THE
QUARTERLY JOURNAL OF ECONOMICS Vol. CXXIV
August 2009
Issue 3
SLUGGISH RESPONSES OF PRICES AND INFLATION TO MONE...

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THE

QUARTERLY JOURNAL OF ECONOMICS Vol. CXXIV

August 2009

Issue 3

SLUGGISH RESPONSES OF PRICES AND INFLATION TO MONETARY SHOCKS IN AN INVENTORY MODEL OF MONEY DEMAND∗ FERNANDO ALVAREZ ANDREW ATKESON CHRIS EDMOND We examine the responses of prices and inflation to monetary shocks in an inventory-theoretic model of money demand. We show that the price level responds sluggishly to an exogenous increase in the money stock because the dynamics of households’ money inventories leads to a partially offsetting endogenous reduction in velocity. We also show that inflation responds sluggishly to an exogenous increase in the nominal interest rate because changes in monetary policy affect the real interest rate. In a quantitative example, we show that this nominal sluggishness is substantial and persistent if inventories in the model are calibrated to match U.S. households’ holdings of M2.

I. INTRODUCTION In this paper, we examine the dynamics of money, velocity, prices, interest rates, and inflation in an inventory-theoretic model of the demand for money.1 We show that our inventorytheoretic model offers new answers to two important questions: why do prices respond sluggishly to changes in money, and why ∗ A previous draft of this paper circulated under the title “Can a Baumol–Tobin Model Account for the Short-Run Behavior of Velocity?” We would like to thank Robert Barro, Michael Dotsey, Tim Fuerst, Robert Lucas, Julio Rotemberg, and several anonymous referees for helpful comments. For financial support, Alvarez thanks the NSF and the Templeton Foundation and Atkeson thanks the NSF. 1. Traditionally, the literature on inventory-theoretic models of money demand has focused on the steady-state implications of these models for money demand (e.g., Barro [1976], Jovanovic [1982], Romer [1986], Chatterjee and Corbae [1992]). Here we examine the implications of an inventory-theoretic model of the demand for money for the dynamics of prices and inflation following a shock to money or to interest rates. C 2009 by the President and Fellows of Harvard College and the Massachusetts Institute of

Technology. The Quarterly Journal of Economics, August 2009

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does inflation respond sluggishly to changes in the short-term nominal interest rate? We first show analytically how prices and inflation are both sluggish in our model, even though price setting is fully flexible. We then show through a quantitative example that this sluggishness is substantial and persistent when our inventory-theoretic model is interpreted as applying to a broad monetary aggregate like M2. Our model is inspired by the analyses of money demand developed by Baumol (1952) and Tobin (1956). In their models, households carry money (despite the fact that money is dominated in rate of return by interest-bearing assets) because they face a fixed cost of trading money and these other assets. Our model is a simplified version of their framework. We study a cash-in-advance model with physically separated asset and goods markets. Households have two financial accounts: a brokerage account in the asset market in which they hold a portfolio of interest-bearing assets and a bank account in the goods market in which they hold money to pay for consumption. We assume that households do not have the opportunity to exchange funds between their brokerage and bank accounts every period. Instead, we assume they have the opportunity to transfer funds between accounts only once every N ≥ 1 periods. Hence, households maintain inventories of money in their bank accounts large enough to pay for consumption expenditures for several periods. They replenish these inventories with transfers from their brokerage accounts once every N periods. As households optimally manage these inventories, their money holdings follow a sawtooth pattern—rising rapidly with each periodic transfer from their brokerage account and then falling slowly as these funds are spent smoothly over time—similar to the sawtooth pattern of money holdings originally derived by Baumol (1952) and Tobin (1956) and more recently by Duffie and Sun (1990) and Abel, Eberly, and Panageas (2007). Here, we focus on the implications of our model for the response of prices to a change in money growth and the response of inflation to a change in interest rates. To highlight the specific mechanisms at work, we make the stark assumptions that price setting is fully flexible and that output in the model is exogenous so that our results can easily be compared to those from a flexible-price, constant-velocity, exogenous output benchmark cash-in-advance model of the effect of monetary policy on prices and inflation. Our first result is that prices respond sluggishly to a change in money in our model, because an exogenous increase in the stock

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of money leads endogenously, through the dynamics of households’ inventories of money, to a partially offsetting decrease in the velocity of money. As a result of this endogenous fall in velocity, prices respond on impact less than one for one to the change in money. Prices respond fully only in the long run when households’ inventories of money, and hence aggregate velocity, settle back down to their steady-state values. The sluggish response of prices to a change in money in our model can thus be understood not as a consequence of a sticky price-setting policy of firms but as a simple consequence of the sluggish response of nominal expenditure to a change in money inherent in an inventory-theoretic approach to money demand. We highlight this implication of our inventory-theoretic model of money demand because a strong negative correlation between fluctuations in money and velocity can be seen clearly in U.S. data. In Figure I, we illustrate this short-run behavior of money and velocity. We plot the ratio of M2 to consumption and the consumption velocity of M2 as deviations from a trend extracted using an HPfilter. These two series are strongly negatively correlated.2 After presenting our analytical results, we examine the extent to which our model can reproduce this comovement of money and velocity in a quantitative example. The mechanism through which our model produces a negative correlation between fluctuations in money and velocity and hence sluggish prices can be understood in two steps. First, consider how aggregate velocity is determined in this inventory-theoretic model of money demand. Households at different points in the cycle of depleting and replenishing their inventories of money in their bank accounts have different propensities to spend the money that they have on hand, or, equivalently, different individual velocities of money. Households that have recently transferred funds from their brokerage accounts to their bank accounts have a large stock of money in their bank account and tend to spend this money slowly to spread their spending smoothly over the interval of time that remains before they next have the opportunity to replenish their bank account. Hence, these households have a relatively low individual velocity of money. In contrast, households that have not transferred funds from their brokerage account in 2. We used the HP-filter smoothing parameter of 34 × 1,600 = 129,600 recommended by Ravn and Uhlig (2002) for monthly data. As discussed in the Appendix, similar results are obtained using alternative measures of the short-run fluctuations in money and velocity.

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FIGURE I Short-Run Negative Correlation of Money/Real Consumption, M/c, and Velocity, v We measure the money supply M as the M2 stock from the Board of Governors of the Federal Reserve System. We measure real consumption c as personal consumption expenditure on nondurables and services from the Bureau of Economic Analysis deflated by the personal consumption expenditures chain-type price index P from the BEA. We define velocity as v ≡ Pc/M. All data are monthly 1959:1– 2006:12 and seasonally adjusted. All variables are reported in logs as deviations from an HP trend with smoothing parameter 34 × 1,600.

the recent past and anticipate having the opportunity to make such a transfer soon tend to spend the money that they have in the bank at a relatively rapid rate, and thus have a relatively high individual velocity of money. Aggregate velocity is given by the weighted average of the individual velocities of money across all households with weights determined by the distribution of money across households. Now consider the effects on aggregate velocity of an increase in the money supply brought about by an open market operation. In this open market operation, the government trades newly created money for interest-bearing securities, and households, on the opposite side of the transaction, trade interest-bearing securities held in their brokerage accounts for newly created money. If the

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nominal interest rate is positive, this new money is purchased only by those households that currently have the opportunity to transfer funds from their brokerage accounts to their bank accounts because these are the only households that currently have the opportunity to begin spending this money. All other households choose not to participate in the open market operation because these households would have to leave this money sitting idle in their brokerage accounts, where it would be dominated in rate of return by interest-bearing securities. Hence, as a result of this open market operation, the fraction of the money stock held by those households currently able to transfer resources from their brokerage account to their bank account rises. Because these households have a lower-than-average propensity to spend this money, aggregate velocity falls. In this way, an exogenous increase in the supply of money leads to an endogenous reduction in the aggregate velocity of money and hence a diminished, or sluggish, response of the price level. To this point we have modeled changes in monetary policy as exogenously specified changes in the money supply. It is now common to model changes in monetary policy not as exogenously specified changes in money but as exogenously specified changes in the short-term nominal interest rate. When we model monetary policy in this way, we find our second result, that expected inflation responds sluggishly to a change in the short-term nominal interest rate. To gain intuition for this result, it is useful to consider the Fisher equation to decompose any change in the nominal interest rate into its two components—a change in the real interest rate and a change in expected inflation. For example, in a standard flexible-price, constant-endowment cash-in-advance model, the real interest rate is always constant, so that, given the Fisher equation, any change in the nominal interest rate must always be accompanied by a matching change in expected inflation. In this sense, in this model, expected inflation must respond immediately to a change in the nominal interest rate. More generally, from the Fisher equation, if a model is to generate a sluggish response of expected inflation to a change in the nominal interest rate caused by a change in monetary policy implemented through open market operations, it must do so because those open market operations generate, at equilibrium, a change in the real interest rate that is roughly as large as the change in the nominal interest rate. In our inventory-theoretic model of money demand, money injections

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implemented through open market operations have an effect on the real interest rate because the asset market is segmented, and it is this effect of open market operations on the real interest rate that is the source of the inflation sluggishness in our model. Asset markets are segmented in our model in the sense that only those agents who currently have the opportunity to transfer money between their brokerage and bank accounts are at the margin in participating in open market operations and in determining asset prices. This asset market segmentation arises naturally in an inventory-theoretic model of the demand for money because those agents who do not have the opportunity to transfer money between the asset and goods markets have no desire to purchase money being injected into the asset market through an open market operation because they have no ability to spend that money in the current period and they find that interest-bearing bonds dominate money as a store of value in the asset market.3 Because only those agents who currently have the opportunity to transfer money from the asset market to the goods market are at the margin in trading money and bonds with the monetary authority, money injections implemented through open market operations have a disproportionate impact on the marginal utility of a dollar for these marginal investors that is manifest as a movement in real interest rates. We first illustrate the mechanisms leading to a sluggish response of prices to money and inflation to interest rates in a specification of our model that is analytically tractable. In this specification of our model, households have log utility and all of the income from selling the households’ endowments is deposited directly into the households’ brokerage accounts. With these assumptions, the model becomes analytically tractable because households in the model choose to spend their inventories of money in their bank accounts at a rate that is independent of expectations of future prices and monetary policies. We show two main results in this analytical version of our model. First, starting from a steady state in which the opportunity cost of holding money in a bank account is low, in response to a 1% exogenous increase in the money stock, on impact, the price level increases by only 1/2 of 1% because velocity falls by 1/2 of 1%. We show how this result 3. These agents choose not to participate in the open market operation as long as the short-term nominal interest rate remains positive. Note that financial intermediaries also choose not to hold money injected through open market operations as long as the short-term nominal interest rate remains positive.

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follows from the basic geometry of money holdings in an inventorytheoretic model of money demand independent of the parameters governing the length of time, in calendar time, between households’ opportunities to transfer cash between their brokerage and bank accounts. Second, also starting from a steady state, in response to a one-percentage-point exogenous change in the nominal interest rate, on impact, the real interest rate responds by one percentage point and expected inflation does not respond at all. We show that this result follows from the asset market segmentation that is inherent in an inventory-theoretic model of money demand, again independent of the parameters governing the length of time, in calendar time, between households’ opportunities to transfer cash between accounts. The parameters governing the length of time between households’ opportunities to transfer money between accounts are important, however, for our model’s implications for the persistence of price and inflation sluggishness. These parameters also determine our model’s implications for steady-state aggregate velocity—the length of calendar time between households’ opportunities to transfer money determines the size of the inventory of money that households must hold to purchase consumption. Thus, the empirical implications of our model for the sluggishness of prices and inflation are largely determined by how we define money (because that definition determines the measure of velocity and hence the magnitude of households’ cash balances). In our model, defining money comes down to answering the question: What assets correspond to those that households hold in their bank accounts, and what assets do households hold and trade less frequently in their brokerage accounts? We examine the implications of our model in a quantitative example using a broad measure of money: U.S. households’ holdings of currency, demand deposits, savings deposits, and time deposits. Here we interpret households’ bank accounts in our model as corresponding to U.S. households’ holdings of deposits in retail commercial banks4 in the data and households’ brokerage 4. In the data, retail banks correspond to a traditional conception of a commercial bank as an institution funded by consumers’ checking, savings, and small time deposits. Clark et al. (2007) provide a useful description of retail banks in our modern financial system. As they describe, “retail banking is the cluster of products and services that banks provide to consumers and small businesses through branches, the Internet, and other channels.” “Organizationally, many large banking companies have a distinct ‘retail banking’ business unit with its own management and financial reporting structure.” “In terms of products and services, deposit taking

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accounts in the model as corresponding to U.S. holdings of other financial assets outside of the retail commercial banking system in the data. In the data, U.S. households hold a large stock of deposits in retail banks, roughly 1/2 to 2/3 of the annual personal consumption expenditure. We argue for the interpretation of this broad collection of accounts in the data as corresponding to bank accounts in our model because we find in the data that U.S. households pay a large opportunity cost in terms of foregone interest to hold such accounts—on the order of 150–200 basis points. This opportunity cost is not substantially different from the opportunity cost U.S. households pay to hold a narrower definition of money such as M1. To parameterize our model to match the ratio of U.S. households’ holdings of broad money relative to personal consumption expenditure, we assume that households transfer funds between their brokerage and bank accounts very infrequently—on the order of once every one-and-one-half to three years. We argue that this assumption is not inconsistent with evidence summarized by Vissing-Jorgensen (2002) regarding the frequency with which U.S. households trade in high-yield assets. Our interpretation of a bank account used for transactions replenished by transfers from a high-yield managed portfolio of risky and riskless assets is the same as used in the models of Duffie and Sun (1990) and Abel, Eberly, and Panageas (2007). We conduct two quantitative exercises with our model. In the first, we feed into the model the shocks to the stock of M2 and aggregate consumption observed in the U.S. economy in monthly data over the past forty years and examine the model’s predictions for velocity in the short run. The model produces fluctuations in velocity that have a surprisingly high correlation of .60 with the fluctuations in velocity observed in the data. This result stands in sharp contrast to the implications of a standard cash-in-advance model (this model with N = 1). In such a model, aggregate velocity is constant regardless of the pattern of money growth. We also find that the short-run fluctuations in velocity in our model are only 40% as large as those in the data. From the finding that is the core retail banking activity on the liability side. Deposit taking includes transactions deposits, such as checking and NOW accounts, and non-transaction deposits, such as savings accounts and time deposits (CDs). Many institutions cite the critical importance of deposits, especially consumer checking account deposits, in generating and maintaining a strong retail franchise. Retail deposits provide a low-cost, stable source of funds and are an important generator of fee income. Checking accounts are also viewed as pivotal because they serve as the anchor tying customers to the bank and allow cross selling opportunities.”

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the short-run fluctuations in velocity in our model are strongly correlated with those observed in the data, we conclude that a substantial portion of the unconditional negative correlation of the ratio of money to consumption and velocity might reasonably be attributed to the response of velocity to exogenous movements in money. From the finding that the short-run fluctuations in velocity in our model are not as large as those in the data, however, we conclude that there may be other shocks to the demand for money that we have not modeled here. In our second quantitative exercise, we consider the response of money, prices, and velocity to an exogenous shock to monetary policy, modeled as an exogenous, persistent shock to the shortterm nominal interest rate similar to that estimated in the literature, which uses vector autoregressions (VARs) to draw inferences about the effects of monetary policy. The consensus in that literature is that the impulse response of inflation to a monetary policy shock is sluggish.5 In our model, we find that the impulse response of inflation is also quite sluggish, as are the responses of money and the price level. All three of these responses from our model are quite similar to the estimated responses of these variables in this VAR literature. Although our model is incomplete in that we have assumed for simplicity that output is exogenous, these findings suggest that our model can account for a substantial portion of the sluggish responses of nominal variables to a change in the nominal interest rate. Our model is related to a growing literature on segmented asset markets. Grossman and Weiss (1983) and Rotemberg (1984) were the first to point out that open market operations could have effects on real interest rates and a delayed impact on the price level in inventory-theoretic models of money demand. The models they present are similar to this model when the parameter N = 2. Those authors examine the impact of a surprise money injection in the context of otherwise deterministic models. Here we study a fully stochastic model as in Alvarez and Atkeson (1997). That model is similar to the one presented here in that agents have separate financial accounts in asset and goods markets and cannot transfer funds between these accounts in every period. In that earlier paper, however, at equilibrium, the individual velocity of money is the same for all households and is constant over time, 5. See Cochrane (1994) and Leeper, Sims, and Zha (1996) for early estimates, Christiano, Eichenbaum, and Evans (1999) and Uhlig (2005) for an overview, and Christiano, Eichenbaum, and Evans (2005) for recent estimates.

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so that aggregate velocity is constant. This result follows from the assumptions in that paper that households have logarithmic utility and a constant probability of being able to transfer money between the asset market and the goods market. The asset pricing implications of our model are closely related to those obtained by Grossman and Weiss (1983), Rotemberg (1984), and Alvarez and Atkeson (1997). In particular, our model has predictions for the effects of money injections on real interest rates arising from the segmentation of the asset market related to the predictions in those papers and those in Alvarez, Lucas, and Weber (2001) and Alvarez, Atkeson, and Kehoe (2002, 2007). Alvarez, Atkeson, and Kehoe (2002, 2007) study the implications of models with segmented asset markets in which households pay a fixed cost to transfer money between bank and brokerage accounts. In that paper, they focus on equilibria in which all households spend all of the money in their bank account every period so that, again, velocity is constant. Two closely related papers build on our framework by endogenizing segmentation (in the spirit of the original Baumol–Tobin model). Chiu (2007) studies a version of our model where households face a fixed utility cost of transferring resources between bank and brokerage accounts. He solves numerically for the equilibrium response of the model to a once-and-for-all increase in the money supply, starting from steady state.6 He finds that the size of the initial money growth shock plays a key role in determining the response to a shock. When the money growth shock is small relative to the fixed cost, households do not pay the fixed cost and the equilibrium dynamics are the same as in an exogenous segmentation model: a money shock leads to an offsetting fall in aggregate velocity, so that the price level responds sluggishly. But for a sufficiently large money injection relative to the fixed cost, all households pay the fixed cost, and so there is no offsetting fall in aggregate velocity and the price level responds one for one to money growth. Because of this, Chiu (2007) concludes that the results from our model are not robust to endogenous segmentation. Khan and Thomas (2007) study a version of our model where households face idiosyncratic fixed costs of transferring resources between the two accounts7 and develop flexible numerical 6. Silva (2008) computes the equilibrium response of prices to an interest rate shock in a closely related continuous time model. 7. Alvarez, Atkeson, and Kehoe (2002, 2007) use idiosyncratic fixed costs to endogenously segment asset markets, but they assume households spend all their

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methods for solving the model. They show that the distribution of the idiosyncratic fixed costs plays an important role in determining the equilibrium responses of the model to a money shock. In their benchmark calibrated example, they find that these costs actually reinforce the sluggishness of prices and reinforce the persistence of liquidity effect relative to our model. The paper proceeds as follows. We present the general model. We next present our results on the impact effects of monetary policy on prices and inflation in the analytically tractable specification of our model. We then present our quantitative exercises. In a final section, we discuss how monetary policy might affect output in a version of our model with production and a discussion of how our results compare with those on price and inflation sluggishness obtained in models with nominal rigidities. II. AN INVENTORY-THEORETIC MODEL OF MONEY DEMAND Consider a cash-in-advance economy in which the asset market and the goods market are physically separated. There is a unit mass of households, each composed of a worker and a shopper. Each household has access to two financial intermediaries: one that manages its portfolio of assets and another that manages its money held in a transactions account in the goods market. We refer to the household’s account with the financial intermediary in the asset market as its brokerage account and its account with the financial intermediary in the goods market as its bank account. There is a government that injects money into the asset market via open market operations. Households that participate in the open market operation purchase this money with assets held in their brokerage accounts. These households must transfer this money to their bank accounts before they can spend it on consumption. Time is discrete and denoted t = 0, 1, 2, . . . . The exogenous shocks in this economy are shocks to the money growth rate μt and shocks to the endowment of each household yt . Because all households receive the same endowment, yt is also the aggregate endowment of goods in the economy. Let ht = (μt , yt ) denote the realized shocks in the current period. The history of shocks is money each period so that aggregate velocity is constant and equal to one. In Khan and Thomas (2007), as in this paper, not all households spend all their money each period, and so there is a nondegenerate cross-sectional distribution of money holdings.

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denoted ht = (h0 , h1 , . . . , ht ) . From the perspective of time zero, the probability distribution over histories ht has density ft (ht ). As in a standard cash-in-advance model, each period is divided into two subperiods. In the first subperiod, each household trades assets held in its brokerage account in the asset market. In the second subperiod, the shopper purchases consumption in the goods market using money held in the household’s bank account, while the worker sells the endowment in the goods market for money Pt (ht )yt (ht ), where Pt (ht ) denotes the price level in the current period. In the next period, a fraction γ ∈ [0, 1] of the worker’s earnings is deposited in the bank account in the goods market, and the remaining 1 − γ of these earnings are deposited in a brokerage account in the asset market. We interpret γ as the fraction of total income that households receive regularly deposited into their transactions accounts or as currency. We refer to γ as the paycheck parameter and to γ Pt−1 (ht−1 )yt−1 (ht−1 ) as the household’s paycheck. We interpret 1 − γ as the fraction of total income that households receive in the form of interest and dividends paid on assets held in their brokerage accounts. Unlike a standard cash-in-advance model, households cannot transfer money between the asset market and the goods market every period. Instead, each household has the opportunity to transfer money between its brokerage account and its bank account only once every N periods. In other periods, a household can trade assets in its brokerage account and use money in its bank account to purchase goods; it simply cannot move money between these two accounts. We refer to households that currently have the opportunity to transfer money between their accounts as active households. Each period a fraction 1/N of the households are active. We index each household by the number of periods since it was last active, here denoted by s = 0, 1, . . . , N − 1. A household of type s < N − 1 in the current period will be type s + 1 in the next period. A household of type s = N − 1 in the current period will be type s = 0 in the next period. Hence, a household of type s = 0 is active in this period, a household of type s = 1 was active last period, and a household of type s = N − 1 will be active next period. In period 0, each household has an initial type s0 , with fraction 1/N of the households of each type s0 = 0, 1, . . . , N − 1. Let S(t, s0 ) denote the type in period t of a household that was initially of type s0 . The quantity of money a household s has on hand in its bank account at the beginning of goods market trade is Mt (s, ht ). The

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shopper in this household spends some of this money on goods, Pt (ht )ct (s, ht ), and the household carries the unspent balance in its bank account into next period, Zt (s, ht ). For an inactive household of type s > 0, the balance in its bank account at the beginning of the period is equal to the quantity of money that it held over in its bank account last period Zt−1 (s − 1, ht−1 ) plus its paycheck γ Pt−1 (ht−1 )yt−1 (ht−1 ). Thus, the evolution of money holdings and consumption for inactive households is (1)

Mt (s, ht ) = Zt−1 (s − 1, ht−1 ) + γ Pt−1 (ht−1 )yt−1 (ht−1 ),

(2)

Mt (s, ht ) ≥ Pt (ht )ct (s, ht ) + Zt (s, ht ).

When a household is of type s = 0, and hence active, it also chooses a transfer of money Pt (ht )xt (ht ) from its brokerage account in the asset market into its bank account in the goods market. Hence, the money holdings and consumption of active households satisfy

(3)

Mt (0, ht ) = Zt−1 (N − 1, ht−1 ) + γ Pt−1 (ht−1 )yt−1 (ht−1 ) + Pt (ht )xt (ht ),

(4)

Mt (0, ht ) ≥ Pt (ht )ct (0, ht ) + Zt (0, ht ).

In addition to the bank account constraints, equations (1)–(4) above, the household also faces a sequence of brokerage account constraints. In each period, the household can trade a complete set of one-period state-contingent bonds that pay one dollar into the household’s brokerage account next period if the relevant contingency is realized. Let Bt−1 (s − 1, ht ) denote the stock of bonds held by households of type s at the beginning of period t following history ht , and let Bt (s, ht , h ) denote bonds purchased at price qt (ht , h ) that will pay off next period if h is realized. Let At (s, ht ) ≥ 0 denote money held by the household in its brokerage account at the end of the period. Because an inactive household of type s > 0 cannot transfer money between its brokerage account and its bank account, this household’s bond and money holdings in its brokerage account must satisfy Bt−1 (s − 1, ht ) + At−1 (s − 1, ht−1 ) (5)

+ (1 − γ )Pt−1 (ht−1 )yt−1 (ht−1 ) − Pt (ht )τt (ht ) ≥ qt (ht , h )Bt (s, ht , h ) dh + At (s, ht ),

where τt (ht ) denotes real lump-sum taxes. Each household’s real bond holdings must remain within arbitrarily large bounds. The

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analogous constraint for active households is

(6)

Bt−1 (N − 1, ht ) + At−1 (N − 1, ht−1 ) + (1 − γ )Pt−1 (ht−1 )yt−1 (ht−1 ) − Pt (ht )τt (ht ) ≥ qt (ht , h )Bt (0, ht , h ) dh + Pt (ht )xt (ht ) + At (0, ht ),

where Pt (ht )xt (ht ) is the active household’s transfer of money from brokerage to bank account. At the beginning of period 0, initially inactive households be¯ 0 (s0 ) in their bank accounts in the gin with exogenous balances M goods market. This quantity is the balance on the left-hand side of (2) in period 0. For initially active households, the initial balance ¯ 0 and ¯ 0 (0, h0 ) in (4) is composed of an exogenous initial balance Z M a transfer P0 (h0 )x0 (h0 ) of their choosing. Each household also be¯ −1 (s0 ) in its brokerage account on gins with exogenous balance B the left-hand side of constraints (5) and (6). The households initially have no money corresponding to A¯ −1 (s0 ) in their brokerage accounts. For each date and state, and taking as given the prices and aggregate variables, each household of initial type s0 chooses complete contingent plans for transfers, consumption, bond, and money holdings to maximize expected utility, ∞

β

t

u[ct (s, ht )] ft (ht ) dht ,

s = S(t, s0 ),

t=0

subject to the constraints (1), (2), and (5) in those periods t in which S(t, s0 ) > 0 and constraints (3), (4), and (6) in those periods t in which S(t, s0 ) = 0. Let Bt (ht ) be the total stock of government bonds. The government faces a sequence of budget constraints, Bt−1 (ht ) = Mt (ht ) − Mt−1 (ht−1 ) + Pt (ht )τt (ht ) + qt (ht , h )Bt (ht , h ) dh , together with arbitrarily large bounds on its real bond issuance. We denote the government’s policy for money injections as μt (ht ) = Mt (ht )/Mt−1 (ht−1 ). In period 0, the initial stock of government debt ¯ −1 and M0 (h0 ) − M ¯ −1 is the initial monetary injection. This is B budget constraint implies that the government pays off its initial

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debt with a combination of lump-sum taxes and money injections achieved through open market operations. An equilibrium of this economy is a collection of prices, complete contingent plans for households, and government policy such that (i) taking as given prices and government policy, the complete contingent plans solve each household’s problem, and (ii) the N−1 ct (s, ht ) = yt (ht ), the money market goods market clears, N1 s=0 N−1 clears, N1 s=0 Mt (s, ht ) + At (s, ht ) = Mt (ht ), and the bond mar N−1 ket clears, N1 s=0 Bt (s, ht , h ) = Bt (ht , h ), for each date and state. To understand equilibrium money demand and asset prices, we examine the household’s first-order conditions. Let ηt (s, ht ) denote Lagrange multipliers on the bank account constraints (2) and (4) of household s, and let λt (s, ht ) denote Lagrange multipliers on the brokerage account constraints (5) and (6). Active households choose transfers xt (ht ) to equate the multipliers on the bank and brokerage accounts: (7)

ηt (0, ht ) = λt (0, ht ).

For households of type s the marginal utility of a dollar satisfies (8)

ηt (s, ht ) = β t

u [ct (s, ht )] ft (ht ). Pt (ht )

The multipliers on the bank accounts satisfy the inequalities t (9) ηt (s, h ) ≥ ηt+1 (s + 1, ht , h ) dh , which hold with equality if Zt (s, ht ) > 0. Combining (8) and (9), we have the consumption Euler equations that determine a household’s money demand, ft+1 (ht , h ) u [ct+1 (s + 1, ht , h )] Pt (ht ) dh , (10) 1≥ β u [ct (s, ht )] Pt+1 (ht , h ) ft (ht ) which again holds with equality if Zt (s, ht ) > 0. The evolution of the marginal utility of a dollar in the brokerage account is determined by state-contingent bond prices: (11)

qt (ht , h ) =

λt+1 (s + 1, ht , h ) . λt (s, ht )

Under the assumption that initial conditions are such that the initial Lagrange multipliers on the brokerage account λ0 (s0 ) are

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the same for all households,8 equations (7), (8), and (11) together imply that state-contingent bond prices are then given by (12)

qt (ht , h ) = β

ft+1 (ht , h ) u [ct+1 (0, ht , h )] Pt (ht ) . u [ct (0, ht )] Pt+1 (ht , h ) ft (ht )

The nominal interest rate is then found from the price of a noncontingent bond paying interest it (ht ) in nominal terms: 1 = qt (ht , h ) dh 1 + it (ht ) ft+1 (ht , h ) u [ct+1 (0, ht , h )] Pt (ht ) dh . (13) = β u [ct (0, ht )] Pt+1 (ht , h ) ft (ht ) In what follows, we will characterize equilibrium in an analytically tractable specification of our model using methods similar to those used in a Lucas-tree economy (see Lucas [1978]). That is, we will find the allocations of money and consumption across households implied by market clearing and then solve for asset prices in terms of marginal utilities using the first-order conditions that link bond prices to ratios of marginal utilities above. To gain intuition as to how these prices lead households to choose to purchase more or less money in an open market operation, as required in equilibrium to match the central bank’s policy for money injections, we find it useful to recast these firstorder conditions in terms of the date-zero asset prices implied by our state-contingent bond prices. Specifically, let Qt (ht ) denote the price in period 0 of one dollar delivered in the asset market in period t following history ht . These prices satisfy the recursion Qt (ht ) = Qt−1 (ht−1 )qt−1 (ht−1 , ht ) for t ≥ 1. From (11) and the recursion for date zero prices we then have that for all households, (14)

Qt (ht ) = λt (s, ht ).

Again, using the assumption that initial conditions are such that the initial Lagrange multipliers on the brokerage account λ0 (s0 ) are the same for all households, from (7) and (8), we have that asset prices are determined by the marginal utility for active ¯ 0 (s0 ) 8. This can be ensured by an appropriate choice of initial bond holdings B or with the assumption that households trade securities contingent on their initial type s0 in an initial asset market before they learn this type.

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households: (15)

Qt (ht ) = β t

u [ct (0, ht )] ft (ht ). Pt (ht )

A large money injection at t and ht is associated with a low datezero price Qt (ht ) and large purchases of money by those households that are currently active (obtained by selling bonds). These active households then transfer this money immediately to their bank accounts and begin spending it, so the low date-zero price Qt (ht ) is associated with high consumption ct (0, ht ) for households that happen to be active at this date. Likewise, a small money injection at t and ht is associated with a high date-zero price Qt (ht ) and small purchases of money and low consumption by those households that are currently active. The mechanism through which money injections in this model have an impact on “real” asset prices is also most easily understood in terms of these date-zero asset prices. We can define a real asset price as the price at date zero of a claim to sufficient cash to purchase one unit of consumption at date t following history ht . This price is given by Qt (ht )Pt (ht ). Note from (15) that this asset price is equal to the marginal utility of consumption of the households that are active at date t. In a standard cash-in-advance model, all households are active at each date and consumption is exogenous, so this real asset price is invariant to the specification of monetary policy. As we show below, in our model, money injections redistribute cash holding across households and thus impact the consumption of the subset of agents who are active at a given date. Corresponding to this redistributive effect, in our model, money injections thus also impact real asset prices in equilibrium. To this point, we have made explicit reference to uncertainty in the notation in order to give a clear characterization of state-contingent asset prices. For the remainder of the paper we suppress reference to histories ht to simplify notation. The inequalities governing money demand can therefore be written u [ct+1 (s + 1)] Pt , (16) 1 ≥ Et β u [ct (s)] Pt+1 with strict equality if Zt (s) > 0, whereas the price for bonds can be written u [ct+1 (0)] Pt 1 . (17) = Et β 1 + it u [ct (0)] Pt+1

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III. HOW THE MODEL WORKS In this section, we solve our model for a special case that is analytically tractable to demonstrate how the model works. In this special case, agents have utility u(c) = log(c) and the paycheck parameter is γ = 0. Given these assumptions, households of type s spend a constant fraction v(s) of their current money holdings and carry the remaining fraction 1 − v(s) into the next period, irrespective of the future paths of money and prices. As a result of the fact that agents choose this simple pattern of expenditure, we can, in this special case, solve analytically for the dynamic, stochastic equilibrium of our model. We use this analytical example to first show how the price level responds sluggishly to an exogenous change in money growth and then show how inflation responds sluggishly to an exogenous change in the nominal interest rate. In the next section, we explore the quantitative implications of our model for illustrative examples in which household expenditure does vary with the future paths of money and prices because agents have preferences other than log utility and/or the paycheck parameter is positive. In presenting this version of the model, we allow the length of a time period to be an arbitrary > 0 units of calendar time (measured in fractions of a year). We continue to use t to count time periods, so after t periods, t units of calendar time have passed. We refer to flow variables such as consumption at annual rates so that ct is consumption in period t. Likewise, the discount factor for the flow utility is β , where β reflects discounting in preferences at an annual rate. We let T > 0 denote the calendar length of time between activity for households, so that N = T / is the number of periods that elapse between activity. We first derive results for an arbitrary length of a period, , and then focus attention on particularly simple formulas that obtain when we let → 0 for fixed T (so that N approaches infinity). We focus on the case of an arbitrarily small time period to show that the time period in our model does not have any economic significance and because this helps simplify the resulting formulas. For purposes of exposition, we leave all the algebraic details to the Appendix. In our analysis here, we assume that, at equilibrium, nominal interest rates are positive, so that households choose not to hold money in their brokerage accounts, where money is dominated in rate of return by bonds, and that the opportunity cost of holding money in a bank account is high, so that those households that

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are about to transfer money between their brokerage and bank accounts do not hold money in their bank accounts. These conditions are analogous to the cash-in-advance constraint binding in a standard cash-in-advance model (this model with N = 1). After solving the model under these assumptions, one can use equations (16) and (17) to check the first-order conditions governing these two assumptions regarding money holdings. III.A. Money and Velocity In our model, households periodically withdraw money from the asset market and then spend that money slowly in the goods market to ensure that it lasts until they have another opportunity to withdraw money from the asset market. As a result, households’ equilibrium paths for money holdings have the familiar saw-toothed shape characteristic of inventory-theoretic models of money demand. Here we discuss how this saw-toothed pattern of money holdings shapes our model’s implications for the dynamics of money, velocity, and prices. Given our assumption that households have utility u(c) = log(c) and the paycheck parameter is γ = 0, households’ money holdings and nominal spending at period t for a period of length are given by (18)

Mt+1 (s + 1) = (1 − v(s))Mt (s) and Pt ct (s) = v(s)Mt (s)

with (19)

v(s) ≡

1 1 − β . 1 − β (N−s)

We refer to the fraction v(s) as the individual velocity of money at an annual rate and to v(s) as the individual velocity in period t. Note that, in this special case of our model, these individual velocities of money are constant over time regardless of expectations for the future path of money and prices. Observe that these individual velocities v(s) converge to 1/(N − s) as β approaches one. In this limiting case, the nominal expenditure of each household is constant over time, as is assumed in the original Baumol–Tobin framework. Given that individual velocities v(s) are constant in this specification of our model, aggregate velocity for any date or state is simply a function of the distribution of money across households with different individual velocities. If the nominal interest rate is

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positive, so that households do not hold any money in the asset market, money market clearing implies Mt =

(20)

N−1 1 Mt (s). N s=0

N−1 Accordingly, we interpret Mt (s)/Mt s=0 as the distribution of money holdings across households. Goods market clearing then implies that the aggregate velocity of money is a weighted average of the individual velocities of money, where the weights are given by the distribution of money holdings across households,

(21)

vt ≡

N−1 N−1 Pt yt 1 Pt ct (s) 1 Mt (s) , = = v(s) Mt N Mt N Mt s=0

s=0

where vt is aggregate velocity at an annual rate. In a steady state with constant money growth, the distribution of money holdings across households of different types is constant. Hence, aggregate velocity is also constant, and the steady-state inflation rate is equal to the money growth rate. Therefore, our model predicts that in the long run, along a steadystate growth path, the price level and the money supply grow together, whereas the aggregate velocity of money stays constant. Out of steady state, however, as a result of the fact that the individual velocities of money v(s) vary across households with different values of s, fluctuations in aggregate money growth cause fluctuations in the distribution of money across households, and this in turn causes fluctuations in aggregate velocity. More specifically, the dynamics of prices, velocity, and money are determined by two factors: first, the differences in individual velocities v(s) across households of different types, and second, the effect of a money injection on the distribution of money holdings across households. How these factors affect fluctuations in aggregate velocity can be understood intuitively as follows. First, consider the differences in individual velocities v(s). These measures of individual velocity equal the flow of consumption obtained by each household relative to its money holdings at the beginning of the period. From (19), we immediately see that v(s) is increasing in s. A household of type s close to zero holds a large stock of money relative to its consumption, whereas

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a household of type s close to N − 1 holds only a small stock of money relative to its consumption. Next consider how a money injection affects the distribution of money across households. From (18), the evolution of the distribution of money for households of type s = 1, . . . , N − 1 is given by (22)

Mt−1 (s − 1) 1 Mt (s) = (1 − v(s − 1)) , Mt Mt−1 μ t

using μt = (Mt /Mt−1 )1/ to denote money growth at an annual rate. Because the distribution of money must sum to one, the money holdings of active households are (23)

N−1 1 Mt (0) 1 Mt−1 (s − 1) 1 =1− (1 − v(s − 1)) . N Mt N Mt−1 μ t s=1

Given an initial distribution of money holdings across households and a process for money growth μt , equations (22) and (23) completely characterize the equilibrium dynamics of the distribution of money holdings across households and hence the equilibrium dynamics of aggregate velocity and the price level. This law of motion for the distribution of money has two key implications. First, in response to an increase in the money supply, aggregate velocity falls and thus the price level responds less than one for one with the money supply. Hence, prices in this model are sluggish in that they move less than would be predicted by the simplest quantity theory. Specifically, the proportional response of prices on impact is roughly half as large as the proportional change in the supply of money. Second, there is a persistently sluggish response of prices to changes in the quantity of money, and the extent of persistence is increasing in the calendar length of time between periods of activity. To see these implications, consider first the impact of a money injection on velocity. By redistributing money toward the active households, an increase in the supply of money tilts the distribution of money holdings toward agents with low individual velocities and away from agents with high individual velocities, lowering aggregate velocity. To see this result more formally, we proceed in two steps. In the first step, we derive the elasticity of velocity with respect to money growth for an arbitrary period length and show that the elasticity is negative—so that on impact,

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velocity declines when money growth increases. In the second step, we consider the case of an arbitrarily small period length. To derive the elasticity of velocity with respect to money growth in period t analytically from equations (21), (22), and (23), observe that

∂ vt μ t = v(0). (24) ∂μ t The elasticity of velocity with respect to money growth in period t is thus given by 1 ∂ log(vt ) v(0) − vt ∂(vt μ t )

= (25) − vt = . v vt ∂μ ∂ log μt t t Because the individual velocity of active households is less than the aggregate velocity (v(0) < vt ), aggregate velocity declines when money growth increases. Given the exchange equation Mt vt = Pt yt , we see that the price level does not respond to impact one for one with an increase in the money supply, because that increase in the money supply leads to an endogenous decrease in aggregate velocity. To quantify this elasticity, we evaluate velocity at steady ¯ To simplify the formulas, we suppose the steadystate, vt = v. state money growth rate is μ¯ = 1 and the time discount factor β → 1, so that the steady-state real return to holding money, β/μ, ¯ also goes to one. In this limiting case, the expenditure of each household is constant over time, as in the original Baumol–Tobin framework. In this limit, individual velocity of active households per period v(0) = /T and steady-state aggregate velocity per period v ¯ = 2/(T / + 1) so that, under these assumptions, the elasticity of aggregate velocity with respect to period money growth is (26)

1 T / − 1 ∂ log(v) =− ∂ log(μ ) 2 T /

and

∂ log(π ) 1 T / + 1 = , ∂ log(μ ) 2 T /

where these derivatives are evaluated at steady state and where π denotes the inflation rate. We can see here that if T = , so that N = 1, as in a standard cash-in-advance model, inflation responds one for one with the shock to money growth and velocity is constant. In contrast, if for fixed T we take → 0, then inflation responds only half as much as money growth. This result follows from the geometry of money

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holdings implied by an inventory-theoretic model—a household that has just replenished its bank account will hold roughly twice as much money as an average household and hence have roughly half the velocity of the average household. Note that here, as we consider the limit as the time period shrinks to zero, we also shrink the magnitude of the money injection to zero. To be able to properly interpret the impact effect, we now specify our model with a small yet finite value of and consider the effect of a sequence of money injections carried out gradually, one per model period, that cumulate over time to a sizable injection. To be specific, we set to correspond to a day and calculate the effects of a total increase in the money supply of 1% accomplished via a sequence of equal-sized money injections, one per model period, over the course of one month, that is, a money injection that increases the money supply by 1/30th of 1% for thirty days, a shock of 0.0333% each day for thirty days. Our analytical results characterize the response of velocity and prices to the money injection on the first day, because we start the model off from a steady state. After the first day, however, the distribution of money holdings across households is no longer in steady state and we must track the impact of the remaining money injections numerically. Figure II illustrates the dynamics of money, velocity, and prices following this shock. In response to this money injection, aggregate velocity falls and the price level responds less than one for one with the change in the money supply. As we showed analytically, the elasticity of velocity with respect to money growth near steady state is approximately −1/2. The impact of the first day’s money injection on velocity is −0.0166%, very close to the analytical value of 0.5 × −0.0333% to be expected. Tracking the effects of the remaining 29 money injections gives the cumulative effect of this sequence of money injections at time t = 30 days on velocity of −0.48%, approximately −1/2 of the cumulative shock of 1.00% that was introduced over those thirty days. In the figure, we trace out the dynamics of money and prices for a total of 300 days (or ten months). Over time, aggregate velocity and prices rise, even overshooting their steady-state levels, and then gradually converge to steady state with dampened oscillations. The results displayed in Figure II regarding the impact of a 1% increase in the money stock carried out over one month are very similar to the results that we obtain when we simply

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FIGURE II Money Up, Velocity Down, Prices Sluggish The dynamics of money, velocity, and prices following a money growth shock. In this exercise, the money growth rate increases by 1/30th of 1% for 30 days. In response to this money injection, aggregate velocity falls and the price level responds less than one for one with the change in the money supply. We showed analytically that the elasticity of velocity with respect to money growth near steady state is approximately −1/2. We find that after thirty days (one month), the cumulative effect of this sequence of money injections on velocity is −0.48%, approximately −1/2 of the cumulative shock of 1% that was introduced over those thirty days. Our analytical results characterize the response of velocity and prices to the money injection on the first day, because we start the model off from a steady state. After the first day, however, the distribution of money holdings across households is no longer in steady state and we must track the impact of the remaining money injections numerically.

set the length of the model period to correspond to one month and calculate the effect of a 1% increase in the money supply accomplished in a single model period (the corresponding figure is available upon request). The dynamics of velocity following a shock can be understood as follows. Because the money growth rate is high for only one month, from (22) we see that the households that were active at the time of the money injection carry an abnormally large stock of money until they next have the opportunity to transfer funds

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from their brokerage accounts. As shown in (19), their individual velocities rise each period until this next visit occurs. Thus, aggregate velocity remains below its steady-state level for a time initially, as these agents have a low individual velocity, and then rises past its steady-state level, as the individual velocity for these agents rises. After N months these agents have spent all of their money and they visit the asset market again. If this were the only effect, we would expect aggregate velocity to return to its steady-state value in N/2 months. However, we show in the Appendix that aggregate velocity remains below its steady-state value for approximately N log(2) months, well over N/2 months (because log(2) ≈ 0.69). In this sense, there is persistence in the sluggish response of prices to changes in the quantity of money and this persistence is increasing in N. The periodic structure of the model introduces a sequence of dampened oscillations in velocity as the changes in the distribution of money holdings work their way through the system. After the first N months, however, these effects are quite small. III.B. Interest Rates and Inflation Until now, we have taken as given the path of money growth and examined our model’s implications for the responses of velocity and the price level to a shock to money growth. An alternative approach is to discuss monetary policy in terms of interest rates and solve endogenously for the responses of money growth, velocity, and inflation consistent with a shock to nominal interest rates. We turn now to such an analysis. Here we show our main result that, on impact, inflation responds sluggishly to a shock to interest rates. We demonstrate analytically that the response of inflation to a change in the nominal interest rate is sluggish in our model when N is large, again under the assumptions that u(c) = log(c) and γ = 0 so that individual velocities v(s) are time-invariant. We solve for the responses of money growth, velocity, and inflation to a change in the nominal interest rate in a deterministic setting. Specifically, we assume the nominal interest rate, inflation, money growth, and the distribution of money holdings across households (and hence velocity) are all initially at steady-state values corresponding to a constant interest rate ¯ı. We fix at t = 0 an increase in the nominal rate above steady state, i0 > ¯ı. We solve for the response of inflation, money growth, and velocity consistent with this change in the nominal interest rate.

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To solve for these responses, we use the pricing formula for nominal bonds (17). In a deterministic setting, this formula can be rewritten as a Fisher equation relating nominal interest rates, real interest rates, and inflation between the current period and the next, (27)

ˆıt = rˆt + πˆ t+1 ,

where a circumflex denotes log deviation from steady state and where we repeatedly use approximations of the form log(1 + it ) ≈ it . We use this Fisher equation to find a path for money growth such that the implied paths for inflation and the real interest rate are consistent with the exogenously specified path for the nominal interest rate. Recall that, in our model, changes in the path of money growth have an impact on velocity, inflation, and real interest rates, with the magnitude of these changes depending on N. As a benchmark, consider first the responses of money growth, velocity, and inflation when N = 1 (so that our model is a standard constant-velocity cash-in-advance model). With N = 1, all households are active, velocity is constant, and the consumption of active households is also constant at ct (0) = y. As a result, in this case, inflation is equal to money growth (πˆ t+1 = μˆ t+1 ) and the real interest rate is constant (ˆrt = 0). With these results, we see that any path of money growth that is consistent with our exogenously specified path of nominal interest rates must have money growth μˆ 1 and inflation πˆ 1 responding one for one to the change in the nominal interest rate in period 0. That is, μˆ 1 = ˆı0 . Clearly, in this case, the response of inflation from period t = 0 to t = 1 anticipated in period t = 0 in response to the change in the nominal interest rate ˆı0 is not at all sluggish. Our solution of the model in this benchmark case with N = 1 is not yet complete, as we have not solved for the equilibrium responses of money growth μˆ 0 and inflation πˆ 0 on impact, at date t = 0. It is well known that in this textbook cash-in-advance model (N = 1), this initial money growth rate and inflation rate are not determinate under an exogenous interest rate rule. We resolve the indeterminacy by choosing the particular path of money growth μˆ 0 so that, on impact, inflation from the last period to the current period does not respond to the change in the nominal interest rate in the current period (i.e., so that πˆ 0 = 0). In the model with N = 1, this is achieved by setting μˆ 0 = 0. This resolution of the

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indeterminacy is equivalent to assuming that the price level in period t = 0 does not respond to the change in the nominal interest rate and hence is consistent with the schemes used to identify shocks to monetary policy discussed in Christiano, Eichenbaum, and Evans (1999). Note that this resolution of the indeterminacy fixes the responses of money growth and inflation at date t = 0 by assumption. Of interest are the equilibrium values of money growth and inflation at date t = 1, μˆ 1 and πˆ 1 . We now turn to the case of a general N > 1. At the end of this section, we show that this indeterminacy of the initial money growth rate μˆ 0 given the exogenous path of the nominal interest rate extends to our setting with N > 1. In particular, we show that, as in the case with N = 1, there is a continuum of paths of money growth consistent with a given path of nominal interest rates. As in the case with N = 1, with N > 1, this continuum has only one dimension; that is, these paths can be indexed by their initial money growth rates μˆ 0 despite the fact that this model has a nondegenerate distribution of money holdings across households as a state variable that is absent from the model with N = 1. Here, we again resolve this indeterminacy by examining the path of money growth consistent with πˆ 0 = 0. Given our assumption of log utility and γ = 0, so that individual velocities are constant over time, this path of money growth has initial money growth at its steady-state level μˆ 0 = 0. Given this result that μˆ 0 = 0 under our resolution of the indeterminacy under an interest rate rule, we solve for the equilibrium responses of money growth μˆ 1 , velocity vˆ1 , and inflation πˆ 1 to the change in the nominal interest rate ˆı0 in period t = 0 by finding the value of money growth μˆ 1 such that the equilibrium responses of the real interest rate rˆ0 and inflation πˆ 1 are consistent with the assumed movement in the nominal interest rate. We solve for each of these responses in turn. Consider first the response of the real interest rate rˆ0 to a change in money growth μˆ 1 . This real interest rate is determined by the growth of the consumption of active households according to rˆ0 = cˆ1 (0) − cˆ0 (0). Given that the individual velocity for active households v(0) is constant over time, the consumption of active households is given by ct (0) = v(0)mt (0)Mt /Pt , where mt (0) = Mt (0)/Mt is the share of the money supply held by active households. The real interest rate can therefore be written (28)

ˆ 1 (0) − m ˆ 0 (0) + μˆ 1 − πˆ 1 . rˆ0 = m

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Given that initial inflation and money growth are at their steadystate values, and given our assumed initial conditions, the distribution of money holdings across households at date t = 0 is equal to its steady-state value, and hence the share of the money supply held by active households, mt (0), and the velocity, vt , are also equal to their steady-state values. Thus, we have m ˆ 0 (0) = 0 and ∂ log(π ) ∂ log(m(0)) +1− μˆ 1 , (29) rˆ0 = ∂ log(μ) ∂ log(μ) where ∂ log(m(0))/∂ log(μ) and ∂ log(π )/∂ log(μ) are the elasticities of the share of money held by active households and of inflation with respect to money growth, both evaluated at the steady state. From (28), these results then imply that the money growth required in period 1 to implement the nominal interest rate ˆı0 in period 0 is given by ⎡ ⎤ (30)

⎢ μˆ 1 = ⎢ ⎣

⎥ 1 ⎥ ˆı0 . ∂ log(m(0)) ⎦ 1+ ∂ log(μ)

Thus, the real interest rate and inflation rate are given by ⎡ ⎡ ⎤ ⎤ ∂ log(π ) ∂ log(π ) ⎢ ⎢ ⎥ ⎥ ∂ log(μ) ∂ log(μ) ⎥ ˆı0 and πˆ 1 = ⎢ ⎥ ˆı0 . rˆ0 = ⎢ ⎣1 − ⎣ ⎦ ∂ log(m(0)) ∂ log(m(0)) ⎦ 1+ 1+ ∂ log(μ) ∂ log(μ) (31) To discuss these formulas, we return to the setting where periods are measured in units of calendar time, with T > 0 denoting the calendar length of time between activity, so that N = T / is the number of periods that elapse between activity. As we can see from these formulas, the difference between our model and the standard model with T = comes through the terms ∂ log(m(0))/∂ log(μ) and ∂ log(π )/∂ log(μ) reflecting the elasticities of the share of money held by active households and of inflation with respect to a money injection. In the standard model with T = (i.e., N = 1), a money injection has no effect in terms of redistributing money holdings across households, so that this elasticity is zero and the elasticity of inflation with respect to money growth is one. Thus, as we have seen, in this case, money growth and inflation respond one for one with the nominal interest rate and the real interest rate remains constant. In contrast, with

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T > (i.e., N > 1), the elasticity of the share of money holdings of active households with respect to money growth is positive and grows large as → 0. Specifically, we show in the Appendix that, taking the limit as β/μ¯ → 1, the elasticity of the money share of active agents is approximately ∂ log(m(0)) T / − 1 = . ∂ log(μ) 2

(32)

And, as we showed above, the elasticity of inflation is ∂ log(π)/∂ log(μ) = (T / + 1)/2(T /), which is less than one for T > and falls toward 1/2 as → 0. Plugging in these expressions for the elasticities gives (33)

μˆ 1 =

2 ˆı0 T / + 1

and

πˆ 1 =

1 ˆı0 T /

and that the real interest rate is (34)

rˆ0 =

T / − 1 ˆı0 . T /

The size of the response of real interest rates to a change in the nominal interest rate on impact is measured by (T / − 1)/(T /), which is decreasing in . For small , a given increase in the nominal interest rate gives rise to a nearly one-for-one increase in the real rate and almost no increase in expected inflation. The small response of inflation to a change in interest rates comes from segmented asset markets: only the fraction /T (i.e., 1/N) of households that are active receive the entire increase in the money supply, and so a given money injection has a disproportionately large impact on the marginal utility of a dollar for these households. Therefore, for small , a given change in nominal interest rates is obtained with a small change in money growth because that small change in the money supply has a large impact on real interest rates. Inflation is sluggish when is small because this small change in money growth leads only to a small change in inflation. In our model, taking → 0 has two effects that together contribute to the sluggish response of inflation—reducing increases the elasticity of the share of money held by active households and lowers the elasticity of inflation with respect to a change in money growth. The more important of these two effects is the first one. To see this, consider a constant velocity model in which agents are permanently divided into a fraction λ who are always active and

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a remaining fraction 1 − λ who are never active, as in Alvarez, Lucas, and Weber (2001). Using the same resolution of the indeterminate price level, the relationship between real and nominal rates on impact is still given by (31) above. Because aggregate velocity is constant in this alternative model, ∂ log(π )/∂ log(μ) = 1. It can also be shown that, in this case, the elasticity of the share of money held by the permanently active agents to money growth is ∂ log(m(0))/∂ log(μ) = (1 − λ)/λ. Therefore, the response of the real rate is rˆ0 = (1 − λ)ˆı0 .

(35)

So if the fraction of agents who are always active in this alternative model is λ = /T (i.e., λ = 1/N), then the alternative model with constant velocity gives the same response of inflation on impact to a change in the nominal interest rate as our model with variable velocity. In this sense, our result that the response of inflation to a change in interest rates is sluggish is driven mainly by asset market segmentation and not variable velocity. For the remainder of this paper, for computational simplicity, we fix the period length to = 1 month so that N = T is the calendar length of time between activity in months. We now present the indeterminacy result that holds in our model. PROPOSITION 1. Let {it∗ }∞ t=0 be a given sequence of nominal inter∗ (s) be the initial distribution of money est rates and M−1 holdings across households. Let {Mt∗ , Mt∗ (s), ct∗ (s), Pt∗ }∞ t=0 be an equilibrium corresponding to this sequence of interest rates and these initial conditions. Then, for each M0 in an open neighborhood of M0∗ , there exists a unique equilibrium {Mt , Mt (s), ct (s), Pt }∞ t=0 consistent with the same path of inand initial distribution of money holdings terest rates {it∗ }∞ t=0 ∗ (s). In this alternative equilibrium, for t ≥ N, the disM−1 tributions of consumption, money growth, and inflation are unchanged in that ct (s) = ct∗ (s),

M∗ Mt+1 = t+1 , Mt Mt∗

and

P∗ Pt+1 = t+1 . Pt Pt∗

For periods t = 0, . . . , N − 1, however, the distributions of consumption, money growth, and inflation all depend on the value of M0 .

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Proof. See the Appendix.

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This indeterminacy result reduces to the standard indeterminacy result when N = 1. (See, e.g., Woodford [2003b, Chapter 2] for an extended discussion.) And because for each M0 there is a unique alternative equilibrium, even for N > 1 the indeterminacy is one-dimensional, as in the standard model. However, for N > 1, this indeterminacy result differs from the standard result in that the distribution of consumption across agents and the path of money growth and inflation differ across these equilibria for the first N periods. Hence, for N > 1, this indeterminacy has implications for real quantities and the real interest rate despite the fact that prices are fully flexible. IV. QUANTITATIVE EXERCISES The setup used in the preceding section, with u(c) = log(c) and γ = 0, simplifies calculations, because individual velocities v(s) are time-invariant. In the case where γ > 0 or for general u(c) the dynamics are more complex, because households’ expenditure decisions will be forward-looking and consequently individual velocities will be time-varying. Below, we examine the quantitative implications of our model for the persistence of the sluggish response of prices to money and inflation to interest rates under alternative parameterizations of our model numerically. We characterize the responses of prices and inflation numerically with values of the parameters N and γ chosen so that our model reproduces both the average level of velocity for a broad monetary aggregate held by U.S. households and the fraction of personal income that is received as wage and salary disbursements.9 We then conduct two exercises with the model to illustrate its quantitative implications. In the first exercise, we examine our model’s quantitative implications for the response of velocity to changes in money growth. In this experiment, we feed into the model the sequences of money growth and aggregate consumption shocks observed in U.S. data and compare the model’s implications for short-run fluctuations 9. The other parameters we need to assign are standard. We set the length of the time period to be a month; the time discount factor β = 0.991/12 , that is, a 1% annual rate; and the steady-state money growth to be μ¯ = 1.011/12 , also a 1% annual rate, which is consistent with a 2% annual opportunity cost of money, as discussed below. We set the coefficient of relative risk aversion to one, that is, log utility.

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in velocity with those observed in the data. We find that velocity in the model is highly correlated with velocity in the data. The magnitude of the fluctuations in the model, however, is significantly smaller than the magnitude of those observed in the data. In the second exercise, we examine the responses of money, prices, and velocity in the model to a monetary policy shock represented as a persistent movement in the nominal interest rate similar to those estimated as the response of the Federal Funds rate to a monetary policy shock in the VAR literature. Here we find that the corresponding impulse responses of money and prices implied by our model are similar to those estimated in the VAR literature. In particular, inflation in the model responds quite sluggishly to the change in interest rates. IV.A. Choosing N and γ In specifying our model, we have assumed that households hold their financial assets in two separate accounts, which we term a bank account and a brokerage account. The bank account is used to purchase consumption and offers a low rate of return on the assets deposited there, whereas the brokerage account can be used to hold a wide array of high-yielding financial assets. Transfers between the two accounts are assumed to be infrequent. To map the parameters of the model to observables in the data, we must interpret the theoretical objects in the model in terms of actual financial institutions in the data. Our preferred interpretation is to map the bank accounts in the model to what is called “retail banking” in the data, whereas the brokerage accounts in the model correspond to the array of actual brokerage accounts, mutual fund shares, pension funds, life insurance reserves, and equity in noncorporate businesses within which households hold claims on financial assets in a form that is not readily accessible for consumption purposes. We choose this interpretation of bank and brokerage accounts in our model based on the observation, documented in the Appendix, that U.S. households pay a substantial cost (on the order of two percentage points) in terms of foregone interest to hold assets in retail banks relative to shortterm Treasury securities. The evidence that we present indicates that there is no substantial difference in the opportunity cost of demand deposits (in M1) and the components of M2 (savings and time deposits) that we consider as part of our monetary aggregate. Our interpretation of bank and brokerage accounts differs from the traditional interpretation of Baumol–Tobin models,

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where withdrawals are made from a safe interest-bearing asset into cash. Instead, we interpret the bank accounts as a broader monetary aggregate, and the account from which these transfers are made as one with high-yield managed portfolios of risky and riskless assets. Our interpretation is similar to those in the models of Duffie and Sun (1990) and Abel, Eberly, and Panageas (2007). We measure U.S. households’ holdings of accounts in retail banks using the flow of funds accounts.10 From the flow of funds accounts, we observe that U.S. households hold a large quantity of such accounts—on the order of 1/2 to 2/3 times annual personal consumption expenditure. We use the implied average annual level of velocity of 1.5 to 2.0 as one statistic to guide our choice of N and γ for the quantitative results that follow. The other statistic that we use is based on our interpretation that the paycheck parameter in the model corresponds to regular wage and salary income automatically deposited in bank accounts in the data. Accordingly, as a baseline, we choose γ = 0.6 to match the fraction of personal income that is received as wage and salary disbursements observed in the data.11 The steady-state velocity implied by our model is a simple function of the parameters N and γ . In particular, holding N fixed, the model’s implications for steady-state velocity are an increasing function of the paycheck parameter γ because the automatic deposit of paychecks into households’ bank accounts allows faster circulation of money. In the example with u(c) = log(c) and γ = 0 that we used for intuition in the preceding sections, with β/μ¯ close to one, aggregate velocity is given by v¯ = 2/(N + 1). With γ > 0, for β/μ¯ close to one, aggregate velocity is well approximated by v¯ = 2/(N + 1)(1 − γ ), which increases as γ increases. Given our choice of γ to match the fraction of personal income that is received as wage and salary disbursements, we choose the 10. In terms of measuring the relative sizes of these accounts using data from the Flow of Funds Accounts of the United States (Federal Reserve Board, 2007), our interpretation corresponds to the following breakdown of the data presented in Table B.100, Balance Sheet of Households and NonProfit Organizations. Total Financial Assets for households are listed on line 8 ($45,405 billion in 2007). We interpret line 9, Deposits ($7,334 billion in 2007), as corresponding to assets held in bank accounts. This category includes checkable deposits and currency, time and savings deposits, and money market shares. We interpret the remaining financial assets listed on line 14, Credit Market Instruments, and lines 23–29 including, among other things, corporate equities, mutual fund shares, life insurance reserves, pension fund reserves, and equity in noncorporate business, as corresponding to assets held in the households’ brokerage accounts. 11. From Table 2.1 of the National Income and Product Accounts of the United States (U.S. Department of Commerce, Bureau of Economic Analysis), we observe that this fraction has been equal to 60% on the average over the period 1959–2007.

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remaining parameter N to match average velocity of 1.5 on an annual basis. We choose the length of a period to be one month and as a baseline use N = 38, so that with γ = 0.6 the model produces an average velocity of 1.5. With these parameters, our model implies that households transfer money between their brokerage accounts and bank accounts very infrequently—on the order of only once every three years. Now we argue that this assumption is not inconsistent with the available microeconomic evidence on the frequency with which agents trade financial assets held outside of their bank accounts. The first set of such microeconomic data concerns the frequency with which households trade equity. Such data are relevant because a household would have to trade equity to rebalance its portfolio between funds held in its bank account and equity held in its brokerage account. The Investment Company Institute (2002) conducted an extensive survey of households’ holdings and trading of equity in 1998 and 2001. They report the frequency with which households traded stocks and stock mutual funds in each year. Averaging across the 1998 and 2001 surveys, 48% of the households neither bought nor sold stocks, and 68% of the households neither bought nor sold stock mutual funds in 1998 and 2001. Because a household would have to buy or sell some of these assets to transfer funds between these higher-yielding assets held in a brokerage account and a lower-yielding bank account, these data, interpreted in the light of our model, would indicate choices of N ranging from roughly 24 (for roughly one-half of households trading these risky assets at least once within the year) to roughly 36 (for roughly one-third of households trading within the year).12 The second set of microeconomic data is that presented by Vissing-Jorgensen (2002). She studies micro data on the frequency of household trading of stocks, bonds, mutual funds, and other risky assets obtained from the Consumer Expenditure Survey. In Figure 6 in her paper, she shows the fraction of households that bought or sold one of these assets over the course of one year 12. These data may also overstate the frequency with which households transfer funds between their equity accounts and their transactions accounts because some of the instances of equity trading are simply reallocations of the equity portfolio. The Investment Company Institute reports that more than 2/3 of those households that sold individual shares of stock in 1998 reinvested all of the proceeds, whereas 57% of those households that sold stock mutual funds reinvested all of the proceeds. In the context of our model, reallocation of the household portfolio in the asset market is costless and does not generate cash that can be used to purchase goods.

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as a function of their financial wealth at the beginning of the year. She finds that the fraction of agents who traded one of these assets ranges from roughly one-third to one-half of the households owning these assets at the beginning of the year. Again, given our interpretation that households hold stocks, bonds, mutual funds, and other risky assets in their brokerage accounts, these data would lead us to choose N between 24 and 36. If a higher proportion of income is automatically available for spending (without the need for a transfer from the brokerage account), so that γ is higher than 0.6, then the chosen value for N needs to be correspondingly higher to keep the steady-state aggregate velocity constant. For example, to match v¯ = 1.5 annual with the higher γ = 0.7 needs about N = 52 months. If we interpret our model in terms of a narrower monetary aggregate with correspondingly higher velocity, then the chosen value of N needs to be lower. For example, to match v¯ = 2.0 annual with our benchmark γ = 0.6 requires N = 30 months, and to match v¯ = 4.0 annual with γ = 0.6 requires N = 15 months. IV.B. The Response of Velocity to U.S. Money and Consumption Shocks We now study the implications of our model for velocity in the short run when we feed in the money growth and aggregate consumption shocks observed in the U.S. data. We use monthly data on M2 as our measure of the monetary aggregate Mt , and we use monthly data on the deviation of the log of real personal consumption expenditure from a linear trend as our measure of the shocks to aggregate endowment yt . To solve for households’ decision rules in the model, we estimate a VAR relating the current money growth rate and aggregate consumption to twelve lags of these variables and use this VAR as the stochastic process governing the exogenous shocks. We then generate the model’s implications for velocity by feeding in the actual series for these shocks. To compare the implications of our model for the dynamics of money and velocity in the short run to the data, we detrend the series implied by the model using the HP-filter. Consider the implications of our model with N = 38 months and γ = 0.6. In Figure III, we show the HP-filtered series for velocity implied by our model with the corresponding HP-filtered series for velocity from the data. The correlation between velocity in the model and the data is .6. In the figure, we have used different scales in plotting the series from the model and the data.

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FIGURE III Model and Data Velocity Results from feeding money growth and endowment shocks as measured in monthly U.S. data into the N = 38, γ = 0.6 model. Money growth shocks are demeaned M2 growth; endowment shocks are the deviations of real personal consumption expenditure from a linear trend. To solve for households’ decision rules in the model, we estimate a VAR relating the current M2 growth rate and real personal consumption expenditure growth rate to 12 lags of these variables and use this VAR as the stochastic process governing the exogenous shocks. All variables are reported in logs as deviations from an HP trend with smoothing parameter 34 × 1,600.

These different scales reflect the fact that the standard deviation of velocity in the model is only 40% of the standard deviation of velocity in the data. Given that we have used nothing but steady-state information to choose the parameters of this model, we regard the high correlation between velocity from the model and the data as a remarkable success. Observe that if we had chosen N = 1, as in a standard cash-in-advance model, velocity as implied by the model would be constant at one regardless of the shock process and, hence, the correlation between velocity in the model and velocity in the data would be zero. We interpret this finding as offering support for the hypothesis that a substantial portion of the negative correlation between the short-run movements of velocity and the ratio of money to consumption is due to the endogenous response of velocity to changes in the ratio of money to consumption.

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We obtain broadly similar results with the alternative values of N and γ discussed above. For example, if we have γ = 0.7 but increase N to 52 to keep v¯ = 1.5 annual, then the correlation of HP-filtered velocity implied by our model and HP-filtered velocity in the data is still .51 (down from 0.60 for the benchmark parameters), whereas the standard deviation of velocity in the model rises slightly, to 45% of the standard deviation of velocity in the data. If instead we keep γ = 0.6 but choose a lower N = 30 to match a higher velocity of v¯ = 2.0 annual, then the correlation of model and data velocity is .56, almost the same as in the benchmark, but the standard deviation of velocity in the model falls to 32% of the data. Similarly, if we choose N = 15 to match even higher velocity of v¯ = 4.0 annual, then the correlation of model and data velocity falls slightly further to .48, whereas the standard deviation of velocity in the model falls to 21% of the data. Reducing N to match the higher velocities implied by narrower monetary aggregates impairs the ability of the model to endogenously produce volatile velocity, but does not substantially alter the correlation between data and model velocity. IV.C. The Response to a Shock to the Interest Rate We now consider the response of inflation to a shock to the nominal interest rate. A large literature estimates the response of the macroeconomy to a monetary policy shock modeled as a shock to the Federal Funds rate. The consensus in this literature is that a monetary policy shock is associated with a persistent increase in the short-term nominal interest rate, a persistent decrease in the money supply, and, at least initially, little or no response in the price level (Christiano, Eichenbaum, and Evans 1999).13 To simulate the effects of a monetary policy shock, we solve for a money growth path consistent with an exogenous, persistent movement in the short-term nominal interest rate. This raises two technical issues. First, recall from Proposition 1 that there is an indeterminacy in this model if the nominal interest rate is exogenous. In equilibrium, there are many paths for money growth, all consistent with the same exogenously specified path for nominal interest rates.14 In the quantitative experiment below, we resolve 13. See Cochrane (1994), Leeper, Sims, and Zha (1996), Christiano, Eichenbaum, and Evans (2005), and Uhlig (2005) for additional examples of such estimates. 14. The indeterminacy result of Section III is for u(c) = log(c) and γ = 0 but extends to the case of general isoelastic preferences and γ > 0.

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this indeterminacy in the same way that we did in Section III. We choose the unique path for money growth that, on impact, leaves the price level unchanged. A second technical issue is that in this model the endogenous dynamics with an exogenous nominal interest rate last exactly N periods. The matrix describing the equilibrium dynamics of endogenous variables has its N eigenvalues all exactly equal to zero. This implies that, if the interest rate is set at its steady-state value but the initial distribution of money holdings is not, then steady state will be reached in exactly N periods. The repetition of the eigenvalues also implies that the matrix that described equilibrium dynamics is not diagonalizable, and hence, this model cannot be solved using standard methods such as those outlined by Blanchard and Kahn (1980) or Uhlig (1999). In an Online Technical Appendix to this paper, we develop a specific solution method for this model based on the use of the generalized Schur form that makes use of the information that the eigenvalues of the matrix describing equilibrium dynamics are all equal to zero.15 We now study the quantitative implications of our model with N = 38 and γ = 0.6, having solved for money growth consistent with the log of the short-term gross interest rate following an AR(1) process with persistence ρ = 0.87. This persistence produces a response of the nominal interest rate to a monetary policy shock similar to that estimated by Christiano, Eichenbaum, and Evans (1999). Figure IV shows the impulse responses of inflation, money growth, and velocity growth following a persistent increase in the nominal interest rate. The model produces a persistent liquidity effect both in the sense that an increase in the nominal interest rate is associated with a fall in money growth and in the sense that an increase in the nominal interest rate is associated, at least initially, with an increase in the real interest rate of roughly the same size. Although it is not plotted separately, the real interest rate in this figure can be read as the difference between the impulse response of the nominal interest rate and the impulse response for inflation. As is clear in the figure, the response of the real interest 15. This Online Technical Appendix is available at http://pages.stern.nyu .edu/∼cedmond/. We also found that direct methods based on use of the generalized Schur form, as suggested by Klein (2000) and others, did not correctly identify that the matrix describing equilibrium dynamics had eigenvalues all equal to zero. This appears to be a numerical issue, because this methodology should work in cases with repeated eigenvalues.

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FIGURE IV Large Liquidity Effects Impulse responses of money growth, inflation, and velocity growth to a persistent nominal interest rate shock in the monthly N = 38, γ = 0.6 model. A unique equilibrium process for money growth is identified by selecting the one consistent with no movement in the price level on impact. All variables are reported as percent deviations from steady state.

rate to the change in the nominal interest rate is quite persistent, and, as a result, inflation is persistently sluggish, responding only slowly to the increase in the nominal interest rate. Figure V shows the same impulse responses, but for the levels of the variables rather than their growth rates. The aggregate price level appears “sticky,” showing little or no response to the shock to interest rates for at least the first twelve months. It is only after twelve months have passed that the money stock and the price level begin to rise together in the manner that would be expected in a flexible price model following a persistent increase in the nominal interest rate. This slow response of the price level simply reflects the persistently sluggish response of inflation. This quantitative exercise indicates that our model can account for a substantial delay in the response of inflation to an

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FIGURE V Sluggish Price Response to Persistent Interest Rate Shock Impulse responses of the money supply, price level, and velocity to a persistent nominal interest rate shock in the monthly N = 38, γ = 0.6 model. A unique equilibrium process for money growth is identified by selecting the one consistent with no movement in the price level on impact. All variables are reported as percent deviations from steady state.

exogenous shock to the nominal interest rate, and it does so because of the persistent response of the real interest rate to the change in the nominal interest rate. V. CONCLUSIONS In this paper, we have put forward a simple inventorytheoretic model of the demand for money and have shown, in that model, that the price level does not respond immediately to an exogenous increase in the money supply and that expected inflation does not respond immediately to an exogenous increase in the nominal interest rate. Instead, there is an extended period of price sluggishness that occurs because the exogenous increase in the money supply leads, at least initially, to an endogenous decrease in the velocity of money and an extended period of inflation

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sluggishness that occurs because of asset market segmentation. We have argued that if this simple model is used to analyze the dynamics of money and velocity using a relatively broad measure of money, then it produces sluggish responses of the price level and inflation similar to that estimated in the VAR literature for the response of the economy to monetary policy shocks. In keeping this model simple, we have abstracted from a number of issues that might play an important role in the development of a more complete model. First, we have simply assumed that households have the opportunity to transfer funds between their brokerage and bank accounts only every N periods and have not allowed households to alter the timing of these transactions after paying some fixed cost. This simplifying assumption allowed us to characterize equilibrium in an analytically tractable specification of our model. A model with explicit consideration of fixed costs of money transfers between accounts must be computed numerically. For work along these lines, see Khan and Thomas (2007). In their benchmark calibrated example, they find that these costs substantially reinforce the sluggishness of prices and the persistence of liquidity effects relative to that seen in our model.16 Second, we have simply assumed that output is exogenous in order to focus on the impact of monetary policy on prices and inflation. The impact of monetary policy shocks on output in a version of our model in which production is endogenous is an important area for future research. We have shown that monetary policy shocks have a direct impact on real asset prices in general and on real interest rates in particular. In a model with endogenous production, these changes in real asset prices would induce firms and workers to shift production and investment through time. The specific results that would be obtained would clearly depend on the exact specification of the production structure of the model. In recent work, Edmond (2003) and King and Thomas (2007) have begun to consider such models. There is a large literature that looks to model the sluggish responses of prices and inflation in an alternative framework in which prices are sticky because firms adjust prices infrequently.17 16. As Khan and Thomas (2007) emphasize, this result is sensitive to the shape of the idiosyncratic distribution of fixed costs facing households. The reason for this sensitivity is a “selection effect” familiar from models of price setting subject to menu costs. 17. This literature includes models in which firms set prices according to time-dependent rules (Fischer 1977; Taylor 1980; Rotemberg 1982; Calvo 1983) or

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Our results on the sluggish responses of prices to changes in money and of inflation to changes in the nominal interest rate arise from theoretical mechanisms that are unrelated to firms’ price-setting decisions. Moreover, the empirical phenomena that motivate our study are also unrelated to the extent of nominal rigidities. Consider first our results on the sluggish response of prices to changes in the stock of money. In our model, prices respond sluggishly to changes in money because nominal expenditure responds sluggishly to changes in money—velocity, which is the ratio of nominal expenditure to money, falls when money rises. The response of nominal expenditure to a change in the stock of money is a feature of money demand, not of the extent of nominal rigidities in terms of firms’ price-setting decisions. For example, if one posits money demand that is interest-inelastic as part of a sticky price model, then nominal expenditure will respond one for one with the stock of money regardless of the extent of nominal rigidities assumed in the model. Thus, modeling money demand in our way in a sticky price setup—where changes in nominal demand become changes in real output—implies that a given money supply shock has a smaller real effect on impact but a more persistent real effect than that obtained using an otherwise standard specification of money demand. Researchers using sticky price models may find it useful to incorporate our model of money demand when they look to account for the impact of a change in the stock of money on the economy. It is clear from our Figure I that this sluggish response of nominal expenditure to money is an important component of understanding the dynamics of prices and money in the unconditional U.S. data. VAR results in Altig et al. (2004) indicate that nominal expenditure also responds sluggishly to a shock to monetary policy. Consider next the relationship between our results and the sluggish response of inflation to changes in the nominal interest rate relative to those in sticky price models. Our model is able to produce a sluggish response of inflation to a persistent shock to the nominal interest rate due to the segmentation of asset markets. The money injections that implement a persistent change in the nominal interest rate also lead to a persistent change in the real state-dependent rules (Caplin and Leahy 1991; Dotsey, King, and Wolman 1999; Midrigan 2006; Golosov and Lucas 2007) or, more recently, on the basis of slowly updated information (Mankiw and Reis 2002; Woodford 2003a).

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interest rate of nearly the same magnitude. Sluggish inflation then follows directly, not as a consequence of sticky prices, but instead as a consequence of the standard Fisher equation linking nominal interest rates, real interest rates, and inflation. In contrast, standard sticky price models have serious problems in reproducing the estimated responses of inflation to a shock to monetary policy modeled as a persistent shock to the nominal interest rate. Mankiw (2001), for example, discusses how a standard sticky price model predicts that the largest response of inflation to a persistent shock to the nominal interest rate occurs on impact, and not in a delayed fashion. He uses this observation to argue for a model with “sticky information.” Sims (1998) makes a similar argument. The difficulty that sticky price models face in generating sluggish inflation arises from the fact that standard sticky price models build on a representative household framework linking the real interest rate to the growth of marginal utility for the representative household, and hence aggregate consumption, through a consumption Euler equation. Thus, in these models, if expected inflation responds sluggishly to a change in the nominal interest rate, then the growth rate of marginal utility for the representative household must respond strongly to a change in the nominal interest rate. Hence, capturing simultaneously a sluggish response of expected inflation and aggregate consumption to a change in the short-term nominal interest rate has been a challenge for these models. Frontier sticky price models, such as Christiano, Eichenbaum, and Evans (2005), use time nonseparable preferences and an elaborate set of adjustment costs and shocks to help their models reproduce a specific set of impulse responses, including the sluggish response of inflation. Canzoneri, Cumby, and Diba (2007), however, observe that standard sticky price models equate the nominal interest rate targeted by the central bank with the interest rate implied by the representative household’s consumption Euler equation and that this assumption fails quite dramatically in the data even if one considers a wide array of time nonseparable preferences for the household. They find a negative correlation between the Federal Funds rate in the data and the short-term nominal interest rates implied by a wide variety of sticky price models’ consumption Euler equations. By contrast, our model abandons the assumption of a representative household for pricing assets. In our model, the real interest rate is linked to the growth of marginal utility for active

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households, not for a representative household consuming aggregate consumption. Hence, as we have seen in our model, we can produce a sluggish response of expected inflation to a change in the nominal interest rate even if aggregate consumption is constant and hence has no response at all to a change in the nominal interest rate. Researchers using models with nominal rigidities may find it useful to incorporate asset market segmentation of the kind we examine here in their models in addressing some of the difficulties their models have with the consumption Euler equation. APPENDIX A. Data All data are monthly 1959:1–2006:12 and seasonally adjusted. We measure the price level P as the personal consumption expenditures chain-type price index with a base year of 2000 from the Bureau of Economic Analysis (BEA). We measure real consumption c as personal consumption expenditure on nondurables and services from the BEA deflated by P. We measure the money supply M as the M2 stock from the Board of Governors of the Federal Reserve System. We define velocity as v ≡ Pc/M. Here we document the robustness of the negative correlation between log(M/c) and log(v) using alternative detrending methods to characterize the short-run fluctuations in money and velocity. We report statistics for HP-filtered data based on the smoothing parameter λ = 1,600 ×34 recommended by Ravn and Uhlig (2002) for monthly data. These are the statistics reported in the main text. In Table A.1, we also report statistics for the lower smoothing parameter λ = 1,600 ×32 and for monthly differences and annual differences. No matter how the short-run fluctuations are measured, we find that there is a pronounced negative correlation between log(M/c) and log(v) and that the standard deviation of log(v) is almost as high as or higher than the standard deviation of log(M/c). We measure the opportunity costs of monetary assets using data collected by the Monetary Services Index project of the Federal Reserve Bank of St. Louis. We measure the opportunity cost of an asset as the short-term Treasury rate less the own rate of return on the asset in question. We take the short-term Treasury rate and own rates of return on currency and demand deposits from the spreadsheet ADJSAM.WKS available from the website

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×32

−.91 1.25

Correlation Standard deviation

Differenced

1,600

×34

Monthly

Annual

−.88 1.01

−.63 0.98

−.86 1.33

Note: Correlation of and relative standard deviation of velocity v to money/real consumption M/c for alternative measures of short-run fluctuations. We measure the money supply M as the M2 stock from the Board of Governors of the Federal Reserve System. We measure real consumption c as personal consumption expenditure on nondurables and services from the Bureau of Economic Analysis deflated by the personal consumption expenditures chain-type price index P from the BEA. We define velocity as v ≡ Pc/M. All data are monthly 1959:1–2006:12 and seasonally adjusted. All variables are reported in logs.

TABLE A.2 OPPORTUNITY COSTS OF MONETARY ASSETS

Currency Demand deposits M2

1959–2006

1959–1990

1990–2006

4.91 1.80 2.08

5.61 2.25 2.30

3.45 0.85 1.64

Note. The opportunity costs of monetary assets in percentage points. We measure opportunity costs as the short-term Treasury rate less the own rate of return on the asset in question. We take the short-term Treasury rate and own rates of return on currency and demand deposits from the Monetary Services Index project of the Federal Reserve Bank of St. Louis. We take the own rate of return on M2 from the Board of Governors of the Federal Reserve System. All data are monthly 1959:1–2006:2 and seasonally adjusted.

of the Federal Reserve Bank of St. Louis. We take the own rate of return on M2 from the Board of Governors of the Federal Reserve System. All opportunity cost data are monthly 1959:1–2006:2 and seasonally adjusted. As is clear from Table A.2, the average opportunity cost of holding demand deposits and M2 is roughly similar, on the order of 200 basis points. Both opportunity costs have fallen somewhat in recent years. B. Algebra of Steady-State Money Distribution and Elasticities Let the length of a period be > 0, measured in fractions of a year. Let the length of time between periods of activity be T , such that the number of periods between periods of inactivity is N = T /. Let period utility be u(c) = log(c) and set the paycheck parameter to γ = 0. In this setting, individual velocity in period t is time-invariant and given by v(s) = (1 − β )/(1 − β (N−s) ) for s = 0, 1, . . . , N − 1.

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For households s = 1, . . . , N − 1, the distribution of money holdings satisfies Mt (s) Mt−1 (s − 1) 1 = [1 − v(s − 1)] , Mt Mt μ t

(36)

with money market clearing implying that N−1 1 Mt−1 (s − 1) 1 1 Mt (0) =1− [1 − v(s − 1)] . N Mt N Mt μ t

(37)

s=1

Now consider a steady state with μt = μ. ¯ Iterating on the steady-state version of (36) and using the formula for individual velocity shows that the steady-state money holdings of household s are related to the holdings of an active household by s−1 1 M(0) M(s) = s . (1 − v(i)) M μ¯ M

(38)

i=0

And because s−1 s−1 1 − β (N−i−1) 1 − β (N−s) (1 − v(i)) = β = β s , (N−i) 1 − β N 1−β i=0 i=0

we have (39)

M(s) = M

s β 1 − β (N−s) M(0) . μ¯ 1 − β N M

We now need to find M(0)/M. We do this using steady-state money market clearing, N−1 1 M(s) 1 M(0) =1− N M N M s=1

(40)

=1−

1 N

N−1 s=1

M(0) M

s β 1 − β (N−s) , μ¯ 1 − β N

and so (41)

N−1 1 M(0) β s 1 − β (N−s) 1= . N M μ¯ 1 − β N s=0

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957

Computing the sums and rearranging gives the solution (42)

−1 1 M(0) ¯ N 1 − (β/μ) ¯ N N N 1 − (1/μ) = (1 − β ) −β . N M 1 − (β/μ) ¯ 1 − (1/μ) ¯

Plugging this formula for M(0)/M into equation (39) gives the complete solution for the steady-state distribution of money holdings. Steady-state aggregate velocity at an annual rate is then given by (43)

v¯ =

N−1 1 M(s) . v(s) N M s=0

We can use the formula for individual velocity in each period to simplify the terms in the sum. For each s we have s M(s) β 1 1 − β 1 − β (N−s) M(0) v(s) = M 1 − β (N−s) μ¯ 1 − β N M s β 1 1−β M(0) = . 1 − β N μ¯ M And so, using the formula for M(0)/M given in equation (42) and then summing over s, we have (44)

−1 ¯ N 1 − (β/μ) ¯ 1 − β N 1 − (1/μ) 1−β . v¯ = 1 − (1/μ) ¯ 1 − (β/μ) ¯ N

To develop intuition, we simplify these formulas by studying a steady state with μ¯ = 1 in the limit as β → 1. We begin with the further special case of = 1 month so that we can quickly derive the main formulas used in the text and then return to the case of general > 0 at the end. With this extra structure, the steady-state money holdings of household s are related to the holdings of an active household by N − s M(0) M(s) = . M N M And so, on using this formula in money market clearing, we also get M(0)/M = 2N/(N + 1), so that we have the complete solution for the distribution of money holdings, (45)

M(s) N−s =2 , M N+1

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for s = 0, 1, . . . , N − 1. Steady-state aggregate velocity is then v=

(46)

N−1 N−1 1 M(s) 1 2 N−s 2 v(s) = = , N M N N−s N+1 N+1 s=0

s=0

as used in the main text. Continuing with this special case of = 1 month, we now derive the elasticity of aggregate velocity with respect to money growth. Specifically, using money market clearing and the law of motion for the money holdings, we have N−1 1 Mt (s) v(s) vt = N Mt s=0 N−1 N−1 1 Mt (s) Mt (s) 1 = v(0) 1 − v(s) + N Mt N Mt s=1

= v(0) + = v(0) +

1 N 1 N

N−1

[v(s) − 1]

s=1 N−1

s=1

Mt (s) Mt

[v(s) − 1][1 − v(s − 1)]

s=1

Mt−1 (s − 1) 1 . Mt−1 μt

And so (47)

vt μt = v(0)μt +

N−1 1 Mt−1 (s − 1) [v(s) − 1][1 − v(s − 1)] , N Mt−1 s=1

which gives the key result (48)

∂ (vt μt ) = v(0), ∂μt

which is a constant for all t. Using the product rule ∂(vt μt )/∂μt = (∂vt /∂μt )μt + vt , we can solve for the elasticity in terms of v(0), a known constant, and aggregate velocity. We evaluate this elasticity at steady state vt = v¯ to get (49)

v(0) 1 N−1 ∂ log(v) = −1=− . ∂ log(μ) v 2 N

And because the aggregate endowment y is constant, the elasticity of inflation with respect to money growth evaluated at steady

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state is (50)

∂ log(π ) ∂ log(v) v(0) 1 N+1 = +1= = . ∂ log(μ) ∂ log(μ) v 2 N

We now derive the elasticity of the share of money held by active households with respect to money growth. Multiplying equation (37) by Mt and differentiating both sides with respect to Mt we get ∂ Mt (0) = N. ∂ Mt Evaluated at steady state, M N+1 N+1 ∂ log(M(0)) =N =N = . ∂ log(μ) M(0) 2N 2 Now let m(0) ≡ M(0)/M denote the steady-state money share. Then we have (51)

∂ log(m(0)) ∂ log(M(0)) N+1 N−1 = −1= −1= . ∂ log(μ) ∂ log(μ) 2 2

To obtain the expressions with arbitrary used in the main text, set N = T / in equations (49)–(51). More formally, use the expression for v¯ in equation (44) and calculate the limit as β/μ¯ → 1 using l’Hˆopital’s rule. C. Dynamic Response of Velocity to a Money Growth Shock Here we analytically characterize the impulse response of velocity to a money growth shock. The dynamics of velocity following a money growth shock are determined by the subsequent evolution of the distribution of money over time. It is easiest to analyze the dynamics of velocity following a shock in a log-linearized version of the model. We proceed in two steps. First, we provide an autoregressive moving average (ARMA) representation of the dynamics of the money distribution. Second, we map the ARMA representation into a formula for the impulse response of velocity that is exact (up to the log-linearization) for the first N − 1 periods after a shock. For simplicity, we consider only the special case of a period length = 1 month. Two sets of equations govern the dynamics of the distribution of money. First, there is an equation requiring that the sum of the log deviations of the fractions of money held by agents of type s be

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zero, 0 = m(0)m ˆ t (0) +

N−1

m(s)m ˆ t (s),

s=1

where steady-state money shares are m(s) ≡ M(s)/M and m ˆ t (s) ≡ log[mt (s)/m(s)]. Second, there is a set of equations for s = 1, . . . , N − 1 governing the evolution of the money shares, ˆ t−1 (s − 1) − μˆ t , m ˆ t (s) = m where these equations follow from the fact that individual velocities v(s) are time-invariant. Rearranging the first equation and using m(s) = 2(N − s)/(N + 1), we have for active households m ˆ t (0) = −

N−1 s=1

N−s m(s) m ˆ t (s) = − m ˆ t (s), m(0) N N−1

s=1

and after iterating on the transitions for inactive households m ˆ t (s) = m ˆ t−s (0) −

s

μˆ t−k+1 ,

k=1

for s = 1, . . . , N − 1. Combining these gives an ARMA representation of the dynamics of the money distribution: m ˆ t (0) = −

N−1 s=1

N−1 s N−s N−s m ˆ t−s (0) + μˆ t−k+1 . N N s=1

k=1

The log deviation of velocity can be written N−1 1 vˆt = m ˆ t (s), N s=0

using v(s)m(s) = 2/(N + 1) = v¯ for all s. Differencing this once and simplifying gives N−1 N−1 1 1 vˆt = m ˆ t (s) = ˆ t−N (0) − (N − 1)μˆ t + μˆ t−s , m ˆ t (0) − m N N s=0

s=1

which repeatedly uses m ˆ t−1 (s − 1) = m ˆ t (s) + μˆ t to cancel terms in the sum. Let the economy start in steady state for t < 0 and consider a given shock μˆ t at date t with μˆ t+k = 0 for all k > 0. For

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the first N − 1 periods after a shock, the terms m ˆ t−N (0) and the N−1 μˆ t−s are zero, so that vˆt = [m ˆ t (0) − (N − 1)μˆ t ]/N. We sum s=1 can solve this for m ˆ t (0) = Nvˆt + (N − 1)μˆ t and use the ARMA representation for the money share of active households to get an ARMA representation of velocity growth that is exact for the first N − 1 periods, vˆt = −

N−1 s=1

N−s 1 N−1 vˆt−s − μˆ t N 2 N

(using μˆ t−s = 0 for the first N − 1 periods). Rearranging terms to write this in levels, we get vˆt =

N−1 1 1 N−1 μˆ t vˆt−s − N 2 N s=1

(this time using vˆt−N = 0 for the first N − 1 periods). When N is large, so that (N − 1)/N ≈ 1, this implies that the impulse response of the log of velocity over the first N − 1 periods is given by 1 k+1 1 1+ − 1. (52) vˆt+k = 2 N This starts with vˆt = −1/2; for large N it crosses zero at roughly k = N log(2) and then rises above zero until k = N. D. Proof of Indeterminacy Proposition Using that u(c) = log(c) and γ = 0, so that Pt ct (0) = v(0)Mt (0), and that u (ct (0)) 1 1 = = , Pt ct (0) Pt v (0) Mt (0)

∞ the sequence of Mt (0) that supports the interest rate it∗ t=0 must satisfy Mt+1 (0) = 1 + it∗ β, Mt (0)

t = 0, 1, . . . ,

or (53)

Mt+1 (0) = M0 (0) β t

t

1 + i ∗j . j=0

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For future reference, we can write equation (53) as

Mt−1−s (0) = M0 (0) β t−1−s−1

(54)

t−1−s−1

1 + i ∗j ,

j=0

which applies if t − 1 − s ≥ 0 or s ≤ t − 1. Now again using that u (c) = log (c) and γ = 0, we have Mt (s) = (1 − v (s − 1)) Mt−1 (s − 1) ,

s = 1, . . . , N,

which we can substitute into

Mt (0) = NMt −

N−1

(1 − v (s − 1)) Mt (s − 1)

s=1

to obtain

(55)

Mt (0) = N ( Mt − Mt−1 ) +

N−1

θs Mt−1−s (0) ,

s=0

where the coefficients θs are given by θs ≡ v(s)[ s−1 j=0 (1 − v( j))] > 0. It is easy to verify that any sequence of {Mt − Mt−1 } for t ≥ 0 and {Mt (0)} for t ≥ −N + 1 that solves equation (55) completely characterizes an equilibrium. Now we specialize equation (55) for three different types of time periods. For t = 0 we have

(56)

N−1 ∗ ∗ M0 (0) = N M0 − M−1 + θs M−1−s (0) . s=0

For t = 1, 2, . . . , N − 1 we can break the sum into two parts and use the expression for Mt−1−s (0) in terms of interest rates,

SLUGGISH RESPONSES OF PRICES AND INFLATION

963

equation (54), so we have Mt (0) t−1

= N ( Mt − Mt−1 ) +

θs Mt−1−s (0) +

= N ( Mt − Mt−1 ) +

θs M0 (0) β t−1−s−1

t−1−s−1

s=0

(57)

+

N−1

∗ θs Mt−1−s (0)

s=t

s=0 t−1

N−1

1 + i ∗j

j=0

∗ θs Mt−1−s (0) ,

s=t

and using the expression for the interest rate equation (53) again, M0 (0) β t−1

t−1

1 + i ∗j j=0 t−1

= N ( Mt − Mt−1 ) +

θs M0 (0) β t−1−s−1

t−1−s−1

s=0

(58)

+

N−1

1 + i ∗j

j=0

∗ θs Mt−1−s (0) .

s=t

Finally, for t = N, N + 1, . . ., we have Mt (0) = N ( Mt − Mt−1 ) +

N−1

θs M0 (0) β t−1−s−1

s=0

t−1−s−1

1 + ij ,

j=0

and inserting the expression for Mt (0) based on the interest rates, M0 (0) β t−1

t−1

1 + i ∗j j=0

(59)

= N ( Mt − Mt−1 ) +

N−1 s=0

θs M0 (0) β t−1−s−1

t−1−s−1

1 + ij .

j=0

Now we are ready to construct the path of the remaining

∞ variables for an equilibrium that supports the interest rate path it∗ t=0 . We do this in three steps, one for each type of time period. We do this for an arbitrary value of M0 .

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Step a. Solve for M0 (0) . For t = 0, M0 (0) is a function of prede∗ termined variables, M−1 , M∗j (0) for j < 0, and M0 . Thus, for the given value of M0 there is a unique value of M0 (0) . Step b. Solve for Mt (0) and Mt for t = 1, . . . , N − 1. Equation (58) gives one equation in one unknown, namely Mt − Mt−1 , given M0 (0) . Using these equations recursively, using the initial conditions M0 found in Step a, we can solve for M1 , . . . , MN−1 . Step c. Solve for Mt for t ≥ N. Given the initial condition MN−1 found in Step b, equation (59) can be used to solve for Mt for t ≥ N. Steps a through c show that for any given M0 there is a unique way to construct an equilibrium that supports the path of interest

∞ rates it∗ t=0 . We now show that any equilibrium that supports the in for ∞ terest rate sequence it∗ t=0 , the distribution of cash Mt (s) /Mt for s = 0, . . . , N − 1 for all t ≥ N is the same. Using equation (53) for t ≥ N in Mt (0) = NMt −

N−1

(1 − v (s − 1)) Mt (s − 1) ,

s=1

we obtain Mt (0) = NMt −

N−1

(1 − v (s − 1))

s=1

s−1

v (k) Mt−k (0) ,

k=1

and using equation (53) we get M0 (0) β t−1

t−1

1 + i ∗j j=0

= NMt −

N−1 s=1

(1 − v (s − 1))

s−1 k=1

v (k) M0 (0) β t−k−1

t−k−1

1 + i ∗j ,

j=0

which shows that the path of Mt is proportional to M0 (0) for t ≥ N. Finally, equation (53) implies that the path of Mt (s) is proportional to M0 (0) , which establishes the desired result. This in turn immediately implies that Mt (s) /Mt = Mt∗ (s) /Mt∗ and Mt+1 /Mt = ∗ ∗ /Mt∗ , and thus that ct (s) = ct∗ (s) Pt+1 /Pt = Pt+1 /Pt∗ for t ≥ N. Mt+1

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965

Finally, the qualification that M0 has to be close to M0∗ ensures that in the values constructed for Mt (0) during the periods t = 0, . . . , N − 1 are all strictly positive. UNIVERSITY OF CHICAGO AND NATIONAL BUREAU OF ECONOMIC RESEARCH UNIVERSITY OF CALIFORNIA–LOS ANGELES, FEDERAL RESERVE BANK OF MINNEAPOLIS, AND NATIONAL BUREAU OF ECONOMIC RESEARCH NEW YORK UNIVERSITY AND UNIVERSITY OF MELBOURNE

REFERENCES Abel, Andrew B., Janice C. Eberly, and Stavros Panageas, “Optimal Inattention to the Stock Market,” American Economic Review, 97 (2007), 244–249. Altig, David, Lawrence J. Christiano, Martin Eichenbaum, and Jesper Linde, “Firm-Specific Capital, Nominal Rigidities and the Business Cycle,” Federal Reserve Bank of Cleveland Working Paper No. 04-16, 2004. Alvarez, Fernando, and Andrew Atkeson, “Money and Exchange Rates in the Grossman–Weiss–Rotemberg Model,” Journal of Monetary Economics, 40 (1997), 619–640. Alvarez, Fernando, Andrew Atkeson, and Patrick J. Kehoe, “Money, Interest Rates, and Exchange Rates with Endogenously Segmented Markets,” Journal of Political Economy, 110 (2002), 73–112. ——, “Time-Varying Risk, Interest Rates, and Exchange Rates in General Equilibrium,” Federal Reserve Bank of Minneapolis Research Department Staff Report No. 371, 2007. Alvarez, Fernando, Robert E. Lucas, Jr., and Warren E. Weber, “Interest Rates and Inflation,” American Economic Review, 91 (2001), 219–225. Barro, Robert J., “Integral Constraints and Aggregation in an Inventory Model of Money Demand,” Journal of Finance, 31 (1976), 77–88. Baumol, William J., “The Transactions Demand for Cash: An Inventory Theoretic Approach,” Quarterly Journal of Economics, 66 (1952), 545–556. Blanchard, Olivier Jean, and Charles M. Kahn, “The Solution of Linear Difference Models under Rational Expectations,” Econometrica, 48 (1980), 1305–1311. Calvo, Guillermo A., “Staggered Prices in a Utility-Maximizing Framework,” Journal of Monetary Economics, 12 (1983), 383–398. Canzoneri, Matthew B., Robert E. Cumby, and Behzad T. Diba, “Euler Equations and Money Market Interest Rates: A Challenge for Monetary Policy Models,” Journal of Monetary Economics, 54 (2007), 1863–1881. Caplin, Andrew, and John Leahy, “State-Dependent Pricing and the Dynamics of Money and Output,” Quarterly Journal of Economics, 106 (1991), 683–708. Chatterjee, Satyajit, and Dean Corbae, “Endogenous Market Participation and the General Equilibrium Value of Money,” Journal of Political Economy, 100 (1992), 615–646. Chiu, Jonathan, “Endogenously Segmented Asset Market in an InventoryTheoretic Model of Money Demand,” Bank of Canada Working Paper No. 2007-46, 2007. Christiano, Lawrence, Martin Eichenbaum, and Charles Evans, “Monetary Policy Shocks: What Have We Learned and to What End?” in Handbook of Macroeconomics, Michael Woodford and John Taylor, eds. (Amsterdam: North-Holland, 1999). ——, “Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy,” Journal of Political Economy, 113 (2005), 1–45. Clark, Timothy, Astrid Dick, Beverly Hirtle, Kevin J. Stiroh, and Robard Williams, “The Role of Retail Banking in the U.S. Banking Industry: Risk, Return, and Industry Structure,” Federal Reserve Bank of New York Economic Policy Review, 13 (2007), 39–56. Cochrane, John H., “Shocks,” Carnegie-Rochester Conference Series on Public Policy, 41 (1994), 295–364.

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Dotsey, Michael, Robert G. King, and Alexander L. Wolman, “State-Dependent Pricing and the General Equilibrium Dynamics of Money and Output,” Quarterly Journal of Economics, 114 (1999), 655–690. Duffie, Darrell, and Tong-Sheng Sun, “Transactions Costs and Portfolio Choice in a Discrete-Continuous-Time Setting,” Journal of Economic Dynamics and Control, 14 (1990), 35–51. Edmond, Chris, “Sticky Prices versus Sticky Demand,” University of Melbourne, Working Paper, 2003. Federal Reserve Board, Flow of Funds Accounts of the United States (Washington, DC: Federal Reserve Board, 2007). Fischer, Stanley, “Long-Term Contracts, Rational Expectations, and the Optimum Money Supply Rule,” Journal of Political Economy, 85 (1977), 191–205. Golosov, Mikhail, and Robert E. Lucas, Jr., “Menu Costs and Phillips Curves,” Journal of Political Economy, 115 (2007), 171–199. Grossman, Sanford J., and Laurence Weiss, “A Transactions-Based Model of the Monetary Transmission Mechanism,” American Economic Review, 73 (1983), 871–880. Investment Company Institute, Equity Ownership in America (Washington, DC: Investment Company Institute, 2002). Jovanovic, Boyan, “Inflation and Welfare in the Steady State,” Journal of Political Economy, 90 (1982), 561–577. Khan, Aubhik, and Julia K. Thomas, “Inflation and Interest Rates with Endogenous Market Segmentation,” Federal Reserve Bank of Philadelphia Working Paper 07-1, 2007. King, Robert G., and Julia K. Thomas, “Breaking the New Keynesian Dichotomy: Asset Market Segmentation and the Monetary Transmission Mechanism,” Ohio State University, Working Paper, 2007. Klein, Paul, “Using the Generalized Schur Form to Solve a Multivariate Linear Rational Expectations Model,” Journal of Economic Dynamics and Control, 24 (2000), 1405–1423. Leeper, Eric M., Christopher A. Sims, and Tao Zha, “What Does Monetary Policy Do?” Brookings Papers on Economic Activity, 2 (1996), 1–78. Lucas, Robert E. Jr., “Asset Prices in an Exchange Economy,” Econometrica, 46 (1978), 1429–1445. Mankiw, N. Gregory, “The Inexorable and Mysterious Tradeoff between Inflation and Unemployment,” Economic Journal, 111 (2001), C45–C61. Mankiw, N. Gregory, and Ricardo Reis, “Sticky Information versus Sticky Prices: A Proposal to Replace the New Keynesian Phillips Curve,” Quarterly Journal of Economics, 117 (2002), 1295–1328. Midrigan, Virgiliu, “Menu Costs, Multi-Product Firms, and Aggregate Fluctuations,” Federal Reserve Bank of Minneapolis, Working Paper, 2006. Ravn, Morten O., and Harald Uhlig, “On Adjusting the Hodrick–Prescott Filter for the Frequency of Observations,” Review of Economics and Statistics, 84 (2002), 371–380. Romer, David, “A Simple General Equilibrium Version of the Baumol–Tobin Model,” Quarterly Journal of Economics, 101 (1986), 663–686. Rotemberg, Julio J., “Monopolistic Price Adjustment and Aggregate Output,” Review of Economic Studies, 49 (1982), 517–531. ——, “A Monetary Equilibrium Model with Transactions Costs,” Journal of Political Economy, 92 (1984), 40–58. Silva, Andr´e C., “Prices and Money after Interest Rate Shocks with Endogenous Market Segmentation,” Universidade Nova de Lisb˜oa, Working Paper, 2008. Sims, Christopher A., “Stickiness,” Carnegie–Rochester Series on Public Policy, 49 (1998), 317–356. Taylor, John B., “Aggregate Dynamics and Staggered Contracts,” Journal of Political Economy, 88 (1980), 1–23. Tobin, James, “The Interest-Elasticity of the Transactions Demand for Cash,” Review of Economics and Statistics, 38 (1956), 241–247. Uhlig, Harald, “A Toolkit for Analysing Nonlinear Dynamic Stochastic Models Easily,” in Computational Methods for the Study of Dynamic Economies, Ramon Marimon and Andrew Scott, eds. (New York: Oxford University Press, 1999).

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E-ZTAX: TAX SALIENCE AND TAX RATES∗ AMY FINKELSTEIN This paper examines whether the salience of a tax system affects equilibrium tax rates. I analyze how tolls change after toll facilities adopt electronic toll collection (ETC); drivers are substantially less aware of tolls paid electronically. I estimate that, in steady state, tolls are 20 to 40 percent higher than they would have been without ETC. Consistent with a salience-based explanation for this toll increase, I find that under ETC, driving becomes less elastic with respect to the toll and toll setting becomes less sensitive to the electoral calendar. Alternative explanations appear unlikely to be able to explain the findings.

I. INTRODUCTION For every dollar of revenue raised by the U.S. income tax system, taxpayers incur about ten cents in private compliance costs associated with record keeping and tax filing (Slemrod 1996). These compliance costs impose a deadweight burden on society. Yet policies that would reduce these costs are frequently opposed by policy makers and economists who believe that compliance costs play an important role in keeping taxes visible and salient to the electorate, who then serve as an important check on attempts to raise the scale of government activity beyond what an informed citizenry would want. For example, Milton Friedman has publicly lamented his inadvertent contribution to the growth of government by encouraging the introduction of the visibility-reducing Federal income tax withholding system during the Second World War (Friedman and Friedman 1998, p. 123). More recently, in 2005, the President’s Advisory Panel on Federal Tax Reform failed to reach consensus on whether to replace part of the existing income tax system with a value-added tax (VAT), in part because of concerns about how ∗ I am grateful to Daron Acemoglu, Gene Amromin, Pol Antras, ` David Autor, Raj Chetty, Peter Diamond, Liran Einav, Hanming Fang, Naomi Feldman, Edward Glaeser, Mike Golosov, Austan Goolsbee, Jerry Hausman, Larry Katz, Erzo Luttmer, Brigitte Madrian, Sean Nicholson, Ben Olken, Jim Poterba, Nancy Rose, Stephen Ryan, Monica Singhal, Heidi Williams, Clifford Winston, two anonymous referees, and seminar participants at Cornell, MIT, Berkeley, Stanford GSB, Yale, the NBER Public Economics Meeting, Harvard, and Stanford for helpful comments; to James Wang and especially Julia Galef for outstanding research assistance; to Tatyana Deryugina, Julia Galef, Stephanie Hurder, and Erin Strumpf for help in conducting the survey of toll awareness; and to the innumerable employees of toll operating authorities around the country who generously took the time to provide data and to answer my many questions.

C 2009 by the President and Fellows of Harvard College and the Massachusetts Institute of

Technology. The Quarterly Journal of Economics, August 2009

969

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the lower visibility of a VAT would affect the size of government. As the Advisory Panel noted in its report: [Some] Panel Members were unwilling to support the [VAT] proposal given the lack of conclusive empirical evidence on the impact of a VAT on the growth of government. Others were more confident that voters could be relied on to understand the amount of tax being paid through a VAT, in part because the proposal studied by the Panel would require the VAT to be separately stated on each sales receipt provided to consumers. These members of the Panel envisioned that voters would appropriately control growth in the size of the federal government through the electoral process. (The President’s Advisory Panel on Federal Tax Reform 2005, pp. 203–204)

The idea that a less visible tax system may fuel the growth of government can be traced back at least to John Stuart Mill’s 1848 Principles of Political Economy. It has its modern roots in the public choice tradition of “fiscal illusion.” In a series of influential books and articles, James Buchanan and co-authors have argued that citizens systematically underestimate the tax price of public sector activities, and that government in turn exploits this misperception to reach a size that is larger than an informed citizenry would want. The extent of the tax misperception—and thus the size of government—is in turn affected by the choice of tax instruments, with more complicated and less visible taxes exacerbating the extent of fiscal illusion and thereby increasing the size of the government (e.g., Buchanan [1967]; Buchanan and Wagner [1977]; Brennan and Buchanan [1980]). Empirical evidence of the impact of tax salience on tax rates, however, has proved extremely elusive. Most of the evidence comes from cross-sectional studies of the relationship between the size of government and the visibility of the tax system, where the direction of causality is far from clear (Oates 1988; Dollery and Worthington 1996). Moreover, as I discuss in more detail below, the sign of any effect of tax salience on tax rates is theoretically ambiguous. The link between tax salience and tax rates is therefore an open empirical question. In this paper, I examine the relationship between tax salience and tax rates empirically by studying the impact of the adoption of electronic toll collection (ETC) on toll rates. Electronic toll collection systems—such as the eponymous E-ZPass in the northeastern United States, I-Pass in Illinois, or Fast-Trak in California—allow automatic deduction of the toll as the car drives through a toll plaza. Because the driver need no longer actively count out and hand over cash for the toll, the toll rate may well be less salient

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to the driver when paying electronically than when paying cash. Indeed, I present survey evidence that indicates a strikingly lower awareness of the amount paid in tolls by those who pay electronically relative to those who pay using cash. This discrepancy in toll awareness exists even among regular commuters on a toll facility. As a result, toll facilities’ adoption of ETC—and the resultant switch by many drivers to paying electronically—provides a setting in which to examine the impact of tax salience on tax rates. Different toll facilities in the United States have adopted ETC at different points in time over the last several decades, and some have not yet adopted it. To study the impact of ETC, I examine the within toll-facility changes in toll rates associated with the adoption and diffusion of ETC. To do so, I collected a new data set on the history of toll rates and ETC installation for 123 toll facilities in the United States. Where they were available, I also collected annual facility-level data on toll traffic, toll revenue, and the share of each that is paid by electronic toll collection. I find robust evidence that toll rates increase after the adoption of electronic toll collection. My estimates suggest that when the proportion of tolls paid using ETC has diffused to its steady state level of about 60 percent, toll rates are 20 to 40 percent higher than they would have been under a fully manual toll collection system. I also present evidence of two potential mechanisms by which reduced salience may contribute to increased toll rates. First, I find that the elasticity of driving with respect to the toll declines (in absolute value) with the adoption of electronic toll collection, suggesting that ETC may raise the optimal level of the toll. Second, I show that under ETC, toll-setting behavior becomes less sensitive to the local election calendar, suggesting that ETC may reduce the political costs of raising tolls. The rest of the paper proceeds as follows. Section II provides a conceptual framework for how tax salience may affect tax rates and the factors that may affect the (ambiguous) sign of this relationship. Section III presents evidence that tolls are less salient when paid by ETC than by cash. Section IV describes the data on toll rates and driving. Section V estimates the impact of ETC on the elasticity of driving with respect to the toll. Section VI estimates the impact of ETC on toll rates. Section VII considers non-salience-based explanations for these empirical findings. The last section concludes.

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II. EFFECTS OF TAX SALIENCE ON CONSUMERS AND GOVERNMENT: CONCEPTUAL FRAMEWORK In a fully salient tax system, individuals are aware of actual taxes as they make economic and political decisions. In a less salient tax system, individuals are not aware of the actual tax (τ ), but instead have a perception of the tax, which I denote by τ˜ . Recent empirical evidence is consistent with individuals misperceiving taxes (Liebman and Zeckhauser 2004; Feldman and Katascak 2005; Chetty, Kroft, and Looney forthcoming) and with the salience of the tax affecting the extent of this misperception (Chetty, Kroft, and Looney forthcoming). This paper focuses on the response of tax rates to tax salience. However, because an input into this response is how consumers’ economic behavior is affected by tax salience, I begin—in both the conceptual framework and the subsequent empirical work—by analyzing the consumers’ response; I then turn to the government’s response. I denote by θ ≥ 0 the (lack of) salience of the tax system. A higher θ corresponds to a less salient tax system; θ = 0 corresponds to a fully salient system. In the empirical application I will examine the move from manual (i.e., cash) toll collection to electronic toll collection (ETC) and interpret this as a move to a less salient tax system (i.e., an increase in θ ); I present survey evidence in Section III that is consistent with the assumption that ETC reduces the salience of tolls. There are two types of tax salience that may affect tax setting: tax salience at the time of the consumption decision for the taxed good, and tax salience at the time of voting. These need not be the same. To capture this, I denote the perceived tax by τ˜ j , where j = {c, v} indicates perceived taxes at the time of consumption and of voting, respectively. For simplicity I assume the perceived tax is a linear function of the actual tax, (1)

τ˜ j (θ ) ≡ δ0 j (θ ) + δ1 j (θ )τ,

and normalize a fully salient system as one in which the perceived and actual tax are the same (i.e., δ0 j (0) = 0 and δ1 j (0) = 1). I assume that δ1 j (θ ) > 0 (i.e., the perceived tax is increasing in the actual tax). I also assume that in a less salient tax system, the link between the perceived and the actual tax is weaker (i.e., δ1 j (θ ) < 0). The effect of the tax salience on the perceived toll level

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is, however, a priori ambiguous; in other words, δ0 j (θ ) can be either sign. For simplicity, I consider only cases of positive taxation (τ > 0), and further assume that τ˜ j > 0. II.A. Response of Consumer Economic Behavior to Tax Salience The individual chooses consumption of the taxed good based on the perceived tax at the time of the consumption decision, τ˜C (θ ). To simplify the analysis, I assume the individual maximizes a utility function that is quasi-linear in the taxed good and exhibits constant elasticity of demand.1 The individual thus solves (2)

( γ1 +1)

max γ0 x1 1 x1

+ x2 subject to x2 + ( p + τ˜C (θ ))x1 ≤ m,

where x1 denotes the taxed good (with producer price p), x2 denotes all other goods (whose price has been normalized to 1), and m is consumer income. I denote by η(τ˜C ) ≡ γ1 the (constant) elasticity of demand for x1 , which I assume is negative. Note that η(τ˜C ) is the elasticity of demand with respect to the perceived price p + τ˜C (θ ); I denote by η(τ ) the elasticity of demand with respect to the actual price p + τ . To see how consumer responsiveness to the tax changes with the salience of the tax, I will estimate empirically how the elasticity of demand with respect to the actual price (η(τ )) varies with the tax salience (θ ). The sign of this relationship (i.e., the sign of ∂η(τ )/∂θ ) is ambiguous. To see this, note that the relationship between η(τ ) (which I will estimate empirically) and η(τ˜C ) (which I have assumed is constant) can be derived as follows: η(τ ) ≡ (3)

∂( p + τ˜C ) ( p + τ ) p + τ˜C ∂ x1 ( p + τ ) ∂ x1 = ∂( p + τ ) x1 ∂( p + τ˜C ) ∂( p + τ ) x1 p + τ˜C p + τ ∂( p + τ˜C ) . = η(τ˜C ) p + τ˜C ∂( p + τ )

Under the assumption of fixed producer prices (i.e., p does not vary with either τ or θ ), the relationship between the perceived tax and actual tax in equation (1) implies that (4)

∂( p + τ˜ ) ∂ τ˜ = = δ1c (θ ). ∂( p + τ ) δτ

1. The assumption of quasi-linear utility seems a reasonable one when the taxed good is a small part of the overall consumer’s budget (such as the toll case I consider). It is not, however, an innocuous assumption for the political response to tax salience; I discuss this in more detail in Section II.B.

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Using (4), we can simplify the relationship between η(τ ) and η(τ˜C ) in (3) to p+τ δ1C (θ ). (5) η(τ ) = η(τ˜C ) p + τ˜C Differentiating both sides of (5) with respect to salience (θ ) gives ∂η(τ ) = η(τ˜C )( p + τ ) ∂θ − ⎛ (6)

⎞

⎜ −1 ⎟ 1 ×⎜ δ1C (θ )τ δ1C (θ ) + δ1C (θ )⎟ . ⎝ ( p + τ˜C )2 δ0C (θ ) + ( p + τ˜C ) ⎠ − + ? −

+

Equation (6) shows that the sign of the impact of tax salience on the elasticity of demand (i.e., the sign of ∂η(τ )/∂θ) is ambiguous, because the impact of salience on the level of the perceived tax (θ ) + δ1C (θ )τ )) is of ambiguous sign.2 In the em(i.e., ∂ τ˜C /∂θ ≡ (δ0C pirical work I find evidence that consumption behavior becomes less elastic as salience decreases (i.e., ∂η(τ )/∂θ > 0). Equation (6) indicates that a sufficient (although not necessary) condition for (θ ) + δ1C (θ )τ > 0 (i.e., the perceived tax is ∂η(τ )/∂θ > 0 is that δ0C increasing as salience decreases). In Section III I present survey evidence that is consistent with this condition, suggesting that these empirical findings are internally consistent. To estimate ∂η(τ )/∂θ empirically, I multiply (5) through by ∂ log( p + τ ) to obtain p+τ δ1C (θ )∂ log( p + τ ). (7) ∂ log x1 = η(τ˜C ) p + τ˜C Taking a linear approximation to (7) around θ = 0 and explicitly separating out the main effects from the interaction effect of interest, I estimate (8)

log(x1 ) = β1 log( p + τ ) + β2 θ + β3 θ log( p + τ ) + ε.

The parameter β1 provides an estimate of the estimated elasticity of demand in a fully salient system (i.e., θ = 0), in which case 2. The other components of (6) are signed by the assumptions discussed earlier in this section.

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η(τ˜C ) = η(τ ) = β1 . The parameter of interest is β3 ; it indicates how the elasticity changes with salience. II.B. Political Response to Tax Salience The political response of tax rates to tax salience may depend not only on how the consumer’s behavioral responsiveness to tax changes with salience (i.e., ∂η(τ )/∂θ) but also on how the political costs of taxes change with tax salience. Section II.A showed that the sign of the effect of tax salience on the consumer’s behavioral responsiveness is ambiguous. Moreover, any effect of tax salience on political costs need not be the same sign as any effect of tax salience on consumer behavioral responsiveness, because salience at the time of consumption and salience at the time of voting may be different; this creates further ambiguity in the sign of the relationship between tax salience and tax rates. This ambiguity motivates the empirical work that is the focus of this paper. To gain some intuition into the determinants of the sign of the relationship between tax salience and tax rates, I consider a government that sets the tax to maximize a weighted sum of some economic objective and the (negative of) any political costs of the tax. For concreteness, I assume the economic objective of the tax is to raise revenue. I discuss other possible economic objectives—and how these affect the implications of tax salience—in Section II.D. The government chooses τ each year to maximize (9)

max λτ Q( p + τ˜C ) − (1 − λ) f (E) C(τ˜v ), τ

where 0 ≤ λ ≤ 1 represents the weight the government places on the economic objective of the tax (i.e., raising revenue) relative to the political cost of the tax, C denotes the political cost of the tax, and E is an indicator variable for whether or not it is an election year. I assume that f (E) > 0 and f (E) > 0; in other words, the political costs of taxes are exogenously higher in election years, so that we expect a “political business cycle” in taxes (Nordhaus 1975); in the empirical work, I provide evidence of a political business cycle in toll setting. The government’s optimization problem yields the first-order condition for the tax rate (10)

τ∗ =

−Q(τ˜C ) (1 − λ) f (E) C (τ˜V ) + , Q (τ˜C ) λQ (τ˜C )

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where to simplify notation I have defined C ≡ (∂C/∂ τ˜ ) (∂ τ˜ /∂τ ) and Q ≡ (∂ Q/∂ τ˜ ) (∂ τ˜ /∂τ ). To ensure an interior solution to the optimal tax, I assume that C > 0 (i.e., political costs are rising in the actual tax) and Q < 0 (i.e., demand is falling in the actual tax). Note that both consumption salience and voting salience affect the choice of tax rate: the amount of revenue raised depends on the perceived tax at the time of the consumption decision (i.e., τ˜C ), and the political cost of the tax depends on the perceived tax at the time of voting (i.e., τ˜v ). Differentiation with respect to θ of the first-order condition for the government’s optimal tax level in (10) indicates that the sign of any effect of tax salience on the choice of tax rate is a priori ambiguous: ⎛ ⎞ ⎛ ∂C Q ⎜ ∂ Q ⎞⎟ ⎜∂ − Q C ⎟ − ∗ ⎜ (1 − λ) f (E) ⎜ ∂θ ∂τ Q ⎟⎟ ∂θ =⎜ + (11) ⎝ ⎠⎟ ⎜ ⎟. 2 ∂θ λ (Q ) ⎜ ∂θ ⎟ ⎝ ⎠ + ? ?

Although the sign of (11) is theoretically ambiguous, there are intuitive findings concerning how the relationship between tax salience and tax rates is likely affected by the effect of salience on the consumer’s behavioral responsiveness to taxes, and by the effect of salience on the political costs of taxes. To see this, consider first the simplest case in which λ = 1, so that the government only maximizes revenue. In that case, the politically optimal tax in equation (10) reduces to the standard inverse elasticity optimal tax equation τ∗ 1 , = p + τ∗ η(τ )

(12)

and thus (under the assumption of fixed producer prices) (13)

sign of

1 ∂η(τ˜C ) ∂τ ∗ = sign of . ∂θ η(τ )2 ∂θ +

?

Equation (13) indicates that, when the government sets taxes to maximize revenue, the sign of how taxes vary with salience is the sign of how the elasticity of demand with respect to the tax varies with salience (which as we saw in (6) can be of either sign). Intuitively, if a decline in salience lowers the behavioral response

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to the tax (i.e., ∂η(τ )/∂θ > 0), then the tax rate set by the government will be rising as salience declines. Note that the assumption of quasi-linear utility is important for this result, as it removes any distortionary effect of reduced salience on consumption of the taxed good that arises from the budgetary consequences of the misperceived tax. In the more general case, where such distortionary effects will exist, Chetty, Kroft, and Looney (forthcoming) show that even if reduced salience reduces the behavioral response to the tax, this is not sufficient for the optimal tax to increase; this is likely to be particularly important for taxes that are a large share of the individual’s budget, such as income taxes. Moreover, if the government puts some weight on the political costs of taxes (i.e., λ < 1), this introduces another source of indeterminacy in the sign of the relationship between tax salience and tax rates. However, the model suggests that we can learn more about the likely sign of ∂τ ∗ /δθ in (11) by examining how any political business cycle in tax setting changes as tax salience declines. To see this, note that ⎛ ⎞ ∂C Q − ∂ Q C 2 ∗ 1 − λ f (E) ⎜ ∂θ ∂ τ ⎟ ∂θ = (14) ⎝ ⎠ ∂θ ∂ E λ (Q )2 + ?

and observe that the first term in parentheses is positive by assumption, and that the second term in parentheses (whose sign is unknown) also appears in (11). Thus if ∂ 2 τ /∂θ ∂ E > 0, this implies that the second term in parentheses in (14) is positive, so that the entire second term in (11) is positive. In other words, if the political business cycle attenuates as salience declines (i.e., ∂ 2 τ /∂θ ∂ E > 0, for which I find evidence in the empirical work below), this makes it more likely that a decline in tax salience raises taxes (i.e., ∂τ ∗ /δθ > 0). To investigate the relationship between tax salience and tax rates empirically, I note that the first-order condition for the tax rate in (10) indicates that the tax rate will depend on tax salience (θ ), whether it is an election year (i.e., E = 1 or E = 0), and the interaction of these two effects. Because of the serial correlation properties of taxes in my empirical application (which I discuss in more detail below), I estimate the relationship between taxes and salience in first differences, estimating that (15)

τ = β1 θ + β2 E + β3 E(θ ) + μ.

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Estimation of (15) allows a comparison of the effect of tax salience on tax rates in nonelection years (i.e., β1 ) and in election years (i.e., β3 ). II.C. Identification An examination of the two main estimating equations— equation (8), which comes from the driver optimization problem and reveals how behavioral responsiveness to the tax changes with salience, and equation (15), which comes from the political optimization problem and reveals how the tax varies with salience—highlights two important identification problems. First, taxes are taken as exogenous to demand in the demand estimation equation (8), but are determined as the endogenous result of the political optimization problem (see (10)). Identification of the demand equation requires that the error term ε in the demand equation (8) be uncorrelated with the error term μ in the taxsetting equation (15); in other words, identification requires that changes in demand do not contemporaneously affect changes in taxes. For example, if demand follows a random walk, then as long as the government tax-setting process takes at least one year to respond to demand, current changes in taxes will be uncorrelated with current changes in demand and the demand equation (8) will be identified.3 This identifying assumption seems reasonable for a (bureaucratic) government that may not be able to make and implement decisions quickly. In the empirical application, I will show that, in practice, taxes are changed only about once a decade, which is consistent with the assumption of a lagged response. Furthermore, any changes in taxes that are driven by changes in any of the nondemand factors that (10) indicates affect tax rates—that is, the sensitivity of political costs to the tax rate (C ), the electoral calendar (E), or the relative weight (λ) that the government places on the political costs of taxes—do not pose a problem for identification (as long as changes in these factors are themselves exogenous to changes in current demand). The second identification problem is that I allow the tax (τ ) to be chosen endogenously by the political optimization problem in (9), but assume that the salience of the tax system (θ ) is 3. In my empirical application I find that changes in (residual) demand have an AR1 coefficient of 0.045, suggesting that demand is (close to) a random walk. I also explore robustness of demand estimation to alternative specifications with weaker identifying assumptions (see Section V).

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exogenously determined. If the government endogenously chooses θ (e.g., on the basis of any of the factors that determine τ ), the taxsetting estimating equation (15) is not identified. The validity of the assumption that the choice of tax salience is exogenous with respect to the choice of tax rate is ultimately an empirical question, and one that I explore in depth in Section VI.A. II.D. Other Government Objective Functions and Normative Implications For concreteness, in Section II.B I assumed the government’s objective function in choosing the tax rate was a weighted average of the revenue raised by the tax (its economic objective) and the (negative of) the political costs of the tax (its political objective). Of course, the government may well have other economic objectives, such as redistributive taxes or Pigouvian corrective taxes; the latter is potentially quite relevant for the toll case that is the subject of the empirical work. As with a revenue-raising tax, the optimal level of these other types of taxes also varies inversely with the behavioral responsiveness to the tax. For example, if the tax is set as an optimal Pigouvian externality correction, the optimal tax will be increasing as the behavioral responsiveness to the tax declines. Therefore the same empirical prediction concerning how the impact of salience on the behavioral responsiveness to the tax likely affects the impact of tax salience on tax rates should apply (qualitatively) to these other economic objectives. In contrast to the positive empirical predictions, the normative implications of any effect of tax salience on tax rates will be quite sensitive to the government’s objective function. One critical issue for the normative implications of tax salience is whether the government operates as a benign social planner or is (partially or fully) maximizing independent objectives (such as keeping politicians in office or increasing the size of government); in the latter case, the government’s response to a decline in salience may be self-serving, but not socially optimal. The evidence I present below that the political business cycle in toll setting attenuates when salience is reduced suggests that part of the impact of tax salience on tax rates comes from reducing the political costs of raising tolls; this suggests that the government’s response to a reduction in tax salience may not be that of a fully benign social planner. Even when the government operates as a fully benign social planner, the normative implications of a decline in salience will also depend on the economic component of the government’s

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objective function. If the economic objective is to raise revenue, then if salience reduces the behavioral responsiveness to the tax, this is likely to be welfare-improving because it allows the government to raise a given amount of revenue at lower distortionary costs. However, if the economic objective of the tax is a Pigouvian externality correction, the normative implications may be quite different. For example, if salience reduces the behavioral responsiveness to the tax, this has no effect on welfare if the tax is set solely as a Pigouvian corrective tax, utility is quasi-linear in the taxed good, and the revenue raised is rebated back to consumers as a lump sum; the government would raise the tax to the (new) higher optimal externality-correction tax and rebate back the resulting (higher) revenue as a lump sum, with no change in aggregate welfare. However, in more general models in which utility is not quasi-linear and/or the government does not rebate back the revenue raised as a lump sum, a lower behavioral responsiveness to the Pigouvian tax due to reduced salience can be welfare-reducing. III. IMPACT OF ETC ON TOLL SALIENCE: SURVEY EVIDENCE The empirical analysis is predicated on the assumption that ETC reduces the salience of the tolls (i.e., increases θ ). I therefore begin by presenting survey evidence consistent with this assumption. Evidence from two separate surveys indicates that individuals are substantially less aware of tolls if they pay them electronically rather than with cash. One survey is an in-person survey that I designed and conducted in May 2007 of 214 individuals who had driven to an antiques show in western Massachusetts on the Massachusetts Turnpike (“MA Survey”). The other is a telephone survey conducted in June and July 2004 of 362 regular users from New Jersey of any of the six bridges or tunnels of the Port Authority of New York and New Jersey that cross the Hudson River (“NYNJ Survey”). More details on the MA Survey can be found in the Online Appendix (Section A); more details on the NYNJ Survey can be found in Holguin-Veras, Kaan, and de Cerrano (2005, especially pp. 116–126 and pp. 383–394). Each survey asked drivers their estimate of the toll paid on their most recent trip on the relevant facility, their method of payment, and a variety of demographic characteristics; information about the exact trip was also collected so that the actual toll paid could be calculated.

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Table I summarizes the results. Both surveys show a strikingly lower awareness of tolls among drivers who paid with ETC than among those who paid with cash. The differences are both economically and statistically significant. In the MA survey, 62% of drivers who paid using ETC responded to the question about their best guess of the toll they paid that day on the Turnpike with “I don’t know” and would not offer a guess without prompting from the surveyor to please “just make your best guess”;4 in contrast, only 2% of drivers who paid with cash had to be prompted to offer a guess. In the NYNJ survey, 38.1% of ETC users reported “do not know” or “refused” when asked how much they paid at the toll in their most recent drive across the Hudson from New Jersey to New York, compared to 20.0% of cash users.5 Moreover, the ETC drivers’ belief that they did not know how much they had paid for the toll was borne out by their subsequent guesses. In the MA Survey, 85% of drivers who paid using ETC estimated the toll they paid incorrectly, compared to only 31% of drivers who paid using cash. In the NYNJ survey, 83% of ETC drivers estimated the toll incorrectly, compared to only 40% of cash drivers. Conditional on making an error, the magnitude of the error was also larger for ETC users; ETC users overestimate tolls by more than cash users.6 These findings of markedly lower knowledge of tolls among people who paid electronically than among those who paid with cash are consistent with the maintained assumption that tolls are less salient under ETC. In other words, the results are consistent with ETC reducing the link between the actual and the perceived toll (i.e., δ1 j (θ ) < 0). These findings are also consistent with other work on “payment decoupling,” which finds that technologies such as credit cards, which decouple the purchase from the payment, reduce awareness of the amount spent and thereby encourage more spending (e.g., Thaler [1999]; Soman [2001]). 4. Indeed, many of the ETC drivers literally responded, “I don’t know, I used EZ-Pass [or Fast Lane].” 5. It is interesting that the discrepancy in toll awareness between ETC and cash drivers is larger in the MA survey. One possible explanation is that the NYNJ Survey asked about the toll paid on a regular commute, whereas the MA Survey asked about the toll paid on a presumably idiosyncratic trip. Differences in the survey method (e.g., telephone vs. in person) may also have an effect on the individual’s willingness to guess. 6. This finding that ETC is associated with overestimation of the toll is consistent with the finding in Section V that ETC is also associated with reduced behavioral responsiveness to the toll. See equation (6) in Section II.A and the discussion that follows it.

0.618 (0.490) 0.851 (0.359) $1.334 (1.850) 68

0.021 (0.142) 0.308 (0.463) $0.162 (0.828) 146

Cash drivers (2)

Covariate adjusted (4) 0.579∗∗∗ (0.060) 0.512∗∗∗ (0.067) $1.01∗∗∗ (0.303)

No covariates (3) 0.597∗∗∗ (0.060) 0.543∗∗∗ (0.058) $1.172∗∗∗ (0.275) 271

0.381 (0.486) 0.826 (0.379) $0.40

ETC drivers (5)

91

0.200 (0.400) 0.395 (0.489) −$0.10

Cash drivers (6)

0.18∗∗∗ (0.05) 0.43∗∗∗ (0.06) $0.50

Difference between ETC and cash drivers (no covariates) (7)

NYNJ survey

Notes. In columns (1), (2), (5), and (6), standard deviations are in parentheses; in columns (3), (4), and (7) robust standard errors are in parentheses and ∗∗∗ , ∗∗ , ∗ denote statistical significance at the 1%, 5%, and 10% levels, respectively. “Error” in the third row is computed as estimated toll − actual toll paid. In the MA Survey an estimate of the toll paid was eventually elicited from all but one of the respondents; however, in the NJNY Survey, an estimate of the toll paid was only elicited for those who did not respond “don’t know” or “refused.” Thus, for the MA Survey, the sample in rows (2) and (3) includes all but one of the respondents in row (1), but for the NYNJ Survey, the sample in rows (2) and (3) includes only those respondents who did not report “don’t know” in row (1). For the NYNJ survey, the cash toll was $6.00, whereas the ETC toll was $5.00 on peak and $4.00 off peak. For the MA survey, the toll depended on the entrance and exit taken. The average toll paid was about $1.15. Less than 10% of drivers in the MA survey sample drove on a portion of the Turnpike in which there are ETC discounts, and the results are not affected by omitting these drivers from the analysis. In column (4), covariates consist of age, age squared, median household income of ZIP code, dealer retail price for the driver’s car (based on information from www.edmunds.com as of October 2007), and indicator variables for sex, whether the driver regularly pays a toll on a commute to work, and highest level of education reached (high school degree or less, college degree, or postcollege degree, where “college degree” includes associates degrees, which were 10% of the college degree sample). Only published summary statistics (as opposed to the underlying microdata) are available for the NYNJ survey, so that the covariate-adjusted difference in means cannot be computed. In addition, the sample sizes by cell for the NYNJ survey had to be approximated based on information in the text on the total sample size (362) and the fraction of drivers that pay by ETC (74.8%). As a result, the standard errors for the NYNJ Survey are also approximated; approximated numbers are shown in italics. I calculated standard deviations for the binary response variables in the NYNJ Survey, but there was not sufficient information available to calculate the standard deviation for the mean error (or the standard error of the difference in mean error).

Fraction who incorrectly estimate toll Mean error, conditional on misreporting N

Fraction who report “don’t know”

ETC drivers (1)

Difference between ETC and cash drivers

MA survey

TABLE I SURVEY EVIDENCE ON DRIVER AWARENESS OF TOLLS, BY PAYMENT METHOD

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Several caveats are in order. First, neither survey is representative of the nationwide population. Nonetheless, it is reassuring that the finding of lower toll awareness among ETC drivers persists in two very different populations, including a population of regular commuters. Second, cross-sectional differences in awareness of tolls between ETC drivers and cash drivers could reflect differences in these drivers besides their payment method. Reassuringly, a comparison of the results in columns (3) and (4) of Table I shows that none of the differences in toll awareness in the MA Survey are sensitive (in either magnitude or statistical significance) to adding controls for demographic characteristics of drivers, including age, sex, education, median household income of ZIP code, and value of their car. Finally, a survey response on toll perception does not necessarily reflect either the perceived toll at the time of consumption (τ˜C ) or the perceived toll at the time of voting (τ˜V ). However, given the large percentage of cash drivers relative to ETC drivers who are spot on in estimating the toll paid correctly, it seems plausible that ETC may reduce one or both of these types of salience. I now turn to direct evidence of the impact of ETC first on consumer behavior and then on toll setting.

IV. DATA AND DESCRIPTIVE STATISTICS This section provides some brief background on the sample construction and variable definitions for the toll facility data; considerably more details on the facilities in the sample and the variable definitions can be found in the Online Appendix (Section B) or in the working paper version of this paper (Finkelstein 2007). IV.A. Sample Construction The target sample was all 183 publicly owned toll facilities in the United States (excluding ferries) that were charging tolls in 1985, which predates the introduction of ETC in the United States. In 1985, toll revenue in states that levied tolls was about 0.8% of state and local tax revenue, roughly the same revenue share as state lotteries (U.S. Census Bureau 1985; U.S. Department of Transportation 1985, 1986; Kearney 2005). Statutory authority for toll setting is usually vested in toll operating authorities. These are typically appointed by state or local governments, which therefore, in practice, retain influence on toll setting.

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1985

1990

1995 ETC start date

2000

2005

FIGURE I Distribution of ETC Start Dates

By contacting each toll authority, I was able to collect data for 123 toll facilities.7 These 123 facilities are run by 49 different operating authorities in 24 different statelike entities; these include 22 states and 2 joint ventures (one between New York and New Jersey and one between New Jersey and Pensylvania). I refer to all 24 hereafter as “states.” On average, the data contain 50 years of toll rates per facility. IV.B. Key Variables ETC Adoption and Diffusion. Figure I shows a histogram of ETC adoption dates, which range from 1987 through 2005, with a median of 1999. By 2005, 87 of the 123 facilities had adopted ETC. Almost all of the variation in whether and when ETC is adopted is between rather than within operating authorities; there is, however, substantial variation across authorities within a state (not shown). On average for a facility with ETC, I observe about six years of ETC. Table II shows that relationship between facility characteristics and ETC adoption. ETC adoption rates are highest in the northeast (78%) and lowest in the west (57%). The high adoption rates in the northeast may reflect greater urbanism (because ETC 7. A toll “facility” is a particular road, bridge, or tunnel; about 60 percent of the responding facilities are bridges or tunnels.

985

E-ZTAX: TAX SALIENCE AND TAX RATES TABLE II WHICH FACILITIES ADOPT ETC?

All By facility type Roads Bridges or tunnels By region of country Northeast Midwest South West

Number of facilities

Probability of adopting ETC by 2005

Average adoption date conditional on adoption

123

.71

1998.2

44 79

.70 .71

1996.4 1999.2

58 10 41 14

.78 .60 .68 .57

1998.7 1996.7 1997 2000.9

may help reduce congestion) as well as higher labor costs (because ETC reduces labor costs of toll collection). ETC is adopted with the same probability on roads as on bridges and tunnels; however, roads that adopt ETC do so about three years earlier on average than bridges or tunnels that adopt ETC. Older facilities are more likely to adopt ETC, and those that do are likely to do so earlier than younger facilities that adopt ETC (not shown). Once a facility adopts ETC, use of the technology diffuses gradually across drivers. I was able to obtain the ETC penetration rate (defined consistently within each facility as either the fraction of toll transactions or the fraction of toll revenue collected by ETC) for about two-thirds of facility-years with ETC. Figure II shows the within-facility ETC diffusion rate. It takes about fourteen years for ETC to reach its steady state penetration rate of 60 percent. Toll Histories. I define the toll as the nominal toll for passenger cars on a full-length trip on a road, or on a round trip on a bridge or tunnel. I collected data on both the “manual” (i.e., cash) toll and any discount offered for the electronic toll; the electronic toll is never more than the cash toll.8 Over half (53 of 87) of facilities with ETC offer a discount at some point. Discounts are presumably offered to encourage use of the technology; indeed, they are more common on facilities that adopt ETC earlier. The discounts may also be rationalized as a Pigouvian subsidy if ETC has positive externalities on congestion reduction. The average discount offered is about 15 percent. 8. High-frequency discounts (i.e., commuter discounts) are not coded. None of the facilities in the sample offer time-of-day varying prices.

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0.7

ETC penetration rate

0.6

0.5

0.4

0.3

0.2

0.1

0 1

2

3

4

5

6

7

8

9 10 11 ETC year

12

13

14

15

16

17

18

19

FIGURE II Within-Facility ETC Diffusion Figure II reports the coefficients on indicator variables for the number of years a facility has had ETC from the following regression: ETC Penetrationit = αi + 19 k=1 βk 1(ETCyear = k), where the αi are facility fixed effects, 1(ETCyear = k) are indicator variables for whether it is the kth year of ETC, and ETC Penetration is defined either as percentage of toll transactions paid by ETC or as percentage of revenue paid by ETC, depending on the facility. The regression is estimated on the sample of facility-years with ETC and data on ETC penetration (N = 467; 84 unique facilities).

The primary toll measure in the analysis is the lower envelope of the manual and electronic tolls (hereafter, “minimum toll”). I also present results for the subsample of facilities that never offer ETC discounts, and for which the minimum and manual toll are therefore always the same. On average, the minimum toll increased by 2.0% per year. This is substantially below the facilityyear-weighted average inflation rate of 4.2%. Toll changes are lumpy; on average only 7.7% of facilities increase their minimum toll and only 1% of facilities decrease it each year. Revenue and Traffic Data. I was able to collect traffic (revenue) data for 76 (45) of the 123 facilities. On average, for a facility with these data, I obtained 34 years of data. V. THE IMPACT OF ETC ON THE ELASTICITY OF DRIVING WITH RESPECT TO THE TOLL CHANGE To examine how ETC affects the elasticity of driving with respect to the tax, I adapt the demand equation (8) to the toll

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987

context as follows: log(traffic)it = γt + β1 log (minimum tollit ) + β2 log (minimum tollit ) ∗ Never ETCi + β3 log (minimum tollit ) ∗ ETC Penetrationit (16)

+ β4 Never ETCi + β5 ETC Penetrationit + εit .

I proxy for demand for the taxed good (i.e., x1 in (8)) with the amount of traffic on facility i in year t (i.e., trafficit ), and for the salience of the tax system (i.e., θ in (8)) with the ETC Penetration rate on facility i in year t (i.e., ETC Penetrationit ). For purposes of practicality, I estimate the demand responsiveness to τ in (16) rather than to p + τ as in (8), because I do not observe the nontax costs ( p) of driving. As long as p does not vary with taxes or with tax salience (i.e., the fixed producer prices assumption discussed in Section II), this modification will affect the magnitude of the estimated elasticities but not their sign. As noted, I use the minimum toll as my measure of τ . Equation (16) examines the relationship between the annual percentage change in a facility’s traffic (log(traffic)it ) and the annual percentage change in its toll (log(minimum toll)it ) and how this relationship changes with the ETC penetration rate. To strengthen the inference, it also allows the elasticity to vary across facilities based on whether the facility ever adopted ETC (Never ETCi is 1 if the facility never adopts ETC and zero otherwise), and it allows for secular changes in demand over time (the γt represent a full set of year fixed effects). The key coefficient of interest is β3 ; this indicates how the elasticity changes at a facility as ETC use diffuses. Finally, εit is a random disturbance term capturing all omitted influences. I allow for an arbitrary variance– covariance matrix within each “state” and give equal weight in the regression to each operating authority. As discussed in Section II.C, identification of (16) is based on the assumption that changes in tolls are not affected by contemporary changes in demand. This is probably a reasonable assumption. Traffic—and presumably underlying demand for driving—changes continuously each year, whereas a facility’s toll is raised on average only every eight to nine years. The infrequency of toll adjustment likely reflects both general lags in price setting by government enterprises and political constraints; for example, I show in Section VI.B that toll increases are significantly lower during state election years. Although tolls may be

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adjusted in part based on past demand shocks (i.e., lagged values of changes in traffic), changes in traffic within a facility show very little serial correlation; a regression of the residuals from (16) on their lags produces a coefficient of only 0.045. Any adjustment of tolls to past changes in demand is therefore unlikely to pose much of a practical problem for the estimation. However, as a robustness check, I also report results in which I limit the sample to the years in which a toll changes or the two years before or after a toll change; I refer to this as the “+2/−2 sample.” The assumption in this more limited sample is that the timing of the toll change is random with respect to short-run traffic changes, although it may reflect longer-run demand changes. I estimate (16) on approximately one-fourth of the facilities in the data. By necessity, the analysis is limited to the approximately 60 percent of facilities for which I obtained traffic data. I further limit the subsample of facilities with traffic data to the approximately 40 percent of them that never offer an ETC discount. This allows me to include the ETC penetration rate directly on the right-hand side, without worrying about omitted variable bias from any potential effect of an ETC discount on both the ETC penetration rate and traffic. An added advantage of looking only at facilities that never offer an ETC discount is that in this sample there is only one toll rate (i.e., the minimum toll and the toll are always the same), which avoids the measurement error that ETC discounts would otherwise introduce in the right-hand-side toll variable once ETC is introduced.9 Table III reports the results. Columns (1) and (2) show the results from regressing log(traffic)it on log(minimum toll)it and year fixed effects. Column (1) shows the results for the full sample of facilities with traffic data, including those that offer ETC discounts. The coefficient on log(minimum toll)it of −0.049 (standard error 0.015) indicates that a 10% increase in tolls is associated with a statistically significant but economically small 0.5% reduction in traffic. Column (2) shows that the result is quite similar for the sample of facilities that never offer ETC discounts; the coefficient on log(minimum toll)it is −0.058 (standard error 9. I show below that the estimated impact of ETC on toll rates is robust to limiting the sample to facilities that never offer discounts. When I limit to those for whom I have traffic data, the effect is very similar in magnitude to the estimates in the full sample, although no longer statistically significant at conventional levels (not shown).

989

E-ZTAX: TAX SALIENCE AND TAX RATES TABLE III THE ELASTICITY OF TRAFFIC WITH RESPECT TO TOLLS (1) log min. tollit

(2)

−0.049 −0.058 (0.015) (0.018) [.004] [.008]

log min. tollit * ETC penetrationit

(3)

(4)

(5)

(6)

−0.061 (0.019) [.009] 0.134 (0.038) [.005]

−0.057 (0.017) [.006]

−0.062 (0.039) [.145] 0.141 (0.076) [.091]

−0.060 (0.037) [.135]

log min. tollit * ETC yearit log min. tollit * never ETCi Mean dep. var. # of states # op. authorities # of facilities N Sample restriction(s)

0.049 21 32 76 2,200

−0.071 (0.136) [.611] 0.042 0.043 12 12 16 16 33 33 727 671 No ETC No ETC discounts discounts

0.006 (0.001) [.002] −0.073 (0.131) [.588] 0.042 12 16 33 727 No ETC discounts

−0.009 (0.209) [.966] 0.040 12 16 33 292 No ETC discounts +2/−2 sample

0.006 (0.003) [.062] −0.006 (0.205) [.976] 0.039 12 16 33 305 No ETC discounts +2/−2 sample

Notes. Table reports results from estimating variants of (16) by OLS. The dependent variable is the change in log traffic. In addition to the covariates reported in the table, all regressions include year fixed effects and a main effect for any variables that are interacted with log(min. toll). The bottom row indicates any sample restrictions. “No ETC discounts” limits facilities to those that never offered an ETC discount. “+2/−2 sample” limits sample to facility-years in which there is a toll change or the two years before or after a facility’s toll change. Never ETCi is an indicator variable for whether facility i never has ETC. ETC penetrationit is the share of tolls paid by ETC on facility i in year t; it is zero in years in which the facility did not have ETC. ETC yearit is the number of years the facility has had ETC; it is zero in any year in which the facility does not have ETC, 1 the year the facility adopts ETC, 2 the second year the facility has ETC, and so forth. Each operating authority receives equal weight. Standard errors (in parentheses) are clustered by state. p-values are reported in square brackets.

= 0.018). These results suggest that tolls are set below the profitmaximizing rate, which is consistent with Peltzman’s (1971) observation that there will be a downward bias in the prices set by government-owned enterprises. More generally, it suggests that— as modeled in Section II.B—the government objective function is not pure revenue maximization.10 10. Of course, I am only measuring the short-run response to a small change in tolls; this behavioral response may merely reflect the route chosen on a particular day. Longer-run responses to (possibly larger) toll changes may be larger, reflecting among other things decisions that affect regular commuting patterns.

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Column (3) shows the results from estimating the complete equation (16). The coefficient on log(minimum tollit ) ∗ ETC penetrationit is 0.134 (standard error 0.038); this indicates that a 5-percentage-point increase in the ETC penetration rate (which is the average increase per year of ETC) is associated with a (statistically significant) 0.0067 decline in the elasticity of driving with respect to the toll, or about 10 percent relative to the average estimated elasticity prior to ETC of −0.061. Column (4) shows the results when the ETC Penetration variable in (16) is replaced by the number of years the facility has had ETC (ETC Year); this variable is zero prior to ETC adoption, 1 in the year of adoption, 2 in the second year of ETC, and so forth. The coefficient on log(minimum tollit ) ∗ ETC Yearit is 0.006 (standard error 0.001), indicating a decline in elasticity of 0.006 per year of ETC quite similar to that estimated in column (3).11 The last two columns of Table III repeat the analysis in columns (3) and (4) on the +2/−2 sample. The point estimates on both the elasticity of driving under manual toll collection and the change in the elasticity associated with ETC Year (or ETC Penetration) remain virtually unchanged. The change in the elasticity associated with ETC remains statistically significant, although at the 10% level in the +2/−2 sample (columns (5) and (6)) rather than at the 1% level as in the larger samples (columns (3) and (4)). As noted in Section II.B, for taxes that are small as a portion of income, if a decline in salience reduces the behavioral responsiveness to the toll, this will tend to cause tolls to rise when salience declines. However, the net impact of salience on toll rates is ambiguous; it also depends on how salience affects the political costs of toll setting. I now turn to an examination first of the net effect of ETC on toll rate and then of the effect of ETC on the political costs of tolls. 11. One potential concern in interpreting these results is that the finding of a decline in the (absolute value) of the elasticity of driving with respect to the toll under ETC might spuriously reflect a general time trend in the elasticity of driving with respect to the toll. To investigate this, I reestimated the regressions shown in columns (3) and (4) of Table III with the inclusion of an additional interaction term log(minimum toll)it * yeart on the right-hand side; this allows for a time trend in the elasticity of driving. The inclusion of this interaction term weakened the precision of the estimated decline (in absolute value) of the driving elasticity under ETC, but did not substantively affect the finding. For example, for the specification shown in column (3), the coefficient on log(minimum tollit ) ∗ ETC penetrationit became 0.137 (standard error 0.067). In column (4), the coefficient on log(minimum tollit ) ∗ ETC Yearit became 0.005 (standard error 0.002).

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VI. THE IMPACT OF ETC ON POLITICAL BEHAVIOR VI.A. The Impact of ETC on Toll Rates Baseline Specification. To estimate the impact of ETC on toll rates, I begin with a simplified version of the estimating equation for tax setting (equation (15)) in which I omit any measure of whether it is an election year from the right-hand side. Because the election calendar is set exogenously, this does not introduce any omitted variable bias, and allows me to capture the average impact of ETC on toll rates; I augment the analysis to include electoral effects in Section VI.B. I therefore begin with the estimating equation: (17)

yit = γt + β1 ETCAdoptit + β2 ETCit + μit .

In the baseline specification, the dependent variable is the change in the log of the minimum toll (log(min toll)it ). I estimate the dependent variable in logs rather than in levels (as in equation (15) in Section II.B) in order not to constrain toll rates in different facilities to grow by the same absolute amount each year; this seems undesirable, given the considerable variation in toll rates across facilities.12 The γt s represent year dummies that control for any common secular changes in toll rates across facilities. The key coefficients of interest are those on ETCAdoptit and ETCit , which represent my parameterization of the change in tax salience (θ in (15)). Specifically, ETCAdoptit is an indicator variable for whether facility i adopted ETC in year t. The coefficient on ETCAdoptit thus measures any level shift in the minimum toll associated with the introduction of ETC; this might include, for example, the effect of any ETC discounts. However, because ETC use among drivers diffuses gradually, it is likely that any impact of ETC on toll rates will also phase in gradually. To capture this, I include the indicator variable ETCit for whether facility i has ETC in year t; it is 1 in the year of ETC adoption and in all subsequent 12. In practice, the sign and statistical significance of the impact of ETC on tolls are robust to specifying the dependent variable as the change in the level of the minimum toll rather than the change in the log of the minimum toll; the magnitude of the effect is slightly more than double in this alternative specification (not shown). One potential concern with the log specification is that the dependent variable is censored when a toll is set to 0. Indeed, 15 of the 123 facilities that were charging a toll in 1985 subsequently set the toll to zero. I treat all facilityyears with zero tolls as censored (both in the log and in the level analysis). This likely biases downward any estimated impact of ETC, because I find that ETC is associated with a negative and marginally statistically significant decline in the probability that the toll rate is changed from nonzero to zero (not shown).

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years. The coefficient on ETCit thus measures the average annual growth in a facility’s toll once it has ETC. Thus I parameterize θ with ETCAdoptit and ETCit in the first year of ETC, and I parameterize θ with ETCit in all subsequent years with ETC. Finally, μit is a random disturbance term capturing all omitted influences.13 I estimate (17), allowing for an arbitrary variance–covariance matrix within each state, and give equal weight in the regression to each operating authority. The first column of Table IV shows the results from estimating (17). The coefficient on ETCit is 0.015 (standard error 0.006). This indicates that once a facility has ETC, its toll increases by 1.5 percentage points more per year than it otherwise would have. This effect is both statistically and economically significant. Relative to the average annual 2% increase in tolls, it implies that after installation of ETC, the facility’s toll rate rises by 75% more per year than it did prior to ETC.14 The toll change in the first year of ETC is given by the sum of the coefficients on ETCAdoptit and ETCit . These indicate that there is a (statistically insignificant) 3.6% decline in tolls the year that ETC is adopted. The results in the next two columns suggest that this decline in the year of ETC adoption is due to ETC discounts. Column (2) shows the results when the dependent variable is the change in the log manual toll; column (3) shows the results when the sample is limited to the approximately 60 percent of facilities that never offered an ETC discount (half of which never adopted ETC), for which the manual and minimum toll are always the same. In these alternative specifications, the sum of the coefficients on ETCAdoptit and ETCit is either positive and insignificant (column (2)) or negative and now both economically and statistically insignificant (column (3)). The fact that the growth in tolls under ETC persists in the “no discount” sample (column (3))—the coefficient on ETCit is statistically significant and slightly larger in magnitude than in the full sample in column (1)—indicates that the estimated growth 13. I estimate (17) in first differences rather than in levels with facility fixed effects because the residuals are much less highly serially correlated in first differences (AR1 coefficient of −0.045) than in the fixed effects version (AR1 coefficient of 0.92), making the first-differenced specification the preferred specification (Wooldridge 2002, pp. 274–281). 14. One might prefer to specify the percentage increase in the toll associated with ETC relative to the average annual growth rate of tolls prior to ETC; this is 1.9%. It is quite similar to the sample average (despite an average annual growth rate of tolls under ETC of 2.8%) because the vast majority of facility-years in the approximately fifty-year toll histories I collected on each facility do not have ETC.

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TABLE IV IMPACT OF ETC ON TOLL RATES log log min. toll manual toll (1) (2) ETCit

0.015 (0.006) [.018]

0.020 (0.006) [.004]

ETC penetrationit −0.051 (0.035) [.158] Mean dep. var. 0.020 # of states 24 # op. authorities 49 # facilities 123 N 5,079 Estimation OLS Sample restriction ETCAdoptit

0.016 (0.032) [.622] 0.022 24 49 123 5,079 OLS

log toll (3)

log toll (4)

log log min. toll min. toll (5) (6)

0.024 (0.012) [.061] 0.623 (0.285) [.044] −0.033 −0.051 (0.019) [0.035] [.097] [.166] 0.017 0.017 17 17 31 31 70 70 2,875 2,751 OLS OLS No ETC No ETC discount discount

0.557 0.501 (0.262) (0.261) [.045] [.067] −0.105 −0.097 (0.109) (0.108) [.348] [.380] 0.020 0.020 24 24 49 49 123 123 4,815 4,815 IV IV

Notes. Table reports results of estimating (17) (columns (1)–(3)) and (19) (columns (4)–(6)). Column headings define the dependent variable; the bottom two rows provide additional information on the estimation technique and sample restriction. ETCAdoptit is an indicator variable for whether facility i adopted ETC in year t. ETCit is an indicator variable for whether the facility has ETC; it is 1 in the year that ETC is adopted and in all subsequent years. ETC penetrationit measures the change in the proportion of tolls on the facility paid by ETC; it is zero if the facility does not have ETC. In column (5), the instrument for ETC penetrationit is ETCit . In column (6), the instrument for ETC penetrationit is a cubic polynomial in the number of years the facility has had ETC. In addition to the covariates shown in the table, all regressions include year fixed effects. Each operating authority receives equal weight. Standard errors (in parentheses) are clustered by state. p-values are reported in square brackets. “No ETC discounts” limits facilities to those that never offered an ETC discount. Declines in sample size in column (4) (compared to column (3)) and in column (5) or (6) (compared to column (1)) reflect missing data on ETC penetration rates (see Section IV).

in tolls after ETC is installed does not merely reflect a recouping of first-year losses from the ETC discount. For facilities that offer ETC discounts, there does not appear to be any systematic change in the discount over time after ETC adoption (not shown). This suggests that in practice increases in the minimum toll reflect a shift of the entire toll schedule, which is consistent with the finding that the manual toll also increases under ETC (column (2)).15 15. Although it might at first appear puzzling that the manual (i.e., cash) toll—which has become no less salient—also increases under ETC, this is easily understood by the necessary linkage between cash and electronic toll rates; were the electronic rate to increase while the cash rate did not, this would presumably discourage use of ETC. The preservation of the ETC discounts once ETC is installed

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The Pattern of ETC Diffusion and Toll Increases. The preceding analysis constrains the effect of ETC to be the same across facilities and over time. However, if ETC increases tolls by reducing their salience, we would expect the effect to be increasing in the ETC penetration rate, whose diffusion rate is not constant over time (see Figure II) or across facilities (not shown). As a stronger test of the salience hypothesis, therefore, I examine how the time pattern of toll changes after ETC adoption compares to the time pattern of ETC diffusion. Specifically, I compare the coefficients from estimating

(18a)

log(min toll)it = γt +

k=9

βk1 ETCYear(k,k+1) + εit

k=−9

and (18b) ETC Penetrationit = γt +

k=9

βk1 ETCYear(k,k+1) + εit ,

k=1

where ETC Penetrationit is the percentage point change in the ETC penetration rate for facility i in year t. The key outcome of interest is a comparison of the time pattern of the coefficients on the indicator variables 1(ETCYear(k,k+1) ) across the two equations. These are indicator variables for whether it is k or k + 1 years since ETC was adopted on the facility. For example, 1(ETCYear(1,2) ) is an indicator variable for whether ETC was adopted this year or last year (i.e., ETC Year is 1 or 2). In (18a), all of the indicator variables represent a two-year interval, except for the first (respectively, last) indicator variable, which is a “catch-all” variable for whether it is 9 or more years before (respectively, after) ETC adoption; the omitted category is the two years prior to adoption (i.e., ETC Year of −1 or −2). In (18b) I include only the post-ETC dummies that are in (18a). Figure IIIA shows the result. The solid black line shows the pattern of the log toll with respect to ETC Year implied by the estimates from (18a) and the dark dashed line shows the corresponding time pattern of ETC diffusion implied by the estimates

likely reflects continued attempts to induce more drivers to switch to ETC; the maximum ETC penetration rate in my sample is only 78%.

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E-ZTAX: TAX SALIENCE AND TAX RATES 0.15

0.55

(A)

ETC penetration rate (right axis)

0.1

0.45

0.05

0.35

0

0.25

–0.05

0.15

Log minimum toll (left axis)

–0.1

0.05

–0.15

–0.05 –8

–6

–4

–2

2

4

6

8

ETC year 0.2

0.55

(B)

0.15

0.45

ETC penetration rate (right axis)

0.1

0.35

0.05 0.25 0

0.15 –0.05

Log minimum toll (left axis)

–0.1

0.05

–0.15

–0.05 –8

–6

–4

–2

2

4

6

8

ETC year

FIGURE III Time Pattern of Toll Changes and ETC Diffusion The solid black line shows the pattern of log minimum toll implied by the estimates from (18a); the light dashed lines show the corresponding 95% confidence interval. The dark dashed line shows the pattern of the ETC penetration rate implied by estimating (18b). ETC year represents the number of years since (or before) ETC adoption. The omitted category (ETC year −2 for (18a) and all years prior to ETC adoption for (18b)) is set to zero. Indicator variables for whether it is nine or more years after ETC adoption are included in the estimating equation but not graphed; in (4a) an indicator variable for whether it is nine or more years before ETC adoption is also included in the regression but not graphed. In Panel B the sample of ETC-adopting facilities is limited to those who adopted in 1998 or earlier. The upper end of the 95% confidence interval for the log minimum toll at eight years is not shown for scale reasons; it is 0.201 (full sample, A) and 0.311 (balanced panel, B). To enhance the readability of the graph, the 95% confidence interval on ETC penetration rate is not shown. For Panel A the upper and lower 95% confidence intervals for ETC penetration rate are as follows: (0.16, 0.378) for ETC year 2, (0.267, 0.484) for ETC year 4, (0.336, 0.565) for ETC year 6, and (0.378, 0.610) for ETC year 8. For Panel B, the analogous confidence intervals are (0.197, 0.283), (0.333, 0.425), (0.389, 0.550), and (0.419, 0.617).

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of (18b).16 The results indicate that, after remaining roughly constant in the pre-ETC period, toll rates decline in the first two years of ETC (reflecting the discounts discussed earlier) and then climb steadily as ETC diffuses across the facility. Of course, the wide confidence intervals on the estimates caution against placing too much weight on the estimated time path. It is nonetheless reassuring that the point estimates suggest that the pattern of toll increases is similar to that of ETC diffusion. A potential concern with this analysis is that the set of facilities that identify the different β ks varies with the ETC year k. It is therefore difficult to distinguish the time path of the effect of ETC on a given facility from potentially heterogeneous effects of ETC across facilities.17 Figure IIIB therefore shows the results from re-estimating (18a) and (18b) when the sample of ETC-adopting facilities is limited to those that adopted ETC in 1998 or earlier. In this balanced panel of facilities, all of the graphed coefficients are identified by a constant set of facilities. The results are quite similar.18 For a more parametric (and higher-powered) analysis of how the time pattern of toll changes after ETC adoption compares with the diffusion of ETC, I estimate a modified version of (17): log(min toll)it = γt + β1 ETCAdoptit + β2 ETC Penetrationit + εit . (19) By replacing the indicator variable for whether the facility has ETC (ETCit ) with the percentage point change in ETC penetration (ETC Penetrationit ), I now allow the effect of ETC to vary over time and across facilities as a function of the diffusion of ETC.19 As discussed, I must estimate equation (19) on 16. The scale of the graph is arbitrary. I set the omitted category to zero. Thus, for example, the log minimum toll in ETC Year 4 is 2∗ β1 . +2∗ β3 and the log minimum toll in ETC Year −4 is 2∗ β−4 . 17. For the same reason, I do not extend the dummies in (18a) or (18b) for more years after ETC is adopted. 18. The point estimates in Figure IIIB indicate no preperiod trend in the balanced panel, which is reassuring relative to the (albeit statistically insignificant) suggestive evidence of some downward preperiod trend in the full sample in Figure IIIA. In Table VI I investigate the issue of potential preperiod trends in more detail, using a more parsimonious specification to increase statistical precision. 19. A more stringent test would be to include both ETC Penetrationit and ETCit on the right-hand side to examine whether the diffusion of ETC has an impact on toll rates that can be distinguished from a linear trend. I find that while the two variables are jointly significant, it is not possible to distinguish the effect of ETC penetration separately from a linear trend (not shown). This is not surprising, because, on average, the data contain about six years of data on a

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the subsample of facilities that never offer an ETC discount, as changes in the ETC discount will affect both the diffusion of ETC and the minimum toll. Column (4) of Table IV shows the results. The coefficient on the change in the ETC penetration rate is 0.623 (standard error 0.285). This indicates that every 10-percentagepoint increase in ETC penetration is associated with a (statistically significant) toll increase of 6.2%. For the full sample of facilities, I estimate (19) instrumenting for ETC Penetrationit with the indicator variable ETCit ; this is equivalent to instrumenting for the change in ETC penetration with a linear trend. Column (5) shows these results. The coefficient on ETC Penetrationit is 0.557 (standard error 0.262), indicating that every 10-percentage-point increase in ETC penetration is associated with a (statistically significant) 5.6% increase in the toll. To allow the effect of ETC to vary over time, in column (6) I instead instrument for the change in ETC penetration with a cubic polynomial in the number of years the facility has had ETC. The coefficient on ETC Penetrationit is now 0.501 (standard error 0.261). The results are also similar if I instead instrument for ETC Penetrationit with a series of indicator variables for the number of years under ETC (not shown). The magnitude of the estimated effect of ETC is quite similar across all of the various specifications shown in Table IV. The results from the baseline specification (Table IV, column (1)) suggest that after 14 years, by which point ETC has diffused to its steady state level (see Figure II), ETC is associated with an increase in the toll rate of 17%, or about one-sixth (∼exp(βETCAdopt + 14∗ βETC )). The IV estimates in columns (5) and (6) suggest that once ETC has diffused to its steady state level of 60%, it is associated with increases in tolls of 26 and 23%, respectively (∼exp(βETCAdopt + 0.6∗ βETC Penetration )). When the sample is limited to facilities without ETC discounts, the implied steady state increase in tolls is 36% when (3) is estimated (column (3)) or 38% when (5) is estimated (column (4)). All of these implied steady state toll increases associated with ETC are statistically significant at at least the 10% level. Taken together, these estimates suggest that the diffusion of ETC to its steady state level is associated with a 20 to 40 percent increase in toll rates. Given the extremely inelastic demand for driving with respect to the toll facility with ETC, and the diffusion pattern of ETC is basically linear for those first six years (see Figure II).

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that I estimate below, these results suggest that the associated increase in revenue for the toll authority is also about 20 to 40 percent. Endogeneity of the Timing of ETC Adoption. I have analyzed the endogenous choice of tax rates while assuming that the choice of the salience of the tax system (i.e., the adoption of ETC) is exogenous. In practice, the decision to adopt ETC does not appear to be random. For example, as previously discussed, higher labor costs in the northeast may have encouraged more ETC adoption. This does not, however, pose a problem for the analysis per se, which requires only that the timing of ETC implementation be uncorrelated with changes in a facility’s toll setting relative to its norm. Nonetheless, the correlation of various observable characteristics with whether or when a facility adopts ETC (see Table II) raises concerns about the identifying assumption that absent the introduction of ETC on facility i in year t, toll rates would not have changed differentially for that facility. I therefore analyze the effect of ETC separately on samples stratified by these characteristics. Table V shows the results. Column (1) replicates the baseline specification (Table IV, column (1)). Columns (2) through (7) show the effects separately by geographic region, by facility type (bridges and tunnels vs. roads), and by facility age. Not only does statistical significance generally persist across the subsamples, but also the point estimates are remarkably similar.20 To more directly control for differences across facilities in the underlying rate of toll growth, column (8) shows that the results are robust to the addition of facility fixed effects to (17), which is equivalent to allowing facility-specific linear trends in toll rates. One specific source of omitted variable bias that the preceding analysis does not directly address is that ETC adoption may be a part of a broader infrastructure project, or a signal that infrastructure modernization is in the works. In this case, the relationship between ETC and toll increases may be spurious, as infrastructure projects may necessitate (or provide political cover for) toll increases. To investigate this possibility, I compiled histories of 20. As a distinct exercise, I was also interested in whether the impact of ETC varied between operating authorities that automatically send monthly statements of expenses to users and authorities from which drivers had to actively request (and in some cases pay for) ETC expense statements. The point estimates did not suggest any economically or statistically differential impact of ETC on toll rates along this dimension, although the standard errors were sufficiently large so that it was not possible to rule out fairly large differences (not shown).

0.020 24 49 123 5,079

0.015 (0.006) [.018] −0.051 (0.035) [.158]

0.022 14 28 68 3,008

0.016 (0.010) [.141] −0.048 (0.054) [.399]

0.017 10 21 55 2,071

0.014 (0.005) [.030] −0.044 (0.027) [.137]

South and west (3)

0.021 18 24 44 1,692

0.015 (0.008) [.067] −0.023 (0.063) [.719]

Roads (4)

0.020 16 31 79 3,387

0.028 (0.010) [.015] −0.086 (0.017) [.000]

Bridges and tunnels (5)

0.019 13 20 43 1,389

0.021 (0.010) [.065] 0.051 (0.079) [.534]

Open after 1960 (6)

0.021 21 39 77 3,690

0.013 (0.007) [.079] −0.084 (0.025) [.003]

Open 1960 or before (7)

0.020 24 49 123 5,079

0.013 (0.007) [.072] −0.053 (0.036) [.147]

Facility fixed effects (8)

−0.055 (0.035) [.124] 0.014 (0.007) [.048] 0.017 (0.014) [.221] −0.003 (0.007) [.659] 0.021 23 46 115 4,712

−0.055 (0.035) [.125] 0.014 (0.007) [.048]

0.021 23 46 115 4,712

(10)

(9)

Facilities with infrastructure data

Notes. Table reports results from estimating variants of (17) by OLS. The dependent variable is the change in the log minimum toll. All regressions include year fixed effects (not shown). Each operating authority receives equal weight. ETCAdoptit is an indicator variable for whether facility i adopted ETC in year t. ETCit is an indicator variable for whether the facility has ETC; it is 1 in the year that ETC is adopted and in all subsequent years. Columns (2) and (3) limit the sample to, respectively, facilities in the northeast and midwest, and facilities in the south and west. Columns (4) and (5) limit the sample to, respectively, roads, and bridges or tunnels. Columns (6) and (7) limit the sample to, respectively, facilities that opened after 1960 and facilities that opened in 1960 or earlier. Column (8) adds facility fixed effects to the right-hand side of (17). In columns (9) and (10) the sample is limited to the 115 facilities for which infrastructure data are available. INFRAAdoptit is an indicator variable for whether facility i started a new infrastructure project in year t. INFRAit is an indicator variable for whether facility i has an infrastructure project in progress in year t; it is 1 in the year that the project is started and in all subsequent years that the project is in progress. All estimates give equal weight to each operating authority. Standard errors in parentheses are clustered by state, and p-values are shown in square brackets.

Mean dep. var. # of states # op. authorities # of facilities N

INFRAit

INFRAADOPTit

ETCAdoptit

ETCit

Baseline (1)

Northeast and midwest (2)

TABLE V IMPACT OF ETC ON TOLL RATES: ROBUSTNESS ANALYSIS

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infrastructure projects on 115 of the 123 individual toll facilities.21 These histories report the timing of a variety of infrastructure projects including renovations, replacements, repairs, widenings, extensions, and other improvements. I constructed indicator variables for whether facility i started an infrastructure project in year t (INFRAAdoptit ) and whether it had a project either started or ongoing in year t (INFRAit ). On average, a project was started in 2.2% of facility-years, and 10.1% of facility-years had an infrastructure project either starting or ongoing. I reestimate the basic relationship between ETC and toll increases (equation (17)) with these two additional variables included as covariates. Column (9) shows that the baseline results (without the additional infrastructure variables) are unaffected by restricting the sample to the 115 facilities for which I have data on infrastructure projects. Column (10) shows that the estimated increase in tolls associated with ETC is not affected in either magnitude or statistical significance by including the two infrastructure variables as controls. This suggests that the increase in tolls associated with ETC is not likely to be spuriously due to a correlation between ETC and infrastructure projects, which themselves are responsible for toll increases; indeed, the results suggest that infrastructure projects are not, in fact, associated with toll increases. There are of course many reasons, besides infrastructure projects, that the timing of ETC adoption might be spuriously correlated with toll increases. For example, facilities may respond to increased congestion by both adopting ETC and by raising tolls as complementary congestion-reducing strategies. This suggests we should observe increases in congestion (or a proxy for it such as traffic) on a facility prior to ETC adoption. Alternatively, facilities might respond to a negative revenue shock by both raising tolls and adopting ETC, with the latter a way to lower revenue losses from the administrative costs of toll collection. This suggests we should observe declining revenue (or declining traffic) on a facility in the years prior to ETC adoption. More generally, we can look for changes in toll rates in the years prior to ETC adoption as a partial test of the identifying assumption that absent the adoption of ETC, a facility would not have experienced differential changes in its toll rate. Of course, if the lower salience of ETC 21. The primary source of data was facility Web pages and annual reports, which often provide detailed histories of work on the facilities. The level of detail and the nature of the projects reported vary across facilities. However, because all of the analysis is within-facility, this should not pose a problem.

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(2)

0.013 (0.010) [.198] ETCAdoptit −0.000 0.000 (0.010) (0.010) [.996] [.978] ETCit −0.006 −0.001 (0.010) (0.010) [.551] [.959] Mean dep. var 0.049 # of states 21 # op. authorities 32 # of facilities 76 N 2,200

Dep. var.: log(revenue) (3) −0.009 (0.016) [.599]

(4)

Dep. var.: log(minimum toll) (5)

(6)

0.004 (0.013) [.777]

0.006 0.009 (0.012) (0.007) [.601] [.242] 0.002 0.002 −0.051 −0.051 (0.025) (0.025) (0.035) (0.035) [.922] [.930] [.158] [.162] 0.028 0.031 0.016 0.017 (0.015) (0.015) (0.006) (0.006) [.090] [.058] [.018] [.008] 0.077 0.020 13 24 19 49 45 123 1,411 5,079

Notes. Table reports results from estimating variants of (17) by OLS. Dependent variables are defined in the column headings. In addition to the covariates shown in the table, all regressions include year fixed effects. Each operating authority receives equal weight. Standard errors (in parentheses) are clustered by state. p-values are reported in square brackets. “1–2 years before ETCAdoptedit ” is an indicator variable for whether it is one to two years before the facility adopts ETC. “1–5 years before ETCAdoptedit ” is an indicator variable for whether it is one to five years before the facility adopts ETC. ETCAdoptit is an indicator variable for whether facility i adopted ETC in year t. ETCit is an indicator variable for whether the facility has ETC; it is 1 in the year that ETC is adopted and in all subsequent years.

made it easier to raise tolls, ETC might be adopted precisely by facilities that were encountering difficulties in making needed toll increases, suggesting that facilities might experience declines in traffic, revenue, or toll increases prior to ETC adoption. Although evidence of such effects would therefore not necessarily be inconsistent with the salience story, the lack of any such evidence reduces concerns about omitted variable bias and spurious findings. Table VI shows the results. I reestimate (17) with three different dependent variables: log(traffic)it (columns (1) and (2)), log(revenue)it (columns (3) and (4)), and log(minimum toll)it (columns (5) and (6)). In addition to the standard regressors (year fixed effects, ETCAdoptit , and ETCit ), I also include an indicator variable for whether it is one to two years prior to ETC adoption (odd columns) or whether it is one to five years prior to ETC

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adoption (even columns). The coefficients on these indicator variables for years just prior to ETC adoption show no statistically or substantively significant evidence of systematic changes in traffic, revenue, or tolls in the years prior to a facility’s adopting ETC. These results are consistent with the results from estimating (18a), which show no systematic preexisting trend in toll rates prior to a facility’s adoption of ETC, particularly in the balanced panel (see Figures IIIA and IIIB). One reason that the various endogeneity concerns may not in practice be a problem is that, as noted in Section IV.B, the different facilities run by a given operating authority tend to adopt ETC all at the same time, and yet may be experiencing different patterns of traffic and tolls.22 There are several other results of interest in Table VI. The finding in columns (3) and (4) that revenue increases by about 3 percent per year under ETC is broadly consistent with the estimated increase in tolls under ETC and the finding that demand for driving is very inelastic with respect to the toll.23 There is also some suggestive evidence in columns (1) and (2) that traffic declines under ETC, although these estimates are not statistically significant and are substantively quite small; a decline in traffic would be consistent with the survey evidence in Section III of overestimation of toll levels by ETC users. VI.B. The Impact of ETC on the Politics of Toll Setting The model in Section II.B suggested two potential mechanisms behind a finding that reduced salience is associated with increased tax rates: (i) a reduced behavioral responsiveness to taxes and (ii) a reduction in the political costs of tolls, particularly in the differential political costs of tolls in election years compared to nonelection years. Section V presented evidence for the first potential mechanism. To investigate the political channel, I examine whether there are political costs to tolls and how these costs change under ETC. Table VII shows the results. Because the political fallout from raising tolls may be concentrated on the extensive margin (i.e., whether tolls are raised), I report results not only for the baseline 22. In a different context, Dusek (2003) examines the impact of the introduction of state income tax withholding on tax rates, but notes that the decision to introduce income tax withholding appears to be correlated with increased demand for bigger government, making the results hard to interpret. 23. For the sample for which I have revenue data, I estimate that ETC is associated with a 2.2% increase in tolls each year (not shown).

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TABLE VII THE IMPACT OF ETC ON THE POLITICS OF TOLL SETTING

ETCit

AnyElec Yearst

log min toll (1)

Min toll raised? (2)

log min. toll (3)

Min toll raised? (4)

log min. toll (5)

Min toll raised? (6)

0.015 (0.006) [.018]

0.073 (0.024) [.006]

0.006 (0.009) [.507] −0.016 (0.004) [.000]

0.044 (0.022) [.042] −0.029 (0.010) [.003]

0.006 (0.009) [.494]

0.044 (0.022) [.042]

−0.016 (0.005) [.001] −0.015 (0.005) [.005]

−0.036 (0.012) [.002] −0.021 (0.012) [.085]

0.004 (0.014) [.791] 0.030 (0.014) [.038]

0.016 (0.033) [.617] 0.094 (0.033) [.005]

GovElec Yearst LegOnly ElecYearst AnyElec Yearst *ETCit GovElec Yearst *ETCit LegOnly ElecYearst *ETCit

0.017 (0.012) [.140]

0.055 (0.027) [.041]

Notes. Columns (1) and (2) report estimates of (17); columns (3)–(6) report estimates of (20). Dependent variable (shown in column heading) is log minimum toll (odd columns) or an indicator variable for whether the minimum toll was raised (even columns). In addition to the covariates shown in the table, all regressions include year fixed effects, ETCAdoptit , and interactions between ETCAdoptit and any indicator variables for the election year included in the regression. Each operating authority receives equal weight. Standard errors (in parentheses) are clustered by state. p-values are in square brackets. “AnyElecYearst ” is an indicator variable for whether state s’s governor or legislature is up for election in year t. “GovElecYearst ” is an indicator variable for whether the governor (and therefore almost always the legislature as well) is up for election. “LegOnlyElecYearst ” is an indicator variable for whether only the legislature is up for election. ETCit is an indicator variable for whether the facility has ETC; it is 1 in the year that ETC is adopted and in all subsequent years. Sample size in all columns is 5,079 facility-years, 123 facilities, 49 operating authorities, and 24 states. The mean of the dependent variable is 0.020 (odd columns) and 0.077 (even columns).

dependent variable log minimum toll (odd columns) but also for the binary dependent variable of whether the minimum toll increased (even columns). Column (1) replicates the baseline results from (17) (see Table IV, column (1)). Column (2) shows the results from estimating (17) with the binary dependent variable for whether the minimum toll was raised that year; the coefficient on ETCit is 0.073 (standard error 0.024). This suggests that, relative to the baseline 7.7% annual probability of a toll increase, the probability of a toll increase almost doubles on a facility once it

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has ETC. Combined with the evidence in column (1), this suggests that the increase in tolls associated with ETC comes about primarily through more frequent toll increases of similar magnitude. I then expand the baseline specification in (17) to include indicator variables for whether it is an election year, and the interactions of these indicators with the change in salience, as proposed in the estimating (15) from Section II.B. This allows me to examine whether there is a political business cycle in toll setting and whether this political business cycle varies under manual toll collection and ETC. Specifically, I estimate yit = γt + β1 ETCAdoptit + β2 ETCit + β3 1(ElecYear)st (20)

+ β4 1(ElecYear)st ∗ ETCAdoptit + β5 1(ElecYear)st ∗ ETCit + εit .

Columns (3) and (4) report results when 1(ElecYear)st is an indicator for whether there is any state election (for either the governor or the legislature) in state s and year t; about half of the facility-years in the data are election years, but the timing of the electoral calendar varies across states. Columns (5) and (6) report results when 1(ElecYear)st is two separate indicators for whether the governor (and therefore almost always the legislature as well) is up for election and for whether only the legislature is up for election; each of these indicator variables is turned on in roughly one-fourth of state years. In all four specifications, the coefficients on all of the election year indicators are negative and statistically significant; this demonstrates the political business cycle under manual toll collection. Given the average annual 2% increase in tolls, the coefficient on the election year dummies of about −0.016 in columns (3) and (5) indicates that toll increases are about 75% lower during election years than during nonelection years under manual toll collection. The interaction term between the election year indicator variables and ETC is always positive; it is statistically significant for legislature-only election years (columns (5) and (6)) and statistically significant (or only marginally insignificant) for any election year (columns (3) and (4)). This suggests that under ETC, tollsetting behavior is less sensitive to the political election calendar (particularly legislature elections) than under manual toll collection. Indeed, there is no evidence that toll increases are lower in election years relative to nonelection years under electronic toll

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collection; the sum of the coefficients on the election year indicator variable and its interaction with ETC (i.e., β3 + β5 ) is almost always positive (and never significantly negative).24 VII. ALTERNATIVE EXPLANATIONS In this section, I briefly consider a range of alternative explanations for the increase in tolls associated with ETC other than the decline in the salience of the toll. I note at the outset that a general point in favor of the salience-based explanation is the finding that toll setting becomes less sensitive to the local election calendar under ETC; this is consistent with a decline in salience reducing the political costs of raising tolls, but would not be predicted by any of the alternative explanations I discuss. VII.A. ETC Lowers the Operating Cost of Toll Collection ETC is associated with substantial reductions in the annual costs of operating and maintaining toll facilities; the ETC cost savings come primarily from reductions in the labor costs associated with manual toll collection (Hau 1992; Pietrzyk and Mierzejewski 1993; Levinson 2002).25 However, for increases in the efficiency of tax collection to increase the equilibrium tax rate requires an improvement in the marginal efficiency of tax collection (Becker and Mulligan 2003). By contrast, ETC improves the fixed component of the efficiency cost of taxation—because the administrative cost savings are independent of the toll rate—which should therefore not prompt an increase in the rate of existing taxes.26 A decline in the fixed administrative costs of tax collection could, however, encourage the introduction of new taxes, such as 24. The “main effect” of ETC, although positive, is no longer statistically significant in columns (3) and (5); toll increases are not statistically significantly larger in nonelection years under ETC than under manual toll collection. However, toll increases are statistically significantly larger in election years under ETC than under manual toll collection; the sum of the coefficients on ETC and the interaction of ETC and election year (i.e., β2 + β5 in (20)) is statistically significant in column (3) and statistically significant for the legislative election year variable in column (5) (not shown). 25. Toll collection costs under manual toll collection can be quite high. A 1995 study of turnpikes in Massachusetts and New Jersey estimated that toll collection costs under manual toll collection were about 6 percent of toll revenue (Friedman and Waldfogel 1995); a 2006 study found that on portions of the Massachusetts Turnpike where there is relatively little traffic, toll collection costs were over onethird of toll revenue (Kriss 2006). 26. Note, moreover, that if operating authorities set tolls to meet an exogenous revenue requirement, the reduction in administrative costs would lower (rather than raise) the equilibrium toll needed to raise a fixed amount of (net) revenue.

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the introduction of tolls on roads that had not been previously been tolled or the construction of new (tolled) roads where no road existed before. Any such effects of ETC, however, would not show up in my analysis, which limits the sample to facilities with preexisting tolls. Lower fixed administrative costs of toll collection could also encourage the installation of more toll collection points on an existing toll facility; however, I find no evidence that ETC had such an effect.27 VII.B. ETC Installation Requires Capital Outlay Although ETC lowers the costs of operating and maintaining toll facilities, installation of ETC requires a capital outlay. It seems unlikely that this capital outlay would require an increase in tolls. Operating authorities can borrow to cover these capital costs, and the capital costs are recouped within a few years by the savings in operating and maintenance costs, and by revenue from the sale or lease of the transponders and interest on prepayments and deposits (Hau 1992; Pietrzyk and Mierzejewski 1993). Of course, it is possible that operating authorities might use the installation costs of ETC as an excuse to raise tolls, even though ETC is selffinancing. Any such excuse might be used for a one-time increase in tolls when ETC comes in; it seems less natural that this excuse could be used for subsequent increases in tolls as ETC use diffuses among drivers. VII.C. Changes in Menu Costs Associated with ETC It is possible that ETC lowers the administrative (menu) cost of toll changes. There could be literal menu cost savings if signs listing the toll rate no longer had to be changed under ETC. Alternatively, ETC might allow smaller increases of non-“round” amounts; unlike manual tolls, this would not impose on drivers that they carry small coins. In practice, however, ETC tolls are not less “round” than manual tolls, except when they are specified as a fixed percentage discount off of the manual toll. In addition, the increase in tolls associated with ETC persists for the subsample of facilities that do not offer discounts; for these facilities, there can be no menu cost savings, as changing the electronic toll 27. I reestimate (17) using as a dependent variable a binary measure for whether there is an increase in the number of toll transactions someone driving a one-way, full-length trip on the facility would have to make. I perform this analysis for the full sample of facilities, and separately both for roads and for bridges and tunnels (not shown).

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requires changing the manual toll, and all facilities continue to have at least some manual payers. Finally, even if ETC did reduce menu costs, this should suggest that ETC would be associated with more frequent toll adjustments, but it is not clear why this would produce a higher equilibrium toll rate. VII.D. ETC Lowers Personal Compliance Costs of Toll Payment ETC reduces the drivers’ compliance costs of paying tolls (Hau 1992; Levinson 2002). Friedman and Waldfogel (1995) estimate that under manual toll collection, these compliance costs—which consist of time spent queuing and paying tolls at the toll plaza— are, on average, about 15% of toll revenue. Reductions in compliance costs of paying tolls may directly increase drivers’ willingness to pay the (monetary) toll, and hence provide an alternative explanation for the observed increase in toll rates. In practice, however, two independent pieces of empirical evidence suggest that toll authorities do not increase tolls in response to reductions in compliance costs; this is consistent with the finding in Section V that they set tolls substantially below the revenue-maximizing rate (i.e., that they implicitly place a relatively large weight on consumer surplus). The first piece of suggestive evidence comes from variation across roads in the number of times an individual must make a toll transaction, and hence variation in the compliance costs savings from ETC. For example, in 1985 an individual made eleven toll transactions while driving the length of the Garden State Parkway, compared to only two on the New Jersey Turnpike. If tolls were increased under ETC in response to the reductions in compliance costs, we would expect greater toll increases on roads with a greater number of toll transactions. In fact, I find weak evidence of the opposite. The second piece of suggestive evidence comes from what happens to toll rates when a bridge or tunnel switches from collecting tolls at both ends of the facility to collecting tolls at only one end; at various times over the course of my sample, about half of the bridges and tunnels (40 of 79) made this switch, which reduced compliance costs on their facility by one-half. I find little evidence of a substantively or statistically significant increase in tolls on a facility following this reduction in compliance costs.28 28. The results of both of these analyses are presented in more detail in the Online Appendix (Section C) and in the working paper version of this paper (Finkelstein 2007).

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VII.E. ETC Raises the Optimal Congestion-Correcting Toll Could the increase in tolls under ETC come entirely from the increase in the optimal congestion externality–reducing toll that results from the reduced consumer responsiveness to tolls? This would suggest that the effect of ETC on toll rates is a salience effect, but one that comes entirely from a reduction in salience at the time of consumption (driving). This seems unlikely given the evidence in Section VI.B that ETC affects the political costs of raising tolls; this suggests that at least some of the toll increase associated with ETC is likely to be due to a decline in voting salience. In addition, as an (admittedly quite) crude test of whether the increase in tolls under ETC is driven by an increase in congestion under ETC, I experimented with controlling for traffic (a proxy for congestion) on the right-hand side of (17). I found that the impact of ETC on the change in tolls is not sensitive to including traffic as a control, suggesting that even conditional on the level of traffic, tolls still rise under ETC (not shown).

VIII. CONCLUSIONS This paper has examined the hypothesis that a less salient tax system can produce a higher equilibrium tax rate. Belief in this possibility has contributed to opposition to tax reforms that are believed to reduce tax salience, such as Federal income tax withholding or partial replacement of the income tax with a valueadded tax. Yet the sign of the effect of tax salience on tax rates is theoretically ambiguous, and empirical evidence has been lacking. I examine the relationship between tax salience and tax rates empirically by looking at the impact of electronic toll collection (ETC) on toll rates. Survey evidence indicates that drivers who pay tolls electronically are substantially less aware of toll rates than those who pay with cash, suggesting that ETC reduces tolls’ salience. To analyze the impact of this reduction in salience, I assembled a new data set on toll rates over the last half century on 123 toll facilities in the United States. Because different toll facilities adopted ETC in different years, and some have not yet adopted it, I am able to examine the within-toll facility change in tolls associated with the introduction of electronic toll collection. I find robust evidence that toll rates increase following the adoption of electronic toll collection. The estimates suggest that after ETC use among drivers has diffused to its steady state level,

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toll rates are 20 to 40 percent higher than they would have been under manual toll collection. I provide evidence of two potential mechanisms by which reduced salience may contribute to increased toll rates: under ETC driving behavior becomes less elastic (in absolute value) with respect to the toll, and toll setting becomes less sensitive to the local election calendar. This decline in the political costs of raising tolls associated with ETC would not be predicted by alternative explanations for the increase in tolls associated with ETC. I also present additional evidence that is not consistent with specific alternative explanations. As previously discussed, the normative implications of these findings are ambiguous. Evidence on what is done with the extra revenue from the higher tolls—in particular, whether it is used for purposes that may be valued by users of the facility such as infrastructure investment or reductions in other highway fees, or whether it primarily serves to increase rents for the governing authority through increased employment or salaries of bureaucrats—could help shed some light on the normative implications of the higher tolls under ETC. Unfortunately, the available data are not sufficient for analysis of this issue. The results also leave open the question of how tax salience affects tax rates in other contexts, such as federal income tax withholding or the replacement of a sales tax with a value added tax. As previously discussed, the sign of the effect of tax salience on tax rates may well differ for taxes that are a larger share of expenditures than tolls. The magnitude of any effect of tax salience is also likely to differ across different political institutions. The results in this paper suggest that the salience of the tax instrument is an important element to consider in both theoretical and empirical investigations of the political economy of tax setting. Relatedly, they suggest that the empirical impact of tax salience in these other specific settings is an interesting and important direction for further work. MASSACHUSETTS INSTITUTE OF TECHNOLOGY AND NBER

REFERENCES Becker, Gary, and Casey Mulligan, “Deadweight Costs and the Size of Government,” Journal of Law and Economics, 46 (2003), 293–340. Brennan, Geoffrey, and James Buchanan, The Power to Tax: Analytical Foundations of a Fiscal Constitution (Cambridge, UK: Cambridge University Press, 1980).

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Buchanan, James, Public Finance in Democratic Process: Fiscal Institutions and the Individual Choice (Chapel Hill: University of North Carolina Press, 1967). Buchanan, James, and Richard E. Wagner, Democracy in Deficit (New York: Academic Press, 1977). Chetty, Raj, Kory Kroft, and Adam Looney, “Salience and Taxation: Theory and Evidence,” American Economic Review, forthcoming. Dollery, Brian, and Andrew Worthington, “The Empirical Analysis of Fiscal Illusion,” Journal of Economic Surveys, 10 (1996), 261–298. Dusek, Libor, Do Governments Grow When They Become More Efficient? Evidence from Tax Withholding, Unpublished Ph.D. Dissertation, University of Chicago, 2003. Feldman, Naomi, and Peter Katuscak, “Should the Average Tax Rate Be Marginalized?” mimeo, Ben Gurion University, 2005. Finkelstein, Amy, “E-Z Tax: Tax Salience and Tax Rates,” Working Paper 12924, National Bureau of Economic Research, 2007. Friedman, David, and Joel Waldfogel, “The Administrative and Compliance Cost of Manual Highway Toll Collection: Evidence from Massachusetts and New Jersey,” National Tax Journal, June 1995. Friedman, Milton, and Rose Friedman, Two Lucky People (Chicago: University of Chicago Press, 1998). Hau, Timothy, “Congestion Charging Mechanisms for Roads: An Evaluation of Current Practice,” Research Paper 1071, The World Bank, 1992. Holguin-Veras, Jose, Ozbay Kaan, and Allison de Cerrano, “Evaluation Study of the Port Authority of New York and New Jersey’s Time of Day Pricing Initiative,” report, Rensselaer Polytechnic Institute, 2005. Kearney, Melissa, “The Economic Winners and Losers of Legalized Gambling,” National Tax Journal, 58 (2005), 281–302. Kriss, Eric, “Turnpike Task Force Final Report,” Pioneer Institute board presentation by Eric Kriss, October 18, 2006. Levinson, David, Financing Transportation Networks (Northampton, MA: Edward Elgar, 2002). Liebman, Jeffrey, and Richard Zeckhauser, “Schmeduling,” unpublished mimeo, Harvard’s Kennedy School of Government, 2004). Nordhaus, William, “The Political Business Cycle,” Review of Economic Studies, 42 (1975), 169–190. Oates, Wallace, “On the Nature and Measurement of Fiscal Illusion: A Survey,” in Taxation and Fiscal Federalism: Essays in Honour of Russell Mathews, Geoffrey Brennan, Bhajan Grewal, and Peter Groenewegen, eds. (Sydney: Australian National University Press, 1988). Peltzman, Sam, “Pricing in Public and Private Enterprises: Electric Utilities in the United States,” Journal of Law and Economics, 14 (1971), 109–147. Pietrzyk, Michael, and Edward Mierzejewski, “Electronic Toll and Traffic Management Systems” (Washington, DC: National Academy Press, 1993). Slemrod, Joel, “Which Is the Simplest Tax System of Them All?” in The Economics of Fundamental Tax Reform, Hank Aaron and William Gale, eds. (Washington, DC: The Brookings Institution, 1996). Soman, Dilip, “Effects of Payment Mechanism on Spending Behavior: The Role of Rehearsal and Immediacy of Payments,” Journal of Consumer Research, 27 (2001), 460–474. Thaler, Richard H., “Mental Accounting Matters,” Journal of Behavioral Decision Making, 12 (1999), 183–206. The President’s Advisory Panel on Federal Tax Reform, Simple, Fair, and ProGrowth: Proposals to Fix America’s Tax System (Washington, DC: U.S. Government Printing Office, 2005). U.S. Census Bureau, “Annual Survey of State and Local Government Finances and Census of Governments,” 1985. U.S. Department of Transportation, “Highway Statistics, YEAR,” various years. Wooldridge, Jeffrey, Econometric Analysis of Cross Section and Panel Data (Cambridge, MA: MIT Press, 2002).

THE BOND MARKET’S q∗ THOMAS PHILIPPON I propose an implementation of the q-theory of investment using bond prices instead of equity prices. Credit risk makes corporate bond prices sensitive to future asset values, and q can be inferred from bond prices. With aggregate U.S. data, the bond market’s q fits the investment equation six times better than the usual measure of q, it drives out cash flows, and it reduces the implied adjustment costs by more than an order of magnitude. Theoretical interpretations for these results are discussed.

I. INTRODUCTION In his 1969 article, James Tobin argued that “the rate of investment—the speed at which investors wish to increase the capital stock—should be related, if to anything, to q, the value of capital relative to its replacement cost” (Tobin 1969, p. 21). Tobin also recognized, however, that q must depend on “expectations, estimates of risk, attitudes towards risk, and a host of other factors,” and he concluded that “it is not to be expected that the essential impact of [. . . ] financial events will be easy to measure in the absence of direct observation of the relevant variables (q in the models).” The quest for an observable proxy for q was therefore recognized as a crucial objective from the very beginning. Subsequent research succeeded in integrating Tobin’s approach with the neoclassical investment theory of Jorgenson (1963). Lucas and Prescott (1971) proposed a dynamic model of investment with convex adjustment costs, and Abel (1979) showed that the rate of investment is optimal when the marginal cost of installment is equal to q − 1. Finally, Hayashi (1982) showed that, under perfect competition and constant returns to scale, marginal q (the market value of an additional unit of capital divided by its replacement cost) is equal to average q (the market value of existing capital divided by its replacement cost). Because average q is observable, the theory became empirically relevant. ∗ This paper was first circulated under the title “The y-Theory of Investment.” I thank Robert Barro (the editor), three anonymous referees, Daron Acemoglu, Mark Aguiar, Manuel Amador, Luca Benzoni, Olivier Blanchard, Xavier Gabaix, Mark Gertler, Simon Gilchrist, Bob Hall, Guido Lorenzoni, Sydney Ludvigson, Pete Kyle, Lasse Pedersen, Christina Romer, David Romer, Ivan Werning, Toni Whited, Jeff Wurgler, Egon Zakrajsek, and seminar participants at NYU, MIT, the SED 2007, London Business School, Ente Einaudi (Rome), University of Salerno, Toulouse University, Duke University, and the NBER Summer Institutes 2006 and 2007. Peter Gross provided excellent research assistance. C 2009 by the President and Fellows of Harvard College and the Massachusetts Institute of

Technology. The Quarterly Journal of Economics, August 2009

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Unfortunately, its implementation proved disappointing. The investment equation fits poorly, leaves large unexplained residuals correlated with cash flows, and implies implausible parameters for the adjustment cost function (see Summers [1981] for an early contribution, and Hassett and Hubbard [1997] and Caballero [1999] for recent literature reviews). Several theories have been proposed to explain this failure. Firms could have market power, and might not operate under constant returns to scale. Adjustment costs might not be convex (Dixit and Pindyck 1994; Caballero and Engle 1999). Firms might be credit-constrained (Fazzari, Hubbard, and Petersen 1988; Bernanke and Gertler 1989). Finally, there could be measurement errors and aggregation biases in the capital stock or the rate of investment. None of these explanations is fully satisfactory, however. The evidence for constant returns and price-taking seems quite strong (Hall 2003). Adjustment costs are certainly not convex at the plant level, but it is not clear that it really matters in the aggregate (Thomas 2002; Hall 2004), although this is still a controversial issue (Bachmann, Caballero, and Engel 2006). Gomes (2001) shows that Tobin’s q should capture most of investment dynamics even when there are credit constraints. Heterogeneity and aggregation do not seem to create strong biases (Hall 2004). In fact, an intriguing message comes out of the more recent empirical research: the market value of equity seems to be the culprit for the empirical failure of the investment equation. Gilchrist and Himmelberg (1995), following Abel and Blanchard (1986), use VARs to forecast cash flows and to construct q, and they find that it performs better than the traditional measure based on equity prices. Cumins, Hasset, and Oliner (2006) use analysts’ forecasts instead of VAR forecasts and reach similar conclusions. Erickson and Whited (2000, 2006) use GMM estimators to purge q from measurement errors. They find that only 40% of observed variations are due to fundamental changes, and, once again, that market values contain large “measurement errors.” Applied research has therefore reached an uncomfortable situation, where the benchmark investment equation appears to be successful only when market prices are not used to construct q. This is unfortunate, because Tobin’s insight was precisely to link observed quantities and market prices. The contribution of this paper is to show that a market-based measure of q can be constructed from corporate bond prices and that this measure performs much better than the traditional one.

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Why would the bond market’s q perform better than the usual measure? There are several possible explanations, two of which are discussed in details in this paper. The first explanation is that total firm value includes the value of growth options, that is, opportunities to expand into new areas and new technologies. With enough skewness, these growth options end up affecting equity prices much more than bond prices. If, in addition, these growth options are unrelated to existing operations, they do not affect current capital expenditures. As a result, bond prices are more closely related to the existing technology’s q, while equity prices reflect organizational rents. A second possible explanation is that the bond market is less susceptible to bubbles than the equity market. In fact, there is empirical and theoretical support for the idea that mispricing is more likely to happen when returns are positively skewed. Barberis and Huang (2007) show that cumulative prospect theory can explain how a positively skewed security becomes overpriced. Brunnermeier, Gollier, and Parker (2007) argue that preference for skewness arises endogenously because investors choose to be optimistic about the states associated with the most skewed Arrow–Debreu securities. Empirically, Mitton and Vorkink (2007) document that underdiversification is largely explained by the fact that investors sacrifice mean–variance efficiency for higher skewness exposure. These insights, combined with the work of Stein (1996) and Gilchrist, Himmelberg, and Huberman (2005) showing why rational managers might not react (or, at least, not much) to asset bubbles, provide another class of explanations.1 Of course, even if we accept the idea that bond prices are somehow more reliable than equity prices, it is far from obvious that it is actually possible to use bond prices to construct q. The contribution of this paper is precisely to show how one can do so, by combining the insights of Black and Scholes (1973) and Merton (1974) with the approach of Abel (1979) and Hayashi (1982). In the Black–Scholes–Merton model, debt and equity are seen as derivatives of the underlying assets. In the simplest case, the market value of corporate debt is a function of its face value, asset 1. Other rational explanations can also be proposed. These explanations typically involve different degrees of asymmetric information, market segmentation, and heterogeneity in adjustment costs and stochastic processes. For instance, firms might be reluctant to use equity to finance capital expenditures, because of adverse selection, in which case the bond market might provide a better measure of investment opportunities (Myers 1984). It is much too early at this stage to take a stand on which explanations are most relevant.

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volatility, and asset value. But one can also invert the function, so that, given asset volatility and the face value of debt, one can construct an estimate of asset value from observed bond prices. I extend this logic to the case where asset value is endogenously determined by capital expenditures decisions. As in Hayashi (1982), I assume constant returns to scale, perfect competition, and convex adjustment costs. There are no taxes and no bankruptcy costs, so the Modigliani–Miller theorem holds, and real investment decisions are independent from capital structure decisions.2 Firms issue long-term, coupon-paying bonds as in Leland (1998), and the default boundary is endogenously determined to maximize equity value, as in Leland and Toft (1996). There are two crucial differences between my model and the usual asset pricing models. First, physical assets change over time. Under constant returns to scale, however, I obtain tractable pricing formulas, where the usual variables are simply scaled by the book value of assets. Thus, book leverage plays the role of the face value of principal outstanding, and q plays the role of total asset value. The second difference is that cash flows are endogenous, because they depend on adjustment costs and investment decisions. I model an economy with a continuum of firms hit by aggregate and idiosyncratic shocks. Even though default is a discrete event at the firm level, the aggregate default rate is a continuous function of the state of the economy. To build economic intuition, I consider first a simple example with one-period debt, constant risk-free rates, and i.i.d. firm-level shocks. I find that, to first order (i.e., for small aggregate shocks), Tobin’s q is a linear function of the spread of corporate bonds over government bonds. The sensitivity of q to bond spreads depends on the risk-neutral default rate, just like the delta of an option in the Black–Scholes formula. In the general case, I choose the parameters of the model to match aggregate and firm level dynamics, estimated with postwar U.S. data. Given book leverage and idiosyncratic volatility, the model produces a nonlinear mapping from bond prices to q. I then use the theoretical mapping to construct a time series for q based on the relative prices of corporate and government bonds, taking into account trends in book leverage and 2. One could introduce taxes and bankruptcy costs if one wanted to derive an optimal capital structure, but this is not the focus of this paper. See Hackbarth, Miao, and Morellec (2006) for such an analysis, with a focus on macroeconomic risk.

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idiosyncractic risk, as well as changes in real risk-free rates. This bond market’s q fits the investment equation quite well with postwar aggregate U.S. data. The R2 is around 60%, cash flows become insignificant, and the implied adjustment costs are more than an order of magnitude smaller than with the usual measure of q. The fit is as good in levels as in differences. The theoretical predictions for the roles of leverage and volatility are supported by the data, as well as the nonlinearities implied by the model. Using simulations, I find that the predictions of the model are robust to specification errors, as well as to taxes and bankruptcy costs. The theoretical predictions for firm level dynamics are consistent with the empirical results of Gilchrist and Zakrajsek (2007), who show that firm-specific interest rates forecast firmlevel investment. The remainder of the paper is organized as follows. Section II presents the setup of the model. Section III uses a simple example to build economic intuition. Section IV presents the numerical solution for the general case. Section V presents the evidence for aggregate U.S. data. Section VI discusses the theoretical interpretations of the results. Section VII discusses the robustness of the results to various changes in the specification of the model. Section VIII concludes. II. MODEL II.A. Firm Value and Investment Time is discrete and runs from t = 0 to ∞. The production technology has constant returns to scale and all markets are perfectly competitive. All factors of production, except physical capital, can be freely adjusted within each period. Physical capital is predetermined in period t and, to make this clear, I denote it by kt−1 . Once other inputs have been chosen optimally, the firm’s profits are therefore equal to pt kt−1 , where pt is the exogenous profit rate in period t. Let the function (kt−1 , kt ) capture the total cost of adjusting the level of capital from kt−1 to kt . For convenience, I include depreciation in the function , and I assume that it is homogeneous of degree one, as in Hayashi (1982).3 3. For instance, the often-used case of quadratic adjustment costs corresponds to (kt , kt+1 ) = kt+1 − (1 − d)kt + 0.5γ2 (kt+1 − kt )2 /kt , where d is the depreciation rate, and γ2 is a constant that pins down the curvature of the adjustment cost function.

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Let rt be the one-period real interest rate, and let Eπ [.] denote expectations under the risk-neutral probability measure π .4 The state of the firm at time t is characterized by the endogenous state variable kt and a vector of exogenous state variables ωt , which follows a Markov process under π . The profit rate and the risk-free rate are functions of ωt . The value of the firm solves the Bellman equation, Eπ [V (kt , ωt+1 ) |ωt ] V (kt−1 , ωt ) = max p(ωt )kt−1 − (kt−1 , kt ) + . kt ≥0 1 + r(ωt ) (1) Because the technology exhibits constant returns to scale, it is convenient to work with the scaled value function, vt ≡

(2)

Vt . kt−1

Similarly, define the growth of k as xt ≡ kt /kt−1 . After dividing both sides of equation (1) by kt−1 , and using the shortcut notation ω for ωt+1 , we obtain x Eπ [v(ω )|ω] , v(ω) = max p(ω) − γ (x) + (3) x≥0 1 + r(ω) where γ is the renormalized version of . The function γ is assumed to be convex and to satisfy limx→0 γ (x) = ∞ and limx→∞ γ (x) = ∞. The optimal investment rate x(ω) solves (4)

∂γ Eπ [v(ω )|ω] (x(ω)) = q(ω) ≡ . ∂x 1 + r(ω)

Equation (4) defines the q-theory of investment: it says that the marginal cost of investment is equal to the expected discounted marginal product of capital. The most important practical issue is the construction of the right-hand side of equation (4). II.B. Measuring q The value of the firm is the value of its debt plus the value of its equity. Let Bt be the market values of the bonds outstanding 4. This is equivalent to using a pricing kernel, but it simplifies the notations and the algebra. If m is the pricing kernel between states ω and ω , then for any random variable z , E[m z |ω] = Eπ [z |ω]/(1 + r(ω)). It is crucial to account for risk premia in any case. Berndt et al. (2005) show that objective probabilities of default are much smaller than risk-adjusted probabilities of default. Lettau and Ludvigson (2002) also emphasize the role of time-varying risk premia.

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at the end of period t, and define bt as the value scaled by end-ofperiod physical assets (5)

bt ≡

Bt . kt

Similarly, let e (ω) be the ex-dividend value of equity, scaled by end-of-period assets. Then q is simply (6)

q(ω) = e(ω) + b(ω).

The most natural way to test the q-theory of investment is therefore to use equation (6) to construct the right-hand side of equation (4). Unfortunately, it fits poorly in practice (Summers 1981; Hassett and Hubbard 1997; Caballero 1999). Equation (6) has been estimated using aggregate and firm-level data, in levels or in first differences, with or without debt on the right-hand side. It leaves large unexplained residuals correlated with cash flows, and it implies implausible values for the adjustment cost function γ (x). As argued in the Introduction, there are potential explanations for this empirical failure, but none is really satisfactory. Moreover, a common finding of the recent research is that “measurement errors” in equity seem to be responsible for the failure of q-theory (Gilchrist and Himmelberg 1995; Erickson and Whited 2000, 2006; Cumins, Hasset, and Oliner 2006). I do not attempt in this paper to explain the meaning of these “measurement errors.” I simply argue that, even if equity prices do not provide a good measure of q, it is still possible to construct another one using observed bond prices. II.C. Corporate Debt I assume that there are no taxes and no deadweight losses from financial distress. The Modigliani–Miller theorem implies that leverage policy does not affect firm value or investment. Leverage does affect bond prices, however, and I must specify debt dynamics before I can use bond prices to estimate q. The model used here belongs to the class of structural models of debt with endogenous default boundary. In this class of models, default is chosen endogenously to maximize equity value (see Leland [2004] for an illuminating discussion). There are many different types of long-term liabilities, and my goal here is not to study all of them, but rather to focus on

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a tractable model of long-term debt. To do so, I use a version of the exponential model introduced in Leland (1994), and used by Leland (1998) and Hackbarth, Miao, and Morellec (2006), among others. In this model, the firm continuously issues and retires bonds. Specifically, a fraction φ of the remaining principal is called at par every period. The retired bonds are replaced by new ones. To understand the timing of cash flows, consider a bond with coupon c and principal normalized to 1, issued at the end of period t. The promised cash flows for this particular bond are as follows: t+1

t+2

...

τ

...

c+φ

(1 − φ)(c + φ)

...

(1 − φ)τ −t−1 (c + φ)

...

Let τ −1 be the sum of the face values of all the bonds outstanding at the beginning of period τ . I use the index τ − 1 to make clear that this variable, just like physical capital, is predetermined at the beginning of each period. The timing of events in each period is the following: 1. The firm enters period τ with capital kτ −1 and total face value of outstanding bonds τ −1 . 2. The state variable ωτ is realized. The value of the firm is then Vτ = vτ kτ −1 , defined in equations (1) and (3). (a) If equity value falls to zero, the firm defaults and the bond holders recover Vτ . (b) Otherwise, the bond holders receive cash flows (c + φ ) τ −1 . 3. At the end of period τ , the capital stock is kτ , the face value of the bonds (including newly issued ones) is τ , and their market value is Bτ = bτ kτ . New issuances represent a principal of τ − (1 − φ ) τ −1 . In Leland (1994) and Leland (1998), book assets are constant, because there is no physical investment, and the firm simply chooses a constant face value . In my setup, the corresponding assumption is that the firm chooses a constant book leverage ratio. In the theoretical analysis, I therefore maintain the following assumption: ASSUMPTION. Firms keep a constant book leverage ratio: ψ ≡ t /kt . A bond issued at the end of period t has a remaining face value of (1 − φ)τ −t−1 at the beginning of period τ . In case of default

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during period τ , all bonds are treated similarly and the bond issued at time t receives (1 − φ)τ −t−1 Vτ / τ −1 . Because all outstanding bonds are treated similarly in case of default, we can characterize the price without specifying when this principal was issued. The following proposition characterizes the debt pricing function. PROPOSITION 1. The scaled value of corporate debt solves the equation (7) b(ω) =

1 Eπ [min{(c + φ)ψ + (1 − φ)b(ω ); v(ω )}|ω]. 1 + r(ω)

Proof. See Appendix. The intuition behind equation (7) is relatively simple. Default happens when equity value falls to zero, that is, when v − (c + φ)ψ − (1 − φ)b = 0. There are no deadweight losses and bondholders simply recover the value of the company. When there is no default, bondholders receive the cash flows (c + φ)ψ and they own (1 − φ) remaining bonds. A few special cases are worth pointing out. Short-term debt corresponds to φ = 1 and c = 0, and the pricing function is simply (8)

bshort (ω) =

1 Eπ [min(ψ; v(ω ))|ω]. 1 + r(ω)

The main difference between short- and long-term debt is the presence of the pricing function b on both sides of equation (7), whereas it appears only on the left-hand side in equation (8). A perpetuity corresponds to φ = 0, and, more generally, 1/φ is the average maturity of the debt. The value of a default-free bond with the same coupon and maturity structure would be (9)

bfree (ω) =

(c + φ)ψ + (1 − φ)Eπ [bfree (ω )|ω] . 1 + r(ω)

With a constant risk-free rate, bfree is simply equal to (c + φ)ψ/ (φ + r). III. SIMPLE EXAMPLE This section presents a simple example in order to build intuition for the more general case. The specific assumptions made in this section, and relaxed later, are that the risk-free rate is constant; firms issue only short-term debt; and idiosyncratic shocks

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are i.i.d. Let us first decompose the state ω into its aggregate component s, and its idiosyncratic component η. The aggregate state follows a discrete Markov chain over the set [1, 2, . . . , S], and it pins down the aggregate profit rate a (s), as well as the conditional risk-neutral expectations. The profit rate of the firm depends on the aggregate state and on the idiosyncratic shock: p(s, η) = a(s) + η.

(10)

The shocks η are independent over time, and distributed according to the density function ζ (.). Because idiosyncratic profitability shocks are i.i.d., the value function is additive and can be written v(s, η) = v(s) + η. I assume that s and η are such that v(s, η) is always positive, so that firms never exit. Tobin’s q is the same for all firms, and I normalize the mean of η to zero; therefore, q(s) =

(11)

Eπ [v(s )|s] . 1+r

Let v¯ ≡ Eπ [v(s)] be the unconditional risk-neutral average asset value, and define q ≡ v/(1 ¯ + r). All the firms choose the same investment rate in this simple example. This will not be true in the general model with persistent idiosyncratic shocks. We can write the value of the aggregate portfolio of corporate bonds by integrating (8) over idiosyncratic shocks: ψ−v(s ) 1 π E ψ+ (12) b(s) = (v(s ) + η − ψ)ζ (η ) dη |s . 1+r −∞ In equation (12), ψ is the promised payment, and the integral measures credit losses. Let δ be the default rate estimated at the risk-neutral average value ψ−v¯ (13) ζ (η ) dη . δ≡ ψ−v¯

−∞

¯ ≡ (ψ + ¯ + η − ψ)ζ (η ) dη )/(1 + r) be the correspondLet b −∞ (v ing price for the aggregate bond portfolio. Using (13) and (11), we can write (12) as (14)

π ¯ = δ(q(s) − q) + E [o(v )] , b(s) − b 1+r

ψ−v where o(v ) ≡ ψ−v¯ (v + η − ψ)ζ (η ) dη is first-order small, in the sense that o(v) ¯ = 0 and ∂o/∂v = 0 when evaluated at v. ¯ When

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aggregate shocks are small, so that v stays relatively close to v, ¯ Eπ [o(v )] is negligible. Equation (14) is the equivalent of the Black–Scholes–Merton formula, applied to Tobin’s q. The value of the option (debt) depends on the value of the underlying (q), and the delta of the option is the probability of default. If this probability is exactly zero, bond prices do not contain information about q. The fact that the sensitivity of b to q is given by δ is intuitive. Indeed, b responds to q precisely because a fraction δ of firms default on average each period. A one-unit move in aggregate q therefore translates into a δ move in the price of a diversified portfolio of bonds. To make equation (14) empirically relevant, we need to express it in terms of bond yields. All the prices we have discussed so far are in real terms, but, in practice, we observe nominal yields. Let r $ be the nominal risk-free rate, and let y$ be the nominal yield on corporate bonds. With short-term debt, the market value is equal to the nominal face value divided by 1 + y$ . Under the assumption we have made in this section, and neglecting the terms that are first-order small, a simple manipulation of equation (14) leads to the following proposition. PROPOSITION 2. To a first-order approximation, Tobin’s q is a linear function of the relative yields of corporate and government bonds,

(15)

qt ≈

1 + rt$ ψ + constant, δ(1 + r) 1 + yt$

where r is the real risk-free rate, ψ is average book leverage, and δ is the risk-neutral default rate. The proposition sheds light on existing empirical studies, such as Bernanke (1983), Stock and Watson (1989), and Lettau and Ludvigson (2002), showing that the spread of corporate bonds over government bonds predicts future output.5 This finding is consistent with q-theory, because the proposition shows that corporate bond spreads are, to first order, proportional to Tobin’s q. 5. In the proposition, I use the relative bond price (the ratio) instead of the spread (the difference) because this is more accurate when inflation is high. The approximation of small aggregate shocks made in this section refers to real shocks, but does not require average inflation to be small.

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IV. LONG-TERM DEBT AND PERSISTENT IDIOSYNCRATIC SHOCKS I now consider the case of long-term debt and persistent firmlevel shocks. The goal is to obtain a mapping from bond yields to Tobin’s q that extends the simple case presented above. As in the previous section, let s denote the aggregate state and let η denote the idiosyncratic component of the profit rate, defined in equation (10). With persistent idiosyncratic shocks, Tobin’s q and the investment rate depend on both s and η, and the value function is no longer additively separable. There is no closed-form solution for bond prices, and the approximation of Proposition 2 is cumbersome because of the fixed point problem in equation (7). I therefore turn directly to numerical simulations. I maintain for now the assumptions of a constant risk-free rate r and of constant book leverage ψ. I use a quadratic adjustment cost function: γ (x) = γ1 x + 0.5γ2 x 2 .

(16)

With this functional form, the investment equation is simply x = (q − γ1 ) /γ2 . Idiosyncratic profitability is assumed to follow an AR(1) process: η

ηt = ρη ηt−1 + ση εt .

(17)

Similarly, I specify aggregate dynamics as at − a¯ = ρa (at−1 − a) ¯ + σa εta .

(18) η

The shocks {εt }η∈[0,1] and εta follow independent normal distributions with zero mean and unit variance. The results discussed below are based on the following parameters: r 3%

ψ 0.45

φ 0.1

γ1 1

γ2 10

ρη 0.47

ση 14%

ρa 0.7

σa 4.5%

a/r ¯ 0.925

c 4.3%

Book leverage is set to 0.45 and average debt maturity to ten years (φ = 0.1), based on Leland (2004), who uses these values as benchmarks for Baa bonds. The parameter γ1 is irrelevant and is normalized to one in this section. There is much disagreement about the parameter γ2 in the literature. Shapiro (1986) estimates a value of around 2.2 years, and Hall (2004) finds even smaller adjustment costs.6 On the other hand, Gilchrist and Himmelberg 6. Shapiro (1986) estimates between 8 and 9 using quarterly data, which corresponds to 2 to 2.2 at annual frequencies.

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(1995) find values of around twenty years, and estimates from macro data are often implausibly high (Summers 1981). I pick a value of γ2 = 10 years, which is in the middle of the set of existing estimates. It turns out, however, that the mapping from bond yields to q is not very sensitive to this parameter. The parameters of equations (17) and (18) are calibrated using U.S. firm and aggregate data, as explained in Section V. Finally, the coupon rate c is chosen so that bonds are issued at par value, as in Leland (1998). We can now use the model to understand the relationship between bond prices and Tobin’s q. The main idea of the paper is to use the price of corporate bonds relative to Treasury to construct a measure of q. The model is simulated with the parameters just described. The processes (17) and (18) are approximated with discrete-state Markov chains using the method in Tauchen (1986). The investment rate x (s, η) and the value of the firm value v (s, η) are obtained by solving the dynamic programming problem in equation (3). Equation (7) is then used to compute the bond pricing function b (s, η). The aggregate bond price b (s) and the aggregate corporate yield y (s) are obtained by integrating over the ergodic distribution of η. Figure I presents the main result. It shows the model-implied aggregate q (s) as a function of the model-implied average relative bond price (φ + r ) / (φ + y (s)). Figure I is generated by considering all the possible values of the aggregate state variable s. Tobin’s q is an increasing and convex function of the relative price of corporate bonds. Figure I therefore extends Proposition 2 to the case of long-term debt, persistent firm-level shocks, and large aggregate shocks. The mapping from bond yields to Tobin’s q is conditional on the calibrated parameters, in particular on book leverage and idiosyncratic volatility. Figure II shows the comparative statics with respect to book leverage (ψ) and firm volatility (ση ). The comparative statics is intuitive. For a given value of q, an increase in leverage leads to more credit risk and lower bond prices, so the mapping shifts left when leverage increases. Similarly, for a given value of q, an increase in idiosyncratic volatility increases credit risk, and the mapping shifts left when volatility increases. In this case, the slope and the curvature of the mapping also change, and the intuition is given by Proposition 2: idiosyncratic volatility increases the delta of the bond with respect to q. In the next section, mappings like the ones displayed in Figure II are used to construct a new measure of q from observed

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1.4 1.3 1.2

Tobin q

1.1 1 0.9 0.8 0.7

0.76

0.78

0.8

0.9 0.82 0.84 0.86 0.88 Relative price of corporate bonds

0.92

0.94

0.96

FIGURE I Aggregate Tobin’s q and the Relative Price of Corporate Bonds The figure shows the implicit mapping between average bond prices and q across aggregate states (with different aggregate profit rates). The price of corporate bonds relative to risk-free bonds is defined as (0.1 + r)/(0.1 + y), where r is the risk-free rate and y is the average yield on corporate bonds. The factor 0.1 reflects the average maturity of 10 years. The mapping is for benchmark values of book leverage, idiosyncratic volatility, and a constant risk-free rate of 3% (see Table II).

bond yields, leverage, and volatility. With respect to leverage, it is important to emphasize the role played by the maintained assumptions of no taxes and no bankruptcy costs. These assumptions imply that capital structure is irrelevant for real decisions (i.e., investment) and for firm value (Modigliani and Miller 1958). Leverage is relevant for bond pricing, however. Bond prices depend on leverage in the same way that they do in the model of Merton (1974): higher leverage increases default risk and therefore decreases the relative price of corporate bonds. Thus, it is crucial to use a mapping that is conditional on leverage to recover the correct value of q. To see why, imagine a world where firms choose their leverage to stabilize their credit spreads. In this case, the correlation between spreads and investment could be arbitrarily small. This would not invalidate the construction of q, however, because the explanatory power would then come from observed changes in leverage. In terms of Figure II, firms would

1025

THE BOND MARKET’S q 1.5 1.4

Leverage 0.4 Leverage 0.5 Leverage 0.6

1.3 1.2

Tobin q

1.1 1 0.9 0.8 0.7 0.6

a 0.5 0.6

0.65

0.7

0.75 0.8 0.85 0.9 Relative price of corporate bonds

0.95

1

0.95

1

1.5 Firm σ 0.1 Firm σ 0.15 Firm σ 0.2

1.4 1.3 1.2

Tobin q

1.1 1 0.9 0.8 0.7 0.6

b 0.5 0.6

0.65

0.7

0.75 0.8 0.85 0.9 Relative price of corporate bonds

FIGURE II Impact of Leverage and Firm Volatility Calibration a in Figure I, except for book leverage in the top panel, and firm volatility in the bottom panel. (a) Mapping for different values of book leverage; (b) mapping for different volatilities of idiosyncratic shocks.

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QUARTERLY JOURNAL OF ECONOMICS TABLE I SUMMARY STATISTICS: QUARTERLY AGGREGATE DATA, 1953:2–2007:2

I/K E(inflation) yBaa r 10 (0.1 + r 10 )/(0.1 + yBaa ) Classic Tobin’s q Bond market’s q

Obs.

Mean

St. dev.

217 217 217 217 217 217 217

0.105 0.037 0.082 0.065 0.908 2.029 1.500

0.010 0.025 0.030 0.027 0.033 0.845 0.117

Min 0.082 −0.016 0.035 0.023 0.796 0.821 1.154

Max 0.125 0.113 0.170 0.148 0.974 4.989 1.720

Notes. Investment and replacement cost of capital are from NIPA. Expected inflation is from the Livingston survey. Yields on 10-year Treasuries and Moody’s Baa index are from FRED. Classic Tobin’s q is computed from the flow of funds, following Hall (2001). Bond market’s q is computed using the structural model, and its mean is normalized to 1.5.

maintain a constant relative price, but their leverage would jump from one mapping to another. I return to this issue in Section VII. V. EMPIRICAL EVIDENCE In this section, I construct a new measure of q using only data from the bond market. I then compare this measure to the usual measure of q, and I assess their respective performances in the aggregate investment equation. The data used in the calibration are summarized in Table I. All the parameters used in the calibration, and the empirical moments used to infer them, are presented in Table II. V.A. Data and Estimation of the Parameters I now describe the data used to estimate the parameters of equations (17) and (18) and the construction of q. Leverage. In the baseline case, book leverage is set to 0.45 based on Leland (2004). Using Compustat, I find a slow increase in average book leverage from 0.4 to 0.55 over the postwar period (Figure IIIa). The sample includes nonfinancial firms, with at least five years of nonmissing values for assets, stock price, operating income, debt, capital expenditures, and property, plants, and equipment. Idiosyncratic Risk. Equation (17) is estimated with firm-level data from Compustat. The profit rate is operating income divided by the net stock of property, plants, and equipment, and η is the idiosyncractic component of this profit rate. Firms in finance and

1027

THE BOND MARKET’S q TABLE II PARAMETERS OF BENCHMARK MODEL Data Parameters chosen exogenously Real risk-free rate r Curvature of adjustment cost function γ2 Average maturity 1/ Book leverage Parameters directly observed in the data Persistence of idiosyncratic profit rate ρη Volatility of idiosyncratic innovations ση Persitence of aggregate profit rate ρa Moments matched Relative bond price (mean) (0.1 + r)/(0.1 + y) Relative bond price (volatility (0.1 + r)/(0.1 + y) of detrended series) Average bond issued at par value E[b]/ f Implied parameters Average profit rate a/r Volatility of aggregate innovations σa Coupon rate c

Model

3% 10 years 10 years 0.45 0.47 0.14 0.7

0.47 0.14 0.7

0.908 0.027

0.908 0.027

1

1

0.925 0.045 0.043

real estate are excluded. The panel regression includes firm fixed effects to remove permanent differences in average profitability across firms or industries due to accounting and technological differences. The estimated baseline parameters, ρη = 0.47 and ση = 14%, are consistent with many previous studies.7 An important issue is that the idiosyncratic volatility of publicly traded companies is not constant. Campbell and Taksler (2003) show that changes in idiosyncratic risk have contributed to changes in yield spreads. The frequency of accounting data is too low to estimate quarterly changes in volatility. In addition, we need a forward-looking measure of idiosyncratic risk to capture market expectations. For all these reasons, the best measure should be based on idiosyncratic stock returns. Following the standard practice in the literature, I use a six-month moving average 7. For instance, Gomes (2001) uses a volatility of 15% and a persistence of 0.62 for the technology shocks. Hennessy, Levy, and Whited (2007) report a persistence of the profit rate of 0.51 and a volatility of 11.85%, which they match with a persistence of 0.684 and a volatility of 11.8% for the technology shocks. Note that in both of these papers, firms operate a technology with decreasing returns. Here, by contrast, the technology has constant returns to scale. This explains why some details of the calibration are different.

1028

0.4

a

0.35

0.8

0.85

0.45

0.9

0.5

0.95

0.55

1

0.6

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1955

1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

Book leverage (right axis)

0.12

0.14

0.16

0.18

Relative bond price

b 1955

1960

1965

1970

1975

1980

Volatility (returns)

1985

1990

1995

2000

2005

Volatility (sales)

FIGURE III The Components of Bond Market q Leverage is average book leverage among nonfinancial firms in Compustat. Idiosyncratic volatility is estimated either from idiosyncratic stock returns or from the dispersion of sales growth. Both measures are then translated into the parameter ση of the model. Relative bond price is the relative price of corporate and government bonds, defined as (0.1 + r)/(0.1 + y), using Moody’s Baa and 10-year Treasury yields. (a) Bond prices and leverage; (b) two measures of idiosyncratic risk.

THE BOND MARKET’S q

1029

of the monthly cross-sectional standard deviation of individual stock returns. I scale this new measure to have a sample mean of η 14% to obtain σˆ t , a time-varying estimate of idiosyncratic risk. As a robustness check, I also consider the cross-sectional standard deviation of the growth rate of sales, measured from Compustat, as a measure of volatility that avoids using stock returns.8 The η two measures of σˆ t are presented in Figure IIIb. Aggregate Bond Prices. Moody’s Baa index, denoted ytBaa , is the main measure of the yield on risky corporate debt. Moody’s index is the equal weighted average of yields on Baa-rated bonds issued by large nonfinancial corporations.9 Following the literature, the 10-year treasury yield is used as the benchmark risk-free rate. Both rt10 and ytBaa are obtained from FRED.10 For equation (18), using annual NIPA data on corporate profits and the stock of nonresidential capital over the postwar period, I estimate ρa = 0.7. The parameters a¯ and σa cannot be calibrated with historical aggregate profit rates because they must capture risk-adjusted values, not historical ones.11 Instead, the model must be consistent with observed bond prices. Three parameters are thus not directly observed in the data: these are c (the coupon rate), a, ¯ and σa . Their values are inferred by matching empirical and simulated moments. The empirical moments are the mean and standard deviation of the price of Baa bonds 8. The dispersion of sales growth is not a perfect measure either, because permanent differences in growth rates would make dispersion positive even if there is no risk. There are other ways to define idiosyncratic risk at the firm level, but they produce similar trends. See Comin and Philippon (2005) for a comparison of various measures of firm volatility. See also Campbell et al. (2001) and Davis et al. (2006) for evidence on privately held companies. 9. To be included in the index, a bond must have a face value of at least 100 million, an initial maturity of at least 20 years, and most importantly, a liquid secondary market. Beyond these characteristics, Moody’s has some discretion on the selection of the bonds. The number of bonds included in the index varies from 75 to 100 in any given year. The main advantages of Moody’s measure are that it is available since 1919, and that it is broadly representative of the U.S. nonfinancial sector, because Baa is close to the median among rated companies. 10. Federal Reserve Economic Data: http://research.stlouisfed.org/fred2/. The issue with using the ten-year treasury bond is that it incorporates a liquidity premium relative to corporate bonds. To adjust for this, it is customary to use the LIBOR/swap rate instead of the treasury rate as a measure of risk-free rate (see Duffie and Singleton [2003] and Lando [2004]), but these rates are only available for relatively recent years. I add 30 basis points to the risk-free rate to adjust for liquidity (see Almeida and Philippon [2007] for a discussion of this issue). 11. Note that, in theory, the same applies to ρa , because persistence under the risk-neutral measure can be different from persistence under the physical measure. In practice, however, the difference for ρa is much smaller than for a¯ or σa . I therefore take the historical persistence to be a good approximation of the risk neutral persistence. Section VII shows that the model is robust to various assumptions regarding aggregate dynamics.

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relative to Treasuries, defined as (φ + rt$ )/(φ + yt$ ), where y$ is the yield on Baa corporate bonds and r $ is the yield on government bonds. The final requirement is that the average bond be issued at par. The three parameters c, a, ¯ and σa are chosen simultaneously to match the par-value requirement and the two empirical moments. The parameters inferred from the simulated moments are c = 4.3%, a/r ¯ = 0.925, and σa = 4.5%. Expected Inflation and Real Rate. The Livingston survey is used to construct expected inflation, and the yield on the ten-year treasury to construct the ex ante real interest rate, rˆtreal . Creating qbond . The model described in Section IV constructs q from the relative price of corporate bonds, conditional on the baseline values for the risk-free rate, book leverage, and idiosyncratic risk. As I have just explained, the risk-free rate, book leverage, and idiosyncratic volatility move over time. Therefore, qbond is a function of four observed inputs: average book leverage ψˆ t , η average idiosyncratic volatility σˆ t , the ex ante real rate rˆtreal , and the relative price of corporate bonds φ + rt10 η ˆ bond real (19) . qt =F ; σˆ t ; ψt ; rˆt φ + ytBaa Figure III displays the three main components: leverage, volatility, and the relative price. In theory, the dynamics of the four inputs must be jointly specified to construct the mapping of equation (19). Quantitatively, however, it turns out that one can estimate mappings with respect to (φ + rt10 )/(φ + ytBaa ) assuming constant values for the other three parameters, as I did in Figure II. For the risk-free rate, this follows from a well-known fact in the bond pricing literature: risk-free rate dynamics plays a negliη gible role in fitting corporate spreads. For σˆ t and ψˆ t , the historical series are so persistent that there is little difference between the mapping assuming a constant value and the mapping conditional on the same value in the time-varying model.12 Classic Measure of Tobin’s q. The usual measure of Tobin’s q is constructed from the flow of funds as in Hall (2001). The usual 12. To check this, I construct an extended Markov model where all the parameters follow AR(1) processes calibrated from the data. I then create mappings conditional on each realization of the parameters and I compare them to the mappings from Figure II. I find that the discrepancies are small for volatility and invisible for book leverage and the risk-free rate. Detailed results and figures are available upon request.

1031

1

2

3

4

5

THE BOND MARKET’S q

1955

1960

1965

1970

1975

1980

Usual q

1985

1990

1995

2000

2005

Bond q

FIGURE IV Usual Measure of q and Bond Market’s q Tobin’s q is constructed from the flow of funds, as in Hall (2001). Bond q is constructed from Moody’s yield on Baa bonds, using the structural model calibrated to the observed evolutions of book leverage and firm volatility, expected inflation from the Livingston survey, and the yield on 10-year Treasury bonds.

measure is the ratio of the value of ownership claims on the firm less the book value of inventories to the reproduction cost of plant and equipment. All the details on the construction of this measure can be found in Hall (2001). Investment and Capital Stock. I use the series on private nonresidential fixed investment and the corresponding current stock of capital from the Bureau of Economic Analysis. Table I displays the summary statistics. V.B. Investment Equations Figure IV shows the two measures of q: qusual , constructed from the flow of funds as in Hall (2001), qbond constructed using bond yields, leverage, idiosyncratic volatility, expected inflation, and the theoretical mappings described in the previous sections. The average value of qbond is arbitrary, because γ1 is a free parameter, and I normalize it to 1.5. Figure IV shows that qusual is approximately seven times more volatile than qbond . The standard deviation of qusual is 0.845, whereas the standard deviation

QUARTERLY JOURNAL OF ECONOMICS

0.08

1

0.09

2

0.1

q

I /K

3

0.11

4

0.12

5

0.13

1032

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

I /K

Usual q

FIGURE V Usual Measure of q and Investment Rate I/K is corporate fixed investment over the replacement cost of equipment and structure. Usual q is constructed from the flow of funds, as in Hall (2001).

of qbond is only 0.117, as reported in Table I. It is also interesting to note that qbond is approximately stationary, because the mappings take into account the evolution of idiosyncratic volatility and book leverage, as explained above. In the short run, qbond depends mostly on the relative price component. Year-to-year changes in (φ + rt10 )/(φ + ytBaa ) account for 85% of the year-to-year changes in qbond . In the long run, leverage and, especially, idiosyncratic risk are also important. Figure V shows qusual and the investment rate in structure and equipment. Figure VI shows qbond and the same investment rate. The corresponding regressions are reported in the upper panel of Table III. They are based on quarterly data. The investment rate in structure and equipment is regressed on the two measures of q, measured at the end of the previous quarter: bond usual + β e qt−1 + εt . xt = α + β bqt−1

The standard errors control for autocorrelation in the error terms up to four quarters. qbond alone accounts for almost 60% of aggregate variations in the investment rate. qusual accounts for only

1033

1.1

0.08

1.2

0.09

1.3

0.1

I /K

1.4 1.5 Bond q

0.11

1.6

0.12

1.7

1.8

0.13

THE BOND MARKET’S q

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

I /K

Bond q

FIGURE VI Bond Market’s q and Investment Rate I/K is corporate fixed investment over the replacement cost of equipment and structure. Bond q is constructed from Moody’s yield on Baa bonds, using the structural model calibrated to the observed evolutions of book leverage and firm volatility, expected inflation from the Livingston survey, and the yield on 10-year Treasury bonds.

10% of aggregate variations. Moreover, once qbond is included, the standard measure has no additional explanatory power. Looking at Figure V, the fit of the investment equation is uniformly good, except in the late 1980s and early 1990s, where, even though the series remain correlated in changes (see below), there is a persistent discrepancy in levels. qbond is more correlated with the investment rate, hence the better fit of the estimated equation, but it is also less volatile than qusual . As a result, the elasticity of investment to q is almost eighteen times higher with this new measure, which is an encouraging result because the low elasticity of investment with respect to q has long been a puzzle in the academic literature. The estimated coefficient still implies adjustment costs that are too high, around 15 years, but, as Erickson and Whited (2000) point out, there are many theoretical and empirical reasons that the inverse of the estimated coefficient is likely to underestimate the true elasticity.13 13. Note that the mapping is calibrated assuming γ2 = 10, so in theory the coefficient should be 0.1. In Table III, it is 0.065. I have also solved for the model

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QUARTERLY JOURNAL OF ECONOMICS TABLE III BENCHMARK REGRESSIONS

Bond q (t − 1) S.e. Classic q (t − 1) S.e. Bond q (t − 1), alt. measure S.e. Observations OLS R2 [bond q] (t − 5, t − 1) S.e. [classic q] (t − 5, t − 1) S.e. [profit rate] (t − 5, t − 1) S.e. [bond q] (t − 5, t − 1), alt. measure S.e. Observations OLS R2

0.0650∗∗∗ (0.00594)

216 .574

Equation in levels: I/K(t) 0.0629∗∗∗ (0.00642) 0.00366∗∗ 0.000928 (0.00155) (0.000970)

216 .095

Estimation in changes: 0.0515∗∗∗ (0.00495) 0.00700∗∗∗ (0.00187)

212 .613

212 .102

216 .580

0.0521∗∗∗ (0.00706) 216 .432

I/K(t) − I/K(t − 4) 0.0471∗∗∗ (0.00584) 0.00240∗ (0.00133) 0.0530 (0.0514) 0.0517∗∗∗

212 .628

(0.00500) 212 .561

Notes. Fixed private nonresidential capital and investment series are from the BEA. Quarterly data, 1953:3 to 2007:2. Classic q is constructed from the flow of funds, as in Hall (2001). Bond q is constructed by applying the structural model to Corporate and Treasury yields, expected inflation, book leverage, and firm volatility measured with idiosyncratic stock returns. The alternate measure of Bond q uses idiosyncratic sales growth volatility as an input. Newey–West standard errors with autocorrelation up to four quarters are reported in parentheses. ∗ , ∗∗ , and ∗∗∗ denote statistical significance at the 10%, 5%, and 1% levels. Constant terms are omitted.

Figure VII shows the four-quarter difference in the investment rate, a measure used by Hassett and Hubbard (1997), among others, because of the high autocorrelation of the series in levels. The corresponding regressions are presented in the bottom panel of Table III. The fit of the equation in difference is even better than the fit in levels, with an R2 above 60%. In the third regression, the change in corporate cash flows over capital is added to the right-hand side of the equation, but it is insignificant and does not improve the fit of the equation. The construction of qbond uses idiosyncratic stock returns to measure firm volatility. Note that using idiosyncratic return volatility is justified even when the aggregate stock market is assuming γ = 15. This makes the theoretical and actual coefficients similar, but does not change anything to the rest of the results. See also Section VII for a discussion of biases.

1035

–0.02

–0.01

0

0.01

0.02

THE BOND MARKET’S q

1955

1960

1965

1970

1975

Change in I /K from t – 4 to t

1980 1985 time

1990

1995

2000

2005

Predicted with lagged bond q

FIGURE VII Four-Quarter Changes in Investment Rate, Actual and Predicted I/K is corporate fixed investment over the replacement cost of equipment and structure. Bond q is constructed from Moody’s yield on Baa bonds, using the structural model calibrated to the observed evolutions of book leverage and firm volatility, expected inflation from the Livingston survey, and the yield on 10-year Treasury bonds.

potentially mispriced. Mispricing across firms is limited by the possibility of arbitrage. In the aggregate, however, arbitrage is much more difficult. There is therefore no inconsistency in using the idiosyncratic component of stock returns to measure idiosyncratic risk, although acknowledging that the aggregate stock market can sometimes be over valued. Nonetheless, one might be concerned about the use of equity returns here, and I have repeated the calibration using the standard deviation of sales growth as a measure of volatility. The results, in the last column of Table III, are somewhat weaker than with the benchmark model. The reason is that sales volatility is a lagging indicator of idiosyncratic risk. Hilscher (2007) shows that the bond market is actually forward-looking for volatility. As a result, using a measure of volatility that lags the true information—and all accounting measures do— creates a specification error. This matters less for the equation in changes because of the smaller role of volatility in that equation.

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The conclusions from this empirical section are the following: • With aggregate U.S. data, qbond fits the investment equation well, both in levels and in differences. • The estimated elasticity of investment to qbond is 18 times higher than the one estimated with qusual . • Corporate cash flows do not have significant explanatory power once qbond is included in the regression. V.C. Further Evidence The evidence presented above is based on the construction of qbond in equation (19). In this section, I provide evidence on the explanatory power of the components separately, and on the role of nonlinearities in the model. I also test the predictive power of the model. The results are in Tables IV and V. Explanatory Power of Individual Components. The econometric literature has studied the predictive power of default spreads for real economic activity.14 Table IV shows the explanatory power of the components of qbond , in levels and in four-quarter differences. Consider first the top part of Table IV, for the regressions in level. Column (1) shows that the Baa spread, by itself, has no explanatory power for investment. The explanatory power appears only when idiosyncratic volatility and leverage are also included, in Column (3). These factors have not been used in the empirical literature. Their empirical importance provides support for the theory developed in this paper. In addition, notice that even when all the components are entered linearly, the explanatory power is only 45%. By contrast, the qbond has an R2 of 57.4% with one degree of freedom instead of four. This shows that the nonlinearities are important in the level equation, as explained below. For the equation in four-quarter differences, the spread by itself has significant explanatory power. This is what one would expect, because the low-frequency movements in leverage and volatility matter less in these regressions. Nonetheless, leverage and volatility are still highly significant. The unrestricted linear 14. Bernanke (1983) notes that the spread of Baa over treasury went “from 2.5 percent during 1929–30 to nearly 8 percent in the mid-1932” and shows that the spread was a useful predictor of industrial production growth. Using monthly data from 1959 to 1988, Stock and Watson (1989) find that the spread between commercial paper and Treasury bills predicts output growth. Some of these relationships are unstable over time (see Stock and Watson [2003] for a survey).

1037

THE BOND MARKET’S q TABLE IV DECOMPOSING BOND q

−0.166 yBaa − r 10 (t − 1) S.e. (0.189) Real risk-free rate (t − 1) S.e. Idiosyncratic volatility (t − 1) S.e. Book leverage (t − 1) S.e. [0.1 + r 10 ]/[0.1 + yBaa ] (t − 1) S.e. Real discount factor (t − 1) S.e. Quadratic term (t − 1) S.e. N 216 .013 OLS R2

Equation in levels: I/K(t) −0.152 −1.051∗∗∗ (0.189) (0.177) −0.0700 −0.0781 (0.0796) (0.0744) 0.278∗∗∗ 0.424∗∗∗

0.407∗∗∗

(0.0759) (0.0672) (0.0690) 0.0910∗∗∗ 0.0633∗∗∗ 0.0727∗∗∗ (0.0214) (0.0172) (0.0159) 0.252∗∗∗ 0.263∗∗∗ (0.0268) 0.203∗∗∗ (0.0673)

216 .023

216 .451

216 .582

Estimation in changes: I/K(t) − I/K(t − 4) [yBaa − r 10 ](t − 5, t − 1) −0.942∗∗∗ −0.953∗∗∗ −0.997∗∗∗ S.e. (0.103) (0.108) (0.0910) [real riskfree rate] −0.0237 −0.00297 (t − 5, t − 1) S.e. (0.0355) (0.0338) 0.265∗∗∗ [idiosyncratic 0.283∗∗∗ volatility] (t − 5, t − 1) S.e. (0.0885) (0.0896) [book leverage] 0.172∗∗∗ 0.142∗∗∗ (t − 5, t − 1) S.e. (0.0516) (0.0515) [(0.1 + r 10 )/ 0.199∗∗∗ (0.1 + yBaa )](t − 5, t − 1) S.e. (0.0195) [real discount factor] 0.0787∗ (t − 5, t − 1) S.e. (0.0419) [quadratic term] (t − 5, t − 1) S.e. Observations 212 212 212 212 .478 .479 .618 .618 OLS R2

(0.0291) 0.187∗∗∗ (0.0649) 1.069∗∗ (0.522) 216 .604

0.270∗∗∗ (0.0912) 0.133∗∗∗ (0.0502) 0.201∗∗∗ (0.0195) 0.0765∗ (0.0412) 0.398 (0.293) 212 .622

Notes. Fixed private nonresidential capital and investment series are from the BEA. Quarterly data, 1953:3 to 2007:2. The ex ante real rate is the nominal rate minus expected inflation from the Livingston survey. The real discount factor is (1 + E[inflation])/(1+nominal rate). Firm volatility is measured with idiosyncratic stock returns. The nominal rates are r 10 for 10-year Treasury bonds, and yBaa for Moody’s index of Baa bonds. Quadratic term is the square of the relative price of Baa bonds minus its mean: [(0.1 + r 10 )/(0.1 + yBaa ) − 0.9]2 . Newey–West standard errors with autocorrelation up to 4 quarters are reported in parentheses. ∗ , ∗∗ , and ∗∗∗ denote statistical significance at the 10%, 5% and 1% levels. Constant terms are omitted.

0.396∗∗∗ (0.0778) 215 .398

0.148∗∗∗ (0.0231)

0.337∗∗∗ (0.0832) 215 .341

0.710∗∗∗ (0.182)

0.131 (0.0935) 215 .430

0.160∗∗∗ (0.0251) 0.760∗∗∗ (0.199)

0.161∗∗∗ (0.0247) 0.797∗∗∗ (0.200) 0.0130 (0.00955) 0.0996 (0.0928) 215 .443 0.0119 (0.00917) 0.169∗∗∗ (0.0585) 0.00976∗∗∗ (0.00279) 0.0206 (0.0832) 215 .149

Growth rate of consumption

0.0279 (0.0417) −0.162 (0.346) 0.0401∗∗ (0.0184) 0.511∗∗∗ (0.0543) 215 .335

Growth rate of residential investment

Notes. Maximum likelihood estimation of coefficients and standard errors, assuming AR(1) model. The R2 is for the corresponding OLS regression with lagged dependent variable on the right-hand side. Fixed private nonresidential investment series is from the BEA. Quarterly data, 1953:3 to 2007:2. Bond q is constructed by applying the structural model to Corporate and Treasury yields, expected inflation, book leverage, and firm volatility measured with idiosyncratic stock returns. Constant terms are omitted.

[bond q] (t − 1) S.e. log[real GDP] (t − 1) S.e. [classic Q] (t − 1) S.e. AR(1) S.e. Observations R2 of OLS

Growth rate of private nonresidential fixed investment

TABLE V PREDICTIVE REGRESSIONS, ONE QUARTER AHEAD: MAXIMUM LIKELIHOOD ESTIMATION OF AUTOREGRESSIVE MODEL

1038 QUARTERLY JOURNAL OF ECONOMICS

THE BOND MARKET’S q

1039

model has an R2 of 61.6%, compared to 61.3% for the bond q model. This suggests that, also as expected, nonlinear effects are not crucial for the specification in changes. Nonlinear Effects. There are several nonlinear effects in the model. Consider equation (4): Tobin’s q has two components, the real discount factor and the expected risk-neutral value of capital, Eπ [v(ω )|ω]. This letter item is a function of the relative price of corporate bonds, as shown in Figures I and II. Thus, the model suggests the use of the relative price (φ + rt10 )/(φ + ytBaa ) instead of the spread ytBaa − rt10 . When rates are stable, the difference between the spread and the relative price is negligible. In the data, however, the level of nominal rates changes a lot. A given change in the spread has a larger impact on the relative price when rates are low than when they are high. Column (4) provides strong support for this first nonlinearity. The relative price does much better than the spread in the level regression.15 The R2 increases from 45.1% to 58.2% because of the nonlinear correction. A second nonlinearity comes from the mapping of Figure I. Tobin’s q is a convex function of the relative bond price. Column (5) shows that this effect is significant, but it only increases the R2 by 2 percentage points. The last column of Table IV can also be compared to the first column of Table III. In level, the structural model has a fit of 57.4%. The unrestricted nonlinear model has a fit of 60.4%. In a statistical sense, the difference is significant, but in an economic sense, it does not appear very important. In differences, the respective performances are 61.3% and 62.2%. These results support the restrictions imposed by the theory. Predictive Regressions. Table V reports the results from predictive regressions of the growth rate of three macroeconomic variables: real corporate investment, real consumption expenditures, and real residential investment. In each case, I run two separate regressions. I estimate an AR(1) model by maximum likelihood to obtain the correct coefficients and standard errors. I also run an OLS regression with the lagged dependent variable on the RHS to get a sense of the R2 of the simple linear regression. 15. Note that, in theory, this could also apply to the real discount factor: (1 + E[inflation])/(1 + r $ ) is not the same as E[inflation] − r $ when nominal shocks are large. Empirically, this nonlinearity seems to matter much less, probably because the real rate is not as volatile as the Baa yield.

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The first column shows that qbond is a very significant predictor of corporate investment growth. It predicts better than the “accelerator” model based on lagged output growth (column (2)). While lagged output growth still has significant marginal forecasting power, it increases the R2 by only 3 percentage points (column (3)). In addition, the coefficient on qbond actually goes up. Column (4) shows that qusual has no predictive power for corporate investment.16 The last two columns focus on consumption and residential investment. Although qbond is the best predictor of corporate investment, it does not predict housing or consumption. qusual , on the other hand, does not predict corporate investment, but it does predict housing and (to some extent) consumption. These results are suggestive of wealth effects from the equity market. They are consistent with the results of Hassett and Hubbard (1997) but clearly inconsistent with the usual implementation of the q-theory. The conclusions from this empirical section are the following: • All the components identified by the theory (bond spreads, volatility, leverage, risk-free rate) are statistically and economically significant. • The fit of the restricted structural model is almost as good as the fit of the unrestricted regressions. • The nonlinearities of the model (relative price instead of spreads, convexity of mapping) are important for the level regressions. • The bond market predicts future corporate investment well, whereas the equity market has no marginal predictive power. VI. THEORETICAL EXPLANATIONS The results so far show that it is possible to link corporate investment and asset prices, using the corporate bond market and modern asset pricing theory. They do not explain why the usual approach fails, however. This section sheds some light on this complex question. 16. Fama (1981) shows that stock prices have little forecasting power for output. Cochrane (1996) finds a significant correlation between stock returns and the growth rate of the aggregate capital stock, but Hassett and Hubbard (1997) argue that it is driven by the correlation with residential investment, not corporate investment. In any case, I find that the bond market’s q outperforms the usual measure both in differences and in levels.

THE BOND MARKET’S q

1041

It is important to recognize that a satisfactory explanation must address two related but distinct issues: 1. Why is qusual more volatile than qbond ? 2. Why does qbond fit the investment equation better? I consider two explanations.17 The first explanation is based on growth options and the distinction between average and marginal q. The second explanation is based on mispricing in the equity market. I chose these explanations because they provide useful benchmarks. They are not mutually exclusive, and they are not the only possible explanations. VI.A. Growth Option Interpretation Suppose that, in addition to the value process in equation (3), the firm also has a growth option of value Gt . Total firm value is then Vt = vt kt−1 + Gt .

(20)

Consider for simplicity the example of Section III, with short-term debt and a constant risk-free rate. The value of short-term debt is (21)

Bt =

1 Eπ [min( t ; vt+1 kt + Gt+1 )]. 1+r t

Let Gt be a binary variable. Gt = GH , with risk-neutral probability λt−1 and GL otherwise. The following proposition states that a growth option with enough skewness can explain why qbond fits better than qusual . PROPOSITION 3. Consider the model of equations (20) and (21). By choosing λt and GL small enough, and GH large enough, the fit of the investment equation can be arbitrarily good for qbond , and arbitrarily poor for qusual . Proof. See the Appendix. The intuition behind Proposition 3 is straightforward. A small probability of a large positive shock has a large impact on equity prices, and almost no impact on bond prices. Because growth options do not depend on the capital stock, news about the likelihood of these future shocks does not affect investment. In essence, 17. For a investigation of whether the same pricing kernel can price bonds and stocks, see Chen, Collin-Dufresne, and Goldstein (forthcoming).

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growth options drive wedges between bond and equity prices, and between marginal and average q. What are the possible interpretations of these shocks? The simplest one is that firms earn organizational rents. Think of a large industrial corporation with outstanding organizational capital. This firm will be able to seize new opportunities if and when they arrive. This might happen through mergers and acquisitions or through internal development of new lines of business. Investing more in the current business and current technology does not improve this option value.18 To summarize, the rational interpretation proposes the following answers to the two questions posed at the beginning of this section: 1. Why is qusual more volatile than qbond ? Because growth options affect stocks much more than bonds. 2. Why does qbond fit the investment equation better? Because growth options are unrelated to current capital expenditures. The example given is obviously extreme, but the lesson is a general one. It is not difficult to come up with a story where current capital expenditures are well explained by the bond market, whereas firm creation, IPOs, and perhaps R&D, are better explained by the equity market. A complete understanding of these joint dynamics is an important topic for future research. VI.B. Mispricing Interpretation Stein (1996) analyzes capital budgeting in the presence of systematic pricing errors by investors, assuming that managers have rational expectations. He emphasizes three crucial aspects of capital budgeting in such a world: (i) the true NPV of investment, (ii) the gains from trading mispriced securities, and (iii) the costs of deviating from an optimal capital structure in order to achieve (i) and (ii). For the purpose of my paper, the most important result is that when capital structure is not a constraint, and when managers have long horizons, real investment decisions are not influenced by mispricing (Stein 1996, Proposition 3). 18. Some other expenditures could be complement with the option value. These could include R&D and reorganizations. At the aggregate level, one might think that new options were realized by new firms. This would explain why IPOs are correlated with the equity market (Jovanovic and Rousseau 2001). For a model of growth option at the firm level, see Abel and Eberly (2005).

THE BOND MARKET’S q

1043

Gilchrist, Himmelberg, and Huberman (2005) consider a model where mispricing comes from heterogeneous beliefs and short sales constraints. They show that increases in dispersion of investor opinion cause stock prices to rise above their fundamental values. This leads to an increase in q, share issues, and real investment. The main difference from Stein (1996) is that they assume that investors do not overvalue cash held in the firm. This assumption rules out the separation of real and financial decisions: managers who seek to exploit mispricing must alter their investment decisions and Proposition 3 in Stein (1996) does not hold. However, Gilchrist, Himmelberg, and Huberman (2005) show that even large pricing errors need not have large effects on investment. Thus, it is possible to explain the fact that investment does not react much to equity mispricing, even when the strict dichotomy of Stein (1996)’s Proposition 3 fails. Neither Stein (1996) nor Gilchrist, Himmelberg, and Huberman (2005) consider the role of bonds and stocks separately, so it appears that the story is still incomplete. It turns out, however, that recent work in behavioral finance has shown that skewed assets are more likely to be mispriced (Barberis and Huang 2007; Brunnermeier, Gollier, and Parker 2007; Mitton and Vorkink 2007). A direct implication is that mispricing is more likely to appear in the equity market than in the bond market. Of course, mispricing can also happen in the bond market. Piazzesi and Schneider (2006), for instance, analyze the consequences for asset prices of disagreement about inflation expectations. To summarize, the behavioral interpretation proposes the following answers to the two questions posed at the beginning of this section: 1. Why is qusual more volatile than qbond ? Because mispricing is more likely in the equity market than in the bond market. 2. Why does qbond fit the investment equation better? Because managers do not react (much) to mispricing. The growth option and mispricing interpretations are not mutually exclusive. In fact, the term Gt in equation (20) is the most likely to be mispriced. The rational and behavioral explanations simply rely on different critical assumptions. In the rational case, Gt must not depend on k, otherwise investment would respond. In the behavioral story, it is important that managers have long horizons.

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VII. THEORETICAL ROBUSTNESS The beauty of the standard q theory is its parsimony. Beyond the assumptions of constant returns and convex costs, it is extremely versatile. In equation (4), the sources of variations in q(ω) include changes in the term structure of risk-free rates, cash flow news that has aggregate, industry, and firm components, and changes in risk premia that separate the market value Eπ [v ] from the objective expectation E[v ]. These multidimensional shocks can be combined in arbitrary ways, and yet their joint impact on investment can be summarized by one real number. Unfortunately, the standard approach fails. The previous section has presented two explanations for this failure, as well as for the (relative) success of the new approach. The new approach, however, is not as model-free as the standard approach. The mappings of Figures I and II are constructed under specific assumptions regarding firm and aggregate dynamics. The goal of this section is to study the theoretical robustness of the new approach. To do so, I focus on three issues: • Is there an exact mapping at the firm level, similar to the one in Figure I, for aggregate q? The answer turns out to be no, but qbond is still a useful measure. • Suppose that aggregate dynamics does not follow a simple autoregressive process under the risk neutral measure. Would the misspecified mapping of Figure I still deliver a good fit? Yes. • What happens when the Modigliani–Miller assumptions do not hold? If anything, the model seems to work better in this case. VII.A. Firm-Level Mappings I first study the extent to which the aggregate mapping of Figure II applies at the firm level. Figure VIII and the left part of Table VI report the results based on a simulated panel of fifty years and 100 firms, using the benchmark model with the parameters in Table II. To get an exact mapping, there must be a monotonic relationship between asset value and bond prices. This is typically the case when there is only one dimension of heterogeneity. In the top left panel of Table VI, the R2 for the aggregate regression is 1 and the estimated elasticity is exactly equal to 1/γ2 (0.1, because γ2 is calibrated to 10 years). At the firm level, there are two sources of

1045

0

0.5

Tobin's q 1

1.5

2

THE BOND MARKET’S q

0.6

0.7 0.8 Relative price of corporate bonds

0.9

1

FIGURE VIII Simulations of a Panel of Firms 5,000 firm–year observations of relative bond price and Tobin’s q. Simulation with constant real rate of 3%, constant idiosyncratic volatility, and constant book leverage.

variation, aggregate and idiosyncratic. Conditional on one shock, there is an exact mapping,19 but there is no guarantee that the ranking would be preserved across several types of shocks. In fact, Figure VIII shows that they are not.20 The bottom left panel of Table VI shows that R2 for firm-level regressions is less than one. In the univariate regression, this does not bias the point estimate. In the multivariate regression, firm-level cash flows are significant, R2 increases, but the point estimate of qbond becomes unreliable. The conclusion is that, at the firm level, the bond q should be significant but cash flows are likely to remain significant as well. These predictions are consistent with the results obtained 19. For instance, fix the aggregate state, and look at the cross section. Then firms with good earnings shocks have high value and high bond prices. Or fix the firm-level shock, and then states with high values have high bond prices. 20. The intuition is the following. Suppose a firm–year observation has a true q of 1.1 based on a good firm shock in a bad aggregate state. Suppose another firm– year observation has a true q of 1.1 based on a medium firm shock in a medium aggregate state. There is no reason to expect them to have the same bond price (for instance, because persistence and volatility are not the same for idiosyncratic and aggregate shocks). As a result, the same value of q for one firm–year observation is associated with several relative prices of bonds. This is what Figure VIII shows.

(0.000148) −0.000318 (0.000312) 100 1.000

(0.000638) 0.0482∗∗∗ (0.000649) 5,000 .943

0.0993∗∗∗ (0.000619) 5,000 .838

(0.000525)

Benchmark model 0.0610∗∗∗

5,000 .879

100 .994

0.0799∗∗∗ (0.000623)

5,000 .883

0.0791∗∗∗ (0.000408)

0.0898∗∗∗ (0.00173) 5,000 .349

0.0703∗∗∗ (0.000276) 0.0434∗∗∗ (0.000498) 5,000 .953

Model B: binary aggregate cash flows

0.0394∗ (0.0222) 100 .031

0.0796∗∗∗ (0.000648) 0.00176 (0.00158) 100 .995

Model B: binary aggregate cash flows

Firm-level regressions: Dependent variable is firm I/K

0.210∗∗∗ (0.000159) 100 .98

0.100∗∗∗

0.1000∗∗∗

100 1.000

(0.00000111)

Benchmark model

Notes. Simulated annual data. The benchmark model is the one used in the main part of the paper, calibrated in Table II. In model B, the aggregate component of the profit rate is either high or low, and the probability of the high state follows a Markov chain under the risk-neutral measure. In both cases, the risk-free rate is constant at 3%, book leverage is constant at 0.45, and idiosyncratic shocks follow the benchmark model. Bond q is constructed using the benchmark mapping of Figure I (it is thus deliberately misspecified for model B). The simulation is for fifty firms and 100 years. OLS standard errors are in parentheses.

Bond q S.e. Profit rate S.e. Observations R2

Bond q S.e. Profit rate S.e. Observations R2

0.100∗∗∗

Aggregate regressions: Dependent variable is aggregate I/K

TABLE VI INVESTMENT REGRESSIONS IN SIMULATED DATA

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by Gilchrist and Zakrajsek (2007) with a large panel data set of firm-level bond prices. They regress the investment rate on a firm-specific measure of the cost of capital, based on firm-level bond yields and industry-specific prices for capital. They find a strong negative relationship between the investment rate and the corporate yields, and they also find that qusual and cash flows remain significant. There are other explanations for the discrepancy between micro and macro results. Returns to scale might be decreasing at the level of an individual firm, even though they are constant for the economy as a whole. This could explain why cash flows are significant in the micro data but not in the macro data. Finally, to the extent that mispricing explains some of the discrepancy between qusual and qbond , the results are consistent with the argument in Lamont and Stein (2006) that there is more mispricing at the aggregate level than at the firm level. VII.B. Robustness to Model Misspecifications I now turn to the issue of the specification of aggregate dynamics. The mapping in Figure I assumes that aggregate dynamics follow an AR(1) process. This is a restrictive assumption, especially under the risk-neutral measure.21 A second model is therefore used to check the robustness of the results. Model B (described in the Appendix) is meant to be the polar opposite to the benchmark model as far as aggregate dynamics are concerned (idiosyncratic shocks are unchanged). This model captures two important ideas. First, cash flows might have a short- and a long-run component, the long-run one being more relevant for valuation and investment. Second, holding constant the objective distribution of cash flows, changes in the market price of risk (due to changes in risk aversion or conditional volatilities) affect the risk-neutral likelihood of good and bad states. In both cases, aggregate cash flows would not summarize the aggregate state. This model is empirically relevant because Vuolteenaho (2002) shows that much of the volatility at the firm level reflects cash-flow news, whereas discount rate shocks are much more important in the aggregate. I simulate a panel similar to the one discussed above (fifty years, 100 firms). I then use the mapping of Figure I to construct 21. Moreover, this assumption implies that the current aggregate profit rate is a sufficient statistic for the current aggregate state, which is clearly unrealistic. This can be seen in the simulated aggregate regressions where aggregate cash flows have an R2 of .98 (Table VI, column (2)).

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q. The model is therefore misspecified because the benchmark mapping is used to construct qbond in a world where aggregate dynamics are substantially different from the benchmark. The first result in Table VI is that the model retains most of its explanatory power. qbond is a reliable predictor even when the model is misspecified. The R2 is still close to one, at 99.4%. The only issue is the bias in the estimated coefficient, which overestimates adjustment costs by about 20%. The second important message of Table VI is that cash flows are not reliable in the aggregate regression. In model B, cash flows have no explanatory power for aggregate investment. At the firm level, cash flows remain significant, as expected, because firm-level dynamics is the same as in the benchmark model. VII.C. Bankruptcy Costs and Leverage The benchmark model is built under the assumptions of no taxes and no bankruptcy costs (Modigliani and Miller 1958).22 I now study how qbond performs if there are taxes and bankruptcy costs. To focus on the crucial issues and to avoid heavy notations, I consider here a simple one-period example. Investment takes place at the beginning of the period, and returns are realized at the end. The risk-free rate is normalized to zero. Profits are taxed at a flat rate, payments to bondholders are deductible, and there are bankruptcy costs. The details of the model are described in the Appendix. Figure IX shows the mappings for different values of distress costs (in the range of values consistent with empirical estimates). Distress costs do not appear to invalidate the approach taken in this paper. The shape of the mapping is similar across the various models.23 If anything, higher bankruptcy costs make the mapping from relative bond prices to q more linear, and thus easier to estimate empirically. VIII. CONCLUSION This paper has shown that it is possible to construct Tobin’s q using bond prices, by bringing the insights of Black and Scholes 22. In such a world, capital structure is irrelevant, and arbitrary changes in leverage are possible without affecting investment. This issue was discussed at the end of Section IV. 23. The fact that one mapping is higher than another on average is irrelevant because it relates only to the average value of q.

THE BOND MARKET’S q

1049

1.6 No distress costs Moderate distress costs Large distress costs

1.5 1.4 1.3

Tobin q

1.2 1.1 1 0.9 0.8 0.7 0.6 0.7

0.75

0.8 0.85 0.9 Relative price of corporate bonds

0.95

FIGURE IX Mappings with Taxes and Bankruptcy Costs Computations for the simple one-period model described in the Appendix, assuming that asset values are lognormally distributed. Moderate distress costs are consistent with the estimates of Andrade and Kaplan (1998).

(1973) and Merton (1974) to the investment models of Abel (1979) and Hayashi (1982). The bond market’s q performs much better than the usual measure of q when used to fit the investment equation using postwar U.S. data. The explanatory power is good (both in level and in differences), cash flows are no longer significant, and the inferred adjustment costs are almost twenty times smaller. Two interpretations of these results are possible. The first is that the equity market is subject to severe mispricing, whereas the bond market is not, or at least not as much. This interpretation is consistent with the arguments in Shiller (2000) and the work of Stein (1996), Gilchrist, Himmelberg, and Huberman (2005), Barberis and Huang (2007), and Brunnermeier, Gollier, and Parker (2007). Another interpretation is that the stock market is mostly right, but that it measures something other than the value of the existing stock of physical capital. This is the view pushed by Hall (2001) and McGrattan and Prescott (2007). According to this

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view, firms accumulate and decumulate large stocks of intangible capital. If the payoffs from intangible capital were highly skewed, then they could affect equity prices more than bond prices, and this could explain the results presented in this paper. The difficulty of this theory, of course, is that it rests on a stock of intangible capital that we cannot readily measure (see Atkeson and Kehoe [2005] for a plant-level analysis). Looking back at Figure IV, it is difficult to imagine a satisfactory answer that does not mix the two theories. Moreover, these theories are not as contradictory as they appear, because the fact that intangible capital is hard to measure increases the scope for disagreement and mispricing. One can hope that future research will be able to reconcile the two explanations. APPENDIX A. Proof of Proposition 1 Let θτ be the marginal default rate during period τ . Let t,τ be the cumulative default rate in periods t + 1 up to τ − 1. In other words, if a bond has not defaulted at time t, the probability that it enters time τ > t is 1 − t,τ . Thus, by definition, t,t+1 = 0 and the default rates

satisfy the recursive structure: 1 − t,τ = (1 − θt+1 ) 1 − t+1,τ . The value at the end of period t of one unit of outstanding principal is

bt1

=

Etπ

∞

(1 − t,τ )

τ =t+1

(22)

+ θτ Vτ / τ −1 ) .

(1 − φ)τ −t−1 ((1 − θτ )(c + φ) (1 + rt,τ )τ −t

Similarly, and just to be clear, the price of one unit of principal at the end of t + 1 is

1 π bt+1 = Et+1

∞

(1 − t+1,τ )

τ =t+2

(23)

+ θτ Vτ / τ −1 ) .

(1 − φ)τ −t−2 ((1 − θτ )(c + φ) (1 + rt+1,τ )τ −t−1

THE BOND MARKET’S q

1051

Using the recursive structure of and the law of iterated expectations, we can substitute (23) into (22) and obtain bt1 = (24)

1 Eπ [(1 − θt+1 )(c + φ) + θt+1 Vt+1 / t ] 1 + rt t 1 − φ π 1 + Et (1 − θt+1 )bt+1 . 1 + rt

Default happens when equity value reaches zero, that is, when

Vt < t−1 φ + c + (1 − φ)bt1 . Therefore, the pricing function satisfies (25)

bt1 =

1 1 Etπ min φ + c + (1 − φ)bt+1 ; Vt+1 / t . 1 + rt

Now recall that bt1 is the price of one unit of outstanding capital. Let us define bt as the value of bonds outstanding at the end of time t, scaled by end-of-period physical assets, bt ≡ ψbt1 ,

(26)

where book leverage was defined in the main text as ψ ≡ t /kt , and assumed to be constant. Multiplying both sides of (25) by ψ, we obtain bt =

1 Eπ [min{(φ + c)ψ + (1 − φ)bt+1 ; vt+1 }]. 1 + rt t

In recursive form, and with constant book leverage, this leads to equation (7). Note that if book leverage were state-contingent, the first term in the min function would simply be (φ + c)ψt + (1 − φ)bt+1 ψt . ψt+1 B. Proof of Proposition 3 Assume that G H > . We can then write the debt pricing formula (21) as (27) Bt =

1 (1 − λt )Etπ min t ; vt+1 kt + GL + λt t . 1+r

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Taking the limit in equation (27) as λt → 0 and GL → 0, it is clear that Bt =

1 Eπ [min( t ; vt+1 kt )]. 1+r t

This is the same pricing formula we used earlier, and we have already seen that one can construct a sufficient statistic for investment in this case. On the other hand, the market value of equity moves when it is revealed that Gt = G H . It is always possible to increase the variance of the shocks by increasing G H . Because these shocks are uncorrelated with investment, the explanatory power of the traditional measure can become arbitrarily small. Note that in a growing economy, it would make sense to index the growth option on aggregate TFP to obtain a model with a balanced growth path. C. Model B In this model, the conditional distribution of cash flows follows a Markov process. Aggregate cash flows can be either high, aH , or low, aL, and the risk-neutral probability of observing a high cash flow is state-dependent: Pr(a = aH ) = f (s). State s follows a four-state Markov process under the risk-neutral measure. The complete aggregate state is (s, a). There are therefore eight possible aggregate states: four states for s and two for a. The persistence in the aggregate time series comes from the persistence in s. Conditional on s, aggregate cash flows are i.i.d. The transition matrix of s is chosen to match the empirical moments in Table II. Firm-level dynamics η are given by equation (17) as in the benchmark model. D. Distress Costs This is a one-period model. Without taxes or bankruptcy costs, the program of the firm is (28)

max Eπ [vk] − k − γ k2 /2, k

where k is investment and v is a random variable. Optimal investment is (29)

k = (q − 1)/γ ,

THE BOND MARKET’S q

1053

where q ≡ Eπ [v]. Now assume that profits are taxed at rate τ , that payments to bondholders are deductible, and that there are proportional bankruptcy costs ϕ. In case of default, a value ϕvk is lost. The firm is financed with debt and equity, and let ψ be book leverage. It is then straightforward to see that (29) still holds, but the definition of q must be adjusted to (30)

q ≡ (1 − τ )Eπ [v] + τ Eπ [min(ψ, v)] − ϕ Eπ [v1v 20 years old) Characteristic

Mean

Age 40.16 Female 0.499 Married 0.703 Illiterate 0.482 Intercollege and up 0.201 Citya Periurban/ large villagea Rurala Ballot success Monthly expenditures 8.678 (log)

Std. dev. 16.244 0.500 0.497 0.458 0.43

0.641

Full sample

Restricted subsample

Mean Std. dev. Mean Std. dev. 54.575 0.490 0.943 0.402 0.178 0.400 0.274

13.240 0.500 0.232 0.490 0.383 0.490 0.460

55.039 0.496 0.948 0.417 0.157 0.372 0.293

13.246 0.500 0.222 0.493 0.364 0.483 0.455

0.325 0.533 8.832

0.470 0.499 0.783

0.335 0.524 8.896

0.472 0.500 0.726

Notes. N = 1,605 for full sample, N = 1,295 for subsample, and N = 29,995 for adult Pakistani population. The Pakistani adult population is from the MICS 2003–4 survey (restricted to the same districts as in our sample). a City, periurban, and rural classifications comparable to our survey data are not available in the MICS.

The initial sampling frame was the list of all Hajj lottery applicants obtained from the Ministry. The survey area was limited for logistic ease to nine administrative districts in the Punjab province.9 Surveyors used addresses and telephone numbers provided in the applications to locate applicants and interview them at their residences. The sample was also restricted to Sunni applicants, because there were too few Shia applicants for meaningful inferences to be drawn. To maximize statistical power, we randomly selected equal numbers of winning and losing parties. Within each party, we randomly selected an individual to interview, and, if other party members of opposite gender were identified as living with the individual, we also selected a second person of the opposite gender. Surveyed applicants are broadly representative of the adult Pakistan population (Table II) with some truncation of the extremes of the socioeconomic distribution, because the poorest cannot afford to go on the Hajj and the rich typically travel on private schemes. Hajj applicants have average education and household 9. The districts were Attock, Islamabad, Rawalpindi, Jhelum, Chakwal, Faisalabad, Sargodha, Multan, and Gujrat.

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QUARTERLY JOURNAL OF ECONOMICS TABLE III SURVEY COMPLETION STATISTICS Panel A: Full sample

Panel B: Restricted subsample

Lottery status

Lottery status

Characteristic

Total Successful Unsuccessful Total Successful Unsuccessful

Selected for interview Raw completed interviews Completion rate (%) Not completed (%) Dead/ill Lives elsewhere Not found Not home Refused

2,537

1,286

1,251

1,995

1,032

963

1,605

855

750

1,295

679

616

63.3

66.5

60.0

64.9

65.8

64.0

2.1 10.4 8.3 7.9 7.9

2.1 10.0 6.4 8.7 6.3

2.1 10.8 10.3 7.2 9.6

2.3 9.8 7.7 8.2 7.2

2.2 9.8 6.6 8.7 6.9

2.3 9.8 8.9 7.6 7.5

Notes. Interview completion percentages from surveyor reports.

expenditures similar to those for the general population, but are older and more likely to be married. Forty percent are from cities, fairly similar to the general population. Surveyors completed interviews with 1,605 applicants, 63% of the 2,537 they attempted to interview (Table III, Panel A). However, only 7.9% of the attempted interviews were refused. In about three-quarters of unsuccessful attempts, surveyors were unable to contact or locate applicants. Some applicants lived in a different (out-of-sample) district from the one provided in their application address (often a relative’s address they wished to travel with), and it was not logistically possible to survey them. In other cases, addresses were incomplete or incorrect or the applicant was not at home despite three separate attempts. Among applicants the survey team could contact (i.e., interviewed plus refusals), the survey completion rate was therefore 88.8%. Successful applicants completed the survey at a 66.5% rate, higher than the 60.0% rate for unsuccessful applicants. This difference is statistically significant at the 1% level (Table III, Panel A). Hajjis were easier to locate, perhaps because their participation in the Hajj made them better known in their localities. Successful applicants also had a slightly lower refusal rate, possibly because they regarded the survey as being more pertinent for those who had actually performed the Hajj.

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The unbalanced interview completion between successful and unsuccessful lottery applicants could potentially introduce selection and bias our estimate of the Hajj effect.10 Therefore, we provide three robustness checks against selection concerns. First, Table I, Panel B, shows that for completed interviews, lottery success is not individually or jointly correlated with observable applicant characteristics. Second, our results are robust to demographic controls. None of our 25 index results qualitatively change with controls for district, urban or periurban location, and individual characteristics.11 Finally, we examine the robustness of our results to a restricted subsample (Table II) that excludes nine out of the 49 tehsils (subdistricts) in our survey area that were particularly difficult to survey. This subsample is balanced on survey completion and reasons for noncompletion. It excludes tehsils with more than 25 selected applicants (tehsils with smaller samples may generate imbalance mechanically) where the completion rate for successful applicants exceeded that for unsuccessful ones by more than 7%. This subsample contains 81% of the total interviews. Although the completion rate was still somewhat higher for successful applicants (65.8% vs. 64.0%), we fail to reject the null hypothesis of an identical completion rate with a p-value of .66. As in the full sample, lottery success in the interviewed subsample is uncorrelated with applicant characteristics (Table I, Panel B). As our results below show, there is no qualitative change in our estimates in the subsample. IV. MAIN RESULTS This section presents our main results on the impact of the Hajj. Sections IV.A–IV.D examine religious behavior and practices, tolerance, gender attitudes, and well-being, respectively. Our 10. A selection effect would imply that the marginal surveyed successful applicant was less willing to give an interview (more uncooperative) and harder to locate. This is because the initial randomization guarantees that successful and unsuccessful applicants are distributed identically along any attribute. If selection is introduced by, for example, successful applicants gaining incremental visibility from traveling, then the marginal successful applicant found is slightly less well known ex ante than the marginal unsuccessful applicant found. However, it is not clear how such potential selection could generate several of our results, such as a shift from localized to global practice or increased tolerance. If anything, one may expect the opposite for the tolerance result, because selection implies that the interviewed successful applicant is marginally less cooperative. 11. We can use additional data such as assets and expenditure from survey data, and the results are robust to these as well. We prefer not to present these as primary controls due to their potential endogeneity.

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QUARTERLY JOURNAL OF ECONOMICS TABLE IV RELIGION AES coefficients

(1) Regarded as religious (2) Global Islamic practice (3) Belief in localized Muslim practices (4) Participation in localized Muslim practices

Base

Controls

Restricted subsample

0.238∗∗∗ (0.06) 0.163∗∗∗ (0.030) −0.101∗∗∗ (0.032) −0.097∗∗ (0.046)

0.230∗∗∗ (0.055) 0.166∗∗∗ (0.029) −0.094∗∗∗ (0.031) −0.097∗∗ (0.045)

0.258∗∗∗ (0.061) 0.171∗∗∗ (0.033) −0.074∗∗ (0.035) −0.085∗ (0.052)

Notes. Columns give AES estimates for our base, control, and restricted subsample specifications. The AES averages the normalized treatment effects obtained from a seemingly unrelated regression in which each dependent variable is a question in the index. All regressions include dummies for place of departure × accommodation category × party size category, as well as dummies for each of the nine districts in the survey. All results come from IV regressions where the instrument is success in the Hajj lottery. Standard errors in parentheses clustered at the party level: Index component questions with number of components indicated in parentheses: Index 1 (1): Do others regard you as religious? Index 2 (10): How frequently do you: pray, do tasbih after prayer, pray in the mosque? Did you pray in the mosque last Sunday? Do you pray optional night prayers? Can you read the Qu’ran? How frequently do you: read the Qu’ran? discuss religious matters? keep fast during Ramadan? keep fast outside Ramadan? Index 3 (10): What is your general view of holy men? Do you regard: visiting holy men as correct? visiting shrines? using amulets? doing a forty-day death ceremony? participating in maulad mehfil (special religious gathering)? Do you believe that: a cap is required for prayer? that dowry is mandatory? that widows have different priority in remarriage? that there can be intercession on Judgment Day? Index 4 (4): Do you actively visit holy men? visit shrines? use amulets? participate in maulad mehfil? ∗ significant at 10%; ∗∗ significant at 5%; ∗∗∗ significant at 1%.

power to detect interaction effects is limited, so we generally do not present interaction results, except in cases where we have strong priors and reasonable power and consistency, as in the case of gender. Our estimates capture the effect of the Hajj five to eight months after pilgrims return. Although this limits our ability to explore persistence of the effects, we do not find any significant changes over the survey period. The rows of Tables IV–VIII present the average effect size (AES) estimates for each index, including the control and restricted subsample specifications. Because the results are very similar, we focus on the base specification. The component questions in each index are described in the notes to the tables. Table IX further presents results for several index component questions of individual interest. A supplemental Online Appendix presents the Hajj impact estimates and definition details for all the component questions.

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TABLE V TOLERANCE AES coefficients

(1) Views of other countries (2) Views of other groups (3) Harmony (4) Peaceful inclination (5) Political Islam index (6) Views of West

Base

Controls

Restricted subsample

0.150∗∗∗ (0.04) 0.131∗∗∗ (0.05) 0.128∗∗∗ (0.04) 0.111∗∗∗ (0.03) −0.050 (0.04) 0.029 (0.04)

0.147∗∗∗ (0.04) 0.108∗∗ (0.05) 0.117∗∗∗ (0.04) 0.121∗∗∗ (0.03) −0.044 (0.03) 0.039 (0.04)

0.151∗∗∗ (0.04) 0.122∗∗ (0.06) 0.126∗∗∗ (0.05) 0.128∗∗∗ (0.04) −0.043 (0.04) 0.011 (0.04)

Notes. See notes to Table IV. Index component questions with number of components indicated in parentheses: Index 1 (6): General view of people from other countries, positive to negative: Saudis, Indonesians, Turks, African, Europeans, Chinese. Index 2 (3): How do members of the following groups compare to your group: different sect? different religion? different ethnicity? Index 3 (4): Do you believe the following groups can live in unity and harmony through compromise over disagreements: sects of Islam? religions? Pakistani ethnic groups? Do you ever pray in a mosque of a different school of thought? Index 4 (8): Belief in incorrectness of: Osama’s goals? Osama’s methods? How important is peace with India for Pakistan? Should the current India/Pakistan boundary be the permanent border if this leads to peace? Should Pakistan not support/only partly support those fighting the Indian government in Kashmir? How incorrect are: suicide attacks? attacks on civilians in war? physical punishment of someone who dishonors family? Index 5 (5): Agree that: government should enforce Islamic injunctions? religious leaders have right to dispense justice? religious leaders should have direct influence on government? better for politicians/officials to have strong religious beliefs? religious beliefs important in voting for candidate? Index 6 (4): Is it bad for Pakistanis to adopt: Western social values? Western technology? Believe there was Western/Jewish role in 9/11 and 2005 London bombing? Believe West does not take into account interests of countries such as Pakistan?

IV.A. Religious Practices and Beliefs Hajjis are 13% more likely to report they are regarded as religious persons, a one-fourth standard deviation increase relative to the control group (Table IV, row (1)). Three indices explore how the Hajj affects religious practice and belief. The first measures global Islamic religious practice, meaning the performance of rites universally acknowledged within the Muslim world. Questions, described in the notes to Table IV, include the applicant’s observance of prayer, fasting, and Qur’anic recitation, etc. The Hajj increases the global religious practice index by 0.16 standard deviations (row (2)). This is a fairly large effect, particularly because it reflects practice five to eight months post-Hajj, and not the fervor of a recently returned

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QUARTERLY JOURNAL OF ECONOMICS TABLE VI GENDER AES coefficients

(1) Views toward women (2) Women’s quality of life (3) Girls’ education (4) Women in workforce/professions (5) Gender authority

Base

Controls

0.120∗∗∗ (0.04) 0.158∗∗∗ (0.05) 0.092∗∗ (0.04) 0.119∗∗∗ (0.04) −0.005 (0.02)

0.116∗∗∗ (0.04) 0.138∗∗∗ (0.05) 0.089∗∗ (0.04) 0.112∗∗∗ (0.04) −0.010 (0.02)

Restricted subsample 0.139∗∗∗ (0.04) 0.166∗∗∗ (0.06) 0.097∗∗ (0.04) 0.091∗∗ (0.04) 0.005 (0.03)

Notes. See notes to Table IV. Index component questions with number of components indicated in parentheses: Index 1 (4): How do men and women compare: mentally/intellectually? spiritually? morally/ethically? Are men and women equal? Index 2 (5): Opinion of quality of women’s lives in following countries/regions relative to Pakistan: Saudi Arabia, Indonesia/Malaysia, West. Think too many crimes against women in Pakistan: overall? relative to men? Index 3 (5): Should girls attend school? Until what level would permit attendance at coeducational schools for: girls? boys? Until what level should coeducational schools be allowed? How many years should girls study relative to boys? Index 4 (3): Like daughters/granddaughter to work? Like a professional occupation for daughters/granddaughters? Good employment important for daughter/granddaughterin-law? Index 5 (7): Women better at managing daily affairs? Wives have equal say in deciding number of children? Is it sometimes correct for: woman to divorce husband? marry against parents wishes? When jobs scarce men should not have more right to one than women? Should daughter have equal inheritence share? Do women count equally to men as witnesses?

pilgrim. The Hajj nearly doubled the rate of regular fasting outside of Ramadan (the obligatory month of fasting) to around 9% and increased praying Tahajjud (supererogatory) prayers by twothirds (Table IX, rows (2) and (3)). In most Muslim countries, there are a variety of Islamic traditions that are not as universally accepted as the global practices examined above. Some of these are specific to particular countries or regions. The Hajj rituals highlight global practices. Local practices might decline because they compete for time and attention with global practices, or because the Hajj induces a shift in belief. We find evidence of an absolute shift away from local beliefs and practices. Although most pilgrims initially have moderately high levels of local beliefs, the Hajj leads to a 0.10–standard deviation reduction in an index of localized beliefs that are fairly common in South Asia but not among Muslims globally (Table IV, row (3)). Some practices, such as visiting the tombs of saints and using amulets, have roots in local Sufi traditions. Others reflect

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TABLE VII WELL-BEING Panel A: AES coefficients Base

Restricted Controls subsample

−0.206∗∗∗ −0.206∗∗∗ −0.200∗∗∗ (0.05) (0.05) (0.05) (2) Positive feelings −0.109∗∗ −0.098∗∗ −0.079 (0.05) (0.04) (0.05) (3) Index of satisfaction −0.010 0.006 0.011 with life and finances (0.04) (0.04) (0.04) (4) Self-rated physical −0.213∗∗∗ −0.219∗∗∗ −0.239∗∗∗ health (0.05) (0.05) (0.06)

(1) Rescaled K6 index

Panel B: AES Main effect −0.369∗∗∗ (0.08) −0.149∗∗ (0.07) −0.028 (0.05) −0.320∗∗∗ (0.07)

Male interaction 0.326∗∗∗ (0.09) 0.079 (0.08) 0.036 (0.08) 0.210∗∗ (0.10)

Notes. See notes for Table IV. In addition, note that Panel A gives AES estimates for our base, control, and restricted subsample specifications, whereas Panel B adds an interaction between Hajj participation and a male variable to the base AES specification. In Panel B, the instruments are success in the Hajj lottery for the main effect and success interacted with male in the interaction specification. Index component questions with number of components indicated in parentheses: Index 1 (6) [rescaled, high value=less distress]: During the past 30 days, how often did you feel: nervous? hopeless? restless or fidgety? so depressed that nothing could cheer you up? everything was an effort? worthless? Index 2 (5): During the past 30 days, how often did you feel: relaxed and peaceful? content? joyous? How much pleasure do you take in life? Altogether, are you very happy/not at all happy (four-point scale)? Index 3 (3): How satisfied with life as a whole are you (ten-point scale)? How much room for improvement in your quality of life? How satisfied are you with finances (ten-point scale)? Index 4 (2): How good is your physical health (four-point scale)? Have you been free of any 7+ day illness/injury in the past year?

local interpretation of Islamic doctrine, such as giving dowry (Islam instead emphasizes mehr, where a man commits to pay his wife in case of divorce) and what remarriage priority should be accorded to widows. Whereas South Asian women often lose status when their husbands die and have little prospect of remarriage, in Islam a widow can readily remarry after a short waiting period. The Hajj similarly reduces an index of localized religious practice, related mainly to the Sufi traditions mentioned above, by 0.10 standard deviations (Table IV, row (4)). As we noted earlier, some have expressed concern about the erosion of local South Asian traditions. We later present evidence suggesting that the Hajj does not produce a shift in favor of a Saudi version of Islam but rather a move toward the global mainstream. IV.B. Tolerance We find that Hajjis display more positive views toward other nationalities and social groups, have greater tolerance, and are more peacefully inclined (Table V).

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QUARTERLY JOURNAL OF ECONOMICS TABLE VIII ENGAGEMENT AND EXPOSURE AES coefficients

(1) Socioeconomic engagement (2) Engagement in politics (3) Formal knowledge of Islam (4) Diversity knowledge (5) Gender knowledge (6) Global knowledge

Base

Controls

Restricted subsample

−0.002 (0.02) −0.011 (0.03) 0.004 (0.04) 0.146∗∗∗ (0.04) 0.125∗∗∗ (0.04) 0.083∗∗ (0.04)

−0.008 (0.02) −0.010 (0.03) 0.000 (0.03) 0.139∗∗∗ (0.04) 0.116∗∗∗ (0.03) 0.086∗∗ (0.03)

0.011 (0.02) −0.024 (0.03) −0.003 (0.04) 0.133∗∗∗ (0.05) 0.104∗∗ (0.04) 0.072 (0.05)

Notes. See notes for Table IV. Index component questions with number of components indicated in parentheses: Index 1 (15): How frequently do you visit: people in your town/village? people outside your town/village? How frequently are you visited by: people in your town/village? people from outside your town/village? How many times in the past year have close family/friends sought advice on: family matters? religious matters? business matters? How many times in the past year have more distant family/friends sought advice on: family matters? religious matters? business matters? Are you a member of following kinds of organizations: religious, professional, school? Do you work as: an employee? for yourself? Index 2 (7): Did you vote in last election? How interested in national affairs? Are you member of political party? Are you a member of a political organization? A social organization? How often do you follow national affairs? Do you have an opinion on how politicians are handling national affairs? Index 3 (10): Name as many of the five pillars of Islam as you can. Correct answer to: How many chapters in the Qu’ran? Can you recite favorite verse of the Qu’ran? What is shortest sura of the Qu’ran? What is longest? How many suras are in the the Qu’ran? What is first revealed verse of the Qu’ran? Is method of prayer described in the Qu’ran? What is percentage required to be given as Zakat (charitable tax)? How long must wealth be held for Zakat to be due? Index 4 (3): Correct answers to: How many accepted schools of thought in Sunni Islam? Is a cap required for prayer? Is saying “talak, talak, talak” sufficient for legal divorce? Index 5 (8): Correct answers to: What was name of prophet’s first wife? How many wives is a man allowed at once? Can a Muslim man marry a Jewish or Christian woman? Is dowry mandatory? Further: Have you heard of Islamic law relating to adultery? Do you have an opinion about women’s lives in: Saudi Arabia? Indonesia/Malaysia? West? Index 6 (6): How many countries share a border with Pakistan? What country has largest percentage Muslim? What percentage of Nigerians are Muslim? What are world’s two most populous countries? Who is the Prime Minister of India? Which is further from Pakistan, England or the United States?

The Hajj increases an index of positive views about people from other countries by 0.15 standard deviations or more than 33% (Table V, row (1)). Hajjis update their beliefs most positively about nationalities they are likely to interact with frequently. The largest positive impact (0.32 standard deviations) is on views toward Indonesians (Table IX, row (4)), the largest non-Saudi pilgrim group and the one Hajjis report as observing the most. Hajjis also have a 0.14–standard deviation more positive view of Saudis (Table IX, row (5)). There is no effect on views of Europeans. Hajjis are also significantly more likely to declare that Indonesians

(10) Do you believe the methods Osama uses in fighting are correct?

(6) In your opinion, overall how are people of a different religion compared to your people? (7) Do you believe that people of different religions can live in unity & agreement (harmony) in a given society by making agreements over their differences? (8) Do you ever pray in the mosque of a different maslak than your own? (9) Do you believe the goals for which Osama is fighting are correct?

(5) Is your general view of Saudi people:

(3) How often did you fast outside of Ramadan during the past year? (4) Is your general view of Indonesian people:

(1) Do you believe others regard you as religious? (2) Do you pray “Tahajjud Namaz”?

Question

.021 .014

.112

0.084 0.063

0.034 0.063

0.051

1 = Yes, 0 = No Binary: 1 = Frequently, 0 = Less often/never 1 = Not correct at all/slightly incorrect, 0 = Correct/absolutely correct 1 = Absolutely never/almost never correct, 0 = To small extent/some extent/strongly correct

.074

.004

.026

.000

0.217 0.110

.006

0.041

.000 .000

0.100 0.184

1 = Religious, 0 = Not religious 1 = Yes (regularly, occasionally), 0 = No (rarely, never) 1 = Several times per month or more, 0 = Once per month or less 2 = Very positive, −2 = Very negative 2 = Very positive, −2 = Very negative 0 = Better or worse, 1 = Same

p-value

Coef.

Coding

TABLE IX SELECTED SURVEY QUESTIONS

0.159

0.068

0.049

0.589

0.389

1.034

0.362

0.049

0.772 0.281

Comp. mean

761

761

1,463

1,270

1,604

1,593

1,583

1,605

1,541 1,605

Obs.

.063

.054

.027

.036

.025

.026

.055

.030

.033 .047

R2 ESTIMATING THE IMPACT OF THE HAJJ

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(17) Do you think there are too many crimes against women in Pakistan? Overall

(16) What is your opinion about the quality of women’s lives in each of the following countries/regions? West

(15) What is your opinion about the quality of women’s lives in each of the following countries/regions? Saudi Arabia

(11) How important do you believe peace with India is for Pakistan’s future? (12) Please tell me what you think about the correctness of the following: family members physically punishing someone who has dishonored the family (13) In your opinion, how do men and women compare to each other with respect to the following traits: spiritually (14) What is your opinion about the quality of women’s lives in each of the following countries/regions? Indonesia/ Malaysia

Question

.145

.051

0.057

0.094

0.051

0.087

0 = Men are better/equal, 1 = Women are better 1 = Greater than in Pakistan, 0 = Lower than or equal that in Pakistan; Base variables 5 = Very high, 1 = Very low 1 = Greater than in Pakistan, 0 = Lower than or equal that in Pakistan; Base variables 5 = Very high, 1 = Very low 1 = Greater than in Pakistan, 0 = Lower than or equal that in Pakistan; Base variables 5 = Very high, 1 = Very low Binary: 0 = No, 1 = Yes 0.052

.088

0.044

0 = Correct, 1 = Never correct

.075

.006

.112

.016

0.044

1 = Important, 0 = Not important

p-value

Coef.

Coding

TABLE IX (CONTINUED)

0.597

0.186

0.322

0.262

0.111

0.261

0.913

Comp. mean

1,605

646

1,180

551

1,497

1,459

1,155

Obs.

.045

.091

.048

.058

.034

.033

.020

R2

1154 QUARTERLY JOURNAL OF ECONOMICS

Coding .052

.039 .036

.024

.156

.073

0.028 0.055

0.059

0.045

0.054

p-value

0.053

Coef.

0.457

0.540

0.729

0.933 0.722

0.171

Comp. mean

R2

1,562 .028

1,605 .029

1,550 .036

1,604 .027 1,550 .035

1,135 .026

Obs.

Notes. Rows contain results from individual IV regressions where the instrument is success in the Hajj lottery, and which include include dummies for place of departure × accommodation category × party size category. p-values are corrected for clustering at the party level.

(18) Do you think there are too many crimes against 1 = Against women score < against women in Pakistan? Relative to men men score, 0 = Against women score ≥ against men score; Base scores 1 = Yes, a lot; 4 = No, not at all (19) In your opinion, girls should attend school Binary: 0 = Disagree, 1 = Agree (20) Until what level would you prefer allow/permit girls 0 = Never, 1 = Primary, secondary, or in your family to attend coeducational schools (boys all levels and girls in the same school)? (21) Until what level would you prefer allow/permit boys 0 = Never, 1 = Primary, secondary, or in your family to attend coeducational schools (boys all levels and girls in the same school)? (22) Would you like for your daughters or female grand- 0 = No, 1 = Yes children to have a career other than caring for the household? (23) How important are the following characteristics in 0 = Not important, 1 = Important your son’s, grandson’s wife?: Good employment or business

Question

TABLE IX (CONTINUED)

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are the best practitioners of Islam (regression not reported). In follow-up open-ended interviews, Pakistani Hajjis also reported positive interactions with Indonesians. For example, one older female Hajji said, “I had a very good experience with female Hajjis from Indonesia. They would make space for me whenever I was walking if I gestured for them to do so. One of them even gave me Vicks VapoRub when she found out that I had the flu.” The Hajj also increases an index of beliefs that adherents of different sects, ethnicities, and religions are equal by 0.13 standard deviations (Table V, row (2)). In contrast to the views on different nationalities, the largest move toward equal status is for people of a different religion (Table IX, row (6)), who would not be encountered during the Hajj, as they aren’t permitted to attend. Hajjis may thus be willing to extend their notions of tolerance beyond the Muslim world. Similarly, the Hajj increases an intergroup harmony index by 0.13 standard deviations (Table V, row (3)). The index solicits applicants’ views on whether people from different ethnic groups, Islamic sects, and religions could live together in harmony in the same society. It also includes a practice-based question about how frequently the respondent prays in a mosque of a different school of thought. The effect is largest for religion, about which the control group has the lowest belief regarding harmony (Table IX, row (7)). The effect on the respondent praying in a mosque of a different school of thought is also large, almost doubling the control group mean of 4.9% (Table IX, row (8)). We complement the harmony index by exploring the extent to which the Hajj leads to greater inclination to peace. The Hajj increases a peaceful inclination index by 0.11 standard deviations (Table V, row (4)). Examining some of the component questions, we find that the Hajj almost doubles the number of respondents who declare that Osama bin Laden’s goals are incorrect, from 6.8% to 13.1%, and increases the fraction declaring his methods incorrect from 16% to 21% (Table IX, rows (9) and (10)).12 The Hajj increases the belief that peace with India is important from 91% to 96% (Table IX, row (11)). Hajjis are also 17% more likely to say it is never correct to physically punish someone who has dishonored the family (Table IX, row (12)). Although these results 12. Slightly more than half say his goals are correct; one-third say his methods are correct; quite a few do not answer.

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are consistent with becoming more tolerant, it is also possible that the Hajj confers religious legitimacy on individuals that allows them to more willingly express previously held views. One might suspect that more orthodox religious practice could be associated with support for political Islam, which advocates a closer relationship between religion and politics and which is often associated with negative perceptions of the West. We see no increase in belief either in the role of religion in politics or in more negative views of the West. It is nonetheless possible that increased tolerance tempers such desires and perceptions, if they do in fact go along with increased orthodoxy. The Hajj reduces support for political Islam, although the effect is only weakly significant at 15% (Table V, row (5)). The political Islam index includes questions on how deeply religion should be involved in politics. Although the average respondent is likely to see a role for religion in matters of the state, Hajjis are no more likely to do so in spite of an increased attachment to global Islam. In fact, the Hajj significantly reduces beliefs that the state should enforce religious injunctions and that religious leaders should be able to dispense justice on their own. The Hajj does not lead to any increase in an index of negative attitudes toward the West (Table V, row (6)) that encompasses views on adopting Western social values and technologies and commonly held suspicions toward the West. We can reject a negative effect of one-twentieth of a standard deviation with 95% confidence. We find no evidence that the Hajj affects the tails of the distribution of attitudes toward political Islam and views toward the West. Moreover, although young people may potentially be more susceptible to intolerance, the six tolerance indices examined don’t show any differential Hajj effect for younger pilgrims (regressions not reported). If anything, the harmony index shows a more positive effect for the young. IV.C. The Hajj and Gender We noted earlier that the Hajj may provide Pakistani pilgrims with a novel opportunity in which men and women interact, perform rituals as equals, and observe the gender roles of other nationalities. Perhaps on account of this, we find that the Hajj causes a 0.12–standard deviation increase in an index of questions about the status of women relative to men along intellectual, spiritual,

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and moral dimensions (Table VI, row (1)). The effect is largest on the spiritual dimension, with an increase of over 50% (from 11% to 17%) in belief that women are better (Table IX, row (13)). Hajjis are also more likely to believe that, although there are gender differences, women’s overall status is equal. The Hajj also increases an index that captures awareness of women’s quality of life issues in Pakistan by 0.16 standard deviations (Table VI, row (2)). The index includes respondents’ ratings of women’s quality of life in other countries relative to Pakistan. The largest effect is on the relative quality of life of Indonesian/Malaysian women being higher, paralleling the previous results on views of other nationalities (Table IX, row (14)). Interestingly, Hajjis show a greater increase in their views on the relative quality of life of women in the West compared to Saudi Arabia (Table IX, rows (15) and (16)). In addition, Hajjis are also more likely to think that crimes against women are high, both on an absolute scale and relative to crimes against men (Table IX, rows (17) and (18)). Do the more favorable assessment of women’s qualities and the greater concern regarding their quality of life in Pakistan go along with a changed view of the role women ought to take in society? We construct three indices to explore the areas of girls’ education, women’s workforce participation and choice of professions, and the willingness to challenge the authority of men relative to women within the household and in social contexts (Table VI, rows (3)–(5)). The Hajj increases favorable views toward education for girls by about 0.09 standard deviations (Table VI, row (3)). We find positive Hajj effects on all components except equal educational attainment across gender. The Hajj increases the desire that girls attend school from 93% to 96% (Table IX, row (19)). Hajjis are 8% more willing to allow both their boys and girls to attend coeducational schools at all levels (Table IX, rows (20) and (21)). Further, the Hajj increases an index of questions about women’s workforce participation and profession choice by 0.12 standard deviations (Table VI, row (4)). The Hajj has a substantial impact on each index component. For example, the Hajj increases the fraction desiring that their daughters/granddaughters work from 54% to 60% (Table IX, row (22)). Hajjis are also 12% more likely to think it is important that their future daughter-in-law be employed (Table IX, row (23)).

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However, Hajjis’ more favorable views of women do not extend to challenging male authority in the household (Table VI, row (5)). The Hajj has little or no impact on an index that includes questions regarding whether the respondent challenges traditional attitudes on women’s roles in domestic matters, such as fertility decisions and marrying against parental wishes, and unequal Islamic rules on gender, such as those related to inheritance laws and providing financial witness. This is perhaps unsurprising given the greater authority and responsibility typically accorded to men along several dimensions within Islam. Nevertheless, the changed perceptions about gender roles do seem to accompany changes in household behavior. The Hajj increased the fraction reporting occasional marital disagreements by 10 percentage points, a large increase relative to the comparison mean of 15% (regression not reported). Because most married couples perform the Hajj together, it is not possible to separate this effect by the respondent’s gender (because it reflects both their own and their spouse’s Hajj impact). Although sample size limitations do not readily allow us to examine heterogeneity of the impact of the Hajj, nevertheless we find that only the girls’ education index shows a smaller increase for men than women, who in any case already have close to 100% agreement with the view that girls should be educated (regressions not reported). In fact, the Hajj leads to somewhat larger changes in the indices of views on women and quality of life for male Hajjis than for female ones. IV.D. Well-Being Hajjis, primarily women, are more likely to report negative feelings that suggest distress, and are less likely to report positive feelings of well-being (Table VII, rows (1), (2), (5), and (6)). This could potentially be due to the changes in Hajjis’ beliefs and frame of reference discussed above (which the psychology literature suggests can lead to stress), to financial stress associated with the cost of the Hajj, or to the impact of the Hajj on physical health. Hajjis report somewhat higher distress, as measured by a version of the K6 screening scale (Kessler et al. 2003).13 The index aggregates respondents’ experience of six negative feelings in the past month, which we rescale so that a higher value represents 13. We should caution that, to our knowledge, the K6 index has not been formally validated for Pakistan.

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less distress. Although applicants had a low level of underlying distress, the Hajj reduces the index by 0.21 standard deviations (Table VII, row (1)). The Hajj also reduces an index of five positive feelings by 0.11 standard deviations (row (2)). In the restricted subsample, the Hajj effect drops slightly to 0.08 standard deviations with a marginal significance of 11%. The increase in distress falls entirely on women (Table VII, rows (5) and (6)). On both the rescaled K6 index and the positive feelings index, there is no significant effect of the Hajj on men. Increased distress might be due to the stark contrast between the typical Pakistani woman’s daily life and the relatively greater equality and integration experienced during the Hajj. The impact of the Hajj on gender attitudes suggests an increased realization that the constraints and restrictions women are accustomed to in Pakistan may not be part of global Islam. The literature in psychology (Crosby 1991; Lantz et al. 2005) suggests that such changes in frame of reference can induce significant stress, although eventually the stress helps deal with the change. Although the Hajj has a negative impact on a female pilgrim’s emotional state, it does not affect overall life satisfaction, either on average, or for women (rows (3) and (7)). We can reject a negative effect on the index of life satisfaction of about one-tenth standard deviation with 95% confidence. Although we cannot rule it out, we do not see much evidence for the hypothesis that the substantial financial expenditure required by the Hajj creates financial stress that accounts for Hajjis’ negative feelings. In fact, we can reject the hypothesis that the Hajj has a negative effect of more than one-twelfth of a standard deviation on the individual component question about satisfaction with finances. The Hajj also does not affect monthly household consumption expenditures or a measure of household assets (regressions not reported). Our interviews reveal that most do not consider the pool of savings for the Hajj as fungible; those unable to go keep these Hajj funds in order to reapply in the future. The Hajj leads to a 0.21–standard deviation reduction in an index of physical health (Table VII, row (4)) that includes selfreported physical health and illness/injury. Although the decrease in self-perceived health could be due to a change in the reference group for Hajjis from local people to those encountered from other countries on the Hajj, it is not clear that this can account for the doubling in reports of serious physical injury or illness.

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The negative physical health effects are also stronger for women (row (8)), suggesting that part of the negative effect of the Hajj on women’s feelings of well-being could be explained by poorer physical health.14 However, the negative point estimates on men’s physical health are larger than the effect on the K6 index (0.11 vs. 0.04 standard deviations), suggesting that the two do not exactly co-move. Also, the coefficient on Hajj lottery success in a regression predicting the K6 index is similar whether or not one controls for physical health, providing further suggestive evidence that the channel for Hajj effects on emotional health is not simply through physical health.

V. POTENTIAL CHANNELS Although our methodology does not provide experimental variation that isolates the potential channels through which the Hajj may impact the pilgrim, we can offer some suggestive evidence. We consider both external channels, which operate by changing the environment a Hajji faces upon return, and internal channels, which reflect changes in Hajjis’ beliefs and preferences. We argue that the evidence points toward the importance of the internal channel and, within that, to exposure to people of differing nationalities, sects, and gender. V.A. External Social Environment Historical accounts suggest that the Hajj confers social prestige and legitimacy (Donnan 1989; Eickelman and Piscatori 1990; Yamba 1995), although some anecdotal evidence suggests that contemporary Hajjis no longer experience this increase in social status (Scupin 1982). A changed social role may bring expectations for the changed behavior and beliefs that are reflected in our results. For example, Hajjis may be expected to be more religious, and may practice more to fulfill that expectation. Alternatively, increased religious legitimacy may allow Hajjis to express longstanding opinions they have not expressed before, such as those opposing Osama Bin Laden. We find no impact of the Hajj on an index of social status and engagement (Table VIII, row (1)). The fifteen components include the frequency of social visits, the giving of advice, and 14. Negative physical health effects are not larger for older people.

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membership in social organizations.15 We might further expect social standing to be reflected in awareness of and engagement in political affairs. In fact, we find no impact of the Hajj on a political engagement index (Table VIII, row (2)) that asks about voting, interest in national affairs, political opinion, and membership in political organizations. It’s possible that the Hajj once led to a much greater change in social roles than it does currently, and that the increased rate of participation in the Hajj due to lower travel costs has reduced the social prestige associated with completing the Hajj. In any case, it does not seem likely that changes in the social role upon return can account for the findings in the previous sections. V.B. Internal State The Hajj may alter an individual’s internal state, changing beliefs and preferences. For example, Hajjis may undergo a change in religious commitment during the pilgrimage that increases orthodoxy in religious practice and leads them to greater tolerance and belief in gender equity consistent with the Qur’an. Alternatively, Hajjis’ increased tolerance and changed gender attitudes may reflect their new exposure to people from different countries and sects and to members of the opposite gender outside their family. Although we cannot rule out the religious dimension, we interpret the evidence as pointing more toward the increased exposure to Muslims from around the world. We find that the Hajj does not increase an index of formal religious knowledge (Table VIII, row (3)) but does increase indices of experiential knowledge about diversity of opinion within Islam, gender within Islam, and the world more broadly (Table VIII, rows (4)–(6)). The changes in experiential knowledge point to the importance of interaction with and observation of other groups.16 Furthermore, to the extent that a spiritual transformation and change in religious commitment would be accompanied by a desire to acquire greater religious knowledge, these results do not suggest that such a change is a primary driver of the findings. 15. All except two component questions are not significant even at the 20% level (Online Appendix 5). These two show that Hajjis are slightly more likely to have visitors from out of town, and slightly more likely to be self-employed ( p-values of .14 each). However, the magnitudes of these effects are small (5% and 3%). 16. Although some of our results could be due to a generic effect of traveling to a different country rather than the experience of the Hajj, it seems unlikely this accounts for all of the results. For example, it is hard to see why a pure travel effect would lead to more positive beliefs about Indonesians.

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The Hajj increases the index measuring knowledge of diversity within Islam by 0.15 standard deviations (Table VIII, row (4)). Index components include questions on how schools of Sunni thought differ, such as whether it is necessary to wear a prayer cap. The index of gender knowledge and awareness, which combines eight questions on gender and marriage in Islam and on having an opinion on women’s issues, increases by 0.13 standard deviations (Table VIII, row (5)).17 Similarly, Hajjis also show an increase of 0.08 standard deviations in the global knowledge index, which reflects general awareness of the world outside Pakistan (Table VIII, row (6)).18 Pilgrims who travel in smaller parties, and thus have more opportunity to interact with non-Pakistanis, experience larger gains in the diversity, gender, and global knowledge indices, as well as in positive views of people from other countries. This is consistent with the idea that the exposure channel is important. The coefficients on the interaction between the Hajj and small party size are large and significant at conventional levels for the gender and global knowledge indices and for positive views of other countries. The small-party interaction effects are 0.13, 0.14, and 0.14 standard deviations, respectively, with p-values of .07, .10, and .06. Point estimates for the group size interaction on other tolerance indices also point to a similar story. The interactions are robust to including other demographic controls and their interactions. However, we cannot rule out that unobservable differences between parties of different size are driving the interaction effects. We would expect Hajj effects to also be larger for those with less prior exposure to situations similar to the Hajj. However, very few respondents had previously traveled outside Pakistan, which limits our power to test this interaction. There are a few robust interactions with literacy and urban residence, though it is unclear if these relate to the prior exposure that is relevant. Although urban applicants do show a smaller decrease in localized beliefs and practices, the literate see larger gains in some of the

17. Four of the eight questions in the gender knowledge and awareness index are about awareness rather than knowledge: whether the respondent has heard of the Islamic law against adultery and whether they have an opinion on women’s lives in three different countries. The Hajj has a somewhat smaller, but still significant, effect on a pure gender knowledge index that is constructed without these questions. 18. We should note that this latter effect falls slightly to 0.07 standard deviations and is marginally significant at 12% in the restricted subsample.

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experiential knowledge measures, suggesting that literacy may partly be picking up other factors such as ability to interact with others. Because party size is often assigned by banks, and is thus less likely to be correlated with unobserved factors, we prefer focusing on it as a test of exposure. Although Hajjis are also exposed to Saudi Arabia and its people, we think this is unlikely to drive our observed effects. Only the move away from localized religious practices seems consistent with a Saudi influence. Saudi Arabia is generally less accepting of other schools of thought and enforces strict gender segregation; Hajj impacts on gender views are more in line with the more liberal attitudes in other Muslim countries.19 Our results thus suggest that Hajjis are likely to be influenced by the practices and beliefs of the typical pilgrim that they encounter during the Hajj, with possibly greater salience to those groups that are more visibly different or are regarded as better in some way, such as in their behavior or organization (factors often mentioned in our interviews). Exposure may therefore induce convergence of belief to the Islamic mean. To the extent that this convergence is a significant force, some of our results may differ for pilgrims from other countries.

VI. CONCLUSIONS Our findings show that the Hajj induces a shift from localized beliefs and practices toward global Islamic practice, increases tolerance and peaceful inclinations, and leads to more favorable attitudes toward women. This demonstrates that deep-rooted attitudes such as religious beliefs and views about others can be changed and also challenges the view that Islamic orthodoxy and extremism are necessarily linked. We conclude with some tentative implications of our results on how social institutions help shape individual beliefs and identity and, at a macro level, how they may foster unity within belief systems. 19. A comparison of gender views across questions from the World Values Surveys shows that Saudis indeed have more conservative gender views than Pakistanis, whereas Pakistanis in turn are more conservative than Indonesians. Fully 62% of Saudis believe a university education is more important for men than women, compared to 24% of Pakistanis and 17% of Indonesians. Similarly, 34% of Saudis do not think that both husband and wife should contribute to household income, compared to 30% of Pakistanis and 15% of Indonesians.

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The social psychology literature suggests that social interactions can lead to either positive or negative feelings toward other groups depending on whether the setting is competitive or cooperative. Several features of the Hajj may create a setting in which the interaction among different groups helps build common purpose and identity. It’s worth noting that other social institutions also share such features with the Hajj. Consider medical education, police/military basic training, and international peace camps. Like the Hajj, participants in these institutions leave their everyday environments and their restrictions on mixing across certain lines, such as ethnicity and social class, to enter a setting in which they collectively perform similar actions, often physically strenuous ones, which require cooperation from others. Furthermore, participants in all these institutions accentuate their similarity, often by taking on common dress or hairstyle during the experience and a common title afterward. It also seems likely that the religious element of the Hajj plays a role beyond providing a cooperative setting. For example, Hajjis’ changed attitudes on gender appear to be circumscribed by those norms broadly accepted in Islam. Further, it is plausible that the religious context provides the legitimacy that makes it acceptable for adherents to alter their views. If a Pakistani woman observes her Indonesian counterpart engaging equally with her spouse without compromising her piety, she may also consider it permissible to do so. If pilgrims see others praying somewhat differently yet without interference in the holiest of Muslim places, they may reason that some degree of religious diversity is acceptable. Our results also shed light on why religions often mandate practices that are costly for individual adherents. Although club good models that apply the framework of individual rationality, as in Iannaccone (1992) and Berman (2000), deliver compelling explanations, additional insights can be obtained using an evolutionary framework in which institutions and prescriptions that reinforce and propagate the religion’s beliefs and practices are more likely to persist. By moving pilgrims toward the religious mainstream, the Hajj may help Islam overcome an evolutionary hurdle faced by world religions: maintaining unity in the face of the divergence of practices and beliefs through local adaptations. A number of religious institutions, including written holy texts and central authorities, can help overcome this hurdle. Sunni

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Islam lacks a central authority, and so the role of pilgrimage may be particularly important. However, achieving convergence and maintaining unity likely require that there be limits to how much diversity is allowed. Too diverse a group may make it difficult to find common ground and too much variance in beliefs increases the likelihood that undesirable religious innovations will spread. It is therefore noteworthy that although people of different faiths made the pilgrimage to Mecca in pre-Islamic times (Armstrong 1997), its institutionalization with Islam’s emergence was accompanied by restricting it to Muslims and disallowing non-Islamic practices that were once elements of the pilgrimage. Both the evolutionary and club good perspectives imply that religions with practices that generate positive externalities for other adherents, provided these are socially efficient, are more likely to persist by raising the attractiveness of being an adherent. Historically, undertaking the Hajj may have created positive externalities for other Muslims both through its effect on tolerance and by facilitating economic trade and the diffusion of economic, cultural, and scientific ideas (Bose 2006). Although we find little evidence of individual medium-term gains in socioeconomic status and engagement in our sample, there is clear evidence for a positive externality in the increased tolerance toward others. Of course, given the significant financial and health costs entailed in undertaking the Hajj, individuals still need to be induced to participate. However, this can be done through religious injunctions, sanctions, and rewards. The Hajj is one of the five pillars of Islam and there is the belief that performing it sincerely cleanses one of all sins. Models of costly religious practices also often argue that these practices signal commitment and screen out those who may free ride on the religious community. Because individuals have already signaled such commitment by applying to the Hajj (less than 1% withdraw), our comparisons between applicants are not influenced by signaling effects. Our results therefore indeed capture a treatment effect. The fact that the Hajj has a direct treatment effect is not surprising, because one would expect that were it only serving a signaling function, it would decline in observance relative to alternate practices that could screen just as well but at a lower cost. The findings in this paper also pose the question of whether pilgrimages or central gatherings may foster such unity in other

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belief systems, religious or otherwise, and conversely, whether their absence increases susceptibility to schisms. The Kumbh Mela, bringing together millions of Hindus every three years, along with Catholic pilgrimages to Lourdes and Rome, may play such a cohesive role. Nonreligious examples include national political conventions in the United States that may promote party unity and exchange among delegates from different regions. Conversely, the split between Judaism and Christianity occurred shortly after the destruction by the Romans of the Jewish temple in Jerusalem, which was a central gathering place, in the year 70 A.D. One may even conjecture whether the multiplication of Protestant sects would have been muted had there been a central holy site for pilgrimage among Protestants. Further insights are likely to come from investigating the impact of the Hajj over different durations and on pilgrims from other countries that differ from Pakistan in their attitudes and exposure, and the impact of other pilgrimages. Because several other countries also allocate Hajj visas by lottery, it should be possible to use the same methodology. More generally, one could use similar approaches to examine the impact of other institutions on social identity. For example, one could use draft lotteries (Angrist 1990) to examine the impact of military service on social identity or regression discontinuity designs to examine the impact of professional training on beliefs and attitudes. Building up evidence from a series of such studies would shed additional light on the broader roles played by institutions, religious and nonreligious, in the shaping of beliefs and identity and the evolution of ideologies and belief systems.

APPENDIX: OUTLINE OF THE HAJJ PILGRIMAGE

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CASE WESTERN RESERVE UNIVERSITY HARVARD UNIVERSITY HARVARD UNIVERSITY, THE BROOKINGS INSTITUTION, AND THE NATIONAL BUREAU OF ECONOMIC RESEARCH

REFERENCES Ahmed, Q. A., Y. M. Arabi, and Z. A. Memish, “Health Risks at the Hajj,” The Lancet, 367 (2006), 1008–1015. Angrist, Joshua, 1990. “Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records,” American Economic Review, 80 (1990), 313–336. Armstrong, K., Jerusalem: One City, Three Faiths (New York: Ballantine Books, 1997). Aronson, E., and S. Patnoe, The Jigsaw Classroom (New York: Longman, 1997). Azarya, V., Aristocrats Facing Change: The Fulbe in Guinea, Nigeria, and Cameroon (Chicago: University of Chicago Press, 1978). Barro, Robert, and R. M. McCleary, “Religion and Economic Growth across Countries,” American Sociological Review, 68 (2003), 760–781. Berman, Eli, “Sect, Subsidy, and Sacrifice: An Economist’s View of Ultra-orthodox Jews,” Quarterly Journal of Economics, 115 (2000), 905–953. Bianchi, R., Guests of God: Pilgrimage and Politics in the Islamic World (Oxford, UK: Oxford University Press, 2004). Boisjoly, J., G. Duncan, M. Kremer, D. Levy, and J. Eccles, “Empathy or Antipathy? The Consequences of Racially and Socially Diverse Peers on Attitudes and Behaviors,” American Economic Review, 96 (2006), 1890–1906. Bose, Sugata, A Hundred Horizons: The Indian Ocean in the Age of Global Empire (Cambridge, MA: Harvard University Press, 2006). Clingingsmith, David, Asim Ijaz Khwaja, and Michael Kremer, “Estimating the Impact of the Hajj: Religion and Tolerance in Islam’s Global Gathering,” KSG Working Paper RWP08-22, 2008. Crosby, F., Juggling: The Unexpected Advantages of Balancing Career and Home for Women and Their Families (New York: Free Press, 1991). DeVries, D. L., and R. E. Slavin, “Teams-Games-Tournaments (TGT): Review of Ten Classroom Experiments,” Journal of Research and Development in Education, 12 (1978), 28–38. Donnan, Hastings, “Symbol and Status: The Significance of the Hajj in Pakistan,” Muslim World, 79 (1989), 205–216. Eickelman, Dale F., and James Piscatori, “Muslim Travellers: Pilgrimage, Migration, and the Religious Imagination,” in Comparative Studies on Muslim Societies, Vol. 9, Barbara D. Metcalf, ed. (Berkeley: University of California Press, 1990). Fisman, Raymond, S. Iyengar, E. Kamenica, and Itamar Simonson, “Racial Preferences in Dating,” Review of Economic Studies, 75 (2008), 117–132. Glaeser, E., and S. Glendon, “Incentives, Predestination and Free Will,” Economic Inquiry, 36 (1998), 429–443. Guiso, Luigi, Paola Sapienza, and Luigi Zingales, “People’s Opium? Religion and Economic Attitudes,” Journal of Monetary Economics, 50 (2003), 225–282. Iannaccone, Laurence R., “Sacrifice and Stigma: Reducing Free-Riding in Cults, Communes, and Other Collectives,” Journal of Political Economy, 100 (1992), 271–291. Ibn Battuta, Tuhfat al-Nuzzar fi Ghara’ib al-Amsar (Beirut: Dar al-Kutub al-’Ilmiyya, 2002 [originally published ca. 1355]). Johnson, D. W., and R. T. Johnson, 1983. “The Socialization and Achievement Crisis: Are Cooperative Learning Experiences the Solution?” in Applied Social Psychology Annual, Vol. 4, L. Bickman, ed. (Beverly Hills, CA: Sage, 1983). Kessler, R. C., P. R. Barker, L. J. Colpe, J. F. Epstein, J. C. Gfroerer, E. Hiripi, M. J. Howes, S-L. T. Normand, R. W. Manderscheid, E. E. Walters, and A. M. Zaslavsky, “Screening for Serious Mental Illness in the General Population,” Archives of General Psychiatry, 60 (2003), 184–189.

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MULTINATIONAL FIRMS, FDI FLOWS, AND IMPERFECT CAPITAL MARKETS∗ ` POL ANTRAS MIHIR A. DESAI C. FRITZ FOLEY This paper examines how costly financial contracting and weak investor protection influence the cross-border operational, financing, and investment decisions of firms. We develop a model in which product developers can play a useful role in monitoring the deployment of their technology abroad. The analysis demonstrates that when firms want to exploit technologies abroad, multinational firm (MNC) activity and foreign direct investment (FDI) flows arise endogenously when monitoring is nonverifiable and financial frictions exist. The mechanism generating MNC activity is not the risk of technological expropriation by local partners but the demands of external funders who require MNC participation to ensure value maximization by local entrepreneurs. The model demonstrates that weak investor protections limit the scale of MNC activity, increase the reliance on FDI flows, and alter the decision to deploy technology through FDI as opposed to arm’s length technology transfers. Several distinctive predictions for the impact of weak investor protection on MNC activity and FDI flows are tested and confirmed using firm-level data.

I. INTRODUCTION Firms globalizing their operations and the associated capital flows have become major features of the world economy. These cross-border activities and capital flows span institutional settings with varying investor protections and levels of capital market development. Although the importance of institutional heterogeneity in dictating economic outcomes has been emphasized, existing analyses typically ignore the global firms and the capital flows that are now commonplace. Investigating how global firms make operational and financing decisions in a world of heterogeneous institutions promises to provide a novel perspective on observed patterns of flows and firm activity. ∗ The statistical analysis of firm-level data on U.S. multinational companies was conducted at the Bureau of Economic Analysis, U.S. Department of Commerce, under arrangements that maintain legal confidentiality requirements. The views expressed are those of the authors and do not reflect official positions of the U.S. Department of Commerce. The authors thank Robert Barro, four anonymous referees, Gita Gopinath, James Markusen, Aleh Tsyvinski, Bill Zeile, and seminar participants at Boston University, Brown University, Hitotsubashi University, MIT, the NBER ITI program meeting, the New York Fed, Oxford, UC Berkeley, UC Boulder, Universidad de Vigo, Universitat Pompeu Fabra, the University of Michigan, and the World Bank for helpful suggestions. Davin Chor provided excellent research assistance. C 2009 by the President and Fellows of Harvard College and the Massachusetts Institute of

Technology. The Quarterly Journal of Economics, August 2009

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This paper develops and tests a model of the operational and financial decisions of firms as they exploit their technologies in countries with differing levels of investor protections. The model demonstrates that multinational firm (MNC) activity and foreign direct investment (FDI) arise endogenously in settings characterized by financial frictions. The model generates several predictions regarding how investor protections influence the use of arm’s length technology transfers, the degree to which MNC activity is financed by capital flows, the extent to which multinationals take ownership in foreign projects, and the scale of multinational operations. These predictions are tested using firm-level data on U.S. MNCs. The model considers the problem of a firm that has developed a proprietary technology and is seeking to deploy this technology abroad with the help of a local entrepreneur. A variety of alternative arrangements, including an arm’s length technology transfer or directly owning and financing the entity that uses it, are considered. External investors are a potential source of funding, but they are concerned with managerial misbehavior, particularly in settings where investor protections are weak. The central premise of the model is that developers of technologies are particularly useful monitors for ensuring that local entrepreneurs are pursuing value maximization. The concerns of external funders regarding managerial misbehavior lead to optimal contracts in which the developer of the technology is required to hold an ownership claim in the foreign project and, in certain cases, this developer is also required to provide financial capital to the local entrepreneur. As such, MNCs and FDI flows arise endogenously in response to concerns over managerial misbehavior and weak investor protections.1 Extending the model to allow for a similar form of monitoring by external investors does not vitiate the primary results. We also show that although simple revenue-sharing agreements may also provide incentives for technology developers to monitor, this type of contract is generally not optimal. 1. The experience of Disney in Japan, as documented in Misawa (2005), provides one example of the mechanism that drives the behavior of external investors. In 1997, Disney was evaluating how to structure a new opportunity with a local partner in Japan. Japanese banks expressed a strong preference for equity participation by Disney over a licensing agreement in order to ensure that Disney had strong incentives to monitor the project and ensure value maximization. The concerns of these lenders and the intuition that Disney would have a unique ability to monitor local partners are reflective of the central ideas of the model.

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The characterization of MNCs as developers of technologies has long been central to models explaining MNC activity. In contrast to those models that emphasize the risk of technology expropriation, the model in this paper emphasizes financial frictions, a cruder form of managerial opportunism and the role of external funders. As such, although technology is central to these other models and the model in this paper, the mechanism generating MNC activity is entirely distinct. Our emphasis on monitoring builds on the theory presented by Holmstrom and Tirole (1997), which captures how monitoring is critical to understanding financial intermediation. Our model delivers several novel predictions about the nature of FDI and patterns of MNC activity. First, the model predicts that arm’s length technology transfers will be more common, relative to the deployment of that technology through affiliate activity, in countries where investor protections are stronger. Second, the share of activity abroad financed by capital flows from the multinational parent will be decreasing in the quality of investor protections in host economies. Third, ownership shares by multinational parents will also be decreasing in the quality of investor protections in host economies. These predictions reflect the fact that monitoring by the developer of the technology is more critical in settings where investor protections are weaker. The model also predicts that the scale of activity based on multinational technologies in host countries will be an increasing function of the quality of the institutional environment. Better investor protections reduce the need for monitoring and therefore allow for a larger scale of activity. We test these predictions using the most comprehensive available data on the activities of U.S. MNCs and on arm’s length technology transfers by U.S. firms. These data provide details on the worldwide operations of U.S. firms, including measures of parental ownership, financing and operational decisions, and information on royalty payments and licensing fees received by U.S. firms from unaffiliated foreign persons. The data enable the use of parentyear fixed effects that implicitly control for a variety of unobserved attributes. The analysis indicates that the likelihood of using arm’s length technology transfer to serve a foreign market increases with measures of investor protections, as suggested by the model. The predictions on parent financing and ownership decisions are also confirmed to be a function of the quality of investor

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protections and the depth of capital markets. The model also suggests that these effects should be most pronounced for technologically advanced firms because these firms are most likely to be able to provide valuable monitoring services. The empirical evidence indicates a differential effect for such firms. Settings where ownership restrictions are liberalized provide an opportunity to test the final prediction of the model. The model implies that ownership liberalizations should have a particularly large effect on multinational affiliate activity in countries with weak investor protections. Our empirical analysis confirms that affiliate activity increases by larger amounts after liberalizations in countries with weaker investor protections. This paper extends the large and growing literature on the effects of investor protections and capital market development on economic outcomes to an open-economy setting where firms make operational and financial decisions across borders. La Porta et al. (1997, 1998) relate investor protections to the concentration of ownership and the depth of capital markets. A large literature, including King and Levine (1993), Levine and Zervos (1998), Rajan and Zingales (1998), Wurgler (2000), and Acemoglu, Johnson, and Mitton (2005), has shown that financial market conditions influence firm investment behavior, economic growth, and industrial structure. By exclusively emphasizing firms with local investment and financing, this literature has neglected how cross-border, intrafirm activity responds to institutional variations. The open-economy dimensions of institutional variations have been explored but overwhelmingly in the context of arm’s-length cross-border lending as in Gertler and Rogoff (1990), Boyd and Smith (1997), and Shleifer and Wolfenzon (2002).2 In related work, Albuquerque (2003) shows that the differential alienability of FDI and portfolio inflows can allow the risk of expropriation to alter the composition of capital inflows. In contrast to this work, we derive the existence of MNCs and FDI flows in response to the possibility of opportunism by private actors. Accordingly, our empirical work employs firm-level data that allow us to 2. Gertler and Rogoff (1990) show how arm’s length lending to entrepreneurs in poor countries is limited by their inability to pledge large amounts of their own wealth. This insight is embedded into an MNC’s production decisions in the model presented here. Our setup also relates to Shleifer and Wolfenzon (2002), who study the interplay between investor protection and equity markets. In contrast, Kraay et al. (2005) emphasize the role of sovereign risk in shaping the structure of world capital flows.

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analyze both patterns of firm activity and financial flows rather than the division of aggregate capital flows between FDI and portfolio flows. In short, we show that weak financial institutions decrease the scale of MNC activity but simultaneously increase the reliance on capital flows from the parent. As such, observed patterns of capital flows reflect these two distinct and contradictory effects. The empirical investigations of microdata provided in the paper indicate that both effects are operative.3 By jointly considering the determinants of MNC activities and the flows of capital that support these activities, the paper also links two literatures—the international trade literature on multinationals and the macroeconomic literature on capital flows. Industrial-organization and international-trade scholars characterize multinationals as having proprietary assets and emphasize the role of market imperfections, such as transport costs and market power, in determining patterns of multinational activity. Recent work on MNCs investigates “horizontal” or “vertical” motivations4 for FDI and explores why alternative productive arrangements, such as whole ownership of foreign affiliates, joint ventures, exports, or arm’s length contracts, are employed.5 Such analyses of MNC activity typically do not consider associated capital flows.6 Research on capital flows typically abstracts 3. It should be emphasized that our model abstracts from any portfolio decision by investors and instead focuses on the financing decisions of firms. Bertaut, Griever, and Tryon (2006) analyze U.S. ownership of foreign securities and conclude that nonfinancial institutions are a fairly small fraction (less than 10%) of overall foreign portfolio investment, and this is when including all securities such as fixed-income investments. As such, our model (unlike the one in Albuquerque [2003]) may not be particularly well suited to interpret cross-country patterns in the composition of capital flows. 4. The horizontal FDI view represents FDI as the replication of capacity in multiple locations in response to factors such as trade costs, as in Markusen (1984), Brainard (1997), Markusen and Venables (2000), and Helpman, Melitz, and Yeaple (2004). The vertical FDI view represents FDI as the geographic distribution of production globally in response to the opportunities afforded by different markets, as in Helpman (1984) and Yeaple (2003). Caves (1996) and Markusen (2002) provide particularly useful overviews of this literature. ` (2003, 2005), Antras ` and Helpman 5. Ethier and Markusen (1996), Antras (2004), Desai, Foley, and Hines (2004a), Grossman and Helpman (2004), and Feenstra and Hanson (2005) analyze the determinants of alternative foreign production arrangements. 6. Several studies linking levels of MNC activity and FDI flows are worth noting. First, high-frequency changes in FDI capital flows have been linked to relative wealth levels through real exchange rate movements (as in Froot and Stein [1991] and Blonigen [1997]), broader measures of stock market wealth (as in Klein and Rosengren [1994] and Baker, Foley, and Wurgler [2009]) and to credit market conditions (as in Klein, Peek, and Rosengren [2002]). Second, MNCs have also been shown to opportunistically employ internal capital markets in weak institutional environments (as in Desai, Foley, and Hines [2004b]) and during currency crises (as in Aguiar and Gopinath [2005] and Desai, Foley, and Forbes [2008]). These

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from firm activity and has focused on the paradox posed by Lucas (1990) of limited capital flows from rich to poor countries in the face of large presumed rate-of-return differentials. Whereas Lucas (1990) emphasizes human-capital externalities to help explain this paradox, Reinhart and Rogoff (2004) review subsequent research on aggregate capital flows and conclude that credit market conditions and political risk play significant roles. By examining firm behavior in a setting with variation in investor protections, this paper attempts to unify an investigation of MNC activity and FDI flows. The rest of the paper is organized as follows. Section II lays out the model and generates several predictions related to the model. Section III provides details on the data employed in the analysis. Section IV presents the results of the empirical analysis, and Section V concludes. II. THEORETICAL FRAMEWORK In this section, we develop a model of financing that builds on and extends the work of Holmstrom and Tirole (1997).7 We illustrate how the model generates both multinational activity as well as FDI flows. Finally, we explore some firm-level empirical predictions that emerge from the model and that we take to the data in later sections. II.A. A Model of Financial Contracting Environment. We consider the problem of an agent—an inventor—who is endowed with an amount W of financial wealth and the technology or knowledge to produce a differentiated good. Consumers in two countries, Home and Foreign, derive utility from consuming this differentiated good. (Appendix I develops a multicountry version of the model.) The good, however, is papers emphasize how heterogeneity in access to capital can interact with MNC production decisions. Marin and Schnitzer (2004) also study the financing decisions of MNCs in a model that stresses managerial incentives. Their model, however, takes the existence of MNCs as given and considers an incomplete-contracting setup, in contrast to our complete-contracting setup. The predictions from their model are quite distinct to the ones we develop here and show to be supported by U.S. data. 7. Our model generalizes the setup in Holmstrom and Tirole (1997) by allowing for diminishing returns to investment and for variable monitoring levels. The scope of the two papers is also very distinct: Holmstrom and Tirole (1997) study the monitoring role of banks in a closed-economy model, whereas our focus is on MNCs.

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prohibitively costly to trade, and thus servicing a particular market requires setting up a production facility in that country. The inventor is located at Home and cannot fully control production in Foreign. Servicing that market thus requires contracting with a foreign agent—an entrepreneur—to manage production there. We assume that entrepreneurs are endowed with no financial wealth and their outside option is normalized to 0. There also exists a continuum of infinitessimal external investors in Foreign that have access to a technology that gives them a gross rate of return equal to 1 on their wealth. All parties are risk neutral and are protected by limited liability. There are three periods: a date-0 contracting stage, a date-1 investment stage, and a date-2 production/consumption stage. Consumer Preferences and Technology. In the main text, we focus on describing production and financing decisions in the Foreign market. For that purpose, we assume that preferences and technology at Home are such that at date 2 the inventor obtains a constant gross return β > 1 for each unit of wealth he invests in production at Home at date 1. We refer to this gross return as the inventor’s shadow value of cash. Our assumption β > 1 implies that the opportunity cost of funds is lower for external investors than for the inventor. In Appendix I, this higher-than-1 value of β is endogenously derived in a multicountry version of the model where consumer preferences, technology, and financial contracting in all countries are fully specified. Note that the provision that β > 1 does not imply that the effective cost of capital provided by external investors is always lower than the effective cost of capital provided by the inventor because informational frictions may drive a wedge between returns earned and the costs borne by the relevant parties. We assume that Foreign preferences are such that cash flows or profits obtained from the sale of the differentiated good in Foreign can be expressed as a strictly increasing and concave function of the quantity produced; that is, R(q), with R (q) > 0 and R (q) ≤ 0. We also assume the standard conditions R(0) = 0, limq→0 R (q) = +∞, and limq→∞ R (q) = 0. These properties of R(q) can be derived from preferences featuring a constant (and higher-than-1) elasticity of substitution across a continuum of differentiated goods produced by different firms. In such case, the elasticity of R(q) with respect to q is constant and given by a parameter α ∈ (0, 1).

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Foreign production is managed by the foreign entrepreneur, who at date 1 can privately choose to behave and enjoy no private benefits, or misbehave and take private benefits. When the manager behaves, the project performs with probability pH , in the sense that when an amount x is invested at date 1, project cash flows at date 2 are equal to R(x) with probability pH and 0 otherwise.8 When the manager misbehaves, the project performs with a lower probability pL < pH and expected cash flows are pL R(x). We assume that the private benefit a manager obtains from misbehaving is increasing in the size of the project, and for simplicity, we specify it as being proportional to the return of the project, that is, BR(x). In Section II.C, we discuss how similar results obtain if private benefits are proportional to the level of investment x. Managerial misbehavior and the associated private benefits can be manifested by choosing to implement the project in a way that generates perquisites for the manager or his associates, in a way that requires less effort, or in a way that is more fun or glamorous. As described below, we relate the ability to engage in such private benefits to the level of investor protections in Foreign as well as to the extent to which the entrepreneur is monitored. The idea is that countries with better investor protections tend to enforce laws that limit the ability of managers to divert funds from the firm or to enjoy private benefits or perquisites. This interpretation parallels the logic in Tirole (2005, p. 359). When investor protections are not perfectly secure, monitoring by third agents is helpful in reducing the extent to which managers are able to divert funds or enjoy private benefits. Following Holmstrom and Tirole (1997), we introduce a monitoring technology that reduces the private benefit of the foreign entrepreneur when he misbehaves. It is reasonable to assume that the inventor can play a particularly useful role in monitoring the behavior of the foreign entrepreneur because the inventor is particularly well informed about how to manage the production of output using its technology. Intuitively, the developer of a technology is in a privileged position to determine if project failure is associated with managerial actions or bad luck.9 We capture this in a 8. This assumes that, when the project succeeds, each unit invested results in a unit of output (q = x), whereas when the project fails, output is zero (q = 0). We relax the latter assumption in Section II.C. 9. An alternative way to interpret monitoring is as follows. Suppose that the foreign entrepreneur can produce the good under a variety (a continuum, actually) of potential techniques indexed by z ∈ [0, B]. Technique 0 entails a probability of success equal to pH and a zero private benefit. All techniques with z > 0 are

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stark way by assuming that no other agent in the economy can productively monitor the foreign entrepreneur, though we discuss a more general setup in Section II.C. We assume that monitoring costs are proportional to the return of the project and when the inventor incurs an effort cost C R(x) in monitoring at date 1, the private benefit for the local entrepreneur is multiplied by a ¯ limC→∞ δ (C ) = 0, factor δ (C ), with δ (C ) < 0, δ (C ) > 0, δ(0) = δ, limC→0 δ (C ) = −∞, and limC→∞ δ (C ) = 0.10 This assumption reflects the idea that larger projects require effort to monitor. Section II.C considers the possibility that effort costs are proportional to investment levels and similar results follow. As mentioned earlier, the scope of private benefits is related to the level of investor protection of the host country by an index γ ∈ (0, 1). In particular, we specify that (1)

B (C; γ ) = (1 − γ ) δ(C).

Note that this formulation implies that ∂ B(·)/∂γ < 0, ∂ B(·)/∂C < 0, and ∂ 2 B(·)/∂C∂γ = −δ (C) > 0. This formulation captures the intuition that the scope for private benefits is decreasing in both investor protection and monitoring and that monitoring has a relatively larger effect on private benefits in countries with poor legal protection of investors. It also implies that parent monitoring substitutes for investor protection. The idea behind this assumption is that both parent monitoring and investor protections constrain managers and that parent monitoring is effective even in imperfect legal environments. This would be the case if, for example, parent monitoring during the production process prevented misbehavior from occurring, thus eliminating any need for legal action after improper behavior occurs. Contracting. We consider optimal contracting between three sets of agents: the inventor, the foreign entrepreneur, and foreign external investors. At date 0, the inventor and the foreign entrepreneur negotiate a contract that stipulates the terms under which the entrepreneur will exploit the technology developed by

associated with a probability of success equal to pL and a private benefit equal to z. Clearly, all techniques with z ∈ (0, B) are dominated from the point of view of the foreign entrepreneur, who will thus effectively (privately) choose either z = 0 or z = B, as assumed in the main text. Under this interpretation, we can think of monitoring as reducing the upper bound of [0, B]. 10. These conditions are sufficient to ensure that the optimal contract is unique and satisfies the second-order conditions.

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the inventor. This contract includes a (possibly negative) date-0 transfer F from the inventor to the entrepreneur, as well as the agents’ date-2 payoffs contingent on the return of the project.11 When F > 0, the date-0 payment represents the extent to which the inventor cofinances the project in the Foreign country. When F < 0, this payment can be thought of as the price or up-front royalties paid for the use of the technology, which the inventor can invest in the Home market at date 1. The contract between the inventor and the entrepreneur also stipulates the date-1 scale of investment x, while the managerial and monitoring efforts of the entrepreneur and inventor, respectively, are unverifiable and thus cannot be part of the contract. Also at date 0, the foreign entrepreneur and external investors sign a financial contract under which the entrepreneur borrows an amount E from the external investors at date 0 in return for a date-2 payment contingent on the return of the project. We consider an optimal contract from the point of view of the inventor and allow the contract between the inventor and the entrepreneur to stipulate the terms of the financial contract between the entrepreneur and foreign external investors. We rule out “direct” financial contracts between the inventor and foreign external investors. This is justified in the extension of the model developed in Appendix I, where the inventor’s shadow value of cash β is endogenized. Given the payoff structure of our setup and our assumptions of risk neutrality and limited liability, it is straightforward to show that an optimal contract is such that all date-2 payoffs can be expressed as shares of the return generated by the project. All agents obtain a payoff equal to zero when the project fails (i.e., when the return is zero) and a positive payoff when the project succeeds (in which case cash flows are positive). When an agent’s share of the date-2 return is positive, this agent thus becomes an equity holder in the entrepreneur’s production facility.12 We define φ I and φ E as the equity shares held by the inventor and external investors, respectively, with the remaining share 1 − φ I − φ E 11. For simplicity, we assume that the inventor’s date-2 return in its Home market (which is not modeled in the main text) is not pledgeable in Foreign. 12. We focus on an interpretation of payoffs resembling the payoffs of an equity contract, but the model is not rich enough to distinguish our optimal contract from a standard debt contract. Our results would survive in a model in which agents randomized between using equity and debt contracts. In any case, we bear this in mind in the empirical section of the paper, where we test the predictions of the model.

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accruing to the foreign entrepreneur. Notice that when φ I is large enough, the entrepreneur’s production facility becomes a subsidiary of the inventor’s firm. II.B. Optimal Contract and Empirical Predictions We next characterize an optimal contract that induces the entrepreneur to behave and the inventor to monitor. This optimal ˜ C} ˜ that solves the ˜ φ˜ I , x, ˜ φ˜ E , E, contract is given by the tuple { F, following program: max

I = φ I pH R(x) + (W − F ) β − C R(x)

s.t.

x ≤ E+ F pH φ E R(x) ≥ E pH (1 − φ E − φ I ) R(x) ≥ 0 ( pH − pL) (1 − φ E − φ I ) R(x) ≥ (1 − γ ) δ (C ) R (x ) ( pH − pL) φ I R(x) ≥ C R(x).

F,φ I ,x,φ E ,E,C

(P1)

(i) (ii) (iii) (iv) (v)

The objective function represents the payoff of the inventor. The first term represents the inventor’s dividends from the expected cash flows of the foreign production facility. The second term represents the gross return from investing his wealth W minus the date-0 transfer F in the Home market.13 The last term represents the monitoring costs. The first constraint is a financing constraint. Because the local entrepreneur has no wealth, his ability to invest at date 1 is limited by the sum of the external investors’ financing E and the cofinancing F by the inventor. The second inequality is the participation constraint of external investors, who need to earn at least an expected gross return on their investments equal to 1. Similarly, the third inequality is the participation constraint of the foreign entrepreneur, given his zero outside option. The fourth inequality is the foreign entrepreneur’s incentive compatibility constraint. This presumes that it is in the interest of the inventor to design a contract in a way that induces the foreign entrepreneur to behave. In Appendix II, we show that this will necessarily be the case, provided that γ is sufficiently large. The final constraint is the inventor’s incentive compatibility constraint: if this condition was not satisfied, the inventor’s payoff would be 13. We assume throughout that W is large enough to ensure that W − F ≥ 0 in equilibrium.

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lower when exerting the monitoring level C˜ than when not doing so.14 In the program above, constraint (iii) will never bind. Intuitively, as is standard in incomplete information problems, the incentive compatibility constraint of the entrepreneur demands that this agent obtains some informational rents in equilibrium, and thus his participation constraint is slack. Conversely, the other four constraints will bind in equilibrium. This is intuitive for the financing constraint (i) and the participation constraint of investors (ii). It is also natural that the optimal contract from the point of view of the inventor will seek to minimize the (incentivecompatible) equity share accruing to the foreign entrepreneur, which explains why constraint (iv) binds. It is perhaps less intuitive that constraint (v) also binds, indicating that the optimal contract minimizes the equity share φ I allocated to the inventor. In particular, it may appear that a large φ I would be attractive because it may foster a larger level of cofinancing F at date 0, thereby encouraging investment. However, inspection of constraint (iv) reveals that a larger φ I decreases the ability of the entrepreneur to borrow from external investors, as it reduces his pledgeable income. Overall, one can show that, for a given level of monitoring, whether utility is transferred through an equity share or a date-0 lump-sum payment has no effect on the scale of the project. In addition, it is clear from the objective function that the inventor strictly prefers a date-0 lump-sum transfer because he can use these funds to invest domestically and obtain a gross rate of return β > 1 on them. Hence, the minimal incentive-compatible inventor equity share φ I is optimal. With these results at hand, it is immediate from constraint (v) that the optimal equity stake held by the inventor will be given by (2)

φ˜ I =

C˜ , pH − pL

which will be positive as long as C˜ is positive. In addition, manipulation of the first-order conditions of program (P1) delivers the following expression that implicitly determines the level of 14. Our derivation of this IC constraint assumes that if the inventor deviates ˜ it does so by setting C = 0 (which for large enough δ¯ would lead to a from C, violation of the entrepreneur’s incentive compatibility constraint). This is without loss of generality because any other deviation C > 0 is dominated.

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monitoring (see Appendix II for details): (3)

˜ = − δ (C)

βpH − pL . (1 − γ )βpH

Straightforward differentiation of (3) together with the convexity of the function δ (·) produces the following result: LEMMA 1. The amount of monitoring C˜ is decreasing in both investor protection γ in Foreign and in the inventor’s shadow value of cash β. The effect of investor protection on monitoring is intuitive. Given our specification of the private benefit function B (·) in (1), the marginal benefit from monitoring is larger, the less developed is the financial system in Foreign (the lower is γ ). Because the marginal cost of monitoring is independent of γ , C˜ and γ are negatively correlated in the optimal contract. The effect of the shadow value of cash β on monitoring is a bit subtler. The intuition behind the result lies in the fact that the larger that β is, the larger is the opportunity cost of remunerating the inventor through ex-post dividends rather than through an ex-ante lump-sum transfer. Because of the tight mapping between φ˜ I and C˜ imposed by the incentive compatibility constraint in (v), we have that a larger β is also associated with a higher shadow cost of monitoring and hence with a lower optimal amount of monitoring. In light of (2), it is clear that our theory has implications for the share of equity held by the inventor that relate closely to the implications for monitoring. In particular, φ˜ I is proportional to the level of monitoring C˜ and thus is affected by the parameters γ and β in the same way as is monitoring. This reflects that equity shares emerge in our model as incentives for the inventor to monitor the foreign entrepreneur. As a result, we can establish the following proposition. PROPOSITION 1. The share of equity held by the inventor is decreasing both in investor protection γ in Foreign and in the inventor’s shadow value of cash β. An immediate corollary of this result follows. COROLLARY 1. Suppose that a transaction is recorded as an FDI transaction only if φ˜ I ≥ φ I .Then, there exists a threshold

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investor protection γ ∗ ∈ 0, 1 such that the optimal contract entails FDI only if γ < γ ∗ . Our theory thus predicts that the prevalence of FDI in a given country should, other things equal, be a decreasing function of the level of investor protection in that country. Manipulation of the first-order conditions of program (P1) also delivers an implicit function of the level of investment as a ˜ function of parameters and the optimal level of monitoring C: (4)

R (x˜ ) =

1 ˜ . ˜ βpH − pL C (1 − γ ) δ C − 1− pH − pL pH − pL βpH

pH

Equation (4) implicitly defines the level of expected sales by the firm, that is, pH R (x˜ ). Differentiating this equation with respect to γ and β, we obtain the following proposition (see Appendix III for details). PROPOSITION 2. Output and cash flows in Foreign are increasing in investor protection γ in Foreign and decreasing in the inventor’s shadow value of cash β. The intuition for the effect of investor protection is straightforward. Despite the fact that the inventor’s monitoring reduces financial frictions, both the foreign entrepreneur’s compensation, as dictated by his incentive compatibility constraint (iv), and monitoring costs are increasing in the scale of operation. In countries with weaker investor protections, the perceived marginal cost of investment is higher, thus reducing equilibrium levels of investment. Using constraints (i), (ii), and (iv), one can also obtain the terms of the optimal financial contract with external investors in terms of C˜ and x: ˜ ˜ C˜ (1 − γ ) δ(C) − , φ˜ E = 1 − pH − pL pH − pL ˜ E˜ = pH φ˜ E R(x). Finally, straightforward manipulation delivers an optimal lumpsum date-0 transfer equal to R (x˜ ) pL ˜ ˜ − 1 x. ˜ C R (x˜ ) − F= β ( pH − pL) R (x˜ ) x˜

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Depending on parameter values, the lump-sum transfer can be positive or negative, and it also varies nonmonotonically with the parameters of the model. We can, however, derive sharper predictions for the share of financing that is provided by the inventor. To see this, focus on the case in which the date-0 payment F˜ is positive and can be interpreted as the level of cofinancing by the inventor. The share of investment financed by the inventor is then given by (5)

pL 1 − α (x˜ ) R (x˜ ) F˜ = − , C˜ x˜ β ( pH − pL) x˜ α (x˜ )

where α(x) ≡ x R (x)/R(x) is the elasticity of revenue to output. As mentioned earlier, when preferences feature a constant elasticity of substitution across a continuum of differentiated goods produced by different firms, α(x) is independent of x, and R(x) can be written as R(x) = Ax α , where A > 0 and α ∈ (0, 1). Notice that the first term in (5) is increasing in C˜ and decreasing in x˜ due to the concavity of R(x). It thus follows from Lemma 1 and Proposition 2 that this first term is necessarily decreasing in γ . As for the second term, it will increase or decrease in x˜ depending on the properties of α(x). In most applications, α(x) will be either independent of x or decreasing in x (e.g., when the firm faces a linear demand function). In those situations, the second term in (5) will also be decreasing in γ and we can conclude the following. ˜ is sufficiently small, the share PROPOSITION 3. Provided that α (x) ˜ x) of inventor financing in total financing ( F/ ˜ is decreasing in investor protection γ . The intuition behind the result is that monitoring by inventors has a relatively high marginal product in countries with weak financial institutions. To induce the inventor to monitor, the optimal contract specifies a relatively steeper payment schedule, with a relatively higher contribution by the inventor at date 0 (a higher ˜ x) F/ ˜ in anticipation of a higher share of the cash flows generated by the project at date 2 (a higher φ˜ I ).15 ˜ x˜ is ambiguous. A 15. The effect of the shadow value of cash on the ratio F/ larger β is associated with a lower monitoring level C˜ (Lemma 1), but also with a lower level of x˜ and thus a higher ratio R (x˜ ) /x˜ (Proposition 2). In addition, β has an additional direct negative effect on the ratio. The overall effect is, in general, ambiguous.

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The fact that the monitoring provided by the inventor is unverifiable by third parties is central to our theory of FDI. In particular, if monitoring was verifiable (and thus contractible), the optimal contract analogous to the one described above would immediately imply an equity share for the inventor equal to zero (see ` Desai, and Foley [2007] for details). Hence, the inventor Antras, would never choose to deploy her technology abroad through FDI. Instead, the inventor would sell the technology to the foreign entrepreneur in exchange for a positive lump-sum fee (and, hence, the inventor would never cofinance the project). In Section IV, we present empirical tests of Propositions 1, 2, and 3, and Corollary 1. Appendix I shows that Propositions 1, 2, and 3 continue to hold in a multicountry version of the model in which the statements apply to cross-sectional variation in investor protections. Our empirical tests exploit variation in the location of affiliates of U.S. MNCs and analyze the effect of investor pro˜ x. ˜ We identify the inventor in tections on proxies for x, ˜ φ˜ I , and F/ the model as being a parent firm and control for other parameters of the model, such as the shadow value of cash β, the concavity of R(x), the monitoring function δ (C ), and the probabilities pH and pL by using fixed effects for each firm in each year and controlling for a wide range of host-country variables. Because our estimation employs parent-firm fixed effects, we are not able to test the predictions regarding the effect of β in Propositions 1, 2, and 3. II.C. Generalizations Before proceeding to the empirical analysis, it is useful to consider the robustness of these results to more general environments. In particular, we consider the degree to which revenue sharing might substitute for equity contracts, the possibility that private benefits and monitoring costs may be proportional to x rather than R(x), and the effects of introducing productive monitoring by external investors. The underlying analysis is provided in Appendix IV. In the model above, we assume that when the project fails, it delivers a level of revenue equal to zero. Such an assumption greatly enhances tractability but suggests that revenue-sharing contracts may provide benefits similar to equity arrangements. This is problematic because it blurs the mapping between φ I in the model and equity shares in the data. More generally, however, revenue-sharing contracts are not optimal when the project delivers a positive level of revenue in case of failure. In fact, a simple

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contract in which external investors are issued secured (or riskfree) debt and the inventor and entrepreneur take equity stakes is optimal.16 To see the intuition for this, consider the same setup as in Section II.A, but now assume that, when the project does not perform, it yields a level of revenue equal to R(x) ∈ (0, R(x)). As is standard in moral hazard problems with risk-neutral agents, the optimal contract calls for the agents undertaking unobservable actions (e.g., effort decisions) to be maximally punished (subject to the limited-liability constraint) whenever a failure of the project is observed. In our particular setup, this would imply that the optimal contract yields both the inventor and the entrepreneur a payoff of zero whenever a project failure is observed. The entire revenue stream R(x) should accrue to external investors. A straightforward way to implement such a contract is for the entrepreneur to issue an amount of secure debt equal to R(x) to external investors and for the inventor and entrepreneur to be equity holders. Once the debt is paid, the inventor and entrepreneur receive a share of zero in case of project failure and a share of the amount R(x) − R(x) in case of project success. The determination of their optimal shares is analogous to that in Section II.A with R(x) − R(x) replacing R(x) (details available upon request). In this more general setting, it is not possible to implement this optimal allocation of payoffs across agents through simple revenue-sharing arrangements. As such, the model can explain why an instrument with the features of equity tends to dominate both fixed-fee and revenue-sharing contracts in financially underdeveloped countries. Such contracts will likely entail an inefficiently low punishment to the inventor when the project does not perform well. We next briefly discuss alternative formulations for the entrepreneur’s private benefit of misbehavior and the inventor’s private cost of monitoring. We have assumed above that these are proportional to the revenue generated by the project in case of success. If instead we specified them as being proportional to x, then the optimal equity share φ˜ I would be given by φ˜ I =

C˜ x˜ ( pH − pL) R (x˜ )

16. A contract in which an entrepreneur issues debt to external investors appears to have empirical validity because most capital provided to affiliates from local sources takes the form of debt.

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and would also depend on x˜ and the concavity of the R(x) ˜ function. One may thus worry that for a sufficiently concave R(x) ˜ function, it could be the case that equity stakes could be low in low-γ countries on account of the low values of x/R ˜ (x˜ ) in those countries. We show in Appendix IV, however, that our main comparative static concerning equity shares holds as long as the elasticity of revenue with respect to output—that is, α (x˜ ) ≡ x˜ R (x˜ ) /R (x˜ )—does not increase in x˜ too quickly. The required condition is analogous to that in Proposition 3 and is satisfied for the case of constant price elasticity and linear demand functions. We finally consider the possibility that local external investors (e.g., banks) also provide useful monitoring, the productivity of which may also be higher in countries with worse investor protections. In Appendix IV, we develop an extension of the model that incorporates monitoring by external investors and that, as with the monitoring by the inventor, is subject to declining marginal benefits. Although the optimal contract is now more complicated, we show that the incentive compatibility constraint for the inventor will continue to bind in equilibrium, implying that the inventor’s equity stake moves proportionally with its level of monitoring. Furthermore, provided that the level of investor protection γ is sufficiently high, the analysis remains qualitatively unaltered by the introduction of local monitoring. The reason for this is that, for large values of γ , the optimal contract already allocates equity stakes φ E to external investors that are large enough to induce them to monitor the entrepreneur.17 As a result, although certain details of the optimal contract change with the possibility of local monitoring, the comparative static results derived in Section II.B continue to hold in this more general model, provided that γ is sufficiently large. III. DATA AND DESCRIPTIVE STATISTICS The empirical work presented in Section IV is based on the most comprehensive available data on the activities of U.S. MNCs and on arm’s length technology transfers by U.S. firms. The Bureau of Economic Analysis (BEA) annual survey of U.S. Direct 17. When the level of investor protection is below a certain threshold, then the incentive compatibility for external investors becomes binding, in which case the analysis becomes more complicated. Without imposing particular functional forms on the monitoring functions, it becomes impossible to derive sharp comparative static results (see Appendix IV).

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Investment Abroad from 1982 through 1999 provides a panel of data on the financial and operating characteristics of U.S. firms operating abroad. U.S. direct investment abroad is defined as the direct or indirect ownership or control by a single U.S. legal entity of at least 10% of the voting securities of an incorporated foreign business enterprise or the equivalent interest in an unincorporated foreign business enterprise. A U.S. multinational entity is the combination of a single U.S. legal entity that has made the direct investment, called the U.S. parent, and at least one foreign business enterprise, called the foreign affiliate.18 The most extensive data for the period examined in this study are available for 1982, 1989, 1994, and 1999 when BEA conducted Benchmark Surveys. Accordingly, the analysis is restricted to benchmark years except when the annual frequency of the data is critical—in the analysis of scale in Section IV.C that uses the liberalizations of ownership restrictions. To analyze arm’s length technology transfers, measures of royalty payments, licensing fees, and other payments for intangible assets received by U.S. firms from unaffiliated foreign persons are drawn from the results of BEA’s annual BE-93 survey. This survey requires that all firms receiving payments above certain thresholds report, regardless of whether the firm is a multinational.19 Table I provides descriptive statistics for the variables used in the analysis employing the benchmark year data (Panel A) and analysis employing the full panel (Panel B). Implementing empirical tests requires mapping the variables of the model to reasonable proxies in the data. To investigate the choice of an inventor to engage in arm’s length technology transfer or FDI (Corollary 1), the analysis uses a dummy variable that is equal to 1 if a U.S. firm receives an arm’s length royalty payment from a country in a given year and 0 if that firm only serves the country through affiliate activity in a particular year. For Proposition 3’s predictions on the share of inventor financing in ˜ x), total financing ( F/ ˜ a variable is defined as the ratio of the sum of parent-provided equity and debt to affiliate assets. Specifically, this share is the ratio of the sum of parent-provided equity and 18. Coverage and methods of the BEA survey are described in Desai, Foley, and Hines (2002). The survey covers all countries and industries, classifying affiliates into industries that are roughly equivalent to three-digit SIC code industries. As a result of confidentiality assurances and penalties for noncompliance, BEA believes that coverage is close to complete and levels of accuracy are high. 19. Because these data have been collected since 1986, data used in the analysis of arm’s length technology transfers cover only 1989, 1994, and 1999.

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Mean

Standard deviation

A: Benchmark year data for Tables II–V Multinational firm variables Arm’s length technology transfer dummy 0.2552 Share of affiliate assets financed by parent 0.4146 Share of affiliate equity owned by parent 0.8991 Log of affiliate sales 9.9024 Log of affiliate employment 4.7601 Affiliate net PPE/assets 0.2355 Log of parent R&D 9.0580

0.4360 0.3267 0.2195 1.7218 1.6060 0.2264 4.3927

Country variables Creditor rights Private credit FDI ownership restrictions Workforce schooling Log of GDP Log of GDP per capita Corporate tax rate Patent protections Property rights Rule of law Risk of expropriation

2.1415 0.7536 0.2247 8.1385 26.8002 9.3995 0.3488 3.2287 4.3767 9.3207 5.1398

1.2100 0.3891 0.4174 2.1739 1.4252 1.1019 0.1060 0.8480 0.8378 1.4088 1.2731

B: Annual data for Table V Log of affiliate sales 10.1285 Log of aggregate affiliate sales 15.7572

2.1426 1.7018

Notes. Panel A provides descriptive statistics for data drawn from the benchmark year survey and used in the analysis presented in Tables II–V. Arm’s length technology transfer dummy is defined for country-year pairs in which a parent has an affiliate or from which a parent receives a royalty payment from an unaffiliated foreign person. This dummy is equal to 1 if the parent receives a royalty payment from an unaffiliated foreign person, and it is otherwise equal to 0. Share of affiliate assets financed by parents is the ratio of parentprovided equity and net parent lending to total affiliate assets. Share of affiliate equity ownership is the equity ownership of the multinational parent. Affiliate net PPE/assets is the ratio of affiliate net property plant and equipment to affiliate assets. Creditor rights is an index of the strength of creditor rights developed in Djankov, McLiesh, and Shleifer (2007); higher levels of the measure indicate stronger legal protections. ¨ ¸Private credit is the ratio of private credit lent by deposit money banks to GDP, as provided in Beck, Demirguc Kunt, and Levine (1999). FDI ownership restrictions is a dummy equal to 0 if two measures of restrictions on foreign ownership as measured by Shatz (2000) are above 3 on a scale of 1 to 5 and 1 otherwise. Workforce schooling is the average schooling years in the population over age 25 years provided in Barro and Lee (2000). Corporate tax rate is the median effective tax rate paid by affiliates in a particular country and year. Patent protections is an index of the strength of patent rights provided in Ginarte and Park (1997). Property rights is an index of the strength of property rights drawn from the 1996 Index of Economic Freedom. Rule of law is an assessment of the strength and impartiality of a country’s overall legal system drawn from the International Country Risk Guide. Risk of expropriation is an index of the risk of outright confiscation or forced nationalization of private enterprise, and it is also drawn from the International Country Risk Guide; higher values of this index reflect lower risks. Panel B provides descriptive statistics for annual data covering the 1982–1999 period that are used in the analysis presented in Table V. Log of aggregate affiliate sales is the log of affiliate sales summed across affiliates in a particular country and year.

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net borrowing by affiliates from the parent to affiliate assets.20 Proposition 1 considers the determinants of the share of equity held by the inventor, φ I , and this variable is measured in the data as the share of affiliate equity owned by the multinational parent. The log of affiliate sales is used to test Proposition 2’s predictions on the scale of affiliate activity. Table I also provides descriptive statistics for a number of other variables. Two measures of investor protections and capital market development are used in the analysis below. Because the model emphasizes the decisions of local lenders, the first measure is creditor rights. This measure is drawn from Djankov, McLiesh, and Shleifer (2007), which extends the sample studied by La Porta et al. (1998) to cover a broader sample of countries over the 1982–1999 period on an annual basis. Creditor rights is an index taking values between 0 and 4 and measures the extent to which the legal system constrains managers from diverting value away from creditors (as a large γ does in the model).21 The second measure is the annual ratio of private credit provided by deposit money banks and other financial institutions ¨ ¸ -Kunt, and Levine to GDP, and it is drawn from Beck, Demirguc (1999). This measure has the advantage of being an objective, continuous measure of the lending environment that captures the willingness of lenders to provide credit in response to investor protections.22 Measures of capital market development are correlated with other measures of economic and institutional development that could affect the outcome studied in ways not considered in the 20. In the model, we have interpreted all sources of financing as equity financing, but as explained in footnote 12, our setup is not rich enough to distinguish equity financing from debt financing. Hence, our empirical tests of Proposition 5 include both. 21. Specifically, the measure is an index formed by adding 1 when (1) the country imposes restrictions, such as creditors’ consent or minimum dividends to file for reorganization; (2) secured creditors are able to gain possession of their security once the reorganization petition has been approved (no automatic stay); (3) secured creditors are ranked first in the distribution of the proceeds that result from the disposition of the assets of a bankrupt firm; and (4) the debtor does not retain the administration of its property pending the resolution of the reorganization. 22. It is possible to employ a measure of shareholder rights to measure investor protections. Creditor rights and private credit are used to measure investor protections for several reasons. First, shareholder rights are only available for a single year near the end of our sample. Second, in our data, there is very little local ownership of affiliate equity, but affiliates do make extensive use of debt borrowed from local sources. As such, using creditor rights and private credit allows us to capitalize on some time-series variation in investor protections and more closely corresponds empirically to the financing choices of affiliates.

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model. Therefore, the regressions control for several measures of economic and institutional variation that might otherwise obscure the analysis. The baseline specifications include controls for FDI ownership restrictions, human capital development, the log of GDP, the log of GDP per capita, and corporate tax rates. A number of countries impose restrictions on the extent to which foreign firms can own local ones. Shatz (2000) documents these restrictions using two distinct measures that capture restrictions on greenfield FDI and cross-border mergers and acquisition activity. The FDI ownership restriction dummy used below is equal to 1 if either of these measures is below 3 and 0 otherwise. Countries with more human capital, with more economic activity, or with a higher level of economic development may be more able to use technology obtained through an arm’s length transfer, and affiliates in these countries may exhibit distinctive financing patterns that reflect the quality of local entrepreneurs as opposed to financial market conditions. To address these possibilities, the specifications include workforce schooling, which measures the average schooling years in the population over 25 years old and is provided in Barro and Lee (2000). Data on the log of GDP and the log of GDP per capita come from the World Development Indicators. Firms could avoid local production or alter their financing patterns in response to tax considerations. Corporate tax rates are imputed from the BEA data by taking the median tax rate paid by affiliates that report positive net income in a particular country and year. Several other controls appear in additional specifications. Firms might choose to deploy technology through affiliate activity as opposed to through an arm’s length transfer, and they might select higher levels of ownership if they fear expropriation by local entrepreneurs (see, for instance, Ethier and Markusen [1986] for a theoretical treatment). Ginarte and Park (1997) provide a measure of the strength of patent protections, and the Index of Economic Freedom provides a measure of more general property rights. Rule of law is an assessment of the strength and impartiality of a country’s legal system, and it is drawn from the International Country Risk Guide (ICRG). Additionally, firms might fear expropriation by foreign governments and might limit foreign activity and make more extensive use of local financing in response. The ICRG also provides an index of the risk of outright

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confiscation or forced nationalization faced by foreign investors. For this measure, higher values indicate lower risks.23 Because the BEA data are a panel measuring activity of individual firms in different countries, they allow for the inclusion of effects for each firm in each year, which we refer to as parent-year fixed effects. These fixed effects help control for other parameters of the model that are likely to be specific to particular firms at particular points in time, such as the shadow value of cash β, the concavity of R(x), the monitoring function δ (C ), and the probabilities pH and pL. The inclusion of these fixed effects implies that the effects of investor protections are identified from within-firm variation in the characteristics of countries in which the firm is active. Although the comprehensive data on MNCs and arm’s length technology transfers do offer a number of advantages, it is worth noting one significant oversight. Neither the model nor the empirical work considers situations in which a firm neither invests in nor transfers technology to a particular location. IV. EMPIRICAL RESULTS Each of the analyses below is composed of a descriptive figure and firm-level regressions. The figures provide a transparent and intuitive perspective on the predictions, and the regressions allow for a full set of controls and subtler tests emphasizing the role of technology intensity. The predictions on the use of arm’s length technology transfers and the financing and ownership of foreign affiliates are investigated by pooling cross sections from the benchmark years. Investigating the effect on scale requires an alternative setup because controlling for the many unobservable characteristics that might determine firm size is problematic. Fortunately, the model provides a stark prediction with respect to scale that can be tested by analyzing responses to the easing of ownership restrictions. IV.A. Arm’s Length Technology Transfer Decisions Figure I provides a preliminary perspective on the extent to which firms deploy technology through arm’s length transfers 23. Some country-level measures of economic and institutional development are highly correlated. The multicollinearity of these variables might cause the standard errors of our key estimates to be large. However, these coefficient estimates remain unbiased.

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FIGURE I Arm’s Length Technology Transfer versus Direct Investment Arm’s length technology transfer share is the ratio of the number of firms that receive a royalty from an unaffiliated foreign person to the sum of the number of such firms and those firms that have an affiliate in a particular country and year. These shares are averaged by quintiles of private credit. Private credit varies by year and is the ratio of private credit lent by deposit money banks to GDP, as ¨ ¸ -Kunt, and Levine (1999). Higher number quintiles provided in Beck, Demirguc relate to higher values of private credit.

relative to direct ownership, across different quintiles of the private credit measure of investor protections. The propensity to use arm’s length technology transfer is computed at the country-year level as the ratio of the number of firms that receive a royalty payment from an unaffiliated foreign person to the number of firms that either receive such an arm’s length royalty or have an affiliate. The average arm’s length royalty share is 0.11 for the lowest private credit quintile of observations while it is 0.27 for the highest quintile. As predicted by the theory, firms appear to make greater use of arm’s length technology transfers, relative to direct ownership, to access countries with more developed capital markets. Table II further explores arm’s length technology transfers through specifications that include various controls and incorporate subtler tests. The dependent variable in these tests, the arm’s length technology transfer dummy, is defined for country-year pairs in which a firm either has an affiliate or receives a royalty payment from an unaffiliated foreign person. The dummy is equal to 1 if the firm receives a royalty payment from an unaffiliated

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TABLE II ARM’S LENGTH TECHNOLOGY TRANSFER VERSUS DIRECT INVESTMENT Dependent variable: Arm’s length technology transfer dummy

Creditor rights

(1)

(2)

(3)

0.0086 (0.0022)

0.0131 (0.0026)

0.0023 (0.0039) 0.0016 (0.0005)

Creditor rights* log of parent R&D Private credit Private credit* log of parent R&D FDI ownership restrictions Workforce schooling

(6)

0.0273 (0.0129)

0.0295 (0.0147)

−0.0606 (0.0133) 0.0117 (0.0020) 0.0020 (0.0097) 0.0103 (0.0024) 0.0243 (0.0039) −0.0223 (0.0077) 0.1588 (0.0438) 0.0158 (0.0066) −0.0086 (0.0066) −0.0040 (0.0046) −0.0080 (0.0055) −0.3923 (0.0968) Y 29,238 .6105

−0.0001 (0.0093) 0.0066 (0.0025) 0.0212 (0.0031) −0.0179 (0.0047) 0.1367 (0.0434)

−0.3780 (0.0840) Y

0.0079 (0.0094) 0.0134 (0.0020) 0.0268 (0.0038) −0.0144 (0.0066) 0.1777 (0.0453) 0.0127 (0.0052) −0.0254 (0.0067) −0.0022 (0.0043) −0.0080 (0.0049) −0.5162 (0.0979) Y

−0.2839 (0.0807) Y

0.0017 (0.0087) 0.0097 (0.0021) 0.0216 (0.0035) −0.0182 (0.0067) 0.1363 (0.0393) 0.0155 (0.0057) −0.0095 (0.0057) −0.0025 (0.0043) −0.0082 (0.0050) −0.2638 (0.0843) Y

37,314 .7628

36,029 .7645

30,954 .6061

34,583 .7598

33,922 .7624

Property rights Rule of law Risk of expropriation

Parent-year fixed effects? No. of obs. R2

(5)

0.0063 (0.0085) 0.0122 (0.0018) 0.0239 (0.0033) −0.0129 (0.0058) 0.1583 (0.0413) 0.0124 (0.0046) −0.0227 (0.0061) −0.0013 (0.0039) −0.0076 (0.0044) −0.3569 (0.0822) Y

0.0098 (0.0089) 0.0069 (0.0019) Log of GDP 0.0238 (0.0032) Log of GDP per capita −0.0148 (0.0039) Corporate tax rate 0.1239 (0.0435) Patent protections

Constant

(4)

Notes. The dependent variable, the arm’s length technology transfer dummy, is defined for country-year pairs in which a parent has an affiliate or from which a parent receives a royalty payment from an unaffiliated foreign person. This dummy is equal to 1 if the parent receives a royalty payment from an unaffiliated foreign person, and it is otherwise equal to 0. Creditor rights is an index of the strength of creditor rights developed in Djankov, McLiesh, and Shleifer (2007); higher levels of the measure indicate stronger legal protections. Private ¨ ¸ -Kunt, credit is the ratio of private credit lent by deposit money banks to GDP, as provided in Beck, Demirguc and Levine (1999). FDI ownership restrictions is a dummy equal to 0 if two measures of restrictions on foreign ownership as measured by Shatz (2000) are above 3 on a scale of 1 to 5 and 1 otherwise. Workforce schooling is the average schooling years in the population over age 25 years provided in Barro and Lee (2000). Corporate tax rate is the median effective tax rate paid by affiliates in a particular country and year. Patent protections is an index of the strength of patent rights provided in Ginarte and Park (1997). Property rights is an index of the strength of property rights drawn from the 1996 Index of Economic Freedom. Rule of law is an assessment of the strength and impartiality of a country’s overall legal system drawn from the International Country Risk Guide. Risk of expropriation is an index of the risk of outright confiscation or forced nationalization of private enterprise, and it is also drawn from the International Country Risk Guide; higher values of this index reflect lower risks. Each specification is an OLS specification that includes parent-year fixed effects. Heteroscedasticity-consistent standard errors that correct for clustering at the country-year level appear in parentheses.

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foreign person, and it is otherwise equal to 0. The inclusion of parent-year fixed effects controls for a variety of unobservable firm characteristics that might otherwise conflate the analysis. All specifications presented in the table also include a measure of the existence of foreign ownership restrictions, workforce schooling, the log of GDP, the log of GDP per capita, and host country tax rates.24 Standard errors are heteroscedasticity-consistent and are clustered at the country-year level. These specifications are linear probability models and are used in order to allow for both parent-year fixed effects and for clustering of standard errors at the country-year level.25 The coefficient on creditor rights in column (1) is positive and significant, affirming the prediction of Corollary 1 that firms are more likely to serve countries with higher levels of investor protections through arm’s length technology transfer as opposed to only through a foreign affiliate. The results also indicate that firms are more likely to engage in arm’s length technology transfer as opposed to just affiliate activity in countries that have a more educated workforce and that have higher corporate tax rates. The predictions of the model relate to credit market development, but the measure of creditor rights may be correlated with more general variation in the institutional environment. The specification presented in column (2) includes additional proxies for the quality of other host country institutions, including indices of patent protections, property rights, the strength and impartiality of the overall legal system, and the risk of expropriation as control variables. The coefficient on creditor rights remains positive and significant with the inclusion of these additional controls, implying that capital market conditions play an economically significant role relative to other host country institutions. The effect of a onestandard-deviation change in creditor rights is approximately one and a half times as large as the effect of a one-standard-deviation change in patent protections, which is also positive and significant in explaining the use of arm’s length technology transfer. 24. For the estimated effects of capital market conditions to be unbiased in this and the subsequent tests, these country characteristics must be exogenous to firms’ decisions to use arm’s length technology transfers as opposed to FDI, and firms’ financing and ownership decisions. 25. Given the limited time dimension of our data set, our linear specification avoids the incidental parameter problem inherent in the estimation of a large number of fixed effects. As a robustness check, these specifications have been run as conditional logit specifications. The resulting coefficients on the measures of financial development are of the same sign and statistical significance as those presented in Table II.

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The specification presented in column (3) provides a subtler test of the model and the particular mechanism that gives rise to FDI as opposed to arm’s length technology transfer. The model implies that the relative value of monitoring should be more pronounced for firms that conduct more research and development (R&D) because these firms are more likely to be deploying novel technologies that require the unique monitoring ability of parents. Alternatively, firms with limited technological capabilities are less likely to be important to external funders as monitors, and the effects of capital market development on the choice to serve a country through arm’s length technology transfer or affiliate activity should be less pronounced for these kinds of firms. The specification presented in column (3) uses the log of parent R&D as a proxy for the degree to which firms are technologically advanced. Because this specification includes parent-year fixed effects, this variable does not enter on its own, but it is interacted with creditor rights.26 The positive coefficient on the interaction term is consistent with the prediction that the value of creating incentives to monitor through ownership in countries with weak financial development is highest for technologically advanced firms. The specifications presented in columns (4)–(6) of Table II repeat those presented in columns (1)–(3), replacing creditor rights with private credit as a measure of financial development. The positive and significant coefficients on private credit in columns (4) and (5) are consistent with the findings in columns (1) and (2) and illustrate that countries with higher levels of financial development are more likely to be served through arm’s length technology transfers as opposed to just affiliate activity. The positive and significant coefficient on private credit interacted with the log of parent R&D presented in column (6) indicates that the effects of capital markets are most pronounced for firms that are R&D intensive.27

26. Because parent characteristics are absorbed by the parent-year fixed effects, the coefficient on this interaction term picks up how the effect of capital market conditions varies across firms. The sample used in this specification and the specification in column (6) includes only MNCs because R&D expenditures are only available in the BEA data for these firms. 27. When running these specifications as conditional logit specifications, the resulting coefficients on these interaction terms are of the same sign and statistical significance as those in the Table II, except for the interaction of creditor rights and the log of parent R&D. The coefficient on this variable is positive, but it is not statistically different from zero at conventional levels.

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FIGURE II Parent Financing of Affiliate Assets Parent financing share is the ratio of the sum of net borrowing from the parent and parent equity provisions to affiliate assets. The bars display medians of the country-level average shares for each quintile of private credit. Private credit is the ratio of private credit lent by deposit money banks to GDP, as provided ¨ ¸ -Kunt, and Levine (1999). Higher number quintiles relate to in Beck, Demirguc higher values of private credit.

IV.B. Financing and Ownership of Foreign Affiliates The analysis presented in Figure II and Table III investigates whether financing and ownership decisions reflect the mechanics emphasized in the model. As depicted in Figure II, parent firms provide financing that averages 45% of affiliate assets in countries in the lowest quintile of private credit but 38% of affiliate assets in countries from the highest quintile of private credit.28 Table III presents the results of more detailed tests of this relation. In addition to a variety of country-level controls, fixed effects for each parent in each year control for differences across firms. The negative and significant coefficient on creditor rights in column (1) 28. More specifically, the values displayed in this chart are computed by first taking average shares of affiliate assets financed by parents for each country in each year. These shares are defined as the ratio of the sum of net borrowing from the parent and parent equity provisions (including both paid-in-capital and retained earnings) to affiliate assets. The bars display medians of the country-level averages for each quintile of private credit.

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TABLE III PARENT FINANCING DECISIONS Dependent variable: Share of affiliate assets financed by parent

Creditor rights

(1)

(2)

(3)

−0.0166 (0.0054)

−0.0164 (0.0051)

−0.0080 (0.0055) −0.0010 (0.0003)

Creditor rights* log of parent R&D Private credit Private credit* log of parent R&D FDI ownership restrictions Workforce schooling

−0.0406 (0.0146) 0.0200 (0.0057) Log of GDP −0.0224 (0.0055) Log of GDP per capita −0.0327 (0.0112) Corporate tax rate −0.1288 (0.0776) Patent protections

(6)

−0.0632 (0.0195)

−0.0384 (0.0215)

−0.0084 (0.0220) −0.0031 (0.0012) −0.0358 (0.0162) 0.0157 (0.0049) −0.0148 (0.0085) 0.0030 (0.0169) −0.1731 (0.0745) −0.0436 (0.0120) −0.0113 (0.0106) 0.0068 (0.0080) 0.0003 (0.0094) 0.8330 (0.1906) Y Y 38,016 .3134

−0.0323 (0.0171) 0.0199 (0.0060) −0.0157 (0.0062) −0.0285 (0.0136) −0.1135 (0.0743)

1.2571 (0.1083) Y

−0.0426 (0.0155) 0.0114 (0.0043) −0.0180 (0.0071) −0.0072 (0.0154) −0.2061 (0.0764) −0.0388 (0.0114) 0.0110 (0.0115) 0.0062 (0.0079) 0.0007 (0.0091) 0.9728 (0.1435) Y

1.0444 (0.1479) Y

−0.0358 (0.0160) 0.0151 (0.0048) −0.0148 (0.0084) 0.0027 (0.0167) −0.1803 (0.0742) −0.0434 (0.0119) −0.0096 (0.0103) 0.0065 (0.0080) 0.0009 (0.0092) 0.8389 (0.1868) Y

N 51,060 .3013

Y 41,232 .3105

Y 40,297 .3071

N 48,183 .3076

Y 38,911 .3167

Rule of law Risk of expropriation

Parent-year fixed effects? Affiliate controls? No. of obs. R2

(5)

−0.0426 (0.0154) 0.0110 (0.0042) −0.0180 (0.0070) −0.0066 (0.0153) −0.2135 (0.0763) −0.0392 (0.0113) 0.0112 (0.0112) 0.0059 (0.0078) 0.0010 (0.0090) 0.9710 (0.1420) Y

Property rights

Constant

(4)

Notes. The dependent variable is the ratio of parent-provided equity and net parent lending to total assets. Creditor rights is an index of the strength of creditor rights developed in Djankov, McLiesh, and Shleifer (2007); higher levels of the measure indicate stronger legal protections. Private credit is the ratio of ¨ ¸ -Kunt, and Levine (1999). private credit lent by deposit money banks to GDP, as provided in Beck, Demirguc FDI ownership restrictions is a dummy equal to 0 if two measures of restrictions on foreign ownership as measured by Shatz (2000) are above 3 on a scale of 1 to 5 and 1 otherwise. Workforce schooling is the average schooling years in the population over age 25 years provided in Barro and Lee (2000). Corporate tax rate is the median effective tax rate paid by affiliates in a particular country and year. Patent protections is an index of the strength of patent rights provided in Ginarte and Park (1997). Property rights is an index of the strength of property rights drawn from the 1996 Index of Economic Freedom. Rule of law is an assessment of the strength and impartiality of a country’s overall legal system drawn from the International Country Risk Guide. Risk of expropriation is an index of the risk of outright confiscation or forced nationalization of private enterprise, and it is also drawn from the International Country Risk Guide; higher values of this index reflect lower risks. Each specification is an OLS specification that includes parent-year fixed effects. As affiliate controls, the specifications presented in columns (2), (3), (5), and (6) include the log of affiliate sales, the log of affiliate employment, and affiliate net PPE/assets. Affiliate net PPE/assets is the ratio of affiliate net property plant and equipment to affiliate assets. Heteroscedasticity-consistent standard errors that correct for clustering at the country-year level appear in parentheses.

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indicates that the share of affiliate assets financed by the parent is higher in countries that do not provide creditors with extensive legal protections. This result is consistent with the prediction contained in Proposition 3 and the pattern depicted in Figure II. The specification in column (2) includes the set of other institutional variables also used in Table II to ensure that proxies for financial development are not proxying for some other kind of institutional development. In addition, this specification also controls for affiliate characteristics that the corporate finance literature suggests might influence the availability of external capital. Harris and Raviv (1991) and Rajan and Zingales (1995) find that larger firms and firms with higher levels of tangible assets are more able to obtain external debt. Two proxies for affiliate size (the log of affiliate sales and the log of affiliate employment) and a proxy for the tangibility of affiliate assets (the ratio of affiliate net property, plant, and equipment to affiliate assets) are included.29 In the specification in column (2), the −0.0164 coefficient on creditor rights implies that the share of affiliate assets financed by the affiliate’s parent is 0.0327, or 7.9% of its mean value, higher for affiliates in countries in the 25th percentile of creditor rights relative to the 75th percentile of creditor rights. The negative and significant coefficient on FDI ownership restrictions is consistent with the hypothesis that such restrictions limit parent capital provisions, and the negative and significant coefficient on the log of GDP suggests that affiliates located in smaller markets are more reliant on their parents for capital. When affiliates borrow, they primarily borrow from external sources, and Desai, Foley, and Hines (2004b) show that affiliates borrow more in high-tax jurisdictions. These facts could explain the negative coefficient on the corporate tax rate in explaining the share of assets financed by the parent.30 Previous theoretical work stressing how concerns over technology expropriation might give rise to multinational activity does not make clear predictions concerning the share of affiliate assets financed by the parent, but it is worth noting that the indices of patent protection and property rights are negative in 29. The affiliate controls included in this specification as well as those in columns (3), (5), and (6) of Table III and columns (2), (3), (5), and (6) of Table IV are potentially endogenous. It is comforting that their inclusion does not typically have a material impact on the estimated effects of capital market conditions. 30. The model’s predictions relate to overall parent capital provision. As such, these specifications differ from the analysis in Desai, Foley, and Hines (2004b), where only borrowing decisions are analyzed.

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the specification in column (2). None of the unreported coefficients on affiliate characteristics is significant. If parent financing creates incentives for monitoring and the effects of monitoring are strongest for firms with more technology, then the effects documented in column (2) should be most pronounced for R&D-intensive firms. The specification in column (3) tests for a differential effect of creditor rights on financing by including creditor rights interacted with the log of parent R&D. The negative and significant coefficient on this interaction term indicates that more technologically advanced firms finance a higher share of affiliate assets in countries with weak credit markets. This finding is not implied by many other intuitions for why investor protections might affect parental financing provisions. The specifications presented in columns (4)–(6) of Table III repeat the analysis presented in columns (1)–(3) substituting measures of private credit for creditor rights. In columns (4) and (5), the coefficient on private credit is negative, and it is significant in column (4) but only marginally significant in column (5). In the specification in column (6), the interaction of private credit and the log of parent R&D is significant. The results obtained when using private credit are also consistent with the prediction of Proposition 3 and with Figure II. The model also predicts that multinational parents should hold larger ownership stakes in affiliates located in countries with weak investor protections. Table IV presents results of using the share of affiliate equity owned by the parent as the dependent variable in specifications that are similar to those presented in Table III. Although parent equity shares are bounded between 0 and 1, and there is a large grouping of affiliates with equity that is 100% owned by a single parent firm, the specifications presented in Table IV are ordinary least squares models that include parent-year fixed effects and that allow standard errors to be clustered at the country-year level.31 In the specifications presented in columns (1), (2), (4), and (5), the proxy for credit market development is negative and significant. Parent companies own higher shares of affiliate equity when affiliates are located in countries where protections extended to creditors are weaker and private credit is scarcer, as predicted by the model. In the specifications 31. Wholly owned affiliates comprise 77.2% of all observations. These results are robust to using an alternative estimation technique. Conditional logit specifications that use a dependent variable that is equal to 1 for wholly owned affiliates and 0 for partially owned affiliates yield similar results.

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QUARTERLY JOURNAL OF ECONOMICS TABLE IV PARENT OWNERSHIP DECISIONS Dependent variable: Share of affiliate equity owned by parent

Creditor rights

(1)

(2)

(3)

−0.0091 (0.0028)

−0.0101 (0.0035)

−0.0010 (0.0031) −0.0010 (0.0003)

Creditor rights* log of parent R&D Private credit Private credit* log of parent R&D FDI ownership restrictions Workforce schooling

−0.0728 (0.0126) 0.0005 (0.0024) Log of GDP −0.0157 (0.0037) Log of GDP per capita 0.0309 (0.0064) Corporate tax rate −0.2633 (0.0638) Patent protections

(6)

−0.0506 (0.0135)

−0.0481 (0.0174)

0.0078 (0.0144) −0.0057 (0.0009) −0.0529 (0.0122) −0.0026 (0.0026) −0.0079 (0.0046) 0.0416 (0.0144) −0.3179 (0.0564) −0.0122 (0.0077) −0.0014 (0.0072) 0.0017 (0.0060) 0.0059 (0.0067) 0.9159 (0.1018) Y Y 38,198 .4217

−0.0622 (0.0117) 0.0007 (0.0026) −0.0110 (0.0035) 0.0381 (0.0078) −0.2778 (0.0584)

1.1593 (0.1006) Y

−0.0611 (0.0134) −0.0044 (0.0025) −0.0116 (0.0045) 0.0363 (0.0132) −0.3391 (0.0700) −0.0137 (0.0072) 0.0044 (0.0075) 0.0012 (0.0061) 0.0050 (0.0068) 1.0675 (0.1121) Y

0.9833 (0.0947) Y

−0.0560 (0.0122) −0.0030 (0.0026) −0.0079 (0.0046) 0.0402 (0.0143) −0.3249 (0.0582) −0.0127 (0.0078) 0.0000 (0.0071) 0.0009 (0.0061) 0.0069 (0.0066) 0.9356 (0.1055) Y

N 51,320 .3974

Y 41,436 .4250

Y 40,498 .4184

N 48,422 .3998

Y 39,096 .4275

Rule of law Risk of expropriation

Parent-year fixed effects? Affiliate controls? No. of obs. R2

(5)

−0.0637 (0.0133) −0.0049 (0.0024) −0.0116 (0.0046) 0.0358 (0.0132) −0.3456 (0.0712) −0.0142 (0.0073) 0.0055 (0.0072) 0.0005 (0.0061) 0.0054 (0.0068) 1.0774 (0.1147) Y

Property rights

Constant

(4)

Notes. The dependent variable is the share of affiliate equity owned by the affiliate’s parent. Creditor rights is an index of the strength of creditor rights developed in Djankov, McLiesh, and Shleifer (2007); higher levels of the measure indicate stronger legal protections. Private credit is the ratio of private credit lent ¨ ¸ -Kunt, and Levine (1999). FDI ownership by deposit money banks to GDP, as provided in Beck, Demirguc restrictions is a dummy equal to 0 if two measures of restrictions on foreign ownership as measured by Shatz (2000) are above 3 on a scale of 1 to 5 and 1 otherwise. Workforce schooling is the average schooling years in the population over age 25 years provided in Barro and Lee (2000). Corporate tax rate is the median effective tax rate paid by affiliates in a particular country and year. Patent protections is an index of the strength of patent rights provided in Ginarte and Park (1997). Property rights is an index of the strength of property rights drawn from the 1996 Index of Economic Freedom. Rule of law is an assessment of the strength and impartiality of a country’s overall legal system drawn from the International Country Risk Guide. Risk of expropriation is an index of the risk of outright confiscation or forced nationalization of private enterprise, and it is also drawn from the International Country Risk Guide; higher values of this index reflect lower risks. Each specification is an OLS specification that includes parent-year fixed effects. As affiliate controls, the specifications presented in columns (2), (3), (5), and (6) include the log of affiliate sales, the log of affiliate employment, and affiliate net PPE/assets. Affiliate net PPE/assets is the ratio of affiliate net property plant and equipment to affiliate assets. Heteroscedasticity-consistent standard errors that correct for clustering at the country-year level appear in parentheses.

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presented in columns (3) and (6), the negative and significant coefficients on the interaction terms indicate that these results are also more pronounced for technologically advanced firms. The results in Table IV also indicate that equity ownership shares are lower in countries with ownership restrictions and countries with higher corporate tax rates. If equity ownership decisions placed strong emphasis on the protection of technology and ownership substituted for weak patent protections, the coefficient on the patent protections variable should be negative and significant. Although the estimated coefficient is negative, it is only marginally significant in some specifications. The results presented in Tables II, III, and IV are robust to a number of concerns. First, it is possible that the estimates of coefficients on capital market conditions interacted with the log of parent R&D may reflect the effect of similar interactions with alternative institutional variables. To consider this possibility, it is useful to consider the inclusion of other interaction terms. For example, when the log of parent R&D interacted with the rule of law index is included in the specifications presented in columns (3) and (6) of the three tables, the interactions that include proxies for capital market development remain significant in all of the tests. When the log of parent R&D interacted with the patent protection index is included in these specifications, the interactions featuring proxies for credit market development remain significant in all of the tests except for the one in column (3) of Table II. As such, it appears that the role of R&D intensity is most pronounced through the channel emphasized in the model, through interactions with capital market conditions. It may also be the case that the share of affiliate assets financed by the parent and parent ownership levels are lower for older affiliates and these affiliates may be more prevalent in countries with better investor protections. Including proxies for affiliate age in the specifications presented in Tables III and IV does not affect the results of interest.32 Similarly, the model does not explicitly consider the possibility that a firm exploits its technology through trade as opposed to through FDI or arm’s length technology transfers. To consider if trade channels could affect the main findings, the log of parent exports to unaffiliated foreign persons 32. The proxies for age are the number of years since an affiliate first reported data to BEA and a dummy equal to 1 if the affiliate first reported in 1982 and 0 otherwise.

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in each country and year is included as a control in each of the specifications. The magnitude and significance of the coefficients on the proxies for capital market conditions and the interactions of these proxies and the log of parent R&D are not materially changed. Finally, contractual forms that are specific to the natural resources sector could affect some of the results. Removing observations of firms in this sector reduces the significance of the results on the effects of private credit in specifications presented in column (5) of Tables II and III, but does not materially change any of the other results on the effects of capital market conditions in Tables II, III, and IV.33 IV.C. Scale of Multinational Activity The model predicts that multinational activity will be of a larger scale in countries with stronger investor protections. Because there are many theories for the determinants of FDI activity, using specifications similar to those presented in Tables II, III, and IV to explore scale is problematic because it is difficult to include a set of controls sufficiently extensive to distinguish between alternative theories.34 Fortunately, a subtler prediction of the model allows for tests of scale effects. Specifically, the model suggests that the response to the liberalizations of ownership restrictions should be larger in host countries with weak investor protections. The intuition for this prediction is that in countries with weak investor protections, ownership restrictions are more likely to bind because ownership is most critical for maximizing the value of the enterprise in these settings. As such, the relaxation of an ownership constraint should have muted effects for affiliates in countries with deep capital markets and more pronounced effects for affiliates in countries with weaker investor protections.35 33. Firms in BEA industries 101–148 and 291–299 are dropped from the sample. The coefficient on private credit in column (5) of Table II, when estimated using the reduced sample, is 0.0292, and it has a t-statistic of 1.92. The coefficient on private credit in column (5) of Table III, when estimated using the reduced sample, is −0.0351, and it has a t-statistic of 1.62. ` Desai, and Foley (2007) presents the results of 34. Appendix Table I in Antras, such an exercise. Although the coefficients on both the creditor rights variables and private credit variables are usually positive in explaining the log of affiliate sales, as Proposition 2 predicts, none of the coefficients on these variables is significant. 35. This prediction can in fact be explicitly derived from the model. In particular, one can envision an ownership restriction as an additional constraint to program (P1), requiring that φ I ≤ φ I for some foreign ownership cap φ I ∈ R. One can then show (details available upon request) that (i) for large enough γ , this constraint will not bind, and thus a removal of the constraint will have no effects

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FIGURE III Liberalizations and Multinational Firm Growth The two lines correspond to averages of an index computed at the country level as the ratio of aggregate affiliate sales in a given year to the level of sales in the year of the liberalization. Countries are split into two samples at the median level of private credit. Private credit is the ratio of private credit lent by deposit money ¨ ¸ -Kunt, and Levine (1999). banks to GDP, as provided in Beck, Demirguc

Figure III illustrates how the scale of multinational activity changes around the time of ownership liberalizations in countries with different levels of capital market development. Liberalizations are defined as the first year in which the FDI ownership restriction dummy described above changes from 1 to 0.36 The

on affiliate activity; (ii) when the constraint binds, the level of affiliate activity x is lower than in the absence of the constraint; and (iii) a marginal increase in φ I (i.e., a relaxation of the restriction) increases x by more, the lower is γ . Hence, the response of affiliate activity to a removal of ownership restrictions will be relatively larger in countries with relatively weaker investor protections. 36. The countries experiencing a liberalization are Argentina (1990), Australia (1987), Colombia (1992), Ecuador (1991), Finland (1990), Honduras (1993), Japan (1993), Malaysia (1987), Mexico (1990), Norway (1995), Peru (1992), Philippines (1992), Portugal (1987), Sweden (1992), Trinidad and Tobago (1994), and Venezuela (1990). Because control variables measuring the development of institutions other than credit markets do not vary much (if at all) through time and are unavailable for six of the sixteen reforming countries, these controls are not included in the analysis of liberalizations. The affiliate fixed effects implicitly control for time-invariant country characteristics, and so this is unlikely to pose a significant problem.

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QUARTERLY JOURNAL OF ECONOMICS TABLE V LIBERALIZATIONS AND MULTINATIONAL FIRM SCALE Dependent variable Log of affiliate sales

Post-liberalization dummy Post-liberalization dummy * low creditor rights dummy Post-liberalization dummy * low private credit dummy Log of GDP

Log of aggregate affiliate sales

(1)

(2)

(3)

(4)

0.0016 (0.0684) 0.3011 (0.0827)

−0.0073 (0.0712)

−0.0633 (0.1230) 0.3682 (0.1552)

−0.1049 (0.1262)

0.3886 (0.3888) Log of GDP per capita 1.3675 (0.3720) Constant −13.5818 (9.2414) Affiliate and year fixed effects? Y Country and year fixed effects? N No. of obs. 180,796 R2 .8035

0.2947 (0.0899) 0.3409 (0.3960) 1.4488 (0.3867) −13.0613 (9.2484) Y N 181,103 .8040

−0.0786 (0.7833) 2.6620 (0.5425) −4.7847 (22.1876) N Y 827 .9243

0.3812 (0.1769) −0.1351 (0.7040) 2.8376 (0.6192) −4.9033 (20.0397) N Y 845 .9251

Notes. The dependent variable in the first two columns is the log of affiliate sales, and the dependent variable in the last two columns is the log of affiliate sales aggregated across affiliates in a particular country. The data are annual data covering the 1982–1999 period. The post-liberalization dummy is equal to 1 for the sixteen countries that liberalize their ownership restrictions in the year of and years following liberalization of foreign ownership restrictions. The low creditor rights dummy is equal to 1 for observations related to countries with below median levels of creditor rights among liberalizing countries measured in the year prior to liberalization and 0 otherwise. The low private credit dummy is equal to 1 for observations related to countries with below median levels of private credit among liberalizing countries measured in the year prior to liberalization and 0 otherwise. Creditor rights is an index of the strength of creditor rights developed in Djankov, McLiesh, and Shleifer (2007). Private credit is the ratio of private credit lent by deposit money ¨ ¸ -Kunt, and Levine (1999). The first two specifications are OLS banks to GDP, as provided in Beck, Demirguc specifications that include affiliate and year fixed effects, and the last two are OLS specifications that include country and year fixed effects. Heteroscedasticity-consistent standard errors that correct for clustering at the country level appear in parentheses.

lines trace out an index that is computed by calculating the ratio of aggregate affiliate sales in a particular country and year to the value of aggregate affiliate sales in that country in the year of liberalization. The line demarcated by squares (triangles) plots the average of this index across countries that have a measure of private credit in the year prior to the liberalization that is equal to or less than (above) the median private credit of liberalizing countries. The lines indicate that affiliate activity increases by a larger margin in countries with low levels of private credit following liberalizations. The specifications presented in Table V investigate whether these differential effects are robust. The dependent variable in

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columns (1) and (2) is the log value of affiliate sales, and the sample consists of the full panel from 1982 to 1999. Given the limited data requirements of these specifications (relative to the variables investigated in Tables II, III, and IV) and the desire to investigate changes within affiliates, the full panel provides a more appropriate setting for these tests. These specifications include affiliate and year fixed effects, and the standard errors are clustered at the country level. The sample includes all countries so that affiliate activity in countries that do not liberalize helps identify the year effects and the coefficients on the income variables. The results are robust to using a sample drawn only from reforming countries. The specifications in columns (1) and (2) include controls for log GDP, log GDP per capita, and the post-liberalization dummy. The coefficient on log GDP per capita is positive and significant indicating that rising incomes are associated with larger levels of affiliate activity. The coefficient of interest in column (1) is the coefficient on the interaction of the post-liberalization dummy and a dummy that is equal to 1 if the country has a value of the creditor rights index in the year before liberalization that is equal to or less than the median value for liberalizing countries. The positive and significant coefficient indicates that affiliates in weak-creditorrights countries grow quickly after liberalizations. The coefficient on the post-liberalization dummy on its own indicates that the effect of liberalizations is negligible and statistically insignificant for affiliates in high-creditor-rights countries. In column (2), these same results are obtained when the measure of private credit is used as the proxy for financial development. At the affiliate level, the model’s predictions regarding how the scale of activity relates to capital market depth are validated using tests that, through the use of affiliate fixed effects and the emphasis on the interaction term, are difficult to reconcile with alternative theories. It is possible that the results presented in columns (1) and (2) inaccurately capture the effects of the liberalizations because they only measure activity on the intensive margin and fail to capture responses on the extensive margin. Entry or exit might accompany liberalizations and might amplify or dampen these results. Figure III suggests this is not the case because it is constructed using data aggregated to the country level. The specifications provided in columns (3) and (4) employ a dependent variable that is the log value of the aggregate value of all sales of U.S. multinational affiliates within a country-year cell. These specifications substitute country fixed effects for affiliate fixed effects but are otherwise similar to the regressions provided in columns (1) and (2).

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In column (3), the coefficient on the interaction term including the creditor rights variable is again positive and significant, indicating that incorporating activity on the extensive margin does not appear to contradict the earlier result. In column (4), the coefficient on the interaction term is again positive and significant. Taken together, the results suggest that the scale of activity is positively related to the quality of investor protections and capital market development, and these results persist when incorporating the effects of entry and exit. V. CONCLUSION Efforts to understand patterns of MNC activity have typically emphasized aspects of technology expropriation rather than the constraints imposed by weak investor protections and shallow capital markets. In the prior literature, MNCs arise because of the risk of a partner expropriating a proprietary technology. In the model presented in this paper, the exploitation of technology is central to understanding MNC activity, but the critical constraint is the nature of capital market development and investor protections in host countries. Entrepreneurs must raise capital to fund projects, and external investors are aware of the possibility that these entrepreneurs might behave opportunistically. Inventors can alleviate financial frictions because they have privileged knowledge of their technology and can thus play a role in monitoring entrepreneurs. As a result, MNC activity and capital flows arise endogenously to ensure that monitoring occurs. External investors demand higher levels of multinational parent firm financial participation in countries with weak investor protections. By placing financial frictions at the center of understanding patterns of activity and flows, the model delivers novel predictions about the use of arm’s length technology transfers and about the financial and investment decisions of MNCs that are validated in firm-level analysis. The use of arm’s length technology transfers is more common in countries with strong investor protections and deep capital markets. Previous findings that FDI flows to developing countries are limited reflect two opposing forces. Weak investor protections and shallow capital markets limit the efficient scale of enterprise but also result in greater parent provision of capital and more parent ownership of affiliate equity. The effects of the institutional setting are more pronounced for R&D-intensive firms because parental monitoring is particularly valuable for the

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investments of these firms. By jointly considering operational and financial decisions, the theory and empirics provide an integrated explanation for patterns of MNC activity and FDI flows that have typically been considered separately. Further consideration of the role of financial frictions on MNC activity along several dimensions may prove fruitful. First, the model presented effectively rules out exports to unrelated parties as a means of serving foreign markets. Incorporating the trade-off between exports and production abroad in a world with financial frictions may yield additional predictions that would help explain the choice between exporting and FDI. Second, exploring the implications of financial frictions for intrafirm trade may help explain how the demands of external funders in weak institutional environments affect the fragmentation of production processes across borders. Finally, the central role of foreign ownership in reducing diversion may lead to significant variation in the relative competitiveness of local and foreign firms that reflects the institutional environment emphasized in this paper. APPENDIX I: THE SHADOW COST OF CASH In the main text, we have treated the shadow value of cash β as exogenous. In this Appendix we briefly illustrate how to endogenize it and show how it relates to characteristics of the Home country and in particular to its level of investor protection. For this purpose, we generalize the setup described in Section II.A and consider the situation in which there are J − 1 Foreign countries, each associated with a level of financial development γ j and a cash flow function R j (x j ).37 The inventor contracts with each of J − 1 foreign entrepreneurs and, as a result of the optimal contracting described above, has an amount of cash equal to W −

˜ j to invest in the Home country. F j= H Preferences and technology at Home are such that the cash flows obtained from the sale of the differentiated good at Home can be expressed as a strictly increasing and concave function of the quantity produced, RH (q H ), satisfying the same properties as the cash flow function in other countries. Home production is managed by the inventor, who can also privately choose to behave or misbehave, with consequences identical to those discussed 37. With some abuse of notation, we use J to denote both the number of countries as well as the set of these countries.

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above: if the inventor behaves, the project performs with probability pH , but if he misbehaves, the project performs with a lower probability pL. In the latter case, however, the inventor obtains a private benefit equal to a fraction 1 − γ H of cash flows, where γ H is an index of investor protection at Home. The inventor sells domestic cash flow rights to a continuum of external investors at Home, who can obtain a rate of return equal to 1 in an alternative investment opportunity.38 We consider an optimal financial contract between the inventor and external investors in which the inventor is granted the ability to make take-it-or-leave-it offers, just as in the main text. The optimal contract specifies the scale of operation x H , the amount of cash Wx that the inventor invests in the project, the share of equity φ EH sold to external investors, and the amount of cash E H provided by external investors. Taking the contracts signed with foreign individuals as given, an optimal financial contract with external investors at Home that induces the inventor to behave is given by the tuple ˜ x , φ˜ H , E˜ H } that solves the following program: {x˜ H , W E max

x H ,Wx ,φ EH ,E H

(P2)

s.t.

I =

j φ I pH − C j R j (x j )

j= H + pH 1 − φ EH RH (x H ) + W − F˜ j − Wx

x H ≤ E H + Wx Wx ≤ W − F˜ j

j= H

j= H

pH φ EH RH (x H ) ≥ E H ( pH − pL) 1 − φ EH RH (x H ) ≥ (1 − γ H )RH (x H ). It is straightforward to show that provided that γ H is low enough (i.e., provided that financial frictions at Home are large enough), all constraints in program (P2) will bind in equilibrium, and the profits of the entrepreneur can be expressed as ⎛ ⎞ j ⎝ W − φ I pH − C j R j (x j ) + β F˜ j ⎠ , (6) I = j= H

j= H

38. For simplicity, we assume that the inventor cannot pledge foreign cash flow rights to its external investors at Home.

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where 1−γH ( pH − pL) βˆ = > 1. H 1−γ x˜ H − 1− pH − pL pH RH (x˜ H ) Notice that the resulting profit function (6) is closely related to that considered in program (P1) in Section II.B, where βˆ now replaces β. There are, however, two important differences between the two profit functions. First, the formulation in (6) considers the case in which the inventor obtains cash flow from the exploitation of the technolˆ ogy in multiple countries. Nevertheless, notice that for a given β, the profit function features separability between these different ˆ the optimal contract sources of dividends. As a result, for a given β, with the entrepreneur and external investors in each country j is as described in Section II.B.39 Hence, Propositions 1, 2, and 3 continue to apply and their statements not only apply to changes in the parameter γ but also to cross-sectional (cross-country) variation in investor protection. In this sense, the tests performed in Section IV are well defined. The second important difference between the profit function in (6) and in program (P1) is that the shadow value of cash βˆ is in fact endogenous, in the sense that it is a function of the scale of operation at Home x H , which in turn will depend on the optimal contracts in the other J countries through the date-0 transfers F˜ j for j = H (as is clear from program (P2)). Hence, βˆ will in general be a function of the vector of country investor protections γ ≡ (γ 1 , . . . , γ J−1 , γ H ). Notice, however, that for large enough J, the effect of a particular investor protection level γ j ( j = H) on the overall shadow value of cash βˆ will tend to be negligible, and thus the comparative static results in Section II.B will continue to apply. To sum up, this Appendix has illustrated that a higher-than1 shadow value of cash can easily be rationalized in a simple 39. Notice also that when βˆ > 1, the inventor is financially constrained at Home, in the sense that external investors at Home are only willing to lend to him a multiple of his pledgeable income (wealth plus date-0 payments). If external investors were to lend a larger amount, the inventor’s incentive-compatibility constraint would be violated. The same would of course apply to external investors in foreign countries. This helps rationalize our assumption in Section II.A that the inventor does not sign bilateral financial contracts with external investors in host countries.

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extension of our initial partial equilibrium model, in which not only foreign entrepreneurs, but also the inventor, face financial constraints. We have seen that endogenizing the shadow value of cash may affect the solution of the optimal contract in subtle ways, but that if the number of host countries in which the inventor exploits his technology is large enough, the comparative static results in Section II.B remain qualitatively valid. APPENDIX II: CHARACTERIZATION OF THE OPTIMAL CONTRACT Let us start by writing the Lagrangian corresponding to program (P1). Letting λk denote the multiplier corresponding to constraint k = 1, 2, 4, 5 (remember constraint (iii) cannot bind), we have L = φ I pH R(x) + (W − F)β − C R(x) + λ1 (E + F − x) + λ2 ( pH φ E R(x) − E) + λ4 (( pH − pL)(1 − φ E − φ I ) C . −(1 − γ )δ(C)) + λ5 φ I − ( pH − pL) The first-order conditions of this program (apart from the standard complementarity slackness conditions) are

(7)

(8)

∂L ∂F ∂L ∂φ I ∂L ∂x ∂L ∂φ E ∂L ∂E ∂L ∂C

= −β + λ1 = 0, = pH R (x˜ ) − λ4 ( pH − pL) + λ5 = 0, = φ˜ I pH R (x˜ ) − C˜ R (x˜ ) − λ1 + λ2 pH φ˜ E R (x˜ ) = 0, = λ2 pH R (x˜ ) − λ4 ( pH − pL) = 0, = λ1 − λ2 = 0, ˜ − = −R (x˜ ) − λ4 (1 − γ ) δ (C)

λ5 = 0. ( pH − pL)

Straightforward manipulation of these conditions delivers λ1 = λ2 = β > 0, pH pH λ2 R (x˜ ) = β R (x˜ ) > 0, λ4 = pH − pL pH − pL λ5 = (β − 1) pH R (x˜ ) > 0,

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from which we conclude that all constraints bind, as claimed in the main text. The fact that λ5 > 1 immediately implies that constraint (v) ˜ ( pH − pL), as indicated in equation (2). binds and we have φ˜ I = C/ Next, plugging the values of the multipliers in (8) yields ˜ = −δ (C)

βpH − pL , (1 − γ ) βpH

as claimed in equation (3) in the main text. Next, plugging the multipliers and φ˜ I into (7) yields R (x˜ ) =

1 ˜ , ˜ C βpH − pL (1 − γ ) δ(C) − 1− pH − pL pH − pL βpH

pH

which corresponds to equation (4) in the main text. Setting the constraints to equality, we can also compute the total payoff obtained by the inventor: R (x˜ ) ˜ (9) I = Wβ + β − x˜ . R (x˜ ) This expression can be used to analyze when it is optimal for the inventor to implement good behavior. To do so, consider the optimal contract that implements bad behavior. It is clear that in this case the inventor has no incentive to exert monitoring effort. It is also immediate that even when the entrepreneur does not obtain any share of the cash flows, her participation constraint will be satisfied, and thus we have that φ˜ IL + φ˜ EL = 1. The program defining the optimal contract can then be written as max

I = φ I pL R(x) + (W − F ) β

s.t.

x ≤ E+ F pL (1 − φ I ) R(x) ≥ E φ I ≥ 0.

F,φ I ,x,E

(P1 L)

(i) (ii) (iii)

Following the same steps as before, we find that all three constraints will bind, and hence C˜ L = φ˜ IL = 0. Furthermore, the optimal level of investment is given by pL R (x˜ L) = 1,

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while the overall payoff obtained by the inventor equals R(x˜ L) L ˜ L = βW + β . (10) − x ˜ R (x˜ L) ˜I > ˜ L if and Comparing equations (9) and (10) we see that only if R(x˜ L) R (x˜ ) − x˜ L. − x ˜ > R (x˜ ) R (x˜ L) However, because R(x)/R (x) − x is strictly increasing in x whenever R (x) < 0, we can conclude that good behavior will be implemented whenever x˜ > x˜ L. Note also that x˜ is increasing in γ (this is formally proved in Appendix III), while x˜ L is independent of γ . Furthermore, when γ → 1, it is necessarily the case that x˜ > x˜ L. Hence, there exists a threshold γ over which it is optimal to implement good behavior. APPENDIX III: PROOFS OF COMPARATIVE STATIC RESULTS The comparative statics in Lemma 1 simply follow from the fact that the right-hand side of equation (3) is increasing in γ and β, while the left-hand side is decreasing in C˜ (given the convexity of δ (·)). The statements of Proposition 1 directly follow from Lemma ˜ 1 because φ˜ I is proportional to C. Consider next the comparative statics in Proposition 2. For that purpose, let ˜ ˜ βpH − pL C (1 − γ ) δ(C) ˜ + , F(γ , β, C(γ , β)) = pH − pL pH − pL βpH so that ˜ , β))] = 1. ˜ − F(γ , β, C(γ pH R (x)[1 Using equation (3), we can establish that ˜ ˜ dC˜ 1 dC˜ δ(C) βpH − pL dF (·) (1 − γ ) δ (C) =− + + dγ pH − pL pH − pL dγ pH − pL βpH dγ ˜ δ(C) < 0; =− pH − pL

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˜ dC˜ βpH − pL 1 dC˜ dF (·) (1 − γ ) δ (C) = + dβ pH − pL dβ pH − pL βpH dβ ˜ pLC˜ pLC = > 0. + ( pH − pL) β 2 pH ( pH − pL) β 2 pH From inspection of (4) and the concavity of R (·), it is then clear that x˜ is increasing in γ and decreasing in β. Finally, the statements in Proposition 3 follow from the discussion in the main text and the fact that R (x˜ ) /x˜ is decreasing in x, ˜ and thus decreasing in γ and increasing in β. APPENDIX IV: GENERALIZATIONS In this Appendix, we provide more details on the generalizations outlined in Section II.C. Consider first the case in which the entrepreneur’s private benefit and the inventor’s private cost of monitoring are proportional to x rather than to R(x). Following the same steps as in the formulation in the main text, we find that the optimal Cˆ and xˆ are now given by ˆ = −δ (C)

βpH − pL βpH (1 − γ )

and pH R (xˆ ) = 1 +

(11)

ˆ pH (1 − γ ) δ(C) (βpH − pL) Cˆ . + β ( pH − pL) pH − pL

Straightforward differentiation indicates that both Cˆ and xˆ continue to be decreasing in γ , as in our paper. Next note that we can use equation (11) to write Cˆ xˆ xˆ R (xˆ ) pH Cˆ Cˆ = ( pH − pL) R (xˆ ) ( pH − pL) R (xˆ ) pH R (xˆ ) −1 ˆ pH xˆ R (xˆ ) 1 pH (1 − γ ) δ(C) (βpH − pL) = . + + β ( pH − pL) ( pH − pL) R (xˆ ) Cˆ ( pH − pL) Cˆ

φˆ I =

It is straightforward to see that the last term continues to be an increasing function of Cˆ and is thus decreasing in γ . This implies that the only way that φˆ I could be increasing in γ would be if ˆ x)— ˆ the elasticity of revenue to output—that is, α(x) ˆ ≡ xˆ R (x)/R( was sufficiently increasing in x. ˆ For a constant-elasticity function, ˆ = α for all xˆ and thus φˆ I continues to be R(x) = Ax α , we have α(x)

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decreasing in γ for any level of concavity of the R(x) function. Remember that the revenue function will be isoelastic whenever the firm faces a demand with constant price elasticity. If the firm were to face a linear demand function, then α(x) ˆ would be decreasing in x, ˆ hence reinforcing the result that φˆ I is decreasing in γ . We next consider the case in which (local) external investors can also serve a monitoring role. In particular, if external investors exert an unverifiable effort cost MR(x), the private benefit is now B (C, M; γ ) = (1 − γ ) (δ (C ) + μ ( M)) , with μ(·) satisfying the same properties as δ(·) above, namely, ¯ lim M→∞ μ(M) = 0, lim M→0 μ μ (M) < 0, μ (M) > 0, μ(0) = μ, (M) = −∞, and lim M→∞ μ (M) = 0. Because local monitoring is not verifiable, the program that determines the optimal contract will need to include a new incentive compatibility constraint for external investors. In particular, an optimal contract that induces the entrepreneur to behave is now given by the tuple ˆ C, ˆ M} ˆ that solves a program analogous to (P1) but ˆ φˆ I , x, ˆ φˆ E , E, { F, with constraints (ii) and (iv) now given by pH φ E R(x) − MR(x) ≥ E

(ii)

( pH − pL) (1 − φ E − φ I ) ≥ (1 − γ ) (δ (C ) + μ ( M))

(iv)

and with the additional constraint φ E ≥ M/ ( pH − pL)

(vi).

Manipulating the first-order conditions of this new program, we obtain λ5 = (β − 1) pH R (xˆ ) + λ6 , which immediately implies that constraint (v) continues to bind even in the case with local monitoring. Consequently, inventor (or parent firm) equity shares continue to move proportionately with the amount of monitoring undertaken by the inventor. Furthermore, provided that the level of investor protection is sufficiently high, the analysis in the main text goes through essentially unaltered. The reason for this is that in such a case, ˆ being constraint (vi) is not binding (λ6 = 0) and we obtain Cˆ and M determined by (12)

ˆ = βpH − pL , − δ (C) (1 − γ ) βpH

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which is identical to (3), and

(13)

ˆ = ( pH − pL) . − μ ( M) (1 − γ ) pH

From the convexity of the monitoring functions, we thus obtain ˆ are decreasing functions of γ . Furthermore, that both Cˆ and M manipulating the first-order conditions we can also easily show that (i) the investment levels (and thus) sales revenue continue ˆ x is still increasing in to be increasing in γ , and (ii) the ratio F/ γ , provided that α (xˆ ) does not increase in xˆ too quickly, just as in the main text (details available upon request). ˆ > Note that equations (12) and (13) also imply that −δ (C) ˆ −μ ( M), and if the functions δ (·) and μ (·) are sufficiently simiˆ > C. ˆ Intuitively, a disproportionate amount of lar we will have M local monitoring may be optimal because it is “cheaper,” as external investors have a lower shadow cost of getting remunerated through equity shares. Still, as long as the equilibrium level of ˆ is sufficiently low (or γ is sufficiently high), the above analyM sis suggests that the inventor equity share comoves with investor protections in the same manner as in our simpler model with only inventor monitoring. For low enough values of γ , however, the above optimal conˆ > ( pH − pL) φ E , which violates constraint (vi). In tract leads to M such a case, we have λ6 > 0. Manipulating the first-order condiˆ are implicitly defined by the tions, one can show that Cˆ and M system ˆ 1 + (1 − γ ) μ ( M) = β, ˆ 1 + (1 − γ ) δ (C) ˆ = (1 − γ )(δ(C) ˆ + μ( M)). ˆ pH − pL − Cˆ − M Unfortunately, without imposing particular functional forms for the functions δ (·) and μ (·), it becomes impossible to characterize how Cˆ (and thus φˆ I ) varies with γ . HARVARD UNIVERSITY AND NBER HARVARD BUSINESS SCHOOL AND NBER HARVARD BUSINESS SCHOOL AND NBER

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REFERENCES Acemoglu, Daron, Simon Johnson, and Todd Mitton, “Determinants of Vertical Integration: Finance Contracts and Regulation,” NBER Working Paper No. 11424, 2005. Aguiar, Mark, and Gita Gopinath, “Fire-Sale FDI and Liquidity Crises,” Review of Economics and Statistics, 87 (2005), 439–452. Albuquerque, Rui, “The Composition of International Capital Flows: Risk Sharing through Foreign Direct Investment,” Journal of International Economics, 61 (2003), 353–383. ` Pol, “Firms, Contracts, and Trade Structure,” Quarterly Journal of EcoAntras, nomics, 118 (2003), 1375–1418. ——, “Incomplete Contracts and the Product Cycle,” American Economic Review, 95 (2005), 1054–1073. ` Pol, and Elhanan Helpman, “Global Sourcing,” Journal of Political EconAntras, omy, 112 (2004), 552–580. ` Pol, Mihir A. Desai, and C. Fritz Foley, “Multinational Firms, FDI Flows Antras, and Imperfect Capital Markets,” NBER Working Paper No. 12855, 2007. Baker, Malcolm, C. Fritz Foley, and Jeffrey Wurgler, “Multinationals as Arbitrageurs? The Effects of Stock Market Valuations on Foreign Direct Investment,” Review of Financial Studies, 22 (2009), 337–369. Barro, Robert J., and Jong-Wha Lee, “International Data on Educational Attainment: Updates and Implications,” CID Working Paper No. 42, 2000. ¨ ¸ -Kunt, and Ross Levine, “A New Database on FiBeck, Thorsten, Asli Demirguc nancial Development and Structure,” World Bank, Policy Research Working Paper No. 2146, 1999. Bertaut, Carol, William L. Griever, and Ralph W. Tryon, “Understanding U.S. Cross-Border Securities Data,” Federal Reserve Bulletin, 92 (2006), A59–A75. Blonigen, Bruce A., “Firm-Specific Assets and the Link Between Exchange Rates and Foreign Direct Investment,” American Economic Review, 87 (1997), 447– 465. Boyd, John H., and Bruce D. Smith, “Capital Market Imperfections, International Credit Markets and Nonconvergence,” Journal of Economic Theory, 73 (1997), 335–364. Brainard, S. Lael, “An Empirical Assessment of the Proximity-Concentration Trade-off between Multinational Sales and Trade,” American Economic Review, 87 (1997), 520–544. Caves, Richard E., Multinational Enterprise and Economic Analysis, 2nd ed. (Cambridge, UK: Cambridge University Press, 1996). Desai, Mihir A., C. Fritz Foley, and Kristin J. Forbes, “Financial Constraints and Growth: Multinational and Local Firm Responses to Currency Depreciations,” Review of Financial Studies, 21 (2008), 2857–2888. Desai, Mihir A., C. Fritz Foley, and James R. Hines, Jr., “Dividend Policy Inside the Firm,” NBER Working Paper No. 8698, 2002. ——, “The Costs of Shared Ownership: Evidence from International Joint Ventures,” Journal of Financial Economics, 73 (2004a), 323–374. ——, “A Multinational Perspective on Capital Structure Choice and Internal Capital Markets,” Journal of Finance, 59 (2004b), 2451–2488. Djankov, Simeon, Caralee McLiesh, and Andrei Shleifer, “Private Credit in 129 Countries,” Journal of Financial Economics, 84 (2007), 299–329. Ethier, Wilfred J., and James R. Markusen, “Multinational Firms, Technology Diffusion and Trade,” Journal of International Economics, 41 (1996), 1–28. Feenstra, Robert, and Gordon Hanson, “Ownership and Control in Outsourcing to China: Estimating the Property-Rights Theory of the Firm,” Quarterly Journal of Economics, 120 (2005), 729–761. Froot, Kenneth A., and Jeremy C. Stein, “Exchange Rates and Foreign Direct Investment: An Imperfect Capital Markets Approach,” Quarterly Journal of Economics, 106 (1991), 1191–1217. Gertler, Mark, and Kenneth S. Rogoff, “North-South Lending and Endogenous Domestic Capital Market Inefficiencies,” Journal of Monetary Economics, 26 (1990), 245–266. Ginarte, Juan Carlos, and Walter Park, “Determinants of Patent Rights: A CrossNational Study,” Research Policy, 26 (1997), 283–301.

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Grossman, Gene M., and Elhanan Helpman, “Managerial Incentives and the International Organization of Production,” Journal of International Economics, 63 (2004), 237–262. Harris, Milton, and Arthur Raviv, “The Theory of Capital Structure,” Journal of Finance, 46 (1991), 297–355. Helpman, Elhanan, “A Simple Theory of International Trade with Multinational Corporations,” Journal of Political Economy, 92 (1984), 451–471. Helpman, Elhanan, Marc J. Melitz, and Stephen R. Yeaple, “Exports versus FDI with Heterogeneous Firms,” American Economic Review, 94 (2004), 300–316. Holmstrom, Bengt, and Jean Tirole, “Financial Intermediation, Loanable Funds, and the Real Sector,” Quarterly Journal of Economics, 112 (1997), 663–691. King, Robert G., and Ross Levine, “Finance and Growth: Schumpeter Might Be Right,” Quarterly Journal of Economics, 108 (1993), 717–738. Klein, Michael W., Joe Peek, and Eric Rosengren, “Troubled Banks, Impaired Foreign Direct Investment: The Role of Relative Access to Credit,” American Economic Review, 92 (2002), 664–682. Klein, Michael W., and Eric Rosengren, “The Real Exchange Rate and Foreign Direct Investment in the United States,” Journal of International Economics, 36 (1994), 373–389. Kraay, Aart, Norman Loayza, Luis Serv´en, and Jaume Ventura, “Country Portfolios,” Journal of the European Economic Association, 3 (2005), 914–945. La Porta, Rafael, Florencio L´opez-de-Silanes, Andrei Shleifer, and Robert W. Vishny, “Legal Determinants of External Finance,” Journal of Finance, 52 (1997), 1131–1150. ——, “Law and Finance,” Journal of Political Economy, 106 (1998), 1113–1155. Levine, Ross, and Sara Zervos, “Stock Markets, Banks, and Economic Growth,” American Economic Review, 88 (1998), 537–558. Lucas, Robert, “Why Doesn’t Capital Flow from Rich to Poor Countries?” American Economic Review, 80 (1990), 92–96. Marin, Dalia, and Monika Schnitzer, “Global versus Local: The Financing of Foreign Direct Investment,” University of Munich, Working Paper, 2004. Markusen, James R., “Multinationals, Multi-Plant Economies, and the Gains from Trade,” Journal of International Economics, 16 (1984), 205–226. ——, Multinational Firms and the Theory of International Trade (Cambridge, MA: MIT Press, 2002). Markusen, James R., and Anthony J. Venables, “The Theory of Endowment, Intraindustry and Multi-national Trade,” Journal of International Economics, 52 (2000), 209–234. Misawa, Mitsuru, “Tokyo Disneyland: Licensing vs. Joint Venture,” Asia Case Research Centre, University of Hong Kong, Case HKU420, 2005. Rajan, Raghuram G., and Luigi Zingales, “What Do We Know about Capital Structure? Some Evidence from International Data,” Journal of Finance, 50 (1995), 1421–1460. ——, “Financial Dependence and Growth,” American Economic Review, 88 (1998), 559–586. Reinhart, Carmen M., and Kenneth S. Rogoff, “Serial Default and the ‘Paradox’ of Rich to Poor Capital Flows,” American Economic Review, 94 (2004), 52–58. Shatz, Howard J., “The Location of U.S. Multinational Affiliates,” Ph.D. Dissertation, Harvard University, 2000. Shleifer, Andrei, and Daniel Wolfenzon, “Investor Protection and Equity Markets,” Journal of Financial Economics, 66 (2002), 3–27. Tirole, Jean, The Theory of Corporate Finance (Princeton, NJ: Princeton University Press, 2005). Wurgler, Jeffrey, “Financial Markets and the Allocation of Capital,” Journal of Financial Economics, 58 (2000), 187–214. Yeaple, Stephen, “The Role of Skill Endowments in the Structure of U.S. Outward FDI,” Review of Economics and Statistics, 85 (2003), 726–734.

PRICE SETTING DURING LOW AND HIGH INFLATION: EVIDENCE FROM MEXICO∗ ETIENNE GAGNON This paper provides new insight into the relationship between inflation and the setting of individual prices by examining a large data set of Mexican consumer prices covering episodes of both low and high inflation. When the annual rate of inflation is low (below 10%–15%), the frequency of price changes comoves weakly with inflation because movements in the frequency of price decreases and increases partly offset each other. In contrast, the average magnitude of price changes correlates strongly with inflation because it is sensitive to movements in the relative shares of price increases and decreases. When inflation rises beyond 10%–15%, few price decreases are observed and both the frequency and average magnitude are important determinants of inflation. I show that a menu-cost model with idiosyncratic technology shocks predicts the average frequency and magnitude of price changes well over a range of inflation similar to that experienced by Mexico.

I. INTRODUCTION This paper presents new evidence on the setting of consumer prices during low and high inflation and sheds light on the empirical plausibility of competing models of price rigidities. It uses a new store-level data set containing over three million individual price quotes that are representative of more than half of Mexican consumers’ expenditures. The data start in January 1994 and end in June 2002. Over that nine-year period, the rate of increase in the official consumer price index (CPI) rose from 6.8% in 1994 to a peak of 41.8% in 1995, before falling to 4.9% in the last year of the sample.1 Given these considerable fluctuations, this data set allows me to document how individual consumer prices are set at various levels of inflation. It also can be used to discriminate among competing models of nominal price rigidities, as these models’ predictions diverge most in the presence of large shocks. ∗ I would like to thank the members of my dissertation committee, Lawrence J. Christiano, Alexander Monge-Naranjo, Sergio Rebelo, and especially my chairperson Martin Eichenbaum, for their continuous guidance and support. I am also grateful to Martin Bodenstein, Jeff Campbell, Reinout DeBock, Rodrigo Garc´ıa ´ Nicolas Vincent, and three anonymous referees for their insightful comVerdu, ments and suggestions. Chris Ahlin and Jos´e Antonio Murillo Garza offered valuable help with the data, and Martha Carillo, Matthew Denes, and Guthrie Dundas provided excellent research assistance. Financial support for this research was provided in part by the Northwestern University Center for International Economics and Development and the Fonds qu´eb´ecois pour les chercheurs et l’aide a` la recherche (FCAR). The views expressed in this paper are solely the responsibility of the author and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System. [email protected] 1. Unless otherwise indicated, all inflation figures are computed using the change in the logarithm of the price index and annualized. C 2009 by the President and Fellows of Harvard College and the Massachusetts Institute of

Technology. The Quarterly Journal of Economics, August 2009

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40 Austria Belgium Finland France Luxembourg Portugal Spain United States Mexico

)

35

30

25

20

15

10

5

0

1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006

Period covered by country studies

FIGURE I Inflation and Time Coverage of U.S., Euro-Area, and Mexican CPI Studies The studies shown are representative of at least 50% of consumer expenditures. Data on inflation come from the OECD Main Economic Indicators, Banco de M´exico, and the U.S. Bureau of Labor Statistics. The sample period for the United States corresponds to the study of Nakamura and Steinsson (2008). Full references to the euro-area country studies can be found in Dhyne et al. (2005).

My data set captures considerably more variation in inflation than do other studies of consumer prices with comparable product coverage.2 As Figure I indicates, inflation was low and stable in the United States and the euro area relative to Mexico throughout the periods covered by the related studies. For high-inflation economies, the evidence is limited mainly to food products in Israel (Lach and Tsiddon 1992; Eden 2001; Baharad and Eden 2004) and Poland (Konieczny and Skrzypacz 2005) and to supermarket products in Argentina (Burstein, Eichenbaum, and Rebelo 2005). My paper differs from these studies because my data set is representative of a much larger set of goods and services in the CPI. The monthly frequency of price changes varied extensively over my sample period. It rose from an average of 22.1% in 1994 2. For studies on the United States, see Bils and Klenow (2004), Klenow and Kryvtsov (2008), and Nakamura and Steinsson (2008). Dhyne et al. (2005) review the main findings for the euro area.

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to a high of 61.9% at the peak of inflation in April 1995, before leveling off around 27.4% in the last year of the sample. I find some important differences in price-setting behaviors across low- and high-inflation periods. When inflation is low (below 10%–15%), the frequency of price changes is only mildly correlated with inflation, especially when I restrict the sample to goods, in which case the correlation almost entirely disappears. On the other hand, the average magnitude of price changes in such a low-inflation environment displays a tight and almost linear relationship with the level of inflation. As a result, movements in the frequency of price changes account for little of the inflation variance: at most 11% for the full sample and 6% for the subsample of goods, figures that are similar to that of Klenow and Kryvtsov (2008) for the United States (about 5%). By contrast, when inflation is high (above 10%–15%), both the frequency and average magnitude of price changes are strongly correlated with inflation. Movements in the frequency of price changes then comprise an important component of inflation variance. When I decompose price changes between price increases and decreases, I find that the frequency of price increases rises steadily as inflation rises from 0% to 10%–15%. This rise is partly offset by a simultaneous decline in the frequency of price decreases, thereby dampening movements in the overall frequency of price changes. This offsetting effect stems from goods, which have the largest proportion of price decreases. By comparison, relatively few price decreases are observed among services. As inflation rises from a low level, the decline in the occurrence of price decreases relative to price increases exacerbates movements in the average magnitude of price changes. In my data set, the change in the composition of price changes largely explains the strong correlation between inflation and the average magnitude of price changes when inflation is low. Once inflation moves beyond 10%–15%, price decreases have largely disappeared from most sectors of the economy, with the exception of some fresh produce. The frequency of price increases continues to rise steadily with inflation, however, and the frequency of price changes thus becomes highly correlated with inflation. Overall, my empirical results suggest that pricing models should endogenize the timing of price changes if they wish to make realistic predictions at both low and high inflation levels. They also present the challenge of finding a model offering empirically plausible predictions at all levels of inflation. To investigate

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whether menu-cost models are consistent with my findings, I calibrate a discrete-time version of the Golosov and Lucas (2007) model. The model features idiosyncratic technology shocks giving rise to a distribution of both positive and negative nominal price adjustments. I show that the model performs well in terms of predicting the average frequency and magnitude of price changes for levels of inflation similar to the ones experienced by Mexico over my sample period. The success of the model comes in part from the presence of offsetting movements in the frequency of price increases and decreases, and highlights the importance of idiosyncratic shocks in this class of models for delivering empirically plausible predictions. The paper is organized as follows. In the next section, I provide a brief overview of the Mexican macroeconomic context over the sample period. In Section III, I describe the assemblage of my data set and discuss features of the data that are important for interpreting my results. Section IV defines the statistics computed in this paper. The main empirical findings are presented in Section V and are then compared to other studies of high-inflation environments in Section VI. In Section VII, I calibrate a discretetime menu-cost model with idiosyncratic technology shocks and investigate its consistency with some key empirical features reported in the paper. The last section provides concluding remarks. II. MACROECONOMIC CONTEXT The sample period was marked by a severe economic downturn in the wake of the December 1994 peso devaluation. To most observers of the Mexican economy, however, 1994 opened rather positively.3 Inflation had been stabilized successfully below 10%, a major achievement in light of the three-digit rates of the late 1980s, and real interest rates also had decreased. The excess return on the three-month, dollar-denominated Tesobonos was only two percentage points above the American T-bill. The budget deficit, seen by many as the culprit of previous economic crises, had been eliminated in 1992. Moreover, the North American Free Trade Agreement had taken effect on January 1, 1994. Foreign capital entered abundantly with a net inflow over 8% of GDP in 1993. However, growth in real GDP per capita remained modest, averaging 2.5% from 1991 to 1993. Many observers saw 3. See Edwards (1998) for a review of observers’ opinions in 1994.

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(b) Inflation rate 140

100

120

80

100

60 %

%

80 60

40 20

40

0

20 0 1994 1995 1996 1997 1998 1999 2000 2001 2002

1994 1995 1996 1997 1998 1999 2000 2001 2002

(d) Money aggregates (logs, 1994M1=0) 80

200 150

60

M1 M4

%

%

100 40

50 20

0

0 1994 1995 1996 1997 1998 1999 2000 2001 2002

1994 1995 1996 1997 1998 1999 2000 2001 2002

(e) Real output (logs, 1994Q1=0)

(f) Real consumption (logs, 1994Q1=0)

40

30

30

20

%

%

20 10

10 0

1994 1995 1996 1997 1998 1999 2000 2001 2002

0

1994 1995 1996 1997 1998 1999 2000 2001 2002

FIGURE II Main Macroeconomic Indicators Source: Banco de M´exico.

this situation as part of a restructuring process that soon would bring strong growth to the country. The devaluation brought a radical change of mood. On December 22, 1994, the exchange rate collapsed and lost more than ` 40% of its value vis-a-vis the U.S. dollar in the week that followed.4 As depicted in Figure II, short-term interest rates were pushed upward substantially as Banco de M´exico tightened the supply of money to prevent further erosion of the peso and capital flight. 4. Mexico pegged its exchange rate to the dollar in May 1992. In February 1994, the country switched to pre-announced crawling bands around the U.S. dollar.

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The devaluation left major stagflation in its wake. Inflation took off almost immediately, increasing from 6.4% in November 1994 to 44.3% in January 1995 before peaking at 92.0% in April 1995. Real output per capita contracted 9.5% in 1995, whereas private consumption per capita fell a solid 13.2%. Mexicans would have to wait until 1998 for real GDP per capita to surpass its 1994 level and until 1999 for inflation to settle below 10%. The decline in aggregate income, coupled with a rise in fiscal evasion, brought a sharp decline in government revenues.5 To prevent further revenue erosion, the government raised the general rate of the value-added tax rate from 10% to 15% on April 1, 1995. This change affected all Mexican regions, with the notable exceptions of Baja California and a corridor along the country’s southern and northern borders where the rate remained at 10%. III. MEXICAN MICRO DATA ON CONSUMER PRICES III.A. Description of Sources The data comprise price quotes collected by Banco de M´exico for computing the Mexican CPI. Most price quotes correspond to narrowly defined items sold in specific outlets (e.g., corn flour, brand Maseca, bag of 1 kg, sold in outlet 1100 in Mexico City). A limited number of quotes are citywide indices, or the average prices of small samples of narrowly defined items belonging to the same category and outlet. Since January 1994, the official gazette of the Mexican government, the Diario Oficial de la Federaci´on, has published price quotes every month. This publication releases each quote with a key linking the item to a specific outlet, city, and product category; these keys allow me to track individual prices over time.6 In this paper, I refer to an item’s complete price history as its price trajectory. The raw data set contains a total of 4.7 million price quotes from January 1994 to June 2002. Banco de M´exico is required to make individual prices available to the public up to six months after their publication, but it does not keep a historical data set of individual prices. The data set was assembled by merging the information released in the Diario. The data for the months of January 1994 to February 1995 could not be extracted electronically, 5. See OECD (2000) for a description of the taxation system. 6. Items from the same outlet are attributed store keys independently to ensure confidentiality.

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so they were typed in from original hard copies of the Diario using double-entry keying, a process ensuring a characterwise accuracy in excess of 99.998%.7 About 430,000 price quotes were added to the database in this way. Precise item descriptions were published in March 1995. The Diario also includes lists of items that are periodically added to or dropped or substituted from the CPI basket. Unlike additions, substitutions are not planned events. They occur when the characteristics of an item (weight, size, model, presentation, etc.) change, when an outlet stops carrying an item, or, in rarer cases, when an outlet goes out of business. The weights used in the CPI are derived from the Survey of Households’ Income and Expenditures (ENIGH). The CPI product categories are representative of all ENIGH categories accounting for at least 0.02% of households’ expenditures. This ensures a coverage of well above 95% of Mexican households’ expenditures. To facilitate comparisons with other studies, I classify each product category according to the euro-area classification of individual consumption by purpose (COICOP). III.B. Sample Coverage In January 1994, the CPI contained 30,692 price quotes spread over 302 product categories. By June 2002, the last month in my sample, it had expanded to nearly 50,000 price quotes distributed over 313 product categories. A major revision of the basket occurred in March 1995 when the number of cities covered in the CPI grew from 35 to 46. At the same time, 29 new product categories were introduced into the basket, and 18 were abandoned. This revision had been planned long before the peso’s devaluation. In July 2002, Banco de M´exico updated the basket again to reflect the structure of Mexican households’ consumption in 2000. I cannot link items before and after the 2002 basket revision because of a change to the item keys. To ensure the greatest comparability across time, I compute my results for a sample covering January 1994 to June 2002 using the expenditure weights implemented in March 1995.8 The sample is further restricted to the product categories comprising individual prices that were unaffected by the 1995 basket revision and I consider only items whose price was 7. I thank Chris Ahlin for lending me original copies of the Diario. 8. These weights are derived from the 1989 ENIGH survey. They were updated using relative prices to reflect consumer expenditures in 1993.

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QUARTERLY JOURNAL OF ECONOMICS TABLE I MAIN SAMPLE STATISTICS Period Price quotes Total Average per month Trajectories Substitutions Product categories

January 1994–June 2002 3,209,947 31,470 44,272 10,457 227

CPI coverage (%)

54.1

Sample composition (%) Unprocessed food Processed food Energy Nonenergy industrial goods Services

26.4 21.7 0.4 26.4 25.1

not regulated. In addition, most education services and clothing items were dropped for reasons detailed below. The final sample contains 3.2 million price quotes from over 44,000 price trajectories and covers 54.1% of CPI expenditures. The main groups of products excluded are rents and homeowners’ imputed rents, clothing (except for a few product categories containing individual observations), and education services, whose weights in the CPI are, respectively, 14.0%, 6.0%, and 3.5%. Food items represent just under half of the expenditures in the final sample, a proportion higher than in most U.S. and euro-area studies. Summary statistics are presented in Table I. III.C. Other Aspects of the Data I now address features of the data that are important to consider in interpreting the results. The most significant issue is price averaging. Banco de M´exico collects prices twice monthly for all items but food; food price collection occurs four times per month.9 The collected prices are then averaged to produce the monthly figures reported in the Diario. Observing the monthly average rather than the actual price of an item complicates the inference about price changes. For example, an average price of $2 for an item is 9. In the United States, the BLS collects prices monthly for food consumed at home, energy, and a few additional items with volatile prices. Other prices are collected monthly for the three largest metropolitan areas (New York, Los Angeles, and Chicago) and every other month for the remaining areas.

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consistent with an actual price of $2 throughout the month. It also is consistent with an actual price of $1.50 in the first half of the month and $2.50 in the second, or any combination of prices with $2 as their average. Moreover, changes to an average-price series are typically more frequent and smaller on average than changes to an actual-price series with the same publication frequency. For example, a price hike from $1.50 to $2.50 in the middle of the month results in an average price of $2, which is $0.50 short of the new actual price, so that another change to the average-price series will likely be recorded in the next month. To make my results as comparable as possible to other studies, which typically do not use averaged price quotes, I have constructed alternative price trajectories that filter out the effect of averaging observations whenever possible. These new series correspond to the end-of-month series, which both are consistent with the published average prices and minimize the number of price changes. Appendix I provides an extensive discussion of how averaging observations affects inferences about the timing and magnitude of price changes, and of how the filter was implemented. I was provided with unpublished semimonthly data by Banco de M´exico, which allows me to directly assess the performance of the filter. Overall, the filtered series are much closer to the end-ofperiod price series that they aim to reproduce. More importantly, the filtered series capture the timing of price changes with great accuracy. All the main patterns described in this paper are found whether prices are filtered or not. Another data issue is that price collectors do not always directly observe prices. Sometimes an item is out of stock, out of season or, in rarer cases, the outlet is closed when the CPI agent visits. In such situations, the price from the previous period is carried forward. Although I cannot identify prices that were imputed in my sample, I do find clear indications that the number of imputations was larger at the beginning of the sample. Item substitutions represented less than 0.1% of all published price quotes in 1994, a proportion that rose to 1.2% in 2001. A more systematic treatment of substitutions was implemented in 2001. Prices can now be carried forward for at most a month and a half before a substitution is sought. If the scarcity is generalized, this allowance can be extended up to three months. This methodological change likely creates a slight downward bias in the estimated frequency of price changes at the beginning of the sample.

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Prices are inclusive of sales as long as they are conditional on the purchase of a single item. For example, in a three-for-two promotion, the regular price would be reported. In the United States, the Bureau of Labor Statistics reports prices net of sales and promotions whenever possible; the same three-for-two promotion would result in a temporary 33% price decrease. There is no variable in the Mexican data set signaling that an item is on sale or that a promotion is going on. Most price quotes for the product categories of textiles, clothing, shoes, and related accessories are averages of small samples of item prices; all items within a sample pertain to the same outlet whenever possible. Banco de M´exico uses store samples to alleviate the problems associated with rapidly appearing and disappearing items due to changes in fashion and the seasons. All such samples were dropped from my analysis to limit the discussion to individual price changes. The decision to include or exclude store samples has little impact on the main findings. All education services observations, which cover registration, activity, and tuition fees, were also dropped from the sample. These services are typically not available for purchase or not sampled during most months of the year. Prices are mechanically carried forward until the start of the next registration period, semester, or academic year. For this reason, one cannot directly interpret the absence of price changes in the monthly series as evidence of price stickiness. A final issue is that item substitutions often accompany changes in product characteristics, thereby raising the question of whether substitutions should be treated as price changes. The Inflation Persistence Network’s approach is to assume that all item substitutions not previously planned by CPI agencies involve a price change, a choice guided in part by the absence of substitution flags in some of the national databases. In this paper, substitutions were instead excluded from the computation of price changes because their treatment varied over the sample period. The main patterns found in this paper are not affected by this choice. IV. INFLATION ACCOUNTING PRINCIPLES Whenever a price is reported for two consecutive months, I create an indicator that a price change has occurred, 1 if pit = pit−1 Iit = 0 if pit = pit−1 ,

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where pit is the price of item i (in logs) during month t. Inflation is defined as πt = i∈ϒt ωit pit , where pit = pit − pit−1 , ωit is the sample weight of item i, and ϒt is the set of all items in the sample for which Iit is defined. For ωit , I use the sample share of spending on the product category to which item i belongs, divided by the number of items in that product category for which I can compute a price change at t. Inflation can also be expressed as

πt =

i∈ϒt ωit pit ωit Iit . i∈ϒt i∈ϒt ωit Iit

fr

t

dpt

The term frt , henceforth referred to as the frequency of price changes, is the share of spending in the sample on items whose price changed at month t. The term dpt is the average magnitude of those price changes. In the popular Taylor (1980) and Calvo (1983) models with uniform staggering of price changes, dpt is the only possible source of variation in πt . It is convenient to decompose inflation further into a weighted sum of price increases and decreases: + i∈ϒt ωit Iit pit + ωit Iit πt = + i∈ϒt i∈ϒt ωit Iit

+ frt

dpt+

− i∈ϒt ωit Iit pit − + ωit Iit . − i∈ϒt i∈ϒt ωit Iit

− frt

dpt−

This decomposition is informative about the relationship between inflation and the distribution of price changes. The computation of inflation statistics for special aggregates, such as goods and services, also follows the approach outlined above. My methodology for computing inflation is similar to the approach taken in most euro-area and U.S. studies of individual price changes but differs from that of Banco de M´exico at the time, which computed inflation as the percentage change in a Laspeyres index. Despite differences in sample coverage, methodology, and filtering of price trajectories, the inflation rate in my sample is strongly correlated with the change in the official CPI:

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The coefficient of correlation is 0.96 over the full sample period and 0.85 over the last three years of the sample.

V. MAIN EMPIRICAL RESULTS This section presents the key empirical findings, focusing on the relationship between inflation and the frequency and average magnitude of price changes. I treat (nonregulated) goods and services separately throughout the discussion due to differences in the way prices are set between the two groups.10 I place a special emphasis on the results for goods, given their predominance in my sample and their greater representativeness. V.A. Setting of Consumer Goods Prices My subsample of goods accounts for 74.9% of all expenditures in my basket and is representative of 77.5% of Mexican consumer expenditures on goods (excluding energy). Most goods left out of the sample pertain to product categories falling under the apparel and related accessories group. Frequency of Goods Price Changes. As seen in the upper panel of Figure III, movements in the frequency of price changes and inflation were very large over the sample period. In April 1995, the rate of inflation in my sample of goods peaked at 86.0% (7.2% in monthly terms). This rate is much higher than the average in 1994 (7.5%) or during the last year of the sample (1.5%). The frequency of price changes also peaked in April 1995, when the price of 64.7% of goods, measured in CPI weights, changed during the month. This number is more than twice the average frequency of 26.8% in 1994. There were large variations in the composition of price changes over the sample period, as shown in the lower panel of Figure III. At the peak of inflation, only 8.9% of price changes were negative, a proportion that rose to 46.0% in the last year of the sample. The corresponding proportion for the full sample of goods and services over the last year of the sample is 43.4%, a figure echoing those from U.S. and euro-area studies. 10. For the products in my sample, the COICOP goods/services classification is almost identical to the Bank of Mexico’s tradables/nontradables classification. The results reported in the paper for goods and services thus have an alternative interpretation in terms of tradables and nontradables.

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PRICE SETTING DURING LOW AND HIGH INFLATION (a) Frequency of price changes and inflation

Frequency Inflation

80

%

60 40 20 0 1994

1995

1996

1997

1998

1999

2000

2001

2002

(b) Frequency of price increases and decreases 60 Increases Decreases

50

%

40 30 20 10 0 1994

1995

1996

1997

1998

1999

2000

2001

2002

FIGURE III Monthly Frequency of Price Changes (Nonregulated Goods) All statistics in the figure, including inflation, are computed using the sample of nonregulated goods.

Positive comovement between frt and πt is clearly visible in Figure III. The correlation coefficient between the two series is 0.91 for the whole period.11 This correlation is largely driven by the high-inflation episode, however; it is about zero if I consider only the last three years of the sample. After mid-1996, it is difficult to spot any downward drift in the frequency of price changes, even though inflation trends down. The reason behind this loose relationship is apparent in the lower panel of Figure III, where I − break down frt into fr+ t and frt . As inflation declined, so did the frequency of price increases. At the same time, price decreases became more frequent, thereby dampening movements in the overall frequency of price changes. A look at the correlation between 11. All correlation statistics presented in this section are computed using linearly detrended series.

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− fr+ t , frt , and πt provides further evidence of these offsetting movements. In the last three years of the sample, the correlation is − 0.59 between fr+ t and πt , and −0.74 between frt and πt . The net result is a relative absence of correlation between frt and πt for my sample of goods over that period. There are a few apparent large negative movements in the inflation series of goods over the low-inflation period, in particular in March 1999, February 2001, July 2001, and February 2002, which are associated with unusually large changes in fresh produce prices. Shocks to the supply of fruits and vegetables, such as unusual weather conditions, can have a notable impact on the price of these items because they are perishable in nature. Some evidence of opposite movements in the frequency of price increases and decreases is apparent for these months. The scatterplot in the upper left panel of Figure IV offers a view from a different angle of the relationship between the monthly frequency of price changes and inflation. Similar scatterplots for price increases and decreases are shown in the middle left and lower left panels, respectively. All panels display linear regression lines that use linear, quadratic, and cubic goods inflation terms as explanatory variables, as well as a full set of year dummies. The dummies are included to account for potential shifts in the relationships over time that are unrelated to inflation, such as fluctuation in aggregate demand, basket composition, and methodology. I present regression lines for two sets of observations. The dashed lines include all monthly observations in the sample. The solid lines exclude April 1995, which was marked by a 5-percentage-point increase in the value-added tax, as well as all periods with negative inflation, which effectively removes all large shocks to food produce mentioned earlier. Variations in the supply of fresh fruits and vegetables and value-added tax changes are shocks that differ in nature from a general rise in the price level. For this reason, my discussion of the scatterplots focuses on the regression results for the smaller sample, as they likely capture the overall relationship between inflation and its components better. All regression statistics can be found in Table II. When inflation is zero, each percentage-point increase in the rate of nonregulated-goods inflation is associated with a 0.35 (0.13)-percentage-point rise in the frequency of price increases and an opposite 0.22 (0.06)-percentage-point decline in the frequency

PRICE SETTING DURING LOW AND HIGH INFLATION (a) Frequency of price changes

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(b) Magnitude of price changes

70

15

10

50

Magnitude (%)

Frequency (%)

60

40 30 20

0

0

Data All observations Excluding π 0 if (u, v) ∈ E and c(u, v) = 0 otherwise. The capacity measures the utility benefits that agents derive from their relationships. For ease of presentation, we assume that the strength of relationships is symmetric, so that c (u, v ) = c (v, u) for all u and v.8 Our model consists of five stages, which are depicted in Figure II. We begin by describing the model and then discuss the economic content of our modeling assumptions. Stage 1: Realization of Needs. Two agents s and t are randomly selected from the social network. Agent t, the lender, has an asset that agent s, the borrower, desires. The lender values the asset at V , and it is assumed that V is drawn from some prior distribution F over [0, ∞). The identity of the borrower and the lender and the value of V are publicly observed by all players. 8. Our results extend to the case where capacities are asymmetric. In that environment, the social network can be represented as a directed graph and the directed network flow determines borrowing.

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Stage 2: Borrowing Arrangement. At this stage, the borrower publicly proposes a transfer arrangement to all agents in the social network. The role of this arrangement is to punish the borrower and compensate the lender in the event of default. A transfer arrangement consists of a set of transfer payments h (u, v ) for all u and v agents involved in the arrangement. Here h (u, v ) is the amount u promises to pay v if the borrower fails to return the asset to the lender. Once the borrower has announced the arrangement, all agents involved have the opportunity to accept or decline. If all involved agents accept, then the asset is borrowed and the borrower earns an income ω (V ), where ω is a nondecreasing function with ω (0) = 0. If some agents decline, then the asset is not lent, and the game moves on directly to stage 5. Stage 3: Repayment. Once the borrower has made use of the asset, he can either return it to the lender or steal it and sell it for a price of V .9 If the borrower returns the asset, then the game moves to the final stage 5. Stage 4: Transfer Payments. All agents observe whether the asset was returned in the previous stage. If the borrower did not return the asset, then the transfer arrangement is activated. Each agent has a binary choice: either he makes the promised payment h (u, v ) in full or he pays nothing. If some agent u fails to make a prescribed transfer h (u, v ) to v, then he loses his friendship with agent v (i.e., the (u, v ) link “goes bad”). If (u, v ) link is lost, then the associated capacity is set to zero for the remainder of the game. We let c (u, v ) denote the new link capacities after these changes. Stage 5: Friendship Utility. At this stage, agents derive utility from their remaining friends. The total utility enjoyed by an agent u from his remaining friends is simply the sum of the values of all c (u, v ). remaining relationships, that is, v Our model is a multistage game with observed actions. Let u denote the set of agent u’s pure strategies and let = ×uu. We focus on the set of pure strategy subgame perfect equilibria below.

III.B. Discussion of Modeling Assumptions We now discuss some of the assumptions underlying our model. 9. As we show in Appendix II, the model can be extended to the case where the liquidation value of the asset is φ · V with φ ≤ 1.

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Social Sanctions. When an agent fails to make a promised transfer, we assume that the associated friendship link automatically goes bad, capturing the idea that friendly feelings often cease to exist if a promise is broken. Appendix II develops explicit micro foundations for this assumption. In these micro foundations, which build on Dixit (2003), failure to make a transfer is a signal that the agent no longer values his friend, in which case these former friends find it optimal not to interact with each other in the future. An alternative justification is that people break a link for emotional or instinctive reasons when a promise is not kept; Fehr and Gachter (2000) provide evidence for such behavior. Circle of Trust. For large social networks it can be unrealistic for the borrower to include socially distant agents in the arrangement. All our results hold if we restrict the set of links over which transfer payments can be proposed to some subgraph of the original network, the “circle of trust,” which may depend on the identity of the borrower and the lender. The only difference in our results is that the network flow measure of the borrowing limit will have to be computed in the subgraph of permissible links. Transfer Arrangement as Social Norms. The transfer arrangement in our model can be interpreted either as an explicit agreement between all parties or as a representation of accepted norms of behavior. In the second interpretation, agents simply share an understanding about what they are expected to do in the event of default. Cash Bonds and Borrowing Constraints. One way to solve the moral hazard problem is to have the borrower post a cash bond to the lender, which is returned only if the borrower does not default on the asset loan. We abstract away from bonds and prepayments by assuming that the borrower is initially cash-constrained. However, we do allow the borrower and other agents to make payments in later stages of the game. This can be justified if agents work or make investments in the initial stage, generating income in later stages; or if transfers are in-kind, for example, helping out with the harvest, where posting a bond may be inefficient or infeasible. III.C. Equilibrium Analysis For what values of V can borrowing be implemented in a subgame perfect equilibrium? We begin answering this question

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by studying equilibria where all promises are kept, that is, where every transfer h (u, v ) is expected to be paid if the borrower fails to return the asset. We later show that focusing on these equilibria is without loss of generality. In any equilibrium where promises are kept, transfers have to satisfy the capacity constraint (1)

h(u, v) ≤ c(u, v).

This is simply an incentive compatibility constraint. If the borrower fails to return the asset, agent u has to decide whether to make his promised transfer payment h (u, v ) to v. The cost of making the payment is h (u, v ); the cost of not making the payment is c (u, v ), because it results in losing the friendship with v. In any equilibrium where promises are kept, u must prefer the friendship over the monetary value of the transfer, leading to (1). Two-Agent Network. To build intuition, we begin the equilibrium analysis with the case where the social network consists only of the borrower s and the lender t. Let σ be a pure strategy subgame perfect equilibrium that implements borrowing where promises are kept. In any such equilibrium, V ≤ h (s, t). To see why, assume that the borrower s defaults on the equilibrium path. Then the lender receives the transfer payment h (s, t) instead of the asset; but he must break even to lend, which yields V ≤ h (s, t). On the other hand, if the borrower returns the asset on the equilibrium path, then he must weakly prefer not to default, which again requires V ≤ h (s, t). Combining this inequality with the capacity constraint (1) then yields (2)

V ≤ c(s, t),

showing that borrowing is limited by the maximum flow in this simple network. It is also easy to see that when (2) is satisfied, there exists an equilibrium that implements borrowing: just set h (s, t) = V .10 Intuitively, the collateral value of friendship can be used to elicit payment and thus solve the agency problem. Four-Agent Network. To gain intuition about borrowing in more general networks, we next consider the network depicted 10. In this equilibrium, all surplus accumulates to the borrower because of our assumption that he proposes the transfer arrangement. In a setup where bargaining power is more evenly distributed, we expect that the surplus would be shared by the agents involved in the transfer arrangements, in a manner similar to Goyal and Vega-Redondo (2007).

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c(

c(

)

c(

)

s

u

t

Borrower

Intermediary

Lender

FIGURE III Borrowing in a Four-Agent Network This figure illustrates borrowing in networks with intermediaries. The arrangement favored in our paper involves transfers flowing from s through u to t in the event of default. In this arrangement the weakest link, min[c(s, u), c(u, t)], determines the borrowing limit. An alternative arrangement, where cousin v promises to punish the borrower s in case of default, sometimes enforces better outcomes. However, this arrangement is not robust to side deals by groups of agents: the borrower and his cousin can jointly deviate, steal the asset, and short-change the lender. As we show in the text, all side deal–proof arrangements satisfy the weakest link requirement.

in Figure III, which consists of four players: the borrower s, the lender t, an intermediate agent u connecting s and t, and an agent v who is connected only to the borrower s. We will refer to v as the “cousin” of s. A natural transfer arrangement that implements borrowing in this network is one where agent u acts as an intermediary who elicits and transits payments from s to t in the case of no compliance, and gets zero net profits. To formalize this arrangement, simply set h (s, u) = h (u, t) = V . For this arrangement to be incentive compatible, the capacity constraint (1) must be satisfied for both links involved: V ≤ c (s, u) must hold so that s delivers the transfer to u, and V ≤ c (u, t) is needed to ensure that u passes on the transfer to t. Combining these yields the “weakest link” inequality (3)

V ≤ min [c (s, u) , c (u, t)] ,

which implies that the maximum flow determines the borrowing limit in this transfer arrangement. However, networks with more than two agents generally admit other subgame perfect equilibria that can implement borrowing even if (3) fails. We argue that these equilibria are implausible, because they fail a natural coalition-proofness requirement. To illustrate, assume that the borrower s has a strong link to his cousin

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v, with a capacity value of c (s, v ) = V + 1. The borrower might then propose an informal arrangement in which he promises to pay his cousin a transfer of h (s, v ) = V + 1 in case he fails to return the asset. This arrangement provides the right incentives to the borrower, and is a subgame perfect equilibrium even if (3) fails. To understand its logic, note that in this arrangement, the borrower essentially makes the following proposal to the lender: “Lend me your asset; if I don’t return it to you, my cousin will be angry with me.” As this interpretation makes it clear, this borrowing arrangement may not be robust to joint deviations where both the borrower and his cousin depart from equilibrium. More concretely, the borrower could circumvent the arrangement by entering a side deal with his cousin, in which he steals the asset and shares the proceeds with the cousin (who in equilibrium would otherwise receive nothing). Due to the possibility of such side deals, we do not find this equilibrium plausible. A similar potential equilibrium is one where the intermediate agent u provides incentives to the borrower but promises a zero transfer to the lender. In this case, the lender effectively “outsources” monitoring to the intermediary, trusting that the borrower will always return the asset rather than pay a high transfer to u. This arrangement is again open to side deals: here s and u can choose to steal the asset jointly and split the proceeds, leaving the lender with nothing. As in the equilibrium with the cousin, the possibility of a side deal arises because nobody “monitors the monitor”: the lender is not fully in control of incentives. When enforcement is outsourced to either the cousin or the intermediary, these agents can team up with the borrower and steal the asset. These examples suggest that when the borrower and other agents can agree to side deals, it may not be in the interest of the lender to provide the asset. This motivates our focus on subgame perfect equilibria that are immune to such side deals. III.D. Side Deal–Proof Equilibrium Consider the subgame starting in stage 2, after the identities of the borrower and the lender and the value of the asset are realized, and for any pure strategy σ ∈ , let Uu (σ ) denote the total utility of agent u in this subgame. We formalize the idea of a side deal as an alternative transfer arrangement h (u, v ) that s proposes to a subset of agents S ⊂ W after the original arrangement is accepted. If this side deal is accepted, agents in S are expected to make transfer payments according to h, whereas agents outside

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S continue to make payments described by h. For the side deal to be credible to all participating agents, it must be accompanied by a proposed path of play that these agents find optimal to follow. This motivates the following definition. DEFINITION 2. A side deal with respect to a pure strategy profile σ is a set of agents S, a transfer arrangement h(u, v) for all u, v ∈ S, and a set of continuation strategies { σu | u ∈ S} proposed by s to agents in S at the end of stage 2, such that σu, σ S\u, σ−S ) ≥ Uu(σu , σ S\u, σ−S ) for all σu and all u ∈ S, (i) Uu( σ S , σ−S ) ≥ Uu (σ S , σ−S ) for all u ∈ S, and (ii) Uu ( (iii) Us ( σ S , σ−S ) > Us (σ S , σ−S ). Condition (i) says that all agents u involved in the side deal are best-responding on the new path of play, that is, that the proposed path of play is an equilibrium for all agents in S conditional on others playing their original strategies σ−S . Condition (ii) says that if any agent u ∈ S refuses to participate in the side deal, then play reverts to the original path of play given by σ . Finally, (iii) ensures that the borrower s strictly benefits from the side deal. DEFINITION 3. A pure strategy profile σ is a side deal–proof equilibrium if it is a subgame perfect equilibrium that admits no side deals. It is easy to see that this condition rules out the equilibria violating the weakest link inequality (3) in Figure III. We now turn to extend this result to general networks.11 III.E. Main Theorem We begin by formally defining the concept of network flows intuitively discussed above. DEFINITION 4. An s → t flow with respect to capacity c is a function f : G × G → R that satisfies the following: (i) Skew symmetry: f (u, v) = − f (v, u). (ii) Capacity constraints: f (u, v) ≤ c(u, v). (iii) Flow conservation: w f (u, w) = 0 unless u = s or u = t. 11. Our definition of side deal–proof equilibrium does not require side deals to be robust to further side deals. However, as the proof in Appendix I makes clear, imposing this requirement would not change any of our results: when there is a deviating side deal, there is also one that is robust to further coalitional deviations, namely the side deal implemented with a network flow.

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The value of a flow is the amount that leaves the borrower s, given by | f | = w f (s, w). Let T st (c) denote the maximum value among all s → t flows. THEOREM 1. There exists a side deal–proof equilibrium that implements borrowing between s and t if and only if the asset value V satisfies (4)

V ≤ T st (c).

This result states that the endogenous borrowing limit equals the value of the maximum flow between borrower s and lender t. We interpret the borrowing limit T st (c) as a measure of networkbased trust: if s can borrow more from t, it must be that t has higher trust in s. The logic of the proof of Theorem 1 is as follows. When V satisfies inequality (4), a side deal–proof equilibrium is easy to construct: by assumption, there exists an s → t flow with value V , and this flow can be used as a transfer arrangement. Flow conservation implies that all intermediate agents break even, confining their role to simply extracting and transmitting the payment V from s to t in case s fails to return the asset. Thus the lender is in full control of incentives; because of this, the equilibrium is easily seen to be side deal–proof. To show that no side deal–proof equilibrium can implement a higher level of borrowing, we build on the maximum flow– minimum cut theorem (Ford and Fulkerson 1956), which states that the maximum network flow between s and t equals the value of the minimum cut. A cut is a disjoint partition of the nodes into two sets G = S ∪ T such that s ∈ S and t ∈ T , and the value of the cut is defined as the sum of c (u, v ) for all links such that u ∈ S and v ∈ T . For any borrowing arrangement violating (4), we can construct a side deal in the following way. Fix a minimum cut (S, T ); the maximum flow–minimum cut theorem implies that the total capacity of all links between S and T is less than V . But then agents in S have a profitable side deal: by defecting as a group, they lose less than V in foregone friendships, but gain V from selling the asset. For a concrete example, consider the network with the cousin in Figure III and suppose that c (s, u) < c (u, t). The minimum cut between s and t has value c (s, u), and the corresponding partition is simply S = (s, v ) and T = (u, t). In any equilibrium where V > c (s, u), that is, where (4) is violated, agents in

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QUARTERLY JOURNAL OF ECONOMICS A. Original network

3

B. Auxiliary network

4 s1

s

2

1 v

4

3

u

t

3.5

s2

3

u

2 2

1

t

v

FIGURE IV Maximum Network Flow with Transfer Constraints This figure illustrates network flow with transfer constraints. Agent s could normally borrow an asset up to value 4 from agent t. However, he faces a binding transfer constraint of 3.5. We can calculate network flow in the constrained graph by drawing an auxiliary network where we split s into two agents s1 and s2 . All incoming links of agent s are connected to s1 and all outgoing links emanate from agent s2 . A directed link from s1 to s2 has capacity equal to the transfer constraint. The network flow from s1 to agent t equals the maximum network flow with transfer constraint.

S have a side deal: the borrower s and his cousin v can team up to steal the asset, because their total repayment is limited by the value of the cut c (s, u). III.F. Extensions: Transfer Constraints and Endogenous Circle of Trust Transfer Constraints. In environments with credit constraints, agents might have limits on the total amount they can borrow or transfer. For example, in Figure IVA, the intermediaries u and v might worry that if the borrower s carried too large a debt burden, he would be unable to pay. We show that the concept of network flows can be used to characterize borrowing in this environment as well. To introduce borrowing and transfer constraints in a simple way, suppose that each agent u can make a total payment of at most ku to others in the network, where the transfer constraints ku are exogenous. Here ku can represent either cash or time constraints.12 How much borrowing can be implemented in this environment? We show that the answer is given by the maximum flow in a modification of the social network, where each agent u is replaced by two identical agents connected by a link with capacity 12. For an intermediate agent (but not for the borrower), incoming transfers may help relax cash constraints. For these intermediate agents, ku represents constraints that remain after incoming payments; for example, these could be time constraints if the transfers were in-kind services, such as helping out, which cannot be easily passed on.

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ku. To formally construct this auxiliary (directed) network G , replace each node u in G with a pair of nodes, u1 and u2 , and replace each (u, v) link with two new directed links, a u2 → v1 link and a v2 → u1 link, each with capacity equal to c(u, v). Finally, for each agent u, create a new u1 → u2 link with capacity equal to the transfer constraint c(u1 , u2 ) = ku. That is, we duplicate all agents u, point all incoming links of u to u1 , have all outgoing links of u originate in u2 , and let the capacity of the u1 → u2 link be ku. For example, consider the network in Figure IVA, where agent s faces a binding transfer constraint of 3.5. The corresponding auxiliary network is drawn in Figure IVB and we can deduce that the constrained network flow equals 3.5, the flow from agent s1 to agent t in the auxiliary graph. In Appendix I we show that in any side deal–proof equilibrium where promises are kept, the borrowing limit in the presence of transfer constraints equals the value of the maximum s1 → t1 flow in G . To understand the intuition, consider a maximal flow. As in the basic model, the amounts assigned to links between agents by this flow can be interpreted as the transfer payments in a candidate transfer arrangement. It remains to verify that, in this arrangement, no agent u exceeds his total transfer constraint ku. But this follows by construction of G . The total transfers promised by u must be equal to the flow leaving u2 in G ; but by flow conservation, this must be equal to the value carried over the u1 → u2 link, which is bounded by the link capacity of ku in G . Circle of Trust. We can endogenize the “circle of trust,” that is, the set of permissible links over which transfer arrangements can be proposed, by assuming that there is a fixed cost associated with proposing various transfer arrangements. For each subgraph G0 ⊆ G, let κ(G0 ) ≥ 0 denote the cost of a transfer arrangement that includes all links in G0 .13 Assume that κ is monotone in the sense that if G0 ⊆ G 0 then κ(G0 ) ≤ κ(G 0 ). The function κ can be interpreted as a characteristic of the community’s social norm; for example, in a kin-based society, we expect κ to be zero or small for most family and relative links. Agent s, who wishes to borrow V from t, must now solve the cost-minimization problem min{κ(G0 )|G0 ⊆ G such that TGst0 ≥ V }, where TGst0 is the trust flow between s and t in G0 . The solution 13. For two networks G = (W, E) and G = (W , E ), we say that G ⊆ G if W ⊆ W and E ⊆ E.

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G∗0 , if it exists, is the minimum cost subgraph where borrowing V can still be supported. Agent s then chooses to borrow if and only if his profit from the loan exceeds the cost, that is, ω(V ) ≥ κ(G∗0 ). Besides its added flexibility, this framework also yields two new implications. (1) The set of people involved in an arrangement is endogenously determined: the greater the profits ω(V ), the more the borrower is willing to extend his circle of trust.14 (2) With positive κ, agents only borrow when profits are high enough; assets that generate low returns are never secured through social collateral. IV. APPLICATIONS IV.A. Network Structure and Welfare We now explore how the network structure affects the payoffs from borrowing in the social collateral model. Because the network is completely summarized by the vector of capacities c, the borrowing limit T st (c) can be viewed as a “trust map” that determines, as a function of the network structure c, how much trust is created between s and t. To see how trust determines payoffs, let st (c) denote the expected payoff of s from borrowing, conditional on the lender being agent t; then z (5) st (c) = (T st (c)), where (z) = ω(v) dF(v), 0

because the payoff is just the expectation of ω(V ) over all values of V that do not exceed the borrowing limit T st (c). Changes in the network affect the payoffs through changes in the trust flow T st (c). Our goal in this section is to characterize these welfare effects.15 Monotonicity. We first explore the effect of increasing connectivity by adding new links or strengthening existing links. We say that the network associated with capacity c1 is more strongly connected than that associated with c2 if no link has lower capacity under c1 than under c2 ; that is, c1 (u, v) ≥ c2 (u, v) for all u, v ∈ W. We then have the following monotonicity result. 14. Formally, an increase in ω(V ) holding fixed V can change the sign of ω(V ) − κ(G∗0 ) from negative to positive and induce borrowing. 15. Besides the profit from borrowing st (c), the borrower s also derives utility from his friends. In the subsequent analysis we focus on the payoff from borrowing.

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PROPOSITION 1. If the social network with capacity c1 is more strongly connected than the network with capacity c2 , then for any borrower s and lender t, both trust and payoffs are higher: T st (c1 ) ≥ T st (c1 ) and st (c1 ) ≥ st (c1 ). Networks with more and stronger links generate more trust and higher payoffs due to the increased supply of social collateral. A large body of work in sociology relies on the result formalized here: Putnam’s (1995), for example, argues that “networks of civic engagement (. . . ) encourage the emergence of social trust.” The fact that this monotonicity emerges naturally in the social collateral model makes it a useful candidate for exploring other questions related to network-based trust. Closure and Structural Holes. We now turn to study how the deeper structure of the network affects payoffs, focusing on changes in network closure, a concept often discussed in the sociology literature. Networks have high closure if the neighborhoods of connected agents have a large overlap. To illustrate, consider the two network neighborhoods of agent s in Figure V, which is a small variation of Figure 1 in Coleman (1988). The neighborhood of s in Figure VB has higher closure, because the friends of s are directly connected. This idea of closure can also be formulated using network paths: a neighborhood has high closure if it connects s to few others through many paths (as in Figure VB), whereas it has low closure if it connects s to many others through fewer paths each (Figure VA). The sociological literature has two views about the benefits of closure. One view, dating back to Coleman (1988), argues that high closure is good because it facilitates sanctions, making it easier for individuals to trust each other. In his discussion of the wholesale diamond market in New York City, Coleman explains that “If any member of this community defected through substituting other stones or stealing stones in his temporary possession, he would lose family, religious and community ties.” Similarly, in the context of Figure V, Coleman argues that in the high closure network of Figure VB, agents t1 and t2 can “combine to provide a collective sanction, or either can reward the other for sanctioning.” In contrast, Granovetter (1973) and Burt (1995) argue that loose networks with low closure lead to higher performance, because they allow agents to reach many others through the network. Burt also emphasizes the role of structural holes, that is, people who bridge otherwise disconnected networks: for example,

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B. High closure

A. Low closure

t3

t4

t3

t4

t1

t2

t1

t2

s

s

FIGURE V Network Neighborhoods with Increasing Network Closure This figure shows network neighborhoods with increasing network closure. The two neighborhoods shown are a small variation on Figure 1 in Coleman (1988). With unit link capacities, agent s is connected through four paths to the rest of the network in both neighborhoods. In a low-value exchange environment, the neighborhood in Panel A is more attractive because it provides access to more people. In a high-value-exchange environment, the neighborhood in Panel B is more attractive, because closure allows borrowing high-valued assets from t1 and t2 .

s is a structural hole in Figure VA but not in VB. According to Burt (2000), these structural holes “broker the flow of information between people, and control the projects that bring together people from opposite sides of the hole.” A key part of this argument is that low-closure networks provide easier access to small favors, advice, information, and other resources. To explore these issues in the social collateral model, we first develop a measure of network closure, building on the idea that high closure is associated with having multiple paths to a smaller set of agents. We begin by counting the total number of paths of an agent, using the concept of network flows. Fix a network with integer-valued capacities c; then the network flow T st (c) is effectively the number of disjoint paths of unit capacity between s and t. Thus, the total path number for s is simply T s (c) = t∈W T st (c). In Figure V, s has a total of four paths in both networks; the difference in closure comes from the fact that in VA, these four paths reach four different people, whereas in VB they reach only

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two people, but there are two paths connecting s with either of them.16 To generalize this observation, let P s (n) denote the share of paths s has with agents to whom he has at least n paths, so that P s (2) = 0 in Figure VA and P s (2) = 1 in Figure VB.17 Clearly, P s (0) = 1 always, and P s (n) is nonincreasing in n. DEFINITION 5. The network neighborhood of s has a higher closure than the neighborhood of s if

(i) T s (c) = T s (c) so that s and s have the same total number of paths; and

(ii) For each n, P s (n) ≥ P s (n), so that a greater share of paths connect s to people with whom he has many paths. These conditions imply that if the neighborhood of s has higher closure, then s is connected to fewer people through many paths.18 This definition allows us to compare high- and low-closure neighborhoods. The key theoretical insight is that higher closure increases trust but reduces access. For example, in Figure VB, two people trust s with assets of value V ≤ 2; although access is low, trust is high in this closed network. In contrast, in Figure VA, s can borrow from four people, but the asset value can be at most 1: access has increased, but at the cost of a reduction in pairwise trust. Due to this trade-off, whether high or low closure is associated with greater welfare depends on what assets are exchanged: trust is more important for high-value assets whereas access matters more for low-value assets. To formalize this trade-off between access and pairwise trust, we let f (v ) denote the density of F (v ) and let ω(V ) = f (V )ω (V ), the frequency-weighted profits from the ability to borrow V . Note that ω(V ) depends both on the probability that an asset of value V is needed ( f (V )), and on the profits this asset generates (ω (V )). We say that the economy is a high-value exchange environment if ω(V ) is increasing: in this case high-value transactions generate greater welfare ω(V ), either because they are more likely or because they are more productive. Conversely, we 16. To see why s has four paths in Figure VB, note that there are two paths connecting s to t1 , the direct one and the indirect one through t2 ; and similarly, two paths connect s to t2 . 17. If arrangements are limited by a circle of trust, then T s (c) and P s (n) need to be computed in the corresponding subgraph of permissible links. 18. Also note that (ii) is equivalent to requiring that the cumulative distribu

tion function 1 − P s (·) first-order stochastically dominates 1 − P s (·).

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say we are in a low-value exchange environment when ω(V ) is decreasing. PROPOSITION 2. In a high-value exchange environment, a neighborhood with higher closure leads to a higher expected payoff to s. Conversely, in a low-value exchange environment, a neighborhood with higher closure leads to a lower expected payoff to s. In a low-value exchange environment, the access provided by low closure is more attractive, because knowing more people directly or indirectly increases the likelihood that s can obtain a low-value asset. This logic is in line with Granovetter’s and Burt’s basic argument about the strength of weak ties and the benefits of a dispersed social network in providing access to assets with low moral hazard, such as small favors, information, or advice.19 In contrast, in a high-value exchange environment, closure is better. Here, a reduction in access is more than compensated for by the fact that, through his dense connections, s will be able to borrow even high-value assets. This finding parallels Coleman’s general argument for network closure, and particularly his example of the wholesale diamond market in New York City, where the exchange of valuable stones requires high trust between dealers.20 The results of Proposition 2 are related to Putnam’s (2000) concepts of bridging and bonding social capital. In Putnam’s view, bonding social capital is associated with dense social networks and is good for generating reciprocity between agents who know each other well. In contrast, the networks underlying bridging social capital are “outward looking and encompass people across diverse social cleavages,” and are good for “linkage to external assets and for information diffusion.” These two concepts parallel our distinction between trust and access; our results thus provide formal foundations as well as network-based measures for bonding and bridging social capital. Community Size and Network Closure. What determines network closure? In Allcott et al. (2007), we argue that in practice, community size should be an important determinant. The 19. Section IV.B develops a variant of our basic setup where exchange of information is explicitly modeled. 20. Vega-Redondo (2006) reports a related finding in a model of repeated games played in networks. He shows that stability of cooperative behavior depends on a certain measure of network cohesiveness.

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Network closure (P s (2)) 0.4 0.6 0.8

1

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0

5

10 Number of friends

Below median size

15

20

Above median size

FIGURE VI Community Size and Network Closure The figure is taken from Allcott et al. (2007). The figure plots average network closure for students by the number of their friends for schools below median size (solid line) and schools above median size (dashed line). For each student s, closure is measured as P s (2), the share of paths s has to others with whom he has at least two paths, within the circle of trust that includes links up to distance 2 from s. See Definition 5 and Section IV.A for details. The figure is constructed using data from 142 U.S. middle and high schools in the National Longitudinal Study of Adolescent Health; observations with number of friends greater than 19 were excluded (less than 1% of total).

intuition is straightforward: in a small community, the pool of potential friends is limited, which makes it more likely that two agents share common friends. In Allcott et al. (2007), we confirm this intuition using data on the social networks of students in the National Longitudinal Study of Adolescent Health (AddHealth).21 Normalizing all link capacities to unity, we build on Definition 5 to measure the closure of the network around a student s with P s (2), the share of all paths that s has that connect him or her with others with whom he or she is connected through at least two paths.22 This quantity is always between zero and one, and higher values represent more closed networks. Figure VI compares this measure 21. AddHealth is a representative sample of 142 U.S. public and private middle and high schools in 1994 and 1995. 22. We also restrict the “circle of trust” to links that are within distance 2 from agent s. The distance of a link (u, v) from s is the arithmetic average of the length of the shortest paths connecting s to u and s to v.

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of closure for schools below and above the median size, for each possible value of a student’s number of friends. This figure confirms that community size is an important predictor of closure in practice: even holding fixed a student’s number of friends, smaller communities exhibit higher network closure. Implications for Organizations. The connection between community size and closure, combined with Proposition 2, has implications for organizational design. In environments where access to small favors such as providing information is important, communities should be larger. This can be achieved through a flat organizational structure where rank does not limit interactions. For example, academic communities in the United States have a relatively informal culture, generating a large community of researchers; this encourages the development of weak ties and creates access to ideas. In contrast, organizations where trust is important can create it by having smaller communities. For instance, the hierarchical structure of armies limits interactions to peers of the same rank, creating networks with high closure and bonding social capital. Our results also help explain the empirical fact that community size is often negatively correlated with prosocial behaviors such as volunteering, work on public projects, and helping friends (Putnam 2000). The traditional explanation is that in large communities people have fewer friends (Jacobs 1993). Our results suggest that even controlling for the number of friends, large communities have less dense social networks, which limits the provision of valuable public goods. IV.B. Job Search and Trust in Recommendations Sociologists have long recognized the importance of networks for finding jobs. For example, in Getting a Job, Granovetter (1974) documents that 56% of his sample of white-collar workers found employment through personal contacts. One possible explanation is that information about job openings often travels through friends and acquaintances. This logic forms the basis of Granovetter’s (1973) “strength of weak ties” theory, formally modeled by Calvo-Armengol and Jackson (2004), which predicts that weak links to agents with whom one has few common friends are most useful for job search, because they provide access to otherwise unobtainable information. However, the evidence about the strength of weak ties is mixed. Studies in U.S. cities (Bridges and

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Villemez 1986; Marsden and Hurlbert 1988) find that both weak and strong ties are important for job search. In Japan, Watanabe (1987) documents that small business employers screen applicants using strong ties. In China, Bian (1997, 1999) argues that the guanxi system of personal relationships allocates jobs using strong ties and paths. Granovetter (1974) provides a second reason for the importance of connections: networks can generate trust in job recommendations. When there is asymmetric information about the skills of job candidates, offers are often made based on the opinions of trusted recommenders. In Granovetter’s sample, such trusted referrals are common: in 60% of all jobs obtained through a network path of length 2 or more, the worker’s direct contact had “put in a good word” for him. Because trusted referrals are more likely to come through strong ties, this logic can help explain why many empirical studies have found strong ties to be more important. We now explore the implications of network-based trust for job search using the social collateral model.23 Consider an employer t who needs to fill a vacancy. Potential employees are either high or low types; if hired, a high type generates total value SH and a low type generates SL, where SH > SL > 0. In the formal labor market, worker types are unobservable, the proportion of high types is π H , and the prevailing market wage rate is w. Thus, hiring from the labor market generates an expected surplus S = π H SH + (1 − π H ) SL, of which S − w accumulates to the employer. However, the employer may be able to hire a known high type through his social network. If s is a high-type job candidate, and his type can be credibly communicated to the employer, then the surplus from hiring s versus hiring from the formal labor market is SH − S. Assuming that this surplus is divided by Nash bargaining, where the bargaining weight of the worker is α, the wage of s if hired is w H = w + α · (SH − S), and the excess profit of the firm relative to hiring from the labor market is (1 − α) · (SH − S). Can the network credibly communicate the worker’s type to the employer? To answer, assume that the type of worker s is only observed by himself and his direct friends, denoted s1 , . . . , sk. Although these friends can, in principle, provide recommendations, 23. Saloner (1985) and Simon and Warner (1992) also study informal recommendations in labor markets. These papers set aside trust considerations by assuming that recommenders and firms have the same objective.

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they face a moral hazard problem: a low-type worker s can bribe them to write good recommendations. Here bribes are interpreted broadly to include in-kind transfers, as well as being nice to the recommender. The amount candidate s is willing to spend on bribes is limited by the attractiveness of the job, α · (SH − S); if he or she offers more, the bribes would exceed the profit from getting the job. This reasoning suggests that the network can only communicate worker type in a credible way when the employer’s trust of recommenders, s1 , . . . , sk exceeds the highest bribe that the worker can pay, α · (SH − S). To formalize these ideas, we modify the basic model as follows. First, we assume that prior to sending recommendations, agents agree on an informal transfer arrangement that is to be activated if the worker turns out to be a low type. This arrangement represents the understanding that recommenders will be held responsible for bad recommendations. Second, we introduce the concept of side deals with bribes, where agent s might propose a new transfer arrangement, together with a set of bribes to be paid to his friends, s1 , . . . , sk, in exchange for their good recommendations.24 Finally, we introduce an auxiliary network, G∞ , where links between s and his friends, s1 , . . . , sk, have infinite capacity, st (c) denotes the trust flow between s and t in this network. and T PROPOSITION 3. In an equilibrium robust to side deals with bribes, low-type workers are never hired through the network. If st (c) ≥ α · (SH − S), there exists an equilibrium and only if T robust to side deals with bribes where a high-type worker s is hired. The result simply states that when network-based trust between the employer and recommenders exceeds the sensitivity of profits to worker type, as measured by the term α · (SH − S), the true type of the worker can be credibly communicated. Several implications about networks and labor markets follow. (1) Networkbased trust should be more important for high-skilled jobs, where the employer’s profits are more sensitive to worker type. Proposition 2 then predicts a trade-off between weak and strong ties: for low-skill jobs, where type matters less, weak connections are best because they maximize access; but for high-skilled jobs, recommendations through strong links embedded in a dense network are more useful. (2) Jobs obtained through the network should 24. The formal details of these modifications are presented in Appendix I.

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earn higher wages than jobs obtained in the market. Simon and Warner (1992) obtain the same prediction, but their mechanism is different: in their work, networks reduce uncertainty about the quality of the match, increasing the reservation wage; in contrast, in our model only high types are hired through the network. (3) Due to the increased importance of trust for high-quality jobs, the wage differential between network-based and market-based hires, w H − w = α · (SH − S), should be positively related to skill intensity. (4) When filling high-skill vacancies, employers should search more through their networks. These predictions are consistent with several empirical facts. The first prediction helps explain the mixed evidence about the strength of weak ties by showing that for many jobs strong ties should be more important; it also implies that the strength of weak ties should vary with the skill intensity of the job, a prediction that awaits empirical testing. Consistent with the second prediction, Granovetter (1974) reports that in his sample, “jobs offering the highest salary are much more prone to be found through contacts than others: whereas less than half of jobs yielding less than $10,000 per year were found by contacts, the figure is more than three-quarters for those paying more than $25,000.” This positive correlation between referrals and salary is also confirmed by Gorcoran, Datcher, and Duncan (1980) and Simon and Warner (1992). Regarding the intensity of network search, Brown (1967) finds that among college professors, personal networks are more frequently used in obtaining jobs of higher rank, smaller teaching loads, and higher salaries and at more prestigious colleges. For these attractive jobs, reducing asymmetric information is likely to be more important, and hence, employers have a stronger preference for searching through their networks. Our predictions would not emerge in a model where the network served purely as a source of information about job vacancies. In such an economy, the network does not reduce information asymmetries; hence the wage differential is zero and the importance of network-based recommendations does not vary with the type of the job. Our results thus suggest that a full analysis of networks in labor markets should incorporate both information transmission and trust in recommendations. Trust and Asymmetric Information. The social collateral model can also be used to study other situations involving asymmetric information. For example, a simple alteration of our job

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search framework shows that network-based recommendations can help identify whether a given borrower is intrinsically a trustworthy type.25 A similar logic applies for transactions of valuable assets such as houses, which involve a potential “lemons” problem: sellers with whom the buyer has a high trust flow are more likely to be honest about the quality of the good, to avoid future retribution through social sanctions.26 We conclude that the implications of social collateral in the presence of asymmetric information are similar to the basic model with moral hazard: higher trust flow can secure transactions where there is greater exposure to asymmetric information. V. MEASURING SOCIAL COLLATERAL IN PERU We now empirically evaluate the social collateral model using a unique data set from two low-income Peruvian shantytown communities, collected by Dean Karlan, Markus Mobius, and Tanya Rosenblat, further described in Karlan et al. (2008). Two key features of these data make them particularly useful for our purposes: (1) information on the social networks of individuals and (2) data on informal loans between friends, relatives, and acquaintances. V.A. Data Description In 2005, a survey was conducted in two communities located in the Northern Cone of Lima. The heads of households and spouses (if available) in 299 households were interviewed. The survey consisted of two components: a household survey and a social network survey. The household survey recorded a list of all members of the household and basic demographic characteristics, including sex, education, occupation, and income; summary statistics for these variables are reported in Table I. Average monthly household income in the two communities was 957 and 840 Peruvian new soles (S/.), respectively, which equals approximately 294 and 258 US$, using the exchange rate in 2005. The social network component of the survey asked the household head and spouse to list up to ten individuals in the community 25. Karlan (2005) documents evidence that there is variation in individuals’ trustworthiness, which is predictive of their financial behavior. 26. In line with this prediction, in the 1996 General Social Survey, 40% of home purchases and 44% of used car purchases involved a direct or indirect network connection between the buyer and seller or realtor (DiMaggio and Louch 1998).

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TRUST AND SOCIAL COLLATERAL TABLE I SUMMARY STATISTICS FOR TWO SHANTYTOWN COMMUNITIES IN PERU Demographic variables

Mean

Female 0.50 Age 35.84 Secondary ed. 0.71 Household inc.(S/.) 887.39 Business-owner 0.20

Standard dev. 0.50 14.37 0.21 1,215.74 0.40

Social network variables Number of contacts Share of “neighbors” Share of “friends” Share of “relatives” Avg. size of loan (S/.) Geographic dist.

Mean

Standard dev.

8.60 4.15 0.59 0.49 0.39 0.49 0.02 0.15 75.88 121.20 41.16 49.17

Note. The table shows summary statistics for adults (age at least 18). Income and loan amounts are reported in Peruvian new soles (S/.). The exchange rate at time of the survey was 3.25 S/. for one US$. Network variables are calculated for the nondirected network where a pair of individuals are classified as connected if one of them names the other as a friend. Geographic distance is reported in meters.

with whom the respondent spent the most time in an average week. We use this data to construct an undirected “OR”-network, where two agents have a link if one of them names the other. Agents have, on average, 8.6 links, and the average geographic distance between connected agents is 42 and 39 m in the two communities; this is considerably less than the geographic distance between two randomly selected addresses, which is 132 and 107 m, respectively.27 About 59% of relationships were classified by respondents as “vecino” (neighbor) and 39% as “amigo” or “compadre” (friend). The share of “relativos” was just 2%.28 Vecinos live slightly closer than amigos/compadres (35 versus 51 m). Over 90% of directly connected people met in the neighborhood for the first time. Importantly for our purposes, the social network survey also recorded, for each responder, the set of friends from whom he or she had borrowed money during the previous twelve months. There were 254 informal loans in the data set; 167 borrowers in 138 households reported having borrowed on average 76 S/. (about 23 US$) from 173 lenders during the past twelve months. Thus, informal borrowing is very common in these communities: 46% of all households have at least one household member who borrowed money in this manner. The mean age of both the borrower and the lender is 39 years and they live, on average, 36 m apart. 27. This is consistent with a body of work showing the importance of social distance in meeting friends, for example, Marmaros and Sacerdote (2006). 28. In the remainder of this section, we use the term “friend” for any network connection, whether vecino, amigo/compadre, or relativo.

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V.B. Empirical Framework Measuring Capacities and Trust Flow. To adapt our model of social collateral to this empirical setting, we need to develop a measure of link capacity. We use the amount of time spent together as a proxy for the strength of a connection, capturing the intuition that link values depend on investment in joint social activity. In the data, the distribution of time spent together is skewed: the average responder spends less than six minutes with the bottom 10% of his/her friends and more than three hours with the top 10%. To obtain a more homogeneous measure, we define normalized time for two connected agents u and v as the value, for the amount of time they spend together, of the empirical cumulative distribution function of time spent together in their community. With this definition, the empirical distribution of normalized time τ (u, v ) across all connected pairs is a discretized uniform distribution on the unit interval in each community. We assume that link capacities are created by an increasing production function g such that c(u, v) = g(τ (u, v)); that is, spending more time together results in stronger links. We compute the network flow between agents s and t by defining the circle of trust to be the subgraph that contains all links of s and t. This circle of trust allows a simple decomposition of the trust flow between s and t as g(min(τ (s, v), τ (v, t))), (6) T st (c) = g(τ (s, t)) + v∈Ns ∩Nt

where the first term represents the direct flow and the second term is the indirect flow. Here Ns is the set of direct friends of agent s. Discrete Choice Framework. A natural approach to estimating the social collateral model is to use observations on how much agents borrow, and to use the loan size as a lower bound for the trust flow. This approach runs into the difficulty that loan amounts are also affected by demand: a borrower might borrow less than the trust flow. To avoid explicitly modeling loan demand, we instead base our estimation on who the agent borrows from, exploiting the idea that people are more likely to borrow from friends who trust them. By conditioning on the borrower, this approach effectively controls for loan demand as a fixed effect. We formulate the borrower’s choice of lender as a discrete choice problem. Consider agent s, who is in need of a loan of size

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V , which he can borrow from potential lenders t1 , . . . , tk. We write the total utility that s enjoys when he borrows from a particular lender t as (7)

ut = u(V, T st (c) + εt ),

where u is increasing and εt represents either measurement error in the trust between s and t, or a supply shock. Appendix II provides micro foundations for this representation by assuming that if V exceeds the level of trust T st , the excess value must be secured using physical collateral that has some opportunity cost. Then, the borrower is more likely to turn to a lender who trusts him more, implying that (8)

preferred lender = arg max[T st (c) + εt ], t

because, conditional on the loan amount, (7) is maximized when trust is highest. Model Predictions. We use the above discrete choice specification to test three predictions of the social collateral model. (1) Agents are more likely to borrow from friends with whom they have a stronger trust flow. This prediction is a direct implication of Theorem 1. (2) The contribution of an indirect path of a given strength is equal to the contribution of a direct link with the same strength. This prediction is made because there are no costs to including intermediate agents within the circle of trust in the borrowing arrangement. In a setup where the circle of trust is endogenized, as in Section III.F, the contribution of indirect paths would be smaller, but still positive. (3) Each indirect path contributes to borrowing through its weakest link. In particular, in decomposition (6), for each indirect s → v → t path, if we have τ (s, v) < τ (v, t), then the contribution of the path to borrowing should only depend on τ (s, v). Some of these predictions are consistent with alternative explanations. Time spent together can be correlated with the strength of altruistic feelings between the two agents and the ease with which information travels between them. Common friends can further strenghten altruism and information transmission. Trust flow can therefore be a proxy for the lender’s altruism toward the borrower and the lender’s ability to learn about the profitability of the borrower’s project. There is no particular reason that in these alternative explanations the weakest link

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Excess propensity to borrow –0.1 0 0.1

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–2

0 1 –1 Excess trust flow (measured as time flow)

2

FIGURE VII Trust Flow and Borrowing This figure is a residual plot, controlling for borrower fixed effects, of the relationship between trust flow, measured as time flow, and borrowing, where time flow is the sum of direct and indirect normalized time spent together. The figure is constructed as follows. For each borrower we calculate mean trust flow with all his or her friends, and define excess trust flow as the deviation from this mean. We similarly construct excess borrowing as the deviation from the average probability of borrowing across all friends. We sort all borrower–lender pairs by excess trust flow, group them into sixteen equal-sized bins, and plot the excess probability of borrowing (vertical axis) against the average excess trust flow (horizontal axis) for each bin.

should determine the strength of altruistic feelings or the strength of information transmission.29 However, without better data, we cannot completely exclude these alternative explanations. V.C. Results Graphical Analysis. We begin with a graphical analysis of trust flow and borrowing to highlight the basic patterns in the data. Assume that the strength of a link is proportional to normalized time: c (u, v ) = c · τ (u, v ). Then trust flow T st can be written as c · τ st , where τ st measures the total (direct plus indirect) “time flow” between agents s and t, computed using equation (6). Figure VII depicts the relationship between trust flow and borrowing in our sample, conditioned on borrower-specific fixed effects. The construction of the figure is the following. We introduce 29. One concrete model of altruism is where the lender cares about the utility of the intermediary who cares about the utility of the borrower. This model predicts that a geometric average of the two link values determines borrowing, which contradicts the weakest link condition of prediction 3. Similarly, if networks matter purely because they transmit information, then the average and not the minimum of link values should determine borrowing.

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TRUST AND SOCIAL COLLATERAL TABLE II BORROWING AS A FUNCTION OF DIRECT AND INDIRECT FLOW Direct time Indirect time

Above average

Below average

Above average

21.0%

42.0%

Below average

14.5%

22.5%

Note. This table shows the role of indirect paths in borrowing. Direct and indirect trust flow are computed as direct and indirect normalized time flow for each borrower and lender pair (see the notes to Figure VI or the text for details.) The construction of the table is as follows. We compute mean direct and indirect flow for each borrower by averaging across his/her friends, and create two indicator variables for whether direct and indirect flow is above or below the average. The table shows how loans are distributed across the resulting four bins (direct flow below or above average × indirect flow below or above average).

an indicator variable Ist , which is one if we observe s borrowing from t. For each borrower s we calculate the mean time τ s he or she spends with her friends, and the share I s of friends he or she borrows from. We then define the borrower’s “excess time flow” with lender t as τ st − τ s , and his or her “excess borrowing” from t by Ist − I s . Figure VII is simply a plot of excess borrowing against excess time flow, where observations are averaged over intervals of excess time flow to smooth out all uncorrelated noise. The figure shows a strong positive relationship, confirming the basic prediction that agents should be more likely to borrow from friends who trust them. Figure VII does not distinguish between direct and indirect flows. To get a sense of the relative contribution of indirect paths, in Table II we group all friends of each borrower into four categories along two dimensions: whether the direct flow between borrower and friend is below or above the average direct flow, and whether the indirect flow between borrower and friend is below or above the average indirect flow. We then calculate the share of loans that fall into each of the resulting four categories. About 14.5 percent of loans involve borrower/lender pairs with both below-average direct flow and below-average indirect flow. Almost double as many loans involve borrower/lender pairs with either above-average direct or above-average indirect flow. About three times as many loans involve borrowers and lenders with both above-average direct and above-average indirect flow. Indirect paths appear to play an important role in creating social collateral for borrowing. Structural Estimation. To analyze the relationship between trust flow and borrowing in greater detail, we now estimate the

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discrete choice model (8). This allows us to measure the relative strength of different network links, as well as to formally test our predictions. We allow capacities to depend on the time spent together in a flexible way, by classifying every link as weak, medium, or strong, depending on whether the time spent together lies in the lowest, medium, or highest third of the time distribution for each of the two communities. Each direct and indirect path between borrower and lender then makes a weak, medium, or strong contribution to total flow, where the strength of these different link types is measured by unknown parameters cW , c M , and c S . Given our definition of the circle of trust, the trust flow T st (c) between s and t, as given by (6), is easily seen to be a linear function of c = (cW , c M , c S ). Assuming that the error term ε has the extreme value distribution, we can then estimate (8) as a conditional logit, (9)

Pr[lender is t] =

exp[(1/λ) · T st (c)] , su u∈Ns exp[(1/λ) · T (c)]

where λ > 0 measures the relative importance of the error term. Given the linearity of T st in c, the unobserved parameters λ and c cannot be separately identified, but we can use the estimates to back out capacity ratios like c S /c M . Table III reports our logit estimates. The first column contains our baseline specification; the coefficient estimates for total weak, medium, and strong flow correspond to cW /λ, c M /λ and c S /λ in the estimating equation. The effect of weak paths on borrowing is insignificant and small: gaining access to lenders through weak ties appears to be relatively less important for obtaining loans. Both medium and strong paths have a highly significant positive effect on borrowing, and the effect of strong paths is significantly greater. One additional medium path to a lender increases the probability of borrowing by a factor of 1.44, whereas an additional strong path increases the probability by a factor of 2.7. The ratio of the point estimates implies that the capacity of strong links is about three times as high as that of medium links: c S /c M ≈ 2.7. These results support prediction 1, that trust flow should be positively related to borrowing, and highlight the importance of strong ties. Is the contribution of an indirect path different from that of a direct path? To compare indirect and direct paths, in column (2) we add the number of indirect medium and strong paths as separate controls in the regression. According to our second prediction,

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TRUST AND SOCIAL COLLATERAL TABLE III TRUST FLOW AND CHOICE OF LENDERS CONDITIONAL LOGIT ESTIMATES

Total weak flow (cW /λ) Total medium flow (c M /λ) Total strong flow (c S /λ)

(1)

(2)

(3)

(4)

0.16 (0.143) 0.365 (0.155)∗ 0.991 (0.163)∗∗

0.151 (0.142) 0.546 (0.266)∗ 1.317 (0.283)∗∗ omitted −.190 (0.319) −.526 (0.363)

0.142 (0.164) 0.341 (0.19) 0.988 (0.165)∗∗

0.147 (0.164) 0.543 (0.267)∗ 1.311 (0.284)∗∗ omitted −.226 (0.379) −.516 (0.368) 0.018 (0.315) 0.06 (0.34) −.006 (0.003)∗ 988

Indirect weak flow Indirect medium flow Indirect strong flow Weak–not weak flow Medium–strong flow Geographic distance Obs.

−.006 (0.003)∗ 988

−.006 (0.003)∗ 988

0.073 (0.313) 0.069 (0.27) −.006 (0.003)∗ 988

Note. Each link is classified as weak, medium, or strong depending on whether the time spent together lies in the lowest third, medium third, or highest third of the time distribution. Weak, medium, and strong total flow are defined by noting that each direct and indirect path between borrower and lender makes either a weak, medium, or strong contribution to total flow. For indirect medium and strong flow we only count indirect paths. Weak–not weak flow counts paths where exactly one link is weak; medium–strong flow counts paths where one link is medium and one link is strong. We do not include indirect weak flow in columns (2) and (4) because we cannot separately identify total and indirect weak flow in our conditional logit estimation, as every potential lender has at least a weak link to the borrower. ∗ 5% significance level. ∗∗ 1% significance level.

the coefficients of these variables should be zero. We find that the estimated coefficients on indirect flow are negative, but not statistically significant, and smaller than the corresponding coefficients on total flow. These results show that both direct and indirect paths have a substantial positive effect on borrowing, confirming the basic intuition that dense networks are better in creating social collateral. The negative estimates of indirect flows, although insignificant, suggest that the effect of indirect paths is slightly smaller, which can be explained in our model by endogenizing the circle of trust as in Section III.F. Combined with the results about strong ties, these estimates suggest that dense networks and bonding social capital are important for obtaining loans in these communities. We now test the prediction about the role of the weakest link in column (3), where we include two new explanatory variables

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in the regression. “Weak-not weak flow” counts the number of indirect paths where one link is weak and the other is medium or strong, whereas “medium-strong flow” counts the number of paths where one link is medium and the other is strong. If prediction 3 is false, then these paths should have a positive effect on borrowing beyond what is predicted by the social collateral “weakest link” theory. The estimated coefficients on these variables are insignificant and small, providing strong evidence for the role of the weakest link in determining social collateral. These results are replicated in column (4), which includes the controls for indirect flows. Our findings about the role of indirect paths and the weakest link property help distinguish our model from other explanations for borrowing, such as altruism and information transmission. One caveat with our econometric analysis is that if time spent together increases due to borrowing, reverse causality confounds the interpretation of the estimates. Thus, the evidence supports, albeit not exclusively, the social collateral model; moreover, strong ties and network closure, that is, bonding social capital, appear to be particularly important for borrowing. Importantly, the theoretical framework provides clear predictions that can be tested in further settings, with perhaps more control over key empirical identification issues. VI. CONCLUSIONS This paper has built a model where agents use their social connections as collateral to secure informal loans. This model naturally leads to a definition of network-based trust, which we then use in applications related to network structure and welfare, trust in job search, and the measurement of social capital. We conclude by sketching three other applications of the social collateral model. VI.A. Network Statistics When informal arrangements are restricted by the circle of trust to connections within a given social distance, our model generates a family of trust measures. Our working paper, Mobius and Szeidl (2007), shows that when all links have equal capacity, these measures are functions of several commonly used network statistics, including (1) number of friends; (2) the clustering coefficient, which is a measure of local network density; (3) the number of common friends of two agents; and (4) the number of transitive triples,

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another measure of network density.30 These results provide social collateral-based foundations for common network statistics. VI.B. Risk Sharing Development economists often emphasize the importance of informal insurance in developing countries. Ambrus, Mobius, and Szeidl (2008) use the social collateral model to explore risksharing in networks. They find that good risk sharing requires networks to be expansive: larger sets of agents should have more connections with the rest of the community. Networks shaped by geographic proximity have this property, because agents tend to have friends at a close distance in multiple directions, helping to explain the observed good risk sharing in village environments. They also find that network-based insurance is local: socially closer agents insure each other more. VI.C. Dynamics of Trust and Panics In the basic social collateral model, link capacities are exogenous. Mobius and Szeidl (2008) show that link values can be endogenized with multiple rounds of exchange. The strength of a relationship is, then, the sum of its direct value, as in the basic model, plus the indirect value, which derives from the ability to conduct transactions through the link in the future. In this framework, fluctuations can be amplified through a network multiplier similar to the social multiplier of Glaeser, Sacerdote, and Scheinkman (2003), because trust withdrawal that constrains exchange locally can lead to further trust withdrawals that ripple through the network. New technologies that limit future social interaction, such as television, can substantially reduce trust and social capital through this mechanism.31 APPENDIX I: PROOFS DEFINITION 6. A weak flow with origin s is a function g : W × W → R with the following properties: (i) Skew symmetry: g(u, v) = −g(v, u). (ii) Capacity constraint: g(u, v) ≤ c(u, v). (iii) Weak flow conservation: w g(u, w) ≤ 0 unless u = s. 30. These measures are used, for example, in Wasserman and Faust (1994), Watts and Strogatz (1998), Glaeser et al. (2000), and Jackson (2006). 31. In related work, Kranton (1996) and Spagnolo (1999) study the interaction between social and business activities.

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A weak flow of origin s can be thought of as taking a certain amount from node s and carrying it to various other nodes in the network. By weak flow conservation, any node other than s receives a nonnegative amount. LEMMA 1. We can decompose any weak flow g as fu, g= u∈V

where for each u, fu is an s → u flow, fu(v, w) = 0 that is, w for all v = u, v = s, and moreover w fu(u, w) = w g(u, w), that is, fu delivers the same amount to u that g does. Proof. Consider vertex u such that w g(u, w) < 0. By weak flow conservation, the amount of the flow that is left at u must be coming from s. Hence, there must be a flow fu ≤ g carrying this amount from s. With fu defined in such a way, repeat the same procedure for the weak flow g − fu with some other vertex u . After fu is defined for all vertices u, the remainder f satisfies flow conservation everywhere and can be added to any of the flows. Implicit summation notation: For a weak flow g and two vertex sets U ⊆ W and V ⊆ W, we use the notation that f (u, v). f (U, V ) = u∈U , v∈V

Proof of Theorem 1. Sufficiency. We begin by showing that when (4) holds, a side deal–proof equilibrium exists. By assumption, there exists an s → t flow with value V . For all u and v, let h (u, v ) equal the value assigned by this flow to the (u, v ) link. Now consider the strategy profile where (1) the borrowing arrangement h is proposed and accepted, (2) the borrower returns the asset, and (3) all transfers are paid if the borrower fails to return the asset. This strategy is clearly an equilibrium. To verify that it is side deal–proof, consider any side deal, and let S denote the set of agents involved. For s to be strictly better off, it must be that he prefers not returning the asset in the side deal. Now consider the ( S, T ) cut. By definition, the amount that flows through this cut under the original arrangement is V ; but then the same amount must flow through the cut in the side deal, as well. This means that s must transfer at least V in the side deal; but then he cannot be better off. More generally, this argument shows that any transfer arrangement that satisfies flow conservation is side deal–proof.

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Necessity. We now show that when (4) is violated, no side deal–proof equilibrium exists. We proceed by assuming to the contrary that a pure strategy side deal–proof equilibrium implements borrowing even though (4) fails. First note that on the equilibrium path, the borrower must weakly prefer not to default. To see why, suppose that the borrower chooses to default on the equilibrium path. Because the lender and all intermediate agents must at least break even, this implies that the borrower has to make a transfer payment of at least V . But then the borrower must weakly prefer not to default, because returning the asset directly has a cost of V . This also implies that all intermediate agents must have a zero payoff. By assumption, there exists an ( S, T ) cut with value c ( S, T ) < V . We now construct a side deal where all intermediate agents in S continue to get zero, but the payoff of s strictly increases. The idea is easiest to understand in an equilibrium where promises are kept, that is, when all transfers satisfy the capacity constraint h (u, v ) ≤ c (u, v ). Then, we simply construct an arrangement that satisfies flow conservation inside S and delivers to the “boundary” of S the exact amount that was promised to be carried over to T under h. More generally, when the capacity constraints fail over some links, the deviation in the side deal can result in some agents in S losing friendships with agents outside S. To compensate for this loss, the side deal must deliver to the “boundary” of S an additional amount that equals the lost friendship value. Formally, let g be a maximal s → t flow and consider the restriction of g to S. Thisis a weak flow, and by the lemma it can be decomposed as g = u∈S gu, where each gu is an s → u flow. Now for each u ∈ S, let g (u, T ) and h (u, T ) denote the amounts leaving S through u under g and h. Moreover, for each u ∈ S, let z (u, T ) denote the total friendship value lost to u in the subgame where the borrower defaults, as a consequence of unkept transfer promises. Because g is a maximum flow and ( S, T ) is a minimal cut, it follows that g (u, T ) ≥ h (u, T ) + z (u, T ). This is because any link between u and T is either represented in h (u, T ), if u pays the transfer, or z (u, T ), if u does not pay and loses the friendship. This inequality implies that, whenever h (u, T ) + z (u, T ) > 0, we also have g (u, T ) > 0. As a result, we can define h =

h(u, T ) + z (u, T ) u∈S

g (u, T )

· gu.

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Note that h is a weak flow in S and delivers exactly h (u, T ) + z (u, T ) to all agents in S. Thus h satisfies flow conservation within S and delivers to the “boundary” of S the sum of two terms: h(u, T ), which is the precise amount to be carried over to T under h, and z (u, T ), which is the loss of friendship u suffers due to not making other promised transfers. We claim that h is a profitable side deal. First, h satisfies all capacity constraints by construction. Second, all agents in S break even under h , as they did in the original equilibrium. Third, the total value delivered by h is at most c ( S, T ) < V , which means that s pays less than V under h , whereas he pays exactly V in the original equilibrium. We have constructed a side deal in which the borrower is better off and all other players are best-responding; hence, the original equilibrium was not side deal–proof. Proof for Section III.F. Transfer Constraints. In this analysis, we use a more stringent equilibrium selection criterion: We look for equilibria where (i) all promised transfers are paid; and (ii) there are no profitable side deals. In the earlier analysis, there was no need to impose (i), because the characterization results showed that any level of borrowing that can be implemented can also be implemented using equilibria where all transfers are paid. With transfer constraints, requiring that all promises be credible has additional bite, because promises that are not credible can generate large punishment in the form of loss of friendship to agents who have small ku. We find it plausible that such agents will not make promises that they know they cannot keep, but instead of providing formal micro foundations for this, we simply restrict ourselves to equilibria that are “credible,” in the sense that all promises are kept. Consider the directed network G defined in the text and let the maximum s1 → t1 flow in G be denoted by T s1 t1 (c). PROPOSITION 4. There exists a side deal–proof equilibrium with credible promises that implements borrowing if and only if (10)

V ≤ T s1 t1 (c).

Proof. Sufficiency. If (10) holds, then take a flow with value V , and let the flow values between different agents define the transfer arrangement in our candidate equilibrium. Note that by construction, this borrowing arrangement satisfies the borrowing

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constraints of all agents u. Moreover, the promised transfers in this arrangement will be kept because they all satisfy the capacity constraint. It remains to be shown that there are no profitable side deals; this follows from the same argument used in the proof of Theorem 1. Necessity. Suppose that (10) fails, and consider an equilibrium where promised transfers are paid and borrowing is implemented. We now show that this equilibrium admits a side deal. Our argument is similar to the proof of Theorem 1, in that we build the side deal using a minimum cut on the network G . However, the present setup has one additional difficulty: we need to make sure that the side deal emerging from the minimum cut does not separate agents from their duplicates. Let (S , T ) be a minimum cut. If for some u = s we have u2 ∈

S , then u1 ∈ S also holds, because u2 has only one incoming link, which originates in u1 . Let S be the union of s and the collection of agents u such that u1 ∈ S . We need to show that agents in S, as a group, do not have the right incentive to return the asset. To / S . It follows see why, consider first an agent u ∈ S such that u2 ∈

that the (S , T ) cut separated u1 from u2 , by cutting the u1 → u2 link. But in this equilibrium, promises are kept, and, hence, the total obligation of u to agents outside S can be at most ku, which is exactly the value of the cut link. Next consider an agent u ∈ S such that u2 ∈ S . For this agent, the total obligations to others outside S are bounded from above by the total value of the links originating in u2 that are cut. Summing over all u ∈ S, we conclude that the total obligations of all agents in S do not exceed the value of the (S , T ) cut, and, hence, are strictly smaller than V . Thus, S, as a group, has an incentive to default. The actual side deal can now be constructed in the same way as in the proof of Theorem 1. Proof of Proposition 1. Consider two capacities c1 ≤ c2 . Any flow between s and t that is feasible under c1 is also feasible under c2 ; hence the maximum flow cannot be lower under c2 than under c1 . Proof of Proposition 2. We denote the share of total paths to agents with whom agent s has precisely j paths with qs ( j). If we treat this function as a probability density function over the nonnegative integers, then an increase in closure is equivalent to a first-order stochastic dominance shift.

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The expected payoff of s, conditional on his being the borrower, can be written as 1 qs ( j) ( j) 1 qs ( j) ( j) = , N j j N j j which can be viewed as the expected value of the function ( j)/j under the probability density qs ( j). In a high-value exchange enω(V ) is increasing; vironment, (V ) is convex because (V ) = this, combined with the fact that (0) = 0, implies that (V )/V is nondecreasing. In this case, a first-order stochastic dominance increase in the probability density qs ( j ) increases the expected payoff by definition. An analogous argument shows that in a lowvalue exchange environment, the same increase in the sense of first-order stochastic dominance reduces the expected payoff of s. Proof of Proposition 3. Preliminaries. The timeline of the model with job search is the following. In stage 1, a set of agents, including s1 , . . . , sk and t, agree on a transfer arrangement that specifies transfers h (u, v ) to be made in the event that s1 , . . . , sk send recommendations, and s is hired and then turns out to be a low type. In stage 2, agents s1 , . . . , sk choose whether to recommend s to the employer t. In stage 3, t decides whether to hire s or not; profits are earned, and the type of s is publicly revealed. In stage 4, if needed, the transfer arrangement is executed; and in stage 5, agents consume the values of remaining links. We consider a class of coalitional deviations that we call side deals with bribes. A side deal with bribes is a new transfer arrangement proposed by s to s1 , . . . , sk and potentially some other agents at the beginning of stage 2, together with a set of bribes b1 , . . . , bk that s pays to s1 , . . . , sk in exchange for their recommendation. For simplicity, we assume that bribes are spot transactions: each agent s j sends the recommendation at the same time that he receives the bribe. We assume that when the surpluses from hiring through the network and in the market are the same, t always hires in the market. Proof. Fix a pure strategy equilibrium robust to side deals with bribes. If a low type is hired in this equilibrium, then the expected surplus from the employment relationship is S, which is the same as hiring in the formal market, and hence t never hires through the network. It follows that in equilibrium only high types

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are hired in the network. Now suppose that in this equilibrium st (c) < α · (SH − S) and the high-type worker is hired. Then the T low type can propose a profitable side deal with bribes. As in the proof of the main theorem, this side deal includes all agents in a minimum cut separating s from t in G∞ and transmits an amount equal to the maximum flow to agents at the boundary of the cut. The bribes in the side deal are specified to equal the amounts that flow through agents s1 , . . . , sk in this flow. It follows that all agents weakly prefer accepting the side deal: intermediate agents at least break even by flow conservation, and the friends of s all break even because the bribes exactly compensate them for the payments to be made in the side deal. This contradiction shows that in any side deal–proof equilibrium where the high type is hired, we must st (c) ≤ α · (SH − S). Finally, if this inequality holds, then have T the transfer arrangement specified by the maximum flow in G∞ is easily seen to be an equilibrium robust to side deals with bribes. APPENDIX II: MICRO FOUNDATIONS FOR SOCIAL SANCTIONS In this Appendix, we develop a model where punishment at the level of the link arises endogenously. There are three key changes relative to the model presented in the main text: (1) with probability p > 0, the asset disappears, for example, is stolen by a third party, after the borrower uses it. (2) Each link “goes bad” with a small probability ε during the model, capturing the idea that friendships can disappear for exogenous reasons. (3) The utility of friendship is modeled using a “friendship game” where agents can choose to interact or stay away from each other. The payoffs of this friendship game depend on the capacity of the link and on whether the link has gone bad. A. Model Setup This model consists of the following six stages: Stage 1: Realization of Needs. Identical to stage 1 in Section III. Stage 2: Borrowing Arrangement. In this model, there is uncertainty about whether the asset disappears after being used. As a result, the arrangement is now a set of state-contingent payments, where the publicly observable state of the world i is either i = 0, if the asset is returned, or i = 1, if the asset is reported stolen. A borrowing agreement consists of two parts. (1) A contract specifying payments yi to be made by the borrower to the

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lender in the two states (i = 0 or 1). This contract can be thought of as a traditional incentive contract to solve the moral hazard problem in lending. If there were a perfect court system in the economy, then this contract would be sufficient to achieve efficient lending. (2) A transfer arrangement specifying payments hi (u, v ) to be made between agents in the social network if the borrower fails to make the payment yi . Here hi (u, v ) denotes a payment to be made by u to v in state i.32 Stage 3: Repayment. If an arrangement was reached in stage 2, the asset is borrowed and s earns an income of ω (V ), where ω(.) is a differentiable, nondecreasing function. Following the use of the asset, with probability p it is stolen. We assume that ω (V ) > pV for all V in the support of F, which guarantees that lending the asset is the socially efficient allocation. Even if the asset is not stolen, the borrower may choose to pretend that it is stolen and sell it at the liquidation value of φ · V , where φ < 1. The borrower then chooses whether to make the payment yi specified in the contract. Stage 4: Bad Links. At this stage, any link in the network may go bad with some small probability. We think of a bad link as the realization by a player that he no longer requires the business or friendship services of his friend. As we describe below, cooperation over bad links in the friendship game is no longer beneficial. Therefore, agents who learn that a link has gone bad will find it optimal not to make a promised transfer along the link. From a technical perspective, bad links are a tool to generate cooperation without repeated play, just like the “Machiavellian types” in Dixit (2003) (see also Benoit and Krishna [1985]). In an equilibrium where promised transfers are expected to be paid, failure by u to make a payment will be interpreted by v as evidence that the link has gone bad. In this case, v will defect in the friendship phase, which reduces the payoff of the deviator u by c (u, v ). To formalize bad links, assume that for every link of every agent, with a small probability ε > 0 independent across agents and links, the player learns that his link has gone bad at this stage. Thus, for any link (u, v ), the probability that the link has not gone bad is (1 − ε)2 ; and for any link (u, v ) where u does not learn that the link has gone bad, u still believes, correctly, that with probability ε the link has gone bad. 32. The circle of trust may restrict the links over which arrangements may be proposed. This case can be treated in the proof by assuming that G denotes the subgraph of permissible links.

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Stage 5: Transfer Payments. If the borrower chose to make payment yi in stage 3, then this stage of the game is skipped, and play moves on to the friendship phase. If the borrower did not make payment yi , then at this stage agents in the social network choose whether to make the prescribed transfers hi (u, v ). Each agent has a binary choice: either he makes the promised payment in full or he pays nothing. Stage 6: Friendship Game. Each link between two agents u and v has a friendship game with an associated value c(u, v). As long as the link is good, the friendship game is a two-player coordination game with two actions, with payoffs C D

C c(u, v) c(u, v) c(u, v)/2 0

D 0 c(u, v)/2 −1 −1

This game has a unique equilibrium (C,C) with payoff c (u, v ) to both parties, which represents the benefit from friendly interactions. A party only derives positive benefits if his or her friend chooses to cooperate; and benefits are highest when there is mutual cooperation. If a link has gone bad, cooperation is no longer beneficial, and the payoffs of the friendship game change: C D

C

D

−1 −1 0 0

0 0 0 0

Here, mutual cooperation leads to the low payoff of −1, capturing the idea that parties who are no longer friends might find it unpleasant to interact. If either party defects, the payoff of both parties is set to zero. The payoffs in the friendship game imply that if a player knows that a link has gone bad with probability 1, a best response is to play D. B. Model Analysis Because there is uncertainty in this model, we need to extend the concept of side deals to Bayesian games. DEFINITION 7. Consider a pure strategy profile σ and a set of beliefs μ. A side deal with respect to (σ, μ) is a set of agents S, a transfer arrangement hi (u, v ) for all u, v ∈ S, and a set of σu, continuation strategies and beliefs {( μu) | u ∈ S} proposed by s to agents at the end of stage 2, such that

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σu, (i) Uu ( σ S−u, σ−S | μu) ≥ Uu σu , σ S−u, σ−S | μu for all σu and all u ∈ S, (ii) The beliefs μ satisfy Bayes’ rule whenever possible if play is determined by ( σ S , σ−S ), (iii) Uu ( σ S , σ−S | μu) ≥ Uu (σ S , σ−S | μ) for all u ∈ S, σ S , σ−S | μu) > Us (σ S , σ−S | μ). (iv) Us ( The only conceptually new condition is (ii), which is clearly needed in a Bayesian environment. Motivated by this definition, our equilibrium concept will be a side deal–proof perfect Bayesian equilibrium. THEOREM 2. There exists a side deal–proof perfect Bayesian equilibrium that implements borrowing between s and t if and only if the asset value V satisfies (11)

V ≤ T st (c) ·

(1 − ε)2 . φ + p(1 − φ)

Proof. We begin by analyzing the optimal incentive contract in the absence of enforcement constraints. Suppose that s makes payments xi (i = 0 or i = 1) in the two states of the world. What values of xi guarantee that s chooses to return the asset and t breaks even? To prevent s from stealing, the excess payment if the asset is reported stolen must exceed the liquidation value φV : x1 − x0 ≥ φV.

(12)

For the lender to break even, he has to receive at least pV in expectation: (13)

px1 + (1 − p) x0 ≥ pV.

The minimum transfers that satisfy (12) and (13) are (14)

x0 = p(1 − φ)V

and

x1 = [φ + p(1 − φ)]V.

When the enforcement constraints are brought back, it is intuitive that borrowing can be implemented in the network as long as max [x0 , x1 ] does not exceed the maximum flow between s and t: in that case, the lender can just transfer xi to the borrower along the network. Because x1 > x0 , this requires that x1 not exceed the maximum flow, or equivalently V ≤ c (s, t) ·

2 (1 − ε) , φ + p(1 − φ)

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which is indeed the condition in the theorem. We now turn to the proof. Sufficiency. We begin by showing that when (11) holds, a side deal–proof equilibrium exists. Let xi be defined by (14) and let yi = xi . By assumption, there exists a flow with respect to the capacity c that carries x1 / (1 − ε)2 from s to t. For all u and v, define h1 (u, v ) to be 1 − ε times the value assigned by this flow to the (u, v ) link. Similarly, let h0 (u, v ) be equal to 1 − ε times a flow that carries x0 / (1 − ε)2 from s to t. Now consider the strategy profile in which (1) the transfer arrangement (xi , hi ) is proposed and accepted, (2) the asset is borrowed and returned unless stolen, (3) every agent u pays every promised transfer hi (u, v ) if necessary, unless he learns that his link with v has gone bad, and (4) all agents play C in the friendship game unless they learn that the link has gone bad, in which case they play D. This strategy profile σ generates beliefs μ, and (σ, μ) constitute a perfect Bayesian equilibrium. To see why, note that conditional on others making the transfer payments, it is optimal for s to make the payments yi and not to steal the asset. Also, because hi (u, v ) ≤ (1 − ε) c (u, v ), all agents find it optimal to make the transfer payments given beliefs. Finally, because on-path play never gets to the transfers, all intermediate agents are indifferent between accepting the deal and rejecting it. In fact, even if the transfers were used in one or both states on path, intermediate agents would still break even, because hi are defined using flows. We also need to verify that the equilibrium proposed here is side deal–proof. Consider any side deal, and let S denote the set of agents involved. Suppose that after the side deal, the borrower reports that the asset is stolen with probability p ≥ p. Let T be the complement of S in W, and consider the ( S, T ) cut. By definition, the expected amount that flows through the ( S, T ) cut in state i if yi is not paid equals xi . If the borrower never chooses to pay yi in the side deal, he will have to make sure that at least p x1 + (1 − p ) x0 gets to the cut in expectation. Because all intermediate agents must break even in expectation, this implies that s’s expected payments must be p x1 + (1 − p ) x0 or more. Thus the side deal comes with a cost increase of ( p − p) [x1 − x0 ]. The increase in expected cost is easily seen to be the same if the borrower chooses to pay yi in one or both states. The expected benefit of the side deal is ( p − p) φV . By equation (12) the expected benefit does not exceed the expected cost; the side deal is not profitable to s, which is a contradiction. Hence the original arrangement was side deal proof.

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Necessity. We now show that when (11) is violated, no side deal–proof equilibrium exists. We proceed by assuming to the contrary that a pure strategy side deal–proof perfect Bayesian equilibrium implements borrowing even though (11) fails. For simplicity, we assume that the equilibrium proposed transfers hi (u, v ) are expected to be paid by all agents u in stage 5 if the borrower chooses not to pay yi directly; that is, we only focus on equilibria where promises are kept. This condition is not necessary to obtain the result, but simplifies the proof somewhat. If this condition holds, then hi (u, v ) ≤ (1 − ε) c (u, v ) holds for all transfers proposed in equilibrium, because the amount by which u can expect to benefit from his friendship with v is at most (1 − ε) c (u, v ). Let χi = 1 if in state i on the equilibrium path, s chooses not to pay yi , and let χi = 0 otherwise. Case I. χ0 = χ1 = 1. In this case, on the equilibrium path, yi are never paid, and instead the transfer arrangements are always used. Define the expected transfer h = ph1 + (1 − p)h0 . By the individual rationality of intermediate agents, h satisfies weak flow conservation, and therefore by the lemma can be decomposed as h=

fu + h ,

u∈V, u=t

where fu is s → u flow and h = ft . In words, the fu flows deliver the expected profits to the intermediate agents, whereas h is an s→ t flow that delivers the expected payoff to the lender. Denote u=t fu = f ; then f is a weak flow delivering the payments to all intermediate agents. Our proof strategy will be the following. First, we take out the profits of all intermediate agents from the capacity c and the transfer h, essentially creating a “reduced” problem where intermediate agents are expected to break even. Then we construct a side deal for this simpler case using the maximum flow–minimum cut theorem, and finally, transform this into a side deal of the original setup. Let c (u, v ) = c (u, v ) − f (u, v ) / (1 − ε) be a capacity on G. Note that any flow g under c can be transformed into a flow g = g + f/ (1 − ε) that satisfies the capacity constraints c. Consider the functions hi = hi − f . It is easy to verify that hi / (1 − ε) satisfy the capacity constraints with respect to c and that h = ph 1 + (1 − p) h 0 . Let ( S, T ) be a minimal cut of the directed flow network with capacity c . By the maximum flow–minimum cut

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theorem, there exists a maximum flow g in the network that uses the full capacity of this cut. By assumption, the value of the cut un2 der h 1 satisfies h 1 (S, T )/ (1 − ε) ≤ g(S, T ) < x1 / (1 − ε) , which implies that (1 − ε) h1 (S, T ) − h0 (S, T ) < φV because (1 − ε) |h| ≥ pV . In words, the value flowing through the minimal cut in the two states does not provide sufficient incentives not to steal the asset. We now construct a side deal for the reduced problem. The idea is to construct a transfer arrangement that satisfies flow conservation inside S and delivers to the “boundary” of S the exact amount that was promised to be carried over to T under h . With such an arrangement, all agents in S will break even in each state, and thus the incentives that applied to S as a group will apply directly to agent s. Because S as a group did not have the right incentives, with the side deal s will not have the right incentives either. Formally, using the implicit summation notation, for each u ∈ S, g(u, T ), h 1 (u, T ), and h 0 (u, T ), let denote the amounts leaving S through u via the maximum flow g, h 1 , and h 0 . Clearly, (1 − ε)g(u, T ) ≥ h 1 (u, T ) and (1 − ε)g(u, T ) ≥ h 0 (u, T ). Now consider the restriction of g to the set S. This isa weak flow, and by as g = u∈S gu. Define the lemma it can be decomposed h

1 = u∈S (h 1 (u, T )/g(u, T )) · gu and h

0 = u∈S (h 0 (u, T )/g(u, T )) · gu. Then h

1 and h

0 are both weak flows in S, they satisfy hi

≤ (1 − ε)c , and they deliver exactly h 1 (u) and h 0 (u) to all u ∈ S. Thus hi

satisfies flow conservation within S, and delivers to the “boundary” of S the amount promised to be carried over to T under h 1 , as desired. The total value delivered by hi

is the value of the cut links under hi ; hence the amount that leaves s in the two states under h

satisfies (1 − ε)[|h

1 | − |h

0 |] < x1 − x0 , that is, is insufficient to provide incentives not to steal the asset. Now go back to the original network, and consider a side deal with all agents in the set S, where these agents are promised a transfer arrangement f + hi

. This is just adding back the profits of all agents to the side deal of the reduced problem. With this definition, the new side deal satisfies the capacity constraints f + hi

≤ (1 − ε)c because hi

≤ (1 − ε)c = (1 − ε)c − f . Second, all agents in S will be indifferent, because they get the same expected profits delivered by f (note that h

is a flow in both states and thus nets to zero state by state). The agents who have links that are in the cut are indifferent because h

is defined so that its inflow equals the required outflow for these agents. Third, the side deal

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does not have enough incentives for s not to steal the asset, because |h

1 | − |h

0 | < φV /(1 − ε). Moreover, if the original deal was beneficial for s, then so is the new deal. This is because the cost of the original deal was | f | + |h |. The cost of the new deal if the borrower follows the honest asset-return policy is | f | + |h

|. But both h and h

are flows, and they are equal on the (S, T ) cut; hence they have equal values. Therefore, by following an honest policy, the borrower will have a cost equal to what he had to pay in the original deal. However, because the incentive compatibility constraint is not satisfied, the borrower is strictly better off always stealing the asset in the side deal. This argument shows that there exists a side deal in which the borrower is strictly better off, and all other players are best-responding; hence the original equilibrium was not side deal proof. It remains to consider the cases where either χ0 or χ1 is equal to zero. In these cases, define the expected transfer payments as h = pχ1 h1 + (1 − p)χ0 h0 . As above, h is a weak flow and thus f , the weak flow delivering the expected profits to all intermediate agents can be defined. Similarly, one can define c and hi , and letting ( S, T ) be the minimal cut of c , h 1 (S, T )/ (1 − ε) < x1 / (1 − ε)2 must hold. Case II. χ0 = 1 and χ1 = 0. Then h = (1 − p)h0 and the decomposition h = f + h yields h0 = f/(1 − p) + h /(1 − p), so that h 0 = h0 − f = f · p/(1 − p) + h /(1 − p) is a weak flow, because it is a sum of two weak flows. It follows that |h0 | = | f | + |h 0 | ≥ | f | + |h 0 (S, T )|. Therefore | f | + |h

0 | ≤ |h0 |, because h

0 is a flow and h

0 = h 0 on the (S, T ) cut. Moreover, incentive compatibility requires y1 − (1 − ε)|h0 | ≥ φV , whereas the break-even constraint of the lender means that py1 + (1 − p)(1 − ε)[|h0 | − | f |/(1 − p)] ≥ pV . Combining these inequalities gives y1 ≥ x1 + (1 − ε)| f |. Now consider the side deal hi

+ f defined as above. Because |h

0 + f | ≤ |h0 | ≤ y0 /(1 − ε) and |h

1 + f | < x1 /(1 − ε) + | f | ≤ y1 /(1 − ε), the borrower will strictly prefer this arrangement to the previous one. Because all intermediate agents get net profits delivered by f in both states in the side deal, they are indifferent. Thus the proposed arrangement is indeed a side deal. Case III. χ0 = 0 and χ1 = 1. Here h1 is a weak flow, which must deliver less than x1 /(1 − ε) to t, because by assumption x1 /(1 − ε) is more than the maximum flow. Thus incentive compatibility fails with the original agreement; even without any side deal, the lender is better off not returning the asset.

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Case IV. χ0 = 0 and χ1 = 0. Here a valid side deal is to pay y0 in state zero and propose the transfer arrangement h

1 for state 1. All intermediate agents are indifferent because they were getting zero in the original arrangement, and because h

1 < x1 / (1 − ε) ≤ y1 / (1 − ε), the expected payment in the side deal is strictly lower than in the original deal. In the proof so far, we have only considered the case where the borrower does not steal the asset on the equilibrium path. If the equilibrium is such that the borrower always steals, then min (1 − ε) |h1 | , y1 ≥ V must hold. If χ1 = 1, then h1 /(1 − ε) is a weak flow with respect to capacity c that must transfer at least V /(1 − ε)2 to t. This leads to a condition on the maximum s → t flow that is stronger than (11). If χ1 = 0, then a valid side deal is to propose the transfer arrangement h

1 for both states. As above, all intermediate agents are indifferent, and h

1 < x1 / (1 − ε) ≤ y1 / (1 − ε) holds, which proves that the expected payment in the side deal is strictly lower than in the original deal. APPENDIX III: EMPIRICAL MODEL The utility function (7) that forms the basis of the discretechoice model can be micro founded in the following way. Suppose that borrower s needs a loan of value V and needs to decide which of his friends to borrow from. Each potential lender t has an opportunity cost k (V ) + ν S of providing the loan, where ν S is a supply shock unobserved to the borrower, which is independent across lenders. If the borrower chooses lender t, he is expected to repay both the value and the lender’s full opportunity cost.33 Beyond the cost of a loan, the choice of lender is also influenced by the level of trust. We assume that the true level of trust between s and t is α + T st (c) + ε M , where α + ε M reflects both measurement error in network-based trust and other sources of trust. When the expected repayment k (V ) + ν S exceeds the level of social trust between borrower and lender, the excess amount must be secured using physical collateral. We assume that providing such physical collateral (e.g., a radio or a bicycle) has an opportunity cost that equals γ times the value of collateral. With these assumptions, 33. In many societies there is a social convention that agents are only to repay the nominal amount borrowed. However, there is often an understanding that lenders should be further compensated using in-kind transfers and gifts. Here we do not distinguish between these different forms of compensation.

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the realized utility of borrowing from t is ω (V ) − γ · max 0, k (V ) + ν S − α − T st (c) − ε M − k (V ) − ν S , where ω (V ) is the utility from borrowing. In this expression ν S is unobservable, and hence s must take expectations over it. After taking expectations, we obtain (15) u V, T st (c) + ε M for some u function that is strictly increasing in the second argument when ν S has full support.34 If we also incorporate observed supply shocks ε S into the analysis, then the final utility representation becomes u V, T st (c) + ε M − ε S − ε S . Assuming that u is close to linear in the second argument, which would be the case if ν S had sufficient variance, letting ε S = (1 + 1/u2 ) ε S , where u2 is the derivative of u in the second argument, we can approximate this total utility as a linear function of T st (c) + ε M − ε S . In this representation, the error term captures a combination of supply shocks and measurement error in trust. YALE UNIVERSITY HARVARD UNIVERSITY AND NBER IOWA STATE UNIVERSITY UNIVERSITY OF CALIFORNIA–BERKELEY

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HOW DOES PARENTAL LEAVE AFFECT FERTILITY AND RETURN TO WORK? EVIDENCE FROM TWO NATURAL EXPERIMENTS∗ ¨ RAFAEL LALIVE AND JOSEF ZWEIMULLER This paper analyzes the effects of changes in the duration of paid, job-protected parental leave on mothers’ higher-order fertility and postbirth labor market careers. Identification is based on a major Austrian reform increasing the duration of parental leave from one year to two years for any child born on or after July 1, 1990. We find that mothers who give birth to their first child immediately after the reform have more second children than prereform mothers, and that extended parental leave significantly reduces return to work. Employment and earnings also decrease in the short run, but not in the long run. Fertility and work responses vary across the population in ways suggesting that both cash transfers and job protection are relevant. Increasing parental leave for a future child increases fertility strongly but leaves short-run postbirth careers relatively unaffected. Partially reversing the 1990 extension, a second 1996 reform improves employment and earnings while compressing the time between births.

I. INTRODUCTION Working parents of a newborn child have to give full attention to their baby and their jobs. Aiming to address this double burden for working parents, most OECD countries offer parental-leave (PL) provisions. However, although countries agree that parents of small children need support, the design of current PL systems differs strongly across countries. The purpose of this paper is to provide information on one key aspect of PL. We ask how PL duration affects a working mother who has just given birth to her first child. By studying the decision to give birth to a second child, we can provide information on the role of PL policy for ∗ We are grateful to Larry Katz and to four anonymous referees for their comments. Johann K. Brunner, Regina Riphahn, and Rainer Winkelmann and participants at seminars in Amsterdam, Basel, Frankfurt, Kobe, Rotterdam, Vienna, Zurich, SOLE 2006, ESSLE 2006, the Vienna Conference on Causal Population Studies, the IZA Prize Conference 2006, and the German Economic Association meeting of 2005 also provided valuable discussion on previous versions of this paper. We bear the sole responsibility for all remaining errors. Beatrice Brunner, ¨ Simone Gaillard, Sandra Hanslin, and Simon Buchi provided excellent research assistance. We are grateful for financial support by the Austrian Science Foundation (FWF) under the National Research Network S103, “The Austrian Center for Labor Economics and the Analysis of the Welfare State,” Subproject “Population Economics.” Further financial support by the Austrian FWF (No. P15422-G05), the Swiss National Science Foundation (No. 8210-67640), and the ForschungsStiftung of the University of Zurich (project “Does Parental Leave Affect Fertility Outcomes?” ) is also acknowledged. [email protected]; [email protected] C 2009 by the President and Fellows of Harvard College and the Massachusetts Institute of

Technology. The Quarterly Journal of Economics, August 2009

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higher-order births. This analysis is important for countries with fertility rates below the replacement level. Studying mothers’ return to work, postbirth employment, and postbirth labor earnings, the paper provides information on how PL duration affects subsequent work careers of working women. This analysis allows assessment of the extent to which extending parental leave facilitates balancing work and life. Moreover, studying the effects of parental leave on both fertility and work allows us to assess whether institutions that shape the terms of postbirth female employment spill over to fertility. Our analysis is based on the Austrian PL system. Under Austrian PL rules women can stay off work and return to the same (or a similar) job at the same employer thereafter. During the leave they receive a flat PL benefit of 340 euros per month. Interestingly, Austrian policymakers implemented two major reforms of the duration of PL—an extension of PL duration in 1990 and a reduction of PL duration in 1996. Specifically, before July 1, 1990, the maximum duration of PL ended with the child’s first birthday. The 1990 reform extended PL until the child’s second birthday for all children born on or after July 1. The 1996 reform partially reversed the extension granted in 1990 by taking away the last six months added in 1990. These policy changes create natural experiments that allow us to assess how changes in PL duration affect fertility decisions of a mother who has just given birth to a newborn child. Extending PL duration affects this decision in two different ways. First, the probability of a higher-order birth is potentially determined by the PL duration for the baby that is already born. This is what we call the current-child effect. This effect is potentially important in the Austrian context because women who give birth no later than 3.5 months after the end of a previous PL are exempt from the work requirement and can automatically renew PL eligibility for the second child. Before the 1990 reform, mothers needed to give birth to a new child within 15.5 months. Such a tight spacing of children is both biologically difficult and not desired by many parents. The 1990 reform increased this period to 27.5 months, thus providing much broader access to automatic renewal. The 1996 reform reduced the automatic renewal period to 21.5 months—a space between births that is biologically feasible and potentially desired. Second, the probability of a higher-order birth is also determined by PL duration for the baby yet to be born. This is what we call the future-child effect. Because PL duration directly

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affects the costs associated with childbearing, the future-child effect is expected to increase fertility. This paper also studies how PL rules affect postbirth labor market careers of mothers with newborn children. The 1990 extension of leave encourages a mother to stay home with her child in the second year after birth and to delay return to work substantially. Future employment and labor earnings will be affected in two ways. First, providing parents with extended PL encourages mothers to stay off work longer and lowers employment and labor earnings immediately after a birth. This short-run effect is mechanical and intended by policy makers. Second, prolonged periods of absence from the workplace may lead to skill depreciation and weaker labor market prospects after labor market reentry. This potential for long-run deterioration of women’s postbirth careers is clearly not intended by policy. Although family policies in many countries are designed to support low-income (and often nonworking) women, the Austrian case is interesting because it affects working women of all income groups. However, it is not a priori clear for which group the PL rules generate the strongest incentives. The flat PL benefit implies that lower-income parents have a higher earnings replacement ratio. To shed light on the importance of cash transfers, we look at differences in response between high- and low-income women. The job protection policy may be more important for career-oriented women. This is because job protection shields working women from future income losses due to firm-specific human capital depreciation or deferred payment contracts. To shed light on the importance of job protection, we look at differences in responses between blue- and white-collar women. As firm-specific human capital and internal labor markets are arguably more important in white-collar professions, we would expect stronger responses from white-collar women. The empirical analysis draws on a unique and very informative data set, the Austrian Social Security Database (ASSD). Set up to provide information to calculate pension benefits for private sector employees (about 80% of Austrian employment), the ASSD collects detailed information on a woman’s earnings and employment history from employers; and it also contains information on take-up of PL benefits and on a woman’s fertility history from the point of time when she first worked in the private sector. We extract information on PL-eligible women who gave birth to the first child observed in ASSD in periods that cover the reform, and we

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analyze subsequent fertility and labor market outcomes both in the short run (three years after the first birth) and in the long run (ten years after the first birth). Our empirical analysis uncovers five key results. First, we find that the extension of PL enacted in July 1990 had a strong impact on subsequent fertility behavior. We find that both the current-child PL effect and the future-child PL effect are quantitatively large. In the short run (within three years) fertility increases by 5 percentage points (15%) as a result of extended leave on the current child and by 7 percentage points (21%) as a result of extending leave for the future child. Second, we find not only that fertility increases temporarily, but also that this increase persists in the long run. Among women eligible for the more generous PL rules, three out of 100 women gave birth to an additional child within ten years after the birth of the first child who would not have done so with short leave. Although we do not observe the completed fertility cycles of mothers, we conclude that it is quite likely that the policy change affected not only the timing but also the number of births. Third, we find that most mothers exhaust the full duration of their leaves and that return to work is substantially delayed even after PL has been exhausted (by 10 percentage points in the short run and by 3 percentage points in the long run). Interestingly, although work experience and earnings decrease strongly in the short run, we do not find that longer leaves have long-run effects on work experience and cumulative earnings. Fourth, there are differential fertility responses of highand low-wage women and blue- and white-collar workers, indicating that both cash transfers and job protection have a sizable impact on fertility and labor market responses. Fifth, we find that the 1996 reduction of PL duration had a significant effect on the timing of subsequent births but no impact on the number of children. The 1996 partial reversal of the extension granted in 1990 also partially undoes the short-run reductions in employment and earnings generated by the 1990 extension of PL duration. This paper contributes to the literature on the impact of cash transfers on fertility behavior (Hardoy and Schøne 2005; Milligan 2005) and to the literature on the effects of welfare reform on fertility behavior of low-income women in the United States (Hoynes 1997; Moffitt 1998; Rosenzweig 1999; Joyce et al. 2004; Kearney 2004).1 Furthermore, Averett and Whittington (2001) study the 1. Bj¨orklund (2007) provides a survey of recent empirical work on the impact of family policies on fertility.

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impact of the Family and Medical Leave Act in 1993 on fertility. Hoem (1993) studies the impact of PL rules (“speed premium”) for Sweden, and Piketty (2003) looks at parental education benefits in France. This paper also contributes to the literature studying the effects of family leave on labor market outcomes. Klerman and Leibowitz (1997, 1999) and Baum (2003) find only weak effects on employment and wages. Berger and Waldfogel (2004) for the United States, Baker and Milligan (2008) for Canada, and Ruhm and Teague (1997) and Ruhm (1998) for European countries find a closer relationship between PL provisions and the labor market attachment of mothers. Albrecht et al. (1998) show that PL-induced career interruptions are not associated with a wage penalty for women in Sweden. Sch¨onberg and Ludsteck (2007) study the causal effects of successive changes in PL duration on employment and earnings in Germany.2 Our paper adds to this literature in at least four ways. First, our empirical analysis provides convincing evidence on the effects of changing PL duration for the current child by adopting a quasiexperimental approach. Second, our study also provides evidence on the effect of changing PL duration on the future child. Understanding these two effects is crucial in PL design. Third, our results speak to the important issue of how policies that enhance the balance between work life and family life affect fertility behavior. This is different from many previous papers that have focused on the effect of cash transfers on fertility. Fourth, our empirical analysis allows assessing the effects of changes in PL on both short- and long-run labor market outcomes for mothers. This allows addressing the frequently raised concern that generous PL policies will harm mothers in the long run because extended periods off work lead to depreciation of human capital and worse future labor market prospects.3 The paper is organized as follows. The next section discusses the institutional setup and develops testable hypotheses as to how the reform might have affected fertility and labor market 2. Several recent papers study the effects of parental leave or child care on child development (Baker and Milligan 2008; Dustmann and Sch¨onberg 2008; Berger, Hill, and Waldfogel 2005; Baker, Gruber, and Milligan 2008). A further related literature analyzes the impact of financial incentives on fertility and labor supply using a structural approach. See Moffitt (1984) for an early approach to this question and Laroque and Salani´e (2005) for a more recent study of the effects of financial transfers on fertility and labor supply. 3. In a companion paper, we discuss how the two Austrian reforms affect the ¨ quality of mothers’ first postbirth jobs (Lalive and Zweimuller 2007). The analysis of the current paper is more comprehensive in providing a detailed assessment of the overall effects of PL on earnings and employment in all postbirth jobs.

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behavior. Section III discusses the data and presents our empirical strategy for measuring the effects of PL duration on the current child and on the future child. Section IV presents the fertility and labor market effects of the increase in PL duration for the current child enacted with the 1990 reform. Section V studies the effect of the 1990 increase in PL duration for the future child. Section VI analyzes the impact of the 1996 reform, and Section VII concludes with a discussion of the relevance of our findings. II. BACKGROUND AND HYPOTHESES This section provides the institutional background of the Austrian PL system and discusses how two reforms in the 1990s may affect higher-order fertility and work careers of mothers. II.A. The Austrian PL System in the 1990s Working women have access to two types of family policies in Austria: maternity leave and parental leave. Maternity leave lasts for sixteen weeks (eight weeks before and eight weeks after the actual birth) and pays the average wage rate over the last quarter before the birth. Before July 1990, PL started after maternity leave ended and lasted until the child’s first birthday. To become eligible for PL a mother had to satisfy a work requirement. Women taking up PL for the first time had to have worked (and paid social security contributions) for at least 52 weeks during the two years prior to birth or be eligible for unemployment benefits—again fulfilling a work requirement of 52 weeks out of the two years prior to entering unemployment. For mothers with at least one previous take-up of PL or first-time mothers below the age of twenty years, the work requirement is reduced to twenty weeks of employment during the last year prior to birth. Moreover, PL is also renewed if the mother gives birth within a “grace period” that extends up to four months after the end of an earlier leave.4 4. The exact legal definition of the length of the grace period is that the work requirement is also abandoned if a new maternity protection period starts within a grace period of six weeks after the formal termination of a previous PL. Because maternity protection starts about eight weeks before the due date, the rules effectively imply that eligibility for PL is renewed for any new child expected to be born within fourteen weeks after the end of the previous leave. Because expected birth dates are not observed in our data, we consider a birth to be realized within the automatic renewal window if it occurs no later than four months after the end of the previous PL. Work exemptions for higher-order births are in place in countries where PL lasts long enough so that women could give

PARENTAL LEAVE, FERTILITY, AND RETURN TO WORK Work required for PL

Maternity leave and PL benefits

0

0

200

10

Weeks

Euros 600 400

20

800

30

1000

1369

0

2

4

6

8

10 12 14 16 18 20 22 24 26 28 30 32 34 36 Time since birth (months)

Before July 1990 July 1990 until June 1996

(A) Monthly transfer income

After July 1996

0

2

4

6

8

10 12 14 16 18 20 22 24 26 28 30 32 34 36 Time since birth (months)

Before July 1990 July 1990 until June 1996

After July 1996

(B) Work requirement for higher-order births

FIGURE I PL Benefits and Work Requirement for Higher-Order Births Figure shows the benefit path for a women earning real 1,000 euros per month before giving birth to her first child (A) and the number of weeks she needs to work for parental leave to cover the subsequent child (B). The parental leave benefit is 340 euros per month irrespective of prebirth monthly income. Dotted line refers to the situation before July 1990, solid line refers to the situation between July 1990 and June 1996, and dashed line refers to the post–July 1996 rules. Source. Austrian federal laws, various years.

PL provisions are twofold. On the one hand, PL protects the previous job. A mother has the right to return to her previous employer until PL ends. Moreover, she cannot be dismissed during the first four weeks after returning to work.5 On the other hand, PL is associated with a government transfer. A mother eligible for PL in 1990 received a PL benefit of about 340 euros per month (31 percent of gross median female earnings). Benefits are not means-tested and not taxed, implying a median net income replacement ratio of more than 40 percent. Single women (or women with a low-income partner) are eligible for higher benefit levels (Sonderunterstutzung). ¨ Figure IA shows the time path of transfer income for a PLeligible woman who has earned 1,000 euros per month during the quarter before birth. Maternity leave transfers amount to 1,000

birth to a new child while being covered by a PL from a previous child. In Germany, job protection is extended when a mother gives birth to a child within a current leave. The “speed premium” in Sweden grants higher PL benefits to parents who have subsequent children within sufficiently short intervals. Also, the PL systems of the Czech Republic, Slovakia, and Estonia feature renewal rules that are very similar to the Austrian system. 5. PL renewal makes mothers eligible for a maternity leave transfer that is eighty percent higher than the regular PL transfer. The maternity leave transfer of mothers who work in between two births equals the average wage in the three months prior to giving birth (the same as for a first birth). PL renewal leaves job protection unchanged.

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euros for a period of about two months after birth.6 After maternity leave has been exhausted, this mother has two options. One is to arrange care for her newborn child and return to her prebirth job earning 1,000 euros per month. This option is complicated by the fact that the Austrian child care system for children under the age of three years is rather limited. Alternatively, she can provide care for her newborn child and take up PL, earning 340 euros per month until her child turns one year old. On her child’s first birthday, she can decide to return to her prebirth job, take up a new job, or continue to provide care for her child. In the event that she gives birth to a new child before her previous child turns 15.5 months old, she has access to renewed leave (Figure IB). Any child born after that date will be covered only if the mother has been working for at least twenty weeks prior to giving birth to the new child. In July 1990, a first PL reform increased the maximum duration of PL to two years and was enacted on July 1, 1990.7 A further reform in 1996 introduced a change in PL duration by introducing a one-partner PL maximum of eighteen months. Because Austrian fathers effectively do not take up PL, the one-partner maximum removed the last six months of PL that were added in 1990.8 6. Because maternity leave is initiated eight weeks prior to expected date of birth, the pre- and postbirth durations of maternity leave vary. 7. In December 1989, the PL system was changed from a “maternity” to a “parental” leave system, allowing for the father to go on PL also. However, this is of no practical consequence. In 1990 fewer than 1% of fathers took advantage of that possibility. A second change was that women in farm households and family businesses, as well as women who did not meet the employment requirements, became eligible for a transfer equal to 50% of regular PL benefits up until the child’s second birthday. This is of no importance in the present analysis because we confine ourselves to behavior of female dependent employees. Furthermore, the reform made it possible to take part-time PL, either between a child’s first and second birthday (by both parents at the same time) or between a child’s first and third birthday (only one parent or both parents alternating). 8. Compared to the U.S. Family and Medical Leave Act (FMLA), the Austrian PL rules are very generous. The FMLA grants twelve weeks of unpaid leave to employees in firms with more than fifty workers. Compared to current OECD systems, the pre-1990 PL system was of average generosity. The rules were very similar to those currently in place in Canada (twelve months PL, cash transfer 55 percent of previous earnings), Australia (twelve months PL, unpaid), or the United Kingdom (eighteen weeks paid maternity leave, thirteen months unpaid PL). Austrian post-1990 rules are more similar to those currently in place in continental Europe. The German system grants three years of PL and a generous cash benefit (100 percent of prior earnings on maternity leave, 67 percent of prior earnings for the first fourteen months of PL, and a flat transfer thereafter). In France mothers get three years of PL, 80 percent of prior earning for the first twelve months, and a flat transfer thereafter. Also, Sweden and Norway offer long leaves and PL benefits replace a very large fraction of prior income. Interestingly, the renewal option is not unique to the Austrian system. The Swedish “speed premium” shares similarities, as PL benefits are extended when an additional

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II.B. Effects on Fertility and Work Careers Extending PL from one year to two years may affect future fertility for two different reasons: (i) a longer PL duration for the current child facilitates access to automatically renewed PL benefits for a new child; and (ii) a longer PL duration for the future child reduces directly the cost of this child. Arguably, taking advantage of PL renewal is difficult when PL leave is short. The one-year policy forces a mother who wants PL protection for the future child to conceive a new child quite early after the birth of the previous child.9 The 1990 reform adds twelve crucial months to the automatic renewal period. Thus, achieving automatic PL coverage for a future child is easier under the two-year policy than under the one-year policy (Figure IB).10 In contrast to the 1990 PL extension, the 1996 PL reduction did not change the biological feasibility of PL renewal. To become eligible without having to go back to work, a mother has to give birth to a new child within 21.5 months. By inducing mothers to give birth to a future child within the automatic renewal period, the 1990 PL extension is likely to change the spacing of births. Note, however, that any shock inducing mothers to give birth to planned children earlier may translate into a long-run increase in the total number of children. As fertility plans are realized earlier, shocks to partnerships, health, etc., that are inducing parents to give up family plans in a one-year system have weaker effects on fertility in a two-year system.11 child is born within two years after the birth of a previous child. The German system also grants the possibility of PL renewal with respect to job protection (but, unlike in the Austrian system, PL benefits do not cease when a parent goes back to work). The PL systems of the Czech Republic and Slovakia are almost identical to the Austrian system and have the PL renewal feature. 9. To see this more clearly, consider a woman who gives birth on September 1, 1988. She would be entitled to PL through September 1, 1989. To qualify for PL renewal, with the eight-week prebirth maternity leave and the six-week post-PL grace period, she would have to give birth by December 14, 1989. Note that this requires conceiving a new child by March 1989, no later than 5.5 months after giving birth to the previous child, implying a space between births of at most 15.5 months. 10. Under the two-year policy, a woman who gives birth on September 1, 1990, qualifies for PL renewal if a second child is conceived by March 1992, or 18 months subsequent to giving birth to the previous child. 11. Notice that when this argument is applied to the 1996 PL reduction, it is not clear whether this reform will lead to more or less children. On the one hand, the 1996 reform requires a tighter space between births for a mother who takes advantage of renewal. On the other hand, although the required space is biologically feasible, it is shorter than before and may induce some mothers to delay a planned birth. The first effect increases and the last effect decreases the number of births.

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Extending PL may also affect higher-order fertility because it lowers the cost of having a future child. Ceteris paribus, a twoyear leave for the future child is more attractive than a one-year leave. Thus, the 1990 reform is expected to increase the number of children born to women exposed to the new policy. The second key aim of PL policies is to facilitate balancing family work and market work. Changes in the duration of PL for the current child may affect mothers’ work careers in two ways. Take-up of extended leaves delays return to work, lowers employment, and lowers labor earnings in the short run (0–36 months after the birth of the current child). Moreover, prolonged career interruptions may also lead to mothers’ postbirth careers deteriorating in the long run (37 to 120 months after the birth of the current child). Changes in PL duration for the future child are expected to affect short-run postbirth work careers only indirectly, via their effect on births. Austrian PL offers two distinct types of benefits: a flat transfer and job protection. Flat transfers translate into strong differences in replacement rates. We therefore expect strong heterogeneity in the responses to changes of PL in mothers with high earnings prior to birth and mothers with low prebirth earnings. Moreover, PL policies target not only costs associated with foregone current income but also costs associated with loss of lifetime income following a job loss. A longer duration of job protection may be particularly beneficial for mothers with firm-specific human capital or mothers who are on deferred payment contracts. To shed light on this issue, we compare women working in white-collar occupations to women in blue-collar jobs. Arguably, job-specific human capital, internal labor market, and career concerns are more important in white-collar jobs, so the job-protection channel should trigger stronger responses for white-collar women than for blue-collar women. III. DATA AND EMPIRICAL STRATEGY In this section we first discuss the available data. We then present the empirical strategies and explain the assumptions under which we identify the causal effect of changes in PL duration on fertility and labor market outcomes. III.A. Data Our empirical analysis is based on the Austrian Social Security Database (ASSD). This database collects information relevant

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to old-age social security benefits. As these benefits depend on individuals’ earnings and employment histories, the database collects information on work histories for the universe of Austrian private sector employees. Furthermore, the database also contains information on exact dates of births. A disadvantage of the ASSD is partial recording of birth histories. ASSD records all births that occur after a woman’s first job in the private sector. This means that we can precisely determine the relative parity of any birth but we cannot determine any birth’s absolute parity.12 Our ASSD extract covers women giving birth to their first ASSD child in the years 1985, 1987, 1990, 1993, and 1996. We observe second-child births, return to work, employment, and earnings for these women until the year 2000, allowing us to analyze about ten years of a woman’s life for the 1990 reform and less than that for the 1996 reform. We focus on mothers who are likely to be at parity one because this yields a comprehensive picture of how changes in PL on this first child affect future fertility and work careers.13 We establish PL eligibility for these women by considering work careers two years prior to their giving birth to the first child. Note that measuring eligibility is complicated because a woman’s work career in the public sector is unobserved (but counts for PL eligibility) and because a woman’s parity is unobserved. Our eligibility indicator allocates a woman into the PL-eligible group if she demonstrates any employment or has ever been eligible for unemployment benefits in the two years prior to giving birth. Clearly, this definition of eligibility may give rise to misclassifying ineligible women into the eligible group, thus reducing take-up. More importantly, this encompassing definition of eligibility allows identification of a group of ineligible women (who neither worked nor received unemployment benefits in the two

12. Partial recording of previous births implies that we cannot precisely determine the parity of a birth. To make things precise, assume a working woman gives birth to a child at age thirty. If this woman is continuously employed in the private sector, we know this birth is her first birth and all subsequent births are recorded in the ASSD. However, if this woman entered the ASSD, say, at age 25 (e.g., because she was previously employed in the public sector and not covered by the ASSD), she could have could have given birth to children before entering the ASSD. More generally, if we observe x previous births in the data, we know that any subsequent birth is of parity x or higher. 13. Our focus here is on mothers, even though fathers could in principle take up PL provisions too. There are two reasons that we do not include fathers in our analysis. First, take-up by fathers is extremely low. Second, our database does not provide information on the dates of birth of a father’s children. Hence, fathers’ reactions to PL policies cannot be addressed in the present context.

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years before giving birth) who do not go on to collect PL in our data. This finding makes us confident that we cleanly identify the group of PL-ineligible women—a group that is of importance in discussing the validity of the empirical strategy measuring the effect of changing PL duration for the future child. Furthermore, in line with demographic research, we restrict attention to women aged 15 to 45 years when giving birth to their first ASSD children. The ASSD allows constructing a set of four key outcome measures. Information on the date of birth of the second ASSD child allows measuring whether a mother gives birth to at least one additional child. Information on the date of return to work allows discussing return-to-work decisions. Information on the woman’s work and earnings career allows assessing employment and earnings in the two years prior to giving birth and up to ten years after birth. In the analysis below, we measure employment and earnings at a yearly frequency relative to the birthday of the first child. The set of conditioning variables comprises information on employment, unemployment, and earnings since entry into ASSD (either 1972 or time of entry into the labor market) and on a woman’s labor market position exactly one year prior to birth (employed or unemployed, industry and region of employer, daily labor income white-collar or blue-collar occupation).14

III.B. Empirical Strategy Our empirical strategy uses the 1990 and 1996 PL reforms to identify the effect of PL duration for the current child and the effect of PL duration for the future child. Table IA shows PL durations for the current and the future child for three cohorts of women who gave birth to a first child at three different dates: July 1990, June 1990, and June 1987.15 July 1990 mothers are eligible for 24 months of PL for the current child and PL renewal takes place when a future child is born within 27.5 months after the July 1990 birth. PL duration is 24 months for any child born within three years. June 1990 mothers are eligible for 12 months of PL for the current child and PL renewal is possible when a future child is born within 15.5 months. PL duration is 24 months for any child born within three years. June 1987 mothers are eligible for 12 months of PL for the current child and any 14. The data do not have information on hours, education, or marital status. 15. Table IB displays the analogous cohorts for the 1996 reform.

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TABLE I EMPIRICAL DESIGN

Current child born

Parental leave current child

Automatic renewal

Parental leave future child (born within 36 months)

June 1987 June 1990 July 1990

(A) 1990 reform 12 months 15.5 months 12 months 15.5 months 24 months 27.5 months

12 months 24 months 24 months

June 1993 June 1996 July 1996

(B) 1996 reform 24 months 27.5 months 24 months 27.5 months 18 months 21.5 months

24 months 18 months 18 months

Source: Austrian Federal Laws, various years.

future child born within 36 months. PL is automatically renewed if the future child is born within 15.5 months. Identifying the Current-Child PL Effect. Can the currentchild PL effect be identified from a comparison of June 1990 mothers with July 1990 mothers? These two groups differ in the duration of the PL renewal period (and the associated PL duration for the first child), but they have the same PL duration for a future child. The crucial identification issue is to what extent mothers could have influenced the date of birth of the current child in anticipation of the policy change. There are at least two reasons that lead us to believe that mothers cannot have “timed” births. First, the conception of a child is an event that cannot be perfectly planned by parents. Second, even if parents could deterministically plan a birth, self-selection requires that parents have been informed of the July 1990 policy reform at the date of conception. We performed a content analysis of the major Austrian newspapers to check the information that potential parents had nine months before the June/July 1990 births, that is, in September/October 1989. The public discussion about the PL reform started in November 11, 1989, but the ruling coalition (social democrats and conservatives) discussed it until April 5, 1990, until it had designed a policy reform apt to find parliamentary approval. Because it was not clear until three months prior to the policy change whether a PL reform would take place and how it would be implemented, the June/July 1990 births were not influenced by anticipation of the July 1990 PL reform. However,

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although anticipation of the PL reform at the date of conception is unlikely, it is still possible that mothers could have influenced the timing of a birth by postponing induced births or planned caesarean sections.16 We assess the presence of such fine tuning in two ways. First, analyzing the number of children born in June and July 1990, we do not find evidence of a spike in births on July 1, 1990. Second, because birth timing is likely to be strongest right around the reform date, we assess the sensitivity of our results by excluding births occurring one week before and one week after July 1, 1990.17 Because babies’ dates of birth assign extended PL and parents could not anticipate extended leave, we can identify the currentchild PL effect by comparing treated mothers giving birth (to the current child) in July 1990 to control mothers giving birth in June 1990.18 Although treatment and control samples are selected over two successive months, we consider their fertility and labor market outcomes over the following 36 months (short-run effects) and the following 120 months (long-run effects). Differences between treated and control mothers cannot be attributed to differences in the environment. In fact, the treated and control mothers are facing different parental leave incentives but practically identical economic conditions following the June/July 1990 birth. Identifying the Future-Child PL Effect. To identify the effect of PL duration on the future child, we compare short-run (0–36 months after birth) and medium-run (37–72 months after birth) outcomes of June 1987 to June 1990 mothers. Identification of the 16. Gans and Leigh (2006) show that the introduction of the Australian baby bonus on July 1, 2004, led to a significant increase in the number of births on that same day, suggesting that parents postponed their births to ensure they were eligible for the bonus. Similarly, Dickert-Conlin and Chandra (1999) show that the U.S. tax system creates an incentive to give birth to a child on the 31st of December rather than on the 1st of January. They find that the probability that a child is born in the last week of December, rather than the first week of January, is positively correlated with tax benefits. 17. Mothers could also have changed prebirth work patterns in order to become eligible for extended leave. Empirical evidence on prebirth employment in Figure VC is not consistent with such qualification effects. 18. This is essentially a regression discontinuity framework (RDD). Denote the treatment status of a mother by D, where D = 1 if a mother has access to a two-year leave, and D = 0 if a mother has access to a one-year leave. Eligibility for treatment is a discontinuous function of the current child’s date of birth T . Denote by t the date when policy changes (July 1, 1990, for the change from the 12-month to the 24-month policy and July 1, 1996, for the change from the 24-month to the 18-month policy). Provided that lim→0 Pr(D = 1|T = t + ) = lim→0 Pr(D = 0|T = t − ), our design satisfies the “fuzzy” RDD assumption (Hahn, Todd, and Klaauw 2001). Figure II is consistent with this assumption being strongly satisfied.

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future-child PL effect requires stronger assumptions than those needed to identify the current-child PL effect. The central identifying assumption is that there are no substantial cohort or time effects that pollute the comparison between June 1987 and June 1990. We propose three ways of assessing the plausibility of this assumption. First, we analyze PL-ineligible women as a control group and check whether outcomes for June 1990 mothers follow a different trend than outcomes for June 1987 mothers, finding no significant time trend. Clearly, this small control group is less than perfect because it encompasses women with weak prebirth labor market attachment. Second, we study time and cohort trends for PL-eligible mothers both before and after the 1990 reform. Third, we also exploit the way PL rules change with time since first birth. Although differences in PL rules between the treated and the control group exist during the first 36 months, the same rules apply 37–72 months after birth. Thus, treated and control mothers should differ in the period 0–36 months after birth but less so in the period 37–72 months after birth. Finally, adding up the effect of extending current leave with the effect of extending future leave allows estimating the total effect of PL duration and PL renewal. Arguably, this total effect comes close to the effects generated by moving fully from a oneyear to a two-year system—an effect of prime policy interest. IV. EXTENDING PL DURATION FOR THE CURRENT CHILD This section discusses the effects of extending PL duration for the current child on fertility and return-to-work behavior. The analysis proceeds in three steps. We first document the fertility effects of changing PL duration for the current child. Next, we turn to labor market responses. And finally, we assess the potential heterogeneity in the responses to the reform by groups that differ in income and in broad occupation IV.A. The Impact on Fertility The ASSD reports information on PL take-up. Focusing on PL eligible mothers of newborn children, Figure II reports average PL take-up (including zeros) associated with a first child born between June 1 and July 30, 1990. June 1990 mothers are eligible for ten months of the parental leave (excluding the first two months of maternity leave). Results indicate that of these ten months, June 1990 mothers take up on average nine months of PL.

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1/6/90

16/6/90

1/7/90 Calendar day Before

16/7/90

31/7/90

After

FIGURE II Parental Leave Taken with Current Child June smoothed backward, July smoothed forward (15-day moving average). Source. ASSD, own calculations. Sample restricted to PL-eligible women giving birth to a child in June 1–30 or July 1–30 of 1990.

In contrast, average PL take-up by July 1990 mothers amounts to 19 months, which is considerably more than for any mother giving birth in June 1990. Interestingly, average PL take-up is about 85 percent of the 22 months covered by PL after the 1990 reform (after two months of maternity leave). This suggests that the second year of leave is valued by the majority of eligible women. Figure II suggests comparing treated mothers who give birth in July 1990 to control mothers who give birth in June 1990. How informative is this contrast on the causal effect of extending PL duration for the current child? Table II provides descriptive evidence on PL take-up by years since birth as well as on key prebirth characteristics. Treated and control mothers are identical with respect to PL take-up in the first year after giving birth to their current child. Both cohorts take up about 9.2 months out of the roughly 10 months offered by the PL system. Striking differences in PL take-up appear in the second year after birth. Whereas treated mothers spend about ten months on PL, control mothers spend less than one month on PL (with their second child).

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TABLE II DESCRIPTIVE STATISTICS, MOTHERS GIVING BIRTH IN JUNE AND JULY 1990 July 1990 Mean Parental leave, yr 1 (mths) Parental leave, yr 2 (mths) Age 20–24 Age 25–29 Age 30–34 Age 35–44

9.208 10.082

SD

June 1990 Mean

(A) Treatment (2.194) 9.196 (3.486)

0.795

(B) Demographics 0.423 (0.494) 0.443 0.346 (0.476) 0.343 0.109 (0.311) 0.087 0.029 (0.167) 0.025

SD

Est

SE

(2.139)

0.012 (0.055)

(2.209)

9.287 (0.074)∗∗∗

(0.497) −0.02 (0.475) 0.004 (0.282) 0.022 (0.156) 0.004

(C) Labor market history Employment (years) 5.846 (3.94) 5.701 (3.792) Unemployment (years) 0.265 (0.543) 0.257 (0.484) Earnings not observed? 0.028 (0.165) 0.026 (0.16) (1 = yes) Daily earnings (euros) 34.49 (42.942) 33.313 (37.719) Employed (1 = yes) White collar (1 = yes) Daily 1989 earnings (euros) Observations

Contrast

(0.013) (0.012) (0.008)∗∗∗ (0.004)

0.144 (0.098) 0.008 (0.013) 0.002 (0.004) 1.178 (1.026)

(D) One year before birth 0.868 (0.339) 0.867 (0.339) 0.001 (0.009) 0.435 (0.496) 0.441 (0.497) −0.006 (0.013) 36.826 (20.935) 36.142 (20.397) 0.684 (0.526) 3,225

2,955

Source: ASSD, own calculations. Sample restricted to PL-eligible women giving birth to a child in June 1–30 or July 1–30 of year 1990. Notes: Mean and standard deviation (in parentheses) for women giving birth to their first child in June 1–30 or July 1–30, 1990. Labor market history covers the period from January 1972 to date of birth in June or July 1990. Labor earnings are unobserved for women coming from the public sector, which is not covered by ASSD. Daily earnings refer to real mean earnings measured in year 2000 euros per day worked—real total labor earnings divided by work experience. Daily 1989 earnings are earnings on the prebirth job measured in year 2000 euros—the job held exactly one year before giving birth. Data also contain information on region and industry of the prebirth employer.

In contrast to PL take-up, both cohorts appear to be quite similar with respect to prebirth characteristics. Both groups show similar amounts of previous work and unemployment experience and previous average labor earnings. Also, labor market status one year before the 1990 birth differs only slightly. Although July 1990 mothers are significantly more likely to be in the age bracket 30–34 years than June 1990 mothers, the overall age composition is quite comparable. Almost 80 percent of all births occur in the age group 20–29 and about 13 percent at ages thirty and older.

1380

25

30

Percent

35

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1/6/90

16/6/90

1/7/90 Calendar day Before

16/7/90

31/7/90

After

FIGURE III How Does Parental Leave Affect Higher-Order Fertility? Figure reports the percentage of women who gave birth to at least one additional child within three years after giving birth in June or July 1990. June smoothed backward, July smoothed forward (15-day moving average). Source. ASSD, own calculations. Sample restricted to PL-eligible women giving birth to a child in June 1–30 or July 1–30 of 1990.

Table II also indicates that there are substantially more births in July 1990 than in June 1990. Is this evidence for birth timing? We investigate this issue by analyzing the number of births in June and July 1990 on a day-to-day basis, finding a steady increase but no discontinuity in the number of births on July 1 (not reported). Thus, comparing June 1990 mothers to July 1990 mothers, we find little evidence of seasonality in the composition of cohorts but strong seasonality in the number of births.19 Figure III presents first evidence on the causal effect of extending PL for the current child on the decision to have an additional child. The vertical axis measures the percentage of women who gave birth to a second child within the 36 months following 19. Indeed, births in July exceed births in June in any given year of our sample period (1985, 1987, 1990, 1993, 1996). Nevertheless, we perform sensitivity tests comparing births that occur, respectively, in the first/second half of June 1990 and the first/second half of July 1990 to assess the sensitivity of our results to short-run timing of births.

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the 1990 birth. To smooth out the noise in date-of-birth data, Figure III presents fifteen-day backward moving averages for June and fifteen-day forward moving averages for July. Results indicate that 32.2 of 100 women in the control group give birth to an additional child within the 36 months. In contrast, almost 36.7 of 100 women do so in the treated group. Thus, almost 5 of 100 women tend to give birth to an additional child in the treated cohort who do not do so in the control group. The magnitude of this effect seems quite robust and varies only slightly over the particular time window one adopts. Table III discusses the validity of this result, explaining the probability of giving birth to an additional child within three years in the context of a linear probability model. Column (1) estimates a baseline difference in short-run higher-order fertility of about 4.5 additional births per hundred mothers. Column (2) includes information on age and prebirth labor market history to assess the sensitivity of the key result to composition of treated and control group mothers. Results indicate that extended PL increases short-run fertility by 4.9 additional children per hundred women. Moreover, estimates indicate that higher-order fertility is lower for older women and for employed women. Column (3) estimates the causal effect of extended leave on births by reducing the width of the baseline window from thirty to fifteen days. Results suggest that about 5.4 children are born to one hundred women with extended leave that are not present under short leave. Anticipating extension of leave, mothers with a strong desire to have two or more children might have timed the birth of their first child to take place on or after July 1, 1990 (by postponing a planned caesarean section or delayed induction of a birth to July 1 or later). Column (4) excludes births taking place one week before and one week after July 1, 1990. Excluding these observations leaves results essentially unchanged; point estimates even slightly increase. The last column of Table III runs a placebo regression where we repeat the regression of column (2) using data on mothers giving birth to their first ASSD child in June and July 1987. These two groups faced identical PL rules and hence we should not see any major differences between them. In fact, the estimated treatment effect is insignificant and the point estimate very close to zero. The empirical analysis has documented a short-run response of higher-order fertility. Does this short-run response persist in the long run? Contrasting June and July 1990 mothers, Figure IV shows how extended leave for the first child affected higher-order

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TABLE III THE THREE-YEAR FERTILITY EFFECT OF EXTENDING PL DURATION FOR THE CURRENT CHILD, JULY 1990 (24 MONTHS PL) VS JUNE 1990 (12 MONTHS PL) Base July

.045 (.012)∗∗∗

No No 0.345

.049 (.012)∗∗∗ .045 (.024)∗ .029 (.028) −.059 (.033)∗ −.111 (.043)∗∗∗ .006 (.006) −.057 (.038) .011 (.022) −1.793 (.694)∗∗∗ −.025 (.045) .000 (.000) −.000 (.000) −.111 (.050)∗∗ −.011 (.017) .002 (.002) −.000 (.002) Yes Yes 0.345

.054 (.017)∗∗∗ .035 (.034) .014 (.039) −.073 (.046) −.116 (.062)∗ .003 (.009) −.048 (.054) .028 (.034) −1.850 (1.202) −.038 (.060) −.000 (.000) .000 (.000) −.036 (.075) −.031 (.024) .001 (.003) .000 (.003) Yes Yes 0.346

.056 (.014)∗∗∗ .042 (.027) .028 (.031) −.058 (.037) −.099 (.049)∗∗ .006 (.007) −.052 (.044) .011 (.025) −1.783 (.752)∗∗ −.004 (.051) .000 (.000) −.000 (.000) −.121 (.057)∗∗ −.004 (.020) .002 (.002) .000 (.002) Yes Yes 0.345

6,180

6,180

3,045

4,757

Age 20–24 Age 25–29 Age 30–34 Age 35–44 Employment (years) Employment sq. Unemployment (years) Unemployment sq. Earnings unobserved Daily earnings (euros) Daily earnings sq. Employed White collar Daily 1989 earnings Daily 1989 earnings sq. Industry Region Mean of dependent variable N

Controls Half-window Anticipation

Placebo .008 (.011) .012 (.021) .048 (.025)∗ .020 (.033) −.125 (.034)∗∗∗ .008 (.007) −.104 (.046)∗∗ −.020 (.028) 1.065 (1.233) .062 (.046) .001 (.000)∗∗ −.000 (.000)∗∗∗ −.099 (.045)∗∗ −.005 (.016) .002 (.002) −.001 (.002) Yes Yes 0.258 6,151

Source: ASSD, own calculations. Sample covers PL-eligible women giving birth to their first child in June 1–30 or July 1–30 of the respective years. Notes: Linear model of the probability of giving birth to a second child within three years of giving birth to a first child in June/July 1990. Standard error in parentheses. ∗ (∗∗ ,∗∗∗ ) denote significance at the 10% (5%, 1%) level, respectively. Inference based on Huber–White standard errors. “Base”: July (24 months PL) vs June (12 months PL). Controls: adds controls (Table II). Half-window: June 16–July 15. Anticipation: June 1–23 and July 8–30. Placebo: June 1987 (12 months PL) vs July 1987 (12 months PL).

1383

0

0

1

20

Percent 40

Percent 2

3

60

4

80

PARENTAL LEAVE, FERTILITY, AND RETURN TO WORK

0

12

24

36

48 60 72 84 Time since birth (months) June 1990

96

July 1990

108

120

0

12

24

36

48 60 72 84 Time since birth (months) June 1990

96

108

120

July 1990

FIGURE IV Additional Births (“Hazard” and Cumulative Proportion), July 1990 (24 Months PL) vs. June 1990 (12 Months PL) Figure reports the additional child hazard, that is, the women giving birth to an additional child in month t as a proportion of those who have not given birth to an additional child up to month t (A), and the cumulative proportion of women giving birth to at least one additional child up to month t (B). Vertical bars indicate end of automatic renewal (dashed for June 1990 mothers, regular for July 1990 mothers). Source. ASSD, own calculations. Sample restricted to PL-eligible women giving birth to a child in June 1–30 or July 1–30 of 1990.

fertility within the ten years following the 1990 birth. Figure IVA shows the second-child hazard rate, that is, the likelihood that a woman gives birth to a second child t months after the 1990 birth conditional on not giving birth to a second child before month t. The control group has a somewhat higher second-child hazard rate between months 12 and 16, whereas the treated group has a much higher hazard between month 18 and month 28. The difference between the two groups is largest during months 22–25, when the additional birth hazard is almost 3.5% for the treated group but less than 2% for the control group. After month 28 there are no major differences between the two groups. This pattern can be rationalized by the PL rules. Recall that the rules grant renewal of PL to control group mothers giving birth before month 16 and to treated mothers giving birth before month 28. Figure IVA shows that the additional-child hazard diverges most strongly when PL renewal is possible to treated mothers but impossible to control mothers. Figure IVB shows the cumulative proportion of women with a second child by time since the 1990 birth. Results indicate that the treated have a lower second-child probability before month 22 but a higher one thereafter. Interestingly, the difference does not erode in the long run. Even ten years after the 1990 birth, the

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TABLE IV SHORT-RUN AND LONG-RUN FERTILITY EFFECTS OF PL DURATION FOR THE CURRENT CHILD, JULY 1990 (24 MONTHS PL) VS JUNE 1990 (12 MONTHS PL) Base Additional birth 0–36 months Additional birth 0–120 months Additional birth 0–16 months Additional birth 17–28 months Additional birth 29–120 months Observations

Controls

Half-window Anticipation Placebo

.045 (.012)∗∗∗ [.345] .03 (.012)∗∗ [.617]

.049 (.012)∗∗∗ [.345] .035 (.012)∗∗∗ [.617]

.054 (.017)∗∗∗ [.346] .03 (.017)∗ [.62]

.056 (.014)∗∗∗ [.345] .048 (.014)∗∗∗ [.617]

.008 (.011) [.258] −.006 (.012) [.556]

−.027 (.006)∗∗∗ [.066] .082 (.01)∗∗∗ [.193] −.024 (.012)∗ [.36]

−.026 (.006)∗∗∗ [.066] .084 (.01)∗∗∗ [.193] −.021 (.012)∗ [.36]

−.029 (.009)∗∗∗ [.067] .084 (.014)∗∗∗ [.195] −.023 (.017) [.359]

−.023 (.007)∗∗∗ [.066] .09 (.011)∗∗∗ [.194] −.018 (.014) [.359]

−.006 (.006) [.069] .011 (.008) [.123] −.011 (.012) [.366]

6,180

6,180

3,045

4,757

6,151

Source. ASSD, own calculations. Sample: PL eligible women giving birth to their first child in June 1–30 (12 months PL) or July 1–30 (24 months PL) in the year 1990. Notes. This table reports the “July 1990” parameter estimate in a linear probability model comparing postbirth fertility of mothers giving birth to their first child in June/July 1990. Standard error in parentheses; mean of dependent variable in brackets. ∗ (∗∗ ,∗∗∗ ) denote significance at the 10% (5%,1%) level, respectively. Inference based on Huber–White standard errors. Base: July (24 months PL) vs. June (12 months PL). Controls: adds controls (Table II). Half-window: June 16–July 15. Anticipation: June 1–23 and July 8–30. Placebo: June 1–23, 1987 (12 months PL) vs. July 8–30, 1987 (12 months PL).

second-child probability of July 1990 mothers is still three percentage points higher than for June 1990 mothers. This suggests that the increase in fertility created by the PL renewal effect affects not just the timing but also the total number of children.20 Table IV provides an econometric assessment of both shortrun and long-run fertility effects using a linear probability model. The first row repeats the results of Table III on short-run fertility. The second row shows the corresponding result for long-run fertility (birth of a second child within 120 months). Column (1) shows that the effect of extending PL for the child born in 1990 20. Note that June 1990 mothers might still catch up to July 1990 mothers after ten years or due to differential third-child fertility. Although our data provide a window that is, arguably, too short to provide a definitive assessment of completed fertility, we believe that this is unlikely to happen. First, June and July 1990 mothers face identical economic and political circumstances on the third child. Second, because only about 65 percent of mothers give birth to two or more children, the third-child treatment effect would have to reach an implausibly large magnitude.

PARENTAL LEAVE, FERTILITY, AND RETURN TO WORK

1385

leads to three additional children being born to one hundred mothers within ten years. Adding controls (column (2)) increases the treatment effect to 3.5 percentage points; halving the estimation window and excluding births closer than seven days before and after July 1, 1990, does not reverse the result. We conclude that extending PL for the current child increases long-run fertility.21 Rows (3)–(5) in Table IV document the timing of excess fertility. Column (1) in Table IV shows that treated mothers reduce future-child fertility by 2.6 percentage points in the period when both treated mothers and control mothers have access to automatic renewal, that is, between months 0 and 16 (row (3)). Then there is a strong increase in fertility by 8.4 percentage points in the period when only treated mothers have access to automatic renewal, that is, months 17–28 (row (4)). Finally, treated mothers are slightly less likely to give birth to a second child between month 29 and month 120 (row (5)). This is the period when neither group has access to automatic renewal. In sum, our results suggest that the short-run change in access to automatic renewal leads to long-run effects on higher-order fertility. The most likely explanation for the high persistence of fertility effects is shocks (to health, partnership, workplace, etc.) that may otherwise induce parents to revise their long-run plans. We show that more generous PL induces parents to realize a planned birth earlier. This means that some shocks that are inducing parents to change family plans in a one-year system no longer affect family planning under a two-year system. This is why short-term gains in fertility also persist in the long run.22 IV.B. Labor Market Outcomes PL rules address the problems of parents in reconciling work and child care. Hence these rules also affect parents’ labor market outcomes. We now explore whether and to what extent extending 21. Although the effect estimated here seems large, our estimated short-run impact is similar in magnitude to that found by Milligan (2005) for pronatalist transfer policies in Quebec where, depending on the parity, parents got a cash transfer up to 8000 CAD. Fertility of those eligible is estimated to have increased 12% on average and 25% for those eligible for the maximum benefit. 22. Although it is true that some women are induced to have a birth within 28 months who would have waited and then never conceived (for preference or biological reasons), there also appear to be some women who are induced to wait beyond 16 months. To the extent that these women experience a negative shock, the net positive effects on the other set of women will be offset. Because there is a positive net fertility effect, the data suggest that any offsetting of this kind is not complete.

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leave from one year to two years affects women’s labor market outcomes, by focusing on three different indicators. (i) Return to work measures the probability that a woman has returned to work at least once after giving birth to her first child in June or July 1990 in the short run (0–36 months after birth) and in the long run (0–120 months after birth). (ii) Employment refers to the months worked per calendar year after birth in the short run (0–36 months after birth) and in the long run (37–120 months after birth). (iii) Earnings measures average pay earned per calendar day after birth in the short run (0–36 months after birth) and in the long run (37–120 months after birth). Note that both employment and earnings are set to zero in periods where a woman does not work and are included in the empirical analysis.23 Figure VA compares the proportion of women returning to work within 36 months after a birth in June and July 1990 by day of birth. Whereas about 62 of 100 women return to work three years after giving birth in June 1990, only about 52 of 100 women do so after giving birth in July 1990, with a strong discontinuity from June 30 to July 1. This suggests a very strong causal impact of PL duration on short-run return-to-work behavior. Figure VB compares the return-to-work profile during the 120 months following the 1990 birth. The figure clearly shows that the maximum length of PL has an extremely strong impact on return-to-work behavior. About 10% of mothers return to work within two months after giving birth (i.e., the end of maternity protection), the same for July 1990 and June 1990 mothers. About 80% of the treated and 83% of the control mothers exhaust the full PL duration. Although a substantial fraction of both treated (20%) and control mothers (25%) return to work exactly when PL has run out, the majority of women (60% among the treated, 58% among controls) stay home after PL has lapsed. Moreover, extended leave for the 1990 child seems to lower the fraction ever returning to work. Whereas 85 of 100 women return to work at least once ten years after the 1990 birth, only 82 of 100 treated women do so. 23. Return to work at date t measures the probability that a woman has stopped her baby break between date 0 and date t. In contrast, employment counts the days at work between date 0 and date t (set to zero when a woman does not work). Because a woman could have returned to work at some date s < t but dropped out of workforce at some later date τ ∈ (s, t), the two indicators differ. Unconditional labor earnings are average earnings per month and set to zero when a woman does not work at all during the respective month. Employment and earnings are available at an annual frequency.

1387

0

40

20

50

Percent 60

Percent 60 40

70

80

80

100

PARENTAL LEAVE, FERTILITY, AND RETURN TO WORK

1/6/90

16/6/90

1/7/90 Calendar day Before

16/7/90

0

31/7/90

12

24

36

After

48 60 72 84 Time since birth (months) June 1990

96

108

120

July 1990

(B) Proportion returning

0

0

2

10

4

Months 6

8

Year 2000 Euros 30 20

10

12

40

(A) Return to work

0

12

24

36 48 60 72 Months since birth

June 1990

84

July 1990

(C) Employment

96

108

120

0

12

24

36 48 60 72 Months since birth

June 1990

84

96

108

120

July 1990

(D) Earnings

FIGURE V Return to Work, Employment, and Labor Earnings, June 1990 vs. July 1990 Panel A reports the percentage of women who have returned to work at least once within three years after the 1990 birth (June smoothed backward, July smoothed forward, fifteen-day moving average); Panel B reports the cumulative proportion of women who have returned to work at least once since the 1990 birth; Panel C reports average months in employment; and Panel D reports mean labor earnings per calendar day since the 1990 birth. (Panels C and D are drawn on an annual frequency; data points at six, eighteen, etc., months refer to the first, second, etc. year after the 1990 birth.) Employment and earnings are set to zero for women who do not hold a job. Zeros are included in all our analyses. Source. ASSD, own calculations. Sample restricted to PL-eligible women giving birth to a child in June 1–30 or July 1–30 of year 1990.

Figure VC explores the effects of extended leave on employment. Employment patterns of women giving birth to their first child are strikingly asymmetric. Whereas paid work takes up about nine to ten months per prebirth year, time spent in the workplace is below seven months in all postbirth years. Interestingly, adverse PL effects on return to work do not translate into lower employment rates. Whereas there is a clear short-run employment disadvantage of treated mothers compared to control mothers in the second year after the 1990 birth, employment is basically the same from the third year onward. Return-to-work

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patterns can be reconciled with employment results as follows. Women eligible for short parental leaves who are planning a further child return to work in the short run temporarily to gain access to renewed parental leave. In contrast, women eligible for long parental leaves can exploit the renewal option and do not have to return. This behavioral pattern explains simultaneously the fact that the fraction ever returning to work is lower in the treated group but long-run employment in months 37–120 remains unchanged. Basically, extending parental leave reduces short-run temporary return to work but does not affect longer-run labor supply decisions. Figure VD displays the evolution of average labor earnings for the two groups. Again, earnings patterns are strikingly asymmetric in periods covering a first-child birth. Whereas women earn about 33 euros per calendar day before birth, mothers of newborn children earn less than 30 euros in all ten postbirth years. In terms of assessing the effects of extended PL on earnings, Figure VD shows that prebirth average earnings are identical between June and July 1990 mothers but diverge strongly immediately after they give birth. Earnings are lower for treated women in the first three years after the 1990 birth. From year four onward, however, treated mothers earn slightly more than control mothers. The positive medium-run earnings effect of extended leave could be driven by various channels: participation in work, length of work, selection into work, and a genuine behavioral effect (more hours, better jobs due to promotions, etc.). Long-run employment results (months 37–120) suggest that the joint effects of participation and length of work are close to zero. There is also a small but insignificant composition effect: women with high prebirth wages return to the job earlier with extended leave than with short parental leave. This implies that the somewhat higher long-run earnings of July 1990 mothers are due to a genuine behavioral effect. Although this effect is small, it seems that those mothers who return after extended leaves work somewhat more and/or are employed in relatively better paid jobs than mothers who return after shorter leaves. Table V uses linear regression to assess the causal effects of the 1990 PL extension for the current child on short- and long-run labor market outcomes. Columns (1)–(5) assess the sensitivity of the results in the same way as the corresponding columns in Table IV on short-run fertility. Treated mothers are significantly less likely to have returned to work three years

PARENTAL LEAVE, FERTILITY, AND RETURN TO WORK

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TABLE V LABOR MARKET EFFECTS OF PL DURATION FOR THE CURRENT CHILD, JULY 1990 (24 MONTHS PL) VS. JUNE 1990 (12 MONTHS PL) Base

Controls Half-window Anticipation

−.109 −.11 −.109 (.013)∗∗∗ (.012)∗∗∗ (.017)∗∗∗ [.564] [.564] [.567] Return to work −.03 −.027 −.046 0–120 months (.009)∗∗∗ (.009)∗∗∗ (.013)∗∗∗ [.847] [.847] [.85] Employment −.999 −1.02 −1.001 0–36 months (.073)∗∗∗ (.071)∗∗∗ (.1)∗∗∗ [2.185] [2.185] [2.194] Employment .07 .074 .047 37–120 months (.111) (.109) (.155) [5.136] [5.136] [5.202] Earnings −2.739 −2.998 −3.156 0–36 months (.335)∗∗∗ (.304)∗∗∗ (.429)∗∗∗ [10.159] [10.159] [10.223] Earnings .852 .545 .195 37–120 months (.563) (.522) (.74) [20.759] [20.759] [21.014] Return to work 0–36 months

Observations

6,180

6,180

3,045

Placebo

−.105 .009 (.014)∗∗∗ (.012) [.561] [.619] −.023 .009 (.01)∗∗ (.009) [.845] [.83] −1.031 −.051 (.081)∗∗∗ (.083) [2.183] [2.908] .09 −.09 (.124) (.111) [5.107] [4.889] −3.044 −.821 (.348)∗∗∗ (.321)∗∗ [10.096] [12.155] .522 −.862 (.598) (.518)∗ [20.658] [19.39] 4,757

6,150

Source: ASSD, own calculations. Sample: PL-eligible women giving birth to their first child in June 1–30 (12 months PL) or July 1–30 (24 months PL) in the year 1990. Notes: This table reports the July 1990 parameter estimate in a linear regression/linear probability model comparing postbirth labor market outcomes of mothers giving birth to their first child in June and July 1990. Standard error in parentheses; mean of dependent variable in brackets. Employment and earnings are set to zero for women who do not hold a job. Zeros are included in all our analyses. ∗ (∗∗ ,∗∗∗ ) denote significance at the 10% (5%,1%) level respectively. Inference based on Huber–White standard errors. Base: July (24 months PL) vs. June (12 months PL). Controls: adds controls (Table II). Half-window: June 16–July 15. Anticipation: June 1–23 and July 8–30. Placebo: June 1987 (12 months PL) vs. July 1987 (12 months PL).

after giving birth to their first in July 1990 (row (1)) and the difference is quantitatively large: An additional 10 of 100 mothers have not returned to work within three years after the 1990 birth. This difference in return to work shrinks over time but a significant three-percentage point difference still remains even after ten years (row (2)). Interestingly, although treated mothers work about one month per year less during the first three years after giving birth (row (3)), there are no long-run employment differences between treated and controls. During months 37–120 after birth, average employment is the same for the two groups (row (4)). A similar finding obtains for earnings per calendar month. Treated mothers earn about three euros less from working on the average day of the three first postbirth years (row (5));

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there is even a positive albeit statistically insignificant earnings differential between treated and control mothers four to ten years after giving birth (months 37–120, row (6)). Thus, although the 1990 reform slightly reduced the number of women ever returning to work, staying out of work for an extended period does not appear to harm employment and earnings of treated mothers. IV.C. Heterogeneous Responses: Income and Occupation Austrian PL provisions offer job protection and a financial transfer during the time a mother stays off work. Although both types of policies reduce the costs of having children, they target quite different dimensions of these costs. Cash transfers help extend the time a mother can stay home with her baby without running into financial distress. This is more likely to help low-income parents. In contrast, job protection extends the time a mother can spend with her baby without losing her job. This is more likely to help career-oriented women, for whom job loss may be very costly. Table VI explores whether extending PL duration affects high- and low-wage women differently. A mother is considered “Hi Wage” if daily earnings on the job held exactly one year prior to giving birth (prebirth job) exceeds the median of daily prebirth earnings (37.12 euros per day worked); and a mother is considered “Lo Wage” otherwise. The flat rate transfer of 340 euros translates into a low replacement rate for high-wage women and a high replacement rate for low-wage women. Moreover, taking occupation as a proxy for the extent of job-specific skills, we also investigate whether the responses for women holding a white-collar occupation one year prior to birth (column (4)) were different from the responses of women holding a blue-collar job (column (5)).24 For comparison purposes, column (1) repeats the baseline result (column (1) of Tables IV and V).25 Results indicate that the 1990 PL reform led to a significant increase in short-run fertility for both high- and low-wage women (Table VI, columns (2) and (3)). Excess short-run fertility amounts 24. Women who did not hold a job one year prior to giving birth to the 1990 child are allocated to the low-wage/blue-collar categories. Results remain qualitatively unchanged if we exclude nonemployed women. 25. Clearly, such rough sample splits along one dimension are likely to be contaminated by imbalance along other dimensions. For instance, 62% of highwage women hold a white-collar occupation, whereas only 44% of all women hold a white-collar occupation. Nevertheless, splitting the sample along these two dimensions allows discussing the relevance of earnings replacement and value of job protection.

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TABLE VI HETEROGENEOUS EFFECTS OF PL DURATION FOR THE CURRENT CHILD (1990 REFORM) All

Hi wage

Lo wage

Wt col

Bl col

(A) Fertility .049 .036 .068 .055 .048 (.012)∗∗∗ (.017)∗∗ (.017)∗∗∗ (.018)∗∗∗ (.016)∗∗∗ [.345] [.351] [.339] [.349] [.342] Additional birth .035 .016 .054 .034 .036 0–120 months (.012)∗∗∗ (.017) (.017)∗∗∗ (.018)∗ (.016)∗∗ [.617] [.616] [.618] [.611] [.622] Additional birth −.026 −.033 −.018 −.018 −.031 0–16 months (.006)∗∗∗ (.009)∗∗∗ (.009)∗ (.009)∗∗ (.009)∗∗∗ [.066] [.06] [.071] [.058] [.072] Additional birth .084 .08 .089 .095 .078 17–28 months (.01)∗∗∗ (.014)∗∗∗ (.014)∗∗∗ (.015)∗∗∗ (.013)∗∗∗ [.193] [.203] [.183] [.206] [.183] Additional birth −.021 −.031 −.013 −.042 −.008 29–120 months (.012)∗ (.017)∗ (.017) (.018)∗∗ (.016) [.36] [.353] [.366] [.348] [.369] (B) Labor market outcomes Return to work −.11 −.103 −.124 −.137 −.094 0–36 months (.012)∗∗∗ (.017)∗∗∗ (.018)∗∗∗ (.018)∗∗∗ (.017)∗∗∗ [.564] [.632] [.496] [.647] [.5] Return to work −.027 −.028 −.029 −.039 −.018 0–120 months (.009)∗∗∗ (.012)∗∗ (.014)∗∗ (.012)∗∗∗ (.013) [.847] [.874] [.82] [.889] [.814] Employment −1.023 −1.186 −1.15 −1.054 −.556 0–36 months (.114)∗∗∗ (.101)∗∗∗ (.114)∗∗∗ (.102)∗∗∗ (.172)∗∗∗ [2.594] [1.984] [2.659] [1.913] [1.505] Employment .2 −.125 .071 .026 .238 37–120 months (.173) (.162) (.171) (.163) (.286) [5.88] [4.762] [5.95] [4.681] [3.92] Earnings −3.548 −2.7 −3.914 −2.347 −2.356 0–36 months (.56)∗∗∗ (.354)∗∗∗ (.564)∗∗∗ (.335)∗∗∗ (.748)∗∗∗ [14.247] [7.183] [13.921] [7.454] [6.508] Earnings 1.142 .311 .45 .895 −.403 37–120 months (.927) (.64) (.923) (.614) (1.465) [26.467] [16.139] [26.336] [16.183] [17.179] Additional birth 0–36 months

Observations

6,180

3,087

3,093

2,705

3,475

Source. ASSD, own calculations. Sample covers women giving birth to their first child in June 1–30 (12 months PL) or July 1–30 (24 months PL) in the year 1990. Notes. This table reports the “July 1990” parameter estimate in linear regressions/linear probability models comparing postbirth labor market outcomes of mothers giving birth to their first child in June and July 1990. Standard error in parentheses; mean of dependent variable in brackets. Employment and earnings are set to zero for women who do not hold a job. Zeros are included in all our analyses. ∗ (∗∗ ,∗∗∗ ) denote significance at the 10% (5%,1%) level, respectively. Inference based on Huber–White standard errors. All: repeats column (2) of Table 4 and column (2) of Table 5 for comparison. Hi/lo wage: median splits for prebirth daily income; Wt/bl col: splits by white- and blue-collar occupation; wage and occupation measured one year prior to birth; women who are not employed one year prior to birth are allocated to the low-wage and blue-collar categories.

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to almost four children per 100 high-wage mothers and to almost seven children per 100 low-wage mothers (row (1)). This result suggests that taking advantage of automatic renewal is less attractive to high-wage women than to low-wage women. Long-run fertility effects disappear for women with high earnings power (1.6-percentage-point difference) but not for women whose prebirth earnings power lies below the median (6.4-percentage-point difference). Rows (3)–(5) in Table VI assess the timing of fertility. High-wage women delay fertility more than low-wage women up to month 16 (when control women also have access to automatic renewal, row (3)). From month 17 to 28 (when the treated have access to automatic renewal but controls do not; row (4)), treated high- and low-wage women display excess fertility of eight and nine children per 100 women, respectively. In the period following month 29, high-wage (but not low-wage) controls have significantly higher fertility (row (5)). In sum, excess fertility for low-wage women results from not delaying initial fertility by the treated and from not catching up by the controls after automatic renewal has lapsed. These differences in fertility timing are likely to be explained by differences in work attachment between high-wage women (63% return to work within three years, row (6), number in brackets) and low-wage women (only 50% return to work within three years, row (6), number in brackets). Because returning to work between children induces a wider space between first birth and second birth, offering automatic renewal compresses the space between children more strongly for the group with a larger ex ante space between births. Interestingly, although there are significant differences in fertility responses between high- and low-wage women, the PL reform affects employment and earnings of high- and low-wage women to a similar extent (Panel B in Table VI). The decrease in return-to-work probabilities is somewhat smaller for high-wage women than for low-wage women in the short run but almost identical in the long run (rows (6) and (7)). The reduction in employment is identical for both groups in the short run and in the long run (rows (8) and (9)). Short-run earnings reductions are greater for high-wage women than for low-wage women (row (10)). However, because employment responses are nearly identical, differential earnings responses arguably reflect ex ante differences in earnings power rather than differential earnings consequences of extending PL duration. There are no significant

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long-run earnings consequences of extended career interruptions (row (11)). Turning to fertility results by occupation reveals that shortrun and long-run fertility responses are quite similar for whitecollar and blue-collar women (columns (4) and (5), rows (1) and (2)): three additional children within 10 years. Yet even though the long-run result is similar, the time pattern of the responses differs somewhat between white- and blue-collar women (rows (3)–(5)). Both blue- and white-collar women delay second-child fertility in the period, giving both treated and control women access to automatic renewal (row (3)); both blue- and white-collar women eligible for extended PL concentrate births of second children in the period with access to automatic renewal (row (4)). Yet whitecollar control women catch up to treated women more strongly than blue-collar control women in the postrenewal period (row (5)). This pattern of results is, again, consistent with differential postbirth labor market attachment between white-collar women (65% return to job within three years, row (6)) and blue-collar women (50% return to job within three years, row (6)). Although occupation does not appear to mediate fertility responses of extended leave strongly, occupation is important for the labor market consequences of extended PL (Panel B in Table VI). About 14 of 100 treated white-collar women do not return to work within three years because of extended PL. In contrast, only 9 of 100 blue-collar women delay return to work in the short run (row (6)). Long-run return to work of blue-collar women is not affected, whereas almost 4 of 100 women in the white-collar group do not return to work within ten years (row (7)). Extended PL reduces employment and earnings more strongly for white-collar women than for blue-collar women in the short run (rows (8) and (10)). However, in the long run PL-induced career interruptions are not harmful (rows (9) and (11)). In sum, the results suggest that labor market outcomes of white-collar women are more sensitive to extending PL. We conclude that the finding of higher fertility responses for low-wage women than for high-wage women suggests that cash transfers (through their impact on replacement ratios) are important determinants of fertility responses. Finding that there are no differences in fertility responses between blue- and whitecollar workers suggests that the job protection provisions are of importance for white-collar women. White-collar women have, on average, higher incomes than blue-collar women and, on the basis

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of their lower average replacement ratios, they should also react less strongly to the PL extension. It seems that lower replacement ratios are compensated by the benefits of job protection. This interpretation is consistent with the idea that internal labor markets and career concerns are more important for white-collar jobs but less relevant for blue-collar workers.26 V. EXTENDING PL DURATION FOR THE FUTURE CHILD This section assesses the effect of extended leave on the future child (“future-child PL effect”).27 To identify this effect we compare the June 1990 cohort (eligible for a one-year PL for the current child but for a two-year PL for the future child) to the June 1987 cohort (one-year PL for the current child and one-year PL for any second child born within three years after the first birth). The June 1990 to June 1987 contrast may be biased due to cohort effects and time trends. Hence Table VII presents a range of supplementary analyses that shed light on the plausibility of the key identifying assumption of identical ex ante fertility plans and labor market trajectories for two cohorts. Assessing the sensitivity of our results to time trends, we provide (i) a placebo estimate of the reform among PL-ineligible mothers (column (3)), (ii) estimates of a three-year postreform time trend that compares July 1993 mothers to July 1990 mothers (column (4)), and (iii) estimates of a two-year prereform time trend that compares June 1987 mothers to June 1985 mothers (column (5)).28 Moreover, 26. Our results also relate to the existing literature on the trade-off between fertility and labor supply. In contrast to our long-run results, Angrist and Evans (1998) find that U.S. women with two children worked less than women with just one child in 1990. There are at least two reasons for the differences in our results. First, Angrist and Evans (1998) do not condition on time since birth. Their finding of a reduction in labor for the average mother could be consistent with a temporary reduction in labor supply in the short run but no reduction of labor supply in the long run—the situation we document for Austria. Second, Austria and the United States differ in terms of female labor force participation. In 1994, the earliest year with comparable OECD statistics, 65% of American working-age women participated in the labor market whereas only 59% of Austrian women did. Because these participation differences presumably reflect differences in the speed of postbirth labor market reentry, a second child is likely to crowd out more employment in the United States than in Austria. Thus, the fertility effects of extended parental leave may come at higher long-run employment cost in countries with high postbirth labor market participation. 27. Note that, although the change in the PL system could in principle also affect first-child, third-child fertility, and so forth, we confine our analysis to the analysis of second-child fertility because for this parity the effects should be most pronounced. 28. The prereform time trend cannot be three years because our ASSD extract starts in 1985.

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PARENTAL LEAVE, FERTILITY, AND RETURN TO WORK TABLE VII THE EFFECT OF PL DURATION FOR THE FUTURE CHILD (1990 REFORM) Base Additional birth

Return to work

Employment

Earnings

Controls

Ineligible

Posttrend

Pretrend

(A) Short-run effects (0–36 months after birth) .069 .068 −.019 −.006 (.012)∗∗∗ (.012)∗∗∗ (.051) (.012) [.286] [.286] [.236] [.364] −.002 −.003 −.053 .008 (.013) (.012) (.038) (.012) [.622] [.622] [.135] [.524] −.183 −.164 −.336 −.103 (.084)∗∗ (.083)∗∗ (.216) (.058)∗ [2.799] [2.799] [.583] [1.71] −.181 −.229 .512 −.75 (.361) (.331) (1.927) (.282)∗∗∗ [11.68] [11.68] [9.031] [8.974]

.001 (.011) [.25] .018 (.012) [.614] −.045 (.086) [2.909] −.589 (.325)∗ [11.849]

(B) Medium-run effects (37–72 months after birth) Additional birth −.019 −.014 −.072 −.011 (.011)∗ (.011) (.047) (.01) [.21] [.21] [.182] [.179] Return to work .028 .024 .011 .022 (.009)∗∗∗ (.01)∗∗ (.043) (.011)∗∗ [.158] [.158] [.156] [.227] Employment −.172 −.191 −.492 .315 (.123) (.122) (.397) (.117)∗∗∗ [4.585] [4.585] [1.599] [4.77] Earnings −.13 −.325 −.252 .441 (.547) (.523) (2.285) (.524) [17.015] [17.015] [13.084] [18.654] Observations

5,977

5,977

274

6,406

.033 (.011)∗∗∗ [.205] .005 (.009) [.144] −.007 (.125) [4.688] .053 (.498) [16.814] 5,892

Source: ASSD, own calculations. Sample covers eligible and ineligible women giving birth to their first child in June or July of the years listed in the notes. Notes: This table reports the “After” parameter estimate in linear regressions/linear probability models comparing postbirth labor market outcomes of mothers giving birth to their first child in June or July of various years. Standard error in parentheses; mean of dependent variable in brackets. Employment and earnings are set to zero for women who do not hold a job. Zeros are included in all our analyses. ∗ (∗∗ ,∗∗∗ ) denote significance at the 10% (5%,1%) level, respectively. Inference based on Huber–White standard errors. Base: eligible, June 1990 (24 months PL for second child, 12 months PL for first child) and June 1987 (12 months PL for first and second child). Controls: adds controls (Table II) to Base. Ineligible: ineligible with controls, June 1990 vs. June 1987. Posttrend: eligible with controls, June 1993 vs. July 1990. Pretrend: eligible with controls, June 1987 vs. June 1985.

Table VII distinguishes between months 0–36 after the first birth (where second-child duration differs) and months 37–72 after the first birth (where second-child duration is identical).29 29. Note that the inverse pattern of eligibility holds for the pre- and postreform trend cohorts. Prereform cohorts are eligible for the same second-child PL duration during months 0–36 after the first birth, but PL duration differs

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Results indicate that the future-child PL effect is quantitatively important (Table VII). Short-run fertility is 7 percentage points higher for June 1990 mothers than for June 1987 mothers (Panel A of Table VII, row (1)). Adding prebirth characteristics does not change this result. We do not find that PL-ineligible June 1990 women tend to give birth to more future children than PL-ineligible June 1987 women (column (3)). We also do not find a high importance of time trends. Higher-order fertility is similar between July 1993 and July 1990 mothers (column (4)) and is also similar between between June 1987 and June 1985 mothers (column (5)). Interestingly, extending leave for the future child does not appear to affect labor market outcomes to any great extent (rows (2)–(4) of Panel A in Table VII). Return to work and earnings do not display statistically significant effects (rows (2) and (4)). Although work experience is reduced significantly, estimates indicate that treated mothers work 0.2 months per year less.30 Panel B in Table VII shows that the short-run fertility effect persists in the medium run. Our results indicate that there is no significant catch-up of control mothers during months 36–72. Although June 1990 mothers give birth to slightly fewer second children than June 1987 mothers, the effect is quite small (1.4 children per 100 women) and not statistically significant. Furthermore, results on PL-ineligible women are insignificant. The last two columns of Panel B of Table VII show time-trend results. More precisely, these results measure time trends plus futurechild differences in PL duration in the medium run. For instance, pretrend estimates compare June 1987 mothers who are covered by a two-year leave in the medium run (months 36–72 cover the period from July 1990 to June 1993) and June 1985 mothers who are covered by a one-year leave for the first two years and a two-year leave for the third year (months 36–72 cover the period from July 1988 to June 1991). Consistent with this pattern of PL eligibility, during months 37–72 after the first birth. In the prereform time trend analysis, for instance, second children of June 1987 mothers are eligible for 24 months of PL duration in months 37–60 after the first birth, whereas second children of June 1985 mothers are still only eligible for 12 months of PL duration. In months 61–72 after the first birth, both second children of both cohorts are eligible for 24 months of PL duration. 30. Note that employment estimates could be spurious because there is a significantly negative postreform trend in employment (column (3), Table VII). Moreover, the coefficients on labor market outcomes are very imprecise, so the data are consistent with zero effects but also with large negative effects on employment and earnings.

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the future-child PL effect is 3 percentage points higher for the June 1987 cohort than for the June 1985 cohort.31 Posttrend estimates capture the fact that second-child leave is reduced from 24 months to 18 months for July 1993 mothers, whereas July 1990 mothers still have access to a two-year leave. Point estimates are quantitatively consistent with the future-child effects estimated above but are not statistically significant. Except for a small increase in return to work, we do not find large future-child PL effect on medium-run labor market outcomes. What can we learn from the current-child and future-child effects? Recall that the current-child estimates compare families with different benefits (in terms of transfers and time for care) for the current child but identical benefits for the future child. Abstracting from automatic renewal, extending parental leave should crowd out short-run postbirth labor market participation but leave fertility decisions unaffected. In contrast, futurechild estimates compare families with different benefits for the future child but identical benefits for the current child. Extending parental leave should affect fertility decisions but not crowd out short-run postbirth labor market participation. Turning to results, we find that extending parental leave for the current child reduces short-run postbirth work experience by one month, whereas the corresponding future-child effect is about one-fifth of a month. Thus, the pattern of labor market results is in line with the pattern of incentives. In contrast, whereas extending parental leave for the future child boosts short-run fertility by 7 percentage points, doing so for the current child also increases short-run fertility by 5 percentage points. Thus, fertility results suggest that access to automatic renewal is valuable; indeed almost as valuable as extended leave for a future child. VI. REDUCING PL DURATION This section discusses the effects of the 1996 reduction of PL. Results comparing mothers giving birth to their first child in July 1996 (eligible for eighteen months of leave) with mothers 31. The effect is about one-half of the short-run estimate in row (1), column (2), of Table VII. This lower importance of extended leave for a future child can probably be explained by two facts. First, the prereform control group of June 1985 mothers gets access to extended leave in the period 61–72 months after birth. Second, mothers might be less responsive to extended leave three to six years after birth than zero to three years after birth.

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TABLE VIII THE EFFECTS OF REDUCING PL DURATION FOR THE CURRENT CHILD (1996 REFORM): JUNE 1996 (24 MONTHS PL) VS. JULY 1996 (18 MONTHS PL) Base

Controls

Half-window Anticipation

(A) Fertility −.001 −.025 (.012) (.017) [.321] [.331] .028 .023 (.009)∗∗∗ (.013)∗ [.152] [.157] −.029 −.032 (.008)∗∗∗ (.011)∗∗∗ [.103] [.109] .005 −.013 (.007) (.01) [.077] [.076]

.003 (.014) [.309] .022 (.01)∗∗ [.148] −.028 (.009)∗∗∗ [.098] .013 (.008)∗ [.076]

(B) Labor market outcomes .051 .053 .058 (.012)∗∗∗ (.012)∗∗∗ (.017)∗∗∗ [.661] [.661] [.66] Employment .675 .684 .703 0–36 months (.069)∗∗∗ (.067)∗∗∗ (.095)∗∗∗ [2.456] [2.456] [2.46] Earnings 2.65 2.697 2.295 0–36 months (.367)∗∗∗ (.321)∗∗∗ (.444)∗∗∗ [12.302] [12.302] [12.148]

.047 (.014)∗∗∗ [.663] .676 (.076)∗∗∗ [2.487] 3.045 (.371)∗∗∗ [12.469]

Additional birth −.003 0–36 months (.012) [.321] Additional birth .028 0–22 months (.009)∗∗∗ [.152] Additional birth −.03 23–28 months (.008)∗∗∗ [.103] Additional birth .004 29–36 months (.007) [.077] Return to work 0–36 months

Placebo −.021 (.012)∗ [.349] −.021 (.009)∗∗ [.151] .001 (.008) [.122] −.003 (.007) [.084] .003 (.012) [.536] .057 (.056) [1.729] −.267 (.264) [9.135]

Source: ASSD, own calculations. Sample: PL-eligible women giving birth to their first child in June 1–30 (24 months PL) or July 1–30 (18 months PL) in the year 1996. Notes. This table reports the “July 1996” parameter estimate in linear regressions/linear probability models comparing outcomes of mothers giving birth to their first child in June or July 1996. Standard error in parentheses; mean of dependent variable in brackets. Employment and earnings are set to zero for women who do not hold a job. Zeros are included in all our analyses. ∗ (∗∗ ,∗∗∗ ) denote significance at the 10% (5%,1%) level, respectively. Inference based on Huber–White standard errors. Base: July (18 months PL) vs. June (24 months PL). Controls: adds controls (Table II). Half-window: June 16–July 15. Anticipation: June 1–23 and July 8–30. Placebo: June 1993 (24 months PL) vs. July 1993 (24 months PL).

giving birth to their first child in June 1996 (eligible for 24 months of leave) indicate, first, that the number of children born within three years is not affected by the partial reversal of the 1990 policy change (Table VIII, row (1)). Second, although the number of children is unaffected, the timing of second-child fertility is significantly altered. There is excess future-child fertility of about 3% before month 22 (when both treated and control mothers have access to PL renewal) and a decrease of the same order of magnitude during months 23–28 (when the treated lose access to PL renewal; Table VIII, rows (2)–(4)). Reducing PL duration strongly affects

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the timing of births but not the number of children being born because, arguably, mothers could take advantage of PL renewal before and after the 1996 reform, whereas the 1990 reform represents a switch from a system where PL renewal was not feasible to a system where it become highly attractive.32 Third, reducing PL duration affects return to work, employment, and earnings considerably. In the short run, 5 of 100 women return to work within three years who would not with extended leave (Table VIII, row (5)). Women on the 18-month leave also work on the average about 0.7 months more per year and earn 3 euros more per day more than women with access to a two-year PL (Table VIII, rows (6) and (7)). Notice that the six-month reduction in PL duration affects return to work, employment, and earnings by about half as much (in absolute value) as the twelvemonth extension of PL duration in 1990. Hence results for the 1996 reform confirm that that PL duration for the current child has a strong impact on short-run labor market outcomes. VII. CONCLUSIONS The focus of this paper is the relevance of the duration of job-protected, paid PL for higher-order fertility and labor market outcomes of working women. The empirical analysis is based on a 1990 extension of PL duration from one year to two years and on a 1996 reduction of PL from two years to eighteen months. We find that extending PL affects fertility via two channels. First, increasing leave for the current child opens up the possibility of renewing PL benefits without going back to work. The resulting tighter spacing of births gives rise to both excess shortrun fertility (5 additional children per 100 women within three years) and excess long-run fertility (3 additional children per 100 women within ten years). Moreover, increasing leave for the future child reduces the cost of care for that child, inducing mothers to give birth to about 7 additional second children per 100 women. This means that extending job-protected paid PL with automatic renewal from one year to two years induces mothers to give birth to about 12 additional children per 100 women. Regarding the labor market consequences of extended leave, we find that most 32. We also investigate the effects of reducing PL duration for the future child by comparing mothers who give birth to a first child in June 1996 to mothers who give birth to a first child in June 1993. Findings indicate that reduced leave on the future child is associated with a decrease in short-run fertility.

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mothers exhaust the full duration of their leaves; that return to work is substantially delayed even after PL has been exhausted; and that prolonging leave leads to significant short-run reductions in employment and earnings but only minor effects in the long run. Fertility and labor market responses are heterogeneous with respect to earnings and occupation on the prebirth job. This is consistent with both replacement rates and job protection mediating the effects of extended leave on fertility and labor market responses. Finally, our findings indicate that the 1996 reduction of PL duration compresses the space between first and second births, but does not have a significant effect on the number of second children born within three years. Moreover, the labor market responses closely mirror those of the 1990 extension of PL duration. Providing causal evidence on how Austrian policy changes affect fertility and labor market careers is interesting and important for the non-Austrian public. In many countries fertility levels have fallen strongly and the question of whether PL policies can help to increase fertility is hotly debated. Our results show that such policies can have a quite strong impact and that both transfers and job protection matter for fertility responses. Our analysis of labor market effects addresses the issue of whether too generous PL rules might have a negative impact on mothers’ subsequent work careers—an issue of paramount importance. We think the Austrian case is interesting in this respect because the 1990 PL reform was a move from a system of average generosity (by current OECD standards) to a system of high generosity. Although we do find that the PL extension increases the proportion of women who never return to work, we do not find detrimental effects on employment and earnings over an extended time horizon. Hence we conclude that generous PL policies do not necessarily harm women’s long-run labor market outcomes. FACULTY OF BUSINESS AND ECONOMICS, UNIVERSITY OF LAUSANNE, CEPR, IFAU, IZA, CESIFO, AND IEW INSTITUTE FOR EMPIRICAL ECONOMIC RESEARCH, UNIVERSITY OF ZURICH, CEPR, IZA, AND CESIFO

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Angrist, Joshua D., and William N. Evans, “Children and Their Parents’ Labor Supply: Evidence from Exogenous Variation in Family Size,” American Economic Review, 88 (1998), 450–477. Averett, Susan L., and Leslie A. Whittington, “Does Maternity Leave Induce Births?” Southern Economic Journal, 68 (2001), 403–417. Baker, Michael, Jonathan Gruber, and Kevin Milligan, “Universal Childcare, Maternal Labor Supply, and Family Well-Being,” Journal of Political Economy, 116 (2008), 709–745. Baker, Michael, and Kevin Milligan, “Maternal Employment, Breastfeeding, and Health: Evidence from Maternity Leave Mandates,” Journal of Health Economics, 27 (2008), 871–887. Baum, Charles L., “The Effect of State Maternity Leave Legislation and the 1993 Family and Medical Leave Act on Employment and Wages,” Labour Economics, 10 (2003), 573–596. Berger, Lawrence M., Jennifer Hill, and Jane Waldfogel, “Maternity Leave, Early Maternal Employment and Child Health and Development in the US,” Economic Journal, 115 (2005), F29–F47. Berger, Lawrence M., and Jane Waldfogel, “Maternity Leave and the Employment of New Mothers in the United States,” Journal of Population Economics, 17 (2004), 331–349. Bj¨orklund, Anders, “Does a Family-Friendly Policy Raise Fertility Levels?” Swedish Institute for European Studies Report No. 3, 2007. Dickert-Conlin, Stacy, and Amitabh Chandra, “Taxes and the Timing of Births,” Journal of Political Economy, 107 (1999), 161–177. Dustmann, Christian, and Uta Sch¨onberg, “The Effect of Expansions in Maternity Leave Coverage on Children’s Long-Term Outcomes,” IZA Discussion Paper No. 3605, 2008. Gans, Joshua S., and Andrew Leigh, “Born on the First of July: An (Un)natural Experiment in Birth Timing,” Australian National University Discussion Paper No. 529, 2006. Hahn, Jinyong, Petra Todd, and Wilbert van der Klaauw, “Identification and Estimation of Treatment Effects with a Regression–Discontinuity Design,” Econometrica, 69 (2001), 201–209. ˚ Schøne, “Cash for Care: More Work for the Stork?” Mimeo, Hardoy, Ines, and Pal Institute for Social Research Oslo, 2005. Hoem, Jan M., “Public Policy as the Fuel of Fertility: Effects of a Policy Reform on the Pace of Childbearing in Sweden in the 1980s,” Acta Sociologica, 36 (1993), 19–31. Hoynes, Hilary W., “Work, Welfare, and Family Structure,” in Fiscal Policy: Lessons From Economic Research, Alan B. Auerbach, ed. (Cambridge, MA: MIT Press, 1997). Joyce, Theodore, Robert Kaestner, Sanders Korenman, and Stanley Henshaw, “Family Cap Provisions and Changes in Births and Abortions,” NBER Working Paper No. W10214, 2004. Kearney, Melissa Schettini, “Is There an Effect of Incremental Welfare Benefits on Fertility Behavior? A Look at the Family Cap,” Journal of Human Resources, 39 (2004), 295–325. Klerman, Jacob A., and Arleen Leibowitz, “Labor Supply Effects of State Maternity Leave Legislation,” in Gender and Family Issues in the Workplace, Francine Blau and Ron Ehrenberg, eds. (New York: Russell Sage Press, 1997). ——, “Job Continuity among New Mothers,” Demography, 36 (1999), 145– 155. ¨ Lalive, Rafael, and Josef Zweimuller, “Parental Leave and Mothers’ Post-Birth Careers,” Mimeo, University of Lausanne, 2007. Laroque, Guy, and Bernard Salani´e, “Fertility and Financial Incentives in France,” CEPR Discussion Paper No. 4064, 2005. Milligan, Kevin, “Subsidizing the Stork: New Evidence on Tax Incentives and Fertility,” Review of Economics and Statistics, 87 (2005), 539–555. Moffitt, Robert A., “Profiles of Fertility, Labour Supply and Wages of Married Women: A Complete Life-Cycle Model,” Review of Economic Studies, 51 (1984), 263–278.

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——, “The Effect of Welfare on Marriage and Fertility,” in Welfare, the Family, and Reproductive Behavior, Robert A. Moffitt, ed. (Washington, DC: National Academy Press, 1998). Piketty, Thomas, “L’Impact de l’Allocation Parentale d’Education sur l’Activit´e Feminine et la Fecondit´e, 1982–2002,” CEPREMAP Working Papers (Couverture Orange) No. 2003-09, 2003. Rosenzweig, Mark R., “Welfare, Marital Prospects, and Nonmarital Childbearing,” Journal of Political Economy, 107 (1999), S3–S32. Ruhm, Christopher, “The Economic Consequences of Parental Leave Mandates: Lessons from Europe,” Quarterly Journal of Economics, 113 (1998), 285–317. Ruhm, Christopher, and Jackqueline L. Teague (1997) “Parental Leave Policies in Europe and North America,” in Gender and Family Issues in the Workplace, Francine D. Blau and Ronald Ehrenberg, eds. (New York: The Russell Sage Foundation Press, 1997). Sch¨onberg, Uta, and Johannes Ludsteck, “Maternity Leave Legislation, Female Labor Supply, and the Family Wage Gap,” IZA Discussion Paper No. 2699, 2007.

QUARTERLY JOURNAL OF ECONOMICS Vol. CXXIV

August 2009

Issue 3

SLUGGISH RESPONSES OF PRICES AND INFLATION TO MONETARY SHOCKS IN AN INVENTORY MODEL OF MONEY DEMAND∗ FERNANDO ALVAREZ ANDREW ATKESON CHRIS EDMOND We examine the responses of prices and inflation to monetary shocks in an inventory-theoretic model of money demand. We show that the price level responds sluggishly to an exogenous increase in the money stock because the dynamics of households’ money inventories leads to a partially offsetting endogenous reduction in velocity. We also show that inflation responds sluggishly to an exogenous increase in the nominal interest rate because changes in monetary policy affect the real interest rate. In a quantitative example, we show that this nominal sluggishness is substantial and persistent if inventories in the model are calibrated to match U.S. households’ holdings of M2.

I. INTRODUCTION In this paper, we examine the dynamics of money, velocity, prices, interest rates, and inflation in an inventory-theoretic model of the demand for money.1 We show that our inventorytheoretic model offers new answers to two important questions: why do prices respond sluggishly to changes in money, and why ∗ A previous draft of this paper circulated under the title “Can a Baumol–Tobin Model Account for the Short-Run Behavior of Velocity?” We would like to thank Robert Barro, Michael Dotsey, Tim Fuerst, Robert Lucas, Julio Rotemberg, and several anonymous referees for helpful comments. For financial support, Alvarez thanks the NSF and the Templeton Foundation and Atkeson thanks the NSF. 1. Traditionally, the literature on inventory-theoretic models of money demand has focused on the steady-state implications of these models for money demand (e.g., Barro [1976], Jovanovic [1982], Romer [1986], Chatterjee and Corbae [1992]). Here we examine the implications of an inventory-theoretic model of the demand for money for the dynamics of prices and inflation following a shock to money or to interest rates. C 2009 by the President and Fellows of Harvard College and the Massachusetts Institute of

Technology. The Quarterly Journal of Economics, August 2009

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does inflation respond sluggishly to changes in the short-term nominal interest rate? We first show analytically how prices and inflation are both sluggish in our model, even though price setting is fully flexible. We then show through a quantitative example that this sluggishness is substantial and persistent when our inventory-theoretic model is interpreted as applying to a broad monetary aggregate like M2. Our model is inspired by the analyses of money demand developed by Baumol (1952) and Tobin (1956). In their models, households carry money (despite the fact that money is dominated in rate of return by interest-bearing assets) because they face a fixed cost of trading money and these other assets. Our model is a simplified version of their framework. We study a cash-in-advance model with physically separated asset and goods markets. Households have two financial accounts: a brokerage account in the asset market in which they hold a portfolio of interest-bearing assets and a bank account in the goods market in which they hold money to pay for consumption. We assume that households do not have the opportunity to exchange funds between their brokerage and bank accounts every period. Instead, we assume they have the opportunity to transfer funds between accounts only once every N ≥ 1 periods. Hence, households maintain inventories of money in their bank accounts large enough to pay for consumption expenditures for several periods. They replenish these inventories with transfers from their brokerage accounts once every N periods. As households optimally manage these inventories, their money holdings follow a sawtooth pattern—rising rapidly with each periodic transfer from their brokerage account and then falling slowly as these funds are spent smoothly over time—similar to the sawtooth pattern of money holdings originally derived by Baumol (1952) and Tobin (1956) and more recently by Duffie and Sun (1990) and Abel, Eberly, and Panageas (2007). Here, we focus on the implications of our model for the response of prices to a change in money growth and the response of inflation to a change in interest rates. To highlight the specific mechanisms at work, we make the stark assumptions that price setting is fully flexible and that output in the model is exogenous so that our results can easily be compared to those from a flexible-price, constant-velocity, exogenous output benchmark cash-in-advance model of the effect of monetary policy on prices and inflation. Our first result is that prices respond sluggishly to a change in money in our model, because an exogenous increase in the stock

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of money leads endogenously, through the dynamics of households’ inventories of money, to a partially offsetting decrease in the velocity of money. As a result of this endogenous fall in velocity, prices respond on impact less than one for one to the change in money. Prices respond fully only in the long run when households’ inventories of money, and hence aggregate velocity, settle back down to their steady-state values. The sluggish response of prices to a change in money in our model can thus be understood not as a consequence of a sticky price-setting policy of firms but as a simple consequence of the sluggish response of nominal expenditure to a change in money inherent in an inventory-theoretic approach to money demand. We highlight this implication of our inventory-theoretic model of money demand because a strong negative correlation between fluctuations in money and velocity can be seen clearly in U.S. data. In Figure I, we illustrate this short-run behavior of money and velocity. We plot the ratio of M2 to consumption and the consumption velocity of M2 as deviations from a trend extracted using an HPfilter. These two series are strongly negatively correlated.2 After presenting our analytical results, we examine the extent to which our model can reproduce this comovement of money and velocity in a quantitative example. The mechanism through which our model produces a negative correlation between fluctuations in money and velocity and hence sluggish prices can be understood in two steps. First, consider how aggregate velocity is determined in this inventory-theoretic model of money demand. Households at different points in the cycle of depleting and replenishing their inventories of money in their bank accounts have different propensities to spend the money that they have on hand, or, equivalently, different individual velocities of money. Households that have recently transferred funds from their brokerage accounts to their bank accounts have a large stock of money in their bank account and tend to spend this money slowly to spread their spending smoothly over the interval of time that remains before they next have the opportunity to replenish their bank account. Hence, these households have a relatively low individual velocity of money. In contrast, households that have not transferred funds from their brokerage account in 2. We used the HP-filter smoothing parameter of 34 × 1,600 = 129,600 recommended by Ravn and Uhlig (2002) for monthly data. As discussed in the Appendix, similar results are obtained using alternative measures of the short-run fluctuations in money and velocity.

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FIGURE I Short-Run Negative Correlation of Money/Real Consumption, M/c, and Velocity, v We measure the money supply M as the M2 stock from the Board of Governors of the Federal Reserve System. We measure real consumption c as personal consumption expenditure on nondurables and services from the Bureau of Economic Analysis deflated by the personal consumption expenditures chain-type price index P from the BEA. We define velocity as v ≡ Pc/M. All data are monthly 1959:1– 2006:12 and seasonally adjusted. All variables are reported in logs as deviations from an HP trend with smoothing parameter 34 × 1,600.

the recent past and anticipate having the opportunity to make such a transfer soon tend to spend the money that they have in the bank at a relatively rapid rate, and thus have a relatively high individual velocity of money. Aggregate velocity is given by the weighted average of the individual velocities of money across all households with weights determined by the distribution of money across households. Now consider the effects on aggregate velocity of an increase in the money supply brought about by an open market operation. In this open market operation, the government trades newly created money for interest-bearing securities, and households, on the opposite side of the transaction, trade interest-bearing securities held in their brokerage accounts for newly created money. If the

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nominal interest rate is positive, this new money is purchased only by those households that currently have the opportunity to transfer funds from their brokerage accounts to their bank accounts because these are the only households that currently have the opportunity to begin spending this money. All other households choose not to participate in the open market operation because these households would have to leave this money sitting idle in their brokerage accounts, where it would be dominated in rate of return by interest-bearing securities. Hence, as a result of this open market operation, the fraction of the money stock held by those households currently able to transfer resources from their brokerage account to their bank account rises. Because these households have a lower-than-average propensity to spend this money, aggregate velocity falls. In this way, an exogenous increase in the supply of money leads to an endogenous reduction in the aggregate velocity of money and hence a diminished, or sluggish, response of the price level. To this point we have modeled changes in monetary policy as exogenously specified changes in the money supply. It is now common to model changes in monetary policy not as exogenously specified changes in money but as exogenously specified changes in the short-term nominal interest rate. When we model monetary policy in this way, we find our second result, that expected inflation responds sluggishly to a change in the short-term nominal interest rate. To gain intuition for this result, it is useful to consider the Fisher equation to decompose any change in the nominal interest rate into its two components—a change in the real interest rate and a change in expected inflation. For example, in a standard flexible-price, constant-endowment cash-in-advance model, the real interest rate is always constant, so that, given the Fisher equation, any change in the nominal interest rate must always be accompanied by a matching change in expected inflation. In this sense, in this model, expected inflation must respond immediately to a change in the nominal interest rate. More generally, from the Fisher equation, if a model is to generate a sluggish response of expected inflation to a change in the nominal interest rate caused by a change in monetary policy implemented through open market operations, it must do so because those open market operations generate, at equilibrium, a change in the real interest rate that is roughly as large as the change in the nominal interest rate. In our inventory-theoretic model of money demand, money injections

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implemented through open market operations have an effect on the real interest rate because the asset market is segmented, and it is this effect of open market operations on the real interest rate that is the source of the inflation sluggishness in our model. Asset markets are segmented in our model in the sense that only those agents who currently have the opportunity to transfer money between their brokerage and bank accounts are at the margin in participating in open market operations and in determining asset prices. This asset market segmentation arises naturally in an inventory-theoretic model of the demand for money because those agents who do not have the opportunity to transfer money between the asset and goods markets have no desire to purchase money being injected into the asset market through an open market operation because they have no ability to spend that money in the current period and they find that interest-bearing bonds dominate money as a store of value in the asset market.3 Because only those agents who currently have the opportunity to transfer money from the asset market to the goods market are at the margin in trading money and bonds with the monetary authority, money injections implemented through open market operations have a disproportionate impact on the marginal utility of a dollar for these marginal investors that is manifest as a movement in real interest rates. We first illustrate the mechanisms leading to a sluggish response of prices to money and inflation to interest rates in a specification of our model that is analytically tractable. In this specification of our model, households have log utility and all of the income from selling the households’ endowments is deposited directly into the households’ brokerage accounts. With these assumptions, the model becomes analytically tractable because households in the model choose to spend their inventories of money in their bank accounts at a rate that is independent of expectations of future prices and monetary policies. We show two main results in this analytical version of our model. First, starting from a steady state in which the opportunity cost of holding money in a bank account is low, in response to a 1% exogenous increase in the money stock, on impact, the price level increases by only 1/2 of 1% because velocity falls by 1/2 of 1%. We show how this result 3. These agents choose not to participate in the open market operation as long as the short-term nominal interest rate remains positive. Note that financial intermediaries also choose not to hold money injected through open market operations as long as the short-term nominal interest rate remains positive.

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follows from the basic geometry of money holdings in an inventorytheoretic model of money demand independent of the parameters governing the length of time, in calendar time, between households’ opportunities to transfer cash between their brokerage and bank accounts. Second, also starting from a steady state, in response to a one-percentage-point exogenous change in the nominal interest rate, on impact, the real interest rate responds by one percentage point and expected inflation does not respond at all. We show that this result follows from the asset market segmentation that is inherent in an inventory-theoretic model of money demand, again independent of the parameters governing the length of time, in calendar time, between households’ opportunities to transfer cash between accounts. The parameters governing the length of time between households’ opportunities to transfer money between accounts are important, however, for our model’s implications for the persistence of price and inflation sluggishness. These parameters also determine our model’s implications for steady-state aggregate velocity—the length of calendar time between households’ opportunities to transfer money determines the size of the inventory of money that households must hold to purchase consumption. Thus, the empirical implications of our model for the sluggishness of prices and inflation are largely determined by how we define money (because that definition determines the measure of velocity and hence the magnitude of households’ cash balances). In our model, defining money comes down to answering the question: What assets correspond to those that households hold in their bank accounts, and what assets do households hold and trade less frequently in their brokerage accounts? We examine the implications of our model in a quantitative example using a broad measure of money: U.S. households’ holdings of currency, demand deposits, savings deposits, and time deposits. Here we interpret households’ bank accounts in our model as corresponding to U.S. households’ holdings of deposits in retail commercial banks4 in the data and households’ brokerage 4. In the data, retail banks correspond to a traditional conception of a commercial bank as an institution funded by consumers’ checking, savings, and small time deposits. Clark et al. (2007) provide a useful description of retail banks in our modern financial system. As they describe, “retail banking is the cluster of products and services that banks provide to consumers and small businesses through branches, the Internet, and other channels.” “Organizationally, many large banking companies have a distinct ‘retail banking’ business unit with its own management and financial reporting structure.” “In terms of products and services, deposit taking

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accounts in the model as corresponding to U.S. holdings of other financial assets outside of the retail commercial banking system in the data. In the data, U.S. households hold a large stock of deposits in retail banks, roughly 1/2 to 2/3 of the annual personal consumption expenditure. We argue for the interpretation of this broad collection of accounts in the data as corresponding to bank accounts in our model because we find in the data that U.S. households pay a large opportunity cost in terms of foregone interest to hold such accounts—on the order of 150–200 basis points. This opportunity cost is not substantially different from the opportunity cost U.S. households pay to hold a narrower definition of money such as M1. To parameterize our model to match the ratio of U.S. households’ holdings of broad money relative to personal consumption expenditure, we assume that households transfer funds between their brokerage and bank accounts very infrequently—on the order of once every one-and-one-half to three years. We argue that this assumption is not inconsistent with evidence summarized by Vissing-Jorgensen (2002) regarding the frequency with which U.S. households trade in high-yield assets. Our interpretation of a bank account used for transactions replenished by transfers from a high-yield managed portfolio of risky and riskless assets is the same as used in the models of Duffie and Sun (1990) and Abel, Eberly, and Panageas (2007). We conduct two quantitative exercises with our model. In the first, we feed into the model the shocks to the stock of M2 and aggregate consumption observed in the U.S. economy in monthly data over the past forty years and examine the model’s predictions for velocity in the short run. The model produces fluctuations in velocity that have a surprisingly high correlation of .60 with the fluctuations in velocity observed in the data. This result stands in sharp contrast to the implications of a standard cash-in-advance model (this model with N = 1). In such a model, aggregate velocity is constant regardless of the pattern of money growth. We also find that the short-run fluctuations in velocity in our model are only 40% as large as those in the data. From the finding that is the core retail banking activity on the liability side. Deposit taking includes transactions deposits, such as checking and NOW accounts, and non-transaction deposits, such as savings accounts and time deposits (CDs). Many institutions cite the critical importance of deposits, especially consumer checking account deposits, in generating and maintaining a strong retail franchise. Retail deposits provide a low-cost, stable source of funds and are an important generator of fee income. Checking accounts are also viewed as pivotal because they serve as the anchor tying customers to the bank and allow cross selling opportunities.”

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the short-run fluctuations in velocity in our model are strongly correlated with those observed in the data, we conclude that a substantial portion of the unconditional negative correlation of the ratio of money to consumption and velocity might reasonably be attributed to the response of velocity to exogenous movements in money. From the finding that the short-run fluctuations in velocity in our model are not as large as those in the data, however, we conclude that there may be other shocks to the demand for money that we have not modeled here. In our second quantitative exercise, we consider the response of money, prices, and velocity to an exogenous shock to monetary policy, modeled as an exogenous, persistent shock to the shortterm nominal interest rate similar to that estimated in the literature, which uses vector autoregressions (VARs) to draw inferences about the effects of monetary policy. The consensus in that literature is that the impulse response of inflation to a monetary policy shock is sluggish.5 In our model, we find that the impulse response of inflation is also quite sluggish, as are the responses of money and the price level. All three of these responses from our model are quite similar to the estimated responses of these variables in this VAR literature. Although our model is incomplete in that we have assumed for simplicity that output is exogenous, these findings suggest that our model can account for a substantial portion of the sluggish responses of nominal variables to a change in the nominal interest rate. Our model is related to a growing literature on segmented asset markets. Grossman and Weiss (1983) and Rotemberg (1984) were the first to point out that open market operations could have effects on real interest rates and a delayed impact on the price level in inventory-theoretic models of money demand. The models they present are similar to this model when the parameter N = 2. Those authors examine the impact of a surprise money injection in the context of otherwise deterministic models. Here we study a fully stochastic model as in Alvarez and Atkeson (1997). That model is similar to the one presented here in that agents have separate financial accounts in asset and goods markets and cannot transfer funds between these accounts in every period. In that earlier paper, however, at equilibrium, the individual velocity of money is the same for all households and is constant over time, 5. See Cochrane (1994) and Leeper, Sims, and Zha (1996) for early estimates, Christiano, Eichenbaum, and Evans (1999) and Uhlig (2005) for an overview, and Christiano, Eichenbaum, and Evans (2005) for recent estimates.

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so that aggregate velocity is constant. This result follows from the assumptions in that paper that households have logarithmic utility and a constant probability of being able to transfer money between the asset market and the goods market. The asset pricing implications of our model are closely related to those obtained by Grossman and Weiss (1983), Rotemberg (1984), and Alvarez and Atkeson (1997). In particular, our model has predictions for the effects of money injections on real interest rates arising from the segmentation of the asset market related to the predictions in those papers and those in Alvarez, Lucas, and Weber (2001) and Alvarez, Atkeson, and Kehoe (2002, 2007). Alvarez, Atkeson, and Kehoe (2002, 2007) study the implications of models with segmented asset markets in which households pay a fixed cost to transfer money between bank and brokerage accounts. In that paper, they focus on equilibria in which all households spend all of the money in their bank account every period so that, again, velocity is constant. Two closely related papers build on our framework by endogenizing segmentation (in the spirit of the original Baumol–Tobin model). Chiu (2007) studies a version of our model where households face a fixed utility cost of transferring resources between bank and brokerage accounts. He solves numerically for the equilibrium response of the model to a once-and-for-all increase in the money supply, starting from steady state.6 He finds that the size of the initial money growth shock plays a key role in determining the response to a shock. When the money growth shock is small relative to the fixed cost, households do not pay the fixed cost and the equilibrium dynamics are the same as in an exogenous segmentation model: a money shock leads to an offsetting fall in aggregate velocity, so that the price level responds sluggishly. But for a sufficiently large money injection relative to the fixed cost, all households pay the fixed cost, and so there is no offsetting fall in aggregate velocity and the price level responds one for one to money growth. Because of this, Chiu (2007) concludes that the results from our model are not robust to endogenous segmentation. Khan and Thomas (2007) study a version of our model where households face idiosyncratic fixed costs of transferring resources between the two accounts7 and develop flexible numerical 6. Silva (2008) computes the equilibrium response of prices to an interest rate shock in a closely related continuous time model. 7. Alvarez, Atkeson, and Kehoe (2002, 2007) use idiosyncratic fixed costs to endogenously segment asset markets, but they assume households spend all their

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methods for solving the model. They show that the distribution of the idiosyncratic fixed costs plays an important role in determining the equilibrium responses of the model to a money shock. In their benchmark calibrated example, they find that these costs actually reinforce the sluggishness of prices and reinforce the persistence of liquidity effect relative to our model. The paper proceeds as follows. We present the general model. We next present our results on the impact effects of monetary policy on prices and inflation in the analytically tractable specification of our model. We then present our quantitative exercises. In a final section, we discuss how monetary policy might affect output in a version of our model with production and a discussion of how our results compare with those on price and inflation sluggishness obtained in models with nominal rigidities. II. AN INVENTORY-THEORETIC MODEL OF MONEY DEMAND Consider a cash-in-advance economy in which the asset market and the goods market are physically separated. There is a unit mass of households, each composed of a worker and a shopper. Each household has access to two financial intermediaries: one that manages its portfolio of assets and another that manages its money held in a transactions account in the goods market. We refer to the household’s account with the financial intermediary in the asset market as its brokerage account and its account with the financial intermediary in the goods market as its bank account. There is a government that injects money into the asset market via open market operations. Households that participate in the open market operation purchase this money with assets held in their brokerage accounts. These households must transfer this money to their bank accounts before they can spend it on consumption. Time is discrete and denoted t = 0, 1, 2, . . . . The exogenous shocks in this economy are shocks to the money growth rate μt and shocks to the endowment of each household yt . Because all households receive the same endowment, yt is also the aggregate endowment of goods in the economy. Let ht = (μt , yt ) denote the realized shocks in the current period. The history of shocks is money each period so that aggregate velocity is constant and equal to one. In Khan and Thomas (2007), as in this paper, not all households spend all their money each period, and so there is a nondegenerate cross-sectional distribution of money holdings.

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denoted ht = (h0 , h1 , . . . , ht ) . From the perspective of time zero, the probability distribution over histories ht has density ft (ht ). As in a standard cash-in-advance model, each period is divided into two subperiods. In the first subperiod, each household trades assets held in its brokerage account in the asset market. In the second subperiod, the shopper purchases consumption in the goods market using money held in the household’s bank account, while the worker sells the endowment in the goods market for money Pt (ht )yt (ht ), where Pt (ht ) denotes the price level in the current period. In the next period, a fraction γ ∈ [0, 1] of the worker’s earnings is deposited in the bank account in the goods market, and the remaining 1 − γ of these earnings are deposited in a brokerage account in the asset market. We interpret γ as the fraction of total income that households receive regularly deposited into their transactions accounts or as currency. We refer to γ as the paycheck parameter and to γ Pt−1 (ht−1 )yt−1 (ht−1 ) as the household’s paycheck. We interpret 1 − γ as the fraction of total income that households receive in the form of interest and dividends paid on assets held in their brokerage accounts. Unlike a standard cash-in-advance model, households cannot transfer money between the asset market and the goods market every period. Instead, each household has the opportunity to transfer money between its brokerage account and its bank account only once every N periods. In other periods, a household can trade assets in its brokerage account and use money in its bank account to purchase goods; it simply cannot move money between these two accounts. We refer to households that currently have the opportunity to transfer money between their accounts as active households. Each period a fraction 1/N of the households are active. We index each household by the number of periods since it was last active, here denoted by s = 0, 1, . . . , N − 1. A household of type s < N − 1 in the current period will be type s + 1 in the next period. A household of type s = N − 1 in the current period will be type s = 0 in the next period. Hence, a household of type s = 0 is active in this period, a household of type s = 1 was active last period, and a household of type s = N − 1 will be active next period. In period 0, each household has an initial type s0 , with fraction 1/N of the households of each type s0 = 0, 1, . . . , N − 1. Let S(t, s0 ) denote the type in period t of a household that was initially of type s0 . The quantity of money a household s has on hand in its bank account at the beginning of goods market trade is Mt (s, ht ). The

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shopper in this household spends some of this money on goods, Pt (ht )ct (s, ht ), and the household carries the unspent balance in its bank account into next period, Zt (s, ht ). For an inactive household of type s > 0, the balance in its bank account at the beginning of the period is equal to the quantity of money that it held over in its bank account last period Zt−1 (s − 1, ht−1 ) plus its paycheck γ Pt−1 (ht−1 )yt−1 (ht−1 ). Thus, the evolution of money holdings and consumption for inactive households is (1)

Mt (s, ht ) = Zt−1 (s − 1, ht−1 ) + γ Pt−1 (ht−1 )yt−1 (ht−1 ),

(2)

Mt (s, ht ) ≥ Pt (ht )ct (s, ht ) + Zt (s, ht ).

When a household is of type s = 0, and hence active, it also chooses a transfer of money Pt (ht )xt (ht ) from its brokerage account in the asset market into its bank account in the goods market. Hence, the money holdings and consumption of active households satisfy

(3)

Mt (0, ht ) = Zt−1 (N − 1, ht−1 ) + γ Pt−1 (ht−1 )yt−1 (ht−1 ) + Pt (ht )xt (ht ),

(4)

Mt (0, ht ) ≥ Pt (ht )ct (0, ht ) + Zt (0, ht ).

In addition to the bank account constraints, equations (1)–(4) above, the household also faces a sequence of brokerage account constraints. In each period, the household can trade a complete set of one-period state-contingent bonds that pay one dollar into the household’s brokerage account next period if the relevant contingency is realized. Let Bt−1 (s − 1, ht ) denote the stock of bonds held by households of type s at the beginning of period t following history ht , and let Bt (s, ht , h ) denote bonds purchased at price qt (ht , h ) that will pay off next period if h is realized. Let At (s, ht ) ≥ 0 denote money held by the household in its brokerage account at the end of the period. Because an inactive household of type s > 0 cannot transfer money between its brokerage account and its bank account, this household’s bond and money holdings in its brokerage account must satisfy Bt−1 (s − 1, ht ) + At−1 (s − 1, ht−1 ) (5)

+ (1 − γ )Pt−1 (ht−1 )yt−1 (ht−1 ) − Pt (ht )τt (ht ) ≥ qt (ht , h )Bt (s, ht , h ) dh + At (s, ht ),

where τt (ht ) denotes real lump-sum taxes. Each household’s real bond holdings must remain within arbitrarily large bounds. The

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analogous constraint for active households is

(6)

Bt−1 (N − 1, ht ) + At−1 (N − 1, ht−1 ) + (1 − γ )Pt−1 (ht−1 )yt−1 (ht−1 ) − Pt (ht )τt (ht ) ≥ qt (ht , h )Bt (0, ht , h ) dh + Pt (ht )xt (ht ) + At (0, ht ),

where Pt (ht )xt (ht ) is the active household’s transfer of money from brokerage to bank account. At the beginning of period 0, initially inactive households be¯ 0 (s0 ) in their bank accounts in the gin with exogenous balances M goods market. This quantity is the balance on the left-hand side of (2) in period 0. For initially active households, the initial balance ¯ 0 and ¯ 0 (0, h0 ) in (4) is composed of an exogenous initial balance Z M a transfer P0 (h0 )x0 (h0 ) of their choosing. Each household also be¯ −1 (s0 ) in its brokerage account on gins with exogenous balance B the left-hand side of constraints (5) and (6). The households initially have no money corresponding to A¯ −1 (s0 ) in their brokerage accounts. For each date and state, and taking as given the prices and aggregate variables, each household of initial type s0 chooses complete contingent plans for transfers, consumption, bond, and money holdings to maximize expected utility, ∞

β

t

u[ct (s, ht )] ft (ht ) dht ,

s = S(t, s0 ),

t=0

subject to the constraints (1), (2), and (5) in those periods t in which S(t, s0 ) > 0 and constraints (3), (4), and (6) in those periods t in which S(t, s0 ) = 0. Let Bt (ht ) be the total stock of government bonds. The government faces a sequence of budget constraints, Bt−1 (ht ) = Mt (ht ) − Mt−1 (ht−1 ) + Pt (ht )τt (ht ) + qt (ht , h )Bt (ht , h ) dh , together with arbitrarily large bounds on its real bond issuance. We denote the government’s policy for money injections as μt (ht ) = Mt (ht )/Mt−1 (ht−1 ). In period 0, the initial stock of government debt ¯ −1 and M0 (h0 ) − M ¯ −1 is the initial monetary injection. This is B budget constraint implies that the government pays off its initial

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debt with a combination of lump-sum taxes and money injections achieved through open market operations. An equilibrium of this economy is a collection of prices, complete contingent plans for households, and government policy such that (i) taking as given prices and government policy, the complete contingent plans solve each household’s problem, and (ii) the N−1 ct (s, ht ) = yt (ht ), the money market goods market clears, N1 s=0 N−1 clears, N1 s=0 Mt (s, ht ) + At (s, ht ) = Mt (ht ), and the bond mar N−1 ket clears, N1 s=0 Bt (s, ht , h ) = Bt (ht , h ), for each date and state. To understand equilibrium money demand and asset prices, we examine the household’s first-order conditions. Let ηt (s, ht ) denote Lagrange multipliers on the bank account constraints (2) and (4) of household s, and let λt (s, ht ) denote Lagrange multipliers on the brokerage account constraints (5) and (6). Active households choose transfers xt (ht ) to equate the multipliers on the bank and brokerage accounts: (7)

ηt (0, ht ) = λt (0, ht ).

For households of type s the marginal utility of a dollar satisfies (8)

ηt (s, ht ) = β t

u [ct (s, ht )] ft (ht ). Pt (ht )

The multipliers on the bank accounts satisfy the inequalities t (9) ηt (s, h ) ≥ ηt+1 (s + 1, ht , h ) dh , which hold with equality if Zt (s, ht ) > 0. Combining (8) and (9), we have the consumption Euler equations that determine a household’s money demand, ft+1 (ht , h ) u [ct+1 (s + 1, ht , h )] Pt (ht ) dh , (10) 1≥ β u [ct (s, ht )] Pt+1 (ht , h ) ft (ht ) which again holds with equality if Zt (s, ht ) > 0. The evolution of the marginal utility of a dollar in the brokerage account is determined by state-contingent bond prices: (11)

qt (ht , h ) =

λt+1 (s + 1, ht , h ) . λt (s, ht )

Under the assumption that initial conditions are such that the initial Lagrange multipliers on the brokerage account λ0 (s0 ) are

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the same for all households,8 equations (7), (8), and (11) together imply that state-contingent bond prices are then given by (12)

qt (ht , h ) = β

ft+1 (ht , h ) u [ct+1 (0, ht , h )] Pt (ht ) . u [ct (0, ht )] Pt+1 (ht , h ) ft (ht )

The nominal interest rate is then found from the price of a noncontingent bond paying interest it (ht ) in nominal terms: 1 = qt (ht , h ) dh 1 + it (ht ) ft+1 (ht , h ) u [ct+1 (0, ht , h )] Pt (ht ) dh . (13) = β u [ct (0, ht )] Pt+1 (ht , h ) ft (ht ) In what follows, we will characterize equilibrium in an analytically tractable specification of our model using methods similar to those used in a Lucas-tree economy (see Lucas [1978]). That is, we will find the allocations of money and consumption across households implied by market clearing and then solve for asset prices in terms of marginal utilities using the first-order conditions that link bond prices to ratios of marginal utilities above. To gain intuition as to how these prices lead households to choose to purchase more or less money in an open market operation, as required in equilibrium to match the central bank’s policy for money injections, we find it useful to recast these firstorder conditions in terms of the date-zero asset prices implied by our state-contingent bond prices. Specifically, let Qt (ht ) denote the price in period 0 of one dollar delivered in the asset market in period t following history ht . These prices satisfy the recursion Qt (ht ) = Qt−1 (ht−1 )qt−1 (ht−1 , ht ) for t ≥ 1. From (11) and the recursion for date zero prices we then have that for all households, (14)

Qt (ht ) = λt (s, ht ).

Again, using the assumption that initial conditions are such that the initial Lagrange multipliers on the brokerage account λ0 (s0 ) are the same for all households, from (7) and (8), we have that asset prices are determined by the marginal utility for active ¯ 0 (s0 ) 8. This can be ensured by an appropriate choice of initial bond holdings B or with the assumption that households trade securities contingent on their initial type s0 in an initial asset market before they learn this type.

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households: (15)

Qt (ht ) = β t

u [ct (0, ht )] ft (ht ). Pt (ht )

A large money injection at t and ht is associated with a low datezero price Qt (ht ) and large purchases of money by those households that are currently active (obtained by selling bonds). These active households then transfer this money immediately to their bank accounts and begin spending it, so the low date-zero price Qt (ht ) is associated with high consumption ct (0, ht ) for households that happen to be active at this date. Likewise, a small money injection at t and ht is associated with a high date-zero price Qt (ht ) and small purchases of money and low consumption by those households that are currently active. The mechanism through which money injections in this model have an impact on “real” asset prices is also most easily understood in terms of these date-zero asset prices. We can define a real asset price as the price at date zero of a claim to sufficient cash to purchase one unit of consumption at date t following history ht . This price is given by Qt (ht )Pt (ht ). Note from (15) that this asset price is equal to the marginal utility of consumption of the households that are active at date t. In a standard cash-in-advance model, all households are active at each date and consumption is exogenous, so this real asset price is invariant to the specification of monetary policy. As we show below, in our model, money injections redistribute cash holding across households and thus impact the consumption of the subset of agents who are active at a given date. Corresponding to this redistributive effect, in our model, money injections thus also impact real asset prices in equilibrium. To this point, we have made explicit reference to uncertainty in the notation in order to give a clear characterization of state-contingent asset prices. For the remainder of the paper we suppress reference to histories ht to simplify notation. The inequalities governing money demand can therefore be written u [ct+1 (s + 1)] Pt , (16) 1 ≥ Et β u [ct (s)] Pt+1 with strict equality if Zt (s) > 0, whereas the price for bonds can be written u [ct+1 (0)] Pt 1 . (17) = Et β 1 + it u [ct (0)] Pt+1

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III. HOW THE MODEL WORKS In this section, we solve our model for a special case that is analytically tractable to demonstrate how the model works. In this special case, agents have utility u(c) = log(c) and the paycheck parameter is γ = 0. Given these assumptions, households of type s spend a constant fraction v(s) of their current money holdings and carry the remaining fraction 1 − v(s) into the next period, irrespective of the future paths of money and prices. As a result of the fact that agents choose this simple pattern of expenditure, we can, in this special case, solve analytically for the dynamic, stochastic equilibrium of our model. We use this analytical example to first show how the price level responds sluggishly to an exogenous change in money growth and then show how inflation responds sluggishly to an exogenous change in the nominal interest rate. In the next section, we explore the quantitative implications of our model for illustrative examples in which household expenditure does vary with the future paths of money and prices because agents have preferences other than log utility and/or the paycheck parameter is positive. In presenting this version of the model, we allow the length of a time period to be an arbitrary > 0 units of calendar time (measured in fractions of a year). We continue to use t to count time periods, so after t periods, t units of calendar time have passed. We refer to flow variables such as consumption at annual rates so that ct is consumption in period t. Likewise, the discount factor for the flow utility is β , where β reflects discounting in preferences at an annual rate. We let T > 0 denote the calendar length of time between activity for households, so that N = T / is the number of periods that elapse between activity. We first derive results for an arbitrary length of a period, , and then focus attention on particularly simple formulas that obtain when we let → 0 for fixed T (so that N approaches infinity). We focus on the case of an arbitrarily small time period to show that the time period in our model does not have any economic significance and because this helps simplify the resulting formulas. For purposes of exposition, we leave all the algebraic details to the Appendix. In our analysis here, we assume that, at equilibrium, nominal interest rates are positive, so that households choose not to hold money in their brokerage accounts, where money is dominated in rate of return by bonds, and that the opportunity cost of holding money in a bank account is high, so that those households that

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are about to transfer money between their brokerage and bank accounts do not hold money in their bank accounts. These conditions are analogous to the cash-in-advance constraint binding in a standard cash-in-advance model (this model with N = 1). After solving the model under these assumptions, one can use equations (16) and (17) to check the first-order conditions governing these two assumptions regarding money holdings. III.A. Money and Velocity In our model, households periodically withdraw money from the asset market and then spend that money slowly in the goods market to ensure that it lasts until they have another opportunity to withdraw money from the asset market. As a result, households’ equilibrium paths for money holdings have the familiar saw-toothed shape characteristic of inventory-theoretic models of money demand. Here we discuss how this saw-toothed pattern of money holdings shapes our model’s implications for the dynamics of money, velocity, and prices. Given our assumption that households have utility u(c) = log(c) and the paycheck parameter is γ = 0, households’ money holdings and nominal spending at period t for a period of length are given by (18)

Mt+1 (s + 1) = (1 − v(s))Mt (s) and Pt ct (s) = v(s)Mt (s)

with (19)

v(s) ≡

1 1 − β . 1 − β (N−s)

We refer to the fraction v(s) as the individual velocity of money at an annual rate and to v(s) as the individual velocity in period t. Note that, in this special case of our model, these individual velocities of money are constant over time regardless of expectations for the future path of money and prices. Observe that these individual velocities v(s) converge to 1/(N − s) as β approaches one. In this limiting case, the nominal expenditure of each household is constant over time, as is assumed in the original Baumol–Tobin framework. Given that individual velocities v(s) are constant in this specification of our model, aggregate velocity for any date or state is simply a function of the distribution of money across households with different individual velocities. If the nominal interest rate is

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positive, so that households do not hold any money in the asset market, money market clearing implies Mt =

(20)

N−1 1 Mt (s). N s=0

N−1 Accordingly, we interpret Mt (s)/Mt s=0 as the distribution of money holdings across households. Goods market clearing then implies that the aggregate velocity of money is a weighted average of the individual velocities of money, where the weights are given by the distribution of money holdings across households,

(21)

vt ≡

N−1 N−1 Pt yt 1 Pt ct (s) 1 Mt (s) , = = v(s) Mt N Mt N Mt s=0

s=0

where vt is aggregate velocity at an annual rate. In a steady state with constant money growth, the distribution of money holdings across households of different types is constant. Hence, aggregate velocity is also constant, and the steady-state inflation rate is equal to the money growth rate. Therefore, our model predicts that in the long run, along a steadystate growth path, the price level and the money supply grow together, whereas the aggregate velocity of money stays constant. Out of steady state, however, as a result of the fact that the individual velocities of money v(s) vary across households with different values of s, fluctuations in aggregate money growth cause fluctuations in the distribution of money across households, and this in turn causes fluctuations in aggregate velocity. More specifically, the dynamics of prices, velocity, and money are determined by two factors: first, the differences in individual velocities v(s) across households of different types, and second, the effect of a money injection on the distribution of money holdings across households. How these factors affect fluctuations in aggregate velocity can be understood intuitively as follows. First, consider the differences in individual velocities v(s). These measures of individual velocity equal the flow of consumption obtained by each household relative to its money holdings at the beginning of the period. From (19), we immediately see that v(s) is increasing in s. A household of type s close to zero holds a large stock of money relative to its consumption, whereas

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a household of type s close to N − 1 holds only a small stock of money relative to its consumption. Next consider how a money injection affects the distribution of money across households. From (18), the evolution of the distribution of money for households of type s = 1, . . . , N − 1 is given by (22)

Mt−1 (s − 1) 1 Mt (s) = (1 − v(s − 1)) , Mt Mt−1 μ t

using μt = (Mt /Mt−1 )1/ to denote money growth at an annual rate. Because the distribution of money must sum to one, the money holdings of active households are (23)

N−1 1 Mt (0) 1 Mt−1 (s − 1) 1 =1− (1 − v(s − 1)) . N Mt N Mt−1 μ t s=1

Given an initial distribution of money holdings across households and a process for money growth μt , equations (22) and (23) completely characterize the equilibrium dynamics of the distribution of money holdings across households and hence the equilibrium dynamics of aggregate velocity and the price level. This law of motion for the distribution of money has two key implications. First, in response to an increase in the money supply, aggregate velocity falls and thus the price level responds less than one for one with the money supply. Hence, prices in this model are sluggish in that they move less than would be predicted by the simplest quantity theory. Specifically, the proportional response of prices on impact is roughly half as large as the proportional change in the supply of money. Second, there is a persistently sluggish response of prices to changes in the quantity of money, and the extent of persistence is increasing in the calendar length of time between periods of activity. To see these implications, consider first the impact of a money injection on velocity. By redistributing money toward the active households, an increase in the supply of money tilts the distribution of money holdings toward agents with low individual velocities and away from agents with high individual velocities, lowering aggregate velocity. To see this result more formally, we proceed in two steps. In the first step, we derive the elasticity of velocity with respect to money growth for an arbitrary period length and show that the elasticity is negative—so that on impact,

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velocity declines when money growth increases. In the second step, we consider the case of an arbitrarily small period length. To derive the elasticity of velocity with respect to money growth in period t analytically from equations (21), (22), and (23), observe that

∂ vt μ t = v(0). (24) ∂μ t The elasticity of velocity with respect to money growth in period t is thus given by 1 ∂ log(vt ) v(0) − vt ∂(vt μ t )

= (25) − vt = . v vt ∂μ ∂ log μt t t Because the individual velocity of active households is less than the aggregate velocity (v(0) < vt ), aggregate velocity declines when money growth increases. Given the exchange equation Mt vt = Pt yt , we see that the price level does not respond to impact one for one with an increase in the money supply, because that increase in the money supply leads to an endogenous decrease in aggregate velocity. To quantify this elasticity, we evaluate velocity at steady ¯ To simplify the formulas, we suppose the steadystate, vt = v. state money growth rate is μ¯ = 1 and the time discount factor β → 1, so that the steady-state real return to holding money, β/μ, ¯ also goes to one. In this limiting case, the expenditure of each household is constant over time, as in the original Baumol–Tobin framework. In this limit, individual velocity of active households per period v(0) = /T and steady-state aggregate velocity per period v ¯ = 2/(T / + 1) so that, under these assumptions, the elasticity of aggregate velocity with respect to period money growth is (26)

1 T / − 1 ∂ log(v) =− ∂ log(μ ) 2 T /

and

∂ log(π ) 1 T / + 1 = , ∂ log(μ ) 2 T /

where these derivatives are evaluated at steady state and where π denotes the inflation rate. We can see here that if T = , so that N = 1, as in a standard cash-in-advance model, inflation responds one for one with the shock to money growth and velocity is constant. In contrast, if for fixed T we take → 0, then inflation responds only half as much as money growth. This result follows from the geometry of money

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holdings implied by an inventory-theoretic model—a household that has just replenished its bank account will hold roughly twice as much money as an average household and hence have roughly half the velocity of the average household. Note that here, as we consider the limit as the time period shrinks to zero, we also shrink the magnitude of the money injection to zero. To be able to properly interpret the impact effect, we now specify our model with a small yet finite value of and consider the effect of a sequence of money injections carried out gradually, one per model period, that cumulate over time to a sizable injection. To be specific, we set to correspond to a day and calculate the effects of a total increase in the money supply of 1% accomplished via a sequence of equal-sized money injections, one per model period, over the course of one month, that is, a money injection that increases the money supply by 1/30th of 1% for thirty days, a shock of 0.0333% each day for thirty days. Our analytical results characterize the response of velocity and prices to the money injection on the first day, because we start the model off from a steady state. After the first day, however, the distribution of money holdings across households is no longer in steady state and we must track the impact of the remaining money injections numerically. Figure II illustrates the dynamics of money, velocity, and prices following this shock. In response to this money injection, aggregate velocity falls and the price level responds less than one for one with the change in the money supply. As we showed analytically, the elasticity of velocity with respect to money growth near steady state is approximately −1/2. The impact of the first day’s money injection on velocity is −0.0166%, very close to the analytical value of 0.5 × −0.0333% to be expected. Tracking the effects of the remaining 29 money injections gives the cumulative effect of this sequence of money injections at time t = 30 days on velocity of −0.48%, approximately −1/2 of the cumulative shock of 1.00% that was introduced over those thirty days. In the figure, we trace out the dynamics of money and prices for a total of 300 days (or ten months). Over time, aggregate velocity and prices rise, even overshooting their steady-state levels, and then gradually converge to steady state with dampened oscillations. The results displayed in Figure II regarding the impact of a 1% increase in the money stock carried out over one month are very similar to the results that we obtain when we simply

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FIGURE II Money Up, Velocity Down, Prices Sluggish The dynamics of money, velocity, and prices following a money growth shock. In this exercise, the money growth rate increases by 1/30th of 1% for 30 days. In response to this money injection, aggregate velocity falls and the price level responds less than one for one with the change in the money supply. We showed analytically that the elasticity of velocity with respect to money growth near steady state is approximately −1/2. We find that after thirty days (one month), the cumulative effect of this sequence of money injections on velocity is −0.48%, approximately −1/2 of the cumulative shock of 1% that was introduced over those thirty days. Our analytical results characterize the response of velocity and prices to the money injection on the first day, because we start the model off from a steady state. After the first day, however, the distribution of money holdings across households is no longer in steady state and we must track the impact of the remaining money injections numerically.

set the length of the model period to correspond to one month and calculate the effect of a 1% increase in the money supply accomplished in a single model period (the corresponding figure is available upon request). The dynamics of velocity following a shock can be understood as follows. Because the money growth rate is high for only one month, from (22) we see that the households that were active at the time of the money injection carry an abnormally large stock of money until they next have the opportunity to transfer funds

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from their brokerage accounts. As shown in (19), their individual velocities rise each period until this next visit occurs. Thus, aggregate velocity remains below its steady-state level for a time initially, as these agents have a low individual velocity, and then rises past its steady-state level, as the individual velocity for these agents rises. After N months these agents have spent all of their money and they visit the asset market again. If this were the only effect, we would expect aggregate velocity to return to its steady-state value in N/2 months. However, we show in the Appendix that aggregate velocity remains below its steady-state value for approximately N log(2) months, well over N/2 months (because log(2) ≈ 0.69). In this sense, there is persistence in the sluggish response of prices to changes in the quantity of money and this persistence is increasing in N. The periodic structure of the model introduces a sequence of dampened oscillations in velocity as the changes in the distribution of money holdings work their way through the system. After the first N months, however, these effects are quite small. III.B. Interest Rates and Inflation Until now, we have taken as given the path of money growth and examined our model’s implications for the responses of velocity and the price level to a shock to money growth. An alternative approach is to discuss monetary policy in terms of interest rates and solve endogenously for the responses of money growth, velocity, and inflation consistent with a shock to nominal interest rates. We turn now to such an analysis. Here we show our main result that, on impact, inflation responds sluggishly to a shock to interest rates. We demonstrate analytically that the response of inflation to a change in the nominal interest rate is sluggish in our model when N is large, again under the assumptions that u(c) = log(c) and γ = 0 so that individual velocities v(s) are time-invariant. We solve for the responses of money growth, velocity, and inflation to a change in the nominal interest rate in a deterministic setting. Specifically, we assume the nominal interest rate, inflation, money growth, and the distribution of money holdings across households (and hence velocity) are all initially at steady-state values corresponding to a constant interest rate ¯ı. We fix at t = 0 an increase in the nominal rate above steady state, i0 > ¯ı. We solve for the response of inflation, money growth, and velocity consistent with this change in the nominal interest rate.

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To solve for these responses, we use the pricing formula for nominal bonds (17). In a deterministic setting, this formula can be rewritten as a Fisher equation relating nominal interest rates, real interest rates, and inflation between the current period and the next, (27)

ˆıt = rˆt + πˆ t+1 ,

where a circumflex denotes log deviation from steady state and where we repeatedly use approximations of the form log(1 + it ) ≈ it . We use this Fisher equation to find a path for money growth such that the implied paths for inflation and the real interest rate are consistent with the exogenously specified path for the nominal interest rate. Recall that, in our model, changes in the path of money growth have an impact on velocity, inflation, and real interest rates, with the magnitude of these changes depending on N. As a benchmark, consider first the responses of money growth, velocity, and inflation when N = 1 (so that our model is a standard constant-velocity cash-in-advance model). With N = 1, all households are active, velocity is constant, and the consumption of active households is also constant at ct (0) = y. As a result, in this case, inflation is equal to money growth (πˆ t+1 = μˆ t+1 ) and the real interest rate is constant (ˆrt = 0). With these results, we see that any path of money growth that is consistent with our exogenously specified path of nominal interest rates must have money growth μˆ 1 and inflation πˆ 1 responding one for one to the change in the nominal interest rate in period 0. That is, μˆ 1 = ˆı0 . Clearly, in this case, the response of inflation from period t = 0 to t = 1 anticipated in period t = 0 in response to the change in the nominal interest rate ˆı0 is not at all sluggish. Our solution of the model in this benchmark case with N = 1 is not yet complete, as we have not solved for the equilibrium responses of money growth μˆ 0 and inflation πˆ 0 on impact, at date t = 0. It is well known that in this textbook cash-in-advance model (N = 1), this initial money growth rate and inflation rate are not determinate under an exogenous interest rate rule. We resolve the indeterminacy by choosing the particular path of money growth μˆ 0 so that, on impact, inflation from the last period to the current period does not respond to the change in the nominal interest rate in the current period (i.e., so that πˆ 0 = 0). In the model with N = 1, this is achieved by setting μˆ 0 = 0. This resolution of the

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indeterminacy is equivalent to assuming that the price level in period t = 0 does not respond to the change in the nominal interest rate and hence is consistent with the schemes used to identify shocks to monetary policy discussed in Christiano, Eichenbaum, and Evans (1999). Note that this resolution of the indeterminacy fixes the responses of money growth and inflation at date t = 0 by assumption. Of interest are the equilibrium values of money growth and inflation at date t = 1, μˆ 1 and πˆ 1 . We now turn to the case of a general N > 1. At the end of this section, we show that this indeterminacy of the initial money growth rate μˆ 0 given the exogenous path of the nominal interest rate extends to our setting with N > 1. In particular, we show that, as in the case with N = 1, there is a continuum of paths of money growth consistent with a given path of nominal interest rates. As in the case with N = 1, with N > 1, this continuum has only one dimension; that is, these paths can be indexed by their initial money growth rates μˆ 0 despite the fact that this model has a nondegenerate distribution of money holdings across households as a state variable that is absent from the model with N = 1. Here, we again resolve this indeterminacy by examining the path of money growth consistent with πˆ 0 = 0. Given our assumption of log utility and γ = 0, so that individual velocities are constant over time, this path of money growth has initial money growth at its steady-state level μˆ 0 = 0. Given this result that μˆ 0 = 0 under our resolution of the indeterminacy under an interest rate rule, we solve for the equilibrium responses of money growth μˆ 1 , velocity vˆ1 , and inflation πˆ 1 to the change in the nominal interest rate ˆı0 in period t = 0 by finding the value of money growth μˆ 1 such that the equilibrium responses of the real interest rate rˆ0 and inflation πˆ 1 are consistent with the assumed movement in the nominal interest rate. We solve for each of these responses in turn. Consider first the response of the real interest rate rˆ0 to a change in money growth μˆ 1 . This real interest rate is determined by the growth of the consumption of active households according to rˆ0 = cˆ1 (0) − cˆ0 (0). Given that the individual velocity for active households v(0) is constant over time, the consumption of active households is given by ct (0) = v(0)mt (0)Mt /Pt , where mt (0) = Mt (0)/Mt is the share of the money supply held by active households. The real interest rate can therefore be written (28)

ˆ 1 (0) − m ˆ 0 (0) + μˆ 1 − πˆ 1 . rˆ0 = m

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Given that initial inflation and money growth are at their steadystate values, and given our assumed initial conditions, the distribution of money holdings across households at date t = 0 is equal to its steady-state value, and hence the share of the money supply held by active households, mt (0), and the velocity, vt , are also equal to their steady-state values. Thus, we have m ˆ 0 (0) = 0 and ∂ log(π ) ∂ log(m(0)) +1− μˆ 1 , (29) rˆ0 = ∂ log(μ) ∂ log(μ) where ∂ log(m(0))/∂ log(μ) and ∂ log(π )/∂ log(μ) are the elasticities of the share of money held by active households and of inflation with respect to money growth, both evaluated at the steady state. From (28), these results then imply that the money growth required in period 1 to implement the nominal interest rate ˆı0 in period 0 is given by ⎡ ⎤ (30)

⎢ μˆ 1 = ⎢ ⎣

⎥ 1 ⎥ ˆı0 . ∂ log(m(0)) ⎦ 1+ ∂ log(μ)

Thus, the real interest rate and inflation rate are given by ⎡ ⎡ ⎤ ⎤ ∂ log(π ) ∂ log(π ) ⎢ ⎢ ⎥ ⎥ ∂ log(μ) ∂ log(μ) ⎥ ˆı0 and πˆ 1 = ⎢ ⎥ ˆı0 . rˆ0 = ⎢ ⎣1 − ⎣ ⎦ ∂ log(m(0)) ∂ log(m(0)) ⎦ 1+ 1+ ∂ log(μ) ∂ log(μ) (31) To discuss these formulas, we return to the setting where periods are measured in units of calendar time, with T > 0 denoting the calendar length of time between activity, so that N = T / is the number of periods that elapse between activity. As we can see from these formulas, the difference between our model and the standard model with T = comes through the terms ∂ log(m(0))/∂ log(μ) and ∂ log(π )/∂ log(μ) reflecting the elasticities of the share of money held by active households and of inflation with respect to a money injection. In the standard model with T = (i.e., N = 1), a money injection has no effect in terms of redistributing money holdings across households, so that this elasticity is zero and the elasticity of inflation with respect to money growth is one. Thus, as we have seen, in this case, money growth and inflation respond one for one with the nominal interest rate and the real interest rate remains constant. In contrast, with

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T > (i.e., N > 1), the elasticity of the share of money holdings of active households with respect to money growth is positive and grows large as → 0. Specifically, we show in the Appendix that, taking the limit as β/μ¯ → 1, the elasticity of the money share of active agents is approximately ∂ log(m(0)) T / − 1 = . ∂ log(μ) 2

(32)

And, as we showed above, the elasticity of inflation is ∂ log(π)/∂ log(μ) = (T / + 1)/2(T /), which is less than one for T > and falls toward 1/2 as → 0. Plugging in these expressions for the elasticities gives (33)

μˆ 1 =

2 ˆı0 T / + 1

and

πˆ 1 =

1 ˆı0 T /

and that the real interest rate is (34)

rˆ0 =

T / − 1 ˆı0 . T /

The size of the response of real interest rates to a change in the nominal interest rate on impact is measured by (T / − 1)/(T /), which is decreasing in . For small , a given increase in the nominal interest rate gives rise to a nearly one-for-one increase in the real rate and almost no increase in expected inflation. The small response of inflation to a change in interest rates comes from segmented asset markets: only the fraction /T (i.e., 1/N) of households that are active receive the entire increase in the money supply, and so a given money injection has a disproportionately large impact on the marginal utility of a dollar for these households. Therefore, for small , a given change in nominal interest rates is obtained with a small change in money growth because that small change in the money supply has a large impact on real interest rates. Inflation is sluggish when is small because this small change in money growth leads only to a small change in inflation. In our model, taking → 0 has two effects that together contribute to the sluggish response of inflation—reducing increases the elasticity of the share of money held by active households and lowers the elasticity of inflation with respect to a change in money growth. The more important of these two effects is the first one. To see this, consider a constant velocity model in which agents are permanently divided into a fraction λ who are always active and

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a remaining fraction 1 − λ who are never active, as in Alvarez, Lucas, and Weber (2001). Using the same resolution of the indeterminate price level, the relationship between real and nominal rates on impact is still given by (31) above. Because aggregate velocity is constant in this alternative model, ∂ log(π )/∂ log(μ) = 1. It can also be shown that, in this case, the elasticity of the share of money held by the permanently active agents to money growth is ∂ log(m(0))/∂ log(μ) = (1 − λ)/λ. Therefore, the response of the real rate is rˆ0 = (1 − λ)ˆı0 .

(35)

So if the fraction of agents who are always active in this alternative model is λ = /T (i.e., λ = 1/N), then the alternative model with constant velocity gives the same response of inflation on impact to a change in the nominal interest rate as our model with variable velocity. In this sense, our result that the response of inflation to a change in interest rates is sluggish is driven mainly by asset market segmentation and not variable velocity. For the remainder of this paper, for computational simplicity, we fix the period length to = 1 month so that N = T is the calendar length of time between activity in months. We now present the indeterminacy result that holds in our model. PROPOSITION 1. Let {it∗ }∞ t=0 be a given sequence of nominal inter∗ (s) be the initial distribution of money est rates and M−1 holdings across households. Let {Mt∗ , Mt∗ (s), ct∗ (s), Pt∗ }∞ t=0 be an equilibrium corresponding to this sequence of interest rates and these initial conditions. Then, for each M0 in an open neighborhood of M0∗ , there exists a unique equilibrium {Mt , Mt (s), ct (s), Pt }∞ t=0 consistent with the same path of inand initial distribution of money holdings terest rates {it∗ }∞ t=0 ∗ (s). In this alternative equilibrium, for t ≥ N, the disM−1 tributions of consumption, money growth, and inflation are unchanged in that ct (s) = ct∗ (s),

M∗ Mt+1 = t+1 , Mt Mt∗

and

P∗ Pt+1 = t+1 . Pt Pt∗

For periods t = 0, . . . , N − 1, however, the distributions of consumption, money growth, and inflation all depend on the value of M0 .

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Proof. See the Appendix.

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This indeterminacy result reduces to the standard indeterminacy result when N = 1. (See, e.g., Woodford [2003b, Chapter 2] for an extended discussion.) And because for each M0 there is a unique alternative equilibrium, even for N > 1 the indeterminacy is one-dimensional, as in the standard model. However, for N > 1, this indeterminacy result differs from the standard result in that the distribution of consumption across agents and the path of money growth and inflation differ across these equilibria for the first N periods. Hence, for N > 1, this indeterminacy has implications for real quantities and the real interest rate despite the fact that prices are fully flexible. IV. QUANTITATIVE EXERCISES The setup used in the preceding section, with u(c) = log(c) and γ = 0, simplifies calculations, because individual velocities v(s) are time-invariant. In the case where γ > 0 or for general u(c) the dynamics are more complex, because households’ expenditure decisions will be forward-looking and consequently individual velocities will be time-varying. Below, we examine the quantitative implications of our model for the persistence of the sluggish response of prices to money and inflation to interest rates under alternative parameterizations of our model numerically. We characterize the responses of prices and inflation numerically with values of the parameters N and γ chosen so that our model reproduces both the average level of velocity for a broad monetary aggregate held by U.S. households and the fraction of personal income that is received as wage and salary disbursements.9 We then conduct two exercises with the model to illustrate its quantitative implications. In the first exercise, we examine our model’s quantitative implications for the response of velocity to changes in money growth. In this experiment, we feed into the model the sequences of money growth and aggregate consumption shocks observed in U.S. data and compare the model’s implications for short-run fluctuations 9. The other parameters we need to assign are standard. We set the length of the time period to be a month; the time discount factor β = 0.991/12 , that is, a 1% annual rate; and the steady-state money growth to be μ¯ = 1.011/12 , also a 1% annual rate, which is consistent with a 2% annual opportunity cost of money, as discussed below. We set the coefficient of relative risk aversion to one, that is, log utility.

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in velocity with those observed in the data. We find that velocity in the model is highly correlated with velocity in the data. The magnitude of the fluctuations in the model, however, is significantly smaller than the magnitude of those observed in the data. In the second exercise, we examine the responses of money, prices, and velocity in the model to a monetary policy shock represented as a persistent movement in the nominal interest rate similar to those estimated as the response of the Federal Funds rate to a monetary policy shock in the VAR literature. Here we find that the corresponding impulse responses of money and prices implied by our model are similar to those estimated in the VAR literature. In particular, inflation in the model responds quite sluggishly to the change in interest rates. IV.A. Choosing N and γ In specifying our model, we have assumed that households hold their financial assets in two separate accounts, which we term a bank account and a brokerage account. The bank account is used to purchase consumption and offers a low rate of return on the assets deposited there, whereas the brokerage account can be used to hold a wide array of high-yielding financial assets. Transfers between the two accounts are assumed to be infrequent. To map the parameters of the model to observables in the data, we must interpret the theoretical objects in the model in terms of actual financial institutions in the data. Our preferred interpretation is to map the bank accounts in the model to what is called “retail banking” in the data, whereas the brokerage accounts in the model correspond to the array of actual brokerage accounts, mutual fund shares, pension funds, life insurance reserves, and equity in noncorporate businesses within which households hold claims on financial assets in a form that is not readily accessible for consumption purposes. We choose this interpretation of bank and brokerage accounts in our model based on the observation, documented in the Appendix, that U.S. households pay a substantial cost (on the order of two percentage points) in terms of foregone interest to hold assets in retail banks relative to shortterm Treasury securities. The evidence that we present indicates that there is no substantial difference in the opportunity cost of demand deposits (in M1) and the components of M2 (savings and time deposits) that we consider as part of our monetary aggregate. Our interpretation of bank and brokerage accounts differs from the traditional interpretation of Baumol–Tobin models,

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where withdrawals are made from a safe interest-bearing asset into cash. Instead, we interpret the bank accounts as a broader monetary aggregate, and the account from which these transfers are made as one with high-yield managed portfolios of risky and riskless assets. Our interpretation is similar to those in the models of Duffie and Sun (1990) and Abel, Eberly, and Panageas (2007). We measure U.S. households’ holdings of accounts in retail banks using the flow of funds accounts.10 From the flow of funds accounts, we observe that U.S. households hold a large quantity of such accounts—on the order of 1/2 to 2/3 times annual personal consumption expenditure. We use the implied average annual level of velocity of 1.5 to 2.0 as one statistic to guide our choice of N and γ for the quantitative results that follow. The other statistic that we use is based on our interpretation that the paycheck parameter in the model corresponds to regular wage and salary income automatically deposited in bank accounts in the data. Accordingly, as a baseline, we choose γ = 0.6 to match the fraction of personal income that is received as wage and salary disbursements observed in the data.11 The steady-state velocity implied by our model is a simple function of the parameters N and γ . In particular, holding N fixed, the model’s implications for steady-state velocity are an increasing function of the paycheck parameter γ because the automatic deposit of paychecks into households’ bank accounts allows faster circulation of money. In the example with u(c) = log(c) and γ = 0 that we used for intuition in the preceding sections, with β/μ¯ close to one, aggregate velocity is given by v¯ = 2/(N + 1). With γ > 0, for β/μ¯ close to one, aggregate velocity is well approximated by v¯ = 2/(N + 1)(1 − γ ), which increases as γ increases. Given our choice of γ to match the fraction of personal income that is received as wage and salary disbursements, we choose the 10. In terms of measuring the relative sizes of these accounts using data from the Flow of Funds Accounts of the United States (Federal Reserve Board, 2007), our interpretation corresponds to the following breakdown of the data presented in Table B.100, Balance Sheet of Households and NonProfit Organizations. Total Financial Assets for households are listed on line 8 ($45,405 billion in 2007). We interpret line 9, Deposits ($7,334 billion in 2007), as corresponding to assets held in bank accounts. This category includes checkable deposits and currency, time and savings deposits, and money market shares. We interpret the remaining financial assets listed on line 14, Credit Market Instruments, and lines 23–29 including, among other things, corporate equities, mutual fund shares, life insurance reserves, pension fund reserves, and equity in noncorporate business, as corresponding to assets held in the households’ brokerage accounts. 11. From Table 2.1 of the National Income and Product Accounts of the United States (U.S. Department of Commerce, Bureau of Economic Analysis), we observe that this fraction has been equal to 60% on the average over the period 1959–2007.

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remaining parameter N to match average velocity of 1.5 on an annual basis. We choose the length of a period to be one month and as a baseline use N = 38, so that with γ = 0.6 the model produces an average velocity of 1.5. With these parameters, our model implies that households transfer money between their brokerage accounts and bank accounts very infrequently—on the order of only once every three years. Now we argue that this assumption is not inconsistent with the available microeconomic evidence on the frequency with which agents trade financial assets held outside of their bank accounts. The first set of such microeconomic data concerns the frequency with which households trade equity. Such data are relevant because a household would have to trade equity to rebalance its portfolio between funds held in its bank account and equity held in its brokerage account. The Investment Company Institute (2002) conducted an extensive survey of households’ holdings and trading of equity in 1998 and 2001. They report the frequency with which households traded stocks and stock mutual funds in each year. Averaging across the 1998 and 2001 surveys, 48% of the households neither bought nor sold stocks, and 68% of the households neither bought nor sold stock mutual funds in 1998 and 2001. Because a household would have to buy or sell some of these assets to transfer funds between these higher-yielding assets held in a brokerage account and a lower-yielding bank account, these data, interpreted in the light of our model, would indicate choices of N ranging from roughly 24 (for roughly one-half of households trading these risky assets at least once within the year) to roughly 36 (for roughly one-third of households trading within the year).12 The second set of microeconomic data is that presented by Vissing-Jorgensen (2002). She studies micro data on the frequency of household trading of stocks, bonds, mutual funds, and other risky assets obtained from the Consumer Expenditure Survey. In Figure 6 in her paper, she shows the fraction of households that bought or sold one of these assets over the course of one year 12. These data may also overstate the frequency with which households transfer funds between their equity accounts and their transactions accounts because some of the instances of equity trading are simply reallocations of the equity portfolio. The Investment Company Institute reports that more than 2/3 of those households that sold individual shares of stock in 1998 reinvested all of the proceeds, whereas 57% of those households that sold stock mutual funds reinvested all of the proceeds. In the context of our model, reallocation of the household portfolio in the asset market is costless and does not generate cash that can be used to purchase goods.

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as a function of their financial wealth at the beginning of the year. She finds that the fraction of agents who traded one of these assets ranges from roughly one-third to one-half of the households owning these assets at the beginning of the year. Again, given our interpretation that households hold stocks, bonds, mutual funds, and other risky assets in their brokerage accounts, these data would lead us to choose N between 24 and 36. If a higher proportion of income is automatically available for spending (without the need for a transfer from the brokerage account), so that γ is higher than 0.6, then the chosen value for N needs to be correspondingly higher to keep the steady-state aggregate velocity constant. For example, to match v¯ = 1.5 annual with the higher γ = 0.7 needs about N = 52 months. If we interpret our model in terms of a narrower monetary aggregate with correspondingly higher velocity, then the chosen value of N needs to be lower. For example, to match v¯ = 2.0 annual with our benchmark γ = 0.6 requires N = 30 months, and to match v¯ = 4.0 annual with γ = 0.6 requires N = 15 months. IV.B. The Response of Velocity to U.S. Money and Consumption Shocks We now study the implications of our model for velocity in the short run when we feed in the money growth and aggregate consumption shocks observed in the U.S. data. We use monthly data on M2 as our measure of the monetary aggregate Mt , and we use monthly data on the deviation of the log of real personal consumption expenditure from a linear trend as our measure of the shocks to aggregate endowment yt . To solve for households’ decision rules in the model, we estimate a VAR relating the current money growth rate and aggregate consumption to twelve lags of these variables and use this VAR as the stochastic process governing the exogenous shocks. We then generate the model’s implications for velocity by feeding in the actual series for these shocks. To compare the implications of our model for the dynamics of money and velocity in the short run to the data, we detrend the series implied by the model using the HP-filter. Consider the implications of our model with N = 38 months and γ = 0.6. In Figure III, we show the HP-filtered series for velocity implied by our model with the corresponding HP-filtered series for velocity from the data. The correlation between velocity in the model and the data is .6. In the figure, we have used different scales in plotting the series from the model and the data.

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FIGURE III Model and Data Velocity Results from feeding money growth and endowment shocks as measured in monthly U.S. data into the N = 38, γ = 0.6 model. Money growth shocks are demeaned M2 growth; endowment shocks are the deviations of real personal consumption expenditure from a linear trend. To solve for households’ decision rules in the model, we estimate a VAR relating the current M2 growth rate and real personal consumption expenditure growth rate to 12 lags of these variables and use this VAR as the stochastic process governing the exogenous shocks. All variables are reported in logs as deviations from an HP trend with smoothing parameter 34 × 1,600.

These different scales reflect the fact that the standard deviation of velocity in the model is only 40% of the standard deviation of velocity in the data. Given that we have used nothing but steady-state information to choose the parameters of this model, we regard the high correlation between velocity from the model and the data as a remarkable success. Observe that if we had chosen N = 1, as in a standard cash-in-advance model, velocity as implied by the model would be constant at one regardless of the shock process and, hence, the correlation between velocity in the model and velocity in the data would be zero. We interpret this finding as offering support for the hypothesis that a substantial portion of the negative correlation between the short-run movements of velocity and the ratio of money to consumption is due to the endogenous response of velocity to changes in the ratio of money to consumption.

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We obtain broadly similar results with the alternative values of N and γ discussed above. For example, if we have γ = 0.7 but increase N to 52 to keep v¯ = 1.5 annual, then the correlation of HP-filtered velocity implied by our model and HP-filtered velocity in the data is still .51 (down from 0.60 for the benchmark parameters), whereas the standard deviation of velocity in the model rises slightly, to 45% of the standard deviation of velocity in the data. If instead we keep γ = 0.6 but choose a lower N = 30 to match a higher velocity of v¯ = 2.0 annual, then the correlation of model and data velocity is .56, almost the same as in the benchmark, but the standard deviation of velocity in the model falls to 32% of the data. Similarly, if we choose N = 15 to match even higher velocity of v¯ = 4.0 annual, then the correlation of model and data velocity falls slightly further to .48, whereas the standard deviation of velocity in the model falls to 21% of the data. Reducing N to match the higher velocities implied by narrower monetary aggregates impairs the ability of the model to endogenously produce volatile velocity, but does not substantially alter the correlation between data and model velocity. IV.C. The Response to a Shock to the Interest Rate We now consider the response of inflation to a shock to the nominal interest rate. A large literature estimates the response of the macroeconomy to a monetary policy shock modeled as a shock to the Federal Funds rate. The consensus in this literature is that a monetary policy shock is associated with a persistent increase in the short-term nominal interest rate, a persistent decrease in the money supply, and, at least initially, little or no response in the price level (Christiano, Eichenbaum, and Evans 1999).13 To simulate the effects of a monetary policy shock, we solve for a money growth path consistent with an exogenous, persistent movement in the short-term nominal interest rate. This raises two technical issues. First, recall from Proposition 1 that there is an indeterminacy in this model if the nominal interest rate is exogenous. In equilibrium, there are many paths for money growth, all consistent with the same exogenously specified path for nominal interest rates.14 In the quantitative experiment below, we resolve 13. See Cochrane (1994), Leeper, Sims, and Zha (1996), Christiano, Eichenbaum, and Evans (2005), and Uhlig (2005) for additional examples of such estimates. 14. The indeterminacy result of Section III is for u(c) = log(c) and γ = 0 but extends to the case of general isoelastic preferences and γ > 0.

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this indeterminacy in the same way that we did in Section III. We choose the unique path for money growth that, on impact, leaves the price level unchanged. A second technical issue is that in this model the endogenous dynamics with an exogenous nominal interest rate last exactly N periods. The matrix describing the equilibrium dynamics of endogenous variables has its N eigenvalues all exactly equal to zero. This implies that, if the interest rate is set at its steady-state value but the initial distribution of money holdings is not, then steady state will be reached in exactly N periods. The repetition of the eigenvalues also implies that the matrix that described equilibrium dynamics is not diagonalizable, and hence, this model cannot be solved using standard methods such as those outlined by Blanchard and Kahn (1980) or Uhlig (1999). In an Online Technical Appendix to this paper, we develop a specific solution method for this model based on the use of the generalized Schur form that makes use of the information that the eigenvalues of the matrix describing equilibrium dynamics are all equal to zero.15 We now study the quantitative implications of our model with N = 38 and γ = 0.6, having solved for money growth consistent with the log of the short-term gross interest rate following an AR(1) process with persistence ρ = 0.87. This persistence produces a response of the nominal interest rate to a monetary policy shock similar to that estimated by Christiano, Eichenbaum, and Evans (1999). Figure IV shows the impulse responses of inflation, money growth, and velocity growth following a persistent increase in the nominal interest rate. The model produces a persistent liquidity effect both in the sense that an increase in the nominal interest rate is associated with a fall in money growth and in the sense that an increase in the nominal interest rate is associated, at least initially, with an increase in the real interest rate of roughly the same size. Although it is not plotted separately, the real interest rate in this figure can be read as the difference between the impulse response of the nominal interest rate and the impulse response for inflation. As is clear in the figure, the response of the real interest 15. This Online Technical Appendix is available at http://pages.stern.nyu .edu/∼cedmond/. We also found that direct methods based on use of the generalized Schur form, as suggested by Klein (2000) and others, did not correctly identify that the matrix describing equilibrium dynamics had eigenvalues all equal to zero. This appears to be a numerical issue, because this methodology should work in cases with repeated eigenvalues.

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FIGURE IV Large Liquidity Effects Impulse responses of money growth, inflation, and velocity growth to a persistent nominal interest rate shock in the monthly N = 38, γ = 0.6 model. A unique equilibrium process for money growth is identified by selecting the one consistent with no movement in the price level on impact. All variables are reported as percent deviations from steady state.

rate to the change in the nominal interest rate is quite persistent, and, as a result, inflation is persistently sluggish, responding only slowly to the increase in the nominal interest rate. Figure V shows the same impulse responses, but for the levels of the variables rather than their growth rates. The aggregate price level appears “sticky,” showing little or no response to the shock to interest rates for at least the first twelve months. It is only after twelve months have passed that the money stock and the price level begin to rise together in the manner that would be expected in a flexible price model following a persistent increase in the nominal interest rate. This slow response of the price level simply reflects the persistently sluggish response of inflation. This quantitative exercise indicates that our model can account for a substantial delay in the response of inflation to an

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FIGURE V Sluggish Price Response to Persistent Interest Rate Shock Impulse responses of the money supply, price level, and velocity to a persistent nominal interest rate shock in the monthly N = 38, γ = 0.6 model. A unique equilibrium process for money growth is identified by selecting the one consistent with no movement in the price level on impact. All variables are reported as percent deviations from steady state.

exogenous shock to the nominal interest rate, and it does so because of the persistent response of the real interest rate to the change in the nominal interest rate. V. CONCLUSIONS In this paper, we have put forward a simple inventorytheoretic model of the demand for money and have shown, in that model, that the price level does not respond immediately to an exogenous increase in the money supply and that expected inflation does not respond immediately to an exogenous increase in the nominal interest rate. Instead, there is an extended period of price sluggishness that occurs because the exogenous increase in the money supply leads, at least initially, to an endogenous decrease in the velocity of money and an extended period of inflation

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sluggishness that occurs because of asset market segmentation. We have argued that if this simple model is used to analyze the dynamics of money and velocity using a relatively broad measure of money, then it produces sluggish responses of the price level and inflation similar to that estimated in the VAR literature for the response of the economy to monetary policy shocks. In keeping this model simple, we have abstracted from a number of issues that might play an important role in the development of a more complete model. First, we have simply assumed that households have the opportunity to transfer funds between their brokerage and bank accounts only every N periods and have not allowed households to alter the timing of these transactions after paying some fixed cost. This simplifying assumption allowed us to characterize equilibrium in an analytically tractable specification of our model. A model with explicit consideration of fixed costs of money transfers between accounts must be computed numerically. For work along these lines, see Khan and Thomas (2007). In their benchmark calibrated example, they find that these costs substantially reinforce the sluggishness of prices and the persistence of liquidity effects relative to that seen in our model.16 Second, we have simply assumed that output is exogenous in order to focus on the impact of monetary policy on prices and inflation. The impact of monetary policy shocks on output in a version of our model in which production is endogenous is an important area for future research. We have shown that monetary policy shocks have a direct impact on real asset prices in general and on real interest rates in particular. In a model with endogenous production, these changes in real asset prices would induce firms and workers to shift production and investment through time. The specific results that would be obtained would clearly depend on the exact specification of the production structure of the model. In recent work, Edmond (2003) and King and Thomas (2007) have begun to consider such models. There is a large literature that looks to model the sluggish responses of prices and inflation in an alternative framework in which prices are sticky because firms adjust prices infrequently.17 16. As Khan and Thomas (2007) emphasize, this result is sensitive to the shape of the idiosyncratic distribution of fixed costs facing households. The reason for this sensitivity is a “selection effect” familiar from models of price setting subject to menu costs. 17. This literature includes models in which firms set prices according to time-dependent rules (Fischer 1977; Taylor 1980; Rotemberg 1982; Calvo 1983) or

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Our results on the sluggish responses of prices to changes in money and of inflation to changes in the nominal interest rate arise from theoretical mechanisms that are unrelated to firms’ price-setting decisions. Moreover, the empirical phenomena that motivate our study are also unrelated to the extent of nominal rigidities. Consider first our results on the sluggish response of prices to changes in the stock of money. In our model, prices respond sluggishly to changes in money because nominal expenditure responds sluggishly to changes in money—velocity, which is the ratio of nominal expenditure to money, falls when money rises. The response of nominal expenditure to a change in the stock of money is a feature of money demand, not of the extent of nominal rigidities in terms of firms’ price-setting decisions. For example, if one posits money demand that is interest-inelastic as part of a sticky price model, then nominal expenditure will respond one for one with the stock of money regardless of the extent of nominal rigidities assumed in the model. Thus, modeling money demand in our way in a sticky price setup—where changes in nominal demand become changes in real output—implies that a given money supply shock has a smaller real effect on impact but a more persistent real effect than that obtained using an otherwise standard specification of money demand. Researchers using sticky price models may find it useful to incorporate our model of money demand when they look to account for the impact of a change in the stock of money on the economy. It is clear from our Figure I that this sluggish response of nominal expenditure to money is an important component of understanding the dynamics of prices and money in the unconditional U.S. data. VAR results in Altig et al. (2004) indicate that nominal expenditure also responds sluggishly to a shock to monetary policy. Consider next the relationship between our results and the sluggish response of inflation to changes in the nominal interest rate relative to those in sticky price models. Our model is able to produce a sluggish response of inflation to a persistent shock to the nominal interest rate due to the segmentation of asset markets. The money injections that implement a persistent change in the nominal interest rate also lead to a persistent change in the real state-dependent rules (Caplin and Leahy 1991; Dotsey, King, and Wolman 1999; Midrigan 2006; Golosov and Lucas 2007) or, more recently, on the basis of slowly updated information (Mankiw and Reis 2002; Woodford 2003a).

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interest rate of nearly the same magnitude. Sluggish inflation then follows directly, not as a consequence of sticky prices, but instead as a consequence of the standard Fisher equation linking nominal interest rates, real interest rates, and inflation. In contrast, standard sticky price models have serious problems in reproducing the estimated responses of inflation to a shock to monetary policy modeled as a persistent shock to the nominal interest rate. Mankiw (2001), for example, discusses how a standard sticky price model predicts that the largest response of inflation to a persistent shock to the nominal interest rate occurs on impact, and not in a delayed fashion. He uses this observation to argue for a model with “sticky information.” Sims (1998) makes a similar argument. The difficulty that sticky price models face in generating sluggish inflation arises from the fact that standard sticky price models build on a representative household framework linking the real interest rate to the growth of marginal utility for the representative household, and hence aggregate consumption, through a consumption Euler equation. Thus, in these models, if expected inflation responds sluggishly to a change in the nominal interest rate, then the growth rate of marginal utility for the representative household must respond strongly to a change in the nominal interest rate. Hence, capturing simultaneously a sluggish response of expected inflation and aggregate consumption to a change in the short-term nominal interest rate has been a challenge for these models. Frontier sticky price models, such as Christiano, Eichenbaum, and Evans (2005), use time nonseparable preferences and an elaborate set of adjustment costs and shocks to help their models reproduce a specific set of impulse responses, including the sluggish response of inflation. Canzoneri, Cumby, and Diba (2007), however, observe that standard sticky price models equate the nominal interest rate targeted by the central bank with the interest rate implied by the representative household’s consumption Euler equation and that this assumption fails quite dramatically in the data even if one considers a wide array of time nonseparable preferences for the household. They find a negative correlation between the Federal Funds rate in the data and the short-term nominal interest rates implied by a wide variety of sticky price models’ consumption Euler equations. By contrast, our model abandons the assumption of a representative household for pricing assets. In our model, the real interest rate is linked to the growth of marginal utility for active

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households, not for a representative household consuming aggregate consumption. Hence, as we have seen in our model, we can produce a sluggish response of expected inflation to a change in the nominal interest rate even if aggregate consumption is constant and hence has no response at all to a change in the nominal interest rate. Researchers using models with nominal rigidities may find it useful to incorporate asset market segmentation of the kind we examine here in their models in addressing some of the difficulties their models have with the consumption Euler equation. APPENDIX A. Data All data are monthly 1959:1–2006:12 and seasonally adjusted. We measure the price level P as the personal consumption expenditures chain-type price index with a base year of 2000 from the Bureau of Economic Analysis (BEA). We measure real consumption c as personal consumption expenditure on nondurables and services from the BEA deflated by P. We measure the money supply M as the M2 stock from the Board of Governors of the Federal Reserve System. We define velocity as v ≡ Pc/M. Here we document the robustness of the negative correlation between log(M/c) and log(v) using alternative detrending methods to characterize the short-run fluctuations in money and velocity. We report statistics for HP-filtered data based on the smoothing parameter λ = 1,600 ×34 recommended by Ravn and Uhlig (2002) for monthly data. These are the statistics reported in the main text. In Table A.1, we also report statistics for the lower smoothing parameter λ = 1,600 ×32 and for monthly differences and annual differences. No matter how the short-run fluctuations are measured, we find that there is a pronounced negative correlation between log(M/c) and log(v) and that the standard deviation of log(v) is almost as high as or higher than the standard deviation of log(M/c). We measure the opportunity costs of monetary assets using data collected by the Monetary Services Index project of the Federal Reserve Bank of St. Louis. We measure the opportunity cost of an asset as the short-term Treasury rate less the own rate of return on the asset in question. We take the short-term Treasury rate and own rates of return on currency and demand deposits from the spreadsheet ADJSAM.WKS available from the website

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×32

−.91 1.25

Correlation Standard deviation

Differenced

1,600

×34

Monthly

Annual

−.88 1.01

−.63 0.98

−.86 1.33

Note: Correlation of and relative standard deviation of velocity v to money/real consumption M/c for alternative measures of short-run fluctuations. We measure the money supply M as the M2 stock from the Board of Governors of the Federal Reserve System. We measure real consumption c as personal consumption expenditure on nondurables and services from the Bureau of Economic Analysis deflated by the personal consumption expenditures chain-type price index P from the BEA. We define velocity as v ≡ Pc/M. All data are monthly 1959:1–2006:12 and seasonally adjusted. All variables are reported in logs.

TABLE A.2 OPPORTUNITY COSTS OF MONETARY ASSETS

Currency Demand deposits M2

1959–2006

1959–1990

1990–2006

4.91 1.80 2.08

5.61 2.25 2.30

3.45 0.85 1.64

Note. The opportunity costs of monetary assets in percentage points. We measure opportunity costs as the short-term Treasury rate less the own rate of return on the asset in question. We take the short-term Treasury rate and own rates of return on currency and demand deposits from the Monetary Services Index project of the Federal Reserve Bank of St. Louis. We take the own rate of return on M2 from the Board of Governors of the Federal Reserve System. All data are monthly 1959:1–2006:2 and seasonally adjusted.

of the Federal Reserve Bank of St. Louis. We take the own rate of return on M2 from the Board of Governors of the Federal Reserve System. All opportunity cost data are monthly 1959:1–2006:2 and seasonally adjusted. As is clear from Table A.2, the average opportunity cost of holding demand deposits and M2 is roughly similar, on the order of 200 basis points. Both opportunity costs have fallen somewhat in recent years. B. Algebra of Steady-State Money Distribution and Elasticities Let the length of a period be > 0, measured in fractions of a year. Let the length of time between periods of activity be T , such that the number of periods between periods of inactivity is N = T /. Let period utility be u(c) = log(c) and set the paycheck parameter to γ = 0. In this setting, individual velocity in period t is time-invariant and given by v(s) = (1 − β )/(1 − β (N−s) ) for s = 0, 1, . . . , N − 1.

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For households s = 1, . . . , N − 1, the distribution of money holdings satisfies Mt (s) Mt−1 (s − 1) 1 = [1 − v(s − 1)] , Mt Mt μ t

(36)

with money market clearing implying that N−1 1 Mt−1 (s − 1) 1 1 Mt (0) =1− [1 − v(s − 1)] . N Mt N Mt μ t

(37)

s=1

Now consider a steady state with μt = μ. ¯ Iterating on the steady-state version of (36) and using the formula for individual velocity shows that the steady-state money holdings of household s are related to the holdings of an active household by s−1 1 M(0) M(s) = s . (1 − v(i)) M μ¯ M

(38)

i=0

And because s−1 s−1 1 − β (N−i−1) 1 − β (N−s) (1 − v(i)) = β = β s , (N−i) 1 − β N 1−β i=0 i=0

we have (39)

M(s) = M

s β 1 − β (N−s) M(0) . μ¯ 1 − β N M

We now need to find M(0)/M. We do this using steady-state money market clearing, N−1 1 M(s) 1 M(0) =1− N M N M s=1

(40)

=1−

1 N

N−1 s=1

M(0) M

s β 1 − β (N−s) , μ¯ 1 − β N

and so (41)

N−1 1 M(0) β s 1 − β (N−s) 1= . N M μ¯ 1 − β N s=0

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957

Computing the sums and rearranging gives the solution (42)

−1 1 M(0) ¯ N 1 − (β/μ) ¯ N N N 1 − (1/μ) = (1 − β ) −β . N M 1 − (β/μ) ¯ 1 − (1/μ) ¯

Plugging this formula for M(0)/M into equation (39) gives the complete solution for the steady-state distribution of money holdings. Steady-state aggregate velocity at an annual rate is then given by (43)

v¯ =

N−1 1 M(s) . v(s) N M s=0

We can use the formula for individual velocity in each period to simplify the terms in the sum. For each s we have s M(s) β 1 1 − β 1 − β (N−s) M(0) v(s) = M 1 − β (N−s) μ¯ 1 − β N M s β 1 1−β M(0) = . 1 − β N μ¯ M And so, using the formula for M(0)/M given in equation (42) and then summing over s, we have (44)

−1 ¯ N 1 − (β/μ) ¯ 1 − β N 1 − (1/μ) 1−β . v¯ = 1 − (1/μ) ¯ 1 − (β/μ) ¯ N

To develop intuition, we simplify these formulas by studying a steady state with μ¯ = 1 in the limit as β → 1. We begin with the further special case of = 1 month so that we can quickly derive the main formulas used in the text and then return to the case of general > 0 at the end. With this extra structure, the steady-state money holdings of household s are related to the holdings of an active household by N − s M(0) M(s) = . M N M And so, on using this formula in money market clearing, we also get M(0)/M = 2N/(N + 1), so that we have the complete solution for the distribution of money holdings, (45)

M(s) N−s =2 , M N+1

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for s = 0, 1, . . . , N − 1. Steady-state aggregate velocity is then v=

(46)

N−1 N−1 1 M(s) 1 2 N−s 2 v(s) = = , N M N N−s N+1 N+1 s=0

s=0

as used in the main text. Continuing with this special case of = 1 month, we now derive the elasticity of aggregate velocity with respect to money growth. Specifically, using money market clearing and the law of motion for the money holdings, we have N−1 1 Mt (s) v(s) vt = N Mt s=0 N−1 N−1 1 Mt (s) Mt (s) 1 = v(0) 1 − v(s) + N Mt N Mt s=1

= v(0) + = v(0) +

1 N 1 N

N−1

[v(s) − 1]

s=1 N−1

s=1

Mt (s) Mt

[v(s) − 1][1 − v(s − 1)]

s=1

Mt−1 (s − 1) 1 . Mt−1 μt

And so (47)

vt μt = v(0)μt +

N−1 1 Mt−1 (s − 1) [v(s) − 1][1 − v(s − 1)] , N Mt−1 s=1

which gives the key result (48)

∂ (vt μt ) = v(0), ∂μt

which is a constant for all t. Using the product rule ∂(vt μt )/∂μt = (∂vt /∂μt )μt + vt , we can solve for the elasticity in terms of v(0), a known constant, and aggregate velocity. We evaluate this elasticity at steady state vt = v¯ to get (49)

v(0) 1 N−1 ∂ log(v) = −1=− . ∂ log(μ) v 2 N

And because the aggregate endowment y is constant, the elasticity of inflation with respect to money growth evaluated at steady

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state is (50)

∂ log(π ) ∂ log(v) v(0) 1 N+1 = +1= = . ∂ log(μ) ∂ log(μ) v 2 N

We now derive the elasticity of the share of money held by active households with respect to money growth. Multiplying equation (37) by Mt and differentiating both sides with respect to Mt we get ∂ Mt (0) = N. ∂ Mt Evaluated at steady state, M N+1 N+1 ∂ log(M(0)) =N =N = . ∂ log(μ) M(0) 2N 2 Now let m(0) ≡ M(0)/M denote the steady-state money share. Then we have (51)

∂ log(m(0)) ∂ log(M(0)) N+1 N−1 = −1= −1= . ∂ log(μ) ∂ log(μ) 2 2

To obtain the expressions with arbitrary used in the main text, set N = T / in equations (49)–(51). More formally, use the expression for v¯ in equation (44) and calculate the limit as β/μ¯ → 1 using l’Hˆopital’s rule. C. Dynamic Response of Velocity to a Money Growth Shock Here we analytically characterize the impulse response of velocity to a money growth shock. The dynamics of velocity following a money growth shock are determined by the subsequent evolution of the distribution of money over time. It is easiest to analyze the dynamics of velocity following a shock in a log-linearized version of the model. We proceed in two steps. First, we provide an autoregressive moving average (ARMA) representation of the dynamics of the money distribution. Second, we map the ARMA representation into a formula for the impulse response of velocity that is exact (up to the log-linearization) for the first N − 1 periods after a shock. For simplicity, we consider only the special case of a period length = 1 month. Two sets of equations govern the dynamics of the distribution of money. First, there is an equation requiring that the sum of the log deviations of the fractions of money held by agents of type s be

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zero, 0 = m(0)m ˆ t (0) +

N−1

m(s)m ˆ t (s),

s=1

where steady-state money shares are m(s) ≡ M(s)/M and m ˆ t (s) ≡ log[mt (s)/m(s)]. Second, there is a set of equations for s = 1, . . . , N − 1 governing the evolution of the money shares, ˆ t−1 (s − 1) − μˆ t , m ˆ t (s) = m where these equations follow from the fact that individual velocities v(s) are time-invariant. Rearranging the first equation and using m(s) = 2(N − s)/(N + 1), we have for active households m ˆ t (0) = −

N−1 s=1

N−s m(s) m ˆ t (s) = − m ˆ t (s), m(0) N N−1

s=1

and after iterating on the transitions for inactive households m ˆ t (s) = m ˆ t−s (0) −

s

μˆ t−k+1 ,

k=1

for s = 1, . . . , N − 1. Combining these gives an ARMA representation of the dynamics of the money distribution: m ˆ t (0) = −

N−1 s=1

N−1 s N−s N−s m ˆ t−s (0) + μˆ t−k+1 . N N s=1

k=1

The log deviation of velocity can be written N−1 1 vˆt = m ˆ t (s), N s=0

using v(s)m(s) = 2/(N + 1) = v¯ for all s. Differencing this once and simplifying gives N−1 N−1 1 1 vˆt = m ˆ t (s) = ˆ t−N (0) − (N − 1)μˆ t + μˆ t−s , m ˆ t (0) − m N N s=0

s=1

which repeatedly uses m ˆ t−1 (s − 1) = m ˆ t (s) + μˆ t to cancel terms in the sum. Let the economy start in steady state for t < 0 and consider a given shock μˆ t at date t with μˆ t+k = 0 for all k > 0. For

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the first N − 1 periods after a shock, the terms m ˆ t−N (0) and the N−1 μˆ t−s are zero, so that vˆt = [m ˆ t (0) − (N − 1)μˆ t ]/N. We sum s=1 can solve this for m ˆ t (0) = Nvˆt + (N − 1)μˆ t and use the ARMA representation for the money share of active households to get an ARMA representation of velocity growth that is exact for the first N − 1 periods, vˆt = −

N−1 s=1

N−s 1 N−1 vˆt−s − μˆ t N 2 N

(using μˆ t−s = 0 for the first N − 1 periods). Rearranging terms to write this in levels, we get vˆt =

N−1 1 1 N−1 μˆ t vˆt−s − N 2 N s=1

(this time using vˆt−N = 0 for the first N − 1 periods). When N is large, so that (N − 1)/N ≈ 1, this implies that the impulse response of the log of velocity over the first N − 1 periods is given by 1 k+1 1 1+ − 1. (52) vˆt+k = 2 N This starts with vˆt = −1/2; for large N it crosses zero at roughly k = N log(2) and then rises above zero until k = N. D. Proof of Indeterminacy Proposition Using that u(c) = log(c) and γ = 0, so that Pt ct (0) = v(0)Mt (0), and that u (ct (0)) 1 1 = = , Pt ct (0) Pt v (0) Mt (0)

∞ the sequence of Mt (0) that supports the interest rate it∗ t=0 must satisfy Mt+1 (0) = 1 + it∗ β, Mt (0)

t = 0, 1, . . . ,

or (53)

Mt+1 (0) = M0 (0) β t

t

1 + i ∗j . j=0

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For future reference, we can write equation (53) as

Mt−1−s (0) = M0 (0) β t−1−s−1

(54)

t−1−s−1

1 + i ∗j ,

j=0

which applies if t − 1 − s ≥ 0 or s ≤ t − 1. Now again using that u (c) = log (c) and γ = 0, we have Mt (s) = (1 − v (s − 1)) Mt−1 (s − 1) ,

s = 1, . . . , N,

which we can substitute into

Mt (0) = NMt −

N−1

(1 − v (s − 1)) Mt (s − 1)

s=1

to obtain

(55)

Mt (0) = N ( Mt − Mt−1 ) +

N−1

θs Mt−1−s (0) ,

s=0

where the coefficients θs are given by θs ≡ v(s)[ s−1 j=0 (1 − v( j))] > 0. It is easy to verify that any sequence of {Mt − Mt−1 } for t ≥ 0 and {Mt (0)} for t ≥ −N + 1 that solves equation (55) completely characterizes an equilibrium. Now we specialize equation (55) for three different types of time periods. For t = 0 we have

(56)

N−1 ∗ ∗ M0 (0) = N M0 − M−1 + θs M−1−s (0) . s=0

For t = 1, 2, . . . , N − 1 we can break the sum into two parts and use the expression for Mt−1−s (0) in terms of interest rates,

SLUGGISH RESPONSES OF PRICES AND INFLATION

963

equation (54), so we have Mt (0) t−1

= N ( Mt − Mt−1 ) +

θs Mt−1−s (0) +

= N ( Mt − Mt−1 ) +

θs M0 (0) β t−1−s−1

t−1−s−1

s=0

(57)

+

N−1

∗ θs Mt−1−s (0)

s=t

s=0 t−1

N−1

1 + i ∗j

j=0

∗ θs Mt−1−s (0) ,

s=t

and using the expression for the interest rate equation (53) again, M0 (0) β t−1

t−1

1 + i ∗j j=0 t−1

= N ( Mt − Mt−1 ) +

θs M0 (0) β t−1−s−1

t−1−s−1

s=0

(58)

+

N−1

1 + i ∗j

j=0

∗ θs Mt−1−s (0) .

s=t

Finally, for t = N, N + 1, . . ., we have Mt (0) = N ( Mt − Mt−1 ) +

N−1

θs M0 (0) β t−1−s−1

s=0

t−1−s−1

1 + ij ,

j=0

and inserting the expression for Mt (0) based on the interest rates, M0 (0) β t−1

t−1

1 + i ∗j j=0

(59)

= N ( Mt − Mt−1 ) +

N−1 s=0

θs M0 (0) β t−1−s−1

t−1−s−1

1 + ij .

j=0

Now we are ready to construct the path of the remaining

∞ variables for an equilibrium that supports the interest rate path it∗ t=0 . We do this in three steps, one for each type of time period. We do this for an arbitrary value of M0 .

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Step a. Solve for M0 (0) . For t = 0, M0 (0) is a function of prede∗ termined variables, M−1 , M∗j (0) for j < 0, and M0 . Thus, for the given value of M0 there is a unique value of M0 (0) . Step b. Solve for Mt (0) and Mt for t = 1, . . . , N − 1. Equation (58) gives one equation in one unknown, namely Mt − Mt−1 , given M0 (0) . Using these equations recursively, using the initial conditions M0 found in Step a, we can solve for M1 , . . . , MN−1 . Step c. Solve for Mt for t ≥ N. Given the initial condition MN−1 found in Step b, equation (59) can be used to solve for Mt for t ≥ N. Steps a through c show that for any given M0 there is a unique way to construct an equilibrium that supports the path of interest

∞ rates it∗ t=0 . We now show that any equilibrium that supports the in for ∞ terest rate sequence it∗ t=0 , the distribution of cash Mt (s) /Mt for s = 0, . . . , N − 1 for all t ≥ N is the same. Using equation (53) for t ≥ N in Mt (0) = NMt −

N−1

(1 − v (s − 1)) Mt (s − 1) ,

s=1

we obtain Mt (0) = NMt −

N−1

(1 − v (s − 1))

s=1

s−1

v (k) Mt−k (0) ,

k=1

and using equation (53) we get M0 (0) β t−1

t−1

1 + i ∗j j=0

= NMt −

N−1 s=1

(1 − v (s − 1))

s−1 k=1

v (k) M0 (0) β t−k−1

t−k−1

1 + i ∗j ,

j=0

which shows that the path of Mt is proportional to M0 (0) for t ≥ N. Finally, equation (53) implies that the path of Mt (s) is proportional to M0 (0) , which establishes the desired result. This in turn immediately implies that Mt (s) /Mt = Mt∗ (s) /Mt∗ and Mt+1 /Mt = ∗ ∗ /Mt∗ , and thus that ct (s) = ct∗ (s) Pt+1 /Pt = Pt+1 /Pt∗ for t ≥ N. Mt+1

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965

Finally, the qualification that M0 has to be close to M0∗ ensures that in the values constructed for Mt (0) during the periods t = 0, . . . , N − 1 are all strictly positive. UNIVERSITY OF CHICAGO AND NATIONAL BUREAU OF ECONOMIC RESEARCH UNIVERSITY OF CALIFORNIA–LOS ANGELES, FEDERAL RESERVE BANK OF MINNEAPOLIS, AND NATIONAL BUREAU OF ECONOMIC RESEARCH NEW YORK UNIVERSITY AND UNIVERSITY OF MELBOURNE

REFERENCES Abel, Andrew B., Janice C. Eberly, and Stavros Panageas, “Optimal Inattention to the Stock Market,” American Economic Review, 97 (2007), 244–249. Altig, David, Lawrence J. Christiano, Martin Eichenbaum, and Jesper Linde, “Firm-Specific Capital, Nominal Rigidities and the Business Cycle,” Federal Reserve Bank of Cleveland Working Paper No. 04-16, 2004. Alvarez, Fernando, and Andrew Atkeson, “Money and Exchange Rates in the Grossman–Weiss–Rotemberg Model,” Journal of Monetary Economics, 40 (1997), 619–640. Alvarez, Fernando, Andrew Atkeson, and Patrick J. Kehoe, “Money, Interest Rates, and Exchange Rates with Endogenously Segmented Markets,” Journal of Political Economy, 110 (2002), 73–112. ——, “Time-Varying Risk, Interest Rates, and Exchange Rates in General Equilibrium,” Federal Reserve Bank of Minneapolis Research Department Staff Report No. 371, 2007. Alvarez, Fernando, Robert E. Lucas, Jr., and Warren E. Weber, “Interest Rates and Inflation,” American Economic Review, 91 (2001), 219–225. Barro, Robert J., “Integral Constraints and Aggregation in an Inventory Model of Money Demand,” Journal of Finance, 31 (1976), 77–88. Baumol, William J., “The Transactions Demand for Cash: An Inventory Theoretic Approach,” Quarterly Journal of Economics, 66 (1952), 545–556. Blanchard, Olivier Jean, and Charles M. Kahn, “The Solution of Linear Difference Models under Rational Expectations,” Econometrica, 48 (1980), 1305–1311. Calvo, Guillermo A., “Staggered Prices in a Utility-Maximizing Framework,” Journal of Monetary Economics, 12 (1983), 383–398. Canzoneri, Matthew B., Robert E. Cumby, and Behzad T. Diba, “Euler Equations and Money Market Interest Rates: A Challenge for Monetary Policy Models,” Journal of Monetary Economics, 54 (2007), 1863–1881. Caplin, Andrew, and John Leahy, “State-Dependent Pricing and the Dynamics of Money and Output,” Quarterly Journal of Economics, 106 (1991), 683–708. Chatterjee, Satyajit, and Dean Corbae, “Endogenous Market Participation and the General Equilibrium Value of Money,” Journal of Political Economy, 100 (1992), 615–646. Chiu, Jonathan, “Endogenously Segmented Asset Market in an InventoryTheoretic Model of Money Demand,” Bank of Canada Working Paper No. 2007-46, 2007. Christiano, Lawrence, Martin Eichenbaum, and Charles Evans, “Monetary Policy Shocks: What Have We Learned and to What End?” in Handbook of Macroeconomics, Michael Woodford and John Taylor, eds. (Amsterdam: North-Holland, 1999). ——, “Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy,” Journal of Political Economy, 113 (2005), 1–45. Clark, Timothy, Astrid Dick, Beverly Hirtle, Kevin J. Stiroh, and Robard Williams, “The Role of Retail Banking in the U.S. Banking Industry: Risk, Return, and Industry Structure,” Federal Reserve Bank of New York Economic Policy Review, 13 (2007), 39–56. Cochrane, John H., “Shocks,” Carnegie-Rochester Conference Series on Public Policy, 41 (1994), 295–364.

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Dotsey, Michael, Robert G. King, and Alexander L. Wolman, “State-Dependent Pricing and the General Equilibrium Dynamics of Money and Output,” Quarterly Journal of Economics, 114 (1999), 655–690. Duffie, Darrell, and Tong-Sheng Sun, “Transactions Costs and Portfolio Choice in a Discrete-Continuous-Time Setting,” Journal of Economic Dynamics and Control, 14 (1990), 35–51. Edmond, Chris, “Sticky Prices versus Sticky Demand,” University of Melbourne, Working Paper, 2003. Federal Reserve Board, Flow of Funds Accounts of the United States (Washington, DC: Federal Reserve Board, 2007). Fischer, Stanley, “Long-Term Contracts, Rational Expectations, and the Optimum Money Supply Rule,” Journal of Political Economy, 85 (1977), 191–205. Golosov, Mikhail, and Robert E. Lucas, Jr., “Menu Costs and Phillips Curves,” Journal of Political Economy, 115 (2007), 171–199. Grossman, Sanford J., and Laurence Weiss, “A Transactions-Based Model of the Monetary Transmission Mechanism,” American Economic Review, 73 (1983), 871–880. Investment Company Institute, Equity Ownership in America (Washington, DC: Investment Company Institute, 2002). Jovanovic, Boyan, “Inflation and Welfare in the Steady State,” Journal of Political Economy, 90 (1982), 561–577. Khan, Aubhik, and Julia K. Thomas, “Inflation and Interest Rates with Endogenous Market Segmentation,” Federal Reserve Bank of Philadelphia Working Paper 07-1, 2007. King, Robert G., and Julia K. Thomas, “Breaking the New Keynesian Dichotomy: Asset Market Segmentation and the Monetary Transmission Mechanism,” Ohio State University, Working Paper, 2007. Klein, Paul, “Using the Generalized Schur Form to Solve a Multivariate Linear Rational Expectations Model,” Journal of Economic Dynamics and Control, 24 (2000), 1405–1423. Leeper, Eric M., Christopher A. Sims, and Tao Zha, “What Does Monetary Policy Do?” Brookings Papers on Economic Activity, 2 (1996), 1–78. Lucas, Robert E. Jr., “Asset Prices in an Exchange Economy,” Econometrica, 46 (1978), 1429–1445. Mankiw, N. Gregory, “The Inexorable and Mysterious Tradeoff between Inflation and Unemployment,” Economic Journal, 111 (2001), C45–C61. Mankiw, N. Gregory, and Ricardo Reis, “Sticky Information versus Sticky Prices: A Proposal to Replace the New Keynesian Phillips Curve,” Quarterly Journal of Economics, 117 (2002), 1295–1328. Midrigan, Virgiliu, “Menu Costs, Multi-Product Firms, and Aggregate Fluctuations,” Federal Reserve Bank of Minneapolis, Working Paper, 2006. Ravn, Morten O., and Harald Uhlig, “On Adjusting the Hodrick–Prescott Filter for the Frequency of Observations,” Review of Economics and Statistics, 84 (2002), 371–380. Romer, David, “A Simple General Equilibrium Version of the Baumol–Tobin Model,” Quarterly Journal of Economics, 101 (1986), 663–686. Rotemberg, Julio J., “Monopolistic Price Adjustment and Aggregate Output,” Review of Economic Studies, 49 (1982), 517–531. ——, “A Monetary Equilibrium Model with Transactions Costs,” Journal of Political Economy, 92 (1984), 40–58. Silva, Andr´e C., “Prices and Money after Interest Rate Shocks with Endogenous Market Segmentation,” Universidade Nova de Lisb˜oa, Working Paper, 2008. Sims, Christopher A., “Stickiness,” Carnegie–Rochester Series on Public Policy, 49 (1998), 317–356. Taylor, John B., “Aggregate Dynamics and Staggered Contracts,” Journal of Political Economy, 88 (1980), 1–23. Tobin, James, “The Interest-Elasticity of the Transactions Demand for Cash,” Review of Economics and Statistics, 38 (1956), 241–247. Uhlig, Harald, “A Toolkit for Analysing Nonlinear Dynamic Stochastic Models Easily,” in Computational Methods for the Study of Dynamic Economies, Ramon Marimon and Andrew Scott, eds. (New York: Oxford University Press, 1999).

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E-ZTAX: TAX SALIENCE AND TAX RATES∗ AMY FINKELSTEIN This paper examines whether the salience of a tax system affects equilibrium tax rates. I analyze how tolls change after toll facilities adopt electronic toll collection (ETC); drivers are substantially less aware of tolls paid electronically. I estimate that, in steady state, tolls are 20 to 40 percent higher than they would have been without ETC. Consistent with a salience-based explanation for this toll increase, I find that under ETC, driving becomes less elastic with respect to the toll and toll setting becomes less sensitive to the electoral calendar. Alternative explanations appear unlikely to be able to explain the findings.

I. INTRODUCTION For every dollar of revenue raised by the U.S. income tax system, taxpayers incur about ten cents in private compliance costs associated with record keeping and tax filing (Slemrod 1996). These compliance costs impose a deadweight burden on society. Yet policies that would reduce these costs are frequently opposed by policy makers and economists who believe that compliance costs play an important role in keeping taxes visible and salient to the electorate, who then serve as an important check on attempts to raise the scale of government activity beyond what an informed citizenry would want. For example, Milton Friedman has publicly lamented his inadvertent contribution to the growth of government by encouraging the introduction of the visibility-reducing Federal income tax withholding system during the Second World War (Friedman and Friedman 1998, p. 123). More recently, in 2005, the President’s Advisory Panel on Federal Tax Reform failed to reach consensus on whether to replace part of the existing income tax system with a value-added tax (VAT), in part because of concerns about how ∗ I am grateful to Daron Acemoglu, Gene Amromin, Pol Antras, ` David Autor, Raj Chetty, Peter Diamond, Liran Einav, Hanming Fang, Naomi Feldman, Edward Glaeser, Mike Golosov, Austan Goolsbee, Jerry Hausman, Larry Katz, Erzo Luttmer, Brigitte Madrian, Sean Nicholson, Ben Olken, Jim Poterba, Nancy Rose, Stephen Ryan, Monica Singhal, Heidi Williams, Clifford Winston, two anonymous referees, and seminar participants at Cornell, MIT, Berkeley, Stanford GSB, Yale, the NBER Public Economics Meeting, Harvard, and Stanford for helpful comments; to James Wang and especially Julia Galef for outstanding research assistance; to Tatyana Deryugina, Julia Galef, Stephanie Hurder, and Erin Strumpf for help in conducting the survey of toll awareness; and to the innumerable employees of toll operating authorities around the country who generously took the time to provide data and to answer my many questions.

C 2009 by the President and Fellows of Harvard College and the Massachusetts Institute of

Technology. The Quarterly Journal of Economics, August 2009

969

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the lower visibility of a VAT would affect the size of government. As the Advisory Panel noted in its report: [Some] Panel Members were unwilling to support the [VAT] proposal given the lack of conclusive empirical evidence on the impact of a VAT on the growth of government. Others were more confident that voters could be relied on to understand the amount of tax being paid through a VAT, in part because the proposal studied by the Panel would require the VAT to be separately stated on each sales receipt provided to consumers. These members of the Panel envisioned that voters would appropriately control growth in the size of the federal government through the electoral process. (The President’s Advisory Panel on Federal Tax Reform 2005, pp. 203–204)

The idea that a less visible tax system may fuel the growth of government can be traced back at least to John Stuart Mill’s 1848 Principles of Political Economy. It has its modern roots in the public choice tradition of “fiscal illusion.” In a series of influential books and articles, James Buchanan and co-authors have argued that citizens systematically underestimate the tax price of public sector activities, and that government in turn exploits this misperception to reach a size that is larger than an informed citizenry would want. The extent of the tax misperception—and thus the size of government—is in turn affected by the choice of tax instruments, with more complicated and less visible taxes exacerbating the extent of fiscal illusion and thereby increasing the size of the government (e.g., Buchanan [1967]; Buchanan and Wagner [1977]; Brennan and Buchanan [1980]). Empirical evidence of the impact of tax salience on tax rates, however, has proved extremely elusive. Most of the evidence comes from cross-sectional studies of the relationship between the size of government and the visibility of the tax system, where the direction of causality is far from clear (Oates 1988; Dollery and Worthington 1996). Moreover, as I discuss in more detail below, the sign of any effect of tax salience on tax rates is theoretically ambiguous. The link between tax salience and tax rates is therefore an open empirical question. In this paper, I examine the relationship between tax salience and tax rates empirically by studying the impact of the adoption of electronic toll collection (ETC) on toll rates. Electronic toll collection systems—such as the eponymous E-ZPass in the northeastern United States, I-Pass in Illinois, or Fast-Trak in California—allow automatic deduction of the toll as the car drives through a toll plaza. Because the driver need no longer actively count out and hand over cash for the toll, the toll rate may well be less salient

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to the driver when paying electronically than when paying cash. Indeed, I present survey evidence that indicates a strikingly lower awareness of the amount paid in tolls by those who pay electronically relative to those who pay using cash. This discrepancy in toll awareness exists even among regular commuters on a toll facility. As a result, toll facilities’ adoption of ETC—and the resultant switch by many drivers to paying electronically—provides a setting in which to examine the impact of tax salience on tax rates. Different toll facilities in the United States have adopted ETC at different points in time over the last several decades, and some have not yet adopted it. To study the impact of ETC, I examine the within toll-facility changes in toll rates associated with the adoption and diffusion of ETC. To do so, I collected a new data set on the history of toll rates and ETC installation for 123 toll facilities in the United States. Where they were available, I also collected annual facility-level data on toll traffic, toll revenue, and the share of each that is paid by electronic toll collection. I find robust evidence that toll rates increase after the adoption of electronic toll collection. My estimates suggest that when the proportion of tolls paid using ETC has diffused to its steady state level of about 60 percent, toll rates are 20 to 40 percent higher than they would have been under a fully manual toll collection system. I also present evidence of two potential mechanisms by which reduced salience may contribute to increased toll rates. First, I find that the elasticity of driving with respect to the toll declines (in absolute value) with the adoption of electronic toll collection, suggesting that ETC may raise the optimal level of the toll. Second, I show that under ETC, toll-setting behavior becomes less sensitive to the local election calendar, suggesting that ETC may reduce the political costs of raising tolls. The rest of the paper proceeds as follows. Section II provides a conceptual framework for how tax salience may affect tax rates and the factors that may affect the (ambiguous) sign of this relationship. Section III presents evidence that tolls are less salient when paid by ETC than by cash. Section IV describes the data on toll rates and driving. Section V estimates the impact of ETC on the elasticity of driving with respect to the toll. Section VI estimates the impact of ETC on toll rates. Section VII considers non-salience-based explanations for these empirical findings. The last section concludes.

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II. EFFECTS OF TAX SALIENCE ON CONSUMERS AND GOVERNMENT: CONCEPTUAL FRAMEWORK In a fully salient tax system, individuals are aware of actual taxes as they make economic and political decisions. In a less salient tax system, individuals are not aware of the actual tax (τ ), but instead have a perception of the tax, which I denote by τ˜ . Recent empirical evidence is consistent with individuals misperceiving taxes (Liebman and Zeckhauser 2004; Feldman and Katascak 2005; Chetty, Kroft, and Looney forthcoming) and with the salience of the tax affecting the extent of this misperception (Chetty, Kroft, and Looney forthcoming). This paper focuses on the response of tax rates to tax salience. However, because an input into this response is how consumers’ economic behavior is affected by tax salience, I begin—in both the conceptual framework and the subsequent empirical work—by analyzing the consumers’ response; I then turn to the government’s response. I denote by θ ≥ 0 the (lack of) salience of the tax system. A higher θ corresponds to a less salient tax system; θ = 0 corresponds to a fully salient system. In the empirical application I will examine the move from manual (i.e., cash) toll collection to electronic toll collection (ETC) and interpret this as a move to a less salient tax system (i.e., an increase in θ ); I present survey evidence in Section III that is consistent with the assumption that ETC reduces the salience of tolls. There are two types of tax salience that may affect tax setting: tax salience at the time of the consumption decision for the taxed good, and tax salience at the time of voting. These need not be the same. To capture this, I denote the perceived tax by τ˜ j , where j = {c, v} indicates perceived taxes at the time of consumption and of voting, respectively. For simplicity I assume the perceived tax is a linear function of the actual tax, (1)

τ˜ j (θ ) ≡ δ0 j (θ ) + δ1 j (θ )τ,

and normalize a fully salient system as one in which the perceived and actual tax are the same (i.e., δ0 j (0) = 0 and δ1 j (0) = 1). I assume that δ1 j (θ ) > 0 (i.e., the perceived tax is increasing in the actual tax). I also assume that in a less salient tax system, the link between the perceived and the actual tax is weaker (i.e., δ1 j (θ ) < 0). The effect of the tax salience on the perceived toll level

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is, however, a priori ambiguous; in other words, δ0 j (θ ) can be either sign. For simplicity, I consider only cases of positive taxation (τ > 0), and further assume that τ˜ j > 0. II.A. Response of Consumer Economic Behavior to Tax Salience The individual chooses consumption of the taxed good based on the perceived tax at the time of the consumption decision, τ˜C (θ ). To simplify the analysis, I assume the individual maximizes a utility function that is quasi-linear in the taxed good and exhibits constant elasticity of demand.1 The individual thus solves (2)

( γ1 +1)

max γ0 x1 1 x1

+ x2 subject to x2 + ( p + τ˜C (θ ))x1 ≤ m,

where x1 denotes the taxed good (with producer price p), x2 denotes all other goods (whose price has been normalized to 1), and m is consumer income. I denote by η(τ˜C ) ≡ γ1 the (constant) elasticity of demand for x1 , which I assume is negative. Note that η(τ˜C ) is the elasticity of demand with respect to the perceived price p + τ˜C (θ ); I denote by η(τ ) the elasticity of demand with respect to the actual price p + τ . To see how consumer responsiveness to the tax changes with the salience of the tax, I will estimate empirically how the elasticity of demand with respect to the actual price (η(τ )) varies with the tax salience (θ ). The sign of this relationship (i.e., the sign of ∂η(τ )/∂θ ) is ambiguous. To see this, note that the relationship between η(τ ) (which I will estimate empirically) and η(τ˜C ) (which I have assumed is constant) can be derived as follows: η(τ ) ≡ (3)

∂( p + τ˜C ) ( p + τ ) p + τ˜C ∂ x1 ( p + τ ) ∂ x1 = ∂( p + τ ) x1 ∂( p + τ˜C ) ∂( p + τ ) x1 p + τ˜C p + τ ∂( p + τ˜C ) . = η(τ˜C ) p + τ˜C ∂( p + τ )

Under the assumption of fixed producer prices (i.e., p does not vary with either τ or θ ), the relationship between the perceived tax and actual tax in equation (1) implies that (4)

∂( p + τ˜ ) ∂ τ˜ = = δ1c (θ ). ∂( p + τ ) δτ

1. The assumption of quasi-linear utility seems a reasonable one when the taxed good is a small part of the overall consumer’s budget (such as the toll case I consider). It is not, however, an innocuous assumption for the political response to tax salience; I discuss this in more detail in Section II.B.

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Using (4), we can simplify the relationship between η(τ ) and η(τ˜C ) in (3) to p+τ δ1C (θ ). (5) η(τ ) = η(τ˜C ) p + τ˜C Differentiating both sides of (5) with respect to salience (θ ) gives ∂η(τ ) = η(τ˜C )( p + τ ) ∂θ − ⎛ (6)

⎞

⎜ −1 ⎟ 1 ×⎜ δ1C (θ )τ δ1C (θ ) + δ1C (θ )⎟ . ⎝ ( p + τ˜C )2 δ0C (θ ) + ( p + τ˜C ) ⎠ − + ? −

+

Equation (6) shows that the sign of the impact of tax salience on the elasticity of demand (i.e., the sign of ∂η(τ )/∂θ) is ambiguous, because the impact of salience on the level of the perceived tax (θ ) + δ1C (θ )τ )) is of ambiguous sign.2 In the em(i.e., ∂ τ˜C /∂θ ≡ (δ0C pirical work I find evidence that consumption behavior becomes less elastic as salience decreases (i.e., ∂η(τ )/∂θ > 0). Equation (6) indicates that a sufficient (although not necessary) condition for (θ ) + δ1C (θ )τ > 0 (i.e., the perceived tax is ∂η(τ )/∂θ > 0 is that δ0C increasing as salience decreases). In Section III I present survey evidence that is consistent with this condition, suggesting that these empirical findings are internally consistent. To estimate ∂η(τ )/∂θ empirically, I multiply (5) through by ∂ log( p + τ ) to obtain p+τ δ1C (θ )∂ log( p + τ ). (7) ∂ log x1 = η(τ˜C ) p + τ˜C Taking a linear approximation to (7) around θ = 0 and explicitly separating out the main effects from the interaction effect of interest, I estimate (8)

log(x1 ) = β1 log( p + τ ) + β2 θ + β3 θ log( p + τ ) + ε.

The parameter β1 provides an estimate of the estimated elasticity of demand in a fully salient system (i.e., θ = 0), in which case 2. The other components of (6) are signed by the assumptions discussed earlier in this section.

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η(τ˜C ) = η(τ ) = β1 . The parameter of interest is β3 ; it indicates how the elasticity changes with salience. II.B. Political Response to Tax Salience The political response of tax rates to tax salience may depend not only on how the consumer’s behavioral responsiveness to tax changes with salience (i.e., ∂η(τ )/∂θ) but also on how the political costs of taxes change with tax salience. Section II.A showed that the sign of the effect of tax salience on the consumer’s behavioral responsiveness is ambiguous. Moreover, any effect of tax salience on political costs need not be the same sign as any effect of tax salience on consumer behavioral responsiveness, because salience at the time of consumption and salience at the time of voting may be different; this creates further ambiguity in the sign of the relationship between tax salience and tax rates. This ambiguity motivates the empirical work that is the focus of this paper. To gain some intuition into the determinants of the sign of the relationship between tax salience and tax rates, I consider a government that sets the tax to maximize a weighted sum of some economic objective and the (negative of) any political costs of the tax. For concreteness, I assume the economic objective of the tax is to raise revenue. I discuss other possible economic objectives—and how these affect the implications of tax salience—in Section II.D. The government chooses τ each year to maximize (9)

max λτ Q( p + τ˜C ) − (1 − λ) f (E) C(τ˜v ), τ

where 0 ≤ λ ≤ 1 represents the weight the government places on the economic objective of the tax (i.e., raising revenue) relative to the political cost of the tax, C denotes the political cost of the tax, and E is an indicator variable for whether or not it is an election year. I assume that f (E) > 0 and f (E) > 0; in other words, the political costs of taxes are exogenously higher in election years, so that we expect a “political business cycle” in taxes (Nordhaus 1975); in the empirical work, I provide evidence of a political business cycle in toll setting. The government’s optimization problem yields the first-order condition for the tax rate (10)

τ∗ =

−Q(τ˜C ) (1 − λ) f (E) C (τ˜V ) + , Q (τ˜C ) λQ (τ˜C )

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where to simplify notation I have defined C ≡ (∂C/∂ τ˜ ) (∂ τ˜ /∂τ ) and Q ≡ (∂ Q/∂ τ˜ ) (∂ τ˜ /∂τ ). To ensure an interior solution to the optimal tax, I assume that C > 0 (i.e., political costs are rising in the actual tax) and Q < 0 (i.e., demand is falling in the actual tax). Note that both consumption salience and voting salience affect the choice of tax rate: the amount of revenue raised depends on the perceived tax at the time of the consumption decision (i.e., τ˜C ), and the political cost of the tax depends on the perceived tax at the time of voting (i.e., τ˜v ). Differentiation with respect to θ of the first-order condition for the government’s optimal tax level in (10) indicates that the sign of any effect of tax salience on the choice of tax rate is a priori ambiguous: ⎛ ⎞ ⎛ ∂C Q ⎜ ∂ Q ⎞⎟ ⎜∂ − Q C ⎟ − ∗ ⎜ (1 − λ) f (E) ⎜ ∂θ ∂τ Q ⎟⎟ ∂θ =⎜ + (11) ⎝ ⎠⎟ ⎜ ⎟. 2 ∂θ λ (Q ) ⎜ ∂θ ⎟ ⎝ ⎠ + ? ?

Although the sign of (11) is theoretically ambiguous, there are intuitive findings concerning how the relationship between tax salience and tax rates is likely affected by the effect of salience on the consumer’s behavioral responsiveness to taxes, and by the effect of salience on the political costs of taxes. To see this, consider first the simplest case in which λ = 1, so that the government only maximizes revenue. In that case, the politically optimal tax in equation (10) reduces to the standard inverse elasticity optimal tax equation τ∗ 1 , = p + τ∗ η(τ )

(12)

and thus (under the assumption of fixed producer prices) (13)

sign of

1 ∂η(τ˜C ) ∂τ ∗ = sign of . ∂θ η(τ )2 ∂θ +

?

Equation (13) indicates that, when the government sets taxes to maximize revenue, the sign of how taxes vary with salience is the sign of how the elasticity of demand with respect to the tax varies with salience (which as we saw in (6) can be of either sign). Intuitively, if a decline in salience lowers the behavioral response

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to the tax (i.e., ∂η(τ )/∂θ > 0), then the tax rate set by the government will be rising as salience declines. Note that the assumption of quasi-linear utility is important for this result, as it removes any distortionary effect of reduced salience on consumption of the taxed good that arises from the budgetary consequences of the misperceived tax. In the more general case, where such distortionary effects will exist, Chetty, Kroft, and Looney (forthcoming) show that even if reduced salience reduces the behavioral response to the tax, this is not sufficient for the optimal tax to increase; this is likely to be particularly important for taxes that are a large share of the individual’s budget, such as income taxes. Moreover, if the government puts some weight on the political costs of taxes (i.e., λ < 1), this introduces another source of indeterminacy in the sign of the relationship between tax salience and tax rates. However, the model suggests that we can learn more about the likely sign of ∂τ ∗ /δθ in (11) by examining how any political business cycle in tax setting changes as tax salience declines. To see this, note that ⎛ ⎞ ∂C Q − ∂ Q C 2 ∗ 1 − λ f (E) ⎜ ∂θ ∂ τ ⎟ ∂θ = (14) ⎝ ⎠ ∂θ ∂ E λ (Q )2 + ?

and observe that the first term in parentheses is positive by assumption, and that the second term in parentheses (whose sign is unknown) also appears in (11). Thus if ∂ 2 τ /∂θ ∂ E > 0, this implies that the second term in parentheses in (14) is positive, so that the entire second term in (11) is positive. In other words, if the political business cycle attenuates as salience declines (i.e., ∂ 2 τ /∂θ ∂ E > 0, for which I find evidence in the empirical work below), this makes it more likely that a decline in tax salience raises taxes (i.e., ∂τ ∗ /δθ > 0). To investigate the relationship between tax salience and tax rates empirically, I note that the first-order condition for the tax rate in (10) indicates that the tax rate will depend on tax salience (θ ), whether it is an election year (i.e., E = 1 or E = 0), and the interaction of these two effects. Because of the serial correlation properties of taxes in my empirical application (which I discuss in more detail below), I estimate the relationship between taxes and salience in first differences, estimating that (15)

τ = β1 θ + β2 E + β3 E(θ ) + μ.

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Estimation of (15) allows a comparison of the effect of tax salience on tax rates in nonelection years (i.e., β1 ) and in election years (i.e., β3 ). II.C. Identification An examination of the two main estimating equations— equation (8), which comes from the driver optimization problem and reveals how behavioral responsiveness to the tax changes with salience, and equation (15), which comes from the political optimization problem and reveals how the tax varies with salience—highlights two important identification problems. First, taxes are taken as exogenous to demand in the demand estimation equation (8), but are determined as the endogenous result of the political optimization problem (see (10)). Identification of the demand equation requires that the error term ε in the demand equation (8) be uncorrelated with the error term μ in the taxsetting equation (15); in other words, identification requires that changes in demand do not contemporaneously affect changes in taxes. For example, if demand follows a random walk, then as long as the government tax-setting process takes at least one year to respond to demand, current changes in taxes will be uncorrelated with current changes in demand and the demand equation (8) will be identified.3 This identifying assumption seems reasonable for a (bureaucratic) government that may not be able to make and implement decisions quickly. In the empirical application, I will show that, in practice, taxes are changed only about once a decade, which is consistent with the assumption of a lagged response. Furthermore, any changes in taxes that are driven by changes in any of the nondemand factors that (10) indicates affect tax rates—that is, the sensitivity of political costs to the tax rate (C ), the electoral calendar (E), or the relative weight (λ) that the government places on the political costs of taxes—do not pose a problem for identification (as long as changes in these factors are themselves exogenous to changes in current demand). The second identification problem is that I allow the tax (τ ) to be chosen endogenously by the political optimization problem in (9), but assume that the salience of the tax system (θ ) is 3. In my empirical application I find that changes in (residual) demand have an AR1 coefficient of 0.045, suggesting that demand is (close to) a random walk. I also explore robustness of demand estimation to alternative specifications with weaker identifying assumptions (see Section V).

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exogenously determined. If the government endogenously chooses θ (e.g., on the basis of any of the factors that determine τ ), the taxsetting estimating equation (15) is not identified. The validity of the assumption that the choice of tax salience is exogenous with respect to the choice of tax rate is ultimately an empirical question, and one that I explore in depth in Section VI.A. II.D. Other Government Objective Functions and Normative Implications For concreteness, in Section II.B I assumed the government’s objective function in choosing the tax rate was a weighted average of the revenue raised by the tax (its economic objective) and the (negative of) the political costs of the tax (its political objective). Of course, the government may well have other economic objectives, such as redistributive taxes or Pigouvian corrective taxes; the latter is potentially quite relevant for the toll case that is the subject of the empirical work. As with a revenue-raising tax, the optimal level of these other types of taxes also varies inversely with the behavioral responsiveness to the tax. For example, if the tax is set as an optimal Pigouvian externality correction, the optimal tax will be increasing as the behavioral responsiveness to the tax declines. Therefore the same empirical prediction concerning how the impact of salience on the behavioral responsiveness to the tax likely affects the impact of tax salience on tax rates should apply (qualitatively) to these other economic objectives. In contrast to the positive empirical predictions, the normative implications of any effect of tax salience on tax rates will be quite sensitive to the government’s objective function. One critical issue for the normative implications of tax salience is whether the government operates as a benign social planner or is (partially or fully) maximizing independent objectives (such as keeping politicians in office or increasing the size of government); in the latter case, the government’s response to a decline in salience may be self-serving, but not socially optimal. The evidence I present below that the political business cycle in toll setting attenuates when salience is reduced suggests that part of the impact of tax salience on tax rates comes from reducing the political costs of raising tolls; this suggests that the government’s response to a reduction in tax salience may not be that of a fully benign social planner. Even when the government operates as a fully benign social planner, the normative implications of a decline in salience will also depend on the economic component of the government’s

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objective function. If the economic objective is to raise revenue, then if salience reduces the behavioral responsiveness to the tax, this is likely to be welfare-improving because it allows the government to raise a given amount of revenue at lower distortionary costs. However, if the economic objective of the tax is a Pigouvian externality correction, the normative implications may be quite different. For example, if salience reduces the behavioral responsiveness to the tax, this has no effect on welfare if the tax is set solely as a Pigouvian corrective tax, utility is quasi-linear in the taxed good, and the revenue raised is rebated back to consumers as a lump sum; the government would raise the tax to the (new) higher optimal externality-correction tax and rebate back the resulting (higher) revenue as a lump sum, with no change in aggregate welfare. However, in more general models in which utility is not quasi-linear and/or the government does not rebate back the revenue raised as a lump sum, a lower behavioral responsiveness to the Pigouvian tax due to reduced salience can be welfare-reducing. III. IMPACT OF ETC ON TOLL SALIENCE: SURVEY EVIDENCE The empirical analysis is predicated on the assumption that ETC reduces the salience of the tolls (i.e., increases θ ). I therefore begin by presenting survey evidence consistent with this assumption. Evidence from two separate surveys indicates that individuals are substantially less aware of tolls if they pay them electronically rather than with cash. One survey is an in-person survey that I designed and conducted in May 2007 of 214 individuals who had driven to an antiques show in western Massachusetts on the Massachusetts Turnpike (“MA Survey”). The other is a telephone survey conducted in June and July 2004 of 362 regular users from New Jersey of any of the six bridges or tunnels of the Port Authority of New York and New Jersey that cross the Hudson River (“NYNJ Survey”). More details on the MA Survey can be found in the Online Appendix (Section A); more details on the NYNJ Survey can be found in Holguin-Veras, Kaan, and de Cerrano (2005, especially pp. 116–126 and pp. 383–394). Each survey asked drivers their estimate of the toll paid on their most recent trip on the relevant facility, their method of payment, and a variety of demographic characteristics; information about the exact trip was also collected so that the actual toll paid could be calculated.

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Table I summarizes the results. Both surveys show a strikingly lower awareness of tolls among drivers who paid with ETC than among those who paid with cash. The differences are both economically and statistically significant. In the MA survey, 62% of drivers who paid using ETC responded to the question about their best guess of the toll they paid that day on the Turnpike with “I don’t know” and would not offer a guess without prompting from the surveyor to please “just make your best guess”;4 in contrast, only 2% of drivers who paid with cash had to be prompted to offer a guess. In the NYNJ survey, 38.1% of ETC users reported “do not know” or “refused” when asked how much they paid at the toll in their most recent drive across the Hudson from New Jersey to New York, compared to 20.0% of cash users.5 Moreover, the ETC drivers’ belief that they did not know how much they had paid for the toll was borne out by their subsequent guesses. In the MA Survey, 85% of drivers who paid using ETC estimated the toll they paid incorrectly, compared to only 31% of drivers who paid using cash. In the NYNJ survey, 83% of ETC drivers estimated the toll incorrectly, compared to only 40% of cash drivers. Conditional on making an error, the magnitude of the error was also larger for ETC users; ETC users overestimate tolls by more than cash users.6 These findings of markedly lower knowledge of tolls among people who paid electronically than among those who paid with cash are consistent with the maintained assumption that tolls are less salient under ETC. In other words, the results are consistent with ETC reducing the link between the actual and the perceived toll (i.e., δ1 j (θ ) < 0). These findings are also consistent with other work on “payment decoupling,” which finds that technologies such as credit cards, which decouple the purchase from the payment, reduce awareness of the amount spent and thereby encourage more spending (e.g., Thaler [1999]; Soman [2001]). 4. Indeed, many of the ETC drivers literally responded, “I don’t know, I used EZ-Pass [or Fast Lane].” 5. It is interesting that the discrepancy in toll awareness between ETC and cash drivers is larger in the MA survey. One possible explanation is that the NYNJ Survey asked about the toll paid on a regular commute, whereas the MA Survey asked about the toll paid on a presumably idiosyncratic trip. Differences in the survey method (e.g., telephone vs. in person) may also have an effect on the individual’s willingness to guess. 6. This finding that ETC is associated with overestimation of the toll is consistent with the finding in Section V that ETC is also associated with reduced behavioral responsiveness to the toll. See equation (6) in Section II.A and the discussion that follows it.

0.618 (0.490) 0.851 (0.359) $1.334 (1.850) 68

0.021 (0.142) 0.308 (0.463) $0.162 (0.828) 146

Cash drivers (2)

Covariate adjusted (4) 0.579∗∗∗ (0.060) 0.512∗∗∗ (0.067) $1.01∗∗∗ (0.303)

No covariates (3) 0.597∗∗∗ (0.060) 0.543∗∗∗ (0.058) $1.172∗∗∗ (0.275) 271

0.381 (0.486) 0.826 (0.379) $0.40

ETC drivers (5)

91

0.200 (0.400) 0.395 (0.489) −$0.10

Cash drivers (6)

0.18∗∗∗ (0.05) 0.43∗∗∗ (0.06) $0.50

Difference between ETC and cash drivers (no covariates) (7)

NYNJ survey

Notes. In columns (1), (2), (5), and (6), standard deviations are in parentheses; in columns (3), (4), and (7) robust standard errors are in parentheses and ∗∗∗ , ∗∗ , ∗ denote statistical significance at the 1%, 5%, and 10% levels, respectively. “Error” in the third row is computed as estimated toll − actual toll paid. In the MA Survey an estimate of the toll paid was eventually elicited from all but one of the respondents; however, in the NJNY Survey, an estimate of the toll paid was only elicited for those who did not respond “don’t know” or “refused.” Thus, for the MA Survey, the sample in rows (2) and (3) includes all but one of the respondents in row (1), but for the NYNJ Survey, the sample in rows (2) and (3) includes only those respondents who did not report “don’t know” in row (1). For the NYNJ survey, the cash toll was $6.00, whereas the ETC toll was $5.00 on peak and $4.00 off peak. For the MA survey, the toll depended on the entrance and exit taken. The average toll paid was about $1.15. Less than 10% of drivers in the MA survey sample drove on a portion of the Turnpike in which there are ETC discounts, and the results are not affected by omitting these drivers from the analysis. In column (4), covariates consist of age, age squared, median household income of ZIP code, dealer retail price for the driver’s car (based on information from www.edmunds.com as of October 2007), and indicator variables for sex, whether the driver regularly pays a toll on a commute to work, and highest level of education reached (high school degree or less, college degree, or postcollege degree, where “college degree” includes associates degrees, which were 10% of the college degree sample). Only published summary statistics (as opposed to the underlying microdata) are available for the NYNJ survey, so that the covariate-adjusted difference in means cannot be computed. In addition, the sample sizes by cell for the NYNJ survey had to be approximated based on information in the text on the total sample size (362) and the fraction of drivers that pay by ETC (74.8%). As a result, the standard errors for the NYNJ Survey are also approximated; approximated numbers are shown in italics. I calculated standard deviations for the binary response variables in the NYNJ Survey, but there was not sufficient information available to calculate the standard deviation for the mean error (or the standard error of the difference in mean error).

Fraction who incorrectly estimate toll Mean error, conditional on misreporting N

Fraction who report “don’t know”

ETC drivers (1)

Difference between ETC and cash drivers

MA survey

TABLE I SURVEY EVIDENCE ON DRIVER AWARENESS OF TOLLS, BY PAYMENT METHOD

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Several caveats are in order. First, neither survey is representative of the nationwide population. Nonetheless, it is reassuring that the finding of lower toll awareness among ETC drivers persists in two very different populations, including a population of regular commuters. Second, cross-sectional differences in awareness of tolls between ETC drivers and cash drivers could reflect differences in these drivers besides their payment method. Reassuringly, a comparison of the results in columns (3) and (4) of Table I shows that none of the differences in toll awareness in the MA Survey are sensitive (in either magnitude or statistical significance) to adding controls for demographic characteristics of drivers, including age, sex, education, median household income of ZIP code, and value of their car. Finally, a survey response on toll perception does not necessarily reflect either the perceived toll at the time of consumption (τ˜C ) or the perceived toll at the time of voting (τ˜V ). However, given the large percentage of cash drivers relative to ETC drivers who are spot on in estimating the toll paid correctly, it seems plausible that ETC may reduce one or both of these types of salience. I now turn to direct evidence of the impact of ETC first on consumer behavior and then on toll setting.

IV. DATA AND DESCRIPTIVE STATISTICS This section provides some brief background on the sample construction and variable definitions for the toll facility data; considerably more details on the facilities in the sample and the variable definitions can be found in the Online Appendix (Section B) or in the working paper version of this paper (Finkelstein 2007). IV.A. Sample Construction The target sample was all 183 publicly owned toll facilities in the United States (excluding ferries) that were charging tolls in 1985, which predates the introduction of ETC in the United States. In 1985, toll revenue in states that levied tolls was about 0.8% of state and local tax revenue, roughly the same revenue share as state lotteries (U.S. Census Bureau 1985; U.S. Department of Transportation 1985, 1986; Kearney 2005). Statutory authority for toll setting is usually vested in toll operating authorities. These are typically appointed by state or local governments, which therefore, in practice, retain influence on toll setting.

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1985

1990

1995 ETC start date

2000

2005

FIGURE I Distribution of ETC Start Dates

By contacting each toll authority, I was able to collect data for 123 toll facilities.7 These 123 facilities are run by 49 different operating authorities in 24 different statelike entities; these include 22 states and 2 joint ventures (one between New York and New Jersey and one between New Jersey and Pensylvania). I refer to all 24 hereafter as “states.” On average, the data contain 50 years of toll rates per facility. IV.B. Key Variables ETC Adoption and Diffusion. Figure I shows a histogram of ETC adoption dates, which range from 1987 through 2005, with a median of 1999. By 2005, 87 of the 123 facilities had adopted ETC. Almost all of the variation in whether and when ETC is adopted is between rather than within operating authorities; there is, however, substantial variation across authorities within a state (not shown). On average for a facility with ETC, I observe about six years of ETC. Table II shows that relationship between facility characteristics and ETC adoption. ETC adoption rates are highest in the northeast (78%) and lowest in the west (57%). The high adoption rates in the northeast may reflect greater urbanism (because ETC 7. A toll “facility” is a particular road, bridge, or tunnel; about 60 percent of the responding facilities are bridges or tunnels.

985

E-ZTAX: TAX SALIENCE AND TAX RATES TABLE II WHICH FACILITIES ADOPT ETC?

All By facility type Roads Bridges or tunnels By region of country Northeast Midwest South West

Number of facilities

Probability of adopting ETC by 2005

Average adoption date conditional on adoption

123

.71

1998.2

44 79

.70 .71

1996.4 1999.2

58 10 41 14

.78 .60 .68 .57

1998.7 1996.7 1997 2000.9

may help reduce congestion) as well as higher labor costs (because ETC reduces labor costs of toll collection). ETC is adopted with the same probability on roads as on bridges and tunnels; however, roads that adopt ETC do so about three years earlier on average than bridges or tunnels that adopt ETC. Older facilities are more likely to adopt ETC, and those that do are likely to do so earlier than younger facilities that adopt ETC (not shown). Once a facility adopts ETC, use of the technology diffuses gradually across drivers. I was able to obtain the ETC penetration rate (defined consistently within each facility as either the fraction of toll transactions or the fraction of toll revenue collected by ETC) for about two-thirds of facility-years with ETC. Figure II shows the within-facility ETC diffusion rate. It takes about fourteen years for ETC to reach its steady state penetration rate of 60 percent. Toll Histories. I define the toll as the nominal toll for passenger cars on a full-length trip on a road, or on a round trip on a bridge or tunnel. I collected data on both the “manual” (i.e., cash) toll and any discount offered for the electronic toll; the electronic toll is never more than the cash toll.8 Over half (53 of 87) of facilities with ETC offer a discount at some point. Discounts are presumably offered to encourage use of the technology; indeed, they are more common on facilities that adopt ETC earlier. The discounts may also be rationalized as a Pigouvian subsidy if ETC has positive externalities on congestion reduction. The average discount offered is about 15 percent. 8. High-frequency discounts (i.e., commuter discounts) are not coded. None of the facilities in the sample offer time-of-day varying prices.

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0.7

ETC penetration rate

0.6

0.5

0.4

0.3

0.2

0.1

0 1

2

3

4

5

6

7

8

9 10 11 ETC year

12

13

14

15

16

17

18

19

FIGURE II Within-Facility ETC Diffusion Figure II reports the coefficients on indicator variables for the number of years a facility has had ETC from the following regression: ETC Penetrationit = αi + 19 k=1 βk 1(ETCyear = k), where the αi are facility fixed effects, 1(ETCyear = k) are indicator variables for whether it is the kth year of ETC, and ETC Penetration is defined either as percentage of toll transactions paid by ETC or as percentage of revenue paid by ETC, depending on the facility. The regression is estimated on the sample of facility-years with ETC and data on ETC penetration (N = 467; 84 unique facilities).

The primary toll measure in the analysis is the lower envelope of the manual and electronic tolls (hereafter, “minimum toll”). I also present results for the subsample of facilities that never offer ETC discounts, and for which the minimum and manual toll are therefore always the same. On average, the minimum toll increased by 2.0% per year. This is substantially below the facilityyear-weighted average inflation rate of 4.2%. Toll changes are lumpy; on average only 7.7% of facilities increase their minimum toll and only 1% of facilities decrease it each year. Revenue and Traffic Data. I was able to collect traffic (revenue) data for 76 (45) of the 123 facilities. On average, for a facility with these data, I obtained 34 years of data. V. THE IMPACT OF ETC ON THE ELASTICITY OF DRIVING WITH RESPECT TO THE TOLL CHANGE To examine how ETC affects the elasticity of driving with respect to the tax, I adapt the demand equation (8) to the toll

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987

context as follows: log(traffic)it = γt + β1 log (minimum tollit ) + β2 log (minimum tollit ) ∗ Never ETCi + β3 log (minimum tollit ) ∗ ETC Penetrationit (16)

+ β4 Never ETCi + β5 ETC Penetrationit + εit .

I proxy for demand for the taxed good (i.e., x1 in (8)) with the amount of traffic on facility i in year t (i.e., trafficit ), and for the salience of the tax system (i.e., θ in (8)) with the ETC Penetration rate on facility i in year t (i.e., ETC Penetrationit ). For purposes of practicality, I estimate the demand responsiveness to τ in (16) rather than to p + τ as in (8), because I do not observe the nontax costs ( p) of driving. As long as p does not vary with taxes or with tax salience (i.e., the fixed producer prices assumption discussed in Section II), this modification will affect the magnitude of the estimated elasticities but not their sign. As noted, I use the minimum toll as my measure of τ . Equation (16) examines the relationship between the annual percentage change in a facility’s traffic (log(traffic)it ) and the annual percentage change in its toll (log(minimum toll)it ) and how this relationship changes with the ETC penetration rate. To strengthen the inference, it also allows the elasticity to vary across facilities based on whether the facility ever adopted ETC (Never ETCi is 1 if the facility never adopts ETC and zero otherwise), and it allows for secular changes in demand over time (the γt represent a full set of year fixed effects). The key coefficient of interest is β3 ; this indicates how the elasticity changes at a facility as ETC use diffuses. Finally, εit is a random disturbance term capturing all omitted influences. I allow for an arbitrary variance– covariance matrix within each “state” and give equal weight in the regression to each operating authority. As discussed in Section II.C, identification of (16) is based on the assumption that changes in tolls are not affected by contemporary changes in demand. This is probably a reasonable assumption. Traffic—and presumably underlying demand for driving—changes continuously each year, whereas a facility’s toll is raised on average only every eight to nine years. The infrequency of toll adjustment likely reflects both general lags in price setting by government enterprises and political constraints; for example, I show in Section VI.B that toll increases are significantly lower during state election years. Although tolls may be

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adjusted in part based on past demand shocks (i.e., lagged values of changes in traffic), changes in traffic within a facility show very little serial correlation; a regression of the residuals from (16) on their lags produces a coefficient of only 0.045. Any adjustment of tolls to past changes in demand is therefore unlikely to pose much of a practical problem for the estimation. However, as a robustness check, I also report results in which I limit the sample to the years in which a toll changes or the two years before or after a toll change; I refer to this as the “+2/−2 sample.” The assumption in this more limited sample is that the timing of the toll change is random with respect to short-run traffic changes, although it may reflect longer-run demand changes. I estimate (16) on approximately one-fourth of the facilities in the data. By necessity, the analysis is limited to the approximately 60 percent of facilities for which I obtained traffic data. I further limit the subsample of facilities with traffic data to the approximately 40 percent of them that never offer an ETC discount. This allows me to include the ETC penetration rate directly on the right-hand side, without worrying about omitted variable bias from any potential effect of an ETC discount on both the ETC penetration rate and traffic. An added advantage of looking only at facilities that never offer an ETC discount is that in this sample there is only one toll rate (i.e., the minimum toll and the toll are always the same), which avoids the measurement error that ETC discounts would otherwise introduce in the right-hand-side toll variable once ETC is introduced.9 Table III reports the results. Columns (1) and (2) show the results from regressing log(traffic)it on log(minimum toll)it and year fixed effects. Column (1) shows the results for the full sample of facilities with traffic data, including those that offer ETC discounts. The coefficient on log(minimum toll)it of −0.049 (standard error 0.015) indicates that a 10% increase in tolls is associated with a statistically significant but economically small 0.5% reduction in traffic. Column (2) shows that the result is quite similar for the sample of facilities that never offer ETC discounts; the coefficient on log(minimum toll)it is −0.058 (standard error 9. I show below that the estimated impact of ETC on toll rates is robust to limiting the sample to facilities that never offer discounts. When I limit to those for whom I have traffic data, the effect is very similar in magnitude to the estimates in the full sample, although no longer statistically significant at conventional levels (not shown).

989

E-ZTAX: TAX SALIENCE AND TAX RATES TABLE III THE ELASTICITY OF TRAFFIC WITH RESPECT TO TOLLS (1) log min. tollit

(2)

−0.049 −0.058 (0.015) (0.018) [.004] [.008]

log min. tollit * ETC penetrationit

(3)

(4)

(5)

(6)

−0.061 (0.019) [.009] 0.134 (0.038) [.005]

−0.057 (0.017) [.006]

−0.062 (0.039) [.145] 0.141 (0.076) [.091]

−0.060 (0.037) [.135]

log min. tollit * ETC yearit log min. tollit * never ETCi Mean dep. var. # of states # op. authorities # of facilities N Sample restriction(s)

0.049 21 32 76 2,200

−0.071 (0.136) [.611] 0.042 0.043 12 12 16 16 33 33 727 671 No ETC No ETC discounts discounts

0.006 (0.001) [.002] −0.073 (0.131) [.588] 0.042 12 16 33 727 No ETC discounts

−0.009 (0.209) [.966] 0.040 12 16 33 292 No ETC discounts +2/−2 sample

0.006 (0.003) [.062] −0.006 (0.205) [.976] 0.039 12 16 33 305 No ETC discounts +2/−2 sample

Notes. Table reports results from estimating variants of (16) by OLS. The dependent variable is the change in log traffic. In addition to the covariates reported in the table, all regressions include year fixed effects and a main effect for any variables that are interacted with log(min. toll). The bottom row indicates any sample restrictions. “No ETC discounts” limits facilities to those that never offered an ETC discount. “+2/−2 sample” limits sample to facility-years in which there is a toll change or the two years before or after a facility’s toll change. Never ETCi is an indicator variable for whether facility i never has ETC. ETC penetrationit is the share of tolls paid by ETC on facility i in year t; it is zero in years in which the facility did not have ETC. ETC yearit is the number of years the facility has had ETC; it is zero in any year in which the facility does not have ETC, 1 the year the facility adopts ETC, 2 the second year the facility has ETC, and so forth. Each operating authority receives equal weight. Standard errors (in parentheses) are clustered by state. p-values are reported in square brackets.

= 0.018). These results suggest that tolls are set below the profitmaximizing rate, which is consistent with Peltzman’s (1971) observation that there will be a downward bias in the prices set by government-owned enterprises. More generally, it suggests that— as modeled in Section II.B—the government objective function is not pure revenue maximization.10 10. Of course, I am only measuring the short-run response to a small change in tolls; this behavioral response may merely reflect the route chosen on a particular day. Longer-run responses to (possibly larger) toll changes may be larger, reflecting among other things decisions that affect regular commuting patterns.

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Column (3) shows the results from estimating the complete equation (16). The coefficient on log(minimum tollit ) ∗ ETC penetrationit is 0.134 (standard error 0.038); this indicates that a 5-percentage-point increase in the ETC penetration rate (which is the average increase per year of ETC) is associated with a (statistically significant) 0.0067 decline in the elasticity of driving with respect to the toll, or about 10 percent relative to the average estimated elasticity prior to ETC of −0.061. Column (4) shows the results when the ETC Penetration variable in (16) is replaced by the number of years the facility has had ETC (ETC Year); this variable is zero prior to ETC adoption, 1 in the year of adoption, 2 in the second year of ETC, and so forth. The coefficient on log(minimum tollit ) ∗ ETC Yearit is 0.006 (standard error 0.001), indicating a decline in elasticity of 0.006 per year of ETC quite similar to that estimated in column (3).11 The last two columns of Table III repeat the analysis in columns (3) and (4) on the +2/−2 sample. The point estimates on both the elasticity of driving under manual toll collection and the change in the elasticity associated with ETC Year (or ETC Penetration) remain virtually unchanged. The change in the elasticity associated with ETC remains statistically significant, although at the 10% level in the +2/−2 sample (columns (5) and (6)) rather than at the 1% level as in the larger samples (columns (3) and (4)). As noted in Section II.B, for taxes that are small as a portion of income, if a decline in salience reduces the behavioral responsiveness to the toll, this will tend to cause tolls to rise when salience declines. However, the net impact of salience on toll rates is ambiguous; it also depends on how salience affects the political costs of toll setting. I now turn to an examination first of the net effect of ETC on toll rate and then of the effect of ETC on the political costs of tolls. 11. One potential concern in interpreting these results is that the finding of a decline in the (absolute value) of the elasticity of driving with respect to the toll under ETC might spuriously reflect a general time trend in the elasticity of driving with respect to the toll. To investigate this, I reestimated the regressions shown in columns (3) and (4) of Table III with the inclusion of an additional interaction term log(minimum toll)it * yeart on the right-hand side; this allows for a time trend in the elasticity of driving. The inclusion of this interaction term weakened the precision of the estimated decline (in absolute value) of the driving elasticity under ETC, but did not substantively affect the finding. For example, for the specification shown in column (3), the coefficient on log(minimum tollit ) ∗ ETC penetrationit became 0.137 (standard error 0.067). In column (4), the coefficient on log(minimum tollit ) ∗ ETC Yearit became 0.005 (standard error 0.002).

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VI. THE IMPACT OF ETC ON POLITICAL BEHAVIOR VI.A. The Impact of ETC on Toll Rates Baseline Specification. To estimate the impact of ETC on toll rates, I begin with a simplified version of the estimating equation for tax setting (equation (15)) in which I omit any measure of whether it is an election year from the right-hand side. Because the election calendar is set exogenously, this does not introduce any omitted variable bias, and allows me to capture the average impact of ETC on toll rates; I augment the analysis to include electoral effects in Section VI.B. I therefore begin with the estimating equation: (17)

yit = γt + β1 ETCAdoptit + β2 ETCit + μit .

In the baseline specification, the dependent variable is the change in the log of the minimum toll (log(min toll)it ). I estimate the dependent variable in logs rather than in levels (as in equation (15) in Section II.B) in order not to constrain toll rates in different facilities to grow by the same absolute amount each year; this seems undesirable, given the considerable variation in toll rates across facilities.12 The γt s represent year dummies that control for any common secular changes in toll rates across facilities. The key coefficients of interest are those on ETCAdoptit and ETCit , which represent my parameterization of the change in tax salience (θ in (15)). Specifically, ETCAdoptit is an indicator variable for whether facility i adopted ETC in year t. The coefficient on ETCAdoptit thus measures any level shift in the minimum toll associated with the introduction of ETC; this might include, for example, the effect of any ETC discounts. However, because ETC use among drivers diffuses gradually, it is likely that any impact of ETC on toll rates will also phase in gradually. To capture this, I include the indicator variable ETCit for whether facility i has ETC in year t; it is 1 in the year of ETC adoption and in all subsequent 12. In practice, the sign and statistical significance of the impact of ETC on tolls are robust to specifying the dependent variable as the change in the level of the minimum toll rather than the change in the log of the minimum toll; the magnitude of the effect is slightly more than double in this alternative specification (not shown). One potential concern with the log specification is that the dependent variable is censored when a toll is set to 0. Indeed, 15 of the 123 facilities that were charging a toll in 1985 subsequently set the toll to zero. I treat all facilityyears with zero tolls as censored (both in the log and in the level analysis). This likely biases downward any estimated impact of ETC, because I find that ETC is associated with a negative and marginally statistically significant decline in the probability that the toll rate is changed from nonzero to zero (not shown).

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years. The coefficient on ETCit thus measures the average annual growth in a facility’s toll once it has ETC. Thus I parameterize θ with ETCAdoptit and ETCit in the first year of ETC, and I parameterize θ with ETCit in all subsequent years with ETC. Finally, μit is a random disturbance term capturing all omitted influences.13 I estimate (17), allowing for an arbitrary variance–covariance matrix within each state, and give equal weight in the regression to each operating authority. The first column of Table IV shows the results from estimating (17). The coefficient on ETCit is 0.015 (standard error 0.006). This indicates that once a facility has ETC, its toll increases by 1.5 percentage points more per year than it otherwise would have. This effect is both statistically and economically significant. Relative to the average annual 2% increase in tolls, it implies that after installation of ETC, the facility’s toll rate rises by 75% more per year than it did prior to ETC.14 The toll change in the first year of ETC is given by the sum of the coefficients on ETCAdoptit and ETCit . These indicate that there is a (statistically insignificant) 3.6% decline in tolls the year that ETC is adopted. The results in the next two columns suggest that this decline in the year of ETC adoption is due to ETC discounts. Column (2) shows the results when the dependent variable is the change in the log manual toll; column (3) shows the results when the sample is limited to the approximately 60 percent of facilities that never offered an ETC discount (half of which never adopted ETC), for which the manual and minimum toll are always the same. In these alternative specifications, the sum of the coefficients on ETCAdoptit and ETCit is either positive and insignificant (column (2)) or negative and now both economically and statistically insignificant (column (3)). The fact that the growth in tolls under ETC persists in the “no discount” sample (column (3))—the coefficient on ETCit is statistically significant and slightly larger in magnitude than in the full sample in column (1)—indicates that the estimated growth 13. I estimate (17) in first differences rather than in levels with facility fixed effects because the residuals are much less highly serially correlated in first differences (AR1 coefficient of −0.045) than in the fixed effects version (AR1 coefficient of 0.92), making the first-differenced specification the preferred specification (Wooldridge 2002, pp. 274–281). 14. One might prefer to specify the percentage increase in the toll associated with ETC relative to the average annual growth rate of tolls prior to ETC; this is 1.9%. It is quite similar to the sample average (despite an average annual growth rate of tolls under ETC of 2.8%) because the vast majority of facility-years in the approximately fifty-year toll histories I collected on each facility do not have ETC.

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TABLE IV IMPACT OF ETC ON TOLL RATES log log min. toll manual toll (1) (2) ETCit

0.015 (0.006) [.018]

0.020 (0.006) [.004]

ETC penetrationit −0.051 (0.035) [.158] Mean dep. var. 0.020 # of states 24 # op. authorities 49 # facilities 123 N 5,079 Estimation OLS Sample restriction ETCAdoptit

0.016 (0.032) [.622] 0.022 24 49 123 5,079 OLS

log toll (3)

log toll (4)

log log min. toll min. toll (5) (6)

0.024 (0.012) [.061] 0.623 (0.285) [.044] −0.033 −0.051 (0.019) [0.035] [.097] [.166] 0.017 0.017 17 17 31 31 70 70 2,875 2,751 OLS OLS No ETC No ETC discount discount

0.557 0.501 (0.262) (0.261) [.045] [.067] −0.105 −0.097 (0.109) (0.108) [.348] [.380] 0.020 0.020 24 24 49 49 123 123 4,815 4,815 IV IV

Notes. Table reports results of estimating (17) (columns (1)–(3)) and (19) (columns (4)–(6)). Column headings define the dependent variable; the bottom two rows provide additional information on the estimation technique and sample restriction. ETCAdoptit is an indicator variable for whether facility i adopted ETC in year t. ETCit is an indicator variable for whether the facility has ETC; it is 1 in the year that ETC is adopted and in all subsequent years. ETC penetrationit measures the change in the proportion of tolls on the facility paid by ETC; it is zero if the facility does not have ETC. In column (5), the instrument for ETC penetrationit is ETCit . In column (6), the instrument for ETC penetrationit is a cubic polynomial in the number of years the facility has had ETC. In addition to the covariates shown in the table, all regressions include year fixed effects. Each operating authority receives equal weight. Standard errors (in parentheses) are clustered by state. p-values are reported in square brackets. “No ETC discounts” limits facilities to those that never offered an ETC discount. Declines in sample size in column (4) (compared to column (3)) and in column (5) or (6) (compared to column (1)) reflect missing data on ETC penetration rates (see Section IV).

in tolls after ETC is installed does not merely reflect a recouping of first-year losses from the ETC discount. For facilities that offer ETC discounts, there does not appear to be any systematic change in the discount over time after ETC adoption (not shown). This suggests that in practice increases in the minimum toll reflect a shift of the entire toll schedule, which is consistent with the finding that the manual toll also increases under ETC (column (2)).15 15. Although it might at first appear puzzling that the manual (i.e., cash) toll—which has become no less salient—also increases under ETC, this is easily understood by the necessary linkage between cash and electronic toll rates; were the electronic rate to increase while the cash rate did not, this would presumably discourage use of ETC. The preservation of the ETC discounts once ETC is installed

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The Pattern of ETC Diffusion and Toll Increases. The preceding analysis constrains the effect of ETC to be the same across facilities and over time. However, if ETC increases tolls by reducing their salience, we would expect the effect to be increasing in the ETC penetration rate, whose diffusion rate is not constant over time (see Figure II) or across facilities (not shown). As a stronger test of the salience hypothesis, therefore, I examine how the time pattern of toll changes after ETC adoption compares to the time pattern of ETC diffusion. Specifically, I compare the coefficients from estimating

(18a)

log(min toll)it = γt +

k=9

βk1 ETCYear(k,k+1) + εit

k=−9

and (18b) ETC Penetrationit = γt +

k=9

βk1 ETCYear(k,k+1) + εit ,

k=1

where ETC Penetrationit is the percentage point change in the ETC penetration rate for facility i in year t. The key outcome of interest is a comparison of the time pattern of the coefficients on the indicator variables 1(ETCYear(k,k+1) ) across the two equations. These are indicator variables for whether it is k or k + 1 years since ETC was adopted on the facility. For example, 1(ETCYear(1,2) ) is an indicator variable for whether ETC was adopted this year or last year (i.e., ETC Year is 1 or 2). In (18a), all of the indicator variables represent a two-year interval, except for the first (respectively, last) indicator variable, which is a “catch-all” variable for whether it is 9 or more years before (respectively, after) ETC adoption; the omitted category is the two years prior to adoption (i.e., ETC Year of −1 or −2). In (18b) I include only the post-ETC dummies that are in (18a). Figure IIIA shows the result. The solid black line shows the pattern of the log toll with respect to ETC Year implied by the estimates from (18a) and the dark dashed line shows the corresponding time pattern of ETC diffusion implied by the estimates

likely reflects continued attempts to induce more drivers to switch to ETC; the maximum ETC penetration rate in my sample is only 78%.

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E-ZTAX: TAX SALIENCE AND TAX RATES 0.15

0.55

(A)

ETC penetration rate (right axis)

0.1

0.45

0.05

0.35

0

0.25

–0.05

0.15

Log minimum toll (left axis)

–0.1

0.05

–0.15

–0.05 –8

–6

–4

–2

2

4

6

8

ETC year 0.2

0.55

(B)

0.15

0.45

ETC penetration rate (right axis)

0.1

0.35

0.05 0.25 0

0.15 –0.05

Log minimum toll (left axis)

–0.1

0.05

–0.15

–0.05 –8

–6

–4

–2

2

4

6

8

ETC year

FIGURE III Time Pattern of Toll Changes and ETC Diffusion The solid black line shows the pattern of log minimum toll implied by the estimates from (18a); the light dashed lines show the corresponding 95% confidence interval. The dark dashed line shows the pattern of the ETC penetration rate implied by estimating (18b). ETC year represents the number of years since (or before) ETC adoption. The omitted category (ETC year −2 for (18a) and all years prior to ETC adoption for (18b)) is set to zero. Indicator variables for whether it is nine or more years after ETC adoption are included in the estimating equation but not graphed; in (4a) an indicator variable for whether it is nine or more years before ETC adoption is also included in the regression but not graphed. In Panel B the sample of ETC-adopting facilities is limited to those who adopted in 1998 or earlier. The upper end of the 95% confidence interval for the log minimum toll at eight years is not shown for scale reasons; it is 0.201 (full sample, A) and 0.311 (balanced panel, B). To enhance the readability of the graph, the 95% confidence interval on ETC penetration rate is not shown. For Panel A the upper and lower 95% confidence intervals for ETC penetration rate are as follows: (0.16, 0.378) for ETC year 2, (0.267, 0.484) for ETC year 4, (0.336, 0.565) for ETC year 6, and (0.378, 0.610) for ETC year 8. For Panel B, the analogous confidence intervals are (0.197, 0.283), (0.333, 0.425), (0.389, 0.550), and (0.419, 0.617).

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of (18b).16 The results indicate that, after remaining roughly constant in the pre-ETC period, toll rates decline in the first two years of ETC (reflecting the discounts discussed earlier) and then climb steadily as ETC diffuses across the facility. Of course, the wide confidence intervals on the estimates caution against placing too much weight on the estimated time path. It is nonetheless reassuring that the point estimates suggest that the pattern of toll increases is similar to that of ETC diffusion. A potential concern with this analysis is that the set of facilities that identify the different β ks varies with the ETC year k. It is therefore difficult to distinguish the time path of the effect of ETC on a given facility from potentially heterogeneous effects of ETC across facilities.17 Figure IIIB therefore shows the results from re-estimating (18a) and (18b) when the sample of ETC-adopting facilities is limited to those that adopted ETC in 1998 or earlier. In this balanced panel of facilities, all of the graphed coefficients are identified by a constant set of facilities. The results are quite similar.18 For a more parametric (and higher-powered) analysis of how the time pattern of toll changes after ETC adoption compares with the diffusion of ETC, I estimate a modified version of (17): log(min toll)it = γt + β1 ETCAdoptit + β2 ETC Penetrationit + εit . (19) By replacing the indicator variable for whether the facility has ETC (ETCit ) with the percentage point change in ETC penetration (ETC Penetrationit ), I now allow the effect of ETC to vary over time and across facilities as a function of the diffusion of ETC.19 As discussed, I must estimate equation (19) on 16. The scale of the graph is arbitrary. I set the omitted category to zero. Thus, for example, the log minimum toll in ETC Year 4 is 2∗ β1 . +2∗ β3 and the log minimum toll in ETC Year −4 is 2∗ β−4 . 17. For the same reason, I do not extend the dummies in (18a) or (18b) for more years after ETC is adopted. 18. The point estimates in Figure IIIB indicate no preperiod trend in the balanced panel, which is reassuring relative to the (albeit statistically insignificant) suggestive evidence of some downward preperiod trend in the full sample in Figure IIIA. In Table VI I investigate the issue of potential preperiod trends in more detail, using a more parsimonious specification to increase statistical precision. 19. A more stringent test would be to include both ETC Penetrationit and ETCit on the right-hand side to examine whether the diffusion of ETC has an impact on toll rates that can be distinguished from a linear trend. I find that while the two variables are jointly significant, it is not possible to distinguish the effect of ETC penetration separately from a linear trend (not shown). This is not surprising, because, on average, the data contain about six years of data on a

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the subsample of facilities that never offer an ETC discount, as changes in the ETC discount will affect both the diffusion of ETC and the minimum toll. Column (4) of Table IV shows the results. The coefficient on the change in the ETC penetration rate is 0.623 (standard error 0.285). This indicates that every 10-percentagepoint increase in ETC penetration is associated with a (statistically significant) toll increase of 6.2%. For the full sample of facilities, I estimate (19) instrumenting for ETC Penetrationit with the indicator variable ETCit ; this is equivalent to instrumenting for the change in ETC penetration with a linear trend. Column (5) shows these results. The coefficient on ETC Penetrationit is 0.557 (standard error 0.262), indicating that every 10-percentage-point increase in ETC penetration is associated with a (statistically significant) 5.6% increase in the toll. To allow the effect of ETC to vary over time, in column (6) I instead instrument for the change in ETC penetration with a cubic polynomial in the number of years the facility has had ETC. The coefficient on ETC Penetrationit is now 0.501 (standard error 0.261). The results are also similar if I instead instrument for ETC Penetrationit with a series of indicator variables for the number of years under ETC (not shown). The magnitude of the estimated effect of ETC is quite similar across all of the various specifications shown in Table IV. The results from the baseline specification (Table IV, column (1)) suggest that after 14 years, by which point ETC has diffused to its steady state level (see Figure II), ETC is associated with an increase in the toll rate of 17%, or about one-sixth (∼exp(βETCAdopt + 14∗ βETC )). The IV estimates in columns (5) and (6) suggest that once ETC has diffused to its steady state level of 60%, it is associated with increases in tolls of 26 and 23%, respectively (∼exp(βETCAdopt + 0.6∗ βETC Penetration )). When the sample is limited to facilities without ETC discounts, the implied steady state increase in tolls is 36% when (3) is estimated (column (3)) or 38% when (5) is estimated (column (4)). All of these implied steady state toll increases associated with ETC are statistically significant at at least the 10% level. Taken together, these estimates suggest that the diffusion of ETC to its steady state level is associated with a 20 to 40 percent increase in toll rates. Given the extremely inelastic demand for driving with respect to the toll facility with ETC, and the diffusion pattern of ETC is basically linear for those first six years (see Figure II).

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that I estimate below, these results suggest that the associated increase in revenue for the toll authority is also about 20 to 40 percent. Endogeneity of the Timing of ETC Adoption. I have analyzed the endogenous choice of tax rates while assuming that the choice of the salience of the tax system (i.e., the adoption of ETC) is exogenous. In practice, the decision to adopt ETC does not appear to be random. For example, as previously discussed, higher labor costs in the northeast may have encouraged more ETC adoption. This does not, however, pose a problem for the analysis per se, which requires only that the timing of ETC implementation be uncorrelated with changes in a facility’s toll setting relative to its norm. Nonetheless, the correlation of various observable characteristics with whether or when a facility adopts ETC (see Table II) raises concerns about the identifying assumption that absent the introduction of ETC on facility i in year t, toll rates would not have changed differentially for that facility. I therefore analyze the effect of ETC separately on samples stratified by these characteristics. Table V shows the results. Column (1) replicates the baseline specification (Table IV, column (1)). Columns (2) through (7) show the effects separately by geographic region, by facility type (bridges and tunnels vs. roads), and by facility age. Not only does statistical significance generally persist across the subsamples, but also the point estimates are remarkably similar.20 To more directly control for differences across facilities in the underlying rate of toll growth, column (8) shows that the results are robust to the addition of facility fixed effects to (17), which is equivalent to allowing facility-specific linear trends in toll rates. One specific source of omitted variable bias that the preceding analysis does not directly address is that ETC adoption may be a part of a broader infrastructure project, or a signal that infrastructure modernization is in the works. In this case, the relationship between ETC and toll increases may be spurious, as infrastructure projects may necessitate (or provide political cover for) toll increases. To investigate this possibility, I compiled histories of 20. As a distinct exercise, I was also interested in whether the impact of ETC varied between operating authorities that automatically send monthly statements of expenses to users and authorities from which drivers had to actively request (and in some cases pay for) ETC expense statements. The point estimates did not suggest any economically or statistically differential impact of ETC on toll rates along this dimension, although the standard errors were sufficiently large so that it was not possible to rule out fairly large differences (not shown).

0.020 24 49 123 5,079

0.015 (0.006) [.018] −0.051 (0.035) [.158]

0.022 14 28 68 3,008

0.016 (0.010) [.141] −0.048 (0.054) [.399]

0.017 10 21 55 2,071

0.014 (0.005) [.030] −0.044 (0.027) [.137]

South and west (3)

0.021 18 24 44 1,692

0.015 (0.008) [.067] −0.023 (0.063) [.719]

Roads (4)

0.020 16 31 79 3,387

0.028 (0.010) [.015] −0.086 (0.017) [.000]

Bridges and tunnels (5)

0.019 13 20 43 1,389

0.021 (0.010) [.065] 0.051 (0.079) [.534]

Open after 1960 (6)

0.021 21 39 77 3,690

0.013 (0.007) [.079] −0.084 (0.025) [.003]

Open 1960 or before (7)

0.020 24 49 123 5,079

0.013 (0.007) [.072] −0.053 (0.036) [.147]

Facility fixed effects (8)

−0.055 (0.035) [.124] 0.014 (0.007) [.048] 0.017 (0.014) [.221] −0.003 (0.007) [.659] 0.021 23 46 115 4,712

−0.055 (0.035) [.125] 0.014 (0.007) [.048]

0.021 23 46 115 4,712

(10)

(9)

Facilities with infrastructure data

Notes. Table reports results from estimating variants of (17) by OLS. The dependent variable is the change in the log minimum toll. All regressions include year fixed effects (not shown). Each operating authority receives equal weight. ETCAdoptit is an indicator variable for whether facility i adopted ETC in year t. ETCit is an indicator variable for whether the facility has ETC; it is 1 in the year that ETC is adopted and in all subsequent years. Columns (2) and (3) limit the sample to, respectively, facilities in the northeast and midwest, and facilities in the south and west. Columns (4) and (5) limit the sample to, respectively, roads, and bridges or tunnels. Columns (6) and (7) limit the sample to, respectively, facilities that opened after 1960 and facilities that opened in 1960 or earlier. Column (8) adds facility fixed effects to the right-hand side of (17). In columns (9) and (10) the sample is limited to the 115 facilities for which infrastructure data are available. INFRAAdoptit is an indicator variable for whether facility i started a new infrastructure project in year t. INFRAit is an indicator variable for whether facility i has an infrastructure project in progress in year t; it is 1 in the year that the project is started and in all subsequent years that the project is in progress. All estimates give equal weight to each operating authority. Standard errors in parentheses are clustered by state, and p-values are shown in square brackets.

Mean dep. var. # of states # op. authorities # of facilities N

INFRAit

INFRAADOPTit

ETCAdoptit

ETCit

Baseline (1)

Northeast and midwest (2)

TABLE V IMPACT OF ETC ON TOLL RATES: ROBUSTNESS ANALYSIS

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infrastructure projects on 115 of the 123 individual toll facilities.21 These histories report the timing of a variety of infrastructure projects including renovations, replacements, repairs, widenings, extensions, and other improvements. I constructed indicator variables for whether facility i started an infrastructure project in year t (INFRAAdoptit ) and whether it had a project either started or ongoing in year t (INFRAit ). On average, a project was started in 2.2% of facility-years, and 10.1% of facility-years had an infrastructure project either starting or ongoing. I reestimate the basic relationship between ETC and toll increases (equation (17)) with these two additional variables included as covariates. Column (9) shows that the baseline results (without the additional infrastructure variables) are unaffected by restricting the sample to the 115 facilities for which I have data on infrastructure projects. Column (10) shows that the estimated increase in tolls associated with ETC is not affected in either magnitude or statistical significance by including the two infrastructure variables as controls. This suggests that the increase in tolls associated with ETC is not likely to be spuriously due to a correlation between ETC and infrastructure projects, which themselves are responsible for toll increases; indeed, the results suggest that infrastructure projects are not, in fact, associated with toll increases. There are of course many reasons, besides infrastructure projects, that the timing of ETC adoption might be spuriously correlated with toll increases. For example, facilities may respond to increased congestion by both adopting ETC and by raising tolls as complementary congestion-reducing strategies. This suggests we should observe increases in congestion (or a proxy for it such as traffic) on a facility prior to ETC adoption. Alternatively, facilities might respond to a negative revenue shock by both raising tolls and adopting ETC, with the latter a way to lower revenue losses from the administrative costs of toll collection. This suggests we should observe declining revenue (or declining traffic) on a facility in the years prior to ETC adoption. More generally, we can look for changes in toll rates in the years prior to ETC adoption as a partial test of the identifying assumption that absent the adoption of ETC, a facility would not have experienced differential changes in its toll rate. Of course, if the lower salience of ETC 21. The primary source of data was facility Web pages and annual reports, which often provide detailed histories of work on the facilities. The level of detail and the nature of the projects reported vary across facilities. However, because all of the analysis is within-facility, this should not pose a problem.

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(2)

0.013 (0.010) [.198] ETCAdoptit −0.000 0.000 (0.010) (0.010) [.996] [.978] ETCit −0.006 −0.001 (0.010) (0.010) [.551] [.959] Mean dep. var 0.049 # of states 21 # op. authorities 32 # of facilities 76 N 2,200

Dep. var.: log(revenue) (3) −0.009 (0.016) [.599]

(4)

Dep. var.: log(minimum toll) (5)

(6)

0.004 (0.013) [.777]

0.006 0.009 (0.012) (0.007) [.601] [.242] 0.002 0.002 −0.051 −0.051 (0.025) (0.025) (0.035) (0.035) [.922] [.930] [.158] [.162] 0.028 0.031 0.016 0.017 (0.015) (0.015) (0.006) (0.006) [.090] [.058] [.018] [.008] 0.077 0.020 13 24 19 49 45 123 1,411 5,079

Notes. Table reports results from estimating variants of (17) by OLS. Dependent variables are defined in the column headings. In addition to the covariates shown in the table, all regressions include year fixed effects. Each operating authority receives equal weight. Standard errors (in parentheses) are clustered by state. p-values are reported in square brackets. “1–2 years before ETCAdoptedit ” is an indicator variable for whether it is one to two years before the facility adopts ETC. “1–5 years before ETCAdoptedit ” is an indicator variable for whether it is one to five years before the facility adopts ETC. ETCAdoptit is an indicator variable for whether facility i adopted ETC in year t. ETCit is an indicator variable for whether the facility has ETC; it is 1 in the year that ETC is adopted and in all subsequent years.

made it easier to raise tolls, ETC might be adopted precisely by facilities that were encountering difficulties in making needed toll increases, suggesting that facilities might experience declines in traffic, revenue, or toll increases prior to ETC adoption. Although evidence of such effects would therefore not necessarily be inconsistent with the salience story, the lack of any such evidence reduces concerns about omitted variable bias and spurious findings. Table VI shows the results. I reestimate (17) with three different dependent variables: log(traffic)it (columns (1) and (2)), log(revenue)it (columns (3) and (4)), and log(minimum toll)it (columns (5) and (6)). In addition to the standard regressors (year fixed effects, ETCAdoptit , and ETCit ), I also include an indicator variable for whether it is one to two years prior to ETC adoption (odd columns) or whether it is one to five years prior to ETC

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adoption (even columns). The coefficients on these indicator variables for years just prior to ETC adoption show no statistically or substantively significant evidence of systematic changes in traffic, revenue, or tolls in the years prior to a facility’s adopting ETC. These results are consistent with the results from estimating (18a), which show no systematic preexisting trend in toll rates prior to a facility’s adoption of ETC, particularly in the balanced panel (see Figures IIIA and IIIB). One reason that the various endogeneity concerns may not in practice be a problem is that, as noted in Section IV.B, the different facilities run by a given operating authority tend to adopt ETC all at the same time, and yet may be experiencing different patterns of traffic and tolls.22 There are several other results of interest in Table VI. The finding in columns (3) and (4) that revenue increases by about 3 percent per year under ETC is broadly consistent with the estimated increase in tolls under ETC and the finding that demand for driving is very inelastic with respect to the toll.23 There is also some suggestive evidence in columns (1) and (2) that traffic declines under ETC, although these estimates are not statistically significant and are substantively quite small; a decline in traffic would be consistent with the survey evidence in Section III of overestimation of toll levels by ETC users. VI.B. The Impact of ETC on the Politics of Toll Setting The model in Section II.B suggested two potential mechanisms behind a finding that reduced salience is associated with increased tax rates: (i) a reduced behavioral responsiveness to taxes and (ii) a reduction in the political costs of tolls, particularly in the differential political costs of tolls in election years compared to nonelection years. Section V presented evidence for the first potential mechanism. To investigate the political channel, I examine whether there are political costs to tolls and how these costs change under ETC. Table VII shows the results. Because the political fallout from raising tolls may be concentrated on the extensive margin (i.e., whether tolls are raised), I report results not only for the baseline 22. In a different context, Dusek (2003) examines the impact of the introduction of state income tax withholding on tax rates, but notes that the decision to introduce income tax withholding appears to be correlated with increased demand for bigger government, making the results hard to interpret. 23. For the sample for which I have revenue data, I estimate that ETC is associated with a 2.2% increase in tolls each year (not shown).

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TABLE VII THE IMPACT OF ETC ON THE POLITICS OF TOLL SETTING

ETCit

AnyElec Yearst

log min toll (1)

Min toll raised? (2)

log min. toll (3)

Min toll raised? (4)

log min. toll (5)

Min toll raised? (6)

0.015 (0.006) [.018]

0.073 (0.024) [.006]

0.006 (0.009) [.507] −0.016 (0.004) [.000]

0.044 (0.022) [.042] −0.029 (0.010) [.003]

0.006 (0.009) [.494]

0.044 (0.022) [.042]

−0.016 (0.005) [.001] −0.015 (0.005) [.005]

−0.036 (0.012) [.002] −0.021 (0.012) [.085]

0.004 (0.014) [.791] 0.030 (0.014) [.038]

0.016 (0.033) [.617] 0.094 (0.033) [.005]

GovElec Yearst LegOnly ElecYearst AnyElec Yearst *ETCit GovElec Yearst *ETCit LegOnly ElecYearst *ETCit

0.017 (0.012) [.140]

0.055 (0.027) [.041]

Notes. Columns (1) and (2) report estimates of (17); columns (3)–(6) report estimates of (20). Dependent variable (shown in column heading) is log minimum toll (odd columns) or an indicator variable for whether the minimum toll was raised (even columns). In addition to the covariates shown in the table, all regressions include year fixed effects, ETCAdoptit , and interactions between ETCAdoptit and any indicator variables for the election year included in the regression. Each operating authority receives equal weight. Standard errors (in parentheses) are clustered by state. p-values are in square brackets. “AnyElecYearst ” is an indicator variable for whether state s’s governor or legislature is up for election in year t. “GovElecYearst ” is an indicator variable for whether the governor (and therefore almost always the legislature as well) is up for election. “LegOnlyElecYearst ” is an indicator variable for whether only the legislature is up for election. ETCit is an indicator variable for whether the facility has ETC; it is 1 in the year that ETC is adopted and in all subsequent years. Sample size in all columns is 5,079 facility-years, 123 facilities, 49 operating authorities, and 24 states. The mean of the dependent variable is 0.020 (odd columns) and 0.077 (even columns).

dependent variable log minimum toll (odd columns) but also for the binary dependent variable of whether the minimum toll increased (even columns). Column (1) replicates the baseline results from (17) (see Table IV, column (1)). Column (2) shows the results from estimating (17) with the binary dependent variable for whether the minimum toll was raised that year; the coefficient on ETCit is 0.073 (standard error 0.024). This suggests that, relative to the baseline 7.7% annual probability of a toll increase, the probability of a toll increase almost doubles on a facility once it

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has ETC. Combined with the evidence in column (1), this suggests that the increase in tolls associated with ETC comes about primarily through more frequent toll increases of similar magnitude. I then expand the baseline specification in (17) to include indicator variables for whether it is an election year, and the interactions of these indicators with the change in salience, as proposed in the estimating (15) from Section II.B. This allows me to examine whether there is a political business cycle in toll setting and whether this political business cycle varies under manual toll collection and ETC. Specifically, I estimate yit = γt + β1 ETCAdoptit + β2 ETCit + β3 1(ElecYear)st (20)

+ β4 1(ElecYear)st ∗ ETCAdoptit + β5 1(ElecYear)st ∗ ETCit + εit .

Columns (3) and (4) report results when 1(ElecYear)st is an indicator for whether there is any state election (for either the governor or the legislature) in state s and year t; about half of the facility-years in the data are election years, but the timing of the electoral calendar varies across states. Columns (5) and (6) report results when 1(ElecYear)st is two separate indicators for whether the governor (and therefore almost always the legislature as well) is up for election and for whether only the legislature is up for election; each of these indicator variables is turned on in roughly one-fourth of state years. In all four specifications, the coefficients on all of the election year indicators are negative and statistically significant; this demonstrates the political business cycle under manual toll collection. Given the average annual 2% increase in tolls, the coefficient on the election year dummies of about −0.016 in columns (3) and (5) indicates that toll increases are about 75% lower during election years than during nonelection years under manual toll collection. The interaction term between the election year indicator variables and ETC is always positive; it is statistically significant for legislature-only election years (columns (5) and (6)) and statistically significant (or only marginally insignificant) for any election year (columns (3) and (4)). This suggests that under ETC, tollsetting behavior is less sensitive to the political election calendar (particularly legislature elections) than under manual toll collection. Indeed, there is no evidence that toll increases are lower in election years relative to nonelection years under electronic toll

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collection; the sum of the coefficients on the election year indicator variable and its interaction with ETC (i.e., β3 + β5 ) is almost always positive (and never significantly negative).24 VII. ALTERNATIVE EXPLANATIONS In this section, I briefly consider a range of alternative explanations for the increase in tolls associated with ETC other than the decline in the salience of the toll. I note at the outset that a general point in favor of the salience-based explanation is the finding that toll setting becomes less sensitive to the local election calendar under ETC; this is consistent with a decline in salience reducing the political costs of raising tolls, but would not be predicted by any of the alternative explanations I discuss. VII.A. ETC Lowers the Operating Cost of Toll Collection ETC is associated with substantial reductions in the annual costs of operating and maintaining toll facilities; the ETC cost savings come primarily from reductions in the labor costs associated with manual toll collection (Hau 1992; Pietrzyk and Mierzejewski 1993; Levinson 2002).25 However, for increases in the efficiency of tax collection to increase the equilibrium tax rate requires an improvement in the marginal efficiency of tax collection (Becker and Mulligan 2003). By contrast, ETC improves the fixed component of the efficiency cost of taxation—because the administrative cost savings are independent of the toll rate—which should therefore not prompt an increase in the rate of existing taxes.26 A decline in the fixed administrative costs of tax collection could, however, encourage the introduction of new taxes, such as 24. The “main effect” of ETC, although positive, is no longer statistically significant in columns (3) and (5); toll increases are not statistically significantly larger in nonelection years under ETC than under manual toll collection. However, toll increases are statistically significantly larger in election years under ETC than under manual toll collection; the sum of the coefficients on ETC and the interaction of ETC and election year (i.e., β2 + β5 in (20)) is statistically significant in column (3) and statistically significant for the legislative election year variable in column (5) (not shown). 25. Toll collection costs under manual toll collection can be quite high. A 1995 study of turnpikes in Massachusetts and New Jersey estimated that toll collection costs under manual toll collection were about 6 percent of toll revenue (Friedman and Waldfogel 1995); a 2006 study found that on portions of the Massachusetts Turnpike where there is relatively little traffic, toll collection costs were over onethird of toll revenue (Kriss 2006). 26. Note, moreover, that if operating authorities set tolls to meet an exogenous revenue requirement, the reduction in administrative costs would lower (rather than raise) the equilibrium toll needed to raise a fixed amount of (net) revenue.

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the introduction of tolls on roads that had not been previously been tolled or the construction of new (tolled) roads where no road existed before. Any such effects of ETC, however, would not show up in my analysis, which limits the sample to facilities with preexisting tolls. Lower fixed administrative costs of toll collection could also encourage the installation of more toll collection points on an existing toll facility; however, I find no evidence that ETC had such an effect.27 VII.B. ETC Installation Requires Capital Outlay Although ETC lowers the costs of operating and maintaining toll facilities, installation of ETC requires a capital outlay. It seems unlikely that this capital outlay would require an increase in tolls. Operating authorities can borrow to cover these capital costs, and the capital costs are recouped within a few years by the savings in operating and maintenance costs, and by revenue from the sale or lease of the transponders and interest on prepayments and deposits (Hau 1992; Pietrzyk and Mierzejewski 1993). Of course, it is possible that operating authorities might use the installation costs of ETC as an excuse to raise tolls, even though ETC is selffinancing. Any such excuse might be used for a one-time increase in tolls when ETC comes in; it seems less natural that this excuse could be used for subsequent increases in tolls as ETC use diffuses among drivers. VII.C. Changes in Menu Costs Associated with ETC It is possible that ETC lowers the administrative (menu) cost of toll changes. There could be literal menu cost savings if signs listing the toll rate no longer had to be changed under ETC. Alternatively, ETC might allow smaller increases of non-“round” amounts; unlike manual tolls, this would not impose on drivers that they carry small coins. In practice, however, ETC tolls are not less “round” than manual tolls, except when they are specified as a fixed percentage discount off of the manual toll. In addition, the increase in tolls associated with ETC persists for the subsample of facilities that do not offer discounts; for these facilities, there can be no menu cost savings, as changing the electronic toll 27. I reestimate (17) using as a dependent variable a binary measure for whether there is an increase in the number of toll transactions someone driving a one-way, full-length trip on the facility would have to make. I perform this analysis for the full sample of facilities, and separately both for roads and for bridges and tunnels (not shown).

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requires changing the manual toll, and all facilities continue to have at least some manual payers. Finally, even if ETC did reduce menu costs, this should suggest that ETC would be associated with more frequent toll adjustments, but it is not clear why this would produce a higher equilibrium toll rate. VII.D. ETC Lowers Personal Compliance Costs of Toll Payment ETC reduces the drivers’ compliance costs of paying tolls (Hau 1992; Levinson 2002). Friedman and Waldfogel (1995) estimate that under manual toll collection, these compliance costs—which consist of time spent queuing and paying tolls at the toll plaza— are, on average, about 15% of toll revenue. Reductions in compliance costs of paying tolls may directly increase drivers’ willingness to pay the (monetary) toll, and hence provide an alternative explanation for the observed increase in toll rates. In practice, however, two independent pieces of empirical evidence suggest that toll authorities do not increase tolls in response to reductions in compliance costs; this is consistent with the finding in Section V that they set tolls substantially below the revenue-maximizing rate (i.e., that they implicitly place a relatively large weight on consumer surplus). The first piece of suggestive evidence comes from variation across roads in the number of times an individual must make a toll transaction, and hence variation in the compliance costs savings from ETC. For example, in 1985 an individual made eleven toll transactions while driving the length of the Garden State Parkway, compared to only two on the New Jersey Turnpike. If tolls were increased under ETC in response to the reductions in compliance costs, we would expect greater toll increases on roads with a greater number of toll transactions. In fact, I find weak evidence of the opposite. The second piece of suggestive evidence comes from what happens to toll rates when a bridge or tunnel switches from collecting tolls at both ends of the facility to collecting tolls at only one end; at various times over the course of my sample, about half of the bridges and tunnels (40 of 79) made this switch, which reduced compliance costs on their facility by one-half. I find little evidence of a substantively or statistically significant increase in tolls on a facility following this reduction in compliance costs.28 28. The results of both of these analyses are presented in more detail in the Online Appendix (Section C) and in the working paper version of this paper (Finkelstein 2007).

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VII.E. ETC Raises the Optimal Congestion-Correcting Toll Could the increase in tolls under ETC come entirely from the increase in the optimal congestion externality–reducing toll that results from the reduced consumer responsiveness to tolls? This would suggest that the effect of ETC on toll rates is a salience effect, but one that comes entirely from a reduction in salience at the time of consumption (driving). This seems unlikely given the evidence in Section VI.B that ETC affects the political costs of raising tolls; this suggests that at least some of the toll increase associated with ETC is likely to be due to a decline in voting salience. In addition, as an (admittedly quite) crude test of whether the increase in tolls under ETC is driven by an increase in congestion under ETC, I experimented with controlling for traffic (a proxy for congestion) on the right-hand side of (17). I found that the impact of ETC on the change in tolls is not sensitive to including traffic as a control, suggesting that even conditional on the level of traffic, tolls still rise under ETC (not shown).

VIII. CONCLUSIONS This paper has examined the hypothesis that a less salient tax system can produce a higher equilibrium tax rate. Belief in this possibility has contributed to opposition to tax reforms that are believed to reduce tax salience, such as Federal income tax withholding or partial replacement of the income tax with a valueadded tax. Yet the sign of the effect of tax salience on tax rates is theoretically ambiguous, and empirical evidence has been lacking. I examine the relationship between tax salience and tax rates empirically by looking at the impact of electronic toll collection (ETC) on toll rates. Survey evidence indicates that drivers who pay tolls electronically are substantially less aware of toll rates than those who pay with cash, suggesting that ETC reduces tolls’ salience. To analyze the impact of this reduction in salience, I assembled a new data set on toll rates over the last half century on 123 toll facilities in the United States. Because different toll facilities adopted ETC in different years, and some have not yet adopted it, I am able to examine the within-toll facility change in tolls associated with the introduction of electronic toll collection. I find robust evidence that toll rates increase following the adoption of electronic toll collection. The estimates suggest that after ETC use among drivers has diffused to its steady state level,

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toll rates are 20 to 40 percent higher than they would have been under manual toll collection. I provide evidence of two potential mechanisms by which reduced salience may contribute to increased toll rates: under ETC driving behavior becomes less elastic (in absolute value) with respect to the toll, and toll setting becomes less sensitive to the local election calendar. This decline in the political costs of raising tolls associated with ETC would not be predicted by alternative explanations for the increase in tolls associated with ETC. I also present additional evidence that is not consistent with specific alternative explanations. As previously discussed, the normative implications of these findings are ambiguous. Evidence on what is done with the extra revenue from the higher tolls—in particular, whether it is used for purposes that may be valued by users of the facility such as infrastructure investment or reductions in other highway fees, or whether it primarily serves to increase rents for the governing authority through increased employment or salaries of bureaucrats—could help shed some light on the normative implications of the higher tolls under ETC. Unfortunately, the available data are not sufficient for analysis of this issue. The results also leave open the question of how tax salience affects tax rates in other contexts, such as federal income tax withholding or the replacement of a sales tax with a value added tax. As previously discussed, the sign of the effect of tax salience on tax rates may well differ for taxes that are a larger share of expenditures than tolls. The magnitude of any effect of tax salience is also likely to differ across different political institutions. The results in this paper suggest that the salience of the tax instrument is an important element to consider in both theoretical and empirical investigations of the political economy of tax setting. Relatedly, they suggest that the empirical impact of tax salience in these other specific settings is an interesting and important direction for further work. MASSACHUSETTS INSTITUTE OF TECHNOLOGY AND NBER

REFERENCES Becker, Gary, and Casey Mulligan, “Deadweight Costs and the Size of Government,” Journal of Law and Economics, 46 (2003), 293–340. Brennan, Geoffrey, and James Buchanan, The Power to Tax: Analytical Foundations of a Fiscal Constitution (Cambridge, UK: Cambridge University Press, 1980).

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Buchanan, James, Public Finance in Democratic Process: Fiscal Institutions and the Individual Choice (Chapel Hill: University of North Carolina Press, 1967). Buchanan, James, and Richard E. Wagner, Democracy in Deficit (New York: Academic Press, 1977). Chetty, Raj, Kory Kroft, and Adam Looney, “Salience and Taxation: Theory and Evidence,” American Economic Review, forthcoming. Dollery, Brian, and Andrew Worthington, “The Empirical Analysis of Fiscal Illusion,” Journal of Economic Surveys, 10 (1996), 261–298. Dusek, Libor, Do Governments Grow When They Become More Efficient? Evidence from Tax Withholding, Unpublished Ph.D. Dissertation, University of Chicago, 2003. Feldman, Naomi, and Peter Katuscak, “Should the Average Tax Rate Be Marginalized?” mimeo, Ben Gurion University, 2005. Finkelstein, Amy, “E-Z Tax: Tax Salience and Tax Rates,” Working Paper 12924, National Bureau of Economic Research, 2007. Friedman, David, and Joel Waldfogel, “The Administrative and Compliance Cost of Manual Highway Toll Collection: Evidence from Massachusetts and New Jersey,” National Tax Journal, June 1995. Friedman, Milton, and Rose Friedman, Two Lucky People (Chicago: University of Chicago Press, 1998). Hau, Timothy, “Congestion Charging Mechanisms for Roads: An Evaluation of Current Practice,” Research Paper 1071, The World Bank, 1992. Holguin-Veras, Jose, Ozbay Kaan, and Allison de Cerrano, “Evaluation Study of the Port Authority of New York and New Jersey’s Time of Day Pricing Initiative,” report, Rensselaer Polytechnic Institute, 2005. Kearney, Melissa, “The Economic Winners and Losers of Legalized Gambling,” National Tax Journal, 58 (2005), 281–302. Kriss, Eric, “Turnpike Task Force Final Report,” Pioneer Institute board presentation by Eric Kriss, October 18, 2006. Levinson, David, Financing Transportation Networks (Northampton, MA: Edward Elgar, 2002). Liebman, Jeffrey, and Richard Zeckhauser, “Schmeduling,” unpublished mimeo, Harvard’s Kennedy School of Government, 2004). Nordhaus, William, “The Political Business Cycle,” Review of Economic Studies, 42 (1975), 169–190. Oates, Wallace, “On the Nature and Measurement of Fiscal Illusion: A Survey,” in Taxation and Fiscal Federalism: Essays in Honour of Russell Mathews, Geoffrey Brennan, Bhajan Grewal, and Peter Groenewegen, eds. (Sydney: Australian National University Press, 1988). Peltzman, Sam, “Pricing in Public and Private Enterprises: Electric Utilities in the United States,” Journal of Law and Economics, 14 (1971), 109–147. Pietrzyk, Michael, and Edward Mierzejewski, “Electronic Toll and Traffic Management Systems” (Washington, DC: National Academy Press, 1993). Slemrod, Joel, “Which Is the Simplest Tax System of Them All?” in The Economics of Fundamental Tax Reform, Hank Aaron and William Gale, eds. (Washington, DC: The Brookings Institution, 1996). Soman, Dilip, “Effects of Payment Mechanism on Spending Behavior: The Role of Rehearsal and Immediacy of Payments,” Journal of Consumer Research, 27 (2001), 460–474. Thaler, Richard H., “Mental Accounting Matters,” Journal of Behavioral Decision Making, 12 (1999), 183–206. The President’s Advisory Panel on Federal Tax Reform, Simple, Fair, and ProGrowth: Proposals to Fix America’s Tax System (Washington, DC: U.S. Government Printing Office, 2005). U.S. Census Bureau, “Annual Survey of State and Local Government Finances and Census of Governments,” 1985. U.S. Department of Transportation, “Highway Statistics, YEAR,” various years. Wooldridge, Jeffrey, Econometric Analysis of Cross Section and Panel Data (Cambridge, MA: MIT Press, 2002).

THE BOND MARKET’S q∗ THOMAS PHILIPPON I propose an implementation of the q-theory of investment using bond prices instead of equity prices. Credit risk makes corporate bond prices sensitive to future asset values, and q can be inferred from bond prices. With aggregate U.S. data, the bond market’s q fits the investment equation six times better than the usual measure of q, it drives out cash flows, and it reduces the implied adjustment costs by more than an order of magnitude. Theoretical interpretations for these results are discussed.

I. INTRODUCTION In his 1969 article, James Tobin argued that “the rate of investment—the speed at which investors wish to increase the capital stock—should be related, if to anything, to q, the value of capital relative to its replacement cost” (Tobin 1969, p. 21). Tobin also recognized, however, that q must depend on “expectations, estimates of risk, attitudes towards risk, and a host of other factors,” and he concluded that “it is not to be expected that the essential impact of [. . . ] financial events will be easy to measure in the absence of direct observation of the relevant variables (q in the models).” The quest for an observable proxy for q was therefore recognized as a crucial objective from the very beginning. Subsequent research succeeded in integrating Tobin’s approach with the neoclassical investment theory of Jorgenson (1963). Lucas and Prescott (1971) proposed a dynamic model of investment with convex adjustment costs, and Abel (1979) showed that the rate of investment is optimal when the marginal cost of installment is equal to q − 1. Finally, Hayashi (1982) showed that, under perfect competition and constant returns to scale, marginal q (the market value of an additional unit of capital divided by its replacement cost) is equal to average q (the market value of existing capital divided by its replacement cost). Because average q is observable, the theory became empirically relevant. ∗ This paper was first circulated under the title “The y-Theory of Investment.” I thank Robert Barro (the editor), three anonymous referees, Daron Acemoglu, Mark Aguiar, Manuel Amador, Luca Benzoni, Olivier Blanchard, Xavier Gabaix, Mark Gertler, Simon Gilchrist, Bob Hall, Guido Lorenzoni, Sydney Ludvigson, Pete Kyle, Lasse Pedersen, Christina Romer, David Romer, Ivan Werning, Toni Whited, Jeff Wurgler, Egon Zakrajsek, and seminar participants at NYU, MIT, the SED 2007, London Business School, Ente Einaudi (Rome), University of Salerno, Toulouse University, Duke University, and the NBER Summer Institutes 2006 and 2007. Peter Gross provided excellent research assistance. C 2009 by the President and Fellows of Harvard College and the Massachusetts Institute of

Technology. The Quarterly Journal of Economics, August 2009

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Unfortunately, its implementation proved disappointing. The investment equation fits poorly, leaves large unexplained residuals correlated with cash flows, and implies implausible parameters for the adjustment cost function (see Summers [1981] for an early contribution, and Hassett and Hubbard [1997] and Caballero [1999] for recent literature reviews). Several theories have been proposed to explain this failure. Firms could have market power, and might not operate under constant returns to scale. Adjustment costs might not be convex (Dixit and Pindyck 1994; Caballero and Engle 1999). Firms might be credit-constrained (Fazzari, Hubbard, and Petersen 1988; Bernanke and Gertler 1989). Finally, there could be measurement errors and aggregation biases in the capital stock or the rate of investment. None of these explanations is fully satisfactory, however. The evidence for constant returns and price-taking seems quite strong (Hall 2003). Adjustment costs are certainly not convex at the plant level, but it is not clear that it really matters in the aggregate (Thomas 2002; Hall 2004), although this is still a controversial issue (Bachmann, Caballero, and Engel 2006). Gomes (2001) shows that Tobin’s q should capture most of investment dynamics even when there are credit constraints. Heterogeneity and aggregation do not seem to create strong biases (Hall 2004). In fact, an intriguing message comes out of the more recent empirical research: the market value of equity seems to be the culprit for the empirical failure of the investment equation. Gilchrist and Himmelberg (1995), following Abel and Blanchard (1986), use VARs to forecast cash flows and to construct q, and they find that it performs better than the traditional measure based on equity prices. Cumins, Hasset, and Oliner (2006) use analysts’ forecasts instead of VAR forecasts and reach similar conclusions. Erickson and Whited (2000, 2006) use GMM estimators to purge q from measurement errors. They find that only 40% of observed variations are due to fundamental changes, and, once again, that market values contain large “measurement errors.” Applied research has therefore reached an uncomfortable situation, where the benchmark investment equation appears to be successful only when market prices are not used to construct q. This is unfortunate, because Tobin’s insight was precisely to link observed quantities and market prices. The contribution of this paper is to show that a market-based measure of q can be constructed from corporate bond prices and that this measure performs much better than the traditional one.

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Why would the bond market’s q perform better than the usual measure? There are several possible explanations, two of which are discussed in details in this paper. The first explanation is that total firm value includes the value of growth options, that is, opportunities to expand into new areas and new technologies. With enough skewness, these growth options end up affecting equity prices much more than bond prices. If, in addition, these growth options are unrelated to existing operations, they do not affect current capital expenditures. As a result, bond prices are more closely related to the existing technology’s q, while equity prices reflect organizational rents. A second possible explanation is that the bond market is less susceptible to bubbles than the equity market. In fact, there is empirical and theoretical support for the idea that mispricing is more likely to happen when returns are positively skewed. Barberis and Huang (2007) show that cumulative prospect theory can explain how a positively skewed security becomes overpriced. Brunnermeier, Gollier, and Parker (2007) argue that preference for skewness arises endogenously because investors choose to be optimistic about the states associated with the most skewed Arrow–Debreu securities. Empirically, Mitton and Vorkink (2007) document that underdiversification is largely explained by the fact that investors sacrifice mean–variance efficiency for higher skewness exposure. These insights, combined with the work of Stein (1996) and Gilchrist, Himmelberg, and Huberman (2005) showing why rational managers might not react (or, at least, not much) to asset bubbles, provide another class of explanations.1 Of course, even if we accept the idea that bond prices are somehow more reliable than equity prices, it is far from obvious that it is actually possible to use bond prices to construct q. The contribution of this paper is precisely to show how one can do so, by combining the insights of Black and Scholes (1973) and Merton (1974) with the approach of Abel (1979) and Hayashi (1982). In the Black–Scholes–Merton model, debt and equity are seen as derivatives of the underlying assets. In the simplest case, the market value of corporate debt is a function of its face value, asset 1. Other rational explanations can also be proposed. These explanations typically involve different degrees of asymmetric information, market segmentation, and heterogeneity in adjustment costs and stochastic processes. For instance, firms might be reluctant to use equity to finance capital expenditures, because of adverse selection, in which case the bond market might provide a better measure of investment opportunities (Myers 1984). It is much too early at this stage to take a stand on which explanations are most relevant.

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volatility, and asset value. But one can also invert the function, so that, given asset volatility and the face value of debt, one can construct an estimate of asset value from observed bond prices. I extend this logic to the case where asset value is endogenously determined by capital expenditures decisions. As in Hayashi (1982), I assume constant returns to scale, perfect competition, and convex adjustment costs. There are no taxes and no bankruptcy costs, so the Modigliani–Miller theorem holds, and real investment decisions are independent from capital structure decisions.2 Firms issue long-term, coupon-paying bonds as in Leland (1998), and the default boundary is endogenously determined to maximize equity value, as in Leland and Toft (1996). There are two crucial differences between my model and the usual asset pricing models. First, physical assets change over time. Under constant returns to scale, however, I obtain tractable pricing formulas, where the usual variables are simply scaled by the book value of assets. Thus, book leverage plays the role of the face value of principal outstanding, and q plays the role of total asset value. The second difference is that cash flows are endogenous, because they depend on adjustment costs and investment decisions. I model an economy with a continuum of firms hit by aggregate and idiosyncratic shocks. Even though default is a discrete event at the firm level, the aggregate default rate is a continuous function of the state of the economy. To build economic intuition, I consider first a simple example with one-period debt, constant risk-free rates, and i.i.d. firm-level shocks. I find that, to first order (i.e., for small aggregate shocks), Tobin’s q is a linear function of the spread of corporate bonds over government bonds. The sensitivity of q to bond spreads depends on the risk-neutral default rate, just like the delta of an option in the Black–Scholes formula. In the general case, I choose the parameters of the model to match aggregate and firm level dynamics, estimated with postwar U.S. data. Given book leverage and idiosyncratic volatility, the model produces a nonlinear mapping from bond prices to q. I then use the theoretical mapping to construct a time series for q based on the relative prices of corporate and government bonds, taking into account trends in book leverage and 2. One could introduce taxes and bankruptcy costs if one wanted to derive an optimal capital structure, but this is not the focus of this paper. See Hackbarth, Miao, and Morellec (2006) for such an analysis, with a focus on macroeconomic risk.

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idiosyncractic risk, as well as changes in real risk-free rates. This bond market’s q fits the investment equation quite well with postwar aggregate U.S. data. The R2 is around 60%, cash flows become insignificant, and the implied adjustment costs are more than an order of magnitude smaller than with the usual measure of q. The fit is as good in levels as in differences. The theoretical predictions for the roles of leverage and volatility are supported by the data, as well as the nonlinearities implied by the model. Using simulations, I find that the predictions of the model are robust to specification errors, as well as to taxes and bankruptcy costs. The theoretical predictions for firm level dynamics are consistent with the empirical results of Gilchrist and Zakrajsek (2007), who show that firm-specific interest rates forecast firmlevel investment. The remainder of the paper is organized as follows. Section II presents the setup of the model. Section III uses a simple example to build economic intuition. Section IV presents the numerical solution for the general case. Section V presents the evidence for aggregate U.S. data. Section VI discusses the theoretical interpretations of the results. Section VII discusses the robustness of the results to various changes in the specification of the model. Section VIII concludes. II. MODEL II.A. Firm Value and Investment Time is discrete and runs from t = 0 to ∞. The production technology has constant returns to scale and all markets are perfectly competitive. All factors of production, except physical capital, can be freely adjusted within each period. Physical capital is predetermined in period t and, to make this clear, I denote it by kt−1 . Once other inputs have been chosen optimally, the firm’s profits are therefore equal to pt kt−1 , where pt is the exogenous profit rate in period t. Let the function (kt−1 , kt ) capture the total cost of adjusting the level of capital from kt−1 to kt . For convenience, I include depreciation in the function , and I assume that it is homogeneous of degree one, as in Hayashi (1982).3 3. For instance, the often-used case of quadratic adjustment costs corresponds to (kt , kt+1 ) = kt+1 − (1 − d)kt + 0.5γ2 (kt+1 − kt )2 /kt , where d is the depreciation rate, and γ2 is a constant that pins down the curvature of the adjustment cost function.

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Let rt be the one-period real interest rate, and let Eπ [.] denote expectations under the risk-neutral probability measure π .4 The state of the firm at time t is characterized by the endogenous state variable kt and a vector of exogenous state variables ωt , which follows a Markov process under π . The profit rate and the risk-free rate are functions of ωt . The value of the firm solves the Bellman equation, Eπ [V (kt , ωt+1 ) |ωt ] V (kt−1 , ωt ) = max p(ωt )kt−1 − (kt−1 , kt ) + . kt ≥0 1 + r(ωt ) (1) Because the technology exhibits constant returns to scale, it is convenient to work with the scaled value function, vt ≡

(2)

Vt . kt−1

Similarly, define the growth of k as xt ≡ kt /kt−1 . After dividing both sides of equation (1) by kt−1 , and using the shortcut notation ω for ωt+1 , we obtain x Eπ [v(ω )|ω] , v(ω) = max p(ω) − γ (x) + (3) x≥0 1 + r(ω) where γ is the renormalized version of . The function γ is assumed to be convex and to satisfy limx→0 γ (x) = ∞ and limx→∞ γ (x) = ∞. The optimal investment rate x(ω) solves (4)

∂γ Eπ [v(ω )|ω] (x(ω)) = q(ω) ≡ . ∂x 1 + r(ω)

Equation (4) defines the q-theory of investment: it says that the marginal cost of investment is equal to the expected discounted marginal product of capital. The most important practical issue is the construction of the right-hand side of equation (4). II.B. Measuring q The value of the firm is the value of its debt plus the value of its equity. Let Bt be the market values of the bonds outstanding 4. This is equivalent to using a pricing kernel, but it simplifies the notations and the algebra. If m is the pricing kernel between states ω and ω , then for any random variable z , E[m z |ω] = Eπ [z |ω]/(1 + r(ω)). It is crucial to account for risk premia in any case. Berndt et al. (2005) show that objective probabilities of default are much smaller than risk-adjusted probabilities of default. Lettau and Ludvigson (2002) also emphasize the role of time-varying risk premia.

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at the end of period t, and define bt as the value scaled by end-ofperiod physical assets (5)

bt ≡

Bt . kt

Similarly, let e (ω) be the ex-dividend value of equity, scaled by end-of-period assets. Then q is simply (6)

q(ω) = e(ω) + b(ω).

The most natural way to test the q-theory of investment is therefore to use equation (6) to construct the right-hand side of equation (4). Unfortunately, it fits poorly in practice (Summers 1981; Hassett and Hubbard 1997; Caballero 1999). Equation (6) has been estimated using aggregate and firm-level data, in levels or in first differences, with or without debt on the right-hand side. It leaves large unexplained residuals correlated with cash flows, and it implies implausible values for the adjustment cost function γ (x). As argued in the Introduction, there are potential explanations for this empirical failure, but none is really satisfactory. Moreover, a common finding of the recent research is that “measurement errors” in equity seem to be responsible for the failure of q-theory (Gilchrist and Himmelberg 1995; Erickson and Whited 2000, 2006; Cumins, Hasset, and Oliner 2006). I do not attempt in this paper to explain the meaning of these “measurement errors.” I simply argue that, even if equity prices do not provide a good measure of q, it is still possible to construct another one using observed bond prices. II.C. Corporate Debt I assume that there are no taxes and no deadweight losses from financial distress. The Modigliani–Miller theorem implies that leverage policy does not affect firm value or investment. Leverage does affect bond prices, however, and I must specify debt dynamics before I can use bond prices to estimate q. The model used here belongs to the class of structural models of debt with endogenous default boundary. In this class of models, default is chosen endogenously to maximize equity value (see Leland [2004] for an illuminating discussion). There are many different types of long-term liabilities, and my goal here is not to study all of them, but rather to focus on

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a tractable model of long-term debt. To do so, I use a version of the exponential model introduced in Leland (1994), and used by Leland (1998) and Hackbarth, Miao, and Morellec (2006), among others. In this model, the firm continuously issues and retires bonds. Specifically, a fraction φ of the remaining principal is called at par every period. The retired bonds are replaced by new ones. To understand the timing of cash flows, consider a bond with coupon c and principal normalized to 1, issued at the end of period t. The promised cash flows for this particular bond are as follows: t+1

t+2

...

τ

...

c+φ

(1 − φ)(c + φ)

...

(1 − φ)τ −t−1 (c + φ)

...

Let τ −1 be the sum of the face values of all the bonds outstanding at the beginning of period τ . I use the index τ − 1 to make clear that this variable, just like physical capital, is predetermined at the beginning of each period. The timing of events in each period is the following: 1. The firm enters period τ with capital kτ −1 and total face value of outstanding bonds τ −1 . 2. The state variable ωτ is realized. The value of the firm is then Vτ = vτ kτ −1 , defined in equations (1) and (3). (a) If equity value falls to zero, the firm defaults and the bond holders recover Vτ . (b) Otherwise, the bond holders receive cash flows (c + φ ) τ −1 . 3. At the end of period τ , the capital stock is kτ , the face value of the bonds (including newly issued ones) is τ , and their market value is Bτ = bτ kτ . New issuances represent a principal of τ − (1 − φ ) τ −1 . In Leland (1994) and Leland (1998), book assets are constant, because there is no physical investment, and the firm simply chooses a constant face value . In my setup, the corresponding assumption is that the firm chooses a constant book leverage ratio. In the theoretical analysis, I therefore maintain the following assumption: ASSUMPTION. Firms keep a constant book leverage ratio: ψ ≡ t /kt . A bond issued at the end of period t has a remaining face value of (1 − φ)τ −t−1 at the beginning of period τ . In case of default

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during period τ , all bonds are treated similarly and the bond issued at time t receives (1 − φ)τ −t−1 Vτ / τ −1 . Because all outstanding bonds are treated similarly in case of default, we can characterize the price without specifying when this principal was issued. The following proposition characterizes the debt pricing function. PROPOSITION 1. The scaled value of corporate debt solves the equation (7) b(ω) =

1 Eπ [min{(c + φ)ψ + (1 − φ)b(ω ); v(ω )}|ω]. 1 + r(ω)

Proof. See Appendix. The intuition behind equation (7) is relatively simple. Default happens when equity value falls to zero, that is, when v − (c + φ)ψ − (1 − φ)b = 0. There are no deadweight losses and bondholders simply recover the value of the company. When there is no default, bondholders receive the cash flows (c + φ)ψ and they own (1 − φ) remaining bonds. A few special cases are worth pointing out. Short-term debt corresponds to φ = 1 and c = 0, and the pricing function is simply (8)

bshort (ω) =

1 Eπ [min(ψ; v(ω ))|ω]. 1 + r(ω)

The main difference between short- and long-term debt is the presence of the pricing function b on both sides of equation (7), whereas it appears only on the left-hand side in equation (8). A perpetuity corresponds to φ = 0, and, more generally, 1/φ is the average maturity of the debt. The value of a default-free bond with the same coupon and maturity structure would be (9)

bfree (ω) =

(c + φ)ψ + (1 − φ)Eπ [bfree (ω )|ω] . 1 + r(ω)

With a constant risk-free rate, bfree is simply equal to (c + φ)ψ/ (φ + r). III. SIMPLE EXAMPLE This section presents a simple example in order to build intuition for the more general case. The specific assumptions made in this section, and relaxed later, are that the risk-free rate is constant; firms issue only short-term debt; and idiosyncratic shocks

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are i.i.d. Let us first decompose the state ω into its aggregate component s, and its idiosyncratic component η. The aggregate state follows a discrete Markov chain over the set [1, 2, . . . , S], and it pins down the aggregate profit rate a (s), as well as the conditional risk-neutral expectations. The profit rate of the firm depends on the aggregate state and on the idiosyncratic shock: p(s, η) = a(s) + η.

(10)

The shocks η are independent over time, and distributed according to the density function ζ (.). Because idiosyncratic profitability shocks are i.i.d., the value function is additive and can be written v(s, η) = v(s) + η. I assume that s and η are such that v(s, η) is always positive, so that firms never exit. Tobin’s q is the same for all firms, and I normalize the mean of η to zero; therefore, q(s) =

(11)

Eπ [v(s )|s] . 1+r

Let v¯ ≡ Eπ [v(s)] be the unconditional risk-neutral average asset value, and define q ≡ v/(1 ¯ + r). All the firms choose the same investment rate in this simple example. This will not be true in the general model with persistent idiosyncratic shocks. We can write the value of the aggregate portfolio of corporate bonds by integrating (8) over idiosyncratic shocks: ψ−v(s ) 1 π E ψ+ (12) b(s) = (v(s ) + η − ψ)ζ (η ) dη |s . 1+r −∞ In equation (12), ψ is the promised payment, and the integral measures credit losses. Let δ be the default rate estimated at the risk-neutral average value ψ−v¯ (13) ζ (η ) dη . δ≡ ψ−v¯

−∞

¯ ≡ (ψ + ¯ + η − ψ)ζ (η ) dη )/(1 + r) be the correspondLet b −∞ (v ing price for the aggregate bond portfolio. Using (13) and (11), we can write (12) as (14)

π ¯ = δ(q(s) − q) + E [o(v )] , b(s) − b 1+r

ψ−v where o(v ) ≡ ψ−v¯ (v + η − ψ)ζ (η ) dη is first-order small, in the sense that o(v) ¯ = 0 and ∂o/∂v = 0 when evaluated at v. ¯ When

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aggregate shocks are small, so that v stays relatively close to v, ¯ Eπ [o(v )] is negligible. Equation (14) is the equivalent of the Black–Scholes–Merton formula, applied to Tobin’s q. The value of the option (debt) depends on the value of the underlying (q), and the delta of the option is the probability of default. If this probability is exactly zero, bond prices do not contain information about q. The fact that the sensitivity of b to q is given by δ is intuitive. Indeed, b responds to q precisely because a fraction δ of firms default on average each period. A one-unit move in aggregate q therefore translates into a δ move in the price of a diversified portfolio of bonds. To make equation (14) empirically relevant, we need to express it in terms of bond yields. All the prices we have discussed so far are in real terms, but, in practice, we observe nominal yields. Let r $ be the nominal risk-free rate, and let y$ be the nominal yield on corporate bonds. With short-term debt, the market value is equal to the nominal face value divided by 1 + y$ . Under the assumption we have made in this section, and neglecting the terms that are first-order small, a simple manipulation of equation (14) leads to the following proposition. PROPOSITION 2. To a first-order approximation, Tobin’s q is a linear function of the relative yields of corporate and government bonds,

(15)

qt ≈

1 + rt$ ψ + constant, δ(1 + r) 1 + yt$

where r is the real risk-free rate, ψ is average book leverage, and δ is the risk-neutral default rate. The proposition sheds light on existing empirical studies, such as Bernanke (1983), Stock and Watson (1989), and Lettau and Ludvigson (2002), showing that the spread of corporate bonds over government bonds predicts future output.5 This finding is consistent with q-theory, because the proposition shows that corporate bond spreads are, to first order, proportional to Tobin’s q. 5. In the proposition, I use the relative bond price (the ratio) instead of the spread (the difference) because this is more accurate when inflation is high. The approximation of small aggregate shocks made in this section refers to real shocks, but does not require average inflation to be small.

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IV. LONG-TERM DEBT AND PERSISTENT IDIOSYNCRATIC SHOCKS I now consider the case of long-term debt and persistent firmlevel shocks. The goal is to obtain a mapping from bond yields to Tobin’s q that extends the simple case presented above. As in the previous section, let s denote the aggregate state and let η denote the idiosyncratic component of the profit rate, defined in equation (10). With persistent idiosyncratic shocks, Tobin’s q and the investment rate depend on both s and η, and the value function is no longer additively separable. There is no closed-form solution for bond prices, and the approximation of Proposition 2 is cumbersome because of the fixed point problem in equation (7). I therefore turn directly to numerical simulations. I maintain for now the assumptions of a constant risk-free rate r and of constant book leverage ψ. I use a quadratic adjustment cost function: γ (x) = γ1 x + 0.5γ2 x 2 .

(16)

With this functional form, the investment equation is simply x = (q − γ1 ) /γ2 . Idiosyncratic profitability is assumed to follow an AR(1) process: η

ηt = ρη ηt−1 + ση εt .

(17)

Similarly, I specify aggregate dynamics as at − a¯ = ρa (at−1 − a) ¯ + σa εta .

(18) η

The shocks {εt }η∈[0,1] and εta follow independent normal distributions with zero mean and unit variance. The results discussed below are based on the following parameters: r 3%

ψ 0.45

φ 0.1

γ1 1

γ2 10

ρη 0.47

ση 14%

ρa 0.7

σa 4.5%

a/r ¯ 0.925

c 4.3%

Book leverage is set to 0.45 and average debt maturity to ten years (φ = 0.1), based on Leland (2004), who uses these values as benchmarks for Baa bonds. The parameter γ1 is irrelevant and is normalized to one in this section. There is much disagreement about the parameter γ2 in the literature. Shapiro (1986) estimates a value of around 2.2 years, and Hall (2004) finds even smaller adjustment costs.6 On the other hand, Gilchrist and Himmelberg 6. Shapiro (1986) estimates between 8 and 9 using quarterly data, which corresponds to 2 to 2.2 at annual frequencies.

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(1995) find values of around twenty years, and estimates from macro data are often implausibly high (Summers 1981). I pick a value of γ2 = 10 years, which is in the middle of the set of existing estimates. It turns out, however, that the mapping from bond yields to q is not very sensitive to this parameter. The parameters of equations (17) and (18) are calibrated using U.S. firm and aggregate data, as explained in Section V. Finally, the coupon rate c is chosen so that bonds are issued at par value, as in Leland (1998). We can now use the model to understand the relationship between bond prices and Tobin’s q. The main idea of the paper is to use the price of corporate bonds relative to Treasury to construct a measure of q. The model is simulated with the parameters just described. The processes (17) and (18) are approximated with discrete-state Markov chains using the method in Tauchen (1986). The investment rate x (s, η) and the value of the firm value v (s, η) are obtained by solving the dynamic programming problem in equation (3). Equation (7) is then used to compute the bond pricing function b (s, η). The aggregate bond price b (s) and the aggregate corporate yield y (s) are obtained by integrating over the ergodic distribution of η. Figure I presents the main result. It shows the model-implied aggregate q (s) as a function of the model-implied average relative bond price (φ + r ) / (φ + y (s)). Figure I is generated by considering all the possible values of the aggregate state variable s. Tobin’s q is an increasing and convex function of the relative price of corporate bonds. Figure I therefore extends Proposition 2 to the case of long-term debt, persistent firm-level shocks, and large aggregate shocks. The mapping from bond yields to Tobin’s q is conditional on the calibrated parameters, in particular on book leverage and idiosyncratic volatility. Figure II shows the comparative statics with respect to book leverage (ψ) and firm volatility (ση ). The comparative statics is intuitive. For a given value of q, an increase in leverage leads to more credit risk and lower bond prices, so the mapping shifts left when leverage increases. Similarly, for a given value of q, an increase in idiosyncratic volatility increases credit risk, and the mapping shifts left when volatility increases. In this case, the slope and the curvature of the mapping also change, and the intuition is given by Proposition 2: idiosyncratic volatility increases the delta of the bond with respect to q. In the next section, mappings like the ones displayed in Figure II are used to construct a new measure of q from observed

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1.4 1.3 1.2

Tobin q

1.1 1 0.9 0.8 0.7

0.76

0.78

0.8

0.9 0.82 0.84 0.86 0.88 Relative price of corporate bonds

0.92

0.94

0.96

FIGURE I Aggregate Tobin’s q and the Relative Price of Corporate Bonds The figure shows the implicit mapping between average bond prices and q across aggregate states (with different aggregate profit rates). The price of corporate bonds relative to risk-free bonds is defined as (0.1 + r)/(0.1 + y), where r is the risk-free rate and y is the average yield on corporate bonds. The factor 0.1 reflects the average maturity of 10 years. The mapping is for benchmark values of book leverage, idiosyncratic volatility, and a constant risk-free rate of 3% (see Table II).

bond yields, leverage, and volatility. With respect to leverage, it is important to emphasize the role played by the maintained assumptions of no taxes and no bankruptcy costs. These assumptions imply that capital structure is irrelevant for real decisions (i.e., investment) and for firm value (Modigliani and Miller 1958). Leverage is relevant for bond pricing, however. Bond prices depend on leverage in the same way that they do in the model of Merton (1974): higher leverage increases default risk and therefore decreases the relative price of corporate bonds. Thus, it is crucial to use a mapping that is conditional on leverage to recover the correct value of q. To see why, imagine a world where firms choose their leverage to stabilize their credit spreads. In this case, the correlation between spreads and investment could be arbitrarily small. This would not invalidate the construction of q, however, because the explanatory power would then come from observed changes in leverage. In terms of Figure II, firms would

1025

THE BOND MARKET’S q 1.5 1.4

Leverage 0.4 Leverage 0.5 Leverage 0.6

1.3 1.2

Tobin q

1.1 1 0.9 0.8 0.7 0.6

a 0.5 0.6

0.65

0.7

0.75 0.8 0.85 0.9 Relative price of corporate bonds

0.95

1

0.95

1

1.5 Firm σ 0.1 Firm σ 0.15 Firm σ 0.2

1.4 1.3 1.2

Tobin q

1.1 1 0.9 0.8 0.7 0.6

b 0.5 0.6

0.65

0.7

0.75 0.8 0.85 0.9 Relative price of corporate bonds

FIGURE II Impact of Leverage and Firm Volatility Calibration a in Figure I, except for book leverage in the top panel, and firm volatility in the bottom panel. (a) Mapping for different values of book leverage; (b) mapping for different volatilities of idiosyncratic shocks.

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QUARTERLY JOURNAL OF ECONOMICS TABLE I SUMMARY STATISTICS: QUARTERLY AGGREGATE DATA, 1953:2–2007:2

I/K E(inflation) yBaa r 10 (0.1 + r 10 )/(0.1 + yBaa ) Classic Tobin’s q Bond market’s q

Obs.

Mean

St. dev.

217 217 217 217 217 217 217

0.105 0.037 0.082 0.065 0.908 2.029 1.500

0.010 0.025 0.030 0.027 0.033 0.845 0.117

Min 0.082 −0.016 0.035 0.023 0.796 0.821 1.154

Max 0.125 0.113 0.170 0.148 0.974 4.989 1.720

Notes. Investment and replacement cost of capital are from NIPA. Expected inflation is from the Livingston survey. Yields on 10-year Treasuries and Moody’s Baa index are from FRED. Classic Tobin’s q is computed from the flow of funds, following Hall (2001). Bond market’s q is computed using the structural model, and its mean is normalized to 1.5.

maintain a constant relative price, but their leverage would jump from one mapping to another. I return to this issue in Section VII. V. EMPIRICAL EVIDENCE In this section, I construct a new measure of q using only data from the bond market. I then compare this measure to the usual measure of q, and I assess their respective performances in the aggregate investment equation. The data used in the calibration are summarized in Table I. All the parameters used in the calibration, and the empirical moments used to infer them, are presented in Table II. V.A. Data and Estimation of the Parameters I now describe the data used to estimate the parameters of equations (17) and (18) and the construction of q. Leverage. In the baseline case, book leverage is set to 0.45 based on Leland (2004). Using Compustat, I find a slow increase in average book leverage from 0.4 to 0.55 over the postwar period (Figure IIIa). The sample includes nonfinancial firms, with at least five years of nonmissing values for assets, stock price, operating income, debt, capital expenditures, and property, plants, and equipment. Idiosyncratic Risk. Equation (17) is estimated with firm-level data from Compustat. The profit rate is operating income divided by the net stock of property, plants, and equipment, and η is the idiosyncractic component of this profit rate. Firms in finance and

1027

THE BOND MARKET’S q TABLE II PARAMETERS OF BENCHMARK MODEL Data Parameters chosen exogenously Real risk-free rate r Curvature of adjustment cost function γ2 Average maturity 1/ Book leverage Parameters directly observed in the data Persistence of idiosyncratic profit rate ρη Volatility of idiosyncratic innovations ση Persitence of aggregate profit rate ρa Moments matched Relative bond price (mean) (0.1 + r)/(0.1 + y) Relative bond price (volatility (0.1 + r)/(0.1 + y) of detrended series) Average bond issued at par value E[b]/ f Implied parameters Average profit rate a/r Volatility of aggregate innovations σa Coupon rate c

Model

3% 10 years 10 years 0.45 0.47 0.14 0.7

0.47 0.14 0.7

0.908 0.027

0.908 0.027

1

1

0.925 0.045 0.043

real estate are excluded. The panel regression includes firm fixed effects to remove permanent differences in average profitability across firms or industries due to accounting and technological differences. The estimated baseline parameters, ρη = 0.47 and ση = 14%, are consistent with many previous studies.7 An important issue is that the idiosyncratic volatility of publicly traded companies is not constant. Campbell and Taksler (2003) show that changes in idiosyncratic risk have contributed to changes in yield spreads. The frequency of accounting data is too low to estimate quarterly changes in volatility. In addition, we need a forward-looking measure of idiosyncratic risk to capture market expectations. For all these reasons, the best measure should be based on idiosyncratic stock returns. Following the standard practice in the literature, I use a six-month moving average 7. For instance, Gomes (2001) uses a volatility of 15% and a persistence of 0.62 for the technology shocks. Hennessy, Levy, and Whited (2007) report a persistence of the profit rate of 0.51 and a volatility of 11.85%, which they match with a persistence of 0.684 and a volatility of 11.8% for the technology shocks. Note that in both of these papers, firms operate a technology with decreasing returns. Here, by contrast, the technology has constant returns to scale. This explains why some details of the calibration are different.

1028

0.4

a

0.35

0.8

0.85

0.45

0.9

0.5

0.95

0.55

1

0.6

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1955

1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

Book leverage (right axis)

0.12

0.14

0.16

0.18

Relative bond price

b 1955

1960

1965

1970

1975

1980

Volatility (returns)

1985

1990

1995

2000

2005

Volatility (sales)

FIGURE III The Components of Bond Market q Leverage is average book leverage among nonfinancial firms in Compustat. Idiosyncratic volatility is estimated either from idiosyncratic stock returns or from the dispersion of sales growth. Both measures are then translated into the parameter ση of the model. Relative bond price is the relative price of corporate and government bonds, defined as (0.1 + r)/(0.1 + y), using Moody’s Baa and 10-year Treasury yields. (a) Bond prices and leverage; (b) two measures of idiosyncratic risk.

THE BOND MARKET’S q

1029

of the monthly cross-sectional standard deviation of individual stock returns. I scale this new measure to have a sample mean of η 14% to obtain σˆ t , a time-varying estimate of idiosyncratic risk. As a robustness check, I also consider the cross-sectional standard deviation of the growth rate of sales, measured from Compustat, as a measure of volatility that avoids using stock returns.8 The η two measures of σˆ t are presented in Figure IIIb. Aggregate Bond Prices. Moody’s Baa index, denoted ytBaa , is the main measure of the yield on risky corporate debt. Moody’s index is the equal weighted average of yields on Baa-rated bonds issued by large nonfinancial corporations.9 Following the literature, the 10-year treasury yield is used as the benchmark risk-free rate. Both rt10 and ytBaa are obtained from FRED.10 For equation (18), using annual NIPA data on corporate profits and the stock of nonresidential capital over the postwar period, I estimate ρa = 0.7. The parameters a¯ and σa cannot be calibrated with historical aggregate profit rates because they must capture risk-adjusted values, not historical ones.11 Instead, the model must be consistent with observed bond prices. Three parameters are thus not directly observed in the data: these are c (the coupon rate), a, ¯ and σa . Their values are inferred by matching empirical and simulated moments. The empirical moments are the mean and standard deviation of the price of Baa bonds 8. The dispersion of sales growth is not a perfect measure either, because permanent differences in growth rates would make dispersion positive even if there is no risk. There are other ways to define idiosyncratic risk at the firm level, but they produce similar trends. See Comin and Philippon (2005) for a comparison of various measures of firm volatility. See also Campbell et al. (2001) and Davis et al. (2006) for evidence on privately held companies. 9. To be included in the index, a bond must have a face value of at least 100 million, an initial maturity of at least 20 years, and most importantly, a liquid secondary market. Beyond these characteristics, Moody’s has some discretion on the selection of the bonds. The number of bonds included in the index varies from 75 to 100 in any given year. The main advantages of Moody’s measure are that it is available since 1919, and that it is broadly representative of the U.S. nonfinancial sector, because Baa is close to the median among rated companies. 10. Federal Reserve Economic Data: http://research.stlouisfed.org/fred2/. The issue with using the ten-year treasury bond is that it incorporates a liquidity premium relative to corporate bonds. To adjust for this, it is customary to use the LIBOR/swap rate instead of the treasury rate as a measure of risk-free rate (see Duffie and Singleton [2003] and Lando [2004]), but these rates are only available for relatively recent years. I add 30 basis points to the risk-free rate to adjust for liquidity (see Almeida and Philippon [2007] for a discussion of this issue). 11. Note that, in theory, the same applies to ρa , because persistence under the risk-neutral measure can be different from persistence under the physical measure. In practice, however, the difference for ρa is much smaller than for a¯ or σa . I therefore take the historical persistence to be a good approximation of the risk neutral persistence. Section VII shows that the model is robust to various assumptions regarding aggregate dynamics.

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relative to Treasuries, defined as (φ + rt$ )/(φ + yt$ ), where y$ is the yield on Baa corporate bonds and r $ is the yield on government bonds. The final requirement is that the average bond be issued at par. The three parameters c, a, ¯ and σa are chosen simultaneously to match the par-value requirement and the two empirical moments. The parameters inferred from the simulated moments are c = 4.3%, a/r ¯ = 0.925, and σa = 4.5%. Expected Inflation and Real Rate. The Livingston survey is used to construct expected inflation, and the yield on the ten-year treasury to construct the ex ante real interest rate, rˆtreal . Creating qbond . The model described in Section IV constructs q from the relative price of corporate bonds, conditional on the baseline values for the risk-free rate, book leverage, and idiosyncratic risk. As I have just explained, the risk-free rate, book leverage, and idiosyncratic volatility move over time. Therefore, qbond is a function of four observed inputs: average book leverage ψˆ t , η average idiosyncratic volatility σˆ t , the ex ante real rate rˆtreal , and the relative price of corporate bonds φ + rt10 η ˆ bond real (19) . qt =F ; σˆ t ; ψt ; rˆt φ + ytBaa Figure III displays the three main components: leverage, volatility, and the relative price. In theory, the dynamics of the four inputs must be jointly specified to construct the mapping of equation (19). Quantitatively, however, it turns out that one can estimate mappings with respect to (φ + rt10 )/(φ + ytBaa ) assuming constant values for the other three parameters, as I did in Figure II. For the risk-free rate, this follows from a well-known fact in the bond pricing literature: risk-free rate dynamics plays a negliη gible role in fitting corporate spreads. For σˆ t and ψˆ t , the historical series are so persistent that there is little difference between the mapping assuming a constant value and the mapping conditional on the same value in the time-varying model.12 Classic Measure of Tobin’s q. The usual measure of Tobin’s q is constructed from the flow of funds as in Hall (2001). The usual 12. To check this, I construct an extended Markov model where all the parameters follow AR(1) processes calibrated from the data. I then create mappings conditional on each realization of the parameters and I compare them to the mappings from Figure II. I find that the discrepancies are small for volatility and invisible for book leverage and the risk-free rate. Detailed results and figures are available upon request.

1031

1

2

3

4

5

THE BOND MARKET’S q

1955

1960

1965

1970

1975

1980

Usual q

1985

1990

1995

2000

2005

Bond q

FIGURE IV Usual Measure of q and Bond Market’s q Tobin’s q is constructed from the flow of funds, as in Hall (2001). Bond q is constructed from Moody’s yield on Baa bonds, using the structural model calibrated to the observed evolutions of book leverage and firm volatility, expected inflation from the Livingston survey, and the yield on 10-year Treasury bonds.

measure is the ratio of the value of ownership claims on the firm less the book value of inventories to the reproduction cost of plant and equipment. All the details on the construction of this measure can be found in Hall (2001). Investment and Capital Stock. I use the series on private nonresidential fixed investment and the corresponding current stock of capital from the Bureau of Economic Analysis. Table I displays the summary statistics. V.B. Investment Equations Figure IV shows the two measures of q: qusual , constructed from the flow of funds as in Hall (2001), qbond constructed using bond yields, leverage, idiosyncratic volatility, expected inflation, and the theoretical mappings described in the previous sections. The average value of qbond is arbitrary, because γ1 is a free parameter, and I normalize it to 1.5. Figure IV shows that qusual is approximately seven times more volatile than qbond . The standard deviation of qusual is 0.845, whereas the standard deviation

QUARTERLY JOURNAL OF ECONOMICS

0.08

1

0.09

2

0.1

q

I /K

3

0.11

4

0.12

5

0.13

1032

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

I /K

Usual q

FIGURE V Usual Measure of q and Investment Rate I/K is corporate fixed investment over the replacement cost of equipment and structure. Usual q is constructed from the flow of funds, as in Hall (2001).

of qbond is only 0.117, as reported in Table I. It is also interesting to note that qbond is approximately stationary, because the mappings take into account the evolution of idiosyncratic volatility and book leverage, as explained above. In the short run, qbond depends mostly on the relative price component. Year-to-year changes in (φ + rt10 )/(φ + ytBaa ) account for 85% of the year-to-year changes in qbond . In the long run, leverage and, especially, idiosyncratic risk are also important. Figure V shows qusual and the investment rate in structure and equipment. Figure VI shows qbond and the same investment rate. The corresponding regressions are reported in the upper panel of Table III. They are based on quarterly data. The investment rate in structure and equipment is regressed on the two measures of q, measured at the end of the previous quarter: bond usual + β e qt−1 + εt . xt = α + β bqt−1

The standard errors control for autocorrelation in the error terms up to four quarters. qbond alone accounts for almost 60% of aggregate variations in the investment rate. qusual accounts for only

1033

1.1

0.08

1.2

0.09

1.3

0.1

I /K

1.4 1.5 Bond q

0.11

1.6

0.12

1.7

1.8

0.13

THE BOND MARKET’S q

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

I /K

Bond q

FIGURE VI Bond Market’s q and Investment Rate I/K is corporate fixed investment over the replacement cost of equipment and structure. Bond q is constructed from Moody’s yield on Baa bonds, using the structural model calibrated to the observed evolutions of book leverage and firm volatility, expected inflation from the Livingston survey, and the yield on 10-year Treasury bonds.

10% of aggregate variations. Moreover, once qbond is included, the standard measure has no additional explanatory power. Looking at Figure V, the fit of the investment equation is uniformly good, except in the late 1980s and early 1990s, where, even though the series remain correlated in changes (see below), there is a persistent discrepancy in levels. qbond is more correlated with the investment rate, hence the better fit of the estimated equation, but it is also less volatile than qusual . As a result, the elasticity of investment to q is almost eighteen times higher with this new measure, which is an encouraging result because the low elasticity of investment with respect to q has long been a puzzle in the academic literature. The estimated coefficient still implies adjustment costs that are too high, around 15 years, but, as Erickson and Whited (2000) point out, there are many theoretical and empirical reasons that the inverse of the estimated coefficient is likely to underestimate the true elasticity.13 13. Note that the mapping is calibrated assuming γ2 = 10, so in theory the coefficient should be 0.1. In Table III, it is 0.065. I have also solved for the model

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QUARTERLY JOURNAL OF ECONOMICS TABLE III BENCHMARK REGRESSIONS

Bond q (t − 1) S.e. Classic q (t − 1) S.e. Bond q (t − 1), alt. measure S.e. Observations OLS R2 [bond q] (t − 5, t − 1) S.e. [classic q] (t − 5, t − 1) S.e. [profit rate] (t − 5, t − 1) S.e. [bond q] (t − 5, t − 1), alt. measure S.e. Observations OLS R2

0.0650∗∗∗ (0.00594)

216 .574

Equation in levels: I/K(t) 0.0629∗∗∗ (0.00642) 0.00366∗∗ 0.000928 (0.00155) (0.000970)

216 .095

Estimation in changes: 0.0515∗∗∗ (0.00495) 0.00700∗∗∗ (0.00187)

212 .613

212 .102

216 .580

0.0521∗∗∗ (0.00706) 216 .432

I/K(t) − I/K(t − 4) 0.0471∗∗∗ (0.00584) 0.00240∗ (0.00133) 0.0530 (0.0514) 0.0517∗∗∗

212 .628

(0.00500) 212 .561

Notes. Fixed private nonresidential capital and investment series are from the BEA. Quarterly data, 1953:3 to 2007:2. Classic q is constructed from the flow of funds, as in Hall (2001). Bond q is constructed by applying the structural model to Corporate and Treasury yields, expected inflation, book leverage, and firm volatility measured with idiosyncratic stock returns. The alternate measure of Bond q uses idiosyncratic sales growth volatility as an input. Newey–West standard errors with autocorrelation up to four quarters are reported in parentheses. ∗ , ∗∗ , and ∗∗∗ denote statistical significance at the 10%, 5%, and 1% levels. Constant terms are omitted.

Figure VII shows the four-quarter difference in the investment rate, a measure used by Hassett and Hubbard (1997), among others, because of the high autocorrelation of the series in levels. The corresponding regressions are presented in the bottom panel of Table III. The fit of the equation in difference is even better than the fit in levels, with an R2 above 60%. In the third regression, the change in corporate cash flows over capital is added to the right-hand side of the equation, but it is insignificant and does not improve the fit of the equation. The construction of qbond uses idiosyncratic stock returns to measure firm volatility. Note that using idiosyncratic return volatility is justified even when the aggregate stock market is assuming γ = 15. This makes the theoretical and actual coefficients similar, but does not change anything to the rest of the results. See also Section VII for a discussion of biases.

1035

–0.02

–0.01

0

0.01

0.02

THE BOND MARKET’S q

1955

1960

1965

1970

1975

Change in I /K from t – 4 to t

1980 1985 time

1990

1995

2000

2005

Predicted with lagged bond q

FIGURE VII Four-Quarter Changes in Investment Rate, Actual and Predicted I/K is corporate fixed investment over the replacement cost of equipment and structure. Bond q is constructed from Moody’s yield on Baa bonds, using the structural model calibrated to the observed evolutions of book leverage and firm volatility, expected inflation from the Livingston survey, and the yield on 10-year Treasury bonds.

potentially mispriced. Mispricing across firms is limited by the possibility of arbitrage. In the aggregate, however, arbitrage is much more difficult. There is therefore no inconsistency in using the idiosyncratic component of stock returns to measure idiosyncratic risk, although acknowledging that the aggregate stock market can sometimes be over valued. Nonetheless, one might be concerned about the use of equity returns here, and I have repeated the calibration using the standard deviation of sales growth as a measure of volatility. The results, in the last column of Table III, are somewhat weaker than with the benchmark model. The reason is that sales volatility is a lagging indicator of idiosyncratic risk. Hilscher (2007) shows that the bond market is actually forward-looking for volatility. As a result, using a measure of volatility that lags the true information—and all accounting measures do— creates a specification error. This matters less for the equation in changes because of the smaller role of volatility in that equation.

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The conclusions from this empirical section are the following: • With aggregate U.S. data, qbond fits the investment equation well, both in levels and in differences. • The estimated elasticity of investment to qbond is 18 times higher than the one estimated with qusual . • Corporate cash flows do not have significant explanatory power once qbond is included in the regression. V.C. Further Evidence The evidence presented above is based on the construction of qbond in equation (19). In this section, I provide evidence on the explanatory power of the components separately, and on the role of nonlinearities in the model. I also test the predictive power of the model. The results are in Tables IV and V. Explanatory Power of Individual Components. The econometric literature has studied the predictive power of default spreads for real economic activity.14 Table IV shows the explanatory power of the components of qbond , in levels and in four-quarter differences. Consider first the top part of Table IV, for the regressions in level. Column (1) shows that the Baa spread, by itself, has no explanatory power for investment. The explanatory power appears only when idiosyncratic volatility and leverage are also included, in Column (3). These factors have not been used in the empirical literature. Their empirical importance provides support for the theory developed in this paper. In addition, notice that even when all the components are entered linearly, the explanatory power is only 45%. By contrast, the qbond has an R2 of 57.4% with one degree of freedom instead of four. This shows that the nonlinearities are important in the level equation, as explained below. For the equation in four-quarter differences, the spread by itself has significant explanatory power. This is what one would expect, because the low-frequency movements in leverage and volatility matter less in these regressions. Nonetheless, leverage and volatility are still highly significant. The unrestricted linear 14. Bernanke (1983) notes that the spread of Baa over treasury went “from 2.5 percent during 1929–30 to nearly 8 percent in the mid-1932” and shows that the spread was a useful predictor of industrial production growth. Using monthly data from 1959 to 1988, Stock and Watson (1989) find that the spread between commercial paper and Treasury bills predicts output growth. Some of these relationships are unstable over time (see Stock and Watson [2003] for a survey).

1037

THE BOND MARKET’S q TABLE IV DECOMPOSING BOND q

−0.166 yBaa − r 10 (t − 1) S.e. (0.189) Real risk-free rate (t − 1) S.e. Idiosyncratic volatility (t − 1) S.e. Book leverage (t − 1) S.e. [0.1 + r 10 ]/[0.1 + yBaa ] (t − 1) S.e. Real discount factor (t − 1) S.e. Quadratic term (t − 1) S.e. N 216 .013 OLS R2

Equation in levels: I/K(t) −0.152 −1.051∗∗∗ (0.189) (0.177) −0.0700 −0.0781 (0.0796) (0.0744) 0.278∗∗∗ 0.424∗∗∗

0.407∗∗∗

(0.0759) (0.0672) (0.0690) 0.0910∗∗∗ 0.0633∗∗∗ 0.0727∗∗∗ (0.0214) (0.0172) (0.0159) 0.252∗∗∗ 0.263∗∗∗ (0.0268) 0.203∗∗∗ (0.0673)

216 .023

216 .451

216 .582

Estimation in changes: I/K(t) − I/K(t − 4) [yBaa − r 10 ](t − 5, t − 1) −0.942∗∗∗ −0.953∗∗∗ −0.997∗∗∗ S.e. (0.103) (0.108) (0.0910) [real riskfree rate] −0.0237 −0.00297 (t − 5, t − 1) S.e. (0.0355) (0.0338) 0.265∗∗∗ [idiosyncratic 0.283∗∗∗ volatility] (t − 5, t − 1) S.e. (0.0885) (0.0896) [book leverage] 0.172∗∗∗ 0.142∗∗∗ (t − 5, t − 1) S.e. (0.0516) (0.0515) [(0.1 + r 10 )/ 0.199∗∗∗ (0.1 + yBaa )](t − 5, t − 1) S.e. (0.0195) [real discount factor] 0.0787∗ (t − 5, t − 1) S.e. (0.0419) [quadratic term] (t − 5, t − 1) S.e. Observations 212 212 212 212 .478 .479 .618 .618 OLS R2

(0.0291) 0.187∗∗∗ (0.0649) 1.069∗∗ (0.522) 216 .604

0.270∗∗∗ (0.0912) 0.133∗∗∗ (0.0502) 0.201∗∗∗ (0.0195) 0.0765∗ (0.0412) 0.398 (0.293) 212 .622

Notes. Fixed private nonresidential capital and investment series are from the BEA. Quarterly data, 1953:3 to 2007:2. The ex ante real rate is the nominal rate minus expected inflation from the Livingston survey. The real discount factor is (1 + E[inflation])/(1+nominal rate). Firm volatility is measured with idiosyncratic stock returns. The nominal rates are r 10 for 10-year Treasury bonds, and yBaa for Moody’s index of Baa bonds. Quadratic term is the square of the relative price of Baa bonds minus its mean: [(0.1 + r 10 )/(0.1 + yBaa ) − 0.9]2 . Newey–West standard errors with autocorrelation up to 4 quarters are reported in parentheses. ∗ , ∗∗ , and ∗∗∗ denote statistical significance at the 10%, 5% and 1% levels. Constant terms are omitted.

0.396∗∗∗ (0.0778) 215 .398

0.148∗∗∗ (0.0231)

0.337∗∗∗ (0.0832) 215 .341

0.710∗∗∗ (0.182)

0.131 (0.0935) 215 .430

0.160∗∗∗ (0.0251) 0.760∗∗∗ (0.199)

0.161∗∗∗ (0.0247) 0.797∗∗∗ (0.200) 0.0130 (0.00955) 0.0996 (0.0928) 215 .443 0.0119 (0.00917) 0.169∗∗∗ (0.0585) 0.00976∗∗∗ (0.00279) 0.0206 (0.0832) 215 .149

Growth rate of consumption

0.0279 (0.0417) −0.162 (0.346) 0.0401∗∗ (0.0184) 0.511∗∗∗ (0.0543) 215 .335

Growth rate of residential investment

Notes. Maximum likelihood estimation of coefficients and standard errors, assuming AR(1) model. The R2 is for the corresponding OLS regression with lagged dependent variable on the right-hand side. Fixed private nonresidential investment series is from the BEA. Quarterly data, 1953:3 to 2007:2. Bond q is constructed by applying the structural model to Corporate and Treasury yields, expected inflation, book leverage, and firm volatility measured with idiosyncratic stock returns. Constant terms are omitted.

[bond q] (t − 1) S.e. log[real GDP] (t − 1) S.e. [classic Q] (t − 1) S.e. AR(1) S.e. Observations R2 of OLS

Growth rate of private nonresidential fixed investment

TABLE V PREDICTIVE REGRESSIONS, ONE QUARTER AHEAD: MAXIMUM LIKELIHOOD ESTIMATION OF AUTOREGRESSIVE MODEL

1038 QUARTERLY JOURNAL OF ECONOMICS

THE BOND MARKET’S q

1039

model has an R2 of 61.6%, compared to 61.3% for the bond q model. This suggests that, also as expected, nonlinear effects are not crucial for the specification in changes. Nonlinear Effects. There are several nonlinear effects in the model. Consider equation (4): Tobin’s q has two components, the real discount factor and the expected risk-neutral value of capital, Eπ [v(ω )|ω]. This letter item is a function of the relative price of corporate bonds, as shown in Figures I and II. Thus, the model suggests the use of the relative price (φ + rt10 )/(φ + ytBaa ) instead of the spread ytBaa − rt10 . When rates are stable, the difference between the spread and the relative price is negligible. In the data, however, the level of nominal rates changes a lot. A given change in the spread has a larger impact on the relative price when rates are low than when they are high. Column (4) provides strong support for this first nonlinearity. The relative price does much better than the spread in the level regression.15 The R2 increases from 45.1% to 58.2% because of the nonlinear correction. A second nonlinearity comes from the mapping of Figure I. Tobin’s q is a convex function of the relative bond price. Column (5) shows that this effect is significant, but it only increases the R2 by 2 percentage points. The last column of Table IV can also be compared to the first column of Table III. In level, the structural model has a fit of 57.4%. The unrestricted nonlinear model has a fit of 60.4%. In a statistical sense, the difference is significant, but in an economic sense, it does not appear very important. In differences, the respective performances are 61.3% and 62.2%. These results support the restrictions imposed by the theory. Predictive Regressions. Table V reports the results from predictive regressions of the growth rate of three macroeconomic variables: real corporate investment, real consumption expenditures, and real residential investment. In each case, I run two separate regressions. I estimate an AR(1) model by maximum likelihood to obtain the correct coefficients and standard errors. I also run an OLS regression with the lagged dependent variable on the RHS to get a sense of the R2 of the simple linear regression. 15. Note that, in theory, this could also apply to the real discount factor: (1 + E[inflation])/(1 + r $ ) is not the same as E[inflation] − r $ when nominal shocks are large. Empirically, this nonlinearity seems to matter much less, probably because the real rate is not as volatile as the Baa yield.

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The first column shows that qbond is a very significant predictor of corporate investment growth. It predicts better than the “accelerator” model based on lagged output growth (column (2)). While lagged output growth still has significant marginal forecasting power, it increases the R2 by only 3 percentage points (column (3)). In addition, the coefficient on qbond actually goes up. Column (4) shows that qusual has no predictive power for corporate investment.16 The last two columns focus on consumption and residential investment. Although qbond is the best predictor of corporate investment, it does not predict housing or consumption. qusual , on the other hand, does not predict corporate investment, but it does predict housing and (to some extent) consumption. These results are suggestive of wealth effects from the equity market. They are consistent with the results of Hassett and Hubbard (1997) but clearly inconsistent with the usual implementation of the q-theory. The conclusions from this empirical section are the following: • All the components identified by the theory (bond spreads, volatility, leverage, risk-free rate) are statistically and economically significant. • The fit of the restricted structural model is almost as good as the fit of the unrestricted regressions. • The nonlinearities of the model (relative price instead of spreads, convexity of mapping) are important for the level regressions. • The bond market predicts future corporate investment well, whereas the equity market has no marginal predictive power. VI. THEORETICAL EXPLANATIONS The results so far show that it is possible to link corporate investment and asset prices, using the corporate bond market and modern asset pricing theory. They do not explain why the usual approach fails, however. This section sheds some light on this complex question. 16. Fama (1981) shows that stock prices have little forecasting power for output. Cochrane (1996) finds a significant correlation between stock returns and the growth rate of the aggregate capital stock, but Hassett and Hubbard (1997) argue that it is driven by the correlation with residential investment, not corporate investment. In any case, I find that the bond market’s q outperforms the usual measure both in differences and in levels.

THE BOND MARKET’S q

1041

It is important to recognize that a satisfactory explanation must address two related but distinct issues: 1. Why is qusual more volatile than qbond ? 2. Why does qbond fit the investment equation better? I consider two explanations.17 The first explanation is based on growth options and the distinction between average and marginal q. The second explanation is based on mispricing in the equity market. I chose these explanations because they provide useful benchmarks. They are not mutually exclusive, and they are not the only possible explanations. VI.A. Growth Option Interpretation Suppose that, in addition to the value process in equation (3), the firm also has a growth option of value Gt . Total firm value is then Vt = vt kt−1 + Gt .

(20)

Consider for simplicity the example of Section III, with short-term debt and a constant risk-free rate. The value of short-term debt is (21)

Bt =

1 Eπ [min( t ; vt+1 kt + Gt+1 )]. 1+r t

Let Gt be a binary variable. Gt = GH , with risk-neutral probability λt−1 and GL otherwise. The following proposition states that a growth option with enough skewness can explain why qbond fits better than qusual . PROPOSITION 3. Consider the model of equations (20) and (21). By choosing λt and GL small enough, and GH large enough, the fit of the investment equation can be arbitrarily good for qbond , and arbitrarily poor for qusual . Proof. See the Appendix. The intuition behind Proposition 3 is straightforward. A small probability of a large positive shock has a large impact on equity prices, and almost no impact on bond prices. Because growth options do not depend on the capital stock, news about the likelihood of these future shocks does not affect investment. In essence, 17. For a investigation of whether the same pricing kernel can price bonds and stocks, see Chen, Collin-Dufresne, and Goldstein (forthcoming).

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growth options drive wedges between bond and equity prices, and between marginal and average q. What are the possible interpretations of these shocks? The simplest one is that firms earn organizational rents. Think of a large industrial corporation with outstanding organizational capital. This firm will be able to seize new opportunities if and when they arrive. This might happen through mergers and acquisitions or through internal development of new lines of business. Investing more in the current business and current technology does not improve this option value.18 To summarize, the rational interpretation proposes the following answers to the two questions posed at the beginning of this section: 1. Why is qusual more volatile than qbond ? Because growth options affect stocks much more than bonds. 2. Why does qbond fit the investment equation better? Because growth options are unrelated to current capital expenditures. The example given is obviously extreme, but the lesson is a general one. It is not difficult to come up with a story where current capital expenditures are well explained by the bond market, whereas firm creation, IPOs, and perhaps R&D, are better explained by the equity market. A complete understanding of these joint dynamics is an important topic for future research. VI.B. Mispricing Interpretation Stein (1996) analyzes capital budgeting in the presence of systematic pricing errors by investors, assuming that managers have rational expectations. He emphasizes three crucial aspects of capital budgeting in such a world: (i) the true NPV of investment, (ii) the gains from trading mispriced securities, and (iii) the costs of deviating from an optimal capital structure in order to achieve (i) and (ii). For the purpose of my paper, the most important result is that when capital structure is not a constraint, and when managers have long horizons, real investment decisions are not influenced by mispricing (Stein 1996, Proposition 3). 18. Some other expenditures could be complement with the option value. These could include R&D and reorganizations. At the aggregate level, one might think that new options were realized by new firms. This would explain why IPOs are correlated with the equity market (Jovanovic and Rousseau 2001). For a model of growth option at the firm level, see Abel and Eberly (2005).

THE BOND MARKET’S q

1043

Gilchrist, Himmelberg, and Huberman (2005) consider a model where mispricing comes from heterogeneous beliefs and short sales constraints. They show that increases in dispersion of investor opinion cause stock prices to rise above their fundamental values. This leads to an increase in q, share issues, and real investment. The main difference from Stein (1996) is that they assume that investors do not overvalue cash held in the firm. This assumption rules out the separation of real and financial decisions: managers who seek to exploit mispricing must alter their investment decisions and Proposition 3 in Stein (1996) does not hold. However, Gilchrist, Himmelberg, and Huberman (2005) show that even large pricing errors need not have large effects on investment. Thus, it is possible to explain the fact that investment does not react much to equity mispricing, even when the strict dichotomy of Stein (1996)’s Proposition 3 fails. Neither Stein (1996) nor Gilchrist, Himmelberg, and Huberman (2005) consider the role of bonds and stocks separately, so it appears that the story is still incomplete. It turns out, however, that recent work in behavioral finance has shown that skewed assets are more likely to be mispriced (Barberis and Huang 2007; Brunnermeier, Gollier, and Parker 2007; Mitton and Vorkink 2007). A direct implication is that mispricing is more likely to appear in the equity market than in the bond market. Of course, mispricing can also happen in the bond market. Piazzesi and Schneider (2006), for instance, analyze the consequences for asset prices of disagreement about inflation expectations. To summarize, the behavioral interpretation proposes the following answers to the two questions posed at the beginning of this section: 1. Why is qusual more volatile than qbond ? Because mispricing is more likely in the equity market than in the bond market. 2. Why does qbond fit the investment equation better? Because managers do not react (much) to mispricing. The growth option and mispricing interpretations are not mutually exclusive. In fact, the term Gt in equation (20) is the most likely to be mispriced. The rational and behavioral explanations simply rely on different critical assumptions. In the rational case, Gt must not depend on k, otherwise investment would respond. In the behavioral story, it is important that managers have long horizons.

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VII. THEORETICAL ROBUSTNESS The beauty of the standard q theory is its parsimony. Beyond the assumptions of constant returns and convex costs, it is extremely versatile. In equation (4), the sources of variations in q(ω) include changes in the term structure of risk-free rates, cash flow news that has aggregate, industry, and firm components, and changes in risk premia that separate the market value Eπ [v ] from the objective expectation E[v ]. These multidimensional shocks can be combined in arbitrary ways, and yet their joint impact on investment can be summarized by one real number. Unfortunately, the standard approach fails. The previous section has presented two explanations for this failure, as well as for the (relative) success of the new approach. The new approach, however, is not as model-free as the standard approach. The mappings of Figures I and II are constructed under specific assumptions regarding firm and aggregate dynamics. The goal of this section is to study the theoretical robustness of the new approach. To do so, I focus on three issues: • Is there an exact mapping at the firm level, similar to the one in Figure I, for aggregate q? The answer turns out to be no, but qbond is still a useful measure. • Suppose that aggregate dynamics does not follow a simple autoregressive process under the risk neutral measure. Would the misspecified mapping of Figure I still deliver a good fit? Yes. • What happens when the Modigliani–Miller assumptions do not hold? If anything, the model seems to work better in this case. VII.A. Firm-Level Mappings I first study the extent to which the aggregate mapping of Figure II applies at the firm level. Figure VIII and the left part of Table VI report the results based on a simulated panel of fifty years and 100 firms, using the benchmark model with the parameters in Table II. To get an exact mapping, there must be a monotonic relationship between asset value and bond prices. This is typically the case when there is only one dimension of heterogeneity. In the top left panel of Table VI, the R2 for the aggregate regression is 1 and the estimated elasticity is exactly equal to 1/γ2 (0.1, because γ2 is calibrated to 10 years). At the firm level, there are two sources of

1045

0

0.5

Tobin's q 1

1.5

2

THE BOND MARKET’S q

0.6

0.7 0.8 Relative price of corporate bonds

0.9

1

FIGURE VIII Simulations of a Panel of Firms 5,000 firm–year observations of relative bond price and Tobin’s q. Simulation with constant real rate of 3%, constant idiosyncratic volatility, and constant book leverage.

variation, aggregate and idiosyncratic. Conditional on one shock, there is an exact mapping,19 but there is no guarantee that the ranking would be preserved across several types of shocks. In fact, Figure VIII shows that they are not.20 The bottom left panel of Table VI shows that R2 for firm-level regressions is less than one. In the univariate regression, this does not bias the point estimate. In the multivariate regression, firm-level cash flows are significant, R2 increases, but the point estimate of qbond becomes unreliable. The conclusion is that, at the firm level, the bond q should be significant but cash flows are likely to remain significant as well. These predictions are consistent with the results obtained 19. For instance, fix the aggregate state, and look at the cross section. Then firms with good earnings shocks have high value and high bond prices. Or fix the firm-level shock, and then states with high values have high bond prices. 20. The intuition is the following. Suppose a firm–year observation has a true q of 1.1 based on a good firm shock in a bad aggregate state. Suppose another firm– year observation has a true q of 1.1 based on a medium firm shock in a medium aggregate state. There is no reason to expect them to have the same bond price (for instance, because persistence and volatility are not the same for idiosyncratic and aggregate shocks). As a result, the same value of q for one firm–year observation is associated with several relative prices of bonds. This is what Figure VIII shows.

(0.000148) −0.000318 (0.000312) 100 1.000

(0.000638) 0.0482∗∗∗ (0.000649) 5,000 .943

0.0993∗∗∗ (0.000619) 5,000 .838

(0.000525)

Benchmark model 0.0610∗∗∗

5,000 .879

100 .994

0.0799∗∗∗ (0.000623)

5,000 .883

0.0791∗∗∗ (0.000408)

0.0898∗∗∗ (0.00173) 5,000 .349

0.0703∗∗∗ (0.000276) 0.0434∗∗∗ (0.000498) 5,000 .953

Model B: binary aggregate cash flows

0.0394∗ (0.0222) 100 .031

0.0796∗∗∗ (0.000648) 0.00176 (0.00158) 100 .995

Model B: binary aggregate cash flows

Firm-level regressions: Dependent variable is firm I/K

0.210∗∗∗ (0.000159) 100 .98

0.100∗∗∗

0.1000∗∗∗

100 1.000

(0.00000111)

Benchmark model

Notes. Simulated annual data. The benchmark model is the one used in the main part of the paper, calibrated in Table II. In model B, the aggregate component of the profit rate is either high or low, and the probability of the high state follows a Markov chain under the risk-neutral measure. In both cases, the risk-free rate is constant at 3%, book leverage is constant at 0.45, and idiosyncratic shocks follow the benchmark model. Bond q is constructed using the benchmark mapping of Figure I (it is thus deliberately misspecified for model B). The simulation is for fifty firms and 100 years. OLS standard errors are in parentheses.

Bond q S.e. Profit rate S.e. Observations R2

Bond q S.e. Profit rate S.e. Observations R2

0.100∗∗∗

Aggregate regressions: Dependent variable is aggregate I/K

TABLE VI INVESTMENT REGRESSIONS IN SIMULATED DATA

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by Gilchrist and Zakrajsek (2007) with a large panel data set of firm-level bond prices. They regress the investment rate on a firm-specific measure of the cost of capital, based on firm-level bond yields and industry-specific prices for capital. They find a strong negative relationship between the investment rate and the corporate yields, and they also find that qusual and cash flows remain significant. There are other explanations for the discrepancy between micro and macro results. Returns to scale might be decreasing at the level of an individual firm, even though they are constant for the economy as a whole. This could explain why cash flows are significant in the micro data but not in the macro data. Finally, to the extent that mispricing explains some of the discrepancy between qusual and qbond , the results are consistent with the argument in Lamont and Stein (2006) that there is more mispricing at the aggregate level than at the firm level. VII.B. Robustness to Model Misspecifications I now turn to the issue of the specification of aggregate dynamics. The mapping in Figure I assumes that aggregate dynamics follow an AR(1) process. This is a restrictive assumption, especially under the risk-neutral measure.21 A second model is therefore used to check the robustness of the results. Model B (described in the Appendix) is meant to be the polar opposite to the benchmark model as far as aggregate dynamics are concerned (idiosyncratic shocks are unchanged). This model captures two important ideas. First, cash flows might have a short- and a long-run component, the long-run one being more relevant for valuation and investment. Second, holding constant the objective distribution of cash flows, changes in the market price of risk (due to changes in risk aversion or conditional volatilities) affect the risk-neutral likelihood of good and bad states. In both cases, aggregate cash flows would not summarize the aggregate state. This model is empirically relevant because Vuolteenaho (2002) shows that much of the volatility at the firm level reflects cash-flow news, whereas discount rate shocks are much more important in the aggregate. I simulate a panel similar to the one discussed above (fifty years, 100 firms). I then use the mapping of Figure I to construct 21. Moreover, this assumption implies that the current aggregate profit rate is a sufficient statistic for the current aggregate state, which is clearly unrealistic. This can be seen in the simulated aggregate regressions where aggregate cash flows have an R2 of .98 (Table VI, column (2)).

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q. The model is therefore misspecified because the benchmark mapping is used to construct qbond in a world where aggregate dynamics are substantially different from the benchmark. The first result in Table VI is that the model retains most of its explanatory power. qbond is a reliable predictor even when the model is misspecified. The R2 is still close to one, at 99.4%. The only issue is the bias in the estimated coefficient, which overestimates adjustment costs by about 20%. The second important message of Table VI is that cash flows are not reliable in the aggregate regression. In model B, cash flows have no explanatory power for aggregate investment. At the firm level, cash flows remain significant, as expected, because firm-level dynamics is the same as in the benchmark model. VII.C. Bankruptcy Costs and Leverage The benchmark model is built under the assumptions of no taxes and no bankruptcy costs (Modigliani and Miller 1958).22 I now study how qbond performs if there are taxes and bankruptcy costs. To focus on the crucial issues and to avoid heavy notations, I consider here a simple one-period example. Investment takes place at the beginning of the period, and returns are realized at the end. The risk-free rate is normalized to zero. Profits are taxed at a flat rate, payments to bondholders are deductible, and there are bankruptcy costs. The details of the model are described in the Appendix. Figure IX shows the mappings for different values of distress costs (in the range of values consistent with empirical estimates). Distress costs do not appear to invalidate the approach taken in this paper. The shape of the mapping is similar across the various models.23 If anything, higher bankruptcy costs make the mapping from relative bond prices to q more linear, and thus easier to estimate empirically. VIII. CONCLUSION This paper has shown that it is possible to construct Tobin’s q using bond prices, by bringing the insights of Black and Scholes 22. In such a world, capital structure is irrelevant, and arbitrary changes in leverage are possible without affecting investment. This issue was discussed at the end of Section IV. 23. The fact that one mapping is higher than another on average is irrelevant because it relates only to the average value of q.

THE BOND MARKET’S q

1049

1.6 No distress costs Moderate distress costs Large distress costs

1.5 1.4 1.3

Tobin q

1.2 1.1 1 0.9 0.8 0.7 0.6 0.7

0.75

0.8 0.85 0.9 Relative price of corporate bonds

0.95

FIGURE IX Mappings with Taxes and Bankruptcy Costs Computations for the simple one-period model described in the Appendix, assuming that asset values are lognormally distributed. Moderate distress costs are consistent with the estimates of Andrade and Kaplan (1998).

(1973) and Merton (1974) to the investment models of Abel (1979) and Hayashi (1982). The bond market’s q performs much better than the usual measure of q when used to fit the investment equation using postwar U.S. data. The explanatory power is good (both in level and in differences), cash flows are no longer significant, and the inferred adjustment costs are almost twenty times smaller. Two interpretations of these results are possible. The first is that the equity market is subject to severe mispricing, whereas the bond market is not, or at least not as much. This interpretation is consistent with the arguments in Shiller (2000) and the work of Stein (1996), Gilchrist, Himmelberg, and Huberman (2005), Barberis and Huang (2007), and Brunnermeier, Gollier, and Parker (2007). Another interpretation is that the stock market is mostly right, but that it measures something other than the value of the existing stock of physical capital. This is the view pushed by Hall (2001) and McGrattan and Prescott (2007). According to this

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view, firms accumulate and decumulate large stocks of intangible capital. If the payoffs from intangible capital were highly skewed, then they could affect equity prices more than bond prices, and this could explain the results presented in this paper. The difficulty of this theory, of course, is that it rests on a stock of intangible capital that we cannot readily measure (see Atkeson and Kehoe [2005] for a plant-level analysis). Looking back at Figure IV, it is difficult to imagine a satisfactory answer that does not mix the two theories. Moreover, these theories are not as contradictory as they appear, because the fact that intangible capital is hard to measure increases the scope for disagreement and mispricing. One can hope that future research will be able to reconcile the two explanations. APPENDIX A. Proof of Proposition 1 Let θτ be the marginal default rate during period τ . Let t,τ be the cumulative default rate in periods t + 1 up to τ − 1. In other words, if a bond has not defaulted at time t, the probability that it enters time τ > t is 1 − t,τ . Thus, by definition, t,t+1 = 0 and the default rates

satisfy the recursive structure: 1 − t,τ = (1 − θt+1 ) 1 − t+1,τ . The value at the end of period t of one unit of outstanding principal is

bt1

=

Etπ

∞

(1 − t,τ )

τ =t+1

(22)

+ θτ Vτ / τ −1 ) .

(1 − φ)τ −t−1 ((1 − θτ )(c + φ) (1 + rt,τ )τ −t

Similarly, and just to be clear, the price of one unit of principal at the end of t + 1 is

1 π bt+1 = Et+1

∞

(1 − t+1,τ )

τ =t+2

(23)

+ θτ Vτ / τ −1 ) .

(1 − φ)τ −t−2 ((1 − θτ )(c + φ) (1 + rt+1,τ )τ −t−1

THE BOND MARKET’S q

1051

Using the recursive structure of and the law of iterated expectations, we can substitute (23) into (22) and obtain bt1 = (24)

1 Eπ [(1 − θt+1 )(c + φ) + θt+1 Vt+1 / t ] 1 + rt t 1 − φ π 1 + Et (1 − θt+1 )bt+1 . 1 + rt

Default happens when equity value reaches zero, that is, when

Vt < t−1 φ + c + (1 − φ)bt1 . Therefore, the pricing function satisfies (25)

bt1 =

1 1 Etπ min φ + c + (1 − φ)bt+1 ; Vt+1 / t . 1 + rt

Now recall that bt1 is the price of one unit of outstanding capital. Let us define bt as the value of bonds outstanding at the end of time t, scaled by end-of-period physical assets, bt ≡ ψbt1 ,

(26)

where book leverage was defined in the main text as ψ ≡ t /kt , and assumed to be constant. Multiplying both sides of (25) by ψ, we obtain bt =

1 Eπ [min{(φ + c)ψ + (1 − φ)bt+1 ; vt+1 }]. 1 + rt t

In recursive form, and with constant book leverage, this leads to equation (7). Note that if book leverage were state-contingent, the first term in the min function would simply be (φ + c)ψt + (1 − φ)bt+1 ψt . ψt+1 B. Proof of Proposition 3 Assume that G H > . We can then write the debt pricing formula (21) as (27) Bt =

1 (1 − λt )Etπ min t ; vt+1 kt + GL + λt t . 1+r

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Taking the limit in equation (27) as λt → 0 and GL → 0, it is clear that Bt =

1 Eπ [min( t ; vt+1 kt )]. 1+r t

This is the same pricing formula we used earlier, and we have already seen that one can construct a sufficient statistic for investment in this case. On the other hand, the market value of equity moves when it is revealed that Gt = G H . It is always possible to increase the variance of the shocks by increasing G H . Because these shocks are uncorrelated with investment, the explanatory power of the traditional measure can become arbitrarily small. Note that in a growing economy, it would make sense to index the growth option on aggregate TFP to obtain a model with a balanced growth path. C. Model B In this model, the conditional distribution of cash flows follows a Markov process. Aggregate cash flows can be either high, aH , or low, aL, and the risk-neutral probability of observing a high cash flow is state-dependent: Pr(a = aH ) = f (s). State s follows a four-state Markov process under the risk-neutral measure. The complete aggregate state is (s, a). There are therefore eight possible aggregate states: four states for s and two for a. The persistence in the aggregate time series comes from the persistence in s. Conditional on s, aggregate cash flows are i.i.d. The transition matrix of s is chosen to match the empirical moments in Table II. Firm-level dynamics η are given by equation (17) as in the benchmark model. D. Distress Costs This is a one-period model. Without taxes or bankruptcy costs, the program of the firm is (28)

max Eπ [vk] − k − γ k2 /2, k

where k is investment and v is a random variable. Optimal investment is (29)

k = (q − 1)/γ ,

THE BOND MARKET’S q

1053

where q ≡ Eπ [v]. Now assume that profits are taxed at rate τ , that payments to bondholders are deductible, and that there are proportional bankruptcy costs ϕ. In case of default, a value ϕvk is lost. The firm is financed with debt and equity, and let ψ be book leverage. It is then straightforward to see that (29) still holds, but the definition of q must be adjusted to (30)

q ≡ (1 − τ )Eπ [v] + τ Eπ [min(ψ, v)] − ϕ Eπ [v1v 20 years old) Characteristic

Mean

Age 40.16 Female 0.499 Married 0.703 Illiterate 0.482 Intercollege and up 0.201 Citya Periurban/ large villagea Rurala Ballot success Monthly expenditures 8.678 (log)

Std. dev. 16.244 0.500 0.497 0.458 0.43

0.641

Full sample

Restricted subsample

Mean Std. dev. Mean Std. dev. 54.575 0.490 0.943 0.402 0.178 0.400 0.274

13.240 0.500 0.232 0.490 0.383 0.490 0.460

55.039 0.496 0.948 0.417 0.157 0.372 0.293

13.246 0.500 0.222 0.493 0.364 0.483 0.455

0.325 0.533 8.832

0.470 0.499 0.783

0.335 0.524 8.896

0.472 0.500 0.726

Notes. N = 1,605 for full sample, N = 1,295 for subsample, and N = 29,995 for adult Pakistani population. The Pakistani adult population is from the MICS 2003–4 survey (restricted to the same districts as in our sample). a City, periurban, and rural classifications comparable to our survey data are not available in the MICS.

The initial sampling frame was the list of all Hajj lottery applicants obtained from the Ministry. The survey area was limited for logistic ease to nine administrative districts in the Punjab province.9 Surveyors used addresses and telephone numbers provided in the applications to locate applicants and interview them at their residences. The sample was also restricted to Sunni applicants, because there were too few Shia applicants for meaningful inferences to be drawn. To maximize statistical power, we randomly selected equal numbers of winning and losing parties. Within each party, we randomly selected an individual to interview, and, if other party members of opposite gender were identified as living with the individual, we also selected a second person of the opposite gender. Surveyed applicants are broadly representative of the adult Pakistan population (Table II) with some truncation of the extremes of the socioeconomic distribution, because the poorest cannot afford to go on the Hajj and the rich typically travel on private schemes. Hajj applicants have average education and household 9. The districts were Attock, Islamabad, Rawalpindi, Jhelum, Chakwal, Faisalabad, Sargodha, Multan, and Gujrat.

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QUARTERLY JOURNAL OF ECONOMICS TABLE III SURVEY COMPLETION STATISTICS Panel A: Full sample

Panel B: Restricted subsample

Lottery status

Lottery status

Characteristic

Total Successful Unsuccessful Total Successful Unsuccessful

Selected for interview Raw completed interviews Completion rate (%) Not completed (%) Dead/ill Lives elsewhere Not found Not home Refused

2,537

1,286

1,251

1,995

1,032

963

1,605

855

750

1,295

679

616

63.3

66.5

60.0

64.9

65.8

64.0

2.1 10.4 8.3 7.9 7.9

2.1 10.0 6.4 8.7 6.3

2.1 10.8 10.3 7.2 9.6

2.3 9.8 7.7 8.2 7.2

2.2 9.8 6.6 8.7 6.9

2.3 9.8 8.9 7.6 7.5

Notes. Interview completion percentages from surveyor reports.

expenditures similar to those for the general population, but are older and more likely to be married. Forty percent are from cities, fairly similar to the general population. Surveyors completed interviews with 1,605 applicants, 63% of the 2,537 they attempted to interview (Table III, Panel A). However, only 7.9% of the attempted interviews were refused. In about three-quarters of unsuccessful attempts, surveyors were unable to contact or locate applicants. Some applicants lived in a different (out-of-sample) district from the one provided in their application address (often a relative’s address they wished to travel with), and it was not logistically possible to survey them. In other cases, addresses were incomplete or incorrect or the applicant was not at home despite three separate attempts. Among applicants the survey team could contact (i.e., interviewed plus refusals), the survey completion rate was therefore 88.8%. Successful applicants completed the survey at a 66.5% rate, higher than the 60.0% rate for unsuccessful applicants. This difference is statistically significant at the 1% level (Table III, Panel A). Hajjis were easier to locate, perhaps because their participation in the Hajj made them better known in their localities. Successful applicants also had a slightly lower refusal rate, possibly because they regarded the survey as being more pertinent for those who had actually performed the Hajj.

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The unbalanced interview completion between successful and unsuccessful lottery applicants could potentially introduce selection and bias our estimate of the Hajj effect.10 Therefore, we provide three robustness checks against selection concerns. First, Table I, Panel B, shows that for completed interviews, lottery success is not individually or jointly correlated with observable applicant characteristics. Second, our results are robust to demographic controls. None of our 25 index results qualitatively change with controls for district, urban or periurban location, and individual characteristics.11 Finally, we examine the robustness of our results to a restricted subsample (Table II) that excludes nine out of the 49 tehsils (subdistricts) in our survey area that were particularly difficult to survey. This subsample is balanced on survey completion and reasons for noncompletion. It excludes tehsils with more than 25 selected applicants (tehsils with smaller samples may generate imbalance mechanically) where the completion rate for successful applicants exceeded that for unsuccessful ones by more than 7%. This subsample contains 81% of the total interviews. Although the completion rate was still somewhat higher for successful applicants (65.8% vs. 64.0%), we fail to reject the null hypothesis of an identical completion rate with a p-value of .66. As in the full sample, lottery success in the interviewed subsample is uncorrelated with applicant characteristics (Table I, Panel B). As our results below show, there is no qualitative change in our estimates in the subsample. IV. MAIN RESULTS This section presents our main results on the impact of the Hajj. Sections IV.A–IV.D examine religious behavior and practices, tolerance, gender attitudes, and well-being, respectively. Our 10. A selection effect would imply that the marginal surveyed successful applicant was less willing to give an interview (more uncooperative) and harder to locate. This is because the initial randomization guarantees that successful and unsuccessful applicants are distributed identically along any attribute. If selection is introduced by, for example, successful applicants gaining incremental visibility from traveling, then the marginal successful applicant found is slightly less well known ex ante than the marginal unsuccessful applicant found. However, it is not clear how such potential selection could generate several of our results, such as a shift from localized to global practice or increased tolerance. If anything, one may expect the opposite for the tolerance result, because selection implies that the interviewed successful applicant is marginally less cooperative. 11. We can use additional data such as assets and expenditure from survey data, and the results are robust to these as well. We prefer not to present these as primary controls due to their potential endogeneity.

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QUARTERLY JOURNAL OF ECONOMICS TABLE IV RELIGION AES coefficients

(1) Regarded as religious (2) Global Islamic practice (3) Belief in localized Muslim practices (4) Participation in localized Muslim practices

Base

Controls

Restricted subsample

0.238∗∗∗ (0.06) 0.163∗∗∗ (0.030) −0.101∗∗∗ (0.032) −0.097∗∗ (0.046)

0.230∗∗∗ (0.055) 0.166∗∗∗ (0.029) −0.094∗∗∗ (0.031) −0.097∗∗ (0.045)

0.258∗∗∗ (0.061) 0.171∗∗∗ (0.033) −0.074∗∗ (0.035) −0.085∗ (0.052)

Notes. Columns give AES estimates for our base, control, and restricted subsample specifications. The AES averages the normalized treatment effects obtained from a seemingly unrelated regression in which each dependent variable is a question in the index. All regressions include dummies for place of departure × accommodation category × party size category, as well as dummies for each of the nine districts in the survey. All results come from IV regressions where the instrument is success in the Hajj lottery. Standard errors in parentheses clustered at the party level: Index component questions with number of components indicated in parentheses: Index 1 (1): Do others regard you as religious? Index 2 (10): How frequently do you: pray, do tasbih after prayer, pray in the mosque? Did you pray in the mosque last Sunday? Do you pray optional night prayers? Can you read the Qu’ran? How frequently do you: read the Qu’ran? discuss religious matters? keep fast during Ramadan? keep fast outside Ramadan? Index 3 (10): What is your general view of holy men? Do you regard: visiting holy men as correct? visiting shrines? using amulets? doing a forty-day death ceremony? participating in maulad mehfil (special religious gathering)? Do you believe that: a cap is required for prayer? that dowry is mandatory? that widows have different priority in remarriage? that there can be intercession on Judgment Day? Index 4 (4): Do you actively visit holy men? visit shrines? use amulets? participate in maulad mehfil? ∗ significant at 10%; ∗∗ significant at 5%; ∗∗∗ significant at 1%.

power to detect interaction effects is limited, so we generally do not present interaction results, except in cases where we have strong priors and reasonable power and consistency, as in the case of gender. Our estimates capture the effect of the Hajj five to eight months after pilgrims return. Although this limits our ability to explore persistence of the effects, we do not find any significant changes over the survey period. The rows of Tables IV–VIII present the average effect size (AES) estimates for each index, including the control and restricted subsample specifications. Because the results are very similar, we focus on the base specification. The component questions in each index are described in the notes to the tables. Table IX further presents results for several index component questions of individual interest. A supplemental Online Appendix presents the Hajj impact estimates and definition details for all the component questions.

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TABLE V TOLERANCE AES coefficients

(1) Views of other countries (2) Views of other groups (3) Harmony (4) Peaceful inclination (5) Political Islam index (6) Views of West

Base

Controls

Restricted subsample

0.150∗∗∗ (0.04) 0.131∗∗∗ (0.05) 0.128∗∗∗ (0.04) 0.111∗∗∗ (0.03) −0.050 (0.04) 0.029 (0.04)

0.147∗∗∗ (0.04) 0.108∗∗ (0.05) 0.117∗∗∗ (0.04) 0.121∗∗∗ (0.03) −0.044 (0.03) 0.039 (0.04)

0.151∗∗∗ (0.04) 0.122∗∗ (0.06) 0.126∗∗∗ (0.05) 0.128∗∗∗ (0.04) −0.043 (0.04) 0.011 (0.04)

Notes. See notes to Table IV. Index component questions with number of components indicated in parentheses: Index 1 (6): General view of people from other countries, positive to negative: Saudis, Indonesians, Turks, African, Europeans, Chinese. Index 2 (3): How do members of the following groups compare to your group: different sect? different religion? different ethnicity? Index 3 (4): Do you believe the following groups can live in unity and harmony through compromise over disagreements: sects of Islam? religions? Pakistani ethnic groups? Do you ever pray in a mosque of a different school of thought? Index 4 (8): Belief in incorrectness of: Osama’s goals? Osama’s methods? How important is peace with India for Pakistan? Should the current India/Pakistan boundary be the permanent border if this leads to peace? Should Pakistan not support/only partly support those fighting the Indian government in Kashmir? How incorrect are: suicide attacks? attacks on civilians in war? physical punishment of someone who dishonors family? Index 5 (5): Agree that: government should enforce Islamic injunctions? religious leaders have right to dispense justice? religious leaders should have direct influence on government? better for politicians/officials to have strong religious beliefs? religious beliefs important in voting for candidate? Index 6 (4): Is it bad for Pakistanis to adopt: Western social values? Western technology? Believe there was Western/Jewish role in 9/11 and 2005 London bombing? Believe West does not take into account interests of countries such as Pakistan?

IV.A. Religious Practices and Beliefs Hajjis are 13% more likely to report they are regarded as religious persons, a one-fourth standard deviation increase relative to the control group (Table IV, row (1)). Three indices explore how the Hajj affects religious practice and belief. The first measures global Islamic religious practice, meaning the performance of rites universally acknowledged within the Muslim world. Questions, described in the notes to Table IV, include the applicant’s observance of prayer, fasting, and Qur’anic recitation, etc. The Hajj increases the global religious practice index by 0.16 standard deviations (row (2)). This is a fairly large effect, particularly because it reflects practice five to eight months post-Hajj, and not the fervor of a recently returned

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QUARTERLY JOURNAL OF ECONOMICS TABLE VI GENDER AES coefficients

(1) Views toward women (2) Women’s quality of life (3) Girls’ education (4) Women in workforce/professions (5) Gender authority

Base

Controls

0.120∗∗∗ (0.04) 0.158∗∗∗ (0.05) 0.092∗∗ (0.04) 0.119∗∗∗ (0.04) −0.005 (0.02)

0.116∗∗∗ (0.04) 0.138∗∗∗ (0.05) 0.089∗∗ (0.04) 0.112∗∗∗ (0.04) −0.010 (0.02)

Restricted subsample 0.139∗∗∗ (0.04) 0.166∗∗∗ (0.06) 0.097∗∗ (0.04) 0.091∗∗ (0.04) 0.005 (0.03)

Notes. See notes to Table IV. Index component questions with number of components indicated in parentheses: Index 1 (4): How do men and women compare: mentally/intellectually? spiritually? morally/ethically? Are men and women equal? Index 2 (5): Opinion of quality of women’s lives in following countries/regions relative to Pakistan: Saudi Arabia, Indonesia/Malaysia, West. Think too many crimes against women in Pakistan: overall? relative to men? Index 3 (5): Should girls attend school? Until what level would permit attendance at coeducational schools for: girls? boys? Until what level should coeducational schools be allowed? How many years should girls study relative to boys? Index 4 (3): Like daughters/granddaughter to work? Like a professional occupation for daughters/granddaughters? Good employment important for daughter/granddaughterin-law? Index 5 (7): Women better at managing daily affairs? Wives have equal say in deciding number of children? Is it sometimes correct for: woman to divorce husband? marry against parents wishes? When jobs scarce men should not have more right to one than women? Should daughter have equal inheritence share? Do women count equally to men as witnesses?

pilgrim. The Hajj nearly doubled the rate of regular fasting outside of Ramadan (the obligatory month of fasting) to around 9% and increased praying Tahajjud (supererogatory) prayers by twothirds (Table IX, rows (2) and (3)). In most Muslim countries, there are a variety of Islamic traditions that are not as universally accepted as the global practices examined above. Some of these are specific to particular countries or regions. The Hajj rituals highlight global practices. Local practices might decline because they compete for time and attention with global practices, or because the Hajj induces a shift in belief. We find evidence of an absolute shift away from local beliefs and practices. Although most pilgrims initially have moderately high levels of local beliefs, the Hajj leads to a 0.10–standard deviation reduction in an index of localized beliefs that are fairly common in South Asia but not among Muslims globally (Table IV, row (3)). Some practices, such as visiting the tombs of saints and using amulets, have roots in local Sufi traditions. Others reflect

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TABLE VII WELL-BEING Panel A: AES coefficients Base

Restricted Controls subsample

−0.206∗∗∗ −0.206∗∗∗ −0.200∗∗∗ (0.05) (0.05) (0.05) (2) Positive feelings −0.109∗∗ −0.098∗∗ −0.079 (0.05) (0.04) (0.05) (3) Index of satisfaction −0.010 0.006 0.011 with life and finances (0.04) (0.04) (0.04) (4) Self-rated physical −0.213∗∗∗ −0.219∗∗∗ −0.239∗∗∗ health (0.05) (0.05) (0.06)

(1) Rescaled K6 index

Panel B: AES Main effect −0.369∗∗∗ (0.08) −0.149∗∗ (0.07) −0.028 (0.05) −0.320∗∗∗ (0.07)

Male interaction 0.326∗∗∗ (0.09) 0.079 (0.08) 0.036 (0.08) 0.210∗∗ (0.10)

Notes. See notes for Table IV. In addition, note that Panel A gives AES estimates for our base, control, and restricted subsample specifications, whereas Panel B adds an interaction between Hajj participation and a male variable to the base AES specification. In Panel B, the instruments are success in the Hajj lottery for the main effect and success interacted with male in the interaction specification. Index component questions with number of components indicated in parentheses: Index 1 (6) [rescaled, high value=less distress]: During the past 30 days, how often did you feel: nervous? hopeless? restless or fidgety? so depressed that nothing could cheer you up? everything was an effort? worthless? Index 2 (5): During the past 30 days, how often did you feel: relaxed and peaceful? content? joyous? How much pleasure do you take in life? Altogether, are you very happy/not at all happy (four-point scale)? Index 3 (3): How satisfied with life as a whole are you (ten-point scale)? How much room for improvement in your quality of life? How satisfied are you with finances (ten-point scale)? Index 4 (2): How good is your physical health (four-point scale)? Have you been free of any 7+ day illness/injury in the past year?

local interpretation of Islamic doctrine, such as giving dowry (Islam instead emphasizes mehr, where a man commits to pay his wife in case of divorce) and what remarriage priority should be accorded to widows. Whereas South Asian women often lose status when their husbands die and have little prospect of remarriage, in Islam a widow can readily remarry after a short waiting period. The Hajj similarly reduces an index of localized religious practice, related mainly to the Sufi traditions mentioned above, by 0.10 standard deviations (Table IV, row (4)). As we noted earlier, some have expressed concern about the erosion of local South Asian traditions. We later present evidence suggesting that the Hajj does not produce a shift in favor of a Saudi version of Islam but rather a move toward the global mainstream. IV.B. Tolerance We find that Hajjis display more positive views toward other nationalities and social groups, have greater tolerance, and are more peacefully inclined (Table V).

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QUARTERLY JOURNAL OF ECONOMICS TABLE VIII ENGAGEMENT AND EXPOSURE AES coefficients

(1) Socioeconomic engagement (2) Engagement in politics (3) Formal knowledge of Islam (4) Diversity knowledge (5) Gender knowledge (6) Global knowledge

Base

Controls

Restricted subsample

−0.002 (0.02) −0.011 (0.03) 0.004 (0.04) 0.146∗∗∗ (0.04) 0.125∗∗∗ (0.04) 0.083∗∗ (0.04)

−0.008 (0.02) −0.010 (0.03) 0.000 (0.03) 0.139∗∗∗ (0.04) 0.116∗∗∗ (0.03) 0.086∗∗ (0.03)

0.011 (0.02) −0.024 (0.03) −0.003 (0.04) 0.133∗∗∗ (0.05) 0.104∗∗ (0.04) 0.072 (0.05)

Notes. See notes for Table IV. Index component questions with number of components indicated in parentheses: Index 1 (15): How frequently do you visit: people in your town/village? people outside your town/village? How frequently are you visited by: people in your town/village? people from outside your town/village? How many times in the past year have close family/friends sought advice on: family matters? religious matters? business matters? How many times in the past year have more distant family/friends sought advice on: family matters? religious matters? business matters? Are you a member of following kinds of organizations: religious, professional, school? Do you work as: an employee? for yourself? Index 2 (7): Did you vote in last election? How interested in national affairs? Are you member of political party? Are you a member of a political organization? A social organization? How often do you follow national affairs? Do you have an opinion on how politicians are handling national affairs? Index 3 (10): Name as many of the five pillars of Islam as you can. Correct answer to: How many chapters in the Qu’ran? Can you recite favorite verse of the Qu’ran? What is shortest sura of the Qu’ran? What is longest? How many suras are in the the Qu’ran? What is first revealed verse of the Qu’ran? Is method of prayer described in the Qu’ran? What is percentage required to be given as Zakat (charitable tax)? How long must wealth be held for Zakat to be due? Index 4 (3): Correct answers to: How many accepted schools of thought in Sunni Islam? Is a cap required for prayer? Is saying “talak, talak, talak” sufficient for legal divorce? Index 5 (8): Correct answers to: What was name of prophet’s first wife? How many wives is a man allowed at once? Can a Muslim man marry a Jewish or Christian woman? Is dowry mandatory? Further: Have you heard of Islamic law relating to adultery? Do you have an opinion about women’s lives in: Saudi Arabia? Indonesia/Malaysia? West? Index 6 (6): How many countries share a border with Pakistan? What country has largest percentage Muslim? What percentage of Nigerians are Muslim? What are world’s two most populous countries? Who is the Prime Minister of India? Which is further from Pakistan, England or the United States?

The Hajj increases an index of positive views about people from other countries by 0.15 standard deviations or more than 33% (Table V, row (1)). Hajjis update their beliefs most positively about nationalities they are likely to interact with frequently. The largest positive impact (0.32 standard deviations) is on views toward Indonesians (Table IX, row (4)), the largest non-Saudi pilgrim group and the one Hajjis report as observing the most. Hajjis also have a 0.14–standard deviation more positive view of Saudis (Table IX, row (5)). There is no effect on views of Europeans. Hajjis are also significantly more likely to declare that Indonesians

(10) Do you believe the methods Osama uses in fighting are correct?

(6) In your opinion, overall how are people of a different religion compared to your people? (7) Do you believe that people of different religions can live in unity & agreement (harmony) in a given society by making agreements over their differences? (8) Do you ever pray in the mosque of a different maslak than your own? (9) Do you believe the goals for which Osama is fighting are correct?

(5) Is your general view of Saudi people:

(3) How often did you fast outside of Ramadan during the past year? (4) Is your general view of Indonesian people:

(1) Do you believe others regard you as religious? (2) Do you pray “Tahajjud Namaz”?

Question

.021 .014

.112

0.084 0.063

0.034 0.063

0.051

1 = Yes, 0 = No Binary: 1 = Frequently, 0 = Less often/never 1 = Not correct at all/slightly incorrect, 0 = Correct/absolutely correct 1 = Absolutely never/almost never correct, 0 = To small extent/some extent/strongly correct

.074

.004

.026

.000

0.217 0.110

.006

0.041

.000 .000

0.100 0.184

1 = Religious, 0 = Not religious 1 = Yes (regularly, occasionally), 0 = No (rarely, never) 1 = Several times per month or more, 0 = Once per month or less 2 = Very positive, −2 = Very negative 2 = Very positive, −2 = Very negative 0 = Better or worse, 1 = Same

p-value

Coef.

Coding

TABLE IX SELECTED SURVEY QUESTIONS

0.159

0.068

0.049

0.589

0.389

1.034

0.362

0.049

0.772 0.281

Comp. mean

761

761

1,463

1,270

1,604

1,593

1,583

1,605

1,541 1,605

Obs.

.063

.054

.027

.036

.025

.026

.055

.030

.033 .047

R2 ESTIMATING THE IMPACT OF THE HAJJ

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(17) Do you think there are too many crimes against women in Pakistan? Overall

(16) What is your opinion about the quality of women’s lives in each of the following countries/regions? West

(15) What is your opinion about the quality of women’s lives in each of the following countries/regions? Saudi Arabia

(11) How important do you believe peace with India is for Pakistan’s future? (12) Please tell me what you think about the correctness of the following: family members physically punishing someone who has dishonored the family (13) In your opinion, how do men and women compare to each other with respect to the following traits: spiritually (14) What is your opinion about the quality of women’s lives in each of the following countries/regions? Indonesia/ Malaysia

Question

.145

.051

0.057

0.094

0.051

0.087

0 = Men are better/equal, 1 = Women are better 1 = Greater than in Pakistan, 0 = Lower than or equal that in Pakistan; Base variables 5 = Very high, 1 = Very low 1 = Greater than in Pakistan, 0 = Lower than or equal that in Pakistan; Base variables 5 = Very high, 1 = Very low 1 = Greater than in Pakistan, 0 = Lower than or equal that in Pakistan; Base variables 5 = Very high, 1 = Very low Binary: 0 = No, 1 = Yes 0.052

.088

0.044

0 = Correct, 1 = Never correct

.075

.006

.112

.016

0.044

1 = Important, 0 = Not important

p-value

Coef.

Coding

TABLE IX (CONTINUED)

0.597

0.186

0.322

0.262

0.111

0.261

0.913

Comp. mean

1,605

646

1,180

551

1,497

1,459

1,155

Obs.

.045

.091

.048

.058

.034

.033

.020

R2

1154 QUARTERLY JOURNAL OF ECONOMICS

Coding .052

.039 .036

.024

.156

.073

0.028 0.055

0.059

0.045

0.054

p-value

0.053

Coef.

0.457

0.540

0.729

0.933 0.722

0.171

Comp. mean

R2

1,562 .028

1,605 .029

1,550 .036

1,604 .027 1,550 .035

1,135 .026

Obs.

Notes. Rows contain results from individual IV regressions where the instrument is success in the Hajj lottery, and which include include dummies for place of departure × accommodation category × party size category. p-values are corrected for clustering at the party level.

(18) Do you think there are too many crimes against 1 = Against women score < against women in Pakistan? Relative to men men score, 0 = Against women score ≥ against men score; Base scores 1 = Yes, a lot; 4 = No, not at all (19) In your opinion, girls should attend school Binary: 0 = Disagree, 1 = Agree (20) Until what level would you prefer allow/permit girls 0 = Never, 1 = Primary, secondary, or in your family to attend coeducational schools (boys all levels and girls in the same school)? (21) Until what level would you prefer allow/permit boys 0 = Never, 1 = Primary, secondary, or in your family to attend coeducational schools (boys all levels and girls in the same school)? (22) Would you like for your daughters or female grand- 0 = No, 1 = Yes children to have a career other than caring for the household? (23) How important are the following characteristics in 0 = Not important, 1 = Important your son’s, grandson’s wife?: Good employment or business

Question

TABLE IX (CONTINUED)

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are the best practitioners of Islam (regression not reported). In follow-up open-ended interviews, Pakistani Hajjis also reported positive interactions with Indonesians. For example, one older female Hajji said, “I had a very good experience with female Hajjis from Indonesia. They would make space for me whenever I was walking if I gestured for them to do so. One of them even gave me Vicks VapoRub when she found out that I had the flu.” The Hajj also increases an index of beliefs that adherents of different sects, ethnicities, and religions are equal by 0.13 standard deviations (Table V, row (2)). In contrast to the views on different nationalities, the largest move toward equal status is for people of a different religion (Table IX, row (6)), who would not be encountered during the Hajj, as they aren’t permitted to attend. Hajjis may thus be willing to extend their notions of tolerance beyond the Muslim world. Similarly, the Hajj increases an intergroup harmony index by 0.13 standard deviations (Table V, row (3)). The index solicits applicants’ views on whether people from different ethnic groups, Islamic sects, and religions could live together in harmony in the same society. It also includes a practice-based question about how frequently the respondent prays in a mosque of a different school of thought. The effect is largest for religion, about which the control group has the lowest belief regarding harmony (Table IX, row (7)). The effect on the respondent praying in a mosque of a different school of thought is also large, almost doubling the control group mean of 4.9% (Table IX, row (8)). We complement the harmony index by exploring the extent to which the Hajj leads to greater inclination to peace. The Hajj increases a peaceful inclination index by 0.11 standard deviations (Table V, row (4)). Examining some of the component questions, we find that the Hajj almost doubles the number of respondents who declare that Osama bin Laden’s goals are incorrect, from 6.8% to 13.1%, and increases the fraction declaring his methods incorrect from 16% to 21% (Table IX, rows (9) and (10)).12 The Hajj increases the belief that peace with India is important from 91% to 96% (Table IX, row (11)). Hajjis are also 17% more likely to say it is never correct to physically punish someone who has dishonored the family (Table IX, row (12)). Although these results 12. Slightly more than half say his goals are correct; one-third say his methods are correct; quite a few do not answer.

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are consistent with becoming more tolerant, it is also possible that the Hajj confers religious legitimacy on individuals that allows them to more willingly express previously held views. One might suspect that more orthodox religious practice could be associated with support for political Islam, which advocates a closer relationship between religion and politics and which is often associated with negative perceptions of the West. We see no increase in belief either in the role of religion in politics or in more negative views of the West. It is nonetheless possible that increased tolerance tempers such desires and perceptions, if they do in fact go along with increased orthodoxy. The Hajj reduces support for political Islam, although the effect is only weakly significant at 15% (Table V, row (5)). The political Islam index includes questions on how deeply religion should be involved in politics. Although the average respondent is likely to see a role for religion in matters of the state, Hajjis are no more likely to do so in spite of an increased attachment to global Islam. In fact, the Hajj significantly reduces beliefs that the state should enforce religious injunctions and that religious leaders should be able to dispense justice on their own. The Hajj does not lead to any increase in an index of negative attitudes toward the West (Table V, row (6)) that encompasses views on adopting Western social values and technologies and commonly held suspicions toward the West. We can reject a negative effect of one-twentieth of a standard deviation with 95% confidence. We find no evidence that the Hajj affects the tails of the distribution of attitudes toward political Islam and views toward the West. Moreover, although young people may potentially be more susceptible to intolerance, the six tolerance indices examined don’t show any differential Hajj effect for younger pilgrims (regressions not reported). If anything, the harmony index shows a more positive effect for the young. IV.C. The Hajj and Gender We noted earlier that the Hajj may provide Pakistani pilgrims with a novel opportunity in which men and women interact, perform rituals as equals, and observe the gender roles of other nationalities. Perhaps on account of this, we find that the Hajj causes a 0.12–standard deviation increase in an index of questions about the status of women relative to men along intellectual, spiritual,

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and moral dimensions (Table VI, row (1)). The effect is largest on the spiritual dimension, with an increase of over 50% (from 11% to 17%) in belief that women are better (Table IX, row (13)). Hajjis are also more likely to believe that, although there are gender differences, women’s overall status is equal. The Hajj also increases an index that captures awareness of women’s quality of life issues in Pakistan by 0.16 standard deviations (Table VI, row (2)). The index includes respondents’ ratings of women’s quality of life in other countries relative to Pakistan. The largest effect is on the relative quality of life of Indonesian/Malaysian women being higher, paralleling the previous results on views of other nationalities (Table IX, row (14)). Interestingly, Hajjis show a greater increase in their views on the relative quality of life of women in the West compared to Saudi Arabia (Table IX, rows (15) and (16)). In addition, Hajjis are also more likely to think that crimes against women are high, both on an absolute scale and relative to crimes against men (Table IX, rows (17) and (18)). Do the more favorable assessment of women’s qualities and the greater concern regarding their quality of life in Pakistan go along with a changed view of the role women ought to take in society? We construct three indices to explore the areas of girls’ education, women’s workforce participation and choice of professions, and the willingness to challenge the authority of men relative to women within the household and in social contexts (Table VI, rows (3)–(5)). The Hajj increases favorable views toward education for girls by about 0.09 standard deviations (Table VI, row (3)). We find positive Hajj effects on all components except equal educational attainment across gender. The Hajj increases the desire that girls attend school from 93% to 96% (Table IX, row (19)). Hajjis are 8% more willing to allow both their boys and girls to attend coeducational schools at all levels (Table IX, rows (20) and (21)). Further, the Hajj increases an index of questions about women’s workforce participation and profession choice by 0.12 standard deviations (Table VI, row (4)). The Hajj has a substantial impact on each index component. For example, the Hajj increases the fraction desiring that their daughters/granddaughters work from 54% to 60% (Table IX, row (22)). Hajjis are also 12% more likely to think it is important that their future daughter-in-law be employed (Table IX, row (23)).

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However, Hajjis’ more favorable views of women do not extend to challenging male authority in the household (Table VI, row (5)). The Hajj has little or no impact on an index that includes questions regarding whether the respondent challenges traditional attitudes on women’s roles in domestic matters, such as fertility decisions and marrying against parental wishes, and unequal Islamic rules on gender, such as those related to inheritance laws and providing financial witness. This is perhaps unsurprising given the greater authority and responsibility typically accorded to men along several dimensions within Islam. Nevertheless, the changed perceptions about gender roles do seem to accompany changes in household behavior. The Hajj increased the fraction reporting occasional marital disagreements by 10 percentage points, a large increase relative to the comparison mean of 15% (regression not reported). Because most married couples perform the Hajj together, it is not possible to separate this effect by the respondent’s gender (because it reflects both their own and their spouse’s Hajj impact). Although sample size limitations do not readily allow us to examine heterogeneity of the impact of the Hajj, nevertheless we find that only the girls’ education index shows a smaller increase for men than women, who in any case already have close to 100% agreement with the view that girls should be educated (regressions not reported). In fact, the Hajj leads to somewhat larger changes in the indices of views on women and quality of life for male Hajjis than for female ones. IV.D. Well-Being Hajjis, primarily women, are more likely to report negative feelings that suggest distress, and are less likely to report positive feelings of well-being (Table VII, rows (1), (2), (5), and (6)). This could potentially be due to the changes in Hajjis’ beliefs and frame of reference discussed above (which the psychology literature suggests can lead to stress), to financial stress associated with the cost of the Hajj, or to the impact of the Hajj on physical health. Hajjis report somewhat higher distress, as measured by a version of the K6 screening scale (Kessler et al. 2003).13 The index aggregates respondents’ experience of six negative feelings in the past month, which we rescale so that a higher value represents 13. We should caution that, to our knowledge, the K6 index has not been formally validated for Pakistan.

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less distress. Although applicants had a low level of underlying distress, the Hajj reduces the index by 0.21 standard deviations (Table VII, row (1)). The Hajj also reduces an index of five positive feelings by 0.11 standard deviations (row (2)). In the restricted subsample, the Hajj effect drops slightly to 0.08 standard deviations with a marginal significance of 11%. The increase in distress falls entirely on women (Table VII, rows (5) and (6)). On both the rescaled K6 index and the positive feelings index, there is no significant effect of the Hajj on men. Increased distress might be due to the stark contrast between the typical Pakistani woman’s daily life and the relatively greater equality and integration experienced during the Hajj. The impact of the Hajj on gender attitudes suggests an increased realization that the constraints and restrictions women are accustomed to in Pakistan may not be part of global Islam. The literature in psychology (Crosby 1991; Lantz et al. 2005) suggests that such changes in frame of reference can induce significant stress, although eventually the stress helps deal with the change. Although the Hajj has a negative impact on a female pilgrim’s emotional state, it does not affect overall life satisfaction, either on average, or for women (rows (3) and (7)). We can reject a negative effect on the index of life satisfaction of about one-tenth standard deviation with 95% confidence. Although we cannot rule it out, we do not see much evidence for the hypothesis that the substantial financial expenditure required by the Hajj creates financial stress that accounts for Hajjis’ negative feelings. In fact, we can reject the hypothesis that the Hajj has a negative effect of more than one-twelfth of a standard deviation on the individual component question about satisfaction with finances. The Hajj also does not affect monthly household consumption expenditures or a measure of household assets (regressions not reported). Our interviews reveal that most do not consider the pool of savings for the Hajj as fungible; those unable to go keep these Hajj funds in order to reapply in the future. The Hajj leads to a 0.21–standard deviation reduction in an index of physical health (Table VII, row (4)) that includes selfreported physical health and illness/injury. Although the decrease in self-perceived health could be due to a change in the reference group for Hajjis from local people to those encountered from other countries on the Hajj, it is not clear that this can account for the doubling in reports of serious physical injury or illness.

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The negative physical health effects are also stronger for women (row (8)), suggesting that part of the negative effect of the Hajj on women’s feelings of well-being could be explained by poorer physical health.14 However, the negative point estimates on men’s physical health are larger than the effect on the K6 index (0.11 vs. 0.04 standard deviations), suggesting that the two do not exactly co-move. Also, the coefficient on Hajj lottery success in a regression predicting the K6 index is similar whether or not one controls for physical health, providing further suggestive evidence that the channel for Hajj effects on emotional health is not simply through physical health.

V. POTENTIAL CHANNELS Although our methodology does not provide experimental variation that isolates the potential channels through which the Hajj may impact the pilgrim, we can offer some suggestive evidence. We consider both external channels, which operate by changing the environment a Hajji faces upon return, and internal channels, which reflect changes in Hajjis’ beliefs and preferences. We argue that the evidence points toward the importance of the internal channel and, within that, to exposure to people of differing nationalities, sects, and gender. V.A. External Social Environment Historical accounts suggest that the Hajj confers social prestige and legitimacy (Donnan 1989; Eickelman and Piscatori 1990; Yamba 1995), although some anecdotal evidence suggests that contemporary Hajjis no longer experience this increase in social status (Scupin 1982). A changed social role may bring expectations for the changed behavior and beliefs that are reflected in our results. For example, Hajjis may be expected to be more religious, and may practice more to fulfill that expectation. Alternatively, increased religious legitimacy may allow Hajjis to express longstanding opinions they have not expressed before, such as those opposing Osama Bin Laden. We find no impact of the Hajj on an index of social status and engagement (Table VIII, row (1)). The fifteen components include the frequency of social visits, the giving of advice, and 14. Negative physical health effects are not larger for older people.

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membership in social organizations.15 We might further expect social standing to be reflected in awareness of and engagement in political affairs. In fact, we find no impact of the Hajj on a political engagement index (Table VIII, row (2)) that asks about voting, interest in national affairs, political opinion, and membership in political organizations. It’s possible that the Hajj once led to a much greater change in social roles than it does currently, and that the increased rate of participation in the Hajj due to lower travel costs has reduced the social prestige associated with completing the Hajj. In any case, it does not seem likely that changes in the social role upon return can account for the findings in the previous sections. V.B. Internal State The Hajj may alter an individual’s internal state, changing beliefs and preferences. For example, Hajjis may undergo a change in religious commitment during the pilgrimage that increases orthodoxy in religious practice and leads them to greater tolerance and belief in gender equity consistent with the Qur’an. Alternatively, Hajjis’ increased tolerance and changed gender attitudes may reflect their new exposure to people from different countries and sects and to members of the opposite gender outside their family. Although we cannot rule out the religious dimension, we interpret the evidence as pointing more toward the increased exposure to Muslims from around the world. We find that the Hajj does not increase an index of formal religious knowledge (Table VIII, row (3)) but does increase indices of experiential knowledge about diversity of opinion within Islam, gender within Islam, and the world more broadly (Table VIII, rows (4)–(6)). The changes in experiential knowledge point to the importance of interaction with and observation of other groups.16 Furthermore, to the extent that a spiritual transformation and change in religious commitment would be accompanied by a desire to acquire greater religious knowledge, these results do not suggest that such a change is a primary driver of the findings. 15. All except two component questions are not significant even at the 20% level (Online Appendix 5). These two show that Hajjis are slightly more likely to have visitors from out of town, and slightly more likely to be self-employed ( p-values of .14 each). However, the magnitudes of these effects are small (5% and 3%). 16. Although some of our results could be due to a generic effect of traveling to a different country rather than the experience of the Hajj, it seems unlikely this accounts for all of the results. For example, it is hard to see why a pure travel effect would lead to more positive beliefs about Indonesians.

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The Hajj increases the index measuring knowledge of diversity within Islam by 0.15 standard deviations (Table VIII, row (4)). Index components include questions on how schools of Sunni thought differ, such as whether it is necessary to wear a prayer cap. The index of gender knowledge and awareness, which combines eight questions on gender and marriage in Islam and on having an opinion on women’s issues, increases by 0.13 standard deviations (Table VIII, row (5)).17 Similarly, Hajjis also show an increase of 0.08 standard deviations in the global knowledge index, which reflects general awareness of the world outside Pakistan (Table VIII, row (6)).18 Pilgrims who travel in smaller parties, and thus have more opportunity to interact with non-Pakistanis, experience larger gains in the diversity, gender, and global knowledge indices, as well as in positive views of people from other countries. This is consistent with the idea that the exposure channel is important. The coefficients on the interaction between the Hajj and small party size are large and significant at conventional levels for the gender and global knowledge indices and for positive views of other countries. The small-party interaction effects are 0.13, 0.14, and 0.14 standard deviations, respectively, with p-values of .07, .10, and .06. Point estimates for the group size interaction on other tolerance indices also point to a similar story. The interactions are robust to including other demographic controls and their interactions. However, we cannot rule out that unobservable differences between parties of different size are driving the interaction effects. We would expect Hajj effects to also be larger for those with less prior exposure to situations similar to the Hajj. However, very few respondents had previously traveled outside Pakistan, which limits our power to test this interaction. There are a few robust interactions with literacy and urban residence, though it is unclear if these relate to the prior exposure that is relevant. Although urban applicants do show a smaller decrease in localized beliefs and practices, the literate see larger gains in some of the

17. Four of the eight questions in the gender knowledge and awareness index are about awareness rather than knowledge: whether the respondent has heard of the Islamic law against adultery and whether they have an opinion on women’s lives in three different countries. The Hajj has a somewhat smaller, but still significant, effect on a pure gender knowledge index that is constructed without these questions. 18. We should note that this latter effect falls slightly to 0.07 standard deviations and is marginally significant at 12% in the restricted subsample.

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experiential knowledge measures, suggesting that literacy may partly be picking up other factors such as ability to interact with others. Because party size is often assigned by banks, and is thus less likely to be correlated with unobserved factors, we prefer focusing on it as a test of exposure. Although Hajjis are also exposed to Saudi Arabia and its people, we think this is unlikely to drive our observed effects. Only the move away from localized religious practices seems consistent with a Saudi influence. Saudi Arabia is generally less accepting of other schools of thought and enforces strict gender segregation; Hajj impacts on gender views are more in line with the more liberal attitudes in other Muslim countries.19 Our results thus suggest that Hajjis are likely to be influenced by the practices and beliefs of the typical pilgrim that they encounter during the Hajj, with possibly greater salience to those groups that are more visibly different or are regarded as better in some way, such as in their behavior or organization (factors often mentioned in our interviews). Exposure may therefore induce convergence of belief to the Islamic mean. To the extent that this convergence is a significant force, some of our results may differ for pilgrims from other countries.

VI. CONCLUSIONS Our findings show that the Hajj induces a shift from localized beliefs and practices toward global Islamic practice, increases tolerance and peaceful inclinations, and leads to more favorable attitudes toward women. This demonstrates that deep-rooted attitudes such as religious beliefs and views about others can be changed and also challenges the view that Islamic orthodoxy and extremism are necessarily linked. We conclude with some tentative implications of our results on how social institutions help shape individual beliefs and identity and, at a macro level, how they may foster unity within belief systems. 19. A comparison of gender views across questions from the World Values Surveys shows that Saudis indeed have more conservative gender views than Pakistanis, whereas Pakistanis in turn are more conservative than Indonesians. Fully 62% of Saudis believe a university education is more important for men than women, compared to 24% of Pakistanis and 17% of Indonesians. Similarly, 34% of Saudis do not think that both husband and wife should contribute to household income, compared to 30% of Pakistanis and 15% of Indonesians.

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The social psychology literature suggests that social interactions can lead to either positive or negative feelings toward other groups depending on whether the setting is competitive or cooperative. Several features of the Hajj may create a setting in which the interaction among different groups helps build common purpose and identity. It’s worth noting that other social institutions also share such features with the Hajj. Consider medical education, police/military basic training, and international peace camps. Like the Hajj, participants in these institutions leave their everyday environments and their restrictions on mixing across certain lines, such as ethnicity and social class, to enter a setting in which they collectively perform similar actions, often physically strenuous ones, which require cooperation from others. Furthermore, participants in all these institutions accentuate their similarity, often by taking on common dress or hairstyle during the experience and a common title afterward. It also seems likely that the religious element of the Hajj plays a role beyond providing a cooperative setting. For example, Hajjis’ changed attitudes on gender appear to be circumscribed by those norms broadly accepted in Islam. Further, it is plausible that the religious context provides the legitimacy that makes it acceptable for adherents to alter their views. If a Pakistani woman observes her Indonesian counterpart engaging equally with her spouse without compromising her piety, she may also consider it permissible to do so. If pilgrims see others praying somewhat differently yet without interference in the holiest of Muslim places, they may reason that some degree of religious diversity is acceptable. Our results also shed light on why religions often mandate practices that are costly for individual adherents. Although club good models that apply the framework of individual rationality, as in Iannaccone (1992) and Berman (2000), deliver compelling explanations, additional insights can be obtained using an evolutionary framework in which institutions and prescriptions that reinforce and propagate the religion’s beliefs and practices are more likely to persist. By moving pilgrims toward the religious mainstream, the Hajj may help Islam overcome an evolutionary hurdle faced by world religions: maintaining unity in the face of the divergence of practices and beliefs through local adaptations. A number of religious institutions, including written holy texts and central authorities, can help overcome this hurdle. Sunni

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Islam lacks a central authority, and so the role of pilgrimage may be particularly important. However, achieving convergence and maintaining unity likely require that there be limits to how much diversity is allowed. Too diverse a group may make it difficult to find common ground and too much variance in beliefs increases the likelihood that undesirable religious innovations will spread. It is therefore noteworthy that although people of different faiths made the pilgrimage to Mecca in pre-Islamic times (Armstrong 1997), its institutionalization with Islam’s emergence was accompanied by restricting it to Muslims and disallowing non-Islamic practices that were once elements of the pilgrimage. Both the evolutionary and club good perspectives imply that religions with practices that generate positive externalities for other adherents, provided these are socially efficient, are more likely to persist by raising the attractiveness of being an adherent. Historically, undertaking the Hajj may have created positive externalities for other Muslims both through its effect on tolerance and by facilitating economic trade and the diffusion of economic, cultural, and scientific ideas (Bose 2006). Although we find little evidence of individual medium-term gains in socioeconomic status and engagement in our sample, there is clear evidence for a positive externality in the increased tolerance toward others. Of course, given the significant financial and health costs entailed in undertaking the Hajj, individuals still need to be induced to participate. However, this can be done through religious injunctions, sanctions, and rewards. The Hajj is one of the five pillars of Islam and there is the belief that performing it sincerely cleanses one of all sins. Models of costly religious practices also often argue that these practices signal commitment and screen out those who may free ride on the religious community. Because individuals have already signaled such commitment by applying to the Hajj (less than 1% withdraw), our comparisons between applicants are not influenced by signaling effects. Our results therefore indeed capture a treatment effect. The fact that the Hajj has a direct treatment effect is not surprising, because one would expect that were it only serving a signaling function, it would decline in observance relative to alternate practices that could screen just as well but at a lower cost. The findings in this paper also pose the question of whether pilgrimages or central gatherings may foster such unity in other

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belief systems, religious or otherwise, and conversely, whether their absence increases susceptibility to schisms. The Kumbh Mela, bringing together millions of Hindus every three years, along with Catholic pilgrimages to Lourdes and Rome, may play such a cohesive role. Nonreligious examples include national political conventions in the United States that may promote party unity and exchange among delegates from different regions. Conversely, the split between Judaism and Christianity occurred shortly after the destruction by the Romans of the Jewish temple in Jerusalem, which was a central gathering place, in the year 70 A.D. One may even conjecture whether the multiplication of Protestant sects would have been muted had there been a central holy site for pilgrimage among Protestants. Further insights are likely to come from investigating the impact of the Hajj over different durations and on pilgrims from other countries that differ from Pakistan in their attitudes and exposure, and the impact of other pilgrimages. Because several other countries also allocate Hajj visas by lottery, it should be possible to use the same methodology. More generally, one could use similar approaches to examine the impact of other institutions on social identity. For example, one could use draft lotteries (Angrist 1990) to examine the impact of military service on social identity or regression discontinuity designs to examine the impact of professional training on beliefs and attitudes. Building up evidence from a series of such studies would shed additional light on the broader roles played by institutions, religious and nonreligious, in the shaping of beliefs and identity and the evolution of ideologies and belief systems.

APPENDIX: OUTLINE OF THE HAJJ PILGRIMAGE

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CASE WESTERN RESERVE UNIVERSITY HARVARD UNIVERSITY HARVARD UNIVERSITY, THE BROOKINGS INSTITUTION, AND THE NATIONAL BUREAU OF ECONOMIC RESEARCH

REFERENCES Ahmed, Q. A., Y. M. Arabi, and Z. A. Memish, “Health Risks at the Hajj,” The Lancet, 367 (2006), 1008–1015. Angrist, Joshua, 1990. “Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records,” American Economic Review, 80 (1990), 313–336. Armstrong, K., Jerusalem: One City, Three Faiths (New York: Ballantine Books, 1997). Aronson, E., and S. Patnoe, The Jigsaw Classroom (New York: Longman, 1997). Azarya, V., Aristocrats Facing Change: The Fulbe in Guinea, Nigeria, and Cameroon (Chicago: University of Chicago Press, 1978). Barro, Robert, and R. M. McCleary, “Religion and Economic Growth across Countries,” American Sociological Review, 68 (2003), 760–781. Berman, Eli, “Sect, Subsidy, and Sacrifice: An Economist’s View of Ultra-orthodox Jews,” Quarterly Journal of Economics, 115 (2000), 905–953. Bianchi, R., Guests of God: Pilgrimage and Politics in the Islamic World (Oxford, UK: Oxford University Press, 2004). Boisjoly, J., G. Duncan, M. Kremer, D. Levy, and J. Eccles, “Empathy or Antipathy? The Consequences of Racially and Socially Diverse Peers on Attitudes and Behaviors,” American Economic Review, 96 (2006), 1890–1906. Bose, Sugata, A Hundred Horizons: The Indian Ocean in the Age of Global Empire (Cambridge, MA: Harvard University Press, 2006). Clingingsmith, David, Asim Ijaz Khwaja, and Michael Kremer, “Estimating the Impact of the Hajj: Religion and Tolerance in Islam’s Global Gathering,” KSG Working Paper RWP08-22, 2008. Crosby, F., Juggling: The Unexpected Advantages of Balancing Career and Home for Women and Their Families (New York: Free Press, 1991). DeVries, D. L., and R. E. Slavin, “Teams-Games-Tournaments (TGT): Review of Ten Classroom Experiments,” Journal of Research and Development in Education, 12 (1978), 28–38. Donnan, Hastings, “Symbol and Status: The Significance of the Hajj in Pakistan,” Muslim World, 79 (1989), 205–216. Eickelman, Dale F., and James Piscatori, “Muslim Travellers: Pilgrimage, Migration, and the Religious Imagination,” in Comparative Studies on Muslim Societies, Vol. 9, Barbara D. Metcalf, ed. (Berkeley: University of California Press, 1990). Fisman, Raymond, S. Iyengar, E. Kamenica, and Itamar Simonson, “Racial Preferences in Dating,” Review of Economic Studies, 75 (2008), 117–132. Glaeser, E., and S. Glendon, “Incentives, Predestination and Free Will,” Economic Inquiry, 36 (1998), 429–443. Guiso, Luigi, Paola Sapienza, and Luigi Zingales, “People’s Opium? Religion and Economic Attitudes,” Journal of Monetary Economics, 50 (2003), 225–282. Iannaccone, Laurence R., “Sacrifice and Stigma: Reducing Free-Riding in Cults, Communes, and Other Collectives,” Journal of Political Economy, 100 (1992), 271–291. Ibn Battuta, Tuhfat al-Nuzzar fi Ghara’ib al-Amsar (Beirut: Dar al-Kutub al-’Ilmiyya, 2002 [originally published ca. 1355]). Johnson, D. W., and R. T. Johnson, 1983. “The Socialization and Achievement Crisis: Are Cooperative Learning Experiences the Solution?” in Applied Social Psychology Annual, Vol. 4, L. Bickman, ed. (Beverly Hills, CA: Sage, 1983). Kessler, R. C., P. R. Barker, L. J. Colpe, J. F. Epstein, J. C. Gfroerer, E. Hiripi, M. J. Howes, S-L. T. Normand, R. W. Manderscheid, E. E. Walters, and A. M. Zaslavsky, “Screening for Serious Mental Illness in the General Population,” Archives of General Psychiatry, 60 (2003), 184–189.

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MULTINATIONAL FIRMS, FDI FLOWS, AND IMPERFECT CAPITAL MARKETS∗ ` POL ANTRAS MIHIR A. DESAI C. FRITZ FOLEY This paper examines how costly financial contracting and weak investor protection influence the cross-border operational, financing, and investment decisions of firms. We develop a model in which product developers can play a useful role in monitoring the deployment of their technology abroad. The analysis demonstrates that when firms want to exploit technologies abroad, multinational firm (MNC) activity and foreign direct investment (FDI) flows arise endogenously when monitoring is nonverifiable and financial frictions exist. The mechanism generating MNC activity is not the risk of technological expropriation by local partners but the demands of external funders who require MNC participation to ensure value maximization by local entrepreneurs. The model demonstrates that weak investor protections limit the scale of MNC activity, increase the reliance on FDI flows, and alter the decision to deploy technology through FDI as opposed to arm’s length technology transfers. Several distinctive predictions for the impact of weak investor protection on MNC activity and FDI flows are tested and confirmed using firm-level data.

I. INTRODUCTION Firms globalizing their operations and the associated capital flows have become major features of the world economy. These cross-border activities and capital flows span institutional settings with varying investor protections and levels of capital market development. Although the importance of institutional heterogeneity in dictating economic outcomes has been emphasized, existing analyses typically ignore the global firms and the capital flows that are now commonplace. Investigating how global firms make operational and financing decisions in a world of heterogeneous institutions promises to provide a novel perspective on observed patterns of flows and firm activity. ∗ The statistical analysis of firm-level data on U.S. multinational companies was conducted at the Bureau of Economic Analysis, U.S. Department of Commerce, under arrangements that maintain legal confidentiality requirements. The views expressed are those of the authors and do not reflect official positions of the U.S. Department of Commerce. The authors thank Robert Barro, four anonymous referees, Gita Gopinath, James Markusen, Aleh Tsyvinski, Bill Zeile, and seminar participants at Boston University, Brown University, Hitotsubashi University, MIT, the NBER ITI program meeting, the New York Fed, Oxford, UC Berkeley, UC Boulder, Universidad de Vigo, Universitat Pompeu Fabra, the University of Michigan, and the World Bank for helpful suggestions. Davin Chor provided excellent research assistance. C 2009 by the President and Fellows of Harvard College and the Massachusetts Institute of

Technology. The Quarterly Journal of Economics, August 2009

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This paper develops and tests a model of the operational and financial decisions of firms as they exploit their technologies in countries with differing levels of investor protections. The model demonstrates that multinational firm (MNC) activity and foreign direct investment (FDI) arise endogenously in settings characterized by financial frictions. The model generates several predictions regarding how investor protections influence the use of arm’s length technology transfers, the degree to which MNC activity is financed by capital flows, the extent to which multinationals take ownership in foreign projects, and the scale of multinational operations. These predictions are tested using firm-level data on U.S. MNCs. The model considers the problem of a firm that has developed a proprietary technology and is seeking to deploy this technology abroad with the help of a local entrepreneur. A variety of alternative arrangements, including an arm’s length technology transfer or directly owning and financing the entity that uses it, are considered. External investors are a potential source of funding, but they are concerned with managerial misbehavior, particularly in settings where investor protections are weak. The central premise of the model is that developers of technologies are particularly useful monitors for ensuring that local entrepreneurs are pursuing value maximization. The concerns of external funders regarding managerial misbehavior lead to optimal contracts in which the developer of the technology is required to hold an ownership claim in the foreign project and, in certain cases, this developer is also required to provide financial capital to the local entrepreneur. As such, MNCs and FDI flows arise endogenously in response to concerns over managerial misbehavior and weak investor protections.1 Extending the model to allow for a similar form of monitoring by external investors does not vitiate the primary results. We also show that although simple revenue-sharing agreements may also provide incentives for technology developers to monitor, this type of contract is generally not optimal. 1. The experience of Disney in Japan, as documented in Misawa (2005), provides one example of the mechanism that drives the behavior of external investors. In 1997, Disney was evaluating how to structure a new opportunity with a local partner in Japan. Japanese banks expressed a strong preference for equity participation by Disney over a licensing agreement in order to ensure that Disney had strong incentives to monitor the project and ensure value maximization. The concerns of these lenders and the intuition that Disney would have a unique ability to monitor local partners are reflective of the central ideas of the model.

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The characterization of MNCs as developers of technologies has long been central to models explaining MNC activity. In contrast to those models that emphasize the risk of technology expropriation, the model in this paper emphasizes financial frictions, a cruder form of managerial opportunism and the role of external funders. As such, although technology is central to these other models and the model in this paper, the mechanism generating MNC activity is entirely distinct. Our emphasis on monitoring builds on the theory presented by Holmstrom and Tirole (1997), which captures how monitoring is critical to understanding financial intermediation. Our model delivers several novel predictions about the nature of FDI and patterns of MNC activity. First, the model predicts that arm’s length technology transfers will be more common, relative to the deployment of that technology through affiliate activity, in countries where investor protections are stronger. Second, the share of activity abroad financed by capital flows from the multinational parent will be decreasing in the quality of investor protections in host economies. Third, ownership shares by multinational parents will also be decreasing in the quality of investor protections in host economies. These predictions reflect the fact that monitoring by the developer of the technology is more critical in settings where investor protections are weaker. The model also predicts that the scale of activity based on multinational technologies in host countries will be an increasing function of the quality of the institutional environment. Better investor protections reduce the need for monitoring and therefore allow for a larger scale of activity. We test these predictions using the most comprehensive available data on the activities of U.S. MNCs and on arm’s length technology transfers by U.S. firms. These data provide details on the worldwide operations of U.S. firms, including measures of parental ownership, financing and operational decisions, and information on royalty payments and licensing fees received by U.S. firms from unaffiliated foreign persons. The data enable the use of parentyear fixed effects that implicitly control for a variety of unobserved attributes. The analysis indicates that the likelihood of using arm’s length technology transfer to serve a foreign market increases with measures of investor protections, as suggested by the model. The predictions on parent financing and ownership decisions are also confirmed to be a function of the quality of investor

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protections and the depth of capital markets. The model also suggests that these effects should be most pronounced for technologically advanced firms because these firms are most likely to be able to provide valuable monitoring services. The empirical evidence indicates a differential effect for such firms. Settings where ownership restrictions are liberalized provide an opportunity to test the final prediction of the model. The model implies that ownership liberalizations should have a particularly large effect on multinational affiliate activity in countries with weak investor protections. Our empirical analysis confirms that affiliate activity increases by larger amounts after liberalizations in countries with weaker investor protections. This paper extends the large and growing literature on the effects of investor protections and capital market development on economic outcomes to an open-economy setting where firms make operational and financial decisions across borders. La Porta et al. (1997, 1998) relate investor protections to the concentration of ownership and the depth of capital markets. A large literature, including King and Levine (1993), Levine and Zervos (1998), Rajan and Zingales (1998), Wurgler (2000), and Acemoglu, Johnson, and Mitton (2005), has shown that financial market conditions influence firm investment behavior, economic growth, and industrial structure. By exclusively emphasizing firms with local investment and financing, this literature has neglected how cross-border, intrafirm activity responds to institutional variations. The open-economy dimensions of institutional variations have been explored but overwhelmingly in the context of arm’s-length cross-border lending as in Gertler and Rogoff (1990), Boyd and Smith (1997), and Shleifer and Wolfenzon (2002).2 In related work, Albuquerque (2003) shows that the differential alienability of FDI and portfolio inflows can allow the risk of expropriation to alter the composition of capital inflows. In contrast to this work, we derive the existence of MNCs and FDI flows in response to the possibility of opportunism by private actors. Accordingly, our empirical work employs firm-level data that allow us to 2. Gertler and Rogoff (1990) show how arm’s length lending to entrepreneurs in poor countries is limited by their inability to pledge large amounts of their own wealth. This insight is embedded into an MNC’s production decisions in the model presented here. Our setup also relates to Shleifer and Wolfenzon (2002), who study the interplay between investor protection and equity markets. In contrast, Kraay et al. (2005) emphasize the role of sovereign risk in shaping the structure of world capital flows.

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analyze both patterns of firm activity and financial flows rather than the division of aggregate capital flows between FDI and portfolio flows. In short, we show that weak financial institutions decrease the scale of MNC activity but simultaneously increase the reliance on capital flows from the parent. As such, observed patterns of capital flows reflect these two distinct and contradictory effects. The empirical investigations of microdata provided in the paper indicate that both effects are operative.3 By jointly considering the determinants of MNC activities and the flows of capital that support these activities, the paper also links two literatures—the international trade literature on multinationals and the macroeconomic literature on capital flows. Industrial-organization and international-trade scholars characterize multinationals as having proprietary assets and emphasize the role of market imperfections, such as transport costs and market power, in determining patterns of multinational activity. Recent work on MNCs investigates “horizontal” or “vertical” motivations4 for FDI and explores why alternative productive arrangements, such as whole ownership of foreign affiliates, joint ventures, exports, or arm’s length contracts, are employed.5 Such analyses of MNC activity typically do not consider associated capital flows.6 Research on capital flows typically abstracts 3. It should be emphasized that our model abstracts from any portfolio decision by investors and instead focuses on the financing decisions of firms. Bertaut, Griever, and Tryon (2006) analyze U.S. ownership of foreign securities and conclude that nonfinancial institutions are a fairly small fraction (less than 10%) of overall foreign portfolio investment, and this is when including all securities such as fixed-income investments. As such, our model (unlike the one in Albuquerque [2003]) may not be particularly well suited to interpret cross-country patterns in the composition of capital flows. 4. The horizontal FDI view represents FDI as the replication of capacity in multiple locations in response to factors such as trade costs, as in Markusen (1984), Brainard (1997), Markusen and Venables (2000), and Helpman, Melitz, and Yeaple (2004). The vertical FDI view represents FDI as the geographic distribution of production globally in response to the opportunities afforded by different markets, as in Helpman (1984) and Yeaple (2003). Caves (1996) and Markusen (2002) provide particularly useful overviews of this literature. ` (2003, 2005), Antras ` and Helpman 5. Ethier and Markusen (1996), Antras (2004), Desai, Foley, and Hines (2004a), Grossman and Helpman (2004), and Feenstra and Hanson (2005) analyze the determinants of alternative foreign production arrangements. 6. Several studies linking levels of MNC activity and FDI flows are worth noting. First, high-frequency changes in FDI capital flows have been linked to relative wealth levels through real exchange rate movements (as in Froot and Stein [1991] and Blonigen [1997]), broader measures of stock market wealth (as in Klein and Rosengren [1994] and Baker, Foley, and Wurgler [2009]) and to credit market conditions (as in Klein, Peek, and Rosengren [2002]). Second, MNCs have also been shown to opportunistically employ internal capital markets in weak institutional environments (as in Desai, Foley, and Hines [2004b]) and during currency crises (as in Aguiar and Gopinath [2005] and Desai, Foley, and Forbes [2008]). These

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from firm activity and has focused on the paradox posed by Lucas (1990) of limited capital flows from rich to poor countries in the face of large presumed rate-of-return differentials. Whereas Lucas (1990) emphasizes human-capital externalities to help explain this paradox, Reinhart and Rogoff (2004) review subsequent research on aggregate capital flows and conclude that credit market conditions and political risk play significant roles. By examining firm behavior in a setting with variation in investor protections, this paper attempts to unify an investigation of MNC activity and FDI flows. The rest of the paper is organized as follows. Section II lays out the model and generates several predictions related to the model. Section III provides details on the data employed in the analysis. Section IV presents the results of the empirical analysis, and Section V concludes. II. THEORETICAL FRAMEWORK In this section, we develop a model of financing that builds on and extends the work of Holmstrom and Tirole (1997).7 We illustrate how the model generates both multinational activity as well as FDI flows. Finally, we explore some firm-level empirical predictions that emerge from the model and that we take to the data in later sections. II.A. A Model of Financial Contracting Environment. We consider the problem of an agent—an inventor—who is endowed with an amount W of financial wealth and the technology or knowledge to produce a differentiated good. Consumers in two countries, Home and Foreign, derive utility from consuming this differentiated good. (Appendix I develops a multicountry version of the model.) The good, however, is papers emphasize how heterogeneity in access to capital can interact with MNC production decisions. Marin and Schnitzer (2004) also study the financing decisions of MNCs in a model that stresses managerial incentives. Their model, however, takes the existence of MNCs as given and considers an incomplete-contracting setup, in contrast to our complete-contracting setup. The predictions from their model are quite distinct to the ones we develop here and show to be supported by U.S. data. 7. Our model generalizes the setup in Holmstrom and Tirole (1997) by allowing for diminishing returns to investment and for variable monitoring levels. The scope of the two papers is also very distinct: Holmstrom and Tirole (1997) study the monitoring role of banks in a closed-economy model, whereas our focus is on MNCs.

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prohibitively costly to trade, and thus servicing a particular market requires setting up a production facility in that country. The inventor is located at Home and cannot fully control production in Foreign. Servicing that market thus requires contracting with a foreign agent—an entrepreneur—to manage production there. We assume that entrepreneurs are endowed with no financial wealth and their outside option is normalized to 0. There also exists a continuum of infinitessimal external investors in Foreign that have access to a technology that gives them a gross rate of return equal to 1 on their wealth. All parties are risk neutral and are protected by limited liability. There are three periods: a date-0 contracting stage, a date-1 investment stage, and a date-2 production/consumption stage. Consumer Preferences and Technology. In the main text, we focus on describing production and financing decisions in the Foreign market. For that purpose, we assume that preferences and technology at Home are such that at date 2 the inventor obtains a constant gross return β > 1 for each unit of wealth he invests in production at Home at date 1. We refer to this gross return as the inventor’s shadow value of cash. Our assumption β > 1 implies that the opportunity cost of funds is lower for external investors than for the inventor. In Appendix I, this higher-than-1 value of β is endogenously derived in a multicountry version of the model where consumer preferences, technology, and financial contracting in all countries are fully specified. Note that the provision that β > 1 does not imply that the effective cost of capital provided by external investors is always lower than the effective cost of capital provided by the inventor because informational frictions may drive a wedge between returns earned and the costs borne by the relevant parties. We assume that Foreign preferences are such that cash flows or profits obtained from the sale of the differentiated good in Foreign can be expressed as a strictly increasing and concave function of the quantity produced; that is, R(q), with R (q) > 0 and R (q) ≤ 0. We also assume the standard conditions R(0) = 0, limq→0 R (q) = +∞, and limq→∞ R (q) = 0. These properties of R(q) can be derived from preferences featuring a constant (and higher-than-1) elasticity of substitution across a continuum of differentiated goods produced by different firms. In such case, the elasticity of R(q) with respect to q is constant and given by a parameter α ∈ (0, 1).

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Foreign production is managed by the foreign entrepreneur, who at date 1 can privately choose to behave and enjoy no private benefits, or misbehave and take private benefits. When the manager behaves, the project performs with probability pH , in the sense that when an amount x is invested at date 1, project cash flows at date 2 are equal to R(x) with probability pH and 0 otherwise.8 When the manager misbehaves, the project performs with a lower probability pL < pH and expected cash flows are pL R(x). We assume that the private benefit a manager obtains from misbehaving is increasing in the size of the project, and for simplicity, we specify it as being proportional to the return of the project, that is, BR(x). In Section II.C, we discuss how similar results obtain if private benefits are proportional to the level of investment x. Managerial misbehavior and the associated private benefits can be manifested by choosing to implement the project in a way that generates perquisites for the manager or his associates, in a way that requires less effort, or in a way that is more fun or glamorous. As described below, we relate the ability to engage in such private benefits to the level of investor protections in Foreign as well as to the extent to which the entrepreneur is monitored. The idea is that countries with better investor protections tend to enforce laws that limit the ability of managers to divert funds from the firm or to enjoy private benefits or perquisites. This interpretation parallels the logic in Tirole (2005, p. 359). When investor protections are not perfectly secure, monitoring by third agents is helpful in reducing the extent to which managers are able to divert funds or enjoy private benefits. Following Holmstrom and Tirole (1997), we introduce a monitoring technology that reduces the private benefit of the foreign entrepreneur when he misbehaves. It is reasonable to assume that the inventor can play a particularly useful role in monitoring the behavior of the foreign entrepreneur because the inventor is particularly well informed about how to manage the production of output using its technology. Intuitively, the developer of a technology is in a privileged position to determine if project failure is associated with managerial actions or bad luck.9 We capture this in a 8. This assumes that, when the project succeeds, each unit invested results in a unit of output (q = x), whereas when the project fails, output is zero (q = 0). We relax the latter assumption in Section II.C. 9. An alternative way to interpret monitoring is as follows. Suppose that the foreign entrepreneur can produce the good under a variety (a continuum, actually) of potential techniques indexed by z ∈ [0, B]. Technique 0 entails a probability of success equal to pH and a zero private benefit. All techniques with z > 0 are

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stark way by assuming that no other agent in the economy can productively monitor the foreign entrepreneur, though we discuss a more general setup in Section II.C. We assume that monitoring costs are proportional to the return of the project and when the inventor incurs an effort cost C R(x) in monitoring at date 1, the private benefit for the local entrepreneur is multiplied by a ¯ limC→∞ δ (C ) = 0, factor δ (C ), with δ (C ) < 0, δ (C ) > 0, δ(0) = δ, limC→0 δ (C ) = −∞, and limC→∞ δ (C ) = 0.10 This assumption reflects the idea that larger projects require effort to monitor. Section II.C considers the possibility that effort costs are proportional to investment levels and similar results follow. As mentioned earlier, the scope of private benefits is related to the level of investor protection of the host country by an index γ ∈ (0, 1). In particular, we specify that (1)

B (C; γ ) = (1 − γ ) δ(C).

Note that this formulation implies that ∂ B(·)/∂γ < 0, ∂ B(·)/∂C < 0, and ∂ 2 B(·)/∂C∂γ = −δ (C) > 0. This formulation captures the intuition that the scope for private benefits is decreasing in both investor protection and monitoring and that monitoring has a relatively larger effect on private benefits in countries with poor legal protection of investors. It also implies that parent monitoring substitutes for investor protection. The idea behind this assumption is that both parent monitoring and investor protections constrain managers and that parent monitoring is effective even in imperfect legal environments. This would be the case if, for example, parent monitoring during the production process prevented misbehavior from occurring, thus eliminating any need for legal action after improper behavior occurs. Contracting. We consider optimal contracting between three sets of agents: the inventor, the foreign entrepreneur, and foreign external investors. At date 0, the inventor and the foreign entrepreneur negotiate a contract that stipulates the terms under which the entrepreneur will exploit the technology developed by

associated with a probability of success equal to pL and a private benefit equal to z. Clearly, all techniques with z ∈ (0, B) are dominated from the point of view of the foreign entrepreneur, who will thus effectively (privately) choose either z = 0 or z = B, as assumed in the main text. Under this interpretation, we can think of monitoring as reducing the upper bound of [0, B]. 10. These conditions are sufficient to ensure that the optimal contract is unique and satisfies the second-order conditions.

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the inventor. This contract includes a (possibly negative) date-0 transfer F from the inventor to the entrepreneur, as well as the agents’ date-2 payoffs contingent on the return of the project.11 When F > 0, the date-0 payment represents the extent to which the inventor cofinances the project in the Foreign country. When F < 0, this payment can be thought of as the price or up-front royalties paid for the use of the technology, which the inventor can invest in the Home market at date 1. The contract between the inventor and the entrepreneur also stipulates the date-1 scale of investment x, while the managerial and monitoring efforts of the entrepreneur and inventor, respectively, are unverifiable and thus cannot be part of the contract. Also at date 0, the foreign entrepreneur and external investors sign a financial contract under which the entrepreneur borrows an amount E from the external investors at date 0 in return for a date-2 payment contingent on the return of the project. We consider an optimal contract from the point of view of the inventor and allow the contract between the inventor and the entrepreneur to stipulate the terms of the financial contract between the entrepreneur and foreign external investors. We rule out “direct” financial contracts between the inventor and foreign external investors. This is justified in the extension of the model developed in Appendix I, where the inventor’s shadow value of cash β is endogenized. Given the payoff structure of our setup and our assumptions of risk neutrality and limited liability, it is straightforward to show that an optimal contract is such that all date-2 payoffs can be expressed as shares of the return generated by the project. All agents obtain a payoff equal to zero when the project fails (i.e., when the return is zero) and a positive payoff when the project succeeds (in which case cash flows are positive). When an agent’s share of the date-2 return is positive, this agent thus becomes an equity holder in the entrepreneur’s production facility.12 We define φ I and φ E as the equity shares held by the inventor and external investors, respectively, with the remaining share 1 − φ I − φ E 11. For simplicity, we assume that the inventor’s date-2 return in its Home market (which is not modeled in the main text) is not pledgeable in Foreign. 12. We focus on an interpretation of payoffs resembling the payoffs of an equity contract, but the model is not rich enough to distinguish our optimal contract from a standard debt contract. Our results would survive in a model in which agents randomized between using equity and debt contracts. In any case, we bear this in mind in the empirical section of the paper, where we test the predictions of the model.

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accruing to the foreign entrepreneur. Notice that when φ I is large enough, the entrepreneur’s production facility becomes a subsidiary of the inventor’s firm. II.B. Optimal Contract and Empirical Predictions We next characterize an optimal contract that induces the entrepreneur to behave and the inventor to monitor. This optimal ˜ C} ˜ that solves the ˜ φ˜ I , x, ˜ φ˜ E , E, contract is given by the tuple { F, following program: max

I = φ I pH R(x) + (W − F ) β − C R(x)

s.t.

x ≤ E+ F pH φ E R(x) ≥ E pH (1 − φ E − φ I ) R(x) ≥ 0 ( pH − pL) (1 − φ E − φ I ) R(x) ≥ (1 − γ ) δ (C ) R (x ) ( pH − pL) φ I R(x) ≥ C R(x).

F,φ I ,x,φ E ,E,C

(P1)

(i) (ii) (iii) (iv) (v)

The objective function represents the payoff of the inventor. The first term represents the inventor’s dividends from the expected cash flows of the foreign production facility. The second term represents the gross return from investing his wealth W minus the date-0 transfer F in the Home market.13 The last term represents the monitoring costs. The first constraint is a financing constraint. Because the local entrepreneur has no wealth, his ability to invest at date 1 is limited by the sum of the external investors’ financing E and the cofinancing F by the inventor. The second inequality is the participation constraint of external investors, who need to earn at least an expected gross return on their investments equal to 1. Similarly, the third inequality is the participation constraint of the foreign entrepreneur, given his zero outside option. The fourth inequality is the foreign entrepreneur’s incentive compatibility constraint. This presumes that it is in the interest of the inventor to design a contract in a way that induces the foreign entrepreneur to behave. In Appendix II, we show that this will necessarily be the case, provided that γ is sufficiently large. The final constraint is the inventor’s incentive compatibility constraint: if this condition was not satisfied, the inventor’s payoff would be 13. We assume throughout that W is large enough to ensure that W − F ≥ 0 in equilibrium.

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lower when exerting the monitoring level C˜ than when not doing so.14 In the program above, constraint (iii) will never bind. Intuitively, as is standard in incomplete information problems, the incentive compatibility constraint of the entrepreneur demands that this agent obtains some informational rents in equilibrium, and thus his participation constraint is slack. Conversely, the other four constraints will bind in equilibrium. This is intuitive for the financing constraint (i) and the participation constraint of investors (ii). It is also natural that the optimal contract from the point of view of the inventor will seek to minimize the (incentivecompatible) equity share accruing to the foreign entrepreneur, which explains why constraint (iv) binds. It is perhaps less intuitive that constraint (v) also binds, indicating that the optimal contract minimizes the equity share φ I allocated to the inventor. In particular, it may appear that a large φ I would be attractive because it may foster a larger level of cofinancing F at date 0, thereby encouraging investment. However, inspection of constraint (iv) reveals that a larger φ I decreases the ability of the entrepreneur to borrow from external investors, as it reduces his pledgeable income. Overall, one can show that, for a given level of monitoring, whether utility is transferred through an equity share or a date-0 lump-sum payment has no effect on the scale of the project. In addition, it is clear from the objective function that the inventor strictly prefers a date-0 lump-sum transfer because he can use these funds to invest domestically and obtain a gross rate of return β > 1 on them. Hence, the minimal incentive-compatible inventor equity share φ I is optimal. With these results at hand, it is immediate from constraint (v) that the optimal equity stake held by the inventor will be given by (2)

φ˜ I =

C˜ , pH − pL

which will be positive as long as C˜ is positive. In addition, manipulation of the first-order conditions of program (P1) delivers the following expression that implicitly determines the level of 14. Our derivation of this IC constraint assumes that if the inventor deviates ˜ it does so by setting C = 0 (which for large enough δ¯ would lead to a from C, violation of the entrepreneur’s incentive compatibility constraint). This is without loss of generality because any other deviation C > 0 is dominated.

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monitoring (see Appendix II for details): (3)

˜ = − δ (C)

βpH − pL . (1 − γ )βpH

Straightforward differentiation of (3) together with the convexity of the function δ (·) produces the following result: LEMMA 1. The amount of monitoring C˜ is decreasing in both investor protection γ in Foreign and in the inventor’s shadow value of cash β. The effect of investor protection on monitoring is intuitive. Given our specification of the private benefit function B (·) in (1), the marginal benefit from monitoring is larger, the less developed is the financial system in Foreign (the lower is γ ). Because the marginal cost of monitoring is independent of γ , C˜ and γ are negatively correlated in the optimal contract. The effect of the shadow value of cash β on monitoring is a bit subtler. The intuition behind the result lies in the fact that the larger that β is, the larger is the opportunity cost of remunerating the inventor through ex-post dividends rather than through an ex-ante lump-sum transfer. Because of the tight mapping between φ˜ I and C˜ imposed by the incentive compatibility constraint in (v), we have that a larger β is also associated with a higher shadow cost of monitoring and hence with a lower optimal amount of monitoring. In light of (2), it is clear that our theory has implications for the share of equity held by the inventor that relate closely to the implications for monitoring. In particular, φ˜ I is proportional to the level of monitoring C˜ and thus is affected by the parameters γ and β in the same way as is monitoring. This reflects that equity shares emerge in our model as incentives for the inventor to monitor the foreign entrepreneur. As a result, we can establish the following proposition. PROPOSITION 1. The share of equity held by the inventor is decreasing both in investor protection γ in Foreign and in the inventor’s shadow value of cash β. An immediate corollary of this result follows. COROLLARY 1. Suppose that a transaction is recorded as an FDI transaction only if φ˜ I ≥ φ I .Then, there exists a threshold

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investor protection γ ∗ ∈ 0, 1 such that the optimal contract entails FDI only if γ < γ ∗ . Our theory thus predicts that the prevalence of FDI in a given country should, other things equal, be a decreasing function of the level of investor protection in that country. Manipulation of the first-order conditions of program (P1) also delivers an implicit function of the level of investment as a ˜ function of parameters and the optimal level of monitoring C: (4)

R (x˜ ) =

1 ˜ . ˜ βpH − pL C (1 − γ ) δ C − 1− pH − pL pH − pL βpH

pH

Equation (4) implicitly defines the level of expected sales by the firm, that is, pH R (x˜ ). Differentiating this equation with respect to γ and β, we obtain the following proposition (see Appendix III for details). PROPOSITION 2. Output and cash flows in Foreign are increasing in investor protection γ in Foreign and decreasing in the inventor’s shadow value of cash β. The intuition for the effect of investor protection is straightforward. Despite the fact that the inventor’s monitoring reduces financial frictions, both the foreign entrepreneur’s compensation, as dictated by his incentive compatibility constraint (iv), and monitoring costs are increasing in the scale of operation. In countries with weaker investor protections, the perceived marginal cost of investment is higher, thus reducing equilibrium levels of investment. Using constraints (i), (ii), and (iv), one can also obtain the terms of the optimal financial contract with external investors in terms of C˜ and x: ˜ ˜ C˜ (1 − γ ) δ(C) − , φ˜ E = 1 − pH − pL pH − pL ˜ E˜ = pH φ˜ E R(x). Finally, straightforward manipulation delivers an optimal lumpsum date-0 transfer equal to R (x˜ ) pL ˜ ˜ − 1 x. ˜ C R (x˜ ) − F= β ( pH − pL) R (x˜ ) x˜

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Depending on parameter values, the lump-sum transfer can be positive or negative, and it also varies nonmonotonically with the parameters of the model. We can, however, derive sharper predictions for the share of financing that is provided by the inventor. To see this, focus on the case in which the date-0 payment F˜ is positive and can be interpreted as the level of cofinancing by the inventor. The share of investment financed by the inventor is then given by (5)

pL 1 − α (x˜ ) R (x˜ ) F˜ = − , C˜ x˜ β ( pH − pL) x˜ α (x˜ )

where α(x) ≡ x R (x)/R(x) is the elasticity of revenue to output. As mentioned earlier, when preferences feature a constant elasticity of substitution across a continuum of differentiated goods produced by different firms, α(x) is independent of x, and R(x) can be written as R(x) = Ax α , where A > 0 and α ∈ (0, 1). Notice that the first term in (5) is increasing in C˜ and decreasing in x˜ due to the concavity of R(x). It thus follows from Lemma 1 and Proposition 2 that this first term is necessarily decreasing in γ . As for the second term, it will increase or decrease in x˜ depending on the properties of α(x). In most applications, α(x) will be either independent of x or decreasing in x (e.g., when the firm faces a linear demand function). In those situations, the second term in (5) will also be decreasing in γ and we can conclude the following. ˜ is sufficiently small, the share PROPOSITION 3. Provided that α (x) ˜ x) of inventor financing in total financing ( F/ ˜ is decreasing in investor protection γ . The intuition behind the result is that monitoring by inventors has a relatively high marginal product in countries with weak financial institutions. To induce the inventor to monitor, the optimal contract specifies a relatively steeper payment schedule, with a relatively higher contribution by the inventor at date 0 (a higher ˜ x) F/ ˜ in anticipation of a higher share of the cash flows generated by the project at date 2 (a higher φ˜ I ).15 ˜ x˜ is ambiguous. A 15. The effect of the shadow value of cash on the ratio F/ larger β is associated with a lower monitoring level C˜ (Lemma 1), but also with a lower level of x˜ and thus a higher ratio R (x˜ ) /x˜ (Proposition 2). In addition, β has an additional direct negative effect on the ratio. The overall effect is, in general, ambiguous.

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The fact that the monitoring provided by the inventor is unverifiable by third parties is central to our theory of FDI. In particular, if monitoring was verifiable (and thus contractible), the optimal contract analogous to the one described above would immediately imply an equity share for the inventor equal to zero (see ` Desai, and Foley [2007] for details). Hence, the inventor Antras, would never choose to deploy her technology abroad through FDI. Instead, the inventor would sell the technology to the foreign entrepreneur in exchange for a positive lump-sum fee (and, hence, the inventor would never cofinance the project). In Section IV, we present empirical tests of Propositions 1, 2, and 3, and Corollary 1. Appendix I shows that Propositions 1, 2, and 3 continue to hold in a multicountry version of the model in which the statements apply to cross-sectional variation in investor protections. Our empirical tests exploit variation in the location of affiliates of U.S. MNCs and analyze the effect of investor pro˜ x. ˜ We identify the inventor in tections on proxies for x, ˜ φ˜ I , and F/ the model as being a parent firm and control for other parameters of the model, such as the shadow value of cash β, the concavity of R(x), the monitoring function δ (C ), and the probabilities pH and pL by using fixed effects for each firm in each year and controlling for a wide range of host-country variables. Because our estimation employs parent-firm fixed effects, we are not able to test the predictions regarding the effect of β in Propositions 1, 2, and 3. II.C. Generalizations Before proceeding to the empirical analysis, it is useful to consider the robustness of these results to more general environments. In particular, we consider the degree to which revenue sharing might substitute for equity contracts, the possibility that private benefits and monitoring costs may be proportional to x rather than R(x), and the effects of introducing productive monitoring by external investors. The underlying analysis is provided in Appendix IV. In the model above, we assume that when the project fails, it delivers a level of revenue equal to zero. Such an assumption greatly enhances tractability but suggests that revenue-sharing contracts may provide benefits similar to equity arrangements. This is problematic because it blurs the mapping between φ I in the model and equity shares in the data. More generally, however, revenue-sharing contracts are not optimal when the project delivers a positive level of revenue in case of failure. In fact, a simple

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contract in which external investors are issued secured (or riskfree) debt and the inventor and entrepreneur take equity stakes is optimal.16 To see the intuition for this, consider the same setup as in Section II.A, but now assume that, when the project does not perform, it yields a level of revenue equal to R(x) ∈ (0, R(x)). As is standard in moral hazard problems with risk-neutral agents, the optimal contract calls for the agents undertaking unobservable actions (e.g., effort decisions) to be maximally punished (subject to the limited-liability constraint) whenever a failure of the project is observed. In our particular setup, this would imply that the optimal contract yields both the inventor and the entrepreneur a payoff of zero whenever a project failure is observed. The entire revenue stream R(x) should accrue to external investors. A straightforward way to implement such a contract is for the entrepreneur to issue an amount of secure debt equal to R(x) to external investors and for the inventor and entrepreneur to be equity holders. Once the debt is paid, the inventor and entrepreneur receive a share of zero in case of project failure and a share of the amount R(x) − R(x) in case of project success. The determination of their optimal shares is analogous to that in Section II.A with R(x) − R(x) replacing R(x) (details available upon request). In this more general setting, it is not possible to implement this optimal allocation of payoffs across agents through simple revenue-sharing arrangements. As such, the model can explain why an instrument with the features of equity tends to dominate both fixed-fee and revenue-sharing contracts in financially underdeveloped countries. Such contracts will likely entail an inefficiently low punishment to the inventor when the project does not perform well. We next briefly discuss alternative formulations for the entrepreneur’s private benefit of misbehavior and the inventor’s private cost of monitoring. We have assumed above that these are proportional to the revenue generated by the project in case of success. If instead we specified them as being proportional to x, then the optimal equity share φ˜ I would be given by φ˜ I =

C˜ x˜ ( pH − pL) R (x˜ )

16. A contract in which an entrepreneur issues debt to external investors appears to have empirical validity because most capital provided to affiliates from local sources takes the form of debt.

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and would also depend on x˜ and the concavity of the R(x) ˜ function. One may thus worry that for a sufficiently concave R(x) ˜ function, it could be the case that equity stakes could be low in low-γ countries on account of the low values of x/R ˜ (x˜ ) in those countries. We show in Appendix IV, however, that our main comparative static concerning equity shares holds as long as the elasticity of revenue with respect to output—that is, α (x˜ ) ≡ x˜ R (x˜ ) /R (x˜ )—does not increase in x˜ too quickly. The required condition is analogous to that in Proposition 3 and is satisfied for the case of constant price elasticity and linear demand functions. We finally consider the possibility that local external investors (e.g., banks) also provide useful monitoring, the productivity of which may also be higher in countries with worse investor protections. In Appendix IV, we develop an extension of the model that incorporates monitoring by external investors and that, as with the monitoring by the inventor, is subject to declining marginal benefits. Although the optimal contract is now more complicated, we show that the incentive compatibility constraint for the inventor will continue to bind in equilibrium, implying that the inventor’s equity stake moves proportionally with its level of monitoring. Furthermore, provided that the level of investor protection γ is sufficiently high, the analysis remains qualitatively unaltered by the introduction of local monitoring. The reason for this is that, for large values of γ , the optimal contract already allocates equity stakes φ E to external investors that are large enough to induce them to monitor the entrepreneur.17 As a result, although certain details of the optimal contract change with the possibility of local monitoring, the comparative static results derived in Section II.B continue to hold in this more general model, provided that γ is sufficiently large. III. DATA AND DESCRIPTIVE STATISTICS The empirical work presented in Section IV is based on the most comprehensive available data on the activities of U.S. MNCs and on arm’s length technology transfers by U.S. firms. The Bureau of Economic Analysis (BEA) annual survey of U.S. Direct 17. When the level of investor protection is below a certain threshold, then the incentive compatibility for external investors becomes binding, in which case the analysis becomes more complicated. Without imposing particular functional forms on the monitoring functions, it becomes impossible to derive sharp comparative static results (see Appendix IV).

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Investment Abroad from 1982 through 1999 provides a panel of data on the financial and operating characteristics of U.S. firms operating abroad. U.S. direct investment abroad is defined as the direct or indirect ownership or control by a single U.S. legal entity of at least 10% of the voting securities of an incorporated foreign business enterprise or the equivalent interest in an unincorporated foreign business enterprise. A U.S. multinational entity is the combination of a single U.S. legal entity that has made the direct investment, called the U.S. parent, and at least one foreign business enterprise, called the foreign affiliate.18 The most extensive data for the period examined in this study are available for 1982, 1989, 1994, and 1999 when BEA conducted Benchmark Surveys. Accordingly, the analysis is restricted to benchmark years except when the annual frequency of the data is critical—in the analysis of scale in Section IV.C that uses the liberalizations of ownership restrictions. To analyze arm’s length technology transfers, measures of royalty payments, licensing fees, and other payments for intangible assets received by U.S. firms from unaffiliated foreign persons are drawn from the results of BEA’s annual BE-93 survey. This survey requires that all firms receiving payments above certain thresholds report, regardless of whether the firm is a multinational.19 Table I provides descriptive statistics for the variables used in the analysis employing the benchmark year data (Panel A) and analysis employing the full panel (Panel B). Implementing empirical tests requires mapping the variables of the model to reasonable proxies in the data. To investigate the choice of an inventor to engage in arm’s length technology transfer or FDI (Corollary 1), the analysis uses a dummy variable that is equal to 1 if a U.S. firm receives an arm’s length royalty payment from a country in a given year and 0 if that firm only serves the country through affiliate activity in a particular year. For Proposition 3’s predictions on the share of inventor financing in ˜ x), total financing ( F/ ˜ a variable is defined as the ratio of the sum of parent-provided equity and debt to affiliate assets. Specifically, this share is the ratio of the sum of parent-provided equity and 18. Coverage and methods of the BEA survey are described in Desai, Foley, and Hines (2002). The survey covers all countries and industries, classifying affiliates into industries that are roughly equivalent to three-digit SIC code industries. As a result of confidentiality assurances and penalties for noncompliance, BEA believes that coverage is close to complete and levels of accuracy are high. 19. Because these data have been collected since 1986, data used in the analysis of arm’s length technology transfers cover only 1989, 1994, and 1999.

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Mean

Standard deviation

A: Benchmark year data for Tables II–V Multinational firm variables Arm’s length technology transfer dummy 0.2552 Share of affiliate assets financed by parent 0.4146 Share of affiliate equity owned by parent 0.8991 Log of affiliate sales 9.9024 Log of affiliate employment 4.7601 Affiliate net PPE/assets 0.2355 Log of parent R&D 9.0580

0.4360 0.3267 0.2195 1.7218 1.6060 0.2264 4.3927

Country variables Creditor rights Private credit FDI ownership restrictions Workforce schooling Log of GDP Log of GDP per capita Corporate tax rate Patent protections Property rights Rule of law Risk of expropriation

2.1415 0.7536 0.2247 8.1385 26.8002 9.3995 0.3488 3.2287 4.3767 9.3207 5.1398

1.2100 0.3891 0.4174 2.1739 1.4252 1.1019 0.1060 0.8480 0.8378 1.4088 1.2731

B: Annual data for Table V Log of affiliate sales 10.1285 Log of aggregate affiliate sales 15.7572

2.1426 1.7018

Notes. Panel A provides descriptive statistics for data drawn from the benchmark year survey and used in the analysis presented in Tables II–V. Arm’s length technology transfer dummy is defined for country-year pairs in which a parent has an affiliate or from which a parent receives a royalty payment from an unaffiliated foreign person. This dummy is equal to 1 if the parent receives a royalty payment from an unaffiliated foreign person, and it is otherwise equal to 0. Share of affiliate assets financed by parents is the ratio of parentprovided equity and net parent lending to total affiliate assets. Share of affiliate equity ownership is the equity ownership of the multinational parent. Affiliate net PPE/assets is the ratio of affiliate net property plant and equipment to affiliate assets. Creditor rights is an index of the strength of creditor rights developed in Djankov, McLiesh, and Shleifer (2007); higher levels of the measure indicate stronger legal protections. ¨ ¸Private credit is the ratio of private credit lent by deposit money banks to GDP, as provided in Beck, Demirguc Kunt, and Levine (1999). FDI ownership restrictions is a dummy equal to 0 if two measures of restrictions on foreign ownership as measured by Shatz (2000) are above 3 on a scale of 1 to 5 and 1 otherwise. Workforce schooling is the average schooling years in the population over age 25 years provided in Barro and Lee (2000). Corporate tax rate is the median effective tax rate paid by affiliates in a particular country and year. Patent protections is an index of the strength of patent rights provided in Ginarte and Park (1997). Property rights is an index of the strength of property rights drawn from the 1996 Index of Economic Freedom. Rule of law is an assessment of the strength and impartiality of a country’s overall legal system drawn from the International Country Risk Guide. Risk of expropriation is an index of the risk of outright confiscation or forced nationalization of private enterprise, and it is also drawn from the International Country Risk Guide; higher values of this index reflect lower risks. Panel B provides descriptive statistics for annual data covering the 1982–1999 period that are used in the analysis presented in Table V. Log of aggregate affiliate sales is the log of affiliate sales summed across affiliates in a particular country and year.

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net borrowing by affiliates from the parent to affiliate assets.20 Proposition 1 considers the determinants of the share of equity held by the inventor, φ I , and this variable is measured in the data as the share of affiliate equity owned by the multinational parent. The log of affiliate sales is used to test Proposition 2’s predictions on the scale of affiliate activity. Table I also provides descriptive statistics for a number of other variables. Two measures of investor protections and capital market development are used in the analysis below. Because the model emphasizes the decisions of local lenders, the first measure is creditor rights. This measure is drawn from Djankov, McLiesh, and Shleifer (2007), which extends the sample studied by La Porta et al. (1998) to cover a broader sample of countries over the 1982–1999 period on an annual basis. Creditor rights is an index taking values between 0 and 4 and measures the extent to which the legal system constrains managers from diverting value away from creditors (as a large γ does in the model).21 The second measure is the annual ratio of private credit provided by deposit money banks and other financial institutions ¨ ¸ -Kunt, and Levine to GDP, and it is drawn from Beck, Demirguc (1999). This measure has the advantage of being an objective, continuous measure of the lending environment that captures the willingness of lenders to provide credit in response to investor protections.22 Measures of capital market development are correlated with other measures of economic and institutional development that could affect the outcome studied in ways not considered in the 20. In the model, we have interpreted all sources of financing as equity financing, but as explained in footnote 12, our setup is not rich enough to distinguish equity financing from debt financing. Hence, our empirical tests of Proposition 5 include both. 21. Specifically, the measure is an index formed by adding 1 when (1) the country imposes restrictions, such as creditors’ consent or minimum dividends to file for reorganization; (2) secured creditors are able to gain possession of their security once the reorganization petition has been approved (no automatic stay); (3) secured creditors are ranked first in the distribution of the proceeds that result from the disposition of the assets of a bankrupt firm; and (4) the debtor does not retain the administration of its property pending the resolution of the reorganization. 22. It is possible to employ a measure of shareholder rights to measure investor protections. Creditor rights and private credit are used to measure investor protections for several reasons. First, shareholder rights are only available for a single year near the end of our sample. Second, in our data, there is very little local ownership of affiliate equity, but affiliates do make extensive use of debt borrowed from local sources. As such, using creditor rights and private credit allows us to capitalize on some time-series variation in investor protections and more closely corresponds empirically to the financing choices of affiliates.

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model. Therefore, the regressions control for several measures of economic and institutional variation that might otherwise obscure the analysis. The baseline specifications include controls for FDI ownership restrictions, human capital development, the log of GDP, the log of GDP per capita, and corporate tax rates. A number of countries impose restrictions on the extent to which foreign firms can own local ones. Shatz (2000) documents these restrictions using two distinct measures that capture restrictions on greenfield FDI and cross-border mergers and acquisition activity. The FDI ownership restriction dummy used below is equal to 1 if either of these measures is below 3 and 0 otherwise. Countries with more human capital, with more economic activity, or with a higher level of economic development may be more able to use technology obtained through an arm’s length transfer, and affiliates in these countries may exhibit distinctive financing patterns that reflect the quality of local entrepreneurs as opposed to financial market conditions. To address these possibilities, the specifications include workforce schooling, which measures the average schooling years in the population over 25 years old and is provided in Barro and Lee (2000). Data on the log of GDP and the log of GDP per capita come from the World Development Indicators. Firms could avoid local production or alter their financing patterns in response to tax considerations. Corporate tax rates are imputed from the BEA data by taking the median tax rate paid by affiliates that report positive net income in a particular country and year. Several other controls appear in additional specifications. Firms might choose to deploy technology through affiliate activity as opposed to through an arm’s length transfer, and they might select higher levels of ownership if they fear expropriation by local entrepreneurs (see, for instance, Ethier and Markusen [1986] for a theoretical treatment). Ginarte and Park (1997) provide a measure of the strength of patent protections, and the Index of Economic Freedom provides a measure of more general property rights. Rule of law is an assessment of the strength and impartiality of a country’s legal system, and it is drawn from the International Country Risk Guide (ICRG). Additionally, firms might fear expropriation by foreign governments and might limit foreign activity and make more extensive use of local financing in response. The ICRG also provides an index of the risk of outright

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confiscation or forced nationalization faced by foreign investors. For this measure, higher values indicate lower risks.23 Because the BEA data are a panel measuring activity of individual firms in different countries, they allow for the inclusion of effects for each firm in each year, which we refer to as parent-year fixed effects. These fixed effects help control for other parameters of the model that are likely to be specific to particular firms at particular points in time, such as the shadow value of cash β, the concavity of R(x), the monitoring function δ (C ), and the probabilities pH and pL. The inclusion of these fixed effects implies that the effects of investor protections are identified from within-firm variation in the characteristics of countries in which the firm is active. Although the comprehensive data on MNCs and arm’s length technology transfers do offer a number of advantages, it is worth noting one significant oversight. Neither the model nor the empirical work considers situations in which a firm neither invests in nor transfers technology to a particular location. IV. EMPIRICAL RESULTS Each of the analyses below is composed of a descriptive figure and firm-level regressions. The figures provide a transparent and intuitive perspective on the predictions, and the regressions allow for a full set of controls and subtler tests emphasizing the role of technology intensity. The predictions on the use of arm’s length technology transfers and the financing and ownership of foreign affiliates are investigated by pooling cross sections from the benchmark years. Investigating the effect on scale requires an alternative setup because controlling for the many unobservable characteristics that might determine firm size is problematic. Fortunately, the model provides a stark prediction with respect to scale that can be tested by analyzing responses to the easing of ownership restrictions. IV.A. Arm’s Length Technology Transfer Decisions Figure I provides a preliminary perspective on the extent to which firms deploy technology through arm’s length transfers 23. Some country-level measures of economic and institutional development are highly correlated. The multicollinearity of these variables might cause the standard errors of our key estimates to be large. However, these coefficient estimates remain unbiased.

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FIGURE I Arm’s Length Technology Transfer versus Direct Investment Arm’s length technology transfer share is the ratio of the number of firms that receive a royalty from an unaffiliated foreign person to the sum of the number of such firms and those firms that have an affiliate in a particular country and year. These shares are averaged by quintiles of private credit. Private credit varies by year and is the ratio of private credit lent by deposit money banks to GDP, as ¨ ¸ -Kunt, and Levine (1999). Higher number quintiles provided in Beck, Demirguc relate to higher values of private credit.

relative to direct ownership, across different quintiles of the private credit measure of investor protections. The propensity to use arm’s length technology transfer is computed at the country-year level as the ratio of the number of firms that receive a royalty payment from an unaffiliated foreign person to the number of firms that either receive such an arm’s length royalty or have an affiliate. The average arm’s length royalty share is 0.11 for the lowest private credit quintile of observations while it is 0.27 for the highest quintile. As predicted by the theory, firms appear to make greater use of arm’s length technology transfers, relative to direct ownership, to access countries with more developed capital markets. Table II further explores arm’s length technology transfers through specifications that include various controls and incorporate subtler tests. The dependent variable in these tests, the arm’s length technology transfer dummy, is defined for country-year pairs in which a firm either has an affiliate or receives a royalty payment from an unaffiliated foreign person. The dummy is equal to 1 if the firm receives a royalty payment from an unaffiliated

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TABLE II ARM’S LENGTH TECHNOLOGY TRANSFER VERSUS DIRECT INVESTMENT Dependent variable: Arm’s length technology transfer dummy

Creditor rights

(1)

(2)

(3)

0.0086 (0.0022)

0.0131 (0.0026)

0.0023 (0.0039) 0.0016 (0.0005)

Creditor rights* log of parent R&D Private credit Private credit* log of parent R&D FDI ownership restrictions Workforce schooling

(6)

0.0273 (0.0129)

0.0295 (0.0147)

−0.0606 (0.0133) 0.0117 (0.0020) 0.0020 (0.0097) 0.0103 (0.0024) 0.0243 (0.0039) −0.0223 (0.0077) 0.1588 (0.0438) 0.0158 (0.0066) −0.0086 (0.0066) −0.0040 (0.0046) −0.0080 (0.0055) −0.3923 (0.0968) Y 29,238 .6105

−0.0001 (0.0093) 0.0066 (0.0025) 0.0212 (0.0031) −0.0179 (0.0047) 0.1367 (0.0434)

−0.3780 (0.0840) Y

0.0079 (0.0094) 0.0134 (0.0020) 0.0268 (0.0038) −0.0144 (0.0066) 0.1777 (0.0453) 0.0127 (0.0052) −0.0254 (0.0067) −0.0022 (0.0043) −0.0080 (0.0049) −0.5162 (0.0979) Y

−0.2839 (0.0807) Y

0.0017 (0.0087) 0.0097 (0.0021) 0.0216 (0.0035) −0.0182 (0.0067) 0.1363 (0.0393) 0.0155 (0.0057) −0.0095 (0.0057) −0.0025 (0.0043) −0.0082 (0.0050) −0.2638 (0.0843) Y

37,314 .7628

36,029 .7645

30,954 .6061

34,583 .7598

33,922 .7624

Property rights Rule of law Risk of expropriation

Parent-year fixed effects? No. of obs. R2

(5)

0.0063 (0.0085) 0.0122 (0.0018) 0.0239 (0.0033) −0.0129 (0.0058) 0.1583 (0.0413) 0.0124 (0.0046) −0.0227 (0.0061) −0.0013 (0.0039) −0.0076 (0.0044) −0.3569 (0.0822) Y

0.0098 (0.0089) 0.0069 (0.0019) Log of GDP 0.0238 (0.0032) Log of GDP per capita −0.0148 (0.0039) Corporate tax rate 0.1239 (0.0435) Patent protections

Constant

(4)

Notes. The dependent variable, the arm’s length technology transfer dummy, is defined for country-year pairs in which a parent has an affiliate or from which a parent receives a royalty payment from an unaffiliated foreign person. This dummy is equal to 1 if the parent receives a royalty payment from an unaffiliated foreign person, and it is otherwise equal to 0. Creditor rights is an index of the strength of creditor rights developed in Djankov, McLiesh, and Shleifer (2007); higher levels of the measure indicate stronger legal protections. Private ¨ ¸ -Kunt, credit is the ratio of private credit lent by deposit money banks to GDP, as provided in Beck, Demirguc and Levine (1999). FDI ownership restrictions is a dummy equal to 0 if two measures of restrictions on foreign ownership as measured by Shatz (2000) are above 3 on a scale of 1 to 5 and 1 otherwise. Workforce schooling is the average schooling years in the population over age 25 years provided in Barro and Lee (2000). Corporate tax rate is the median effective tax rate paid by affiliates in a particular country and year. Patent protections is an index of the strength of patent rights provided in Ginarte and Park (1997). Property rights is an index of the strength of property rights drawn from the 1996 Index of Economic Freedom. Rule of law is an assessment of the strength and impartiality of a country’s overall legal system drawn from the International Country Risk Guide. Risk of expropriation is an index of the risk of outright confiscation or forced nationalization of private enterprise, and it is also drawn from the International Country Risk Guide; higher values of this index reflect lower risks. Each specification is an OLS specification that includes parent-year fixed effects. Heteroscedasticity-consistent standard errors that correct for clustering at the country-year level appear in parentheses.

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foreign person, and it is otherwise equal to 0. The inclusion of parent-year fixed effects controls for a variety of unobservable firm characteristics that might otherwise conflate the analysis. All specifications presented in the table also include a measure of the existence of foreign ownership restrictions, workforce schooling, the log of GDP, the log of GDP per capita, and host country tax rates.24 Standard errors are heteroscedasticity-consistent and are clustered at the country-year level. These specifications are linear probability models and are used in order to allow for both parent-year fixed effects and for clustering of standard errors at the country-year level.25 The coefficient on creditor rights in column (1) is positive and significant, affirming the prediction of Corollary 1 that firms are more likely to serve countries with higher levels of investor protections through arm’s length technology transfer as opposed to only through a foreign affiliate. The results also indicate that firms are more likely to engage in arm’s length technology transfer as opposed to just affiliate activity in countries that have a more educated workforce and that have higher corporate tax rates. The predictions of the model relate to credit market development, but the measure of creditor rights may be correlated with more general variation in the institutional environment. The specification presented in column (2) includes additional proxies for the quality of other host country institutions, including indices of patent protections, property rights, the strength and impartiality of the overall legal system, and the risk of expropriation as control variables. The coefficient on creditor rights remains positive and significant with the inclusion of these additional controls, implying that capital market conditions play an economically significant role relative to other host country institutions. The effect of a onestandard-deviation change in creditor rights is approximately one and a half times as large as the effect of a one-standard-deviation change in patent protections, which is also positive and significant in explaining the use of arm’s length technology transfer. 24. For the estimated effects of capital market conditions to be unbiased in this and the subsequent tests, these country characteristics must be exogenous to firms’ decisions to use arm’s length technology transfers as opposed to FDI, and firms’ financing and ownership decisions. 25. Given the limited time dimension of our data set, our linear specification avoids the incidental parameter problem inherent in the estimation of a large number of fixed effects. As a robustness check, these specifications have been run as conditional logit specifications. The resulting coefficients on the measures of financial development are of the same sign and statistical significance as those presented in Table II.

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The specification presented in column (3) provides a subtler test of the model and the particular mechanism that gives rise to FDI as opposed to arm’s length technology transfer. The model implies that the relative value of monitoring should be more pronounced for firms that conduct more research and development (R&D) because these firms are more likely to be deploying novel technologies that require the unique monitoring ability of parents. Alternatively, firms with limited technological capabilities are less likely to be important to external funders as monitors, and the effects of capital market development on the choice to serve a country through arm’s length technology transfer or affiliate activity should be less pronounced for these kinds of firms. The specification presented in column (3) uses the log of parent R&D as a proxy for the degree to which firms are technologically advanced. Because this specification includes parent-year fixed effects, this variable does not enter on its own, but it is interacted with creditor rights.26 The positive coefficient on the interaction term is consistent with the prediction that the value of creating incentives to monitor through ownership in countries with weak financial development is highest for technologically advanced firms. The specifications presented in columns (4)–(6) of Table II repeat those presented in columns (1)–(3), replacing creditor rights with private credit as a measure of financial development. The positive and significant coefficients on private credit in columns (4) and (5) are consistent with the findings in columns (1) and (2) and illustrate that countries with higher levels of financial development are more likely to be served through arm’s length technology transfers as opposed to just affiliate activity. The positive and significant coefficient on private credit interacted with the log of parent R&D presented in column (6) indicates that the effects of capital markets are most pronounced for firms that are R&D intensive.27

26. Because parent characteristics are absorbed by the parent-year fixed effects, the coefficient on this interaction term picks up how the effect of capital market conditions varies across firms. The sample used in this specification and the specification in column (6) includes only MNCs because R&D expenditures are only available in the BEA data for these firms. 27. When running these specifications as conditional logit specifications, the resulting coefficients on these interaction terms are of the same sign and statistical significance as those in the Table II, except for the interaction of creditor rights and the log of parent R&D. The coefficient on this variable is positive, but it is not statistically different from zero at conventional levels.

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FIGURE II Parent Financing of Affiliate Assets Parent financing share is the ratio of the sum of net borrowing from the parent and parent equity provisions to affiliate assets. The bars display medians of the country-level average shares for each quintile of private credit. Private credit is the ratio of private credit lent by deposit money banks to GDP, as provided ¨ ¸ -Kunt, and Levine (1999). Higher number quintiles relate to in Beck, Demirguc higher values of private credit.

IV.B. Financing and Ownership of Foreign Affiliates The analysis presented in Figure II and Table III investigates whether financing and ownership decisions reflect the mechanics emphasized in the model. As depicted in Figure II, parent firms provide financing that averages 45% of affiliate assets in countries in the lowest quintile of private credit but 38% of affiliate assets in countries from the highest quintile of private credit.28 Table III presents the results of more detailed tests of this relation. In addition to a variety of country-level controls, fixed effects for each parent in each year control for differences across firms. The negative and significant coefficient on creditor rights in column (1) 28. More specifically, the values displayed in this chart are computed by first taking average shares of affiliate assets financed by parents for each country in each year. These shares are defined as the ratio of the sum of net borrowing from the parent and parent equity provisions (including both paid-in-capital and retained earnings) to affiliate assets. The bars display medians of the country-level averages for each quintile of private credit.

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TABLE III PARENT FINANCING DECISIONS Dependent variable: Share of affiliate assets financed by parent

Creditor rights

(1)

(2)

(3)

−0.0166 (0.0054)

−0.0164 (0.0051)

−0.0080 (0.0055) −0.0010 (0.0003)

Creditor rights* log of parent R&D Private credit Private credit* log of parent R&D FDI ownership restrictions Workforce schooling

−0.0406 (0.0146) 0.0200 (0.0057) Log of GDP −0.0224 (0.0055) Log of GDP per capita −0.0327 (0.0112) Corporate tax rate −0.1288 (0.0776) Patent protections

(6)

−0.0632 (0.0195)

−0.0384 (0.0215)

−0.0084 (0.0220) −0.0031 (0.0012) −0.0358 (0.0162) 0.0157 (0.0049) −0.0148 (0.0085) 0.0030 (0.0169) −0.1731 (0.0745) −0.0436 (0.0120) −0.0113 (0.0106) 0.0068 (0.0080) 0.0003 (0.0094) 0.8330 (0.1906) Y Y 38,016 .3134

−0.0323 (0.0171) 0.0199 (0.0060) −0.0157 (0.0062) −0.0285 (0.0136) −0.1135 (0.0743)

1.2571 (0.1083) Y

−0.0426 (0.0155) 0.0114 (0.0043) −0.0180 (0.0071) −0.0072 (0.0154) −0.2061 (0.0764) −0.0388 (0.0114) 0.0110 (0.0115) 0.0062 (0.0079) 0.0007 (0.0091) 0.9728 (0.1435) Y

1.0444 (0.1479) Y

−0.0358 (0.0160) 0.0151 (0.0048) −0.0148 (0.0084) 0.0027 (0.0167) −0.1803 (0.0742) −0.0434 (0.0119) −0.0096 (0.0103) 0.0065 (0.0080) 0.0009 (0.0092) 0.8389 (0.1868) Y

N 51,060 .3013

Y 41,232 .3105

Y 40,297 .3071

N 48,183 .3076

Y 38,911 .3167

Rule of law Risk of expropriation

Parent-year fixed effects? Affiliate controls? No. of obs. R2

(5)

−0.0426 (0.0154) 0.0110 (0.0042) −0.0180 (0.0070) −0.0066 (0.0153) −0.2135 (0.0763) −0.0392 (0.0113) 0.0112 (0.0112) 0.0059 (0.0078) 0.0010 (0.0090) 0.9710 (0.1420) Y

Property rights

Constant

(4)

Notes. The dependent variable is the ratio of parent-provided equity and net parent lending to total assets. Creditor rights is an index of the strength of creditor rights developed in Djankov, McLiesh, and Shleifer (2007); higher levels of the measure indicate stronger legal protections. Private credit is the ratio of ¨ ¸ -Kunt, and Levine (1999). private credit lent by deposit money banks to GDP, as provided in Beck, Demirguc FDI ownership restrictions is a dummy equal to 0 if two measures of restrictions on foreign ownership as measured by Shatz (2000) are above 3 on a scale of 1 to 5 and 1 otherwise. Workforce schooling is the average schooling years in the population over age 25 years provided in Barro and Lee (2000). Corporate tax rate is the median effective tax rate paid by affiliates in a particular country and year. Patent protections is an index of the strength of patent rights provided in Ginarte and Park (1997). Property rights is an index of the strength of property rights drawn from the 1996 Index of Economic Freedom. Rule of law is an assessment of the strength and impartiality of a country’s overall legal system drawn from the International Country Risk Guide. Risk of expropriation is an index of the risk of outright confiscation or forced nationalization of private enterprise, and it is also drawn from the International Country Risk Guide; higher values of this index reflect lower risks. Each specification is an OLS specification that includes parent-year fixed effects. As affiliate controls, the specifications presented in columns (2), (3), (5), and (6) include the log of affiliate sales, the log of affiliate employment, and affiliate net PPE/assets. Affiliate net PPE/assets is the ratio of affiliate net property plant and equipment to affiliate assets. Heteroscedasticity-consistent standard errors that correct for clustering at the country-year level appear in parentheses.

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indicates that the share of affiliate assets financed by the parent is higher in countries that do not provide creditors with extensive legal protections. This result is consistent with the prediction contained in Proposition 3 and the pattern depicted in Figure II. The specification in column (2) includes the set of other institutional variables also used in Table II to ensure that proxies for financial development are not proxying for some other kind of institutional development. In addition, this specification also controls for affiliate characteristics that the corporate finance literature suggests might influence the availability of external capital. Harris and Raviv (1991) and Rajan and Zingales (1995) find that larger firms and firms with higher levels of tangible assets are more able to obtain external debt. Two proxies for affiliate size (the log of affiliate sales and the log of affiliate employment) and a proxy for the tangibility of affiliate assets (the ratio of affiliate net property, plant, and equipment to affiliate assets) are included.29 In the specification in column (2), the −0.0164 coefficient on creditor rights implies that the share of affiliate assets financed by the affiliate’s parent is 0.0327, or 7.9% of its mean value, higher for affiliates in countries in the 25th percentile of creditor rights relative to the 75th percentile of creditor rights. The negative and significant coefficient on FDI ownership restrictions is consistent with the hypothesis that such restrictions limit parent capital provisions, and the negative and significant coefficient on the log of GDP suggests that affiliates located in smaller markets are more reliant on their parents for capital. When affiliates borrow, they primarily borrow from external sources, and Desai, Foley, and Hines (2004b) show that affiliates borrow more in high-tax jurisdictions. These facts could explain the negative coefficient on the corporate tax rate in explaining the share of assets financed by the parent.30 Previous theoretical work stressing how concerns over technology expropriation might give rise to multinational activity does not make clear predictions concerning the share of affiliate assets financed by the parent, but it is worth noting that the indices of patent protection and property rights are negative in 29. The affiliate controls included in this specification as well as those in columns (3), (5), and (6) of Table III and columns (2), (3), (5), and (6) of Table IV are potentially endogenous. It is comforting that their inclusion does not typically have a material impact on the estimated effects of capital market conditions. 30. The model’s predictions relate to overall parent capital provision. As such, these specifications differ from the analysis in Desai, Foley, and Hines (2004b), where only borrowing decisions are analyzed.

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the specification in column (2). None of the unreported coefficients on affiliate characteristics is significant. If parent financing creates incentives for monitoring and the effects of monitoring are strongest for firms with more technology, then the effects documented in column (2) should be most pronounced for R&D-intensive firms. The specification in column (3) tests for a differential effect of creditor rights on financing by including creditor rights interacted with the log of parent R&D. The negative and significant coefficient on this interaction term indicates that more technologically advanced firms finance a higher share of affiliate assets in countries with weak credit markets. This finding is not implied by many other intuitions for why investor protections might affect parental financing provisions. The specifications presented in columns (4)–(6) of Table III repeat the analysis presented in columns (1)–(3) substituting measures of private credit for creditor rights. In columns (4) and (5), the coefficient on private credit is negative, and it is significant in column (4) but only marginally significant in column (5). In the specification in column (6), the interaction of private credit and the log of parent R&D is significant. The results obtained when using private credit are also consistent with the prediction of Proposition 3 and with Figure II. The model also predicts that multinational parents should hold larger ownership stakes in affiliates located in countries with weak investor protections. Table IV presents results of using the share of affiliate equity owned by the parent as the dependent variable in specifications that are similar to those presented in Table III. Although parent equity shares are bounded between 0 and 1, and there is a large grouping of affiliates with equity that is 100% owned by a single parent firm, the specifications presented in Table IV are ordinary least squares models that include parent-year fixed effects and that allow standard errors to be clustered at the country-year level.31 In the specifications presented in columns (1), (2), (4), and (5), the proxy for credit market development is negative and significant. Parent companies own higher shares of affiliate equity when affiliates are located in countries where protections extended to creditors are weaker and private credit is scarcer, as predicted by the model. In the specifications 31. Wholly owned affiliates comprise 77.2% of all observations. These results are robust to using an alternative estimation technique. Conditional logit specifications that use a dependent variable that is equal to 1 for wholly owned affiliates and 0 for partially owned affiliates yield similar results.

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QUARTERLY JOURNAL OF ECONOMICS TABLE IV PARENT OWNERSHIP DECISIONS Dependent variable: Share of affiliate equity owned by parent

Creditor rights

(1)

(2)

(3)

−0.0091 (0.0028)

−0.0101 (0.0035)

−0.0010 (0.0031) −0.0010 (0.0003)

Creditor rights* log of parent R&D Private credit Private credit* log of parent R&D FDI ownership restrictions Workforce schooling

−0.0728 (0.0126) 0.0005 (0.0024) Log of GDP −0.0157 (0.0037) Log of GDP per capita 0.0309 (0.0064) Corporate tax rate −0.2633 (0.0638) Patent protections

(6)

−0.0506 (0.0135)

−0.0481 (0.0174)

0.0078 (0.0144) −0.0057 (0.0009) −0.0529 (0.0122) −0.0026 (0.0026) −0.0079 (0.0046) 0.0416 (0.0144) −0.3179 (0.0564) −0.0122 (0.0077) −0.0014 (0.0072) 0.0017 (0.0060) 0.0059 (0.0067) 0.9159 (0.1018) Y Y 38,198 .4217

−0.0622 (0.0117) 0.0007 (0.0026) −0.0110 (0.0035) 0.0381 (0.0078) −0.2778 (0.0584)

1.1593 (0.1006) Y

−0.0611 (0.0134) −0.0044 (0.0025) −0.0116 (0.0045) 0.0363 (0.0132) −0.3391 (0.0700) −0.0137 (0.0072) 0.0044 (0.0075) 0.0012 (0.0061) 0.0050 (0.0068) 1.0675 (0.1121) Y

0.9833 (0.0947) Y

−0.0560 (0.0122) −0.0030 (0.0026) −0.0079 (0.0046) 0.0402 (0.0143) −0.3249 (0.0582) −0.0127 (0.0078) 0.0000 (0.0071) 0.0009 (0.0061) 0.0069 (0.0066) 0.9356 (0.1055) Y

N 51,320 .3974

Y 41,436 .4250

Y 40,498 .4184

N 48,422 .3998

Y 39,096 .4275

Rule of law Risk of expropriation

Parent-year fixed effects? Affiliate controls? No. of obs. R2

(5)

−0.0637 (0.0133) −0.0049 (0.0024) −0.0116 (0.0046) 0.0358 (0.0132) −0.3456 (0.0712) −0.0142 (0.0073) 0.0055 (0.0072) 0.0005 (0.0061) 0.0054 (0.0068) 1.0774 (0.1147) Y

Property rights

Constant

(4)

Notes. The dependent variable is the share of affiliate equity owned by the affiliate’s parent. Creditor rights is an index of the strength of creditor rights developed in Djankov, McLiesh, and Shleifer (2007); higher levels of the measure indicate stronger legal protections. Private credit is the ratio of private credit lent ¨ ¸ -Kunt, and Levine (1999). FDI ownership by deposit money banks to GDP, as provided in Beck, Demirguc restrictions is a dummy equal to 0 if two measures of restrictions on foreign ownership as measured by Shatz (2000) are above 3 on a scale of 1 to 5 and 1 otherwise. Workforce schooling is the average schooling years in the population over age 25 years provided in Barro and Lee (2000). Corporate tax rate is the median effective tax rate paid by affiliates in a particular country and year. Patent protections is an index of the strength of patent rights provided in Ginarte and Park (1997). Property rights is an index of the strength of property rights drawn from the 1996 Index of Economic Freedom. Rule of law is an assessment of the strength and impartiality of a country’s overall legal system drawn from the International Country Risk Guide. Risk of expropriation is an index of the risk of outright confiscation or forced nationalization of private enterprise, and it is also drawn from the International Country Risk Guide; higher values of this index reflect lower risks. Each specification is an OLS specification that includes parent-year fixed effects. As affiliate controls, the specifications presented in columns (2), (3), (5), and (6) include the log of affiliate sales, the log of affiliate employment, and affiliate net PPE/assets. Affiliate net PPE/assets is the ratio of affiliate net property plant and equipment to affiliate assets. Heteroscedasticity-consistent standard errors that correct for clustering at the country-year level appear in parentheses.

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presented in columns (3) and (6), the negative and significant coefficients on the interaction terms indicate that these results are also more pronounced for technologically advanced firms. The results in Table IV also indicate that equity ownership shares are lower in countries with ownership restrictions and countries with higher corporate tax rates. If equity ownership decisions placed strong emphasis on the protection of technology and ownership substituted for weak patent protections, the coefficient on the patent protections variable should be negative and significant. Although the estimated coefficient is negative, it is only marginally significant in some specifications. The results presented in Tables II, III, and IV are robust to a number of concerns. First, it is possible that the estimates of coefficients on capital market conditions interacted with the log of parent R&D may reflect the effect of similar interactions with alternative institutional variables. To consider this possibility, it is useful to consider the inclusion of other interaction terms. For example, when the log of parent R&D interacted with the rule of law index is included in the specifications presented in columns (3) and (6) of the three tables, the interactions that include proxies for capital market development remain significant in all of the tests. When the log of parent R&D interacted with the patent protection index is included in these specifications, the interactions featuring proxies for credit market development remain significant in all of the tests except for the one in column (3) of Table II. As such, it appears that the role of R&D intensity is most pronounced through the channel emphasized in the model, through interactions with capital market conditions. It may also be the case that the share of affiliate assets financed by the parent and parent ownership levels are lower for older affiliates and these affiliates may be more prevalent in countries with better investor protections. Including proxies for affiliate age in the specifications presented in Tables III and IV does not affect the results of interest.32 Similarly, the model does not explicitly consider the possibility that a firm exploits its technology through trade as opposed to through FDI or arm’s length technology transfers. To consider if trade channels could affect the main findings, the log of parent exports to unaffiliated foreign persons 32. The proxies for age are the number of years since an affiliate first reported data to BEA and a dummy equal to 1 if the affiliate first reported in 1982 and 0 otherwise.

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in each country and year is included as a control in each of the specifications. The magnitude and significance of the coefficients on the proxies for capital market conditions and the interactions of these proxies and the log of parent R&D are not materially changed. Finally, contractual forms that are specific to the natural resources sector could affect some of the results. Removing observations of firms in this sector reduces the significance of the results on the effects of private credit in specifications presented in column (5) of Tables II and III, but does not materially change any of the other results on the effects of capital market conditions in Tables II, III, and IV.33 IV.C. Scale of Multinational Activity The model predicts that multinational activity will be of a larger scale in countries with stronger investor protections. Because there are many theories for the determinants of FDI activity, using specifications similar to those presented in Tables II, III, and IV to explore scale is problematic because it is difficult to include a set of controls sufficiently extensive to distinguish between alternative theories.34 Fortunately, a subtler prediction of the model allows for tests of scale effects. Specifically, the model suggests that the response to the liberalizations of ownership restrictions should be larger in host countries with weak investor protections. The intuition for this prediction is that in countries with weak investor protections, ownership restrictions are more likely to bind because ownership is most critical for maximizing the value of the enterprise in these settings. As such, the relaxation of an ownership constraint should have muted effects for affiliates in countries with deep capital markets and more pronounced effects for affiliates in countries with weaker investor protections.35 33. Firms in BEA industries 101–148 and 291–299 are dropped from the sample. The coefficient on private credit in column (5) of Table II, when estimated using the reduced sample, is 0.0292, and it has a t-statistic of 1.92. The coefficient on private credit in column (5) of Table III, when estimated using the reduced sample, is −0.0351, and it has a t-statistic of 1.62. ` Desai, and Foley (2007) presents the results of 34. Appendix Table I in Antras, such an exercise. Although the coefficients on both the creditor rights variables and private credit variables are usually positive in explaining the log of affiliate sales, as Proposition 2 predicts, none of the coefficients on these variables is significant. 35. This prediction can in fact be explicitly derived from the model. In particular, one can envision an ownership restriction as an additional constraint to program (P1), requiring that φ I ≤ φ I for some foreign ownership cap φ I ∈ R. One can then show (details available upon request) that (i) for large enough γ , this constraint will not bind, and thus a removal of the constraint will have no effects

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FIGURE III Liberalizations and Multinational Firm Growth The two lines correspond to averages of an index computed at the country level as the ratio of aggregate affiliate sales in a given year to the level of sales in the year of the liberalization. Countries are split into two samples at the median level of private credit. Private credit is the ratio of private credit lent by deposit money ¨ ¸ -Kunt, and Levine (1999). banks to GDP, as provided in Beck, Demirguc

Figure III illustrates how the scale of multinational activity changes around the time of ownership liberalizations in countries with different levels of capital market development. Liberalizations are defined as the first year in which the FDI ownership restriction dummy described above changes from 1 to 0.36 The

on affiliate activity; (ii) when the constraint binds, the level of affiliate activity x is lower than in the absence of the constraint; and (iii) a marginal increase in φ I (i.e., a relaxation of the restriction) increases x by more, the lower is γ . Hence, the response of affiliate activity to a removal of ownership restrictions will be relatively larger in countries with relatively weaker investor protections. 36. The countries experiencing a liberalization are Argentina (1990), Australia (1987), Colombia (1992), Ecuador (1991), Finland (1990), Honduras (1993), Japan (1993), Malaysia (1987), Mexico (1990), Norway (1995), Peru (1992), Philippines (1992), Portugal (1987), Sweden (1992), Trinidad and Tobago (1994), and Venezuela (1990). Because control variables measuring the development of institutions other than credit markets do not vary much (if at all) through time and are unavailable for six of the sixteen reforming countries, these controls are not included in the analysis of liberalizations. The affiliate fixed effects implicitly control for time-invariant country characteristics, and so this is unlikely to pose a significant problem.

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QUARTERLY JOURNAL OF ECONOMICS TABLE V LIBERALIZATIONS AND MULTINATIONAL FIRM SCALE Dependent variable Log of affiliate sales

Post-liberalization dummy Post-liberalization dummy * low creditor rights dummy Post-liberalization dummy * low private credit dummy Log of GDP

Log of aggregate affiliate sales

(1)

(2)

(3)

(4)

0.0016 (0.0684) 0.3011 (0.0827)

−0.0073 (0.0712)

−0.0633 (0.1230) 0.3682 (0.1552)

−0.1049 (0.1262)

0.3886 (0.3888) Log of GDP per capita 1.3675 (0.3720) Constant −13.5818 (9.2414) Affiliate and year fixed effects? Y Country and year fixed effects? N No. of obs. 180,796 R2 .8035

0.2947 (0.0899) 0.3409 (0.3960) 1.4488 (0.3867) −13.0613 (9.2484) Y N 181,103 .8040

−0.0786 (0.7833) 2.6620 (0.5425) −4.7847 (22.1876) N Y 827 .9243

0.3812 (0.1769) −0.1351 (0.7040) 2.8376 (0.6192) −4.9033 (20.0397) N Y 845 .9251

Notes. The dependent variable in the first two columns is the log of affiliate sales, and the dependent variable in the last two columns is the log of affiliate sales aggregated across affiliates in a particular country. The data are annual data covering the 1982–1999 period. The post-liberalization dummy is equal to 1 for the sixteen countries that liberalize their ownership restrictions in the year of and years following liberalization of foreign ownership restrictions. The low creditor rights dummy is equal to 1 for observations related to countries with below median levels of creditor rights among liberalizing countries measured in the year prior to liberalization and 0 otherwise. The low private credit dummy is equal to 1 for observations related to countries with below median levels of private credit among liberalizing countries measured in the year prior to liberalization and 0 otherwise. Creditor rights is an index of the strength of creditor rights developed in Djankov, McLiesh, and Shleifer (2007). Private credit is the ratio of private credit lent by deposit money ¨ ¸ -Kunt, and Levine (1999). The first two specifications are OLS banks to GDP, as provided in Beck, Demirguc specifications that include affiliate and year fixed effects, and the last two are OLS specifications that include country and year fixed effects. Heteroscedasticity-consistent standard errors that correct for clustering at the country level appear in parentheses.

lines trace out an index that is computed by calculating the ratio of aggregate affiliate sales in a particular country and year to the value of aggregate affiliate sales in that country in the year of liberalization. The line demarcated by squares (triangles) plots the average of this index across countries that have a measure of private credit in the year prior to the liberalization that is equal to or less than (above) the median private credit of liberalizing countries. The lines indicate that affiliate activity increases by a larger margin in countries with low levels of private credit following liberalizations. The specifications presented in Table V investigate whether these differential effects are robust. The dependent variable in

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columns (1) and (2) is the log value of affiliate sales, and the sample consists of the full panel from 1982 to 1999. Given the limited data requirements of these specifications (relative to the variables investigated in Tables II, III, and IV) and the desire to investigate changes within affiliates, the full panel provides a more appropriate setting for these tests. These specifications include affiliate and year fixed effects, and the standard errors are clustered at the country level. The sample includes all countries so that affiliate activity in countries that do not liberalize helps identify the year effects and the coefficients on the income variables. The results are robust to using a sample drawn only from reforming countries. The specifications in columns (1) and (2) include controls for log GDP, log GDP per capita, and the post-liberalization dummy. The coefficient on log GDP per capita is positive and significant indicating that rising incomes are associated with larger levels of affiliate activity. The coefficient of interest in column (1) is the coefficient on the interaction of the post-liberalization dummy and a dummy that is equal to 1 if the country has a value of the creditor rights index in the year before liberalization that is equal to or less than the median value for liberalizing countries. The positive and significant coefficient indicates that affiliates in weak-creditorrights countries grow quickly after liberalizations. The coefficient on the post-liberalization dummy on its own indicates that the effect of liberalizations is negligible and statistically insignificant for affiliates in high-creditor-rights countries. In column (2), these same results are obtained when the measure of private credit is used as the proxy for financial development. At the affiliate level, the model’s predictions regarding how the scale of activity relates to capital market depth are validated using tests that, through the use of affiliate fixed effects and the emphasis on the interaction term, are difficult to reconcile with alternative theories. It is possible that the results presented in columns (1) and (2) inaccurately capture the effects of the liberalizations because they only measure activity on the intensive margin and fail to capture responses on the extensive margin. Entry or exit might accompany liberalizations and might amplify or dampen these results. Figure III suggests this is not the case because it is constructed using data aggregated to the country level. The specifications provided in columns (3) and (4) employ a dependent variable that is the log value of the aggregate value of all sales of U.S. multinational affiliates within a country-year cell. These specifications substitute country fixed effects for affiliate fixed effects but are otherwise similar to the regressions provided in columns (1) and (2).

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In column (3), the coefficient on the interaction term including the creditor rights variable is again positive and significant, indicating that incorporating activity on the extensive margin does not appear to contradict the earlier result. In column (4), the coefficient on the interaction term is again positive and significant. Taken together, the results suggest that the scale of activity is positively related to the quality of investor protections and capital market development, and these results persist when incorporating the effects of entry and exit. V. CONCLUSION Efforts to understand patterns of MNC activity have typically emphasized aspects of technology expropriation rather than the constraints imposed by weak investor protections and shallow capital markets. In the prior literature, MNCs arise because of the risk of a partner expropriating a proprietary technology. In the model presented in this paper, the exploitation of technology is central to understanding MNC activity, but the critical constraint is the nature of capital market development and investor protections in host countries. Entrepreneurs must raise capital to fund projects, and external investors are aware of the possibility that these entrepreneurs might behave opportunistically. Inventors can alleviate financial frictions because they have privileged knowledge of their technology and can thus play a role in monitoring entrepreneurs. As a result, MNC activity and capital flows arise endogenously to ensure that monitoring occurs. External investors demand higher levels of multinational parent firm financial participation in countries with weak investor protections. By placing financial frictions at the center of understanding patterns of activity and flows, the model delivers novel predictions about the use of arm’s length technology transfers and about the financial and investment decisions of MNCs that are validated in firm-level analysis. The use of arm’s length technology transfers is more common in countries with strong investor protections and deep capital markets. Previous findings that FDI flows to developing countries are limited reflect two opposing forces. Weak investor protections and shallow capital markets limit the efficient scale of enterprise but also result in greater parent provision of capital and more parent ownership of affiliate equity. The effects of the institutional setting are more pronounced for R&D-intensive firms because parental monitoring is particularly valuable for the

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investments of these firms. By jointly considering operational and financial decisions, the theory and empirics provide an integrated explanation for patterns of MNC activity and FDI flows that have typically been considered separately. Further consideration of the role of financial frictions on MNC activity along several dimensions may prove fruitful. First, the model presented effectively rules out exports to unrelated parties as a means of serving foreign markets. Incorporating the trade-off between exports and production abroad in a world with financial frictions may yield additional predictions that would help explain the choice between exporting and FDI. Second, exploring the implications of financial frictions for intrafirm trade may help explain how the demands of external funders in weak institutional environments affect the fragmentation of production processes across borders. Finally, the central role of foreign ownership in reducing diversion may lead to significant variation in the relative competitiveness of local and foreign firms that reflects the institutional environment emphasized in this paper. APPENDIX I: THE SHADOW COST OF CASH In the main text, we have treated the shadow value of cash β as exogenous. In this Appendix we briefly illustrate how to endogenize it and show how it relates to characteristics of the Home country and in particular to its level of investor protection. For this purpose, we generalize the setup described in Section II.A and consider the situation in which there are J − 1 Foreign countries, each associated with a level of financial development γ j and a cash flow function R j (x j ).37 The inventor contracts with each of J − 1 foreign entrepreneurs and, as a result of the optimal contracting described above, has an amount of cash equal to W −

˜ j to invest in the Home country. F j= H Preferences and technology at Home are such that the cash flows obtained from the sale of the differentiated good at Home can be expressed as a strictly increasing and concave function of the quantity produced, RH (q H ), satisfying the same properties as the cash flow function in other countries. Home production is managed by the inventor, who can also privately choose to behave or misbehave, with consequences identical to those discussed 37. With some abuse of notation, we use J to denote both the number of countries as well as the set of these countries.

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above: if the inventor behaves, the project performs with probability pH , but if he misbehaves, the project performs with a lower probability pL. In the latter case, however, the inventor obtains a private benefit equal to a fraction 1 − γ H of cash flows, where γ H is an index of investor protection at Home. The inventor sells domestic cash flow rights to a continuum of external investors at Home, who can obtain a rate of return equal to 1 in an alternative investment opportunity.38 We consider an optimal financial contract between the inventor and external investors in which the inventor is granted the ability to make take-it-or-leave-it offers, just as in the main text. The optimal contract specifies the scale of operation x H , the amount of cash Wx that the inventor invests in the project, the share of equity φ EH sold to external investors, and the amount of cash E H provided by external investors. Taking the contracts signed with foreign individuals as given, an optimal financial contract with external investors at Home that induces the inventor to behave is given by the tuple ˜ x , φ˜ H , E˜ H } that solves the following program: {x˜ H , W E max

x H ,Wx ,φ EH ,E H

(P2)

s.t.

I =

j φ I pH − C j R j (x j )

j= H + pH 1 − φ EH RH (x H ) + W − F˜ j − Wx

x H ≤ E H + Wx Wx ≤ W − F˜ j

j= H

j= H

pH φ EH RH (x H ) ≥ E H ( pH − pL) 1 − φ EH RH (x H ) ≥ (1 − γ H )RH (x H ). It is straightforward to show that provided that γ H is low enough (i.e., provided that financial frictions at Home are large enough), all constraints in program (P2) will bind in equilibrium, and the profits of the entrepreneur can be expressed as ⎛ ⎞ j ⎝ W − φ I pH − C j R j (x j ) + β F˜ j ⎠ , (6) I = j= H

j= H

38. For simplicity, we assume that the inventor cannot pledge foreign cash flow rights to its external investors at Home.

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where 1−γH ( pH − pL) βˆ = > 1. H 1−γ x˜ H − 1− pH − pL pH RH (x˜ H ) Notice that the resulting profit function (6) is closely related to that considered in program (P1) in Section II.B, where βˆ now replaces β. There are, however, two important differences between the two profit functions. First, the formulation in (6) considers the case in which the inventor obtains cash flow from the exploitation of the technolˆ ogy in multiple countries. Nevertheless, notice that for a given β, the profit function features separability between these different ˆ the optimal contract sources of dividends. As a result, for a given β, with the entrepreneur and external investors in each country j is as described in Section II.B.39 Hence, Propositions 1, 2, and 3 continue to apply and their statements not only apply to changes in the parameter γ but also to cross-sectional (cross-country) variation in investor protection. In this sense, the tests performed in Section IV are well defined. The second important difference between the profit function in (6) and in program (P1) is that the shadow value of cash βˆ is in fact endogenous, in the sense that it is a function of the scale of operation at Home x H , which in turn will depend on the optimal contracts in the other J countries through the date-0 transfers F˜ j for j = H (as is clear from program (P2)). Hence, βˆ will in general be a function of the vector of country investor protections γ ≡ (γ 1 , . . . , γ J−1 , γ H ). Notice, however, that for large enough J, the effect of a particular investor protection level γ j ( j = H) on the overall shadow value of cash βˆ will tend to be negligible, and thus the comparative static results in Section II.B will continue to apply. To sum up, this Appendix has illustrated that a higher-than1 shadow value of cash can easily be rationalized in a simple 39. Notice also that when βˆ > 1, the inventor is financially constrained at Home, in the sense that external investors at Home are only willing to lend to him a multiple of his pledgeable income (wealth plus date-0 payments). If external investors were to lend a larger amount, the inventor’s incentive-compatibility constraint would be violated. The same would of course apply to external investors in foreign countries. This helps rationalize our assumption in Section II.A that the inventor does not sign bilateral financial contracts with external investors in host countries.

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extension of our initial partial equilibrium model, in which not only foreign entrepreneurs, but also the inventor, face financial constraints. We have seen that endogenizing the shadow value of cash may affect the solution of the optimal contract in subtle ways, but that if the number of host countries in which the inventor exploits his technology is large enough, the comparative static results in Section II.B remain qualitatively valid. APPENDIX II: CHARACTERIZATION OF THE OPTIMAL CONTRACT Let us start by writing the Lagrangian corresponding to program (P1). Letting λk denote the multiplier corresponding to constraint k = 1, 2, 4, 5 (remember constraint (iii) cannot bind), we have L = φ I pH R(x) + (W − F)β − C R(x) + λ1 (E + F − x) + λ2 ( pH φ E R(x) − E) + λ4 (( pH − pL)(1 − φ E − φ I ) C . −(1 − γ )δ(C)) + λ5 φ I − ( pH − pL) The first-order conditions of this program (apart from the standard complementarity slackness conditions) are

(7)

(8)

∂L ∂F ∂L ∂φ I ∂L ∂x ∂L ∂φ E ∂L ∂E ∂L ∂C

= −β + λ1 = 0, = pH R (x˜ ) − λ4 ( pH − pL) + λ5 = 0, = φ˜ I pH R (x˜ ) − C˜ R (x˜ ) − λ1 + λ2 pH φ˜ E R (x˜ ) = 0, = λ2 pH R (x˜ ) − λ4 ( pH − pL) = 0, = λ1 − λ2 = 0, ˜ − = −R (x˜ ) − λ4 (1 − γ ) δ (C)

λ5 = 0. ( pH − pL)

Straightforward manipulation of these conditions delivers λ1 = λ2 = β > 0, pH pH λ2 R (x˜ ) = β R (x˜ ) > 0, λ4 = pH − pL pH − pL λ5 = (β − 1) pH R (x˜ ) > 0,

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from which we conclude that all constraints bind, as claimed in the main text. The fact that λ5 > 1 immediately implies that constraint (v) ˜ ( pH − pL), as indicated in equation (2). binds and we have φ˜ I = C/ Next, plugging the values of the multipliers in (8) yields ˜ = −δ (C)

βpH − pL , (1 − γ ) βpH

as claimed in equation (3) in the main text. Next, plugging the multipliers and φ˜ I into (7) yields R (x˜ ) =

1 ˜ , ˜ C βpH − pL (1 − γ ) δ(C) − 1− pH − pL pH − pL βpH

pH

which corresponds to equation (4) in the main text. Setting the constraints to equality, we can also compute the total payoff obtained by the inventor: R (x˜ ) ˜ (9) I = Wβ + β − x˜ . R (x˜ ) This expression can be used to analyze when it is optimal for the inventor to implement good behavior. To do so, consider the optimal contract that implements bad behavior. It is clear that in this case the inventor has no incentive to exert monitoring effort. It is also immediate that even when the entrepreneur does not obtain any share of the cash flows, her participation constraint will be satisfied, and thus we have that φ˜ IL + φ˜ EL = 1. The program defining the optimal contract can then be written as max

I = φ I pL R(x) + (W − F ) β

s.t.

x ≤ E+ F pL (1 − φ I ) R(x) ≥ E φ I ≥ 0.

F,φ I ,x,E

(P1 L)

(i) (ii) (iii)

Following the same steps as before, we find that all three constraints will bind, and hence C˜ L = φ˜ IL = 0. Furthermore, the optimal level of investment is given by pL R (x˜ L) = 1,

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while the overall payoff obtained by the inventor equals R(x˜ L) L ˜ L = βW + β . (10) − x ˜ R (x˜ L) ˜I > ˜ L if and Comparing equations (9) and (10) we see that only if R(x˜ L) R (x˜ ) − x˜ L. − x ˜ > R (x˜ ) R (x˜ L) However, because R(x)/R (x) − x is strictly increasing in x whenever R (x) < 0, we can conclude that good behavior will be implemented whenever x˜ > x˜ L. Note also that x˜ is increasing in γ (this is formally proved in Appendix III), while x˜ L is independent of γ . Furthermore, when γ → 1, it is necessarily the case that x˜ > x˜ L. Hence, there exists a threshold γ over which it is optimal to implement good behavior. APPENDIX III: PROOFS OF COMPARATIVE STATIC RESULTS The comparative statics in Lemma 1 simply follow from the fact that the right-hand side of equation (3) is increasing in γ and β, while the left-hand side is decreasing in C˜ (given the convexity of δ (·)). The statements of Proposition 1 directly follow from Lemma ˜ 1 because φ˜ I is proportional to C. Consider next the comparative statics in Proposition 2. For that purpose, let ˜ ˜ βpH − pL C (1 − γ ) δ(C) ˜ + , F(γ , β, C(γ , β)) = pH − pL pH − pL βpH so that ˜ , β))] = 1. ˜ − F(γ , β, C(γ pH R (x)[1 Using equation (3), we can establish that ˜ ˜ dC˜ 1 dC˜ δ(C) βpH − pL dF (·) (1 − γ ) δ (C) =− + + dγ pH − pL pH − pL dγ pH − pL βpH dγ ˜ δ(C) < 0; =− pH − pL

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˜ dC˜ βpH − pL 1 dC˜ dF (·) (1 − γ ) δ (C) = + dβ pH − pL dβ pH − pL βpH dβ ˜ pLC˜ pLC = > 0. + ( pH − pL) β 2 pH ( pH − pL) β 2 pH From inspection of (4) and the concavity of R (·), it is then clear that x˜ is increasing in γ and decreasing in β. Finally, the statements in Proposition 3 follow from the discussion in the main text and the fact that R (x˜ ) /x˜ is decreasing in x, ˜ and thus decreasing in γ and increasing in β. APPENDIX IV: GENERALIZATIONS In this Appendix, we provide more details on the generalizations outlined in Section II.C. Consider first the case in which the entrepreneur’s private benefit and the inventor’s private cost of monitoring are proportional to x rather than to R(x). Following the same steps as in the formulation in the main text, we find that the optimal Cˆ and xˆ are now given by ˆ = −δ (C)

βpH − pL βpH (1 − γ )

and pH R (xˆ ) = 1 +

(11)

ˆ pH (1 − γ ) δ(C) (βpH − pL) Cˆ . + β ( pH − pL) pH − pL

Straightforward differentiation indicates that both Cˆ and xˆ continue to be decreasing in γ , as in our paper. Next note that we can use equation (11) to write Cˆ xˆ xˆ R (xˆ ) pH Cˆ Cˆ = ( pH − pL) R (xˆ ) ( pH − pL) R (xˆ ) pH R (xˆ ) −1 ˆ pH xˆ R (xˆ ) 1 pH (1 − γ ) δ(C) (βpH − pL) = . + + β ( pH − pL) ( pH − pL) R (xˆ ) Cˆ ( pH − pL) Cˆ

φˆ I =

It is straightforward to see that the last term continues to be an increasing function of Cˆ and is thus decreasing in γ . This implies that the only way that φˆ I could be increasing in γ would be if ˆ x)— ˆ the elasticity of revenue to output—that is, α(x) ˆ ≡ xˆ R (x)/R( was sufficiently increasing in x. ˆ For a constant-elasticity function, ˆ = α for all xˆ and thus φˆ I continues to be R(x) = Ax α , we have α(x)

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decreasing in γ for any level of concavity of the R(x) function. Remember that the revenue function will be isoelastic whenever the firm faces a demand with constant price elasticity. If the firm were to face a linear demand function, then α(x) ˆ would be decreasing in x, ˆ hence reinforcing the result that φˆ I is decreasing in γ . We next consider the case in which (local) external investors can also serve a monitoring role. In particular, if external investors exert an unverifiable effort cost MR(x), the private benefit is now B (C, M; γ ) = (1 − γ ) (δ (C ) + μ ( M)) , with μ(·) satisfying the same properties as δ(·) above, namely, ¯ lim M→∞ μ(M) = 0, lim M→0 μ μ (M) < 0, μ (M) > 0, μ(0) = μ, (M) = −∞, and lim M→∞ μ (M) = 0. Because local monitoring is not verifiable, the program that determines the optimal contract will need to include a new incentive compatibility constraint for external investors. In particular, an optimal contract that induces the entrepreneur to behave is now given by the tuple ˆ C, ˆ M} ˆ that solves a program analogous to (P1) but ˆ φˆ I , x, ˆ φˆ E , E, { F, with constraints (ii) and (iv) now given by pH φ E R(x) − MR(x) ≥ E

(ii)

( pH − pL) (1 − φ E − φ I ) ≥ (1 − γ ) (δ (C ) + μ ( M))

(iv)

and with the additional constraint φ E ≥ M/ ( pH − pL)

(vi).

Manipulating the first-order conditions of this new program, we obtain λ5 = (β − 1) pH R (xˆ ) + λ6 , which immediately implies that constraint (v) continues to bind even in the case with local monitoring. Consequently, inventor (or parent firm) equity shares continue to move proportionately with the amount of monitoring undertaken by the inventor. Furthermore, provided that the level of investor protection is sufficiently high, the analysis in the main text goes through essentially unaltered. The reason for this is that in such a case, ˆ being constraint (vi) is not binding (λ6 = 0) and we obtain Cˆ and M determined by (12)

ˆ = βpH − pL , − δ (C) (1 − γ ) βpH

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which is identical to (3), and

(13)

ˆ = ( pH − pL) . − μ ( M) (1 − γ ) pH

From the convexity of the monitoring functions, we thus obtain ˆ are decreasing functions of γ . Furthermore, that both Cˆ and M manipulating the first-order conditions we can also easily show that (i) the investment levels (and thus) sales revenue continue ˆ x is still increasing in to be increasing in γ , and (ii) the ratio F/ γ , provided that α (xˆ ) does not increase in xˆ too quickly, just as in the main text (details available upon request). ˆ > Note that equations (12) and (13) also imply that −δ (C) ˆ −μ ( M), and if the functions δ (·) and μ (·) are sufficiently simiˆ > C. ˆ Intuitively, a disproportionate amount of lar we will have M local monitoring may be optimal because it is “cheaper,” as external investors have a lower shadow cost of getting remunerated through equity shares. Still, as long as the equilibrium level of ˆ is sufficiently low (or γ is sufficiently high), the above analyM sis suggests that the inventor equity share comoves with investor protections in the same manner as in our simpler model with only inventor monitoring. For low enough values of γ , however, the above optimal conˆ > ( pH − pL) φ E , which violates constraint (vi). In tract leads to M such a case, we have λ6 > 0. Manipulating the first-order condiˆ are implicitly defined by the tions, one can show that Cˆ and M system ˆ 1 + (1 − γ ) μ ( M) = β, ˆ 1 + (1 − γ ) δ (C) ˆ = (1 − γ )(δ(C) ˆ + μ( M)). ˆ pH − pL − Cˆ − M Unfortunately, without imposing particular functional forms for the functions δ (·) and μ (·), it becomes impossible to characterize how Cˆ (and thus φˆ I ) varies with γ . HARVARD UNIVERSITY AND NBER HARVARD BUSINESS SCHOOL AND NBER HARVARD BUSINESS SCHOOL AND NBER

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REFERENCES Acemoglu, Daron, Simon Johnson, and Todd Mitton, “Determinants of Vertical Integration: Finance Contracts and Regulation,” NBER Working Paper No. 11424, 2005. Aguiar, Mark, and Gita Gopinath, “Fire-Sale FDI and Liquidity Crises,” Review of Economics and Statistics, 87 (2005), 439–452. Albuquerque, Rui, “The Composition of International Capital Flows: Risk Sharing through Foreign Direct Investment,” Journal of International Economics, 61 (2003), 353–383. ` Pol, “Firms, Contracts, and Trade Structure,” Quarterly Journal of EcoAntras, nomics, 118 (2003), 1375–1418. ——, “Incomplete Contracts and the Product Cycle,” American Economic Review, 95 (2005), 1054–1073. ` Pol, and Elhanan Helpman, “Global Sourcing,” Journal of Political EconAntras, omy, 112 (2004), 552–580. ` Pol, Mihir A. Desai, and C. Fritz Foley, “Multinational Firms, FDI Flows Antras, and Imperfect Capital Markets,” NBER Working Paper No. 12855, 2007. Baker, Malcolm, C. Fritz Foley, and Jeffrey Wurgler, “Multinationals as Arbitrageurs? The Effects of Stock Market Valuations on Foreign Direct Investment,” Review of Financial Studies, 22 (2009), 337–369. Barro, Robert J., and Jong-Wha Lee, “International Data on Educational Attainment: Updates and Implications,” CID Working Paper No. 42, 2000. ¨ ¸ -Kunt, and Ross Levine, “A New Database on FiBeck, Thorsten, Asli Demirguc nancial Development and Structure,” World Bank, Policy Research Working Paper No. 2146, 1999. Bertaut, Carol, William L. Griever, and Ralph W. Tryon, “Understanding U.S. Cross-Border Securities Data,” Federal Reserve Bulletin, 92 (2006), A59–A75. Blonigen, Bruce A., “Firm-Specific Assets and the Link Between Exchange Rates and Foreign Direct Investment,” American Economic Review, 87 (1997), 447– 465. Boyd, John H., and Bruce D. Smith, “Capital Market Imperfections, International Credit Markets and Nonconvergence,” Journal of Economic Theory, 73 (1997), 335–364. Brainard, S. Lael, “An Empirical Assessment of the Proximity-Concentration Trade-off between Multinational Sales and Trade,” American Economic Review, 87 (1997), 520–544. Caves, Richard E., Multinational Enterprise and Economic Analysis, 2nd ed. (Cambridge, UK: Cambridge University Press, 1996). Desai, Mihir A., C. Fritz Foley, and Kristin J. Forbes, “Financial Constraints and Growth: Multinational and Local Firm Responses to Currency Depreciations,” Review of Financial Studies, 21 (2008), 2857–2888. Desai, Mihir A., C. Fritz Foley, and James R. Hines, Jr., “Dividend Policy Inside the Firm,” NBER Working Paper No. 8698, 2002. ——, “The Costs of Shared Ownership: Evidence from International Joint Ventures,” Journal of Financial Economics, 73 (2004a), 323–374. ——, “A Multinational Perspective on Capital Structure Choice and Internal Capital Markets,” Journal of Finance, 59 (2004b), 2451–2488. Djankov, Simeon, Caralee McLiesh, and Andrei Shleifer, “Private Credit in 129 Countries,” Journal of Financial Economics, 84 (2007), 299–329. Ethier, Wilfred J., and James R. Markusen, “Multinational Firms, Technology Diffusion and Trade,” Journal of International Economics, 41 (1996), 1–28. Feenstra, Robert, and Gordon Hanson, “Ownership and Control in Outsourcing to China: Estimating the Property-Rights Theory of the Firm,” Quarterly Journal of Economics, 120 (2005), 729–761. Froot, Kenneth A., and Jeremy C. Stein, “Exchange Rates and Foreign Direct Investment: An Imperfect Capital Markets Approach,” Quarterly Journal of Economics, 106 (1991), 1191–1217. Gertler, Mark, and Kenneth S. Rogoff, “North-South Lending and Endogenous Domestic Capital Market Inefficiencies,” Journal of Monetary Economics, 26 (1990), 245–266. Ginarte, Juan Carlos, and Walter Park, “Determinants of Patent Rights: A CrossNational Study,” Research Policy, 26 (1997), 283–301.

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Grossman, Gene M., and Elhanan Helpman, “Managerial Incentives and the International Organization of Production,” Journal of International Economics, 63 (2004), 237–262. Harris, Milton, and Arthur Raviv, “The Theory of Capital Structure,” Journal of Finance, 46 (1991), 297–355. Helpman, Elhanan, “A Simple Theory of International Trade with Multinational Corporations,” Journal of Political Economy, 92 (1984), 451–471. Helpman, Elhanan, Marc J. Melitz, and Stephen R. Yeaple, “Exports versus FDI with Heterogeneous Firms,” American Economic Review, 94 (2004), 300–316. Holmstrom, Bengt, and Jean Tirole, “Financial Intermediation, Loanable Funds, and the Real Sector,” Quarterly Journal of Economics, 112 (1997), 663–691. King, Robert G., and Ross Levine, “Finance and Growth: Schumpeter Might Be Right,” Quarterly Journal of Economics, 108 (1993), 717–738. Klein, Michael W., Joe Peek, and Eric Rosengren, “Troubled Banks, Impaired Foreign Direct Investment: The Role of Relative Access to Credit,” American Economic Review, 92 (2002), 664–682. Klein, Michael W., and Eric Rosengren, “The Real Exchange Rate and Foreign Direct Investment in the United States,” Journal of International Economics, 36 (1994), 373–389. Kraay, Aart, Norman Loayza, Luis Serv´en, and Jaume Ventura, “Country Portfolios,” Journal of the European Economic Association, 3 (2005), 914–945. La Porta, Rafael, Florencio L´opez-de-Silanes, Andrei Shleifer, and Robert W. Vishny, “Legal Determinants of External Finance,” Journal of Finance, 52 (1997), 1131–1150. ——, “Law and Finance,” Journal of Political Economy, 106 (1998), 1113–1155. Levine, Ross, and Sara Zervos, “Stock Markets, Banks, and Economic Growth,” American Economic Review, 88 (1998), 537–558. Lucas, Robert, “Why Doesn’t Capital Flow from Rich to Poor Countries?” American Economic Review, 80 (1990), 92–96. Marin, Dalia, and Monika Schnitzer, “Global versus Local: The Financing of Foreign Direct Investment,” University of Munich, Working Paper, 2004. Markusen, James R., “Multinationals, Multi-Plant Economies, and the Gains from Trade,” Journal of International Economics, 16 (1984), 205–226. ——, Multinational Firms and the Theory of International Trade (Cambridge, MA: MIT Press, 2002). Markusen, James R., and Anthony J. Venables, “The Theory of Endowment, Intraindustry and Multi-national Trade,” Journal of International Economics, 52 (2000), 209–234. Misawa, Mitsuru, “Tokyo Disneyland: Licensing vs. Joint Venture,” Asia Case Research Centre, University of Hong Kong, Case HKU420, 2005. Rajan, Raghuram G., and Luigi Zingales, “What Do We Know about Capital Structure? Some Evidence from International Data,” Journal of Finance, 50 (1995), 1421–1460. ——, “Financial Dependence and Growth,” American Economic Review, 88 (1998), 559–586. Reinhart, Carmen M., and Kenneth S. Rogoff, “Serial Default and the ‘Paradox’ of Rich to Poor Capital Flows,” American Economic Review, 94 (2004), 52–58. Shatz, Howard J., “The Location of U.S. Multinational Affiliates,” Ph.D. Dissertation, Harvard University, 2000. Shleifer, Andrei, and Daniel Wolfenzon, “Investor Protection and Equity Markets,” Journal of Financial Economics, 66 (2002), 3–27. Tirole, Jean, The Theory of Corporate Finance (Princeton, NJ: Princeton University Press, 2005). Wurgler, Jeffrey, “Financial Markets and the Allocation of Capital,” Journal of Financial Economics, 58 (2000), 187–214. Yeaple, Stephen, “The Role of Skill Endowments in the Structure of U.S. Outward FDI,” Review of Economics and Statistics, 85 (2003), 726–734.

PRICE SETTING DURING LOW AND HIGH INFLATION: EVIDENCE FROM MEXICO∗ ETIENNE GAGNON This paper provides new insight into the relationship between inflation and the setting of individual prices by examining a large data set of Mexican consumer prices covering episodes of both low and high inflation. When the annual rate of inflation is low (below 10%–15%), the frequency of price changes comoves weakly with inflation because movements in the frequency of price decreases and increases partly offset each other. In contrast, the average magnitude of price changes correlates strongly with inflation because it is sensitive to movements in the relative shares of price increases and decreases. When inflation rises beyond 10%–15%, few price decreases are observed and both the frequency and average magnitude are important determinants of inflation. I show that a menu-cost model with idiosyncratic technology shocks predicts the average frequency and magnitude of price changes well over a range of inflation similar to that experienced by Mexico.

I. INTRODUCTION This paper presents new evidence on the setting of consumer prices during low and high inflation and sheds light on the empirical plausibility of competing models of price rigidities. It uses a new store-level data set containing over three million individual price quotes that are representative of more than half of Mexican consumers’ expenditures. The data start in January 1994 and end in June 2002. Over that nine-year period, the rate of increase in the official consumer price index (CPI) rose from 6.8% in 1994 to a peak of 41.8% in 1995, before falling to 4.9% in the last year of the sample.1 Given these considerable fluctuations, this data set allows me to document how individual consumer prices are set at various levels of inflation. It also can be used to discriminate among competing models of nominal price rigidities, as these models’ predictions diverge most in the presence of large shocks. ∗ I would like to thank the members of my dissertation committee, Lawrence J. Christiano, Alexander Monge-Naranjo, Sergio Rebelo, and especially my chairperson Martin Eichenbaum, for their continuous guidance and support. I am also grateful to Martin Bodenstein, Jeff Campbell, Reinout DeBock, Rodrigo Garc´ıa ´ Nicolas Vincent, and three anonymous referees for their insightful comVerdu, ments and suggestions. Chris Ahlin and Jos´e Antonio Murillo Garza offered valuable help with the data, and Martha Carillo, Matthew Denes, and Guthrie Dundas provided excellent research assistance. Financial support for this research was provided in part by the Northwestern University Center for International Economics and Development and the Fonds qu´eb´ecois pour les chercheurs et l’aide a` la recherche (FCAR). The views expressed in this paper are solely the responsibility of the author and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System. [email protected] 1. Unless otherwise indicated, all inflation figures are computed using the change in the logarithm of the price index and annualized. C 2009 by the President and Fellows of Harvard College and the Massachusetts Institute of

Technology. The Quarterly Journal of Economics, August 2009

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40 Austria Belgium Finland France Luxembourg Portugal Spain United States Mexico

)

35

30

25

20

15

10

5

0

1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006

Period covered by country studies

FIGURE I Inflation and Time Coverage of U.S., Euro-Area, and Mexican CPI Studies The studies shown are representative of at least 50% of consumer expenditures. Data on inflation come from the OECD Main Economic Indicators, Banco de M´exico, and the U.S. Bureau of Labor Statistics. The sample period for the United States corresponds to the study of Nakamura and Steinsson (2008). Full references to the euro-area country studies can be found in Dhyne et al. (2005).

My data set captures considerably more variation in inflation than do other studies of consumer prices with comparable product coverage.2 As Figure I indicates, inflation was low and stable in the United States and the euro area relative to Mexico throughout the periods covered by the related studies. For high-inflation economies, the evidence is limited mainly to food products in Israel (Lach and Tsiddon 1992; Eden 2001; Baharad and Eden 2004) and Poland (Konieczny and Skrzypacz 2005) and to supermarket products in Argentina (Burstein, Eichenbaum, and Rebelo 2005). My paper differs from these studies because my data set is representative of a much larger set of goods and services in the CPI. The monthly frequency of price changes varied extensively over my sample period. It rose from an average of 22.1% in 1994 2. For studies on the United States, see Bils and Klenow (2004), Klenow and Kryvtsov (2008), and Nakamura and Steinsson (2008). Dhyne et al. (2005) review the main findings for the euro area.

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to a high of 61.9% at the peak of inflation in April 1995, before leveling off around 27.4% in the last year of the sample. I find some important differences in price-setting behaviors across low- and high-inflation periods. When inflation is low (below 10%–15%), the frequency of price changes is only mildly correlated with inflation, especially when I restrict the sample to goods, in which case the correlation almost entirely disappears. On the other hand, the average magnitude of price changes in such a low-inflation environment displays a tight and almost linear relationship with the level of inflation. As a result, movements in the frequency of price changes account for little of the inflation variance: at most 11% for the full sample and 6% for the subsample of goods, figures that are similar to that of Klenow and Kryvtsov (2008) for the United States (about 5%). By contrast, when inflation is high (above 10%–15%), both the frequency and average magnitude of price changes are strongly correlated with inflation. Movements in the frequency of price changes then comprise an important component of inflation variance. When I decompose price changes between price increases and decreases, I find that the frequency of price increases rises steadily as inflation rises from 0% to 10%–15%. This rise is partly offset by a simultaneous decline in the frequency of price decreases, thereby dampening movements in the overall frequency of price changes. This offsetting effect stems from goods, which have the largest proportion of price decreases. By comparison, relatively few price decreases are observed among services. As inflation rises from a low level, the decline in the occurrence of price decreases relative to price increases exacerbates movements in the average magnitude of price changes. In my data set, the change in the composition of price changes largely explains the strong correlation between inflation and the average magnitude of price changes when inflation is low. Once inflation moves beyond 10%–15%, price decreases have largely disappeared from most sectors of the economy, with the exception of some fresh produce. The frequency of price increases continues to rise steadily with inflation, however, and the frequency of price changes thus becomes highly correlated with inflation. Overall, my empirical results suggest that pricing models should endogenize the timing of price changes if they wish to make realistic predictions at both low and high inflation levels. They also present the challenge of finding a model offering empirically plausible predictions at all levels of inflation. To investigate

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whether menu-cost models are consistent with my findings, I calibrate a discrete-time version of the Golosov and Lucas (2007) model. The model features idiosyncratic technology shocks giving rise to a distribution of both positive and negative nominal price adjustments. I show that the model performs well in terms of predicting the average frequency and magnitude of price changes for levels of inflation similar to the ones experienced by Mexico over my sample period. The success of the model comes in part from the presence of offsetting movements in the frequency of price increases and decreases, and highlights the importance of idiosyncratic shocks in this class of models for delivering empirically plausible predictions. The paper is organized as follows. In the next section, I provide a brief overview of the Mexican macroeconomic context over the sample period. In Section III, I describe the assemblage of my data set and discuss features of the data that are important for interpreting my results. Section IV defines the statistics computed in this paper. The main empirical findings are presented in Section V and are then compared to other studies of high-inflation environments in Section VI. In Section VII, I calibrate a discretetime menu-cost model with idiosyncratic technology shocks and investigate its consistency with some key empirical features reported in the paper. The last section provides concluding remarks. II. MACROECONOMIC CONTEXT The sample period was marked by a severe economic downturn in the wake of the December 1994 peso devaluation. To most observers of the Mexican economy, however, 1994 opened rather positively.3 Inflation had been stabilized successfully below 10%, a major achievement in light of the three-digit rates of the late 1980s, and real interest rates also had decreased. The excess return on the three-month, dollar-denominated Tesobonos was only two percentage points above the American T-bill. The budget deficit, seen by many as the culprit of previous economic crises, had been eliminated in 1992. Moreover, the North American Free Trade Agreement had taken effect on January 1, 1994. Foreign capital entered abundantly with a net inflow over 8% of GDP in 1993. However, growth in real GDP per capita remained modest, averaging 2.5% from 1991 to 1993. Many observers saw 3. See Edwards (1998) for a review of observers’ opinions in 1994.

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(b) Inflation rate 140

100

120

80

100

60 %

%

80 60

40 20

40

0

20 0 1994 1995 1996 1997 1998 1999 2000 2001 2002

1994 1995 1996 1997 1998 1999 2000 2001 2002

(d) Money aggregates (logs, 1994M1=0) 80

200 150

60

M1 M4

%

%

100 40

50 20

0

0 1994 1995 1996 1997 1998 1999 2000 2001 2002

1994 1995 1996 1997 1998 1999 2000 2001 2002

(e) Real output (logs, 1994Q1=0)

(f) Real consumption (logs, 1994Q1=0)

40

30

30

20

%

%

20 10

10 0

1994 1995 1996 1997 1998 1999 2000 2001 2002

0

1994 1995 1996 1997 1998 1999 2000 2001 2002

FIGURE II Main Macroeconomic Indicators Source: Banco de M´exico.

this situation as part of a restructuring process that soon would bring strong growth to the country. The devaluation brought a radical change of mood. On December 22, 1994, the exchange rate collapsed and lost more than ` 40% of its value vis-a-vis the U.S. dollar in the week that followed.4 As depicted in Figure II, short-term interest rates were pushed upward substantially as Banco de M´exico tightened the supply of money to prevent further erosion of the peso and capital flight. 4. Mexico pegged its exchange rate to the dollar in May 1992. In February 1994, the country switched to pre-announced crawling bands around the U.S. dollar.

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The devaluation left major stagflation in its wake. Inflation took off almost immediately, increasing from 6.4% in November 1994 to 44.3% in January 1995 before peaking at 92.0% in April 1995. Real output per capita contracted 9.5% in 1995, whereas private consumption per capita fell a solid 13.2%. Mexicans would have to wait until 1998 for real GDP per capita to surpass its 1994 level and until 1999 for inflation to settle below 10%. The decline in aggregate income, coupled with a rise in fiscal evasion, brought a sharp decline in government revenues.5 To prevent further revenue erosion, the government raised the general rate of the value-added tax rate from 10% to 15% on April 1, 1995. This change affected all Mexican regions, with the notable exceptions of Baja California and a corridor along the country’s southern and northern borders where the rate remained at 10%. III. MEXICAN MICRO DATA ON CONSUMER PRICES III.A. Description of Sources The data comprise price quotes collected by Banco de M´exico for computing the Mexican CPI. Most price quotes correspond to narrowly defined items sold in specific outlets (e.g., corn flour, brand Maseca, bag of 1 kg, sold in outlet 1100 in Mexico City). A limited number of quotes are citywide indices, or the average prices of small samples of narrowly defined items belonging to the same category and outlet. Since January 1994, the official gazette of the Mexican government, the Diario Oficial de la Federaci´on, has published price quotes every month. This publication releases each quote with a key linking the item to a specific outlet, city, and product category; these keys allow me to track individual prices over time.6 In this paper, I refer to an item’s complete price history as its price trajectory. The raw data set contains a total of 4.7 million price quotes from January 1994 to June 2002. Banco de M´exico is required to make individual prices available to the public up to six months after their publication, but it does not keep a historical data set of individual prices. The data set was assembled by merging the information released in the Diario. The data for the months of January 1994 to February 1995 could not be extracted electronically, 5. See OECD (2000) for a description of the taxation system. 6. Items from the same outlet are attributed store keys independently to ensure confidentiality.

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so they were typed in from original hard copies of the Diario using double-entry keying, a process ensuring a characterwise accuracy in excess of 99.998%.7 About 430,000 price quotes were added to the database in this way. Precise item descriptions were published in March 1995. The Diario also includes lists of items that are periodically added to or dropped or substituted from the CPI basket. Unlike additions, substitutions are not planned events. They occur when the characteristics of an item (weight, size, model, presentation, etc.) change, when an outlet stops carrying an item, or, in rarer cases, when an outlet goes out of business. The weights used in the CPI are derived from the Survey of Households’ Income and Expenditures (ENIGH). The CPI product categories are representative of all ENIGH categories accounting for at least 0.02% of households’ expenditures. This ensures a coverage of well above 95% of Mexican households’ expenditures. To facilitate comparisons with other studies, I classify each product category according to the euro-area classification of individual consumption by purpose (COICOP). III.B. Sample Coverage In January 1994, the CPI contained 30,692 price quotes spread over 302 product categories. By June 2002, the last month in my sample, it had expanded to nearly 50,000 price quotes distributed over 313 product categories. A major revision of the basket occurred in March 1995 when the number of cities covered in the CPI grew from 35 to 46. At the same time, 29 new product categories were introduced into the basket, and 18 were abandoned. This revision had been planned long before the peso’s devaluation. In July 2002, Banco de M´exico updated the basket again to reflect the structure of Mexican households’ consumption in 2000. I cannot link items before and after the 2002 basket revision because of a change to the item keys. To ensure the greatest comparability across time, I compute my results for a sample covering January 1994 to June 2002 using the expenditure weights implemented in March 1995.8 The sample is further restricted to the product categories comprising individual prices that were unaffected by the 1995 basket revision and I consider only items whose price was 7. I thank Chris Ahlin for lending me original copies of the Diario. 8. These weights are derived from the 1989 ENIGH survey. They were updated using relative prices to reflect consumer expenditures in 1993.

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QUARTERLY JOURNAL OF ECONOMICS TABLE I MAIN SAMPLE STATISTICS Period Price quotes Total Average per month Trajectories Substitutions Product categories

January 1994–June 2002 3,209,947 31,470 44,272 10,457 227

CPI coverage (%)

54.1

Sample composition (%) Unprocessed food Processed food Energy Nonenergy industrial goods Services

26.4 21.7 0.4 26.4 25.1

not regulated. In addition, most education services and clothing items were dropped for reasons detailed below. The final sample contains 3.2 million price quotes from over 44,000 price trajectories and covers 54.1% of CPI expenditures. The main groups of products excluded are rents and homeowners’ imputed rents, clothing (except for a few product categories containing individual observations), and education services, whose weights in the CPI are, respectively, 14.0%, 6.0%, and 3.5%. Food items represent just under half of the expenditures in the final sample, a proportion higher than in most U.S. and euro-area studies. Summary statistics are presented in Table I. III.C. Other Aspects of the Data I now address features of the data that are important to consider in interpreting the results. The most significant issue is price averaging. Banco de M´exico collects prices twice monthly for all items but food; food price collection occurs four times per month.9 The collected prices are then averaged to produce the monthly figures reported in the Diario. Observing the monthly average rather than the actual price of an item complicates the inference about price changes. For example, an average price of $2 for an item is 9. In the United States, the BLS collects prices monthly for food consumed at home, energy, and a few additional items with volatile prices. Other prices are collected monthly for the three largest metropolitan areas (New York, Los Angeles, and Chicago) and every other month for the remaining areas.

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consistent with an actual price of $2 throughout the month. It also is consistent with an actual price of $1.50 in the first half of the month and $2.50 in the second, or any combination of prices with $2 as their average. Moreover, changes to an average-price series are typically more frequent and smaller on average than changes to an actual-price series with the same publication frequency. For example, a price hike from $1.50 to $2.50 in the middle of the month results in an average price of $2, which is $0.50 short of the new actual price, so that another change to the average-price series will likely be recorded in the next month. To make my results as comparable as possible to other studies, which typically do not use averaged price quotes, I have constructed alternative price trajectories that filter out the effect of averaging observations whenever possible. These new series correspond to the end-of-month series, which both are consistent with the published average prices and minimize the number of price changes. Appendix I provides an extensive discussion of how averaging observations affects inferences about the timing and magnitude of price changes, and of how the filter was implemented. I was provided with unpublished semimonthly data by Banco de M´exico, which allows me to directly assess the performance of the filter. Overall, the filtered series are much closer to the end-ofperiod price series that they aim to reproduce. More importantly, the filtered series capture the timing of price changes with great accuracy. All the main patterns described in this paper are found whether prices are filtered or not. Another data issue is that price collectors do not always directly observe prices. Sometimes an item is out of stock, out of season or, in rarer cases, the outlet is closed when the CPI agent visits. In such situations, the price from the previous period is carried forward. Although I cannot identify prices that were imputed in my sample, I do find clear indications that the number of imputations was larger at the beginning of the sample. Item substitutions represented less than 0.1% of all published price quotes in 1994, a proportion that rose to 1.2% in 2001. A more systematic treatment of substitutions was implemented in 2001. Prices can now be carried forward for at most a month and a half before a substitution is sought. If the scarcity is generalized, this allowance can be extended up to three months. This methodological change likely creates a slight downward bias in the estimated frequency of price changes at the beginning of the sample.

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Prices are inclusive of sales as long as they are conditional on the purchase of a single item. For example, in a three-for-two promotion, the regular price would be reported. In the United States, the Bureau of Labor Statistics reports prices net of sales and promotions whenever possible; the same three-for-two promotion would result in a temporary 33% price decrease. There is no variable in the Mexican data set signaling that an item is on sale or that a promotion is going on. Most price quotes for the product categories of textiles, clothing, shoes, and related accessories are averages of small samples of item prices; all items within a sample pertain to the same outlet whenever possible. Banco de M´exico uses store samples to alleviate the problems associated with rapidly appearing and disappearing items due to changes in fashion and the seasons. All such samples were dropped from my analysis to limit the discussion to individual price changes. The decision to include or exclude store samples has little impact on the main findings. All education services observations, which cover registration, activity, and tuition fees, were also dropped from the sample. These services are typically not available for purchase or not sampled during most months of the year. Prices are mechanically carried forward until the start of the next registration period, semester, or academic year. For this reason, one cannot directly interpret the absence of price changes in the monthly series as evidence of price stickiness. A final issue is that item substitutions often accompany changes in product characteristics, thereby raising the question of whether substitutions should be treated as price changes. The Inflation Persistence Network’s approach is to assume that all item substitutions not previously planned by CPI agencies involve a price change, a choice guided in part by the absence of substitution flags in some of the national databases. In this paper, substitutions were instead excluded from the computation of price changes because their treatment varied over the sample period. The main patterns found in this paper are not affected by this choice. IV. INFLATION ACCOUNTING PRINCIPLES Whenever a price is reported for two consecutive months, I create an indicator that a price change has occurred, 1 if pit = pit−1 Iit = 0 if pit = pit−1 ,

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where pit is the price of item i (in logs) during month t. Inflation is defined as πt = i∈ϒt ωit pit , where pit = pit − pit−1 , ωit is the sample weight of item i, and ϒt is the set of all items in the sample for which Iit is defined. For ωit , I use the sample share of spending on the product category to which item i belongs, divided by the number of items in that product category for which I can compute a price change at t. Inflation can also be expressed as

πt =

i∈ϒt ωit pit ωit Iit . i∈ϒt i∈ϒt ωit Iit

fr

t

dpt

The term frt , henceforth referred to as the frequency of price changes, is the share of spending in the sample on items whose price changed at month t. The term dpt is the average magnitude of those price changes. In the popular Taylor (1980) and Calvo (1983) models with uniform staggering of price changes, dpt is the only possible source of variation in πt . It is convenient to decompose inflation further into a weighted sum of price increases and decreases: + i∈ϒt ωit Iit pit + ωit Iit πt = + i∈ϒt i∈ϒt ωit Iit

+ frt

dpt+

− i∈ϒt ωit Iit pit − + ωit Iit . − i∈ϒt i∈ϒt ωit Iit

− frt

dpt−

This decomposition is informative about the relationship between inflation and the distribution of price changes. The computation of inflation statistics for special aggregates, such as goods and services, also follows the approach outlined above. My methodology for computing inflation is similar to the approach taken in most euro-area and U.S. studies of individual price changes but differs from that of Banco de M´exico at the time, which computed inflation as the percentage change in a Laspeyres index. Despite differences in sample coverage, methodology, and filtering of price trajectories, the inflation rate in my sample is strongly correlated with the change in the official CPI:

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The coefficient of correlation is 0.96 over the full sample period and 0.85 over the last three years of the sample.

V. MAIN EMPIRICAL RESULTS This section presents the key empirical findings, focusing on the relationship between inflation and the frequency and average magnitude of price changes. I treat (nonregulated) goods and services separately throughout the discussion due to differences in the way prices are set between the two groups.10 I place a special emphasis on the results for goods, given their predominance in my sample and their greater representativeness. V.A. Setting of Consumer Goods Prices My subsample of goods accounts for 74.9% of all expenditures in my basket and is representative of 77.5% of Mexican consumer expenditures on goods (excluding energy). Most goods left out of the sample pertain to product categories falling under the apparel and related accessories group. Frequency of Goods Price Changes. As seen in the upper panel of Figure III, movements in the frequency of price changes and inflation were very large over the sample period. In April 1995, the rate of inflation in my sample of goods peaked at 86.0% (7.2% in monthly terms). This rate is much higher than the average in 1994 (7.5%) or during the last year of the sample (1.5%). The frequency of price changes also peaked in April 1995, when the price of 64.7% of goods, measured in CPI weights, changed during the month. This number is more than twice the average frequency of 26.8% in 1994. There were large variations in the composition of price changes over the sample period, as shown in the lower panel of Figure III. At the peak of inflation, only 8.9% of price changes were negative, a proportion that rose to 46.0% in the last year of the sample. The corresponding proportion for the full sample of goods and services over the last year of the sample is 43.4%, a figure echoing those from U.S. and euro-area studies. 10. For the products in my sample, the COICOP goods/services classification is almost identical to the Bank of Mexico’s tradables/nontradables classification. The results reported in the paper for goods and services thus have an alternative interpretation in terms of tradables and nontradables.

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PRICE SETTING DURING LOW AND HIGH INFLATION (a) Frequency of price changes and inflation

Frequency Inflation

80

%

60 40 20 0 1994

1995

1996

1997

1998

1999

2000

2001

2002

(b) Frequency of price increases and decreases 60 Increases Decreases

50

%

40 30 20 10 0 1994

1995

1996

1997

1998

1999

2000

2001

2002

FIGURE III Monthly Frequency of Price Changes (Nonregulated Goods) All statistics in the figure, including inflation, are computed using the sample of nonregulated goods.

Positive comovement between frt and πt is clearly visible in Figure III. The correlation coefficient between the two series is 0.91 for the whole period.11 This correlation is largely driven by the high-inflation episode, however; it is about zero if I consider only the last three years of the sample. After mid-1996, it is difficult to spot any downward drift in the frequency of price changes, even though inflation trends down. The reason behind this loose relationship is apparent in the lower panel of Figure III, where I − break down frt into fr+ t and frt . As inflation declined, so did the frequency of price increases. At the same time, price decreases became more frequent, thereby dampening movements in the overall frequency of price changes. A look at the correlation between 11. All correlation statistics presented in this section are computed using linearly detrended series.

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− fr+ t , frt , and πt provides further evidence of these offsetting movements. In the last three years of the sample, the correlation is − 0.59 between fr+ t and πt , and −0.74 between frt and πt . The net result is a relative absence of correlation between frt and πt for my sample of goods over that period. There are a few apparent large negative movements in the inflation series of goods over the low-inflation period, in particular in March 1999, February 2001, July 2001, and February 2002, which are associated with unusually large changes in fresh produce prices. Shocks to the supply of fruits and vegetables, such as unusual weather conditions, can have a notable impact on the price of these items because they are perishable in nature. Some evidence of opposite movements in the frequency of price increases and decreases is apparent for these months. The scatterplot in the upper left panel of Figure IV offers a view from a different angle of the relationship between the monthly frequency of price changes and inflation. Similar scatterplots for price increases and decreases are shown in the middle left and lower left panels, respectively. All panels display linear regression lines that use linear, quadratic, and cubic goods inflation terms as explanatory variables, as well as a full set of year dummies. The dummies are included to account for potential shifts in the relationships over time that are unrelated to inflation, such as fluctuation in aggregate demand, basket composition, and methodology. I present regression lines for two sets of observations. The dashed lines include all monthly observations in the sample. The solid lines exclude April 1995, which was marked by a 5-percentage-point increase in the value-added tax, as well as all periods with negative inflation, which effectively removes all large shocks to food produce mentioned earlier. Variations in the supply of fresh fruits and vegetables and value-added tax changes are shocks that differ in nature from a general rise in the price level. For this reason, my discussion of the scatterplots focuses on the regression results for the smaller sample, as they likely capture the overall relationship between inflation and its components better. All regression statistics can be found in Table II. When inflation is zero, each percentage-point increase in the rate of nonregulated-goods inflation is associated with a 0.35 (0.13)-percentage-point rise in the frequency of price increases and an opposite 0.22 (0.06)-percentage-point decline in the frequency

PRICE SETTING DURING LOW AND HIGH INFLATION (a) Frequency of price changes

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(b) Magnitude of price changes

70

15

10

50

Magnitude (%)

Frequency (%)

60

40 30 20

0

0

Data All observations Excluding π 0 if (u, v) ∈ E and c(u, v) = 0 otherwise. The capacity measures the utility benefits that agents derive from their relationships. For ease of presentation, we assume that the strength of relationships is symmetric, so that c (u, v ) = c (v, u) for all u and v.8 Our model consists of five stages, which are depicted in Figure II. We begin by describing the model and then discuss the economic content of our modeling assumptions. Stage 1: Realization of Needs. Two agents s and t are randomly selected from the social network. Agent t, the lender, has an asset that agent s, the borrower, desires. The lender values the asset at V , and it is assumed that V is drawn from some prior distribution F over [0, ∞). The identity of the borrower and the lender and the value of V are publicly observed by all players. 8. Our results extend to the case where capacities are asymmetric. In that environment, the social network can be represented as a directed graph and the directed network flow determines borrowing.

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Stage 2: Borrowing Arrangement. At this stage, the borrower publicly proposes a transfer arrangement to all agents in the social network. The role of this arrangement is to punish the borrower and compensate the lender in the event of default. A transfer arrangement consists of a set of transfer payments h (u, v ) for all u and v agents involved in the arrangement. Here h (u, v ) is the amount u promises to pay v if the borrower fails to return the asset to the lender. Once the borrower has announced the arrangement, all agents involved have the opportunity to accept or decline. If all involved agents accept, then the asset is borrowed and the borrower earns an income ω (V ), where ω is a nondecreasing function with ω (0) = 0. If some agents decline, then the asset is not lent, and the game moves on directly to stage 5. Stage 3: Repayment. Once the borrower has made use of the asset, he can either return it to the lender or steal it and sell it for a price of V .9 If the borrower returns the asset, then the game moves to the final stage 5. Stage 4: Transfer Payments. All agents observe whether the asset was returned in the previous stage. If the borrower did not return the asset, then the transfer arrangement is activated. Each agent has a binary choice: either he makes the promised payment h (u, v ) in full or he pays nothing. If some agent u fails to make a prescribed transfer h (u, v ) to v, then he loses his friendship with agent v (i.e., the (u, v ) link “goes bad”). If (u, v ) link is lost, then the associated capacity is set to zero for the remainder of the game. We let c (u, v ) denote the new link capacities after these changes. Stage 5: Friendship Utility. At this stage, agents derive utility from their remaining friends. The total utility enjoyed by an agent u from his remaining friends is simply the sum of the values of all c (u, v ). remaining relationships, that is, v Our model is a multistage game with observed actions. Let u denote the set of agent u’s pure strategies and let = ×uu. We focus on the set of pure strategy subgame perfect equilibria below.

III.B. Discussion of Modeling Assumptions We now discuss some of the assumptions underlying our model. 9. As we show in Appendix II, the model can be extended to the case where the liquidation value of the asset is φ · V with φ ≤ 1.

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Social Sanctions. When an agent fails to make a promised transfer, we assume that the associated friendship link automatically goes bad, capturing the idea that friendly feelings often cease to exist if a promise is broken. Appendix II develops explicit micro foundations for this assumption. In these micro foundations, which build on Dixit (2003), failure to make a transfer is a signal that the agent no longer values his friend, in which case these former friends find it optimal not to interact with each other in the future. An alternative justification is that people break a link for emotional or instinctive reasons when a promise is not kept; Fehr and Gachter (2000) provide evidence for such behavior. Circle of Trust. For large social networks it can be unrealistic for the borrower to include socially distant agents in the arrangement. All our results hold if we restrict the set of links over which transfer payments can be proposed to some subgraph of the original network, the “circle of trust,” which may depend on the identity of the borrower and the lender. The only difference in our results is that the network flow measure of the borrowing limit will have to be computed in the subgraph of permissible links. Transfer Arrangement as Social Norms. The transfer arrangement in our model can be interpreted either as an explicit agreement between all parties or as a representation of accepted norms of behavior. In the second interpretation, agents simply share an understanding about what they are expected to do in the event of default. Cash Bonds and Borrowing Constraints. One way to solve the moral hazard problem is to have the borrower post a cash bond to the lender, which is returned only if the borrower does not default on the asset loan. We abstract away from bonds and prepayments by assuming that the borrower is initially cash-constrained. However, we do allow the borrower and other agents to make payments in later stages of the game. This can be justified if agents work or make investments in the initial stage, generating income in later stages; or if transfers are in-kind, for example, helping out with the harvest, where posting a bond may be inefficient or infeasible. III.C. Equilibrium Analysis For what values of V can borrowing be implemented in a subgame perfect equilibrium? We begin answering this question

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by studying equilibria where all promises are kept, that is, where every transfer h (u, v ) is expected to be paid if the borrower fails to return the asset. We later show that focusing on these equilibria is without loss of generality. In any equilibrium where promises are kept, transfers have to satisfy the capacity constraint (1)

h(u, v) ≤ c(u, v).

This is simply an incentive compatibility constraint. If the borrower fails to return the asset, agent u has to decide whether to make his promised transfer payment h (u, v ) to v. The cost of making the payment is h (u, v ); the cost of not making the payment is c (u, v ), because it results in losing the friendship with v. In any equilibrium where promises are kept, u must prefer the friendship over the monetary value of the transfer, leading to (1). Two-Agent Network. To build intuition, we begin the equilibrium analysis with the case where the social network consists only of the borrower s and the lender t. Let σ be a pure strategy subgame perfect equilibrium that implements borrowing where promises are kept. In any such equilibrium, V ≤ h (s, t). To see why, assume that the borrower s defaults on the equilibrium path. Then the lender receives the transfer payment h (s, t) instead of the asset; but he must break even to lend, which yields V ≤ h (s, t). On the other hand, if the borrower returns the asset on the equilibrium path, then he must weakly prefer not to default, which again requires V ≤ h (s, t). Combining this inequality with the capacity constraint (1) then yields (2)

V ≤ c(s, t),

showing that borrowing is limited by the maximum flow in this simple network. It is also easy to see that when (2) is satisfied, there exists an equilibrium that implements borrowing: just set h (s, t) = V .10 Intuitively, the collateral value of friendship can be used to elicit payment and thus solve the agency problem. Four-Agent Network. To gain intuition about borrowing in more general networks, we next consider the network depicted 10. In this equilibrium, all surplus accumulates to the borrower because of our assumption that he proposes the transfer arrangement. In a setup where bargaining power is more evenly distributed, we expect that the surplus would be shared by the agents involved in the transfer arrangements, in a manner similar to Goyal and Vega-Redondo (2007).

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c(

c(

)

c(

)

s

u

t

Borrower

Intermediary

Lender

FIGURE III Borrowing in a Four-Agent Network This figure illustrates borrowing in networks with intermediaries. The arrangement favored in our paper involves transfers flowing from s through u to t in the event of default. In this arrangement the weakest link, min[c(s, u), c(u, t)], determines the borrowing limit. An alternative arrangement, where cousin v promises to punish the borrower s in case of default, sometimes enforces better outcomes. However, this arrangement is not robust to side deals by groups of agents: the borrower and his cousin can jointly deviate, steal the asset, and short-change the lender. As we show in the text, all side deal–proof arrangements satisfy the weakest link requirement.

in Figure III, which consists of four players: the borrower s, the lender t, an intermediate agent u connecting s and t, and an agent v who is connected only to the borrower s. We will refer to v as the “cousin” of s. A natural transfer arrangement that implements borrowing in this network is one where agent u acts as an intermediary who elicits and transits payments from s to t in the case of no compliance, and gets zero net profits. To formalize this arrangement, simply set h (s, u) = h (u, t) = V . For this arrangement to be incentive compatible, the capacity constraint (1) must be satisfied for both links involved: V ≤ c (s, u) must hold so that s delivers the transfer to u, and V ≤ c (u, t) is needed to ensure that u passes on the transfer to t. Combining these yields the “weakest link” inequality (3)

V ≤ min [c (s, u) , c (u, t)] ,

which implies that the maximum flow determines the borrowing limit in this transfer arrangement. However, networks with more than two agents generally admit other subgame perfect equilibria that can implement borrowing even if (3) fails. We argue that these equilibria are implausible, because they fail a natural coalition-proofness requirement. To illustrate, assume that the borrower s has a strong link to his cousin

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v, with a capacity value of c (s, v ) = V + 1. The borrower might then propose an informal arrangement in which he promises to pay his cousin a transfer of h (s, v ) = V + 1 in case he fails to return the asset. This arrangement provides the right incentives to the borrower, and is a subgame perfect equilibrium even if (3) fails. To understand its logic, note that in this arrangement, the borrower essentially makes the following proposal to the lender: “Lend me your asset; if I don’t return it to you, my cousin will be angry with me.” As this interpretation makes it clear, this borrowing arrangement may not be robust to joint deviations where both the borrower and his cousin depart from equilibrium. More concretely, the borrower could circumvent the arrangement by entering a side deal with his cousin, in which he steals the asset and shares the proceeds with the cousin (who in equilibrium would otherwise receive nothing). Due to the possibility of such side deals, we do not find this equilibrium plausible. A similar potential equilibrium is one where the intermediate agent u provides incentives to the borrower but promises a zero transfer to the lender. In this case, the lender effectively “outsources” monitoring to the intermediary, trusting that the borrower will always return the asset rather than pay a high transfer to u. This arrangement is again open to side deals: here s and u can choose to steal the asset jointly and split the proceeds, leaving the lender with nothing. As in the equilibrium with the cousin, the possibility of a side deal arises because nobody “monitors the monitor”: the lender is not fully in control of incentives. When enforcement is outsourced to either the cousin or the intermediary, these agents can team up with the borrower and steal the asset. These examples suggest that when the borrower and other agents can agree to side deals, it may not be in the interest of the lender to provide the asset. This motivates our focus on subgame perfect equilibria that are immune to such side deals. III.D. Side Deal–Proof Equilibrium Consider the subgame starting in stage 2, after the identities of the borrower and the lender and the value of the asset are realized, and for any pure strategy σ ∈ , let Uu (σ ) denote the total utility of agent u in this subgame. We formalize the idea of a side deal as an alternative transfer arrangement h (u, v ) that s proposes to a subset of agents S ⊂ W after the original arrangement is accepted. If this side deal is accepted, agents in S are expected to make transfer payments according to h, whereas agents outside

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S continue to make payments described by h. For the side deal to be credible to all participating agents, it must be accompanied by a proposed path of play that these agents find optimal to follow. This motivates the following definition. DEFINITION 2. A side deal with respect to a pure strategy profile σ is a set of agents S, a transfer arrangement h(u, v) for all u, v ∈ S, and a set of continuation strategies { σu | u ∈ S} proposed by s to agents in S at the end of stage 2, such that σu, σ S\u, σ−S ) ≥ Uu(σu , σ S\u, σ−S ) for all σu and all u ∈ S, (i) Uu( σ S , σ−S ) ≥ Uu (σ S , σ−S ) for all u ∈ S, and (ii) Uu ( (iii) Us ( σ S , σ−S ) > Us (σ S , σ−S ). Condition (i) says that all agents u involved in the side deal are best-responding on the new path of play, that is, that the proposed path of play is an equilibrium for all agents in S conditional on others playing their original strategies σ−S . Condition (ii) says that if any agent u ∈ S refuses to participate in the side deal, then play reverts to the original path of play given by σ . Finally, (iii) ensures that the borrower s strictly benefits from the side deal. DEFINITION 3. A pure strategy profile σ is a side deal–proof equilibrium if it is a subgame perfect equilibrium that admits no side deals. It is easy to see that this condition rules out the equilibria violating the weakest link inequality (3) in Figure III. We now turn to extend this result to general networks.11 III.E. Main Theorem We begin by formally defining the concept of network flows intuitively discussed above. DEFINITION 4. An s → t flow with respect to capacity c is a function f : G × G → R that satisfies the following: (i) Skew symmetry: f (u, v) = − f (v, u). (ii) Capacity constraints: f (u, v) ≤ c(u, v). (iii) Flow conservation: w f (u, w) = 0 unless u = s or u = t. 11. Our definition of side deal–proof equilibrium does not require side deals to be robust to further side deals. However, as the proof in Appendix I makes clear, imposing this requirement would not change any of our results: when there is a deviating side deal, there is also one that is robust to further coalitional deviations, namely the side deal implemented with a network flow.

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The value of a flow is the amount that leaves the borrower s, given by | f | = w f (s, w). Let T st (c) denote the maximum value among all s → t flows. THEOREM 1. There exists a side deal–proof equilibrium that implements borrowing between s and t if and only if the asset value V satisfies (4)

V ≤ T st (c).

This result states that the endogenous borrowing limit equals the value of the maximum flow between borrower s and lender t. We interpret the borrowing limit T st (c) as a measure of networkbased trust: if s can borrow more from t, it must be that t has higher trust in s. The logic of the proof of Theorem 1 is as follows. When V satisfies inequality (4), a side deal–proof equilibrium is easy to construct: by assumption, there exists an s → t flow with value V , and this flow can be used as a transfer arrangement. Flow conservation implies that all intermediate agents break even, confining their role to simply extracting and transmitting the payment V from s to t in case s fails to return the asset. Thus the lender is in full control of incentives; because of this, the equilibrium is easily seen to be side deal–proof. To show that no side deal–proof equilibrium can implement a higher level of borrowing, we build on the maximum flow– minimum cut theorem (Ford and Fulkerson 1956), which states that the maximum network flow between s and t equals the value of the minimum cut. A cut is a disjoint partition of the nodes into two sets G = S ∪ T such that s ∈ S and t ∈ T , and the value of the cut is defined as the sum of c (u, v ) for all links such that u ∈ S and v ∈ T . For any borrowing arrangement violating (4), we can construct a side deal in the following way. Fix a minimum cut (S, T ); the maximum flow–minimum cut theorem implies that the total capacity of all links between S and T is less than V . But then agents in S have a profitable side deal: by defecting as a group, they lose less than V in foregone friendships, but gain V from selling the asset. For a concrete example, consider the network with the cousin in Figure III and suppose that c (s, u) < c (u, t). The minimum cut between s and t has value c (s, u), and the corresponding partition is simply S = (s, v ) and T = (u, t). In any equilibrium where V > c (s, u), that is, where (4) is violated, agents in

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QUARTERLY JOURNAL OF ECONOMICS A. Original network

3

B. Auxiliary network

4 s1

s

2

1 v

4

3

u

t

3.5

s2

3

u

2 2

1

t

v

FIGURE IV Maximum Network Flow with Transfer Constraints This figure illustrates network flow with transfer constraints. Agent s could normally borrow an asset up to value 4 from agent t. However, he faces a binding transfer constraint of 3.5. We can calculate network flow in the constrained graph by drawing an auxiliary network where we split s into two agents s1 and s2 . All incoming links of agent s are connected to s1 and all outgoing links emanate from agent s2 . A directed link from s1 to s2 has capacity equal to the transfer constraint. The network flow from s1 to agent t equals the maximum network flow with transfer constraint.

S have a side deal: the borrower s and his cousin v can team up to steal the asset, because their total repayment is limited by the value of the cut c (s, u). III.F. Extensions: Transfer Constraints and Endogenous Circle of Trust Transfer Constraints. In environments with credit constraints, agents might have limits on the total amount they can borrow or transfer. For example, in Figure IVA, the intermediaries u and v might worry that if the borrower s carried too large a debt burden, he would be unable to pay. We show that the concept of network flows can be used to characterize borrowing in this environment as well. To introduce borrowing and transfer constraints in a simple way, suppose that each agent u can make a total payment of at most ku to others in the network, where the transfer constraints ku are exogenous. Here ku can represent either cash or time constraints.12 How much borrowing can be implemented in this environment? We show that the answer is given by the maximum flow in a modification of the social network, where each agent u is replaced by two identical agents connected by a link with capacity 12. For an intermediate agent (but not for the borrower), incoming transfers may help relax cash constraints. For these intermediate agents, ku represents constraints that remain after incoming payments; for example, these could be time constraints if the transfers were in-kind services, such as helping out, which cannot be easily passed on.

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ku. To formally construct this auxiliary (directed) network G , replace each node u in G with a pair of nodes, u1 and u2 , and replace each (u, v) link with two new directed links, a u2 → v1 link and a v2 → u1 link, each with capacity equal to c(u, v). Finally, for each agent u, create a new u1 → u2 link with capacity equal to the transfer constraint c(u1 , u2 ) = ku. That is, we duplicate all agents u, point all incoming links of u to u1 , have all outgoing links of u originate in u2 , and let the capacity of the u1 → u2 link be ku. For example, consider the network in Figure IVA, where agent s faces a binding transfer constraint of 3.5. The corresponding auxiliary network is drawn in Figure IVB and we can deduce that the constrained network flow equals 3.5, the flow from agent s1 to agent t in the auxiliary graph. In Appendix I we show that in any side deal–proof equilibrium where promises are kept, the borrowing limit in the presence of transfer constraints equals the value of the maximum s1 → t1 flow in G . To understand the intuition, consider a maximal flow. As in the basic model, the amounts assigned to links between agents by this flow can be interpreted as the transfer payments in a candidate transfer arrangement. It remains to verify that, in this arrangement, no agent u exceeds his total transfer constraint ku. But this follows by construction of G . The total transfers promised by u must be equal to the flow leaving u2 in G ; but by flow conservation, this must be equal to the value carried over the u1 → u2 link, which is bounded by the link capacity of ku in G . Circle of Trust. We can endogenize the “circle of trust,” that is, the set of permissible links over which transfer arrangements can be proposed, by assuming that there is a fixed cost associated with proposing various transfer arrangements. For each subgraph G0 ⊆ G, let κ(G0 ) ≥ 0 denote the cost of a transfer arrangement that includes all links in G0 .13 Assume that κ is monotone in the sense that if G0 ⊆ G 0 then κ(G0 ) ≤ κ(G 0 ). The function κ can be interpreted as a characteristic of the community’s social norm; for example, in a kin-based society, we expect κ to be zero or small for most family and relative links. Agent s, who wishes to borrow V from t, must now solve the cost-minimization problem min{κ(G0 )|G0 ⊆ G such that TGst0 ≥ V }, where TGst0 is the trust flow between s and t in G0 . The solution 13. For two networks G = (W, E) and G = (W , E ), we say that G ⊆ G if W ⊆ W and E ⊆ E.

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G∗0 , if it exists, is the minimum cost subgraph where borrowing V can still be supported. Agent s then chooses to borrow if and only if his profit from the loan exceeds the cost, that is, ω(V ) ≥ κ(G∗0 ). Besides its added flexibility, this framework also yields two new implications. (1) The set of people involved in an arrangement is endogenously determined: the greater the profits ω(V ), the more the borrower is willing to extend his circle of trust.14 (2) With positive κ, agents only borrow when profits are high enough; assets that generate low returns are never secured through social collateral. IV. APPLICATIONS IV.A. Network Structure and Welfare We now explore how the network structure affects the payoffs from borrowing in the social collateral model. Because the network is completely summarized by the vector of capacities c, the borrowing limit T st (c) can be viewed as a “trust map” that determines, as a function of the network structure c, how much trust is created between s and t. To see how trust determines payoffs, let st (c) denote the expected payoff of s from borrowing, conditional on the lender being agent t; then z (5) st (c) = (T st (c)), where (z) = ω(v) dF(v), 0

because the payoff is just the expectation of ω(V ) over all values of V that do not exceed the borrowing limit T st (c). Changes in the network affect the payoffs through changes in the trust flow T st (c). Our goal in this section is to characterize these welfare effects.15 Monotonicity. We first explore the effect of increasing connectivity by adding new links or strengthening existing links. We say that the network associated with capacity c1 is more strongly connected than that associated with c2 if no link has lower capacity under c1 than under c2 ; that is, c1 (u, v) ≥ c2 (u, v) for all u, v ∈ W. We then have the following monotonicity result. 14. Formally, an increase in ω(V ) holding fixed V can change the sign of ω(V ) − κ(G∗0 ) from negative to positive and induce borrowing. 15. Besides the profit from borrowing st (c), the borrower s also derives utility from his friends. In the subsequent analysis we focus on the payoff from borrowing.

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PROPOSITION 1. If the social network with capacity c1 is more strongly connected than the network with capacity c2 , then for any borrower s and lender t, both trust and payoffs are higher: T st (c1 ) ≥ T st (c1 ) and st (c1 ) ≥ st (c1 ). Networks with more and stronger links generate more trust and higher payoffs due to the increased supply of social collateral. A large body of work in sociology relies on the result formalized here: Putnam’s (1995), for example, argues that “networks of civic engagement (. . . ) encourage the emergence of social trust.” The fact that this monotonicity emerges naturally in the social collateral model makes it a useful candidate for exploring other questions related to network-based trust. Closure and Structural Holes. We now turn to study how the deeper structure of the network affects payoffs, focusing on changes in network closure, a concept often discussed in the sociology literature. Networks have high closure if the neighborhoods of connected agents have a large overlap. To illustrate, consider the two network neighborhoods of agent s in Figure V, which is a small variation of Figure 1 in Coleman (1988). The neighborhood of s in Figure VB has higher closure, because the friends of s are directly connected. This idea of closure can also be formulated using network paths: a neighborhood has high closure if it connects s to few others through many paths (as in Figure VB), whereas it has low closure if it connects s to many others through fewer paths each (Figure VA). The sociological literature has two views about the benefits of closure. One view, dating back to Coleman (1988), argues that high closure is good because it facilitates sanctions, making it easier for individuals to trust each other. In his discussion of the wholesale diamond market in New York City, Coleman explains that “If any member of this community defected through substituting other stones or stealing stones in his temporary possession, he would lose family, religious and community ties.” Similarly, in the context of Figure V, Coleman argues that in the high closure network of Figure VB, agents t1 and t2 can “combine to provide a collective sanction, or either can reward the other for sanctioning.” In contrast, Granovetter (1973) and Burt (1995) argue that loose networks with low closure lead to higher performance, because they allow agents to reach many others through the network. Burt also emphasizes the role of structural holes, that is, people who bridge otherwise disconnected networks: for example,

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B. High closure

A. Low closure

t3

t4

t3

t4

t1

t2

t1

t2

s

s

FIGURE V Network Neighborhoods with Increasing Network Closure This figure shows network neighborhoods with increasing network closure. The two neighborhoods shown are a small variation on Figure 1 in Coleman (1988). With unit link capacities, agent s is connected through four paths to the rest of the network in both neighborhoods. In a low-value exchange environment, the neighborhood in Panel A is more attractive because it provides access to more people. In a high-value-exchange environment, the neighborhood in Panel B is more attractive, because closure allows borrowing high-valued assets from t1 and t2 .

s is a structural hole in Figure VA but not in VB. According to Burt (2000), these structural holes “broker the flow of information between people, and control the projects that bring together people from opposite sides of the hole.” A key part of this argument is that low-closure networks provide easier access to small favors, advice, information, and other resources. To explore these issues in the social collateral model, we first develop a measure of network closure, building on the idea that high closure is associated with having multiple paths to a smaller set of agents. We begin by counting the total number of paths of an agent, using the concept of network flows. Fix a network with integer-valued capacities c; then the network flow T st (c) is effectively the number of disjoint paths of unit capacity between s and t. Thus, the total path number for s is simply T s (c) = t∈W T st (c). In Figure V, s has a total of four paths in both networks; the difference in closure comes from the fact that in VA, these four paths reach four different people, whereas in VB they reach only

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two people, but there are two paths connecting s with either of them.16 To generalize this observation, let P s (n) denote the share of paths s has with agents to whom he has at least n paths, so that P s (2) = 0 in Figure VA and P s (2) = 1 in Figure VB.17 Clearly, P s (0) = 1 always, and P s (n) is nonincreasing in n. DEFINITION 5. The network neighborhood of s has a higher closure than the neighborhood of s if

(i) T s (c) = T s (c) so that s and s have the same total number of paths; and

(ii) For each n, P s (n) ≥ P s (n), so that a greater share of paths connect s to people with whom he has many paths. These conditions imply that if the neighborhood of s has higher closure, then s is connected to fewer people through many paths.18 This definition allows us to compare high- and low-closure neighborhoods. The key theoretical insight is that higher closure increases trust but reduces access. For example, in Figure VB, two people trust s with assets of value V ≤ 2; although access is low, trust is high in this closed network. In contrast, in Figure VA, s can borrow from four people, but the asset value can be at most 1: access has increased, but at the cost of a reduction in pairwise trust. Due to this trade-off, whether high or low closure is associated with greater welfare depends on what assets are exchanged: trust is more important for high-value assets whereas access matters more for low-value assets. To formalize this trade-off between access and pairwise trust, we let f (v ) denote the density of F (v ) and let ω(V ) = f (V )ω (V ), the frequency-weighted profits from the ability to borrow V . Note that ω(V ) depends both on the probability that an asset of value V is needed ( f (V )), and on the profits this asset generates (ω (V )). We say that the economy is a high-value exchange environment if ω(V ) is increasing: in this case high-value transactions generate greater welfare ω(V ), either because they are more likely or because they are more productive. Conversely, we 16. To see why s has four paths in Figure VB, note that there are two paths connecting s to t1 , the direct one and the indirect one through t2 ; and similarly, two paths connect s to t2 . 17. If arrangements are limited by a circle of trust, then T s (c) and P s (n) need to be computed in the corresponding subgraph of permissible links. 18. Also note that (ii) is equivalent to requiring that the cumulative distribu

tion function 1 − P s (·) first-order stochastically dominates 1 − P s (·).

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say we are in a low-value exchange environment when ω(V ) is decreasing. PROPOSITION 2. In a high-value exchange environment, a neighborhood with higher closure leads to a higher expected payoff to s. Conversely, in a low-value exchange environment, a neighborhood with higher closure leads to a lower expected payoff to s. In a low-value exchange environment, the access provided by low closure is more attractive, because knowing more people directly or indirectly increases the likelihood that s can obtain a low-value asset. This logic is in line with Granovetter’s and Burt’s basic argument about the strength of weak ties and the benefits of a dispersed social network in providing access to assets with low moral hazard, such as small favors, information, or advice.19 In contrast, in a high-value exchange environment, closure is better. Here, a reduction in access is more than compensated for by the fact that, through his dense connections, s will be able to borrow even high-value assets. This finding parallels Coleman’s general argument for network closure, and particularly his example of the wholesale diamond market in New York City, where the exchange of valuable stones requires high trust between dealers.20 The results of Proposition 2 are related to Putnam’s (2000) concepts of bridging and bonding social capital. In Putnam’s view, bonding social capital is associated with dense social networks and is good for generating reciprocity between agents who know each other well. In contrast, the networks underlying bridging social capital are “outward looking and encompass people across diverse social cleavages,” and are good for “linkage to external assets and for information diffusion.” These two concepts parallel our distinction between trust and access; our results thus provide formal foundations as well as network-based measures for bonding and bridging social capital. Community Size and Network Closure. What determines network closure? In Allcott et al. (2007), we argue that in practice, community size should be an important determinant. The 19. Section IV.B develops a variant of our basic setup where exchange of information is explicitly modeled. 20. Vega-Redondo (2006) reports a related finding in a model of repeated games played in networks. He shows that stability of cooperative behavior depends on a certain measure of network cohesiveness.

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Network closure (P s (2)) 0.4 0.6 0.8

1

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0

5

10 Number of friends

Below median size

15

20

Above median size

FIGURE VI Community Size and Network Closure The figure is taken from Allcott et al. (2007). The figure plots average network closure for students by the number of their friends for schools below median size (solid line) and schools above median size (dashed line). For each student s, closure is measured as P s (2), the share of paths s has to others with whom he has at least two paths, within the circle of trust that includes links up to distance 2 from s. See Definition 5 and Section IV.A for details. The figure is constructed using data from 142 U.S. middle and high schools in the National Longitudinal Study of Adolescent Health; observations with number of friends greater than 19 were excluded (less than 1% of total).

intuition is straightforward: in a small community, the pool of potential friends is limited, which makes it more likely that two agents share common friends. In Allcott et al. (2007), we confirm this intuition using data on the social networks of students in the National Longitudinal Study of Adolescent Health (AddHealth).21 Normalizing all link capacities to unity, we build on Definition 5 to measure the closure of the network around a student s with P s (2), the share of all paths that s has that connect him or her with others with whom he or she is connected through at least two paths.22 This quantity is always between zero and one, and higher values represent more closed networks. Figure VI compares this measure 21. AddHealth is a representative sample of 142 U.S. public and private middle and high schools in 1994 and 1995. 22. We also restrict the “circle of trust” to links that are within distance 2 from agent s. The distance of a link (u, v) from s is the arithmetic average of the length of the shortest paths connecting s to u and s to v.

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of closure for schools below and above the median size, for each possible value of a student’s number of friends. This figure confirms that community size is an important predictor of closure in practice: even holding fixed a student’s number of friends, smaller communities exhibit higher network closure. Implications for Organizations. The connection between community size and closure, combined with Proposition 2, has implications for organizational design. In environments where access to small favors such as providing information is important, communities should be larger. This can be achieved through a flat organizational structure where rank does not limit interactions. For example, academic communities in the United States have a relatively informal culture, generating a large community of researchers; this encourages the development of weak ties and creates access to ideas. In contrast, organizations where trust is important can create it by having smaller communities. For instance, the hierarchical structure of armies limits interactions to peers of the same rank, creating networks with high closure and bonding social capital. Our results also help explain the empirical fact that community size is often negatively correlated with prosocial behaviors such as volunteering, work on public projects, and helping friends (Putnam 2000). The traditional explanation is that in large communities people have fewer friends (Jacobs 1993). Our results suggest that even controlling for the number of friends, large communities have less dense social networks, which limits the provision of valuable public goods. IV.B. Job Search and Trust in Recommendations Sociologists have long recognized the importance of networks for finding jobs. For example, in Getting a Job, Granovetter (1974) documents that 56% of his sample of white-collar workers found employment through personal contacts. One possible explanation is that information about job openings often travels through friends and acquaintances. This logic forms the basis of Granovetter’s (1973) “strength of weak ties” theory, formally modeled by Calvo-Armengol and Jackson (2004), which predicts that weak links to agents with whom one has few common friends are most useful for job search, because they provide access to otherwise unobtainable information. However, the evidence about the strength of weak ties is mixed. Studies in U.S. cities (Bridges and

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Villemez 1986; Marsden and Hurlbert 1988) find that both weak and strong ties are important for job search. In Japan, Watanabe (1987) documents that small business employers screen applicants using strong ties. In China, Bian (1997, 1999) argues that the guanxi system of personal relationships allocates jobs using strong ties and paths. Granovetter (1974) provides a second reason for the importance of connections: networks can generate trust in job recommendations. When there is asymmetric information about the skills of job candidates, offers are often made based on the opinions of trusted recommenders. In Granovetter’s sample, such trusted referrals are common: in 60% of all jobs obtained through a network path of length 2 or more, the worker’s direct contact had “put in a good word” for him. Because trusted referrals are more likely to come through strong ties, this logic can help explain why many empirical studies have found strong ties to be more important. We now explore the implications of network-based trust for job search using the social collateral model.23 Consider an employer t who needs to fill a vacancy. Potential employees are either high or low types; if hired, a high type generates total value SH and a low type generates SL, where SH > SL > 0. In the formal labor market, worker types are unobservable, the proportion of high types is π H , and the prevailing market wage rate is w. Thus, hiring from the labor market generates an expected surplus S = π H SH + (1 − π H ) SL, of which S − w accumulates to the employer. However, the employer may be able to hire a known high type through his social network. If s is a high-type job candidate, and his type can be credibly communicated to the employer, then the surplus from hiring s versus hiring from the formal labor market is SH − S. Assuming that this surplus is divided by Nash bargaining, where the bargaining weight of the worker is α, the wage of s if hired is w H = w + α · (SH − S), and the excess profit of the firm relative to hiring from the labor market is (1 − α) · (SH − S). Can the network credibly communicate the worker’s type to the employer? To answer, assume that the type of worker s is only observed by himself and his direct friends, denoted s1 , . . . , sk. Although these friends can, in principle, provide recommendations, 23. Saloner (1985) and Simon and Warner (1992) also study informal recommendations in labor markets. These papers set aside trust considerations by assuming that recommenders and firms have the same objective.

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they face a moral hazard problem: a low-type worker s can bribe them to write good recommendations. Here bribes are interpreted broadly to include in-kind transfers, as well as being nice to the recommender. The amount candidate s is willing to spend on bribes is limited by the attractiveness of the job, α · (SH − S); if he or she offers more, the bribes would exceed the profit from getting the job. This reasoning suggests that the network can only communicate worker type in a credible way when the employer’s trust of recommenders, s1 , . . . , sk exceeds the highest bribe that the worker can pay, α · (SH − S). To formalize these ideas, we modify the basic model as follows. First, we assume that prior to sending recommendations, agents agree on an informal transfer arrangement that is to be activated if the worker turns out to be a low type. This arrangement represents the understanding that recommenders will be held responsible for bad recommendations. Second, we introduce the concept of side deals with bribes, where agent s might propose a new transfer arrangement, together with a set of bribes to be paid to his friends, s1 , . . . , sk, in exchange for their good recommendations.24 Finally, we introduce an auxiliary network, G∞ , where links between s and his friends, s1 , . . . , sk, have infinite capacity, st (c) denotes the trust flow between s and t in this network. and T PROPOSITION 3. In an equilibrium robust to side deals with bribes, low-type workers are never hired through the network. If st (c) ≥ α · (SH − S), there exists an equilibrium and only if T robust to side deals with bribes where a high-type worker s is hired. The result simply states that when network-based trust between the employer and recommenders exceeds the sensitivity of profits to worker type, as measured by the term α · (SH − S), the true type of the worker can be credibly communicated. Several implications about networks and labor markets follow. (1) Networkbased trust should be more important for high-skilled jobs, where the employer’s profits are more sensitive to worker type. Proposition 2 then predicts a trade-off between weak and strong ties: for low-skill jobs, where type matters less, weak connections are best because they maximize access; but for high-skilled jobs, recommendations through strong links embedded in a dense network are more useful. (2) Jobs obtained through the network should 24. The formal details of these modifications are presented in Appendix I.

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earn higher wages than jobs obtained in the market. Simon and Warner (1992) obtain the same prediction, but their mechanism is different: in their work, networks reduce uncertainty about the quality of the match, increasing the reservation wage; in contrast, in our model only high types are hired through the network. (3) Due to the increased importance of trust for high-quality jobs, the wage differential between network-based and market-based hires, w H − w = α · (SH − S), should be positively related to skill intensity. (4) When filling high-skill vacancies, employers should search more through their networks. These predictions are consistent with several empirical facts. The first prediction helps explain the mixed evidence about the strength of weak ties by showing that for many jobs strong ties should be more important; it also implies that the strength of weak ties should vary with the skill intensity of the job, a prediction that awaits empirical testing. Consistent with the second prediction, Granovetter (1974) reports that in his sample, “jobs offering the highest salary are much more prone to be found through contacts than others: whereas less than half of jobs yielding less than $10,000 per year were found by contacts, the figure is more than three-quarters for those paying more than $25,000.” This positive correlation between referrals and salary is also confirmed by Gorcoran, Datcher, and Duncan (1980) and Simon and Warner (1992). Regarding the intensity of network search, Brown (1967) finds that among college professors, personal networks are more frequently used in obtaining jobs of higher rank, smaller teaching loads, and higher salaries and at more prestigious colleges. For these attractive jobs, reducing asymmetric information is likely to be more important, and hence, employers have a stronger preference for searching through their networks. Our predictions would not emerge in a model where the network served purely as a source of information about job vacancies. In such an economy, the network does not reduce information asymmetries; hence the wage differential is zero and the importance of network-based recommendations does not vary with the type of the job. Our results thus suggest that a full analysis of networks in labor markets should incorporate both information transmission and trust in recommendations. Trust and Asymmetric Information. The social collateral model can also be used to study other situations involving asymmetric information. For example, a simple alteration of our job

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search framework shows that network-based recommendations can help identify whether a given borrower is intrinsically a trustworthy type.25 A similar logic applies for transactions of valuable assets such as houses, which involve a potential “lemons” problem: sellers with whom the buyer has a high trust flow are more likely to be honest about the quality of the good, to avoid future retribution through social sanctions.26 We conclude that the implications of social collateral in the presence of asymmetric information are similar to the basic model with moral hazard: higher trust flow can secure transactions where there is greater exposure to asymmetric information. V. MEASURING SOCIAL COLLATERAL IN PERU We now empirically evaluate the social collateral model using a unique data set from two low-income Peruvian shantytown communities, collected by Dean Karlan, Markus Mobius, and Tanya Rosenblat, further described in Karlan et al. (2008). Two key features of these data make them particularly useful for our purposes: (1) information on the social networks of individuals and (2) data on informal loans between friends, relatives, and acquaintances. V.A. Data Description In 2005, a survey was conducted in two communities located in the Northern Cone of Lima. The heads of households and spouses (if available) in 299 households were interviewed. The survey consisted of two components: a household survey and a social network survey. The household survey recorded a list of all members of the household and basic demographic characteristics, including sex, education, occupation, and income; summary statistics for these variables are reported in Table I. Average monthly household income in the two communities was 957 and 840 Peruvian new soles (S/.), respectively, which equals approximately 294 and 258 US$, using the exchange rate in 2005. The social network component of the survey asked the household head and spouse to list up to ten individuals in the community 25. Karlan (2005) documents evidence that there is variation in individuals’ trustworthiness, which is predictive of their financial behavior. 26. In line with this prediction, in the 1996 General Social Survey, 40% of home purchases and 44% of used car purchases involved a direct or indirect network connection between the buyer and seller or realtor (DiMaggio and Louch 1998).

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TRUST AND SOCIAL COLLATERAL TABLE I SUMMARY STATISTICS FOR TWO SHANTYTOWN COMMUNITIES IN PERU Demographic variables

Mean

Female 0.50 Age 35.84 Secondary ed. 0.71 Household inc.(S/.) 887.39 Business-owner 0.20

Standard dev. 0.50 14.37 0.21 1,215.74 0.40

Social network variables Number of contacts Share of “neighbors” Share of “friends” Share of “relatives” Avg. size of loan (S/.) Geographic dist.

Mean

Standard dev.

8.60 4.15 0.59 0.49 0.39 0.49 0.02 0.15 75.88 121.20 41.16 49.17

Note. The table shows summary statistics for adults (age at least 18). Income and loan amounts are reported in Peruvian new soles (S/.). The exchange rate at time of the survey was 3.25 S/. for one US$. Network variables are calculated for the nondirected network where a pair of individuals are classified as connected if one of them names the other as a friend. Geographic distance is reported in meters.

with whom the respondent spent the most time in an average week. We use this data to construct an undirected “OR”-network, where two agents have a link if one of them names the other. Agents have, on average, 8.6 links, and the average geographic distance between connected agents is 42 and 39 m in the two communities; this is considerably less than the geographic distance between two randomly selected addresses, which is 132 and 107 m, respectively.27 About 59% of relationships were classified by respondents as “vecino” (neighbor) and 39% as “amigo” or “compadre” (friend). The share of “relativos” was just 2%.28 Vecinos live slightly closer than amigos/compadres (35 versus 51 m). Over 90% of directly connected people met in the neighborhood for the first time. Importantly for our purposes, the social network survey also recorded, for each responder, the set of friends from whom he or she had borrowed money during the previous twelve months. There were 254 informal loans in the data set; 167 borrowers in 138 households reported having borrowed on average 76 S/. (about 23 US$) from 173 lenders during the past twelve months. Thus, informal borrowing is very common in these communities: 46% of all households have at least one household member who borrowed money in this manner. The mean age of both the borrower and the lender is 39 years and they live, on average, 36 m apart. 27. This is consistent with a body of work showing the importance of social distance in meeting friends, for example, Marmaros and Sacerdote (2006). 28. In the remainder of this section, we use the term “friend” for any network connection, whether vecino, amigo/compadre, or relativo.

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V.B. Empirical Framework Measuring Capacities and Trust Flow. To adapt our model of social collateral to this empirical setting, we need to develop a measure of link capacity. We use the amount of time spent together as a proxy for the strength of a connection, capturing the intuition that link values depend on investment in joint social activity. In the data, the distribution of time spent together is skewed: the average responder spends less than six minutes with the bottom 10% of his/her friends and more than three hours with the top 10%. To obtain a more homogeneous measure, we define normalized time for two connected agents u and v as the value, for the amount of time they spend together, of the empirical cumulative distribution function of time spent together in their community. With this definition, the empirical distribution of normalized time τ (u, v ) across all connected pairs is a discretized uniform distribution on the unit interval in each community. We assume that link capacities are created by an increasing production function g such that c(u, v) = g(τ (u, v)); that is, spending more time together results in stronger links. We compute the network flow between agents s and t by defining the circle of trust to be the subgraph that contains all links of s and t. This circle of trust allows a simple decomposition of the trust flow between s and t as g(min(τ (s, v), τ (v, t))), (6) T st (c) = g(τ (s, t)) + v∈Ns ∩Nt

where the first term represents the direct flow and the second term is the indirect flow. Here Ns is the set of direct friends of agent s. Discrete Choice Framework. A natural approach to estimating the social collateral model is to use observations on how much agents borrow, and to use the loan size as a lower bound for the trust flow. This approach runs into the difficulty that loan amounts are also affected by demand: a borrower might borrow less than the trust flow. To avoid explicitly modeling loan demand, we instead base our estimation on who the agent borrows from, exploiting the idea that people are more likely to borrow from friends who trust them. By conditioning on the borrower, this approach effectively controls for loan demand as a fixed effect. We formulate the borrower’s choice of lender as a discrete choice problem. Consider agent s, who is in need of a loan of size

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V , which he can borrow from potential lenders t1 , . . . , tk. We write the total utility that s enjoys when he borrows from a particular lender t as (7)

ut = u(V, T st (c) + εt ),

where u is increasing and εt represents either measurement error in the trust between s and t, or a supply shock. Appendix II provides micro foundations for this representation by assuming that if V exceeds the level of trust T st , the excess value must be secured using physical collateral that has some opportunity cost. Then, the borrower is more likely to turn to a lender who trusts him more, implying that (8)

preferred lender = arg max[T st (c) + εt ], t

because, conditional on the loan amount, (7) is maximized when trust is highest. Model Predictions. We use the above discrete choice specification to test three predictions of the social collateral model. (1) Agents are more likely to borrow from friends with whom they have a stronger trust flow. This prediction is a direct implication of Theorem 1. (2) The contribution of an indirect path of a given strength is equal to the contribution of a direct link with the same strength. This prediction is made because there are no costs to including intermediate agents within the circle of trust in the borrowing arrangement. In a setup where the circle of trust is endogenized, as in Section III.F, the contribution of indirect paths would be smaller, but still positive. (3) Each indirect path contributes to borrowing through its weakest link. In particular, in decomposition (6), for each indirect s → v → t path, if we have τ (s, v) < τ (v, t), then the contribution of the path to borrowing should only depend on τ (s, v). Some of these predictions are consistent with alternative explanations. Time spent together can be correlated with the strength of altruistic feelings between the two agents and the ease with which information travels between them. Common friends can further strenghten altruism and information transmission. Trust flow can therefore be a proxy for the lender’s altruism toward the borrower and the lender’s ability to learn about the profitability of the borrower’s project. There is no particular reason that in these alternative explanations the weakest link

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Excess propensity to borrow –0.1 0 0.1

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–2

0 1 –1 Excess trust flow (measured as time flow)

2

FIGURE VII Trust Flow and Borrowing This figure is a residual plot, controlling for borrower fixed effects, of the relationship between trust flow, measured as time flow, and borrowing, where time flow is the sum of direct and indirect normalized time spent together. The figure is constructed as follows. For each borrower we calculate mean trust flow with all his or her friends, and define excess trust flow as the deviation from this mean. We similarly construct excess borrowing as the deviation from the average probability of borrowing across all friends. We sort all borrower–lender pairs by excess trust flow, group them into sixteen equal-sized bins, and plot the excess probability of borrowing (vertical axis) against the average excess trust flow (horizontal axis) for each bin.

should determine the strength of altruistic feelings or the strength of information transmission.29 However, without better data, we cannot completely exclude these alternative explanations. V.C. Results Graphical Analysis. We begin with a graphical analysis of trust flow and borrowing to highlight the basic patterns in the data. Assume that the strength of a link is proportional to normalized time: c (u, v ) = c · τ (u, v ). Then trust flow T st can be written as c · τ st , where τ st measures the total (direct plus indirect) “time flow” between agents s and t, computed using equation (6). Figure VII depicts the relationship between trust flow and borrowing in our sample, conditioned on borrower-specific fixed effects. The construction of the figure is the following. We introduce 29. One concrete model of altruism is where the lender cares about the utility of the intermediary who cares about the utility of the borrower. This model predicts that a geometric average of the two link values determines borrowing, which contradicts the weakest link condition of prediction 3. Similarly, if networks matter purely because they transmit information, then the average and not the minimum of link values should determine borrowing.

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TRUST AND SOCIAL COLLATERAL TABLE II BORROWING AS A FUNCTION OF DIRECT AND INDIRECT FLOW Direct time Indirect time

Above average

Below average

Above average

21.0%

42.0%

Below average

14.5%

22.5%

Note. This table shows the role of indirect paths in borrowing. Direct and indirect trust flow are computed as direct and indirect normalized time flow for each borrower and lender pair (see the notes to Figure VI or the text for details.) The construction of the table is as follows. We compute mean direct and indirect flow for each borrower by averaging across his/her friends, and create two indicator variables for whether direct and indirect flow is above or below the average. The table shows how loans are distributed across the resulting four bins (direct flow below or above average × indirect flow below or above average).

an indicator variable Ist , which is one if we observe s borrowing from t. For each borrower s we calculate the mean time τ s he or she spends with her friends, and the share I s of friends he or she borrows from. We then define the borrower’s “excess time flow” with lender t as τ st − τ s , and his or her “excess borrowing” from t by Ist − I s . Figure VII is simply a plot of excess borrowing against excess time flow, where observations are averaged over intervals of excess time flow to smooth out all uncorrelated noise. The figure shows a strong positive relationship, confirming the basic prediction that agents should be more likely to borrow from friends who trust them. Figure VII does not distinguish between direct and indirect flows. To get a sense of the relative contribution of indirect paths, in Table II we group all friends of each borrower into four categories along two dimensions: whether the direct flow between borrower and friend is below or above the average direct flow, and whether the indirect flow between borrower and friend is below or above the average indirect flow. We then calculate the share of loans that fall into each of the resulting four categories. About 14.5 percent of loans involve borrower/lender pairs with both below-average direct flow and below-average indirect flow. Almost double as many loans involve borrower/lender pairs with either above-average direct or above-average indirect flow. About three times as many loans involve borrowers and lenders with both above-average direct and above-average indirect flow. Indirect paths appear to play an important role in creating social collateral for borrowing. Structural Estimation. To analyze the relationship between trust flow and borrowing in greater detail, we now estimate the

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discrete choice model (8). This allows us to measure the relative strength of different network links, as well as to formally test our predictions. We allow capacities to depend on the time spent together in a flexible way, by classifying every link as weak, medium, or strong, depending on whether the time spent together lies in the lowest, medium, or highest third of the time distribution for each of the two communities. Each direct and indirect path between borrower and lender then makes a weak, medium, or strong contribution to total flow, where the strength of these different link types is measured by unknown parameters cW , c M , and c S . Given our definition of the circle of trust, the trust flow T st (c) between s and t, as given by (6), is easily seen to be a linear function of c = (cW , c M , c S ). Assuming that the error term ε has the extreme value distribution, we can then estimate (8) as a conditional logit, (9)

Pr[lender is t] =

exp[(1/λ) · T st (c)] , su u∈Ns exp[(1/λ) · T (c)]

where λ > 0 measures the relative importance of the error term. Given the linearity of T st in c, the unobserved parameters λ and c cannot be separately identified, but we can use the estimates to back out capacity ratios like c S /c M . Table III reports our logit estimates. The first column contains our baseline specification; the coefficient estimates for total weak, medium, and strong flow correspond to cW /λ, c M /λ and c S /λ in the estimating equation. The effect of weak paths on borrowing is insignificant and small: gaining access to lenders through weak ties appears to be relatively less important for obtaining loans. Both medium and strong paths have a highly significant positive effect on borrowing, and the effect of strong paths is significantly greater. One additional medium path to a lender increases the probability of borrowing by a factor of 1.44, whereas an additional strong path increases the probability by a factor of 2.7. The ratio of the point estimates implies that the capacity of strong links is about three times as high as that of medium links: c S /c M ≈ 2.7. These results support prediction 1, that trust flow should be positively related to borrowing, and highlight the importance of strong ties. Is the contribution of an indirect path different from that of a direct path? To compare indirect and direct paths, in column (2) we add the number of indirect medium and strong paths as separate controls in the regression. According to our second prediction,

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TRUST AND SOCIAL COLLATERAL TABLE III TRUST FLOW AND CHOICE OF LENDERS CONDITIONAL LOGIT ESTIMATES

Total weak flow (cW /λ) Total medium flow (c M /λ) Total strong flow (c S /λ)

(1)

(2)

(3)

(4)

0.16 (0.143) 0.365 (0.155)∗ 0.991 (0.163)∗∗

0.151 (0.142) 0.546 (0.266)∗ 1.317 (0.283)∗∗ omitted −.190 (0.319) −.526 (0.363)

0.142 (0.164) 0.341 (0.19) 0.988 (0.165)∗∗

0.147 (0.164) 0.543 (0.267)∗ 1.311 (0.284)∗∗ omitted −.226 (0.379) −.516 (0.368) 0.018 (0.315) 0.06 (0.34) −.006 (0.003)∗ 988

Indirect weak flow Indirect medium flow Indirect strong flow Weak–not weak flow Medium–strong flow Geographic distance Obs.

−.006 (0.003)∗ 988

−.006 (0.003)∗ 988

0.073 (0.313) 0.069 (0.27) −.006 (0.003)∗ 988

Note. Each link is classified as weak, medium, or strong depending on whether the time spent together lies in the lowest third, medium third, or highest third of the time distribution. Weak, medium, and strong total flow are defined by noting that each direct and indirect path between borrower and lender makes either a weak, medium, or strong contribution to total flow. For indirect medium and strong flow we only count indirect paths. Weak–not weak flow counts paths where exactly one link is weak; medium–strong flow counts paths where one link is medium and one link is strong. We do not include indirect weak flow in columns (2) and (4) because we cannot separately identify total and indirect weak flow in our conditional logit estimation, as every potential lender has at least a weak link to the borrower. ∗ 5% significance level. ∗∗ 1% significance level.

the coefficients of these variables should be zero. We find that the estimated coefficients on indirect flow are negative, but not statistically significant, and smaller than the corresponding coefficients on total flow. These results show that both direct and indirect paths have a substantial positive effect on borrowing, confirming the basic intuition that dense networks are better in creating social collateral. The negative estimates of indirect flows, although insignificant, suggest that the effect of indirect paths is slightly smaller, which can be explained in our model by endogenizing the circle of trust as in Section III.F. Combined with the results about strong ties, these estimates suggest that dense networks and bonding social capital are important for obtaining loans in these communities. We now test the prediction about the role of the weakest link in column (3), where we include two new explanatory variables

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in the regression. “Weak-not weak flow” counts the number of indirect paths where one link is weak and the other is medium or strong, whereas “medium-strong flow” counts the number of paths where one link is medium and the other is strong. If prediction 3 is false, then these paths should have a positive effect on borrowing beyond what is predicted by the social collateral “weakest link” theory. The estimated coefficients on these variables are insignificant and small, providing strong evidence for the role of the weakest link in determining social collateral. These results are replicated in column (4), which includes the controls for indirect flows. Our findings about the role of indirect paths and the weakest link property help distinguish our model from other explanations for borrowing, such as altruism and information transmission. One caveat with our econometric analysis is that if time spent together increases due to borrowing, reverse causality confounds the interpretation of the estimates. Thus, the evidence supports, albeit not exclusively, the social collateral model; moreover, strong ties and network closure, that is, bonding social capital, appear to be particularly important for borrowing. Importantly, the theoretical framework provides clear predictions that can be tested in further settings, with perhaps more control over key empirical identification issues. VI. CONCLUSIONS This paper has built a model where agents use their social connections as collateral to secure informal loans. This model naturally leads to a definition of network-based trust, which we then use in applications related to network structure and welfare, trust in job search, and the measurement of social capital. We conclude by sketching three other applications of the social collateral model. VI.A. Network Statistics When informal arrangements are restricted by the circle of trust to connections within a given social distance, our model generates a family of trust measures. Our working paper, Mobius and Szeidl (2007), shows that when all links have equal capacity, these measures are functions of several commonly used network statistics, including (1) number of friends; (2) the clustering coefficient, which is a measure of local network density; (3) the number of common friends of two agents; and (4) the number of transitive triples,

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another measure of network density.30 These results provide social collateral-based foundations for common network statistics. VI.B. Risk Sharing Development economists often emphasize the importance of informal insurance in developing countries. Ambrus, Mobius, and Szeidl (2008) use the social collateral model to explore risksharing in networks. They find that good risk sharing requires networks to be expansive: larger sets of agents should have more connections with the rest of the community. Networks shaped by geographic proximity have this property, because agents tend to have friends at a close distance in multiple directions, helping to explain the observed good risk sharing in village environments. They also find that network-based insurance is local: socially closer agents insure each other more. VI.C. Dynamics of Trust and Panics In the basic social collateral model, link capacities are exogenous. Mobius and Szeidl (2008) show that link values can be endogenized with multiple rounds of exchange. The strength of a relationship is, then, the sum of its direct value, as in the basic model, plus the indirect value, which derives from the ability to conduct transactions through the link in the future. In this framework, fluctuations can be amplified through a network multiplier similar to the social multiplier of Glaeser, Sacerdote, and Scheinkman (2003), because trust withdrawal that constrains exchange locally can lead to further trust withdrawals that ripple through the network. New technologies that limit future social interaction, such as television, can substantially reduce trust and social capital through this mechanism.31 APPENDIX I: PROOFS DEFINITION 6. A weak flow with origin s is a function g : W × W → R with the following properties: (i) Skew symmetry: g(u, v) = −g(v, u). (ii) Capacity constraint: g(u, v) ≤ c(u, v). (iii) Weak flow conservation: w g(u, w) ≤ 0 unless u = s. 30. These measures are used, for example, in Wasserman and Faust (1994), Watts and Strogatz (1998), Glaeser et al. (2000), and Jackson (2006). 31. In related work, Kranton (1996) and Spagnolo (1999) study the interaction between social and business activities.

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A weak flow of origin s can be thought of as taking a certain amount from node s and carrying it to various other nodes in the network. By weak flow conservation, any node other than s receives a nonnegative amount. LEMMA 1. We can decompose any weak flow g as fu, g= u∈V

where for each u, fu is an s → u flow, fu(v, w) = 0 that is, w for all v = u, v = s, and moreover w fu(u, w) = w g(u, w), that is, fu delivers the same amount to u that g does. Proof. Consider vertex u such that w g(u, w) < 0. By weak flow conservation, the amount of the flow that is left at u must be coming from s. Hence, there must be a flow fu ≤ g carrying this amount from s. With fu defined in such a way, repeat the same procedure for the weak flow g − fu with some other vertex u . After fu is defined for all vertices u, the remainder f satisfies flow conservation everywhere and can be added to any of the flows. Implicit summation notation: For a weak flow g and two vertex sets U ⊆ W and V ⊆ W, we use the notation that f (u, v). f (U, V ) = u∈U , v∈V

Proof of Theorem 1. Sufficiency. We begin by showing that when (4) holds, a side deal–proof equilibrium exists. By assumption, there exists an s → t flow with value V . For all u and v, let h (u, v ) equal the value assigned by this flow to the (u, v ) link. Now consider the strategy profile where (1) the borrowing arrangement h is proposed and accepted, (2) the borrower returns the asset, and (3) all transfers are paid if the borrower fails to return the asset. This strategy is clearly an equilibrium. To verify that it is side deal–proof, consider any side deal, and let S denote the set of agents involved. For s to be strictly better off, it must be that he prefers not returning the asset in the side deal. Now consider the ( S, T ) cut. By definition, the amount that flows through this cut under the original arrangement is V ; but then the same amount must flow through the cut in the side deal, as well. This means that s must transfer at least V in the side deal; but then he cannot be better off. More generally, this argument shows that any transfer arrangement that satisfies flow conservation is side deal–proof.

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Necessity. We now show that when (4) is violated, no side deal–proof equilibrium exists. We proceed by assuming to the contrary that a pure strategy side deal–proof equilibrium implements borrowing even though (4) fails. First note that on the equilibrium path, the borrower must weakly prefer not to default. To see why, suppose that the borrower chooses to default on the equilibrium path. Because the lender and all intermediate agents must at least break even, this implies that the borrower has to make a transfer payment of at least V . But then the borrower must weakly prefer not to default, because returning the asset directly has a cost of V . This also implies that all intermediate agents must have a zero payoff. By assumption, there exists an ( S, T ) cut with value c ( S, T ) < V . We now construct a side deal where all intermediate agents in S continue to get zero, but the payoff of s strictly increases. The idea is easiest to understand in an equilibrium where promises are kept, that is, when all transfers satisfy the capacity constraint h (u, v ) ≤ c (u, v ). Then, we simply construct an arrangement that satisfies flow conservation inside S and delivers to the “boundary” of S the exact amount that was promised to be carried over to T under h. More generally, when the capacity constraints fail over some links, the deviation in the side deal can result in some agents in S losing friendships with agents outside S. To compensate for this loss, the side deal must deliver to the “boundary” of S an additional amount that equals the lost friendship value. Formally, let g be a maximal s → t flow and consider the restriction of g to S. Thisis a weak flow, and by the lemma it can be decomposed as g = u∈S gu, where each gu is an s → u flow. Now for each u ∈ S, let g (u, T ) and h (u, T ) denote the amounts leaving S through u under g and h. Moreover, for each u ∈ S, let z (u, T ) denote the total friendship value lost to u in the subgame where the borrower defaults, as a consequence of unkept transfer promises. Because g is a maximum flow and ( S, T ) is a minimal cut, it follows that g (u, T ) ≥ h (u, T ) + z (u, T ). This is because any link between u and T is either represented in h (u, T ), if u pays the transfer, or z (u, T ), if u does not pay and loses the friendship. This inequality implies that, whenever h (u, T ) + z (u, T ) > 0, we also have g (u, T ) > 0. As a result, we can define h =

h(u, T ) + z (u, T ) u∈S

g (u, T )

· gu.

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Note that h is a weak flow in S and delivers exactly h (u, T ) + z (u, T ) to all agents in S. Thus h satisfies flow conservation within S and delivers to the “boundary” of S the sum of two terms: h(u, T ), which is the precise amount to be carried over to T under h, and z (u, T ), which is the loss of friendship u suffers due to not making other promised transfers. We claim that h is a profitable side deal. First, h satisfies all capacity constraints by construction. Second, all agents in S break even under h , as they did in the original equilibrium. Third, the total value delivered by h is at most c ( S, T ) < V , which means that s pays less than V under h , whereas he pays exactly V in the original equilibrium. We have constructed a side deal in which the borrower is better off and all other players are best-responding; hence, the original equilibrium was not side deal–proof. Proof for Section III.F. Transfer Constraints. In this analysis, we use a more stringent equilibrium selection criterion: We look for equilibria where (i) all promised transfers are paid; and (ii) there are no profitable side deals. In the earlier analysis, there was no need to impose (i), because the characterization results showed that any level of borrowing that can be implemented can also be implemented using equilibria where all transfers are paid. With transfer constraints, requiring that all promises be credible has additional bite, because promises that are not credible can generate large punishment in the form of loss of friendship to agents who have small ku. We find it plausible that such agents will not make promises that they know they cannot keep, but instead of providing formal micro foundations for this, we simply restrict ourselves to equilibria that are “credible,” in the sense that all promises are kept. Consider the directed network G defined in the text and let the maximum s1 → t1 flow in G be denoted by T s1 t1 (c). PROPOSITION 4. There exists a side deal–proof equilibrium with credible promises that implements borrowing if and only if (10)

V ≤ T s1 t1 (c).

Proof. Sufficiency. If (10) holds, then take a flow with value V , and let the flow values between different agents define the transfer arrangement in our candidate equilibrium. Note that by construction, this borrowing arrangement satisfies the borrowing

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constraints of all agents u. Moreover, the promised transfers in this arrangement will be kept because they all satisfy the capacity constraint. It remains to be shown that there are no profitable side deals; this follows from the same argument used in the proof of Theorem 1. Necessity. Suppose that (10) fails, and consider an equilibrium where promised transfers are paid and borrowing is implemented. We now show that this equilibrium admits a side deal. Our argument is similar to the proof of Theorem 1, in that we build the side deal using a minimum cut on the network G . However, the present setup has one additional difficulty: we need to make sure that the side deal emerging from the minimum cut does not separate agents from their duplicates. Let (S , T ) be a minimum cut. If for some u = s we have u2 ∈

S , then u1 ∈ S also holds, because u2 has only one incoming link, which originates in u1 . Let S be the union of s and the collection of agents u such that u1 ∈ S . We need to show that agents in S, as a group, do not have the right incentive to return the asset. To / S . It follows see why, consider first an agent u ∈ S such that u2 ∈

that the (S , T ) cut separated u1 from u2 , by cutting the u1 → u2 link. But in this equilibrium, promises are kept, and, hence, the total obligation of u to agents outside S can be at most ku, which is exactly the value of the cut link. Next consider an agent u ∈ S such that u2 ∈ S . For this agent, the total obligations to others outside S are bounded from above by the total value of the links originating in u2 that are cut. Summing over all u ∈ S, we conclude that the total obligations of all agents in S do not exceed the value of the (S , T ) cut, and, hence, are strictly smaller than V . Thus, S, as a group, has an incentive to default. The actual side deal can now be constructed in the same way as in the proof of Theorem 1. Proof of Proposition 1. Consider two capacities c1 ≤ c2 . Any flow between s and t that is feasible under c1 is also feasible under c2 ; hence the maximum flow cannot be lower under c2 than under c1 . Proof of Proposition 2. We denote the share of total paths to agents with whom agent s has precisely j paths with qs ( j). If we treat this function as a probability density function over the nonnegative integers, then an increase in closure is equivalent to a first-order stochastic dominance shift.

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The expected payoff of s, conditional on his being the borrower, can be written as 1 qs ( j) ( j) 1 qs ( j) ( j) = , N j j N j j which can be viewed as the expected value of the function ( j)/j under the probability density qs ( j). In a high-value exchange enω(V ) is increasing; vironment, (V ) is convex because (V ) = this, combined with the fact that (0) = 0, implies that (V )/V is nondecreasing. In this case, a first-order stochastic dominance increase in the probability density qs ( j ) increases the expected payoff by definition. An analogous argument shows that in a lowvalue exchange environment, the same increase in the sense of first-order stochastic dominance reduces the expected payoff of s. Proof of Proposition 3. Preliminaries. The timeline of the model with job search is the following. In stage 1, a set of agents, including s1 , . . . , sk and t, agree on a transfer arrangement that specifies transfers h (u, v ) to be made in the event that s1 , . . . , sk send recommendations, and s is hired and then turns out to be a low type. In stage 2, agents s1 , . . . , sk choose whether to recommend s to the employer t. In stage 3, t decides whether to hire s or not; profits are earned, and the type of s is publicly revealed. In stage 4, if needed, the transfer arrangement is executed; and in stage 5, agents consume the values of remaining links. We consider a class of coalitional deviations that we call side deals with bribes. A side deal with bribes is a new transfer arrangement proposed by s to s1 , . . . , sk and potentially some other agents at the beginning of stage 2, together with a set of bribes b1 , . . . , bk that s pays to s1 , . . . , sk in exchange for their recommendation. For simplicity, we assume that bribes are spot transactions: each agent s j sends the recommendation at the same time that he receives the bribe. We assume that when the surpluses from hiring through the network and in the market are the same, t always hires in the market. Proof. Fix a pure strategy equilibrium robust to side deals with bribes. If a low type is hired in this equilibrium, then the expected surplus from the employment relationship is S, which is the same as hiring in the formal market, and hence t never hires through the network. It follows that in equilibrium only high types

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are hired in the network. Now suppose that in this equilibrium st (c) < α · (SH − S) and the high-type worker is hired. Then the T low type can propose a profitable side deal with bribes. As in the proof of the main theorem, this side deal includes all agents in a minimum cut separating s from t in G∞ and transmits an amount equal to the maximum flow to agents at the boundary of the cut. The bribes in the side deal are specified to equal the amounts that flow through agents s1 , . . . , sk in this flow. It follows that all agents weakly prefer accepting the side deal: intermediate agents at least break even by flow conservation, and the friends of s all break even because the bribes exactly compensate them for the payments to be made in the side deal. This contradiction shows that in any side deal–proof equilibrium where the high type is hired, we must st (c) ≤ α · (SH − S). Finally, if this inequality holds, then have T the transfer arrangement specified by the maximum flow in G∞ is easily seen to be an equilibrium robust to side deals with bribes. APPENDIX II: MICRO FOUNDATIONS FOR SOCIAL SANCTIONS In this Appendix, we develop a model where punishment at the level of the link arises endogenously. There are three key changes relative to the model presented in the main text: (1) with probability p > 0, the asset disappears, for example, is stolen by a third party, after the borrower uses it. (2) Each link “goes bad” with a small probability ε during the model, capturing the idea that friendships can disappear for exogenous reasons. (3) The utility of friendship is modeled using a “friendship game” where agents can choose to interact or stay away from each other. The payoffs of this friendship game depend on the capacity of the link and on whether the link has gone bad. A. Model Setup This model consists of the following six stages: Stage 1: Realization of Needs. Identical to stage 1 in Section III. Stage 2: Borrowing Arrangement. In this model, there is uncertainty about whether the asset disappears after being used. As a result, the arrangement is now a set of state-contingent payments, where the publicly observable state of the world i is either i = 0, if the asset is returned, or i = 1, if the asset is reported stolen. A borrowing agreement consists of two parts. (1) A contract specifying payments yi to be made by the borrower to the

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lender in the two states (i = 0 or 1). This contract can be thought of as a traditional incentive contract to solve the moral hazard problem in lending. If there were a perfect court system in the economy, then this contract would be sufficient to achieve efficient lending. (2) A transfer arrangement specifying payments hi (u, v ) to be made between agents in the social network if the borrower fails to make the payment yi . Here hi (u, v ) denotes a payment to be made by u to v in state i.32 Stage 3: Repayment. If an arrangement was reached in stage 2, the asset is borrowed and s earns an income of ω (V ), where ω(.) is a differentiable, nondecreasing function. Following the use of the asset, with probability p it is stolen. We assume that ω (V ) > pV for all V in the support of F, which guarantees that lending the asset is the socially efficient allocation. Even if the asset is not stolen, the borrower may choose to pretend that it is stolen and sell it at the liquidation value of φ · V , where φ < 1. The borrower then chooses whether to make the payment yi specified in the contract. Stage 4: Bad Links. At this stage, any link in the network may go bad with some small probability. We think of a bad link as the realization by a player that he no longer requires the business or friendship services of his friend. As we describe below, cooperation over bad links in the friendship game is no longer beneficial. Therefore, agents who learn that a link has gone bad will find it optimal not to make a promised transfer along the link. From a technical perspective, bad links are a tool to generate cooperation without repeated play, just like the “Machiavellian types” in Dixit (2003) (see also Benoit and Krishna [1985]). In an equilibrium where promised transfers are expected to be paid, failure by u to make a payment will be interpreted by v as evidence that the link has gone bad. In this case, v will defect in the friendship phase, which reduces the payoff of the deviator u by c (u, v ). To formalize bad links, assume that for every link of every agent, with a small probability ε > 0 independent across agents and links, the player learns that his link has gone bad at this stage. Thus, for any link (u, v ), the probability that the link has not gone bad is (1 − ε)2 ; and for any link (u, v ) where u does not learn that the link has gone bad, u still believes, correctly, that with probability ε the link has gone bad. 32. The circle of trust may restrict the links over which arrangements may be proposed. This case can be treated in the proof by assuming that G denotes the subgraph of permissible links.

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Stage 5: Transfer Payments. If the borrower chose to make payment yi in stage 3, then this stage of the game is skipped, and play moves on to the friendship phase. If the borrower did not make payment yi , then at this stage agents in the social network choose whether to make the prescribed transfers hi (u, v ). Each agent has a binary choice: either he makes the promised payment in full or he pays nothing. Stage 6: Friendship Game. Each link between two agents u and v has a friendship game with an associated value c(u, v). As long as the link is good, the friendship game is a two-player coordination game with two actions, with payoffs C D

C c(u, v) c(u, v) c(u, v)/2 0

D 0 c(u, v)/2 −1 −1

This game has a unique equilibrium (C,C) with payoff c (u, v ) to both parties, which represents the benefit from friendly interactions. A party only derives positive benefits if his or her friend chooses to cooperate; and benefits are highest when there is mutual cooperation. If a link has gone bad, cooperation is no longer beneficial, and the payoffs of the friendship game change: C D

C

D

−1 −1 0 0

0 0 0 0

Here, mutual cooperation leads to the low payoff of −1, capturing the idea that parties who are no longer friends might find it unpleasant to interact. If either party defects, the payoff of both parties is set to zero. The payoffs in the friendship game imply that if a player knows that a link has gone bad with probability 1, a best response is to play D. B. Model Analysis Because there is uncertainty in this model, we need to extend the concept of side deals to Bayesian games. DEFINITION 7. Consider a pure strategy profile σ and a set of beliefs μ. A side deal with respect to (σ, μ) is a set of agents S, a transfer arrangement hi (u, v ) for all u, v ∈ S, and a set of σu, continuation strategies and beliefs {( μu) | u ∈ S} proposed by s to agents at the end of stage 2, such that

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σu, (i) Uu ( σ S−u, σ−S | μu) ≥ Uu σu , σ S−u, σ−S | μu for all σu and all u ∈ S, (ii) The beliefs μ satisfy Bayes’ rule whenever possible if play is determined by ( σ S , σ−S ), (iii) Uu ( σ S , σ−S | μu) ≥ Uu (σ S , σ−S | μ) for all u ∈ S, σ S , σ−S | μu) > Us (σ S , σ−S | μ). (iv) Us ( The only conceptually new condition is (ii), which is clearly needed in a Bayesian environment. Motivated by this definition, our equilibrium concept will be a side deal–proof perfect Bayesian equilibrium. THEOREM 2. There exists a side deal–proof perfect Bayesian equilibrium that implements borrowing between s and t if and only if the asset value V satisfies (11)

V ≤ T st (c) ·

(1 − ε)2 . φ + p(1 − φ)

Proof. We begin by analyzing the optimal incentive contract in the absence of enforcement constraints. Suppose that s makes payments xi (i = 0 or i = 1) in the two states of the world. What values of xi guarantee that s chooses to return the asset and t breaks even? To prevent s from stealing, the excess payment if the asset is reported stolen must exceed the liquidation value φV : x1 − x0 ≥ φV.

(12)

For the lender to break even, he has to receive at least pV in expectation: (13)

px1 + (1 − p) x0 ≥ pV.

The minimum transfers that satisfy (12) and (13) are (14)

x0 = p(1 − φ)V

and

x1 = [φ + p(1 − φ)]V.

When the enforcement constraints are brought back, it is intuitive that borrowing can be implemented in the network as long as max [x0 , x1 ] does not exceed the maximum flow between s and t: in that case, the lender can just transfer xi to the borrower along the network. Because x1 > x0 , this requires that x1 not exceed the maximum flow, or equivalently V ≤ c (s, t) ·

2 (1 − ε) , φ + p(1 − φ)

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which is indeed the condition in the theorem. We now turn to the proof. Sufficiency. We begin by showing that when (11) holds, a side deal–proof equilibrium exists. Let xi be defined by (14) and let yi = xi . By assumption, there exists a flow with respect to the capacity c that carries x1 / (1 − ε)2 from s to t. For all u and v, define h1 (u, v ) to be 1 − ε times the value assigned by this flow to the (u, v ) link. Similarly, let h0 (u, v ) be equal to 1 − ε times a flow that carries x0 / (1 − ε)2 from s to t. Now consider the strategy profile in which (1) the transfer arrangement (xi , hi ) is proposed and accepted, (2) the asset is borrowed and returned unless stolen, (3) every agent u pays every promised transfer hi (u, v ) if necessary, unless he learns that his link with v has gone bad, and (4) all agents play C in the friendship game unless they learn that the link has gone bad, in which case they play D. This strategy profile σ generates beliefs μ, and (σ, μ) constitute a perfect Bayesian equilibrium. To see why, note that conditional on others making the transfer payments, it is optimal for s to make the payments yi and not to steal the asset. Also, because hi (u, v ) ≤ (1 − ε) c (u, v ), all agents find it optimal to make the transfer payments given beliefs. Finally, because on-path play never gets to the transfers, all intermediate agents are indifferent between accepting the deal and rejecting it. In fact, even if the transfers were used in one or both states on path, intermediate agents would still break even, because hi are defined using flows. We also need to verify that the equilibrium proposed here is side deal–proof. Consider any side deal, and let S denote the set of agents involved. Suppose that after the side deal, the borrower reports that the asset is stolen with probability p ≥ p. Let T be the complement of S in W, and consider the ( S, T ) cut. By definition, the expected amount that flows through the ( S, T ) cut in state i if yi is not paid equals xi . If the borrower never chooses to pay yi in the side deal, he will have to make sure that at least p x1 + (1 − p ) x0 gets to the cut in expectation. Because all intermediate agents must break even in expectation, this implies that s’s expected payments must be p x1 + (1 − p ) x0 or more. Thus the side deal comes with a cost increase of ( p − p) [x1 − x0 ]. The increase in expected cost is easily seen to be the same if the borrower chooses to pay yi in one or both states. The expected benefit of the side deal is ( p − p) φV . By equation (12) the expected benefit does not exceed the expected cost; the side deal is not profitable to s, which is a contradiction. Hence the original arrangement was side deal proof.

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Necessity. We now show that when (11) is violated, no side deal–proof equilibrium exists. We proceed by assuming to the contrary that a pure strategy side deal–proof perfect Bayesian equilibrium implements borrowing even though (11) fails. For simplicity, we assume that the equilibrium proposed transfers hi (u, v ) are expected to be paid by all agents u in stage 5 if the borrower chooses not to pay yi directly; that is, we only focus on equilibria where promises are kept. This condition is not necessary to obtain the result, but simplifies the proof somewhat. If this condition holds, then hi (u, v ) ≤ (1 − ε) c (u, v ) holds for all transfers proposed in equilibrium, because the amount by which u can expect to benefit from his friendship with v is at most (1 − ε) c (u, v ). Let χi = 1 if in state i on the equilibrium path, s chooses not to pay yi , and let χi = 0 otherwise. Case I. χ0 = χ1 = 1. In this case, on the equilibrium path, yi are never paid, and instead the transfer arrangements are always used. Define the expected transfer h = ph1 + (1 − p)h0 . By the individual rationality of intermediate agents, h satisfies weak flow conservation, and therefore by the lemma can be decomposed as h=

fu + h ,

u∈V, u=t

where fu is s → u flow and h = ft . In words, the fu flows deliver the expected profits to the intermediate agents, whereas h is an s→ t flow that delivers the expected payoff to the lender. Denote u=t fu = f ; then f is a weak flow delivering the payments to all intermediate agents. Our proof strategy will be the following. First, we take out the profits of all intermediate agents from the capacity c and the transfer h, essentially creating a “reduced” problem where intermediate agents are expected to break even. Then we construct a side deal for this simpler case using the maximum flow–minimum cut theorem, and finally, transform this into a side deal of the original setup. Let c (u, v ) = c (u, v ) − f (u, v ) / (1 − ε) be a capacity on G. Note that any flow g under c can be transformed into a flow g = g + f/ (1 − ε) that satisfies the capacity constraints c. Consider the functions hi = hi − f . It is easy to verify that hi / (1 − ε) satisfy the capacity constraints with respect to c and that h = ph 1 + (1 − p) h 0 . Let ( S, T ) be a minimal cut of the directed flow network with capacity c . By the maximum flow–minimum cut

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theorem, there exists a maximum flow g in the network that uses the full capacity of this cut. By assumption, the value of the cut un2 der h 1 satisfies h 1 (S, T )/ (1 − ε) ≤ g(S, T ) < x1 / (1 − ε) , which implies that (1 − ε) h1 (S, T ) − h0 (S, T ) < φV because (1 − ε) |h| ≥ pV . In words, the value flowing through the minimal cut in the two states does not provide sufficient incentives not to steal the asset. We now construct a side deal for the reduced problem. The idea is to construct a transfer arrangement that satisfies flow conservation inside S and delivers to the “boundary” of S the exact amount that was promised to be carried over to T under h . With such an arrangement, all agents in S will break even in each state, and thus the incentives that applied to S as a group will apply directly to agent s. Because S as a group did not have the right incentives, with the side deal s will not have the right incentives either. Formally, using the implicit summation notation, for each u ∈ S, g(u, T ), h 1 (u, T ), and h 0 (u, T ), let denote the amounts leaving S through u via the maximum flow g, h 1 , and h 0 . Clearly, (1 − ε)g(u, T ) ≥ h 1 (u, T ) and (1 − ε)g(u, T ) ≥ h 0 (u, T ). Now consider the restriction of g to the set S. This isa weak flow, and by as g = u∈S gu. Define the lemma it can be decomposed h

1 = u∈S (h 1 (u, T )/g(u, T )) · gu and h

0 = u∈S (h 0 (u, T )/g(u, T )) · gu. Then h

1 and h

0 are both weak flows in S, they satisfy hi

≤ (1 − ε)c , and they deliver exactly h 1 (u) and h 0 (u) to all u ∈ S. Thus hi

satisfies flow conservation within S, and delivers to the “boundary” of S the amount promised to be carried over to T under h 1 , as desired. The total value delivered by hi

is the value of the cut links under hi ; hence the amount that leaves s in the two states under h

satisfies (1 − ε)[|h

1 | − |h

0 |] < x1 − x0 , that is, is insufficient to provide incentives not to steal the asset. Now go back to the original network, and consider a side deal with all agents in the set S, where these agents are promised a transfer arrangement f + hi

. This is just adding back the profits of all agents to the side deal of the reduced problem. With this definition, the new side deal satisfies the capacity constraints f + hi

≤ (1 − ε)c because hi

≤ (1 − ε)c = (1 − ε)c − f . Second, all agents in S will be indifferent, because they get the same expected profits delivered by f (note that h

is a flow in both states and thus nets to zero state by state). The agents who have links that are in the cut are indifferent because h

is defined so that its inflow equals the required outflow for these agents. Third, the side deal

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does not have enough incentives for s not to steal the asset, because |h

1 | − |h

0 | < φV /(1 − ε). Moreover, if the original deal was beneficial for s, then so is the new deal. This is because the cost of the original deal was | f | + |h |. The cost of the new deal if the borrower follows the honest asset-return policy is | f | + |h

|. But both h and h

are flows, and they are equal on the (S, T ) cut; hence they have equal values. Therefore, by following an honest policy, the borrower will have a cost equal to what he had to pay in the original deal. However, because the incentive compatibility constraint is not satisfied, the borrower is strictly better off always stealing the asset in the side deal. This argument shows that there exists a side deal in which the borrower is strictly better off, and all other players are best-responding; hence the original equilibrium was not side deal proof. It remains to consider the cases where either χ0 or χ1 is equal to zero. In these cases, define the expected transfer payments as h = pχ1 h1 + (1 − p)χ0 h0 . As above, h is a weak flow and thus f , the weak flow delivering the expected profits to all intermediate agents can be defined. Similarly, one can define c and hi , and letting ( S, T ) be the minimal cut of c , h 1 (S, T )/ (1 − ε) < x1 / (1 − ε)2 must hold. Case II. χ0 = 1 and χ1 = 0. Then h = (1 − p)h0 and the decomposition h = f + h yields h0 = f/(1 − p) + h /(1 − p), so that h 0 = h0 − f = f · p/(1 − p) + h /(1 − p) is a weak flow, because it is a sum of two weak flows. It follows that |h0 | = | f | + |h 0 | ≥ | f | + |h 0 (S, T )|. Therefore | f | + |h

0 | ≤ |h0 |, because h

0 is a flow and h

0 = h 0 on the (S, T ) cut. Moreover, incentive compatibility requires y1 − (1 − ε)|h0 | ≥ φV , whereas the break-even constraint of the lender means that py1 + (1 − p)(1 − ε)[|h0 | − | f |/(1 − p)] ≥ pV . Combining these inequalities gives y1 ≥ x1 + (1 − ε)| f |. Now consider the side deal hi

+ f defined as above. Because |h

0 + f | ≤ |h0 | ≤ y0 /(1 − ε) and |h

1 + f | < x1 /(1 − ε) + | f | ≤ y1 /(1 − ε), the borrower will strictly prefer this arrangement to the previous one. Because all intermediate agents get net profits delivered by f in both states in the side deal, they are indifferent. Thus the proposed arrangement is indeed a side deal. Case III. χ0 = 0 and χ1 = 1. Here h1 is a weak flow, which must deliver less than x1 /(1 − ε) to t, because by assumption x1 /(1 − ε) is more than the maximum flow. Thus incentive compatibility fails with the original agreement; even without any side deal, the lender is better off not returning the asset.

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Case IV. χ0 = 0 and χ1 = 0. Here a valid side deal is to pay y0 in state zero and propose the transfer arrangement h

1 for state 1. All intermediate agents are indifferent because they were getting zero in the original arrangement, and because h

1 < x1 / (1 − ε) ≤ y1 / (1 − ε), the expected payment in the side deal is strictly lower than in the original deal. In the proof so far, we have only considered the case where the borrower does not steal the asset on the equilibrium path. If the equilibrium is such that the borrower always steals, then min (1 − ε) |h1 | , y1 ≥ V must hold. If χ1 = 1, then h1 /(1 − ε) is a weak flow with respect to capacity c that must transfer at least V /(1 − ε)2 to t. This leads to a condition on the maximum s → t flow that is stronger than (11). If χ1 = 0, then a valid side deal is to propose the transfer arrangement h

1 for both states. As above, all intermediate agents are indifferent, and h

1 < x1 / (1 − ε) ≤ y1 / (1 − ε) holds, which proves that the expected payment in the side deal is strictly lower than in the original deal. APPENDIX III: EMPIRICAL MODEL The utility function (7) that forms the basis of the discretechoice model can be micro founded in the following way. Suppose that borrower s needs a loan of value V and needs to decide which of his friends to borrow from. Each potential lender t has an opportunity cost k (V ) + ν S of providing the loan, where ν S is a supply shock unobserved to the borrower, which is independent across lenders. If the borrower chooses lender t, he is expected to repay both the value and the lender’s full opportunity cost.33 Beyond the cost of a loan, the choice of lender is also influenced by the level of trust. We assume that the true level of trust between s and t is α + T st (c) + ε M , where α + ε M reflects both measurement error in network-based trust and other sources of trust. When the expected repayment k (V ) + ν S exceeds the level of social trust between borrower and lender, the excess amount must be secured using physical collateral. We assume that providing such physical collateral (e.g., a radio or a bicycle) has an opportunity cost that equals γ times the value of collateral. With these assumptions, 33. In many societies there is a social convention that agents are only to repay the nominal amount borrowed. However, there is often an understanding that lenders should be further compensated using in-kind transfers and gifts. Here we do not distinguish between these different forms of compensation.

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the realized utility of borrowing from t is ω (V ) − γ · max 0, k (V ) + ν S − α − T st (c) − ε M − k (V ) − ν S , where ω (V ) is the utility from borrowing. In this expression ν S is unobservable, and hence s must take expectations over it. After taking expectations, we obtain (15) u V, T st (c) + ε M for some u function that is strictly increasing in the second argument when ν S has full support.34 If we also incorporate observed supply shocks ε S into the analysis, then the final utility representation becomes u V, T st (c) + ε M − ε S − ε S . Assuming that u is close to linear in the second argument, which would be the case if ν S had sufficient variance, letting ε S = (1 + 1/u2 ) ε S , where u2 is the derivative of u in the second argument, we can approximate this total utility as a linear function of T st (c) + ε M − ε S . In this representation, the error term captures a combination of supply shocks and measurement error in trust. YALE UNIVERSITY HARVARD UNIVERSITY AND NBER IOWA STATE UNIVERSITY UNIVERSITY OF CALIFORNIA–BERKELEY

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HOW DOES PARENTAL LEAVE AFFECT FERTILITY AND RETURN TO WORK? EVIDENCE FROM TWO NATURAL EXPERIMENTS∗ ¨ RAFAEL LALIVE AND JOSEF ZWEIMULLER This paper analyzes the effects of changes in the duration of paid, job-protected parental leave on mothers’ higher-order fertility and postbirth labor market careers. Identification is based on a major Austrian reform increasing the duration of parental leave from one year to two years for any child born on or after July 1, 1990. We find that mothers who give birth to their first child immediately after the reform have more second children than prereform mothers, and that extended parental leave significantly reduces return to work. Employment and earnings also decrease in the short run, but not in the long run. Fertility and work responses vary across the population in ways suggesting that both cash transfers and job protection are relevant. Increasing parental leave for a future child increases fertility strongly but leaves short-run postbirth careers relatively unaffected. Partially reversing the 1990 extension, a second 1996 reform improves employment and earnings while compressing the time between births.

I. INTRODUCTION Working parents of a newborn child have to give full attention to their baby and their jobs. Aiming to address this double burden for working parents, most OECD countries offer parental-leave (PL) provisions. However, although countries agree that parents of small children need support, the design of current PL systems differs strongly across countries. The purpose of this paper is to provide information on one key aspect of PL. We ask how PL duration affects a working mother who has just given birth to her first child. By studying the decision to give birth to a second child, we can provide information on the role of PL policy for ∗ We are grateful to Larry Katz and to four anonymous referees for their comments. Johann K. Brunner, Regina Riphahn, and Rainer Winkelmann and participants at seminars in Amsterdam, Basel, Frankfurt, Kobe, Rotterdam, Vienna, Zurich, SOLE 2006, ESSLE 2006, the Vienna Conference on Causal Population Studies, the IZA Prize Conference 2006, and the German Economic Association meeting of 2005 also provided valuable discussion on previous versions of this paper. We bear the sole responsibility for all remaining errors. Beatrice Brunner, ¨ Simone Gaillard, Sandra Hanslin, and Simon Buchi provided excellent research assistance. We are grateful for financial support by the Austrian Science Foundation (FWF) under the National Research Network S103, “The Austrian Center for Labor Economics and the Analysis of the Welfare State,” Subproject “Population Economics.” Further financial support by the Austrian FWF (No. P15422-G05), the Swiss National Science Foundation (No. 8210-67640), and the ForschungsStiftung of the University of Zurich (project “Does Parental Leave Affect Fertility Outcomes?” ) is also acknowledged. [email protected]; [email protected] C 2009 by the President and Fellows of Harvard College and the Massachusetts Institute of

Technology. The Quarterly Journal of Economics, August 2009

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higher-order births. This analysis is important for countries with fertility rates below the replacement level. Studying mothers’ return to work, postbirth employment, and postbirth labor earnings, the paper provides information on how PL duration affects subsequent work careers of working women. This analysis allows assessment of the extent to which extending parental leave facilitates balancing work and life. Moreover, studying the effects of parental leave on both fertility and work allows us to assess whether institutions that shape the terms of postbirth female employment spill over to fertility. Our analysis is based on the Austrian PL system. Under Austrian PL rules women can stay off work and return to the same (or a similar) job at the same employer thereafter. During the leave they receive a flat PL benefit of 340 euros per month. Interestingly, Austrian policymakers implemented two major reforms of the duration of PL—an extension of PL duration in 1990 and a reduction of PL duration in 1996. Specifically, before July 1, 1990, the maximum duration of PL ended with the child’s first birthday. The 1990 reform extended PL until the child’s second birthday for all children born on or after July 1. The 1996 reform partially reversed the extension granted in 1990 by taking away the last six months added in 1990. These policy changes create natural experiments that allow us to assess how changes in PL duration affect fertility decisions of a mother who has just given birth to a newborn child. Extending PL duration affects this decision in two different ways. First, the probability of a higher-order birth is potentially determined by the PL duration for the baby that is already born. This is what we call the current-child effect. This effect is potentially important in the Austrian context because women who give birth no later than 3.5 months after the end of a previous PL are exempt from the work requirement and can automatically renew PL eligibility for the second child. Before the 1990 reform, mothers needed to give birth to a new child within 15.5 months. Such a tight spacing of children is both biologically difficult and not desired by many parents. The 1990 reform increased this period to 27.5 months, thus providing much broader access to automatic renewal. The 1996 reform reduced the automatic renewal period to 21.5 months—a space between births that is biologically feasible and potentially desired. Second, the probability of a higher-order birth is also determined by PL duration for the baby yet to be born. This is what we call the future-child effect. Because PL duration directly

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affects the costs associated with childbearing, the future-child effect is expected to increase fertility. This paper also studies how PL rules affect postbirth labor market careers of mothers with newborn children. The 1990 extension of leave encourages a mother to stay home with her child in the second year after birth and to delay return to work substantially. Future employment and labor earnings will be affected in two ways. First, providing parents with extended PL encourages mothers to stay off work longer and lowers employment and labor earnings immediately after a birth. This short-run effect is mechanical and intended by policy makers. Second, prolonged periods of absence from the workplace may lead to skill depreciation and weaker labor market prospects after labor market reentry. This potential for long-run deterioration of women’s postbirth careers is clearly not intended by policy. Although family policies in many countries are designed to support low-income (and often nonworking) women, the Austrian case is interesting because it affects working women of all income groups. However, it is not a priori clear for which group the PL rules generate the strongest incentives. The flat PL benefit implies that lower-income parents have a higher earnings replacement ratio. To shed light on the importance of cash transfers, we look at differences in response between high- and low-income women. The job protection policy may be more important for career-oriented women. This is because job protection shields working women from future income losses due to firm-specific human capital depreciation or deferred payment contracts. To shed light on the importance of job protection, we look at differences in responses between blue- and white-collar women. As firm-specific human capital and internal labor markets are arguably more important in white-collar professions, we would expect stronger responses from white-collar women. The empirical analysis draws on a unique and very informative data set, the Austrian Social Security Database (ASSD). Set up to provide information to calculate pension benefits for private sector employees (about 80% of Austrian employment), the ASSD collects detailed information on a woman’s earnings and employment history from employers; and it also contains information on take-up of PL benefits and on a woman’s fertility history from the point of time when she first worked in the private sector. We extract information on PL-eligible women who gave birth to the first child observed in ASSD in periods that cover the reform, and we

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analyze subsequent fertility and labor market outcomes both in the short run (three years after the first birth) and in the long run (ten years after the first birth). Our empirical analysis uncovers five key results. First, we find that the extension of PL enacted in July 1990 had a strong impact on subsequent fertility behavior. We find that both the current-child PL effect and the future-child PL effect are quantitatively large. In the short run (within three years) fertility increases by 5 percentage points (15%) as a result of extended leave on the current child and by 7 percentage points (21%) as a result of extending leave for the future child. Second, we find not only that fertility increases temporarily, but also that this increase persists in the long run. Among women eligible for the more generous PL rules, three out of 100 women gave birth to an additional child within ten years after the birth of the first child who would not have done so with short leave. Although we do not observe the completed fertility cycles of mothers, we conclude that it is quite likely that the policy change affected not only the timing but also the number of births. Third, we find that most mothers exhaust the full duration of their leaves and that return to work is substantially delayed even after PL has been exhausted (by 10 percentage points in the short run and by 3 percentage points in the long run). Interestingly, although work experience and earnings decrease strongly in the short run, we do not find that longer leaves have long-run effects on work experience and cumulative earnings. Fourth, there are differential fertility responses of highand low-wage women and blue- and white-collar workers, indicating that both cash transfers and job protection have a sizable impact on fertility and labor market responses. Fifth, we find that the 1996 reduction of PL duration had a significant effect on the timing of subsequent births but no impact on the number of children. The 1996 partial reversal of the extension granted in 1990 also partially undoes the short-run reductions in employment and earnings generated by the 1990 extension of PL duration. This paper contributes to the literature on the impact of cash transfers on fertility behavior (Hardoy and Schøne 2005; Milligan 2005) and to the literature on the effects of welfare reform on fertility behavior of low-income women in the United States (Hoynes 1997; Moffitt 1998; Rosenzweig 1999; Joyce et al. 2004; Kearney 2004).1 Furthermore, Averett and Whittington (2001) study the 1. Bj¨orklund (2007) provides a survey of recent empirical work on the impact of family policies on fertility.

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impact of the Family and Medical Leave Act in 1993 on fertility. Hoem (1993) studies the impact of PL rules (“speed premium”) for Sweden, and Piketty (2003) looks at parental education benefits in France. This paper also contributes to the literature studying the effects of family leave on labor market outcomes. Klerman and Leibowitz (1997, 1999) and Baum (2003) find only weak effects on employment and wages. Berger and Waldfogel (2004) for the United States, Baker and Milligan (2008) for Canada, and Ruhm and Teague (1997) and Ruhm (1998) for European countries find a closer relationship between PL provisions and the labor market attachment of mothers. Albrecht et al. (1998) show that PL-induced career interruptions are not associated with a wage penalty for women in Sweden. Sch¨onberg and Ludsteck (2007) study the causal effects of successive changes in PL duration on employment and earnings in Germany.2 Our paper adds to this literature in at least four ways. First, our empirical analysis provides convincing evidence on the effects of changing PL duration for the current child by adopting a quasiexperimental approach. Second, our study also provides evidence on the effect of changing PL duration on the future child. Understanding these two effects is crucial in PL design. Third, our results speak to the important issue of how policies that enhance the balance between work life and family life affect fertility behavior. This is different from many previous papers that have focused on the effect of cash transfers on fertility. Fourth, our empirical analysis allows assessing the effects of changes in PL on both short- and long-run labor market outcomes for mothers. This allows addressing the frequently raised concern that generous PL policies will harm mothers in the long run because extended periods off work lead to depreciation of human capital and worse future labor market prospects.3 The paper is organized as follows. The next section discusses the institutional setup and develops testable hypotheses as to how the reform might have affected fertility and labor market 2. Several recent papers study the effects of parental leave or child care on child development (Baker and Milligan 2008; Dustmann and Sch¨onberg 2008; Berger, Hill, and Waldfogel 2005; Baker, Gruber, and Milligan 2008). A further related literature analyzes the impact of financial incentives on fertility and labor supply using a structural approach. See Moffitt (1984) for an early approach to this question and Laroque and Salani´e (2005) for a more recent study of the effects of financial transfers on fertility and labor supply. 3. In a companion paper, we discuss how the two Austrian reforms affect the ¨ quality of mothers’ first postbirth jobs (Lalive and Zweimuller 2007). The analysis of the current paper is more comprehensive in providing a detailed assessment of the overall effects of PL on earnings and employment in all postbirth jobs.

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behavior. Section III discusses the data and presents our empirical strategy for measuring the effects of PL duration on the current child and on the future child. Section IV presents the fertility and labor market effects of the increase in PL duration for the current child enacted with the 1990 reform. Section V studies the effect of the 1990 increase in PL duration for the future child. Section VI analyzes the impact of the 1996 reform, and Section VII concludes with a discussion of the relevance of our findings. II. BACKGROUND AND HYPOTHESES This section provides the institutional background of the Austrian PL system and discusses how two reforms in the 1990s may affect higher-order fertility and work careers of mothers. II.A. The Austrian PL System in the 1990s Working women have access to two types of family policies in Austria: maternity leave and parental leave. Maternity leave lasts for sixteen weeks (eight weeks before and eight weeks after the actual birth) and pays the average wage rate over the last quarter before the birth. Before July 1990, PL started after maternity leave ended and lasted until the child’s first birthday. To become eligible for PL a mother had to satisfy a work requirement. Women taking up PL for the first time had to have worked (and paid social security contributions) for at least 52 weeks during the two years prior to birth or be eligible for unemployment benefits—again fulfilling a work requirement of 52 weeks out of the two years prior to entering unemployment. For mothers with at least one previous take-up of PL or first-time mothers below the age of twenty years, the work requirement is reduced to twenty weeks of employment during the last year prior to birth. Moreover, PL is also renewed if the mother gives birth within a “grace period” that extends up to four months after the end of an earlier leave.4 4. The exact legal definition of the length of the grace period is that the work requirement is also abandoned if a new maternity protection period starts within a grace period of six weeks after the formal termination of a previous PL. Because maternity protection starts about eight weeks before the due date, the rules effectively imply that eligibility for PL is renewed for any new child expected to be born within fourteen weeks after the end of the previous leave. Because expected birth dates are not observed in our data, we consider a birth to be realized within the automatic renewal window if it occurs no later than four months after the end of the previous PL. Work exemptions for higher-order births are in place in countries where PL lasts long enough so that women could give

PARENTAL LEAVE, FERTILITY, AND RETURN TO WORK Work required for PL

Maternity leave and PL benefits

0

0

200

10

Weeks

Euros 600 400

20

800

30

1000

1369

0

2

4

6

8

10 12 14 16 18 20 22 24 26 28 30 32 34 36 Time since birth (months)

Before July 1990 July 1990 until June 1996

(A) Monthly transfer income

After July 1996

0

2

4

6

8

10 12 14 16 18 20 22 24 26 28 30 32 34 36 Time since birth (months)

Before July 1990 July 1990 until June 1996

After July 1996

(B) Work requirement for higher-order births

FIGURE I PL Benefits and Work Requirement for Higher-Order Births Figure shows the benefit path for a women earning real 1,000 euros per month before giving birth to her first child (A) and the number of weeks she needs to work for parental leave to cover the subsequent child (B). The parental leave benefit is 340 euros per month irrespective of prebirth monthly income. Dotted line refers to the situation before July 1990, solid line refers to the situation between July 1990 and June 1996, and dashed line refers to the post–July 1996 rules. Source. Austrian federal laws, various years.

PL provisions are twofold. On the one hand, PL protects the previous job. A mother has the right to return to her previous employer until PL ends. Moreover, she cannot be dismissed during the first four weeks after returning to work.5 On the other hand, PL is associated with a government transfer. A mother eligible for PL in 1990 received a PL benefit of about 340 euros per month (31 percent of gross median female earnings). Benefits are not means-tested and not taxed, implying a median net income replacement ratio of more than 40 percent. Single women (or women with a low-income partner) are eligible for higher benefit levels (Sonderunterstutzung). ¨ Figure IA shows the time path of transfer income for a PLeligible woman who has earned 1,000 euros per month during the quarter before birth. Maternity leave transfers amount to 1,000

birth to a new child while being covered by a PL from a previous child. In Germany, job protection is extended when a mother gives birth to a child within a current leave. The “speed premium” in Sweden grants higher PL benefits to parents who have subsequent children within sufficiently short intervals. Also, the PL systems of the Czech Republic, Slovakia, and Estonia feature renewal rules that are very similar to the Austrian system. 5. PL renewal makes mothers eligible for a maternity leave transfer that is eighty percent higher than the regular PL transfer. The maternity leave transfer of mothers who work in between two births equals the average wage in the three months prior to giving birth (the same as for a first birth). PL renewal leaves job protection unchanged.

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euros for a period of about two months after birth.6 After maternity leave has been exhausted, this mother has two options. One is to arrange care for her newborn child and return to her prebirth job earning 1,000 euros per month. This option is complicated by the fact that the Austrian child care system for children under the age of three years is rather limited. Alternatively, she can provide care for her newborn child and take up PL, earning 340 euros per month until her child turns one year old. On her child’s first birthday, she can decide to return to her prebirth job, take up a new job, or continue to provide care for her child. In the event that she gives birth to a new child before her previous child turns 15.5 months old, she has access to renewed leave (Figure IB). Any child born after that date will be covered only if the mother has been working for at least twenty weeks prior to giving birth to the new child. In July 1990, a first PL reform increased the maximum duration of PL to two years and was enacted on July 1, 1990.7 A further reform in 1996 introduced a change in PL duration by introducing a one-partner PL maximum of eighteen months. Because Austrian fathers effectively do not take up PL, the one-partner maximum removed the last six months of PL that were added in 1990.8 6. Because maternity leave is initiated eight weeks prior to expected date of birth, the pre- and postbirth durations of maternity leave vary. 7. In December 1989, the PL system was changed from a “maternity” to a “parental” leave system, allowing for the father to go on PL also. However, this is of no practical consequence. In 1990 fewer than 1% of fathers took advantage of that possibility. A second change was that women in farm households and family businesses, as well as women who did not meet the employment requirements, became eligible for a transfer equal to 50% of regular PL benefits up until the child’s second birthday. This is of no importance in the present analysis because we confine ourselves to behavior of female dependent employees. Furthermore, the reform made it possible to take part-time PL, either between a child’s first and second birthday (by both parents at the same time) or between a child’s first and third birthday (only one parent or both parents alternating). 8. Compared to the U.S. Family and Medical Leave Act (FMLA), the Austrian PL rules are very generous. The FMLA grants twelve weeks of unpaid leave to employees in firms with more than fifty workers. Compared to current OECD systems, the pre-1990 PL system was of average generosity. The rules were very similar to those currently in place in Canada (twelve months PL, cash transfer 55 percent of previous earnings), Australia (twelve months PL, unpaid), or the United Kingdom (eighteen weeks paid maternity leave, thirteen months unpaid PL). Austrian post-1990 rules are more similar to those currently in place in continental Europe. The German system grants three years of PL and a generous cash benefit (100 percent of prior earnings on maternity leave, 67 percent of prior earnings for the first fourteen months of PL, and a flat transfer thereafter). In France mothers get three years of PL, 80 percent of prior earning for the first twelve months, and a flat transfer thereafter. Also, Sweden and Norway offer long leaves and PL benefits replace a very large fraction of prior income. Interestingly, the renewal option is not unique to the Austrian system. The Swedish “speed premium” shares similarities, as PL benefits are extended when an additional

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II.B. Effects on Fertility and Work Careers Extending PL from one year to two years may affect future fertility for two different reasons: (i) a longer PL duration for the current child facilitates access to automatically renewed PL benefits for a new child; and (ii) a longer PL duration for the future child reduces directly the cost of this child. Arguably, taking advantage of PL renewal is difficult when PL leave is short. The one-year policy forces a mother who wants PL protection for the future child to conceive a new child quite early after the birth of the previous child.9 The 1990 reform adds twelve crucial months to the automatic renewal period. Thus, achieving automatic PL coverage for a future child is easier under the two-year policy than under the one-year policy (Figure IB).10 In contrast to the 1990 PL extension, the 1996 PL reduction did not change the biological feasibility of PL renewal. To become eligible without having to go back to work, a mother has to give birth to a new child within 21.5 months. By inducing mothers to give birth to a future child within the automatic renewal period, the 1990 PL extension is likely to change the spacing of births. Note, however, that any shock inducing mothers to give birth to planned children earlier may translate into a long-run increase in the total number of children. As fertility plans are realized earlier, shocks to partnerships, health, etc., that are inducing parents to give up family plans in a one-year system have weaker effects on fertility in a two-year system.11 child is born within two years after the birth of a previous child. The German system also grants the possibility of PL renewal with respect to job protection (but, unlike in the Austrian system, PL benefits do not cease when a parent goes back to work). The PL systems of the Czech Republic and Slovakia are almost identical to the Austrian system and have the PL renewal feature. 9. To see this more clearly, consider a woman who gives birth on September 1, 1988. She would be entitled to PL through September 1, 1989. To qualify for PL renewal, with the eight-week prebirth maternity leave and the six-week post-PL grace period, she would have to give birth by December 14, 1989. Note that this requires conceiving a new child by March 1989, no later than 5.5 months after giving birth to the previous child, implying a space between births of at most 15.5 months. 10. Under the two-year policy, a woman who gives birth on September 1, 1990, qualifies for PL renewal if a second child is conceived by March 1992, or 18 months subsequent to giving birth to the previous child. 11. Notice that when this argument is applied to the 1996 PL reduction, it is not clear whether this reform will lead to more or less children. On the one hand, the 1996 reform requires a tighter space between births for a mother who takes advantage of renewal. On the other hand, although the required space is biologically feasible, it is shorter than before and may induce some mothers to delay a planned birth. The first effect increases and the last effect decreases the number of births.

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Extending PL may also affect higher-order fertility because it lowers the cost of having a future child. Ceteris paribus, a twoyear leave for the future child is more attractive than a one-year leave. Thus, the 1990 reform is expected to increase the number of children born to women exposed to the new policy. The second key aim of PL policies is to facilitate balancing family work and market work. Changes in the duration of PL for the current child may affect mothers’ work careers in two ways. Take-up of extended leaves delays return to work, lowers employment, and lowers labor earnings in the short run (0–36 months after the birth of the current child). Moreover, prolonged career interruptions may also lead to mothers’ postbirth careers deteriorating in the long run (37 to 120 months after the birth of the current child). Changes in PL duration for the future child are expected to affect short-run postbirth work careers only indirectly, via their effect on births. Austrian PL offers two distinct types of benefits: a flat transfer and job protection. Flat transfers translate into strong differences in replacement rates. We therefore expect strong heterogeneity in the responses to changes of PL in mothers with high earnings prior to birth and mothers with low prebirth earnings. Moreover, PL policies target not only costs associated with foregone current income but also costs associated with loss of lifetime income following a job loss. A longer duration of job protection may be particularly beneficial for mothers with firm-specific human capital or mothers who are on deferred payment contracts. To shed light on this issue, we compare women working in white-collar occupations to women in blue-collar jobs. Arguably, job-specific human capital, internal labor market, and career concerns are more important in white-collar jobs, so the job-protection channel should trigger stronger responses for white-collar women than for blue-collar women. III. DATA AND EMPIRICAL STRATEGY In this section we first discuss the available data. We then present the empirical strategies and explain the assumptions under which we identify the causal effect of changes in PL duration on fertility and labor market outcomes. III.A. Data Our empirical analysis is based on the Austrian Social Security Database (ASSD). This database collects information relevant

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to old-age social security benefits. As these benefits depend on individuals’ earnings and employment histories, the database collects information on work histories for the universe of Austrian private sector employees. Furthermore, the database also contains information on exact dates of births. A disadvantage of the ASSD is partial recording of birth histories. ASSD records all births that occur after a woman’s first job in the private sector. This means that we can precisely determine the relative parity of any birth but we cannot determine any birth’s absolute parity.12 Our ASSD extract covers women giving birth to their first ASSD child in the years 1985, 1987, 1990, 1993, and 1996. We observe second-child births, return to work, employment, and earnings for these women until the year 2000, allowing us to analyze about ten years of a woman’s life for the 1990 reform and less than that for the 1996 reform. We focus on mothers who are likely to be at parity one because this yields a comprehensive picture of how changes in PL on this first child affect future fertility and work careers.13 We establish PL eligibility for these women by considering work careers two years prior to their giving birth to the first child. Note that measuring eligibility is complicated because a woman’s work career in the public sector is unobserved (but counts for PL eligibility) and because a woman’s parity is unobserved. Our eligibility indicator allocates a woman into the PL-eligible group if she demonstrates any employment or has ever been eligible for unemployment benefits in the two years prior to giving birth. Clearly, this definition of eligibility may give rise to misclassifying ineligible women into the eligible group, thus reducing take-up. More importantly, this encompassing definition of eligibility allows identification of a group of ineligible women (who neither worked nor received unemployment benefits in the two

12. Partial recording of previous births implies that we cannot precisely determine the parity of a birth. To make things precise, assume a working woman gives birth to a child at age thirty. If this woman is continuously employed in the private sector, we know this birth is her first birth and all subsequent births are recorded in the ASSD. However, if this woman entered the ASSD, say, at age 25 (e.g., because she was previously employed in the public sector and not covered by the ASSD), she could have could have given birth to children before entering the ASSD. More generally, if we observe x previous births in the data, we know that any subsequent birth is of parity x or higher. 13. Our focus here is on mothers, even though fathers could in principle take up PL provisions too. There are two reasons that we do not include fathers in our analysis. First, take-up by fathers is extremely low. Second, our database does not provide information on the dates of birth of a father’s children. Hence, fathers’ reactions to PL policies cannot be addressed in the present context.

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years before giving birth) who do not go on to collect PL in our data. This finding makes us confident that we cleanly identify the group of PL-ineligible women—a group that is of importance in discussing the validity of the empirical strategy measuring the effect of changing PL duration for the future child. Furthermore, in line with demographic research, we restrict attention to women aged 15 to 45 years when giving birth to their first ASSD children. The ASSD allows constructing a set of four key outcome measures. Information on the date of birth of the second ASSD child allows measuring whether a mother gives birth to at least one additional child. Information on the date of return to work allows discussing return-to-work decisions. Information on the woman’s work and earnings career allows assessing employment and earnings in the two years prior to giving birth and up to ten years after birth. In the analysis below, we measure employment and earnings at a yearly frequency relative to the birthday of the first child. The set of conditioning variables comprises information on employment, unemployment, and earnings since entry into ASSD (either 1972 or time of entry into the labor market) and on a woman’s labor market position exactly one year prior to birth (employed or unemployed, industry and region of employer, daily labor income white-collar or blue-collar occupation).14

III.B. Empirical Strategy Our empirical strategy uses the 1990 and 1996 PL reforms to identify the effect of PL duration for the current child and the effect of PL duration for the future child. Table IA shows PL durations for the current and the future child for three cohorts of women who gave birth to a first child at three different dates: July 1990, June 1990, and June 1987.15 July 1990 mothers are eligible for 24 months of PL for the current child and PL renewal takes place when a future child is born within 27.5 months after the July 1990 birth. PL duration is 24 months for any child born within three years. June 1990 mothers are eligible for 12 months of PL for the current child and PL renewal is possible when a future child is born within 15.5 months. PL duration is 24 months for any child born within three years. June 1987 mothers are eligible for 12 months of PL for the current child and any 14. The data do not have information on hours, education, or marital status. 15. Table IB displays the analogous cohorts for the 1996 reform.

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TABLE I EMPIRICAL DESIGN

Current child born

Parental leave current child

Automatic renewal

Parental leave future child (born within 36 months)

June 1987 June 1990 July 1990

(A) 1990 reform 12 months 15.5 months 12 months 15.5 months 24 months 27.5 months

12 months 24 months 24 months

June 1993 June 1996 July 1996

(B) 1996 reform 24 months 27.5 months 24 months 27.5 months 18 months 21.5 months

24 months 18 months 18 months

Source: Austrian Federal Laws, various years.

future child born within 36 months. PL is automatically renewed if the future child is born within 15.5 months. Identifying the Current-Child PL Effect. Can the currentchild PL effect be identified from a comparison of June 1990 mothers with July 1990 mothers? These two groups differ in the duration of the PL renewal period (and the associated PL duration for the first child), but they have the same PL duration for a future child. The crucial identification issue is to what extent mothers could have influenced the date of birth of the current child in anticipation of the policy change. There are at least two reasons that lead us to believe that mothers cannot have “timed” births. First, the conception of a child is an event that cannot be perfectly planned by parents. Second, even if parents could deterministically plan a birth, self-selection requires that parents have been informed of the July 1990 policy reform at the date of conception. We performed a content analysis of the major Austrian newspapers to check the information that potential parents had nine months before the June/July 1990 births, that is, in September/October 1989. The public discussion about the PL reform started in November 11, 1989, but the ruling coalition (social democrats and conservatives) discussed it until April 5, 1990, until it had designed a policy reform apt to find parliamentary approval. Because it was not clear until three months prior to the policy change whether a PL reform would take place and how it would be implemented, the June/July 1990 births were not influenced by anticipation of the July 1990 PL reform. However,

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although anticipation of the PL reform at the date of conception is unlikely, it is still possible that mothers could have influenced the timing of a birth by postponing induced births or planned caesarean sections.16 We assess the presence of such fine tuning in two ways. First, analyzing the number of children born in June and July 1990, we do not find evidence of a spike in births on July 1, 1990. Second, because birth timing is likely to be strongest right around the reform date, we assess the sensitivity of our results by excluding births occurring one week before and one week after July 1, 1990.17 Because babies’ dates of birth assign extended PL and parents could not anticipate extended leave, we can identify the currentchild PL effect by comparing treated mothers giving birth (to the current child) in July 1990 to control mothers giving birth in June 1990.18 Although treatment and control samples are selected over two successive months, we consider their fertility and labor market outcomes over the following 36 months (short-run effects) and the following 120 months (long-run effects). Differences between treated and control mothers cannot be attributed to differences in the environment. In fact, the treated and control mothers are facing different parental leave incentives but practically identical economic conditions following the June/July 1990 birth. Identifying the Future-Child PL Effect. To identify the effect of PL duration on the future child, we compare short-run (0–36 months after birth) and medium-run (37–72 months after birth) outcomes of June 1987 to June 1990 mothers. Identification of the 16. Gans and Leigh (2006) show that the introduction of the Australian baby bonus on July 1, 2004, led to a significant increase in the number of births on that same day, suggesting that parents postponed their births to ensure they were eligible for the bonus. Similarly, Dickert-Conlin and Chandra (1999) show that the U.S. tax system creates an incentive to give birth to a child on the 31st of December rather than on the 1st of January. They find that the probability that a child is born in the last week of December, rather than the first week of January, is positively correlated with tax benefits. 17. Mothers could also have changed prebirth work patterns in order to become eligible for extended leave. Empirical evidence on prebirth employment in Figure VC is not consistent with such qualification effects. 18. This is essentially a regression discontinuity framework (RDD). Denote the treatment status of a mother by D, where D = 1 if a mother has access to a two-year leave, and D = 0 if a mother has access to a one-year leave. Eligibility for treatment is a discontinuous function of the current child’s date of birth T . Denote by t the date when policy changes (July 1, 1990, for the change from the 12-month to the 24-month policy and July 1, 1996, for the change from the 24-month to the 18-month policy). Provided that lim→0 Pr(D = 1|T = t + ) = lim→0 Pr(D = 0|T = t − ), our design satisfies the “fuzzy” RDD assumption (Hahn, Todd, and Klaauw 2001). Figure II is consistent with this assumption being strongly satisfied.

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future-child PL effect requires stronger assumptions than those needed to identify the current-child PL effect. The central identifying assumption is that there are no substantial cohort or time effects that pollute the comparison between June 1987 and June 1990. We propose three ways of assessing the plausibility of this assumption. First, we analyze PL-ineligible women as a control group and check whether outcomes for June 1990 mothers follow a different trend than outcomes for June 1987 mothers, finding no significant time trend. Clearly, this small control group is less than perfect because it encompasses women with weak prebirth labor market attachment. Second, we study time and cohort trends for PL-eligible mothers both before and after the 1990 reform. Third, we also exploit the way PL rules change with time since first birth. Although differences in PL rules between the treated and the control group exist during the first 36 months, the same rules apply 37–72 months after birth. Thus, treated and control mothers should differ in the period 0–36 months after birth but less so in the period 37–72 months after birth. Finally, adding up the effect of extending current leave with the effect of extending future leave allows estimating the total effect of PL duration and PL renewal. Arguably, this total effect comes close to the effects generated by moving fully from a oneyear to a two-year system—an effect of prime policy interest. IV. EXTENDING PL DURATION FOR THE CURRENT CHILD This section discusses the effects of extending PL duration for the current child on fertility and return-to-work behavior. The analysis proceeds in three steps. We first document the fertility effects of changing PL duration for the current child. Next, we turn to labor market responses. And finally, we assess the potential heterogeneity in the responses to the reform by groups that differ in income and in broad occupation IV.A. The Impact on Fertility The ASSD reports information on PL take-up. Focusing on PL eligible mothers of newborn children, Figure II reports average PL take-up (including zeros) associated with a first child born between June 1 and July 30, 1990. June 1990 mothers are eligible for ten months of the parental leave (excluding the first two months of maternity leave). Results indicate that of these ten months, June 1990 mothers take up on average nine months of PL.

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1/6/90

16/6/90

1/7/90 Calendar day Before

16/7/90

31/7/90

After

FIGURE II Parental Leave Taken with Current Child June smoothed backward, July smoothed forward (15-day moving average). Source. ASSD, own calculations. Sample restricted to PL-eligible women giving birth to a child in June 1–30 or July 1–30 of 1990.

In contrast, average PL take-up by July 1990 mothers amounts to 19 months, which is considerably more than for any mother giving birth in June 1990. Interestingly, average PL take-up is about 85 percent of the 22 months covered by PL after the 1990 reform (after two months of maternity leave). This suggests that the second year of leave is valued by the majority of eligible women. Figure II suggests comparing treated mothers who give birth in July 1990 to control mothers who give birth in June 1990. How informative is this contrast on the causal effect of extending PL duration for the current child? Table II provides descriptive evidence on PL take-up by years since birth as well as on key prebirth characteristics. Treated and control mothers are identical with respect to PL take-up in the first year after giving birth to their current child. Both cohorts take up about 9.2 months out of the roughly 10 months offered by the PL system. Striking differences in PL take-up appear in the second year after birth. Whereas treated mothers spend about ten months on PL, control mothers spend less than one month on PL (with their second child).

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TABLE II DESCRIPTIVE STATISTICS, MOTHERS GIVING BIRTH IN JUNE AND JULY 1990 July 1990 Mean Parental leave, yr 1 (mths) Parental leave, yr 2 (mths) Age 20–24 Age 25–29 Age 30–34 Age 35–44

9.208 10.082

SD

June 1990 Mean

(A) Treatment (2.194) 9.196 (3.486)

0.795

(B) Demographics 0.423 (0.494) 0.443 0.346 (0.476) 0.343 0.109 (0.311) 0.087 0.029 (0.167) 0.025

SD

Est

SE

(2.139)

0.012 (0.055)

(2.209)

9.287 (0.074)∗∗∗

(0.497) −0.02 (0.475) 0.004 (0.282) 0.022 (0.156) 0.004

(C) Labor market history Employment (years) 5.846 (3.94) 5.701 (3.792) Unemployment (years) 0.265 (0.543) 0.257 (0.484) Earnings not observed? 0.028 (0.165) 0.026 (0.16) (1 = yes) Daily earnings (euros) 34.49 (42.942) 33.313 (37.719) Employed (1 = yes) White collar (1 = yes) Daily 1989 earnings (euros) Observations

Contrast

(0.013) (0.012) (0.008)∗∗∗ (0.004)

0.144 (0.098) 0.008 (0.013) 0.002 (0.004) 1.178 (1.026)

(D) One year before birth 0.868 (0.339) 0.867 (0.339) 0.001 (0.009) 0.435 (0.496) 0.441 (0.497) −0.006 (0.013) 36.826 (20.935) 36.142 (20.397) 0.684 (0.526) 3,225

2,955

Source: ASSD, own calculations. Sample restricted to PL-eligible women giving birth to a child in June 1–30 or July 1–30 of year 1990. Notes: Mean and standard deviation (in parentheses) for women giving birth to their first child in June 1–30 or July 1–30, 1990. Labor market history covers the period from January 1972 to date of birth in June or July 1990. Labor earnings are unobserved for women coming from the public sector, which is not covered by ASSD. Daily earnings refer to real mean earnings measured in year 2000 euros per day worked—real total labor earnings divided by work experience. Daily 1989 earnings are earnings on the prebirth job measured in year 2000 euros—the job held exactly one year before giving birth. Data also contain information on region and industry of the prebirth employer.

In contrast to PL take-up, both cohorts appear to be quite similar with respect to prebirth characteristics. Both groups show similar amounts of previous work and unemployment experience and previous average labor earnings. Also, labor market status one year before the 1990 birth differs only slightly. Although July 1990 mothers are significantly more likely to be in the age bracket 30–34 years than June 1990 mothers, the overall age composition is quite comparable. Almost 80 percent of all births occur in the age group 20–29 and about 13 percent at ages thirty and older.

1380

25

30

Percent

35

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1/6/90

16/6/90

1/7/90 Calendar day Before

16/7/90

31/7/90

After

FIGURE III How Does Parental Leave Affect Higher-Order Fertility? Figure reports the percentage of women who gave birth to at least one additional child within three years after giving birth in June or July 1990. June smoothed backward, July smoothed forward (15-day moving average). Source. ASSD, own calculations. Sample restricted to PL-eligible women giving birth to a child in June 1–30 or July 1–30 of 1990.

Table II also indicates that there are substantially more births in July 1990 than in June 1990. Is this evidence for birth timing? We investigate this issue by analyzing the number of births in June and July 1990 on a day-to-day basis, finding a steady increase but no discontinuity in the number of births on July 1 (not reported). Thus, comparing June 1990 mothers to July 1990 mothers, we find little evidence of seasonality in the composition of cohorts but strong seasonality in the number of births.19 Figure III presents first evidence on the causal effect of extending PL for the current child on the decision to have an additional child. The vertical axis measures the percentage of women who gave birth to a second child within the 36 months following 19. Indeed, births in July exceed births in June in any given year of our sample period (1985, 1987, 1990, 1993, 1996). Nevertheless, we perform sensitivity tests comparing births that occur, respectively, in the first/second half of June 1990 and the first/second half of July 1990 to assess the sensitivity of our results to short-run timing of births.

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the 1990 birth. To smooth out the noise in date-of-birth data, Figure III presents fifteen-day backward moving averages for June and fifteen-day forward moving averages for July. Results indicate that 32.2 of 100 women in the control group give birth to an additional child within the 36 months. In contrast, almost 36.7 of 100 women do so in the treated group. Thus, almost 5 of 100 women tend to give birth to an additional child in the treated cohort who do not do so in the control group. The magnitude of this effect seems quite robust and varies only slightly over the particular time window one adopts. Table III discusses the validity of this result, explaining the probability of giving birth to an additional child within three years in the context of a linear probability model. Column (1) estimates a baseline difference in short-run higher-order fertility of about 4.5 additional births per hundred mothers. Column (2) includes information on age and prebirth labor market history to assess the sensitivity of the key result to composition of treated and control group mothers. Results indicate that extended PL increases short-run fertility by 4.9 additional children per hundred women. Moreover, estimates indicate that higher-order fertility is lower for older women and for employed women. Column (3) estimates the causal effect of extended leave on births by reducing the width of the baseline window from thirty to fifteen days. Results suggest that about 5.4 children are born to one hundred women with extended leave that are not present under short leave. Anticipating extension of leave, mothers with a strong desire to have two or more children might have timed the birth of their first child to take place on or after July 1, 1990 (by postponing a planned caesarean section or delayed induction of a birth to July 1 or later). Column (4) excludes births taking place one week before and one week after July 1, 1990. Excluding these observations leaves results essentially unchanged; point estimates even slightly increase. The last column of Table III runs a placebo regression where we repeat the regression of column (2) using data on mothers giving birth to their first ASSD child in June and July 1987. These two groups faced identical PL rules and hence we should not see any major differences between them. In fact, the estimated treatment effect is insignificant and the point estimate very close to zero. The empirical analysis has documented a short-run response of higher-order fertility. Does this short-run response persist in the long run? Contrasting June and July 1990 mothers, Figure IV shows how extended leave for the first child affected higher-order

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TABLE III THE THREE-YEAR FERTILITY EFFECT OF EXTENDING PL DURATION FOR THE CURRENT CHILD, JULY 1990 (24 MONTHS PL) VS JUNE 1990 (12 MONTHS PL) Base July

.045 (.012)∗∗∗

No No 0.345

.049 (.012)∗∗∗ .045 (.024)∗ .029 (.028) −.059 (.033)∗ −.111 (.043)∗∗∗ .006 (.006) −.057 (.038) .011 (.022) −1.793 (.694)∗∗∗ −.025 (.045) .000 (.000) −.000 (.000) −.111 (.050)∗∗ −.011 (.017) .002 (.002) −.000 (.002) Yes Yes 0.345

.054 (.017)∗∗∗ .035 (.034) .014 (.039) −.073 (.046) −.116 (.062)∗ .003 (.009) −.048 (.054) .028 (.034) −1.850 (1.202) −.038 (.060) −.000 (.000) .000 (.000) −.036 (.075) −.031 (.024) .001 (.003) .000 (.003) Yes Yes 0.346

.056 (.014)∗∗∗ .042 (.027) .028 (.031) −.058 (.037) −.099 (.049)∗∗ .006 (.007) −.052 (.044) .011 (.025) −1.783 (.752)∗∗ −.004 (.051) .000 (.000) −.000 (.000) −.121 (.057)∗∗ −.004 (.020) .002 (.002) .000 (.002) Yes Yes 0.345

6,180

6,180

3,045

4,757

Age 20–24 Age 25–29 Age 30–34 Age 35–44 Employment (years) Employment sq. Unemployment (years) Unemployment sq. Earnings unobserved Daily earnings (euros) Daily earnings sq. Employed White collar Daily 1989 earnings Daily 1989 earnings sq. Industry Region Mean of dependent variable N

Controls Half-window Anticipation

Placebo .008 (.011) .012 (.021) .048 (.025)∗ .020 (.033) −.125 (.034)∗∗∗ .008 (.007) −.104 (.046)∗∗ −.020 (.028) 1.065 (1.233) .062 (.046) .001 (.000)∗∗ −.000 (.000)∗∗∗ −.099 (.045)∗∗ −.005 (.016) .002 (.002) −.001 (.002) Yes Yes 0.258 6,151

Source: ASSD, own calculations. Sample covers PL-eligible women giving birth to their first child in June 1–30 or July 1–30 of the respective years. Notes: Linear model of the probability of giving birth to a second child within three years of giving birth to a first child in June/July 1990. Standard error in parentheses. ∗ (∗∗ ,∗∗∗ ) denote significance at the 10% (5%, 1%) level, respectively. Inference based on Huber–White standard errors. “Base”: July (24 months PL) vs June (12 months PL). Controls: adds controls (Table II). Half-window: June 16–July 15. Anticipation: June 1–23 and July 8–30. Placebo: June 1987 (12 months PL) vs July 1987 (12 months PL).

1383

0

0

1

20

Percent 40

Percent 2

3

60

4

80

PARENTAL LEAVE, FERTILITY, AND RETURN TO WORK

0

12

24

36

48 60 72 84 Time since birth (months) June 1990

96

July 1990

108

120

0

12

24

36

48 60 72 84 Time since birth (months) June 1990

96

108

120

July 1990

FIGURE IV Additional Births (“Hazard” and Cumulative Proportion), July 1990 (24 Months PL) vs. June 1990 (12 Months PL) Figure reports the additional child hazard, that is, the women giving birth to an additional child in month t as a proportion of those who have not given birth to an additional child up to month t (A), and the cumulative proportion of women giving birth to at least one additional child up to month t (B). Vertical bars indicate end of automatic renewal (dashed for June 1990 mothers, regular for July 1990 mothers). Source. ASSD, own calculations. Sample restricted to PL-eligible women giving birth to a child in June 1–30 or July 1–30 of 1990.

fertility within the ten years following the 1990 birth. Figure IVA shows the second-child hazard rate, that is, the likelihood that a woman gives birth to a second child t months after the 1990 birth conditional on not giving birth to a second child before month t. The control group has a somewhat higher second-child hazard rate between months 12 and 16, whereas the treated group has a much higher hazard between month 18 and month 28. The difference between the two groups is largest during months 22–25, when the additional birth hazard is almost 3.5% for the treated group but less than 2% for the control group. After month 28 there are no major differences between the two groups. This pattern can be rationalized by the PL rules. Recall that the rules grant renewal of PL to control group mothers giving birth before month 16 and to treated mothers giving birth before month 28. Figure IVA shows that the additional-child hazard diverges most strongly when PL renewal is possible to treated mothers but impossible to control mothers. Figure IVB shows the cumulative proportion of women with a second child by time since the 1990 birth. Results indicate that the treated have a lower second-child probability before month 22 but a higher one thereafter. Interestingly, the difference does not erode in the long run. Even ten years after the 1990 birth, the

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TABLE IV SHORT-RUN AND LONG-RUN FERTILITY EFFECTS OF PL DURATION FOR THE CURRENT CHILD, JULY 1990 (24 MONTHS PL) VS JUNE 1990 (12 MONTHS PL) Base Additional birth 0–36 months Additional birth 0–120 months Additional birth 0–16 months Additional birth 17–28 months Additional birth 29–120 months Observations

Controls

Half-window Anticipation Placebo

.045 (.012)∗∗∗ [.345] .03 (.012)∗∗ [.617]

.049 (.012)∗∗∗ [.345] .035 (.012)∗∗∗ [.617]

.054 (.017)∗∗∗ [.346] .03 (.017)∗ [.62]

.056 (.014)∗∗∗ [.345] .048 (.014)∗∗∗ [.617]

.008 (.011) [.258] −.006 (.012) [.556]

−.027 (.006)∗∗∗ [.066] .082 (.01)∗∗∗ [.193] −.024 (.012)∗ [.36]

−.026 (.006)∗∗∗ [.066] .084 (.01)∗∗∗ [.193] −.021 (.012)∗ [.36]

−.029 (.009)∗∗∗ [.067] .084 (.014)∗∗∗ [.195] −.023 (.017) [.359]

−.023 (.007)∗∗∗ [.066] .09 (.011)∗∗∗ [.194] −.018 (.014) [.359]

−.006 (.006) [.069] .011 (.008) [.123] −.011 (.012) [.366]

6,180

6,180

3,045

4,757

6,151

Source. ASSD, own calculations. Sample: PL eligible women giving birth to their first child in June 1–30 (12 months PL) or July 1–30 (24 months PL) in the year 1990. Notes. This table reports the “July 1990” parameter estimate in a linear probability model comparing postbirth fertility of mothers giving birth to their first child in June/July 1990. Standard error in parentheses; mean of dependent variable in brackets. ∗ (∗∗ ,∗∗∗ ) denote significance at the 10% (5%,1%) level, respectively. Inference based on Huber–White standard errors. Base: July (24 months PL) vs. June (12 months PL). Controls: adds controls (Table II). Half-window: June 16–July 15. Anticipation: June 1–23 and July 8–30. Placebo: June 1–23, 1987 (12 months PL) vs. July 8–30, 1987 (12 months PL).

second-child probability of July 1990 mothers is still three percentage points higher than for June 1990 mothers. This suggests that the increase in fertility created by the PL renewal effect affects not just the timing but also the total number of children.20 Table IV provides an econometric assessment of both shortrun and long-run fertility effects using a linear probability model. The first row repeats the results of Table III on short-run fertility. The second row shows the corresponding result for long-run fertility (birth of a second child within 120 months). Column (1) shows that the effect of extending PL for the child born in 1990 20. Note that June 1990 mothers might still catch up to July 1990 mothers after ten years or due to differential third-child fertility. Although our data provide a window that is, arguably, too short to provide a definitive assessment of completed fertility, we believe that this is unlikely to happen. First, June and July 1990 mothers face identical economic and political circumstances on the third child. Second, because only about 65 percent of mothers give birth to two or more children, the third-child treatment effect would have to reach an implausibly large magnitude.

PARENTAL LEAVE, FERTILITY, AND RETURN TO WORK

1385

leads to three additional children being born to one hundred mothers within ten years. Adding controls (column (2)) increases the treatment effect to 3.5 percentage points; halving the estimation window and excluding births closer than seven days before and after July 1, 1990, does not reverse the result. We conclude that extending PL for the current child increases long-run fertility.21 Rows (3)–(5) in Table IV document the timing of excess fertility. Column (1) in Table IV shows that treated mothers reduce future-child fertility by 2.6 percentage points in the period when both treated mothers and control mothers have access to automatic renewal, that is, between months 0 and 16 (row (3)). Then there is a strong increase in fertility by 8.4 percentage points in the period when only treated mothers have access to automatic renewal, that is, months 17–28 (row (4)). Finally, treated mothers are slightly less likely to give birth to a second child between month 29 and month 120 (row (5)). This is the period when neither group has access to automatic renewal. In sum, our results suggest that the short-run change in access to automatic renewal leads to long-run effects on higher-order fertility. The most likely explanation for the high persistence of fertility effects is shocks (to health, partnership, workplace, etc.) that may otherwise induce parents to revise their long-run plans. We show that more generous PL induces parents to realize a planned birth earlier. This means that some shocks that are inducing parents to change family plans in a one-year system no longer affect family planning under a two-year system. This is why short-term gains in fertility also persist in the long run.22 IV.B. Labor Market Outcomes PL rules address the problems of parents in reconciling work and child care. Hence these rules also affect parents’ labor market outcomes. We now explore whether and to what extent extending 21. Although the effect estimated here seems large, our estimated short-run impact is similar in magnitude to that found by Milligan (2005) for pronatalist transfer policies in Quebec where, depending on the parity, parents got a cash transfer up to 8000 CAD. Fertility of those eligible is estimated to have increased 12% on average and 25% for those eligible for the maximum benefit. 22. Although it is true that some women are induced to have a birth within 28 months who would have waited and then never conceived (for preference or biological reasons), there also appear to be some women who are induced to wait beyond 16 months. To the extent that these women experience a negative shock, the net positive effects on the other set of women will be offset. Because there is a positive net fertility effect, the data suggest that any offsetting of this kind is not complete.

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leave from one year to two years affects women’s labor market outcomes, by focusing on three different indicators. (i) Return to work measures the probability that a woman has returned to work at least once after giving birth to her first child in June or July 1990 in the short run (0–36 months after birth) and in the long run (0–120 months after birth). (ii) Employment refers to the months worked per calendar year after birth in the short run (0–36 months after birth) and in the long run (37–120 months after birth). (iii) Earnings measures average pay earned per calendar day after birth in the short run (0–36 months after birth) and in the long run (37–120 months after birth). Note that both employment and earnings are set to zero in periods where a woman does not work and are included in the empirical analysis.23 Figure VA compares the proportion of women returning to work within 36 months after a birth in June and July 1990 by day of birth. Whereas about 62 of 100 women return to work three years after giving birth in June 1990, only about 52 of 100 women do so after giving birth in July 1990, with a strong discontinuity from June 30 to July 1. This suggests a very strong causal impact of PL duration on short-run return-to-work behavior. Figure VB compares the return-to-work profile during the 120 months following the 1990 birth. The figure clearly shows that the maximum length of PL has an extremely strong impact on return-to-work behavior. About 10% of mothers return to work within two months after giving birth (i.e., the end of maternity protection), the same for July 1990 and June 1990 mothers. About 80% of the treated and 83% of the control mothers exhaust the full PL duration. Although a substantial fraction of both treated (20%) and control mothers (25%) return to work exactly when PL has run out, the majority of women (60% among the treated, 58% among controls) stay home after PL has lapsed. Moreover, extended leave for the 1990 child seems to lower the fraction ever returning to work. Whereas 85 of 100 women return to work at least once ten years after the 1990 birth, only 82 of 100 treated women do so. 23. Return to work at date t measures the probability that a woman has stopped her baby break between date 0 and date t. In contrast, employment counts the days at work between date 0 and date t (set to zero when a woman does not work). Because a woman could have returned to work at some date s < t but dropped out of workforce at some later date τ ∈ (s, t), the two indicators differ. Unconditional labor earnings are average earnings per month and set to zero when a woman does not work at all during the respective month. Employment and earnings are available at an annual frequency.

1387

0

40

20

50

Percent 60

Percent 60 40

70

80

80

100

PARENTAL LEAVE, FERTILITY, AND RETURN TO WORK

1/6/90

16/6/90

1/7/90 Calendar day Before

16/7/90

0

31/7/90

12

24

36

After

48 60 72 84 Time since birth (months) June 1990

96

108

120

July 1990

(B) Proportion returning

0

0

2

10

4

Months 6

8

Year 2000 Euros 30 20

10

12

40

(A) Return to work

0

12

24

36 48 60 72 Months since birth

June 1990

84

July 1990

(C) Employment

96

108

120

0

12

24

36 48 60 72 Months since birth

June 1990

84

96

108

120

July 1990

(D) Earnings

FIGURE V Return to Work, Employment, and Labor Earnings, June 1990 vs. July 1990 Panel A reports the percentage of women who have returned to work at least once within three years after the 1990 birth (June smoothed backward, July smoothed forward, fifteen-day moving average); Panel B reports the cumulative proportion of women who have returned to work at least once since the 1990 birth; Panel C reports average months in employment; and Panel D reports mean labor earnings per calendar day since the 1990 birth. (Panels C and D are drawn on an annual frequency; data points at six, eighteen, etc., months refer to the first, second, etc. year after the 1990 birth.) Employment and earnings are set to zero for women who do not hold a job. Zeros are included in all our analyses. Source. ASSD, own calculations. Sample restricted to PL-eligible women giving birth to a child in June 1–30 or July 1–30 of year 1990.

Figure VC explores the effects of extended leave on employment. Employment patterns of women giving birth to their first child are strikingly asymmetric. Whereas paid work takes up about nine to ten months per prebirth year, time spent in the workplace is below seven months in all postbirth years. Interestingly, adverse PL effects on return to work do not translate into lower employment rates. Whereas there is a clear short-run employment disadvantage of treated mothers compared to control mothers in the second year after the 1990 birth, employment is basically the same from the third year onward. Return-to-work

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patterns can be reconciled with employment results as follows. Women eligible for short parental leaves who are planning a further child return to work in the short run temporarily to gain access to renewed parental leave. In contrast, women eligible for long parental leaves can exploit the renewal option and do not have to return. This behavioral pattern explains simultaneously the fact that the fraction ever returning to work is lower in the treated group but long-run employment in months 37–120 remains unchanged. Basically, extending parental leave reduces short-run temporary return to work but does not affect longer-run labor supply decisions. Figure VD displays the evolution of average labor earnings for the two groups. Again, earnings patterns are strikingly asymmetric in periods covering a first-child birth. Whereas women earn about 33 euros per calendar day before birth, mothers of newborn children earn less than 30 euros in all ten postbirth years. In terms of assessing the effects of extended PL on earnings, Figure VD shows that prebirth average earnings are identical between June and July 1990 mothers but diverge strongly immediately after they give birth. Earnings are lower for treated women in the first three years after the 1990 birth. From year four onward, however, treated mothers earn slightly more than control mothers. The positive medium-run earnings effect of extended leave could be driven by various channels: participation in work, length of work, selection into work, and a genuine behavioral effect (more hours, better jobs due to promotions, etc.). Long-run employment results (months 37–120) suggest that the joint effects of participation and length of work are close to zero. There is also a small but insignificant composition effect: women with high prebirth wages return to the job earlier with extended leave than with short parental leave. This implies that the somewhat higher long-run earnings of July 1990 mothers are due to a genuine behavioral effect. Although this effect is small, it seems that those mothers who return after extended leaves work somewhat more and/or are employed in relatively better paid jobs than mothers who return after shorter leaves. Table V uses linear regression to assess the causal effects of the 1990 PL extension for the current child on short- and long-run labor market outcomes. Columns (1)–(5) assess the sensitivity of the results in the same way as the corresponding columns in Table IV on short-run fertility. Treated mothers are significantly less likely to have returned to work three years

PARENTAL LEAVE, FERTILITY, AND RETURN TO WORK

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TABLE V LABOR MARKET EFFECTS OF PL DURATION FOR THE CURRENT CHILD, JULY 1990 (24 MONTHS PL) VS. JUNE 1990 (12 MONTHS PL) Base

Controls Half-window Anticipation

−.109 −.11 −.109 (.013)∗∗∗ (.012)∗∗∗ (.017)∗∗∗ [.564] [.564] [.567] Return to work −.03 −.027 −.046 0–120 months (.009)∗∗∗ (.009)∗∗∗ (.013)∗∗∗ [.847] [.847] [.85] Employment −.999 −1.02 −1.001 0–36 months (.073)∗∗∗ (.071)∗∗∗ (.1)∗∗∗ [2.185] [2.185] [2.194] Employment .07 .074 .047 37–120 months (.111) (.109) (.155) [5.136] [5.136] [5.202] Earnings −2.739 −2.998 −3.156 0–36 months (.335)∗∗∗ (.304)∗∗∗ (.429)∗∗∗ [10.159] [10.159] [10.223] Earnings .852 .545 .195 37–120 months (.563) (.522) (.74) [20.759] [20.759] [21.014] Return to work 0–36 months

Observations

6,180

6,180

3,045

Placebo

−.105 .009 (.014)∗∗∗ (.012) [.561] [.619] −.023 .009 (.01)∗∗ (.009) [.845] [.83] −1.031 −.051 (.081)∗∗∗ (.083) [2.183] [2.908] .09 −.09 (.124) (.111) [5.107] [4.889] −3.044 −.821 (.348)∗∗∗ (.321)∗∗ [10.096] [12.155] .522 −.862 (.598) (.518)∗ [20.658] [19.39] 4,757

6,150

Source: ASSD, own calculations. Sample: PL-eligible women giving birth to their first child in June 1–30 (12 months PL) or July 1–30 (24 months PL) in the year 1990. Notes: This table reports the July 1990 parameter estimate in a linear regression/linear probability model comparing postbirth labor market outcomes of mothers giving birth to their first child in June and July 1990. Standard error in parentheses; mean of dependent variable in brackets. Employment and earnings are set to zero for women who do not hold a job. Zeros are included in all our analyses. ∗ (∗∗ ,∗∗∗ ) denote significance at the 10% (5%,1%) level respectively. Inference based on Huber–White standard errors. Base: July (24 months PL) vs. June (12 months PL). Controls: adds controls (Table II). Half-window: June 16–July 15. Anticipation: June 1–23 and July 8–30. Placebo: June 1987 (12 months PL) vs. July 1987 (12 months PL).

after giving birth to their first in July 1990 (row (1)) and the difference is quantitatively large: An additional 10 of 100 mothers have not returned to work within three years after the 1990 birth. This difference in return to work shrinks over time but a significant three-percentage point difference still remains even after ten years (row (2)). Interestingly, although treated mothers work about one month per year less during the first three years after giving birth (row (3)), there are no long-run employment differences between treated and controls. During months 37–120 after birth, average employment is the same for the two groups (row (4)). A similar finding obtains for earnings per calendar month. Treated mothers earn about three euros less from working on the average day of the three first postbirth years (row (5));

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there is even a positive albeit statistically insignificant earnings differential between treated and control mothers four to ten years after giving birth (months 37–120, row (6)). Thus, although the 1990 reform slightly reduced the number of women ever returning to work, staying out of work for an extended period does not appear to harm employment and earnings of treated mothers. IV.C. Heterogeneous Responses: Income and Occupation Austrian PL provisions offer job protection and a financial transfer during the time a mother stays off work. Although both types of policies reduce the costs of having children, they target quite different dimensions of these costs. Cash transfers help extend the time a mother can stay home with her baby without running into financial distress. This is more likely to help low-income parents. In contrast, job protection extends the time a mother can spend with her baby without losing her job. This is more likely to help career-oriented women, for whom job loss may be very costly. Table VI explores whether extending PL duration affects high- and low-wage women differently. A mother is considered “Hi Wage” if daily earnings on the job held exactly one year prior to giving birth (prebirth job) exceeds the median of daily prebirth earnings (37.12 euros per day worked); and a mother is considered “Lo Wage” otherwise. The flat rate transfer of 340 euros translates into a low replacement rate for high-wage women and a high replacement rate for low-wage women. Moreover, taking occupation as a proxy for the extent of job-specific skills, we also investigate whether the responses for women holding a white-collar occupation one year prior to birth (column (4)) were different from the responses of women holding a blue-collar job (column (5)).24 For comparison purposes, column (1) repeats the baseline result (column (1) of Tables IV and V).25 Results indicate that the 1990 PL reform led to a significant increase in short-run fertility for both high- and low-wage women (Table VI, columns (2) and (3)). Excess short-run fertility amounts 24. Women who did not hold a job one year prior to giving birth to the 1990 child are allocated to the low-wage/blue-collar categories. Results remain qualitatively unchanged if we exclude nonemployed women. 25. Clearly, such rough sample splits along one dimension are likely to be contaminated by imbalance along other dimensions. For instance, 62% of highwage women hold a white-collar occupation, whereas only 44% of all women hold a white-collar occupation. Nevertheless, splitting the sample along these two dimensions allows discussing the relevance of earnings replacement and value of job protection.

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TABLE VI HETEROGENEOUS EFFECTS OF PL DURATION FOR THE CURRENT CHILD (1990 REFORM) All

Hi wage

Lo wage

Wt col

Bl col

(A) Fertility .049 .036 .068 .055 .048 (.012)∗∗∗ (.017)∗∗ (.017)∗∗∗ (.018)∗∗∗ (.016)∗∗∗ [.345] [.351] [.339] [.349] [.342] Additional birth .035 .016 .054 .034 .036 0–120 months (.012)∗∗∗ (.017) (.017)∗∗∗ (.018)∗ (.016)∗∗ [.617] [.616] [.618] [.611] [.622] Additional birth −.026 −.033 −.018 −.018 −.031 0–16 months (.006)∗∗∗ (.009)∗∗∗ (.009)∗ (.009)∗∗ (.009)∗∗∗ [.066] [.06] [.071] [.058] [.072] Additional birth .084 .08 .089 .095 .078 17–28 months (.01)∗∗∗ (.014)∗∗∗ (.014)∗∗∗ (.015)∗∗∗ (.013)∗∗∗ [.193] [.203] [.183] [.206] [.183] Additional birth −.021 −.031 −.013 −.042 −.008 29–120 months (.012)∗ (.017)∗ (.017) (.018)∗∗ (.016) [.36] [.353] [.366] [.348] [.369] (B) Labor market outcomes Return to work −.11 −.103 −.124 −.137 −.094 0–36 months (.012)∗∗∗ (.017)∗∗∗ (.018)∗∗∗ (.018)∗∗∗ (.017)∗∗∗ [.564] [.632] [.496] [.647] [.5] Return to work −.027 −.028 −.029 −.039 −.018 0–120 months (.009)∗∗∗ (.012)∗∗ (.014)∗∗ (.012)∗∗∗ (.013) [.847] [.874] [.82] [.889] [.814] Employment −1.023 −1.186 −1.15 −1.054 −.556 0–36 months (.114)∗∗∗ (.101)∗∗∗ (.114)∗∗∗ (.102)∗∗∗ (.172)∗∗∗ [2.594] [1.984] [2.659] [1.913] [1.505] Employment .2 −.125 .071 .026 .238 37–120 months (.173) (.162) (.171) (.163) (.286) [5.88] [4.762] [5.95] [4.681] [3.92] Earnings −3.548 −2.7 −3.914 −2.347 −2.356 0–36 months (.56)∗∗∗ (.354)∗∗∗ (.564)∗∗∗ (.335)∗∗∗ (.748)∗∗∗ [14.247] [7.183] [13.921] [7.454] [6.508] Earnings 1.142 .311 .45 .895 −.403 37–120 months (.927) (.64) (.923) (.614) (1.465) [26.467] [16.139] [26.336] [16.183] [17.179] Additional birth 0–36 months

Observations

6,180

3,087

3,093

2,705

3,475

Source. ASSD, own calculations. Sample covers women giving birth to their first child in June 1–30 (12 months PL) or July 1–30 (24 months PL) in the year 1990. Notes. This table reports the “July 1990” parameter estimate in linear regressions/linear probability models comparing postbirth labor market outcomes of mothers giving birth to their first child in June and July 1990. Standard error in parentheses; mean of dependent variable in brackets. Employment and earnings are set to zero for women who do not hold a job. Zeros are included in all our analyses. ∗ (∗∗ ,∗∗∗ ) denote significance at the 10% (5%,1%) level, respectively. Inference based on Huber–White standard errors. All: repeats column (2) of Table 4 and column (2) of Table 5 for comparison. Hi/lo wage: median splits for prebirth daily income; Wt/bl col: splits by white- and blue-collar occupation; wage and occupation measured one year prior to birth; women who are not employed one year prior to birth are allocated to the low-wage and blue-collar categories.

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to almost four children per 100 high-wage mothers and to almost seven children per 100 low-wage mothers (row (1)). This result suggests that taking advantage of automatic renewal is less attractive to high-wage women than to low-wage women. Long-run fertility effects disappear for women with high earnings power (1.6-percentage-point difference) but not for women whose prebirth earnings power lies below the median (6.4-percentage-point difference). Rows (3)–(5) in Table VI assess the timing of fertility. High-wage women delay fertility more than low-wage women up to month 16 (when control women also have access to automatic renewal, row (3)). From month 17 to 28 (when the treated have access to automatic renewal but controls do not; row (4)), treated high- and low-wage women display excess fertility of eight and nine children per 100 women, respectively. In the period following month 29, high-wage (but not low-wage) controls have significantly higher fertility (row (5)). In sum, excess fertility for low-wage women results from not delaying initial fertility by the treated and from not catching up by the controls after automatic renewal has lapsed. These differences in fertility timing are likely to be explained by differences in work attachment between high-wage women (63% return to work within three years, row (6), number in brackets) and low-wage women (only 50% return to work within three years, row (6), number in brackets). Because returning to work between children induces a wider space between first birth and second birth, offering automatic renewal compresses the space between children more strongly for the group with a larger ex ante space between births. Interestingly, although there are significant differences in fertility responses between high- and low-wage women, the PL reform affects employment and earnings of high- and low-wage women to a similar extent (Panel B in Table VI). The decrease in return-to-work probabilities is somewhat smaller for high-wage women than for low-wage women in the short run but almost identical in the long run (rows (6) and (7)). The reduction in employment is identical for both groups in the short run and in the long run (rows (8) and (9)). Short-run earnings reductions are greater for high-wage women than for low-wage women (row (10)). However, because employment responses are nearly identical, differential earnings responses arguably reflect ex ante differences in earnings power rather than differential earnings consequences of extending PL duration. There are no significant

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long-run earnings consequences of extended career interruptions (row (11)). Turning to fertility results by occupation reveals that shortrun and long-run fertility responses are quite similar for whitecollar and blue-collar women (columns (4) and (5), rows (1) and (2)): three additional children within 10 years. Yet even though the long-run result is similar, the time pattern of the responses differs somewhat between white- and blue-collar women (rows (3)–(5)). Both blue- and white-collar women delay second-child fertility in the period, giving both treated and control women access to automatic renewal (row (3)); both blue- and white-collar women eligible for extended PL concentrate births of second children in the period with access to automatic renewal (row (4)). Yet whitecollar control women catch up to treated women more strongly than blue-collar control women in the postrenewal period (row (5)). This pattern of results is, again, consistent with differential postbirth labor market attachment between white-collar women (65% return to job within three years, row (6)) and blue-collar women (50% return to job within three years, row (6)). Although occupation does not appear to mediate fertility responses of extended leave strongly, occupation is important for the labor market consequences of extended PL (Panel B in Table VI). About 14 of 100 treated white-collar women do not return to work within three years because of extended PL. In contrast, only 9 of 100 blue-collar women delay return to work in the short run (row (6)). Long-run return to work of blue-collar women is not affected, whereas almost 4 of 100 women in the white-collar group do not return to work within ten years (row (7)). Extended PL reduces employment and earnings more strongly for white-collar women than for blue-collar women in the short run (rows (8) and (10)). However, in the long run PL-induced career interruptions are not harmful (rows (9) and (11)). In sum, the results suggest that labor market outcomes of white-collar women are more sensitive to extending PL. We conclude that the finding of higher fertility responses for low-wage women than for high-wage women suggests that cash transfers (through their impact on replacement ratios) are important determinants of fertility responses. Finding that there are no differences in fertility responses between blue- and whitecollar workers suggests that the job protection provisions are of importance for white-collar women. White-collar women have, on average, higher incomes than blue-collar women and, on the basis

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of their lower average replacement ratios, they should also react less strongly to the PL extension. It seems that lower replacement ratios are compensated by the benefits of job protection. This interpretation is consistent with the idea that internal labor markets and career concerns are more important for white-collar jobs but less relevant for blue-collar workers.26 V. EXTENDING PL DURATION FOR THE FUTURE CHILD This section assesses the effect of extended leave on the future child (“future-child PL effect”).27 To identify this effect we compare the June 1990 cohort (eligible for a one-year PL for the current child but for a two-year PL for the future child) to the June 1987 cohort (one-year PL for the current child and one-year PL for any second child born within three years after the first birth). The June 1990 to June 1987 contrast may be biased due to cohort effects and time trends. Hence Table VII presents a range of supplementary analyses that shed light on the plausibility of the key identifying assumption of identical ex ante fertility plans and labor market trajectories for two cohorts. Assessing the sensitivity of our results to time trends, we provide (i) a placebo estimate of the reform among PL-ineligible mothers (column (3)), (ii) estimates of a three-year postreform time trend that compares July 1993 mothers to July 1990 mothers (column (4)), and (iii) estimates of a two-year prereform time trend that compares June 1987 mothers to June 1985 mothers (column (5)).28 Moreover, 26. Our results also relate to the existing literature on the trade-off between fertility and labor supply. In contrast to our long-run results, Angrist and Evans (1998) find that U.S. women with two children worked less than women with just one child in 1990. There are at least two reasons for the differences in our results. First, Angrist and Evans (1998) do not condition on time since birth. Their finding of a reduction in labor for the average mother could be consistent with a temporary reduction in labor supply in the short run but no reduction of labor supply in the long run—the situation we document for Austria. Second, Austria and the United States differ in terms of female labor force participation. In 1994, the earliest year with comparable OECD statistics, 65% of American working-age women participated in the labor market whereas only 59% of Austrian women did. Because these participation differences presumably reflect differences in the speed of postbirth labor market reentry, a second child is likely to crowd out more employment in the United States than in Austria. Thus, the fertility effects of extended parental leave may come at higher long-run employment cost in countries with high postbirth labor market participation. 27. Note that, although the change in the PL system could in principle also affect first-child, third-child fertility, and so forth, we confine our analysis to the analysis of second-child fertility because for this parity the effects should be most pronounced. 28. The prereform time trend cannot be three years because our ASSD extract starts in 1985.

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PARENTAL LEAVE, FERTILITY, AND RETURN TO WORK TABLE VII THE EFFECT OF PL DURATION FOR THE FUTURE CHILD (1990 REFORM) Base Additional birth

Return to work

Employment

Earnings

Controls

Ineligible

Posttrend

Pretrend

(A) Short-run effects (0–36 months after birth) .069 .068 −.019 −.006 (.012)∗∗∗ (.012)∗∗∗ (.051) (.012) [.286] [.286] [.236] [.364] −.002 −.003 −.053 .008 (.013) (.012) (.038) (.012) [.622] [.622] [.135] [.524] −.183 −.164 −.336 −.103 (.084)∗∗ (.083)∗∗ (.216) (.058)∗ [2.799] [2.799] [.583] [1.71] −.181 −.229 .512 −.75 (.361) (.331) (1.927) (.282)∗∗∗ [11.68] [11.68] [9.031] [8.974]

.001 (.011) [.25] .018 (.012) [.614] −.045 (.086) [2.909] −.589 (.325)∗ [11.849]

(B) Medium-run effects (37–72 months after birth) Additional birth −.019 −.014 −.072 −.011 (.011)∗ (.011) (.047) (.01) [.21] [.21] [.182] [.179] Return to work .028 .024 .011 .022 (.009)∗∗∗ (.01)∗∗ (.043) (.011)∗∗ [.158] [.158] [.156] [.227] Employment −.172 −.191 −.492 .315 (.123) (.122) (.397) (.117)∗∗∗ [4.585] [4.585] [1.599] [4.77] Earnings −.13 −.325 −.252 .441 (.547) (.523) (2.285) (.524) [17.015] [17.015] [13.084] [18.654] Observations

5,977

5,977

274

6,406

.033 (.011)∗∗∗ [.205] .005 (.009) [.144] −.007 (.125) [4.688] .053 (.498) [16.814] 5,892

Source: ASSD, own calculations. Sample covers eligible and ineligible women giving birth to their first child in June or July of the years listed in the notes. Notes: This table reports the “After” parameter estimate in linear regressions/linear probability models comparing postbirth labor market outcomes of mothers giving birth to their first child in June or July of various years. Standard error in parentheses; mean of dependent variable in brackets. Employment and earnings are set to zero for women who do not hold a job. Zeros are included in all our analyses. ∗ (∗∗ ,∗∗∗ ) denote significance at the 10% (5%,1%) level, respectively. Inference based on Huber–White standard errors. Base: eligible, June 1990 (24 months PL for second child, 12 months PL for first child) and June 1987 (12 months PL for first and second child). Controls: adds controls (Table II) to Base. Ineligible: ineligible with controls, June 1990 vs. June 1987. Posttrend: eligible with controls, June 1993 vs. July 1990. Pretrend: eligible with controls, June 1987 vs. June 1985.

Table VII distinguishes between months 0–36 after the first birth (where second-child duration differs) and months 37–72 after the first birth (where second-child duration is identical).29 29. Note that the inverse pattern of eligibility holds for the pre- and postreform trend cohorts. Prereform cohorts are eligible for the same second-child PL duration during months 0–36 after the first birth, but PL duration differs

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Results indicate that the future-child PL effect is quantitatively important (Table VII). Short-run fertility is 7 percentage points higher for June 1990 mothers than for June 1987 mothers (Panel A of Table VII, row (1)). Adding prebirth characteristics does not change this result. We do not find that PL-ineligible June 1990 women tend to give birth to more future children than PL-ineligible June 1987 women (column (3)). We also do not find a high importance of time trends. Higher-order fertility is similar between July 1993 and July 1990 mothers (column (4)) and is also similar between between June 1987 and June 1985 mothers (column (5)). Interestingly, extending leave for the future child does not appear to affect labor market outcomes to any great extent (rows (2)–(4) of Panel A in Table VII). Return to work and earnings do not display statistically significant effects (rows (2) and (4)). Although work experience is reduced significantly, estimates indicate that treated mothers work 0.2 months per year less.30 Panel B in Table VII shows that the short-run fertility effect persists in the medium run. Our results indicate that there is no significant catch-up of control mothers during months 36–72. Although June 1990 mothers give birth to slightly fewer second children than June 1987 mothers, the effect is quite small (1.4 children per 100 women) and not statistically significant. Furthermore, results on PL-ineligible women are insignificant. The last two columns of Panel B of Table VII show time-trend results. More precisely, these results measure time trends plus futurechild differences in PL duration in the medium run. For instance, pretrend estimates compare June 1987 mothers who are covered by a two-year leave in the medium run (months 36–72 cover the period from July 1990 to June 1993) and June 1985 mothers who are covered by a one-year leave for the first two years and a two-year leave for the third year (months 36–72 cover the period from July 1988 to June 1991). Consistent with this pattern of PL eligibility, during months 37–72 after the first birth. In the prereform time trend analysis, for instance, second children of June 1987 mothers are eligible for 24 months of PL duration in months 37–60 after the first birth, whereas second children of June 1985 mothers are still only eligible for 12 months of PL duration. In months 61–72 after the first birth, both second children of both cohorts are eligible for 24 months of PL duration. 30. Note that employment estimates could be spurious because there is a significantly negative postreform trend in employment (column (3), Table VII). Moreover, the coefficients on labor market outcomes are very imprecise, so the data are consistent with zero effects but also with large negative effects on employment and earnings.

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the future-child PL effect is 3 percentage points higher for the June 1987 cohort than for the June 1985 cohort.31 Posttrend estimates capture the fact that second-child leave is reduced from 24 months to 18 months for July 1993 mothers, whereas July 1990 mothers still have access to a two-year leave. Point estimates are quantitatively consistent with the future-child effects estimated above but are not statistically significant. Except for a small increase in return to work, we do not find large future-child PL effect on medium-run labor market outcomes. What can we learn from the current-child and future-child effects? Recall that the current-child estimates compare families with different benefits (in terms of transfers and time for care) for the current child but identical benefits for the future child. Abstracting from automatic renewal, extending parental leave should crowd out short-run postbirth labor market participation but leave fertility decisions unaffected. In contrast, futurechild estimates compare families with different benefits for the future child but identical benefits for the current child. Extending parental leave should affect fertility decisions but not crowd out short-run postbirth labor market participation. Turning to results, we find that extending parental leave for the current child reduces short-run postbirth work experience by one month, whereas the corresponding future-child effect is about one-fifth of a month. Thus, the pattern of labor market results is in line with the pattern of incentives. In contrast, whereas extending parental leave for the future child boosts short-run fertility by 7 percentage points, doing so for the current child also increases short-run fertility by 5 percentage points. Thus, fertility results suggest that access to automatic renewal is valuable; indeed almost as valuable as extended leave for a future child. VI. REDUCING PL DURATION This section discusses the effects of the 1996 reduction of PL. Results comparing mothers giving birth to their first child in July 1996 (eligible for eighteen months of leave) with mothers 31. The effect is about one-half of the short-run estimate in row (1), column (2), of Table VII. This lower importance of extended leave for a future child can probably be explained by two facts. First, the prereform control group of June 1985 mothers gets access to extended leave in the period 61–72 months after birth. Second, mothers might be less responsive to extended leave three to six years after birth than zero to three years after birth.

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TABLE VIII THE EFFECTS OF REDUCING PL DURATION FOR THE CURRENT CHILD (1996 REFORM): JUNE 1996 (24 MONTHS PL) VS. JULY 1996 (18 MONTHS PL) Base

Controls

Half-window Anticipation

(A) Fertility −.001 −.025 (.012) (.017) [.321] [.331] .028 .023 (.009)∗∗∗ (.013)∗ [.152] [.157] −.029 −.032 (.008)∗∗∗ (.011)∗∗∗ [.103] [.109] .005 −.013 (.007) (.01) [.077] [.076]

.003 (.014) [.309] .022 (.01)∗∗ [.148] −.028 (.009)∗∗∗ [.098] .013 (.008)∗ [.076]

(B) Labor market outcomes .051 .053 .058 (.012)∗∗∗ (.012)∗∗∗ (.017)∗∗∗ [.661] [.661] [.66] Employment .675 .684 .703 0–36 months (.069)∗∗∗ (.067)∗∗∗ (.095)∗∗∗ [2.456] [2.456] [2.46] Earnings 2.65 2.697 2.295 0–36 months (.367)∗∗∗ (.321)∗∗∗ (.444)∗∗∗ [12.302] [12.302] [12.148]

.047 (.014)∗∗∗ [.663] .676 (.076)∗∗∗ [2.487] 3.045 (.371)∗∗∗ [12.469]

Additional birth −.003 0–36 months (.012) [.321] Additional birth .028 0–22 months (.009)∗∗∗ [.152] Additional birth −.03 23–28 months (.008)∗∗∗ [.103] Additional birth .004 29–36 months (.007) [.077] Return to work 0–36 months

Placebo −.021 (.012)∗ [.349] −.021 (.009)∗∗ [.151] .001 (.008) [.122] −.003 (.007) [.084] .003 (.012) [.536] .057 (.056) [1.729] −.267 (.264) [9.135]

Source: ASSD, own calculations. Sample: PL-eligible women giving birth to their first child in June 1–30 (24 months PL) or July 1–30 (18 months PL) in the year 1996. Notes. This table reports the “July 1996” parameter estimate in linear regressions/linear probability models comparing outcomes of mothers giving birth to their first child in June or July 1996. Standard error in parentheses; mean of dependent variable in brackets. Employment and earnings are set to zero for women who do not hold a job. Zeros are included in all our analyses. ∗ (∗∗ ,∗∗∗ ) denote significance at the 10% (5%,1%) level, respectively. Inference based on Huber–White standard errors. Base: July (18 months PL) vs. June (24 months PL). Controls: adds controls (Table II). Half-window: June 16–July 15. Anticipation: June 1–23 and July 8–30. Placebo: June 1993 (24 months PL) vs. July 1993 (24 months PL).

giving birth to their first child in June 1996 (eligible for 24 months of leave) indicate, first, that the number of children born within three years is not affected by the partial reversal of the 1990 policy change (Table VIII, row (1)). Second, although the number of children is unaffected, the timing of second-child fertility is significantly altered. There is excess future-child fertility of about 3% before month 22 (when both treated and control mothers have access to PL renewal) and a decrease of the same order of magnitude during months 23–28 (when the treated lose access to PL renewal; Table VIII, rows (2)–(4)). Reducing PL duration strongly affects

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the timing of births but not the number of children being born because, arguably, mothers could take advantage of PL renewal before and after the 1996 reform, whereas the 1990 reform represents a switch from a system where PL renewal was not feasible to a system where it become highly attractive.32 Third, reducing PL duration affects return to work, employment, and earnings considerably. In the short run, 5 of 100 women return to work within three years who would not with extended leave (Table VIII, row (5)). Women on the 18-month leave also work on the average about 0.7 months more per year and earn 3 euros more per day more than women with access to a two-year PL (Table VIII, rows (6) and (7)). Notice that the six-month reduction in PL duration affects return to work, employment, and earnings by about half as much (in absolute value) as the twelvemonth extension of PL duration in 1990. Hence results for the 1996 reform confirm that that PL duration for the current child has a strong impact on short-run labor market outcomes. VII. CONCLUSIONS The focus of this paper is the relevance of the duration of job-protected, paid PL for higher-order fertility and labor market outcomes of working women. The empirical analysis is based on a 1990 extension of PL duration from one year to two years and on a 1996 reduction of PL from two years to eighteen months. We find that extending PL affects fertility via two channels. First, increasing leave for the current child opens up the possibility of renewing PL benefits without going back to work. The resulting tighter spacing of births gives rise to both excess shortrun fertility (5 additional children per 100 women within three years) and excess long-run fertility (3 additional children per 100 women within ten years). Moreover, increasing leave for the future child reduces the cost of care for that child, inducing mothers to give birth to about 7 additional second children per 100 women. This means that extending job-protected paid PL with automatic renewal from one year to two years induces mothers to give birth to about 12 additional children per 100 women. Regarding the labor market consequences of extended leave, we find that most 32. We also investigate the effects of reducing PL duration for the future child by comparing mothers who give birth to a first child in June 1996 to mothers who give birth to a first child in June 1993. Findings indicate that reduced leave on the future child is associated with a decrease in short-run fertility.

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mothers exhaust the full duration of their leaves; that return to work is substantially delayed even after PL has been exhausted; and that prolonging leave leads to significant short-run reductions in employment and earnings but only minor effects in the long run. Fertility and labor market responses are heterogeneous with respect to earnings and occupation on the prebirth job. This is consistent with both replacement rates and job protection mediating the effects of extended leave on fertility and labor market responses. Finally, our findings indicate that the 1996 reduction of PL duration compresses the space between first and second births, but does not have a significant effect on the number of second children born within three years. Moreover, the labor market responses closely mirror those of the 1990 extension of PL duration. Providing causal evidence on how Austrian policy changes affect fertility and labor market careers is interesting and important for the non-Austrian public. In many countries fertility levels have fallen strongly and the question of whether PL policies can help to increase fertility is hotly debated. Our results show that such policies can have a quite strong impact and that both transfers and job protection matter for fertility responses. Our analysis of labor market effects addresses the issue of whether too generous PL rules might have a negative impact on mothers’ subsequent work careers—an issue of paramount importance. We think the Austrian case is interesting in this respect because the 1990 PL reform was a move from a system of average generosity (by current OECD standards) to a system of high generosity. Although we do find that the PL extension increases the proportion of women who never return to work, we do not find detrimental effects on employment and earnings over an extended time horizon. Hence we conclude that generous PL policies do not necessarily harm women’s long-run labor market outcomes. FACULTY OF BUSINESS AND ECONOMICS, UNIVERSITY OF LAUSANNE, CEPR, IFAU, IZA, CESIFO, AND IEW INSTITUTE FOR EMPIRICAL ECONOMIC RESEARCH, UNIVERSITY OF ZURICH, CEPR, IZA, AND CESIFO

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Angrist, Joshua D., and William N. Evans, “Children and Their Parents’ Labor Supply: Evidence from Exogenous Variation in Family Size,” American Economic Review, 88 (1998), 450–477. Averett, Susan L., and Leslie A. Whittington, “Does Maternity Leave Induce Births?” Southern Economic Journal, 68 (2001), 403–417. Baker, Michael, Jonathan Gruber, and Kevin Milligan, “Universal Childcare, Maternal Labor Supply, and Family Well-Being,” Journal of Political Economy, 116 (2008), 709–745. Baker, Michael, and Kevin Milligan, “Maternal Employment, Breastfeeding, and Health: Evidence from Maternity Leave Mandates,” Journal of Health Economics, 27 (2008), 871–887. Baum, Charles L., “The Effect of State Maternity Leave Legislation and the 1993 Family and Medical Leave Act on Employment and Wages,” Labour Economics, 10 (2003), 573–596. Berger, Lawrence M., Jennifer Hill, and Jane Waldfogel, “Maternity Leave, Early Maternal Employment and Child Health and Development in the US,” Economic Journal, 115 (2005), F29–F47. Berger, Lawrence M., and Jane Waldfogel, “Maternity Leave and the Employment of New Mothers in the United States,” Journal of Population Economics, 17 (2004), 331–349. Bj¨orklund, Anders, “Does a Family-Friendly Policy Raise Fertility Levels?” Swedish Institute for European Studies Report No. 3, 2007. Dickert-Conlin, Stacy, and Amitabh Chandra, “Taxes and the Timing of Births,” Journal of Political Economy, 107 (1999), 161–177. Dustmann, Christian, and Uta Sch¨onberg, “The Effect of Expansions in Maternity Leave Coverage on Children’s Long-Term Outcomes,” IZA Discussion Paper No. 3605, 2008. Gans, Joshua S., and Andrew Leigh, “Born on the First of July: An (Un)natural Experiment in Birth Timing,” Australian National University Discussion Paper No. 529, 2006. Hahn, Jinyong, Petra Todd, and Wilbert van der Klaauw, “Identification and Estimation of Treatment Effects with a Regression–Discontinuity Design,” Econometrica, 69 (2001), 201–209. ˚ Schøne, “Cash for Care: More Work for the Stork?” Mimeo, Hardoy, Ines, and Pal Institute for Social Research Oslo, 2005. Hoem, Jan M., “Public Policy as the Fuel of Fertility: Effects of a Policy Reform on the Pace of Childbearing in Sweden in the 1980s,” Acta Sociologica, 36 (1993), 19–31. Hoynes, Hilary W., “Work, Welfare, and Family Structure,” in Fiscal Policy: Lessons From Economic Research, Alan B. Auerbach, ed. (Cambridge, MA: MIT Press, 1997). Joyce, Theodore, Robert Kaestner, Sanders Korenman, and Stanley Henshaw, “Family Cap Provisions and Changes in Births and Abortions,” NBER Working Paper No. W10214, 2004. Kearney, Melissa Schettini, “Is There an Effect of Incremental Welfare Benefits on Fertility Behavior? A Look at the Family Cap,” Journal of Human Resources, 39 (2004), 295–325. Klerman, Jacob A., and Arleen Leibowitz, “Labor Supply Effects of State Maternity Leave Legislation,” in Gender and Family Issues in the Workplace, Francine Blau and Ron Ehrenberg, eds. (New York: Russell Sage Press, 1997). ——, “Job Continuity among New Mothers,” Demography, 36 (1999), 145– 155. ¨ Lalive, Rafael, and Josef Zweimuller, “Parental Leave and Mothers’ Post-Birth Careers,” Mimeo, University of Lausanne, 2007. Laroque, Guy, and Bernard Salani´e, “Fertility and Financial Incentives in France,” CEPR Discussion Paper No. 4064, 2005. Milligan, Kevin, “Subsidizing the Stork: New Evidence on Tax Incentives and Fertility,” Review of Economics and Statistics, 87 (2005), 539–555. Moffitt, Robert A., “Profiles of Fertility, Labour Supply and Wages of Married Women: A Complete Life-Cycle Model,” Review of Economic Studies, 51 (1984), 263–278.

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——, “The Effect of Welfare on Marriage and Fertility,” in Welfare, the Family, and Reproductive Behavior, Robert A. Moffitt, ed. (Washington, DC: National Academy Press, 1998). Piketty, Thomas, “L’Impact de l’Allocation Parentale d’Education sur l’Activit´e Feminine et la Fecondit´e, 1982–2002,” CEPREMAP Working Papers (Couverture Orange) No. 2003-09, 2003. Rosenzweig, Mark R., “Welfare, Marital Prospects, and Nonmarital Childbearing,” Journal of Political Economy, 107 (1999), S3–S32. Ruhm, Christopher, “The Economic Consequences of Parental Leave Mandates: Lessons from Europe,” Quarterly Journal of Economics, 113 (1998), 285–317. Ruhm, Christopher, and Jackqueline L. Teague (1997) “Parental Leave Policies in Europe and North America,” in Gender and Family Issues in the Workplace, Francine D. Blau and Ronald Ehrenberg, eds. (New York: The Russell Sage Foundation Press, 1997). Sch¨onberg, Uta, and Johannes Ludsteck, “Maternity Leave Legislation, Female Labor Supply, and the Family Wage Gap,” IZA Discussion Paper No. 2699, 2007.

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