INTRODUCTION
TO THE SERIES
The aim of the Handbooks in Economics series is to produce Handbooks for various branches of economics, each of which is a definitive source, reference, and teaching supplement for use by professional researchers and advanced graduate students. Each Handbook provides self-contained surveys of the current state of a branch of economics in the form of chapters prepared by leading specialists on various aspects of this branch of economics. These surveys summarize not only received results but also newer developments, from recent journal articles and discussion papers. Some original material is also included, but the main goal is to provide comprehensive and accessible surveys. The Handbooks are intended to provide not only useful reference volumes for professional collections but also possible supplementary readings for advanced courses for graduate students in economics. KENNETH J. ARROW and MICHAEL D. INTRILIGATOR
PUBLISHER'S
NOTE
For a complete overview of the Handbooks in Economics Series, please refer to the listing at the end of this volume.
CONTENTS OF THE HANDBOOK
VOLUME 1A PART 1 - E M P I R I C A L A N D H I S T O R I C A L P E R F O R M A N C E
Chapter 1 Business Cycle Fluctuations in US Macroeconomic Time Series JAMES H. STOCK and MARK W WATSON
Chapter 2 Monetary Policy Shocks: What Have we Learned and to What End? LAWRENCE J. CHRISTIANO, MARTIN EICHENBAUM and CHARLES L. EVANS
Chapter 3 Monetary Policy Regimes and Economic Performance: The Historical Record MICHAEL D. BORDO AND ANNA J. SCHWARTZ
Chapter 4 The New Empirics of Economic Growth STEVEN N. DURLAUF and DANNY T. QUAH PART 2 - M E T H O D S O F D Y N A M I C A N A L Y S I S
Chapter 5 Numerical Solution of Dynamic Economic Models MANUEL S. SANTOS
Chapter 6 Indeterminacy and Sunspots in Macroeconomics JESS BENHABIB and ROGER E.A. FARMER
Chapter 7 Learning Dynamics GEORGE W. EVANS and SEPPO HONKAPOHJA
Chapter 8 Micro Data and General Equilibrium Models MARTIN BROWNING, LARS PETER HANSEN and JAMES J. HECKMAN
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viii PART 3 - M O D E L S O F E C O N O M I C G R O W T H
Chapter 9 Neoclassical Growth Theory ROBERT M. SOLOW
Chapter 10 Explaining Cross-Country Income Differences ELLEN R. McGRATTAN and JAMES A. SCHMITZ, Jr.
VOLUME 1B PART 4 - C O N S U M P T I O N A N D I N V E S T M E N T
Chapter 11 Consumption ORAZIO R ATTANASIO
Chapter 12 Aggregate Investment RICARDO J. CABALLERO
Chapter 13 Inventories VALERIE A. RAMEY and KE;NNETH D. WEST PART 5 - M O D E L S O F E C O N O M I C F L U C T U A T I O N S
Chapter 14 Resuscitating Real Business Cycles ROBERT G. KING AND SERG10 T. REBELO
Chapter 15 Staggered Price and Wage Setting in Macroeconomics JOHN B. TAYLOR
Chapter 16 The Cyclical Behavior of Prices and Costs JULIO J. ROTEMBERG and MICHAEL WOODFORD
Chapter 17 Labor-Market Frictions and Employment Fluctuations ROBERT E. HALL
Chapter 18 Job Reallocation, Employmant Fluctuations and Unemployment DALE T. MORTENSEN and CHRISTOPHER A. PISSARIDES
Contents of the Handbook
Contents of the Handbook
VOLUME 1C PART 6 - F I N A N C I A L M A R K E T S A N D T H E M A C R O E C O N O M Y
Chapter 19 Asset Prices, Consumption, and the Business Cycle JOHN Y. CAMPBELL
Chapter 20 Human Behavior and the Efficiency of the Financial System ROBERT J. SHILLER
Chapter 21 The Financial Accelerator in a Quantitative Business Cycle Framework BEN S. BERNANKE, MARK GERTLER and SIMON G1LCHRIST PART 7 - M O N E T A R Y A N D F I S C A L P O L I C Y
Chapter 22 Political Economics and Macroeconomic Policy TORSTEN PERSSON and GUIDO TABELLINI
Chapter 23 Issues in the Design of Monetary Policy Rules BENNETT T. McCALLUM
Chapter 24 Inflation Stabilization and BOP Crises in Developing Countries GUILLERMO A. CALVO and CARLOS A. VI~GH
Chapter 25 Government Debt DOUGLAS W ELMENDORF AND N. GREGORY MANKIW
Chapter 26 Optimal Fiscal and Monetary Policy V.V CHARI and PATRICK J. KEHOE
ix
PREFACE TO THE HANDBOOK
Purpose The Handbook of Macroeconomics aims to provide a survey of the state of knowledge in the broad area that includes the theories and facts of economic growth and economic fluctuations, as well as the consequences of monetary and fiscal policies for general economic conditions.
Progress in Macroeconomics Macroeconomic issues are central concerns in economics. Hence it is surprising that (with the exception of the subset of these topics addressed in the Handbook of Monetary Economics) no review of this area has been undertaken in the Handbook of Economics series until now. Surprising or not, we find that now is an especially auspicious time to present such a review of the field. Macroeconomics underwent a revolution in the 1970's and 1980's, due to the introduction of the methods of rational expectations, dynamic optimization, and general equilibrium analysis into macroeconomic models, to the development of new theories of economic fluctuations, and to the introduction of sophisticated methods for the analysis of economic time series. These developments were both important and exciting. However, the rapid change in methods and theories led to considerable disagreement, especially in the 1980's, as to whether there was any core of common beliefs, even about the defining problems of the subject, that united macroeconomists any longer. The 1990's have also been exciting, but for a different reason. In our view, the modern methods of analysis have progressed to the point where they are now much better able to address practical or substantive macroeconomic questions - whether traditional, new, empirical, or policy-related. Indeed, we find that it is no longer necessary to choose between more powerful methods and practical policy concerns. We believe that both the progress and the focus on substantive problems has led to a situation in macroeconomics where the area of common ground is considerable, though we cannot yet announce a "new synthesis" that could be endorsed by most scholars working in the field. For this reason, we have organized this Handbook around substantive macroeconomic problems, and not around alternative methodological approaches or schools of thought.
xi
xii
Prefiwe
The extent to which the field has changed over the past decade is considerable, and we think that there is a great need for the survey of the current state ofmacroeconomics that we and the other contributors to this book have attempted here. We hope that the Handbook of Macroeconomics will be useful as a teaching supplement in graduate courses in the field, and also as a reference that will assist researchers in one area of macroeconomics to become better acquainted with developments in other branches of the field. Overview
The Handbook of" Macroeconomics includes 26 chapters, arranged into seven parts. Part 1 reviews evidence on the Empirical and Historical PerJbrmance of the aggregate economy, to provide factual background for tile modeling efforts and policy discussion of the remaining chapters. It includes evidence on the character of business fluctuations, on long-run economic growth and the persistence of crosscountry differences in income levels, and on economic performance under alternative policy regimes. Part 2 on Methods of Dynamic Analysis treats several technical issues that arise in the study of economic models which are dynamic and in which agents' expectations about the future are critical to equilibrium determination. These include methods for the calibration and computation of models with intertemporal equilibria, the analysis of the determinacy of equilibria, and the use of "learning" dynamics to consider the stability of such equilibria. These topics are important for economic theory in general, and some are also treated in the Handbook of Mathematical Economics, The Handbook of Econometrics, and the Handbook of Computational Economics, for example, from a somewhat different perspective. Here we emphasize results - such as the problems associated with the calibration of general equilibrium models using microeconomic studies - that have particular application to macroeconomic models. The Handbook then turns to a review of theoretical models of macroeconomic phenomena. Part 3 reviews Models" of Economic Growth, including both the determinants of long-run levels of income per capita and the sources of cross-country income differences. Both "neoclassical" and "endogenous" theories of growth are discussed. Part 4 treats models of Consumption and Investment demand, from the point of view of intertemporal optimization. Part 5 covers Models" of Economic Fluctuations. In the chapters in this part we see a common approach to model formulation and testing, emphasizing intertemporal optimization, quantitative general equilibrium modeling, and the systematic comparison of model predictions with economic time series. This common approach allows for consideration of a variety of views about the ultimate sources of economic fluctuations and of the efficiency of the market mechanisms that amplify and propagate them. Part 6 treats Financial Markets and the Macroeconomy. The chapters in this part consider the relation between financial market developments and aggregate economic
Preface
xiii
activity, both from the point of view of how business fluctuations affect financial markets, and how financial market disturbances affect overall economic activity. These chapters also delve into the question of whether financial market behavior can be understood in terms of the postulates of rational expectations and intertemporal optimization that are used so extensively in modern macroeconomics-an issue of fundamental importance to our subject that can be, and has been, subject to special scrutiny kn the area of financial economics because of the unusual quality of available data. Finally, Part 7 reviews a number of Monetary and Fiscal Policy issues. Here we consider both the positive theory (or political economics) of government policymaking and the normative theory. Both the nature of ideal (or second-best) outcomes according to economic theory and the choice of simple rules that may offer practical guidance for policymakers are discussed. Lessons from economic theory and from experience with alternative policy regimes are reviewed. None of the chapters in this part focus entirely on international, or open economy, macroeconomic policies, because many such issues are addressed in the Handbook of International Economics. Nevertheless, open-economy issues cannot be separated from closed-economy issues as the analysis of disinflation policies and currency crises in this part of the Handbook of Macroeconomics, or the analysis of policy regimes in the Part I of the Handbook of Macroeconomics make clear.
Acknowledgements Our use of the pronoun "we" in this preface should not, of course, be taken to suggest that much, if any, of the credit for what is useful in these volumes is due to the Handbook's editors. We wish to acknowledge the tremendous debt we owe to the authors of the chapters in this Handbook, who not only prepared the individual chapters, but also provided us with much useful advice about the organization of the overall project. We are grateful for their efforts and for their patience with our slow progress toward completion of the Handbook. We hope that they will find that the final product justifies their efforts. We also wish to thank the Federal Reserve Bank of New York, the Federal Reserve Bank of San Francisco, and the Center for Economic Policy Research at Stanford University for financial support for two conferences on "Recent Developments in Macroeconomics" at which drafts of the Handbook chapters were presented and discussed, and especially to Jack Beebe and Rick Mishkin who made these two useful conferences happen. The deadlines, feedback, and commentary at these conferences were essential to the successful completion of the Handbook. We also would like to thank Jean Koentop for managing the manuscript as it neared completion. Stanford, California Princeton, New Jersey
John B. Taylor Michael Woodford
Chapter 19
A S S E T PRICES, C O N S U M P T I O N , A N D THE BUSINESS CYCLE * JOHN Y. CAMPBELL Harvard University and NBER. Department of Economics, Littauer Center, Harvard University, Cambridge, MA 02138, USA
Contents Abstract Keywords 1. Introduction 2. International asset market data 3. The equity p r e m i u m puzzle 3.1. The stochastic discount factor 3.2. Consumption-based asset pricing with power utility 3.3. The riskfree rate puzzle 3.4. Bond returns and the equity premium and riskfrce rate puzzles 3.5. Separating risk aversion and intertemporal substitution 4. The d y n a m i c s o f asset returns and c o n s u m p t i o n 4.1. Time-variation in conditional expectations 4.2. A loglinear asset pricing framework 4.3. The stock market volatility puzzle 4.4. Implications for the equity premium puzzle 4.5. What does the stock market forecast? 4.6. Changing volatility in stock returns 4.7. What does the bond market forecast? 5. C y c l i c a l variation in the price o f risk 5.1. Habit formation 5.2. Models with heterogeneous agents
1232 1232 1233 1238 1245 1245 1249 1252 1255 1256 1260 1260 1264 1268 1272 1275 1277 1280 1284 1284 1290
* This chapter draws heavily on John Y. Campbell, "Consumption and the Stock Market: Interpreting International Experience", Swedish Economic Policy Review 3:251-299, Autumn 1996. I am grateful to the National Science Foundation for financial support, to Tim Chue, Vassil Konstantinov, and Luis Viceira for able research assistance, to Andrew Abel, Olivier Blanchard, Ricardo Caballero, Robert Shiller, Andrei Shleifer, John Taylor, and Michael Woodford for helpful comments, and to Barclays de Zoete Wedd Securities Limited, Morgan Stanley Capital International, David Barr, Bjorn Hansson, and Paul S6derlind for providing data. Handbook of Mactveconomics, Volume 1, Edited by J.B. lhylor and M. WoodJbrd © 1999 Elsevier Science B.V. All tqghts reserved 1231
1232 5.3. Irrational expectations 6. Some implications for macroeconomics References
J..Y Campbell 1293 1296 1298
Abstract This chapter reviews the behavior of financial asset prices in relation to consumption. The chapter lists some important stylized facts that characterize US data, and relates them to recent developments in equilibrium asset pricing theory. Data from other countries are examined to see which features of the US experience apply more generally. The chapter argues that to make sense of asset market behavior one needs a model in which the market price of risk is high, time-varying, and correlated with the state of the economy. Models that have this feature, including models with habitformation in utility, heterogeneous investors, and irrational expectations, are discussed. The main focus is on stock returns and short-term real interest rates, but bond returns are also considered.
Keywords JEL classification: G12
Ch. 19." Asset Prices, Consumption, and the Business Cycle
1233
1. Introduction
The behavior of aggregate stock prices is a subject of enduring fascination to investors, policymakers, and economists. In recent years stock markets have continued to show some familiar patterns, including high average returns and volatile and procyclical price movements. Economists have struggled to understand these patterns. If stock prices are determined by fundamentals, then what exactly are these fundamentals and what is the mechanism by which they move prices? Researchers, working primarily with US data, have documented a host of interesting stylized facts about the stock market and its relation to short-term interest rates and aggregate consumption: (1) The average real return on stock is high. In quarterly US data over the period 1947.2 to 1996.4, a standard data set that is used throughout this chapter, the average real stock return has been 7.6% at an annual rate. (Here and throughout the chapter, the word return is used to mean a log or continuously compounded return unless otherwise stated.) (2) The average riskless real interest rate is low. 3-month Treasury bills deliver a return that is riskless in nominal terms and close to riskless in real terms because there is only modest uncertainty about inflation at a 3-month horizon. In the postwar quarterly US data, the average real return on 3-month Treasury bills has been 0.8% per year. (3) Real stock returns are volatile, with an annualized standard deviation of 15.5% in the US data. (4) The real interest rate is much less volatile. The annualized standard deviation of the ex post real return on US Treasury bills is 1.8%, and much of this is due to short-run inflation risk. Less than half the variance of the real bill return is forecastable, so the standard deviation of the ex ante real interest rate is considerably smaller than 1.8%. (5) Real consumption growth is very smooth. The annualized standard deviation of the growth rate of seasonally adjusted real consumption of nondurables and services is 1.1% in the US data. (6) Real dividend growth is extremely volatile at short horizons because dividend data are not adjusted to remove seasonality in dividend payments. The annualized quarterly standard deviation of real dividend growth is 28.8% in the US data. At longer horizons, however, the volatility of dividend growth is intermediate between the volatility of stock returns and the volatility of consumption growth. At an annual frequency, for example, the volatility of real dividend growth is only 6% in the US data. (7) Quarterly real consumption growth and real dividend growth have a very weak correlation of 0.06 in the US data, but the correlation increases at lower frequencies to just over 0.25 at a 4-year horizon. (8) Real consumption growth and real stock returns have a quarterly correlation of 0.22 in the US data. The correlation increases to 0.33 at a 1-year horizon, and declines at longer horizons.
1234
J.Y. Campbell
(9)
Quarterly real dividend growth and real stock returns have a very weak correlation of 0.04 in the US data, but the correlation increases dramatically at lower frequencies to reach 0.51 at a 4-year horizon. (10) Real US consumption growth is not well forecast by its own history or by the stock market. The first-order autocorrelation of the quarterly growth rate of real nondurables and services consumption is a modest 0.2, and the log pricedividend ratio forecasts less than 5% of the variation of real consumption growth at horizons of 1 to 4 years. (11) Real US dividend growth has some short-run forecastability arising from the seasonality of dividend payments. But it is not well forecast by the stock market. The log price-dividend ratio forecasts no more than about 8% of the variation of real dividend growth at horizons of 1 to 4 years. (12) The real interest rate has some positive serial correlation; its first-order autocorrelation in postwar quarterly US data is 0.5. However the real interest rate is not well forecast by the stock market, since the log price-dividend ratio forecasts less than 1% of the variation of the real interest rate at horizons of 1 to 4 years. (13) Excess returns on US stock over Treasury bills are highly forecastable. The log price-dividend ratio forecasts 18% of the variance of the excess return at a 1-year horizon, 34% at a 2-year horizon, and 51% at a 4-year horizon. These facts raise two important questions for students of macroeconomics and finance: • Why is the average real stock return so high in relation to the average short-term real interest rate? • Why is the volatility of real stock returns so high in relation to the volatility of the short-term real interest rate? Mehra and Prescott (1985) call the first question the "equity premium puzzle". 1 Finance theory explains the expected excess return on any risky asset over the riskless interest rate as the quantity of risk times the price of risk. In a standard consumptionbased asset pricing model of the type studied by Hansen and Singleton (1983), the quantity of stock market risk is measured by the covariance of the excess stock return with consumption growth, while the price of risk is the coefficient of relative risk aversion of a representative investor. The high average stock return and low riskless interest rate (stylized facts 1 and 2) imply that the expected excess return on stock, the equity premium, is high. But the smoothness of consumption (stylized fact 5) makes the covariance of stock returns with consumption low; hence the equity premium can only be explained by a very high coefficient of risk aversion. Shiller (1982), Hansen and Jagannathan (1991), and Cochrane and Hansen (1992) have related the equity premium puzzle to the volatility of the stochastic discount factor, or equivalently the volatility of the intertemporal marginal rate of substitution of a representative investor. Expressed in these terms, the equity premium puzzle is
I For excellent recent surveys, see Cochrane and l-lansen (1992) or Kocherlakota(1996).
Ch. 19:
Asset Prices, Consumption, and the Business Cycle
1235
that an extremely volatile stochastic discount factor is required to match the ratio of the equity premium to the standard deviation of stock returns (the Sharpe ratio of the stock market). Some authors, such as Kandel and Stambaugh (1991), have responded to the equity premium puzzle by arguing that risk aversion is indeed much higher than traditionally thought. However this can lead to the "riskfree rate puzzle" of Weil (1989). If investors are very risk averse, then they have a strong desire to transfer wealth from periods with high consumption to periods with low consumption. Since consumption has tended to grow steadily over time, high risk aversion makes investors want to borrow to reduce the discrepancy between future consumption and present consumption. To reconcile this with the low real interest rate we observe, we must postulate that investors are extremely patient; their preferences give future consumption almost as much weight as current consumption, or even greater weight than current consumption. In other words they have a low or even negative rate of time preference. I will call the second question the "stock market volatility puzzle". To understand the puzzle, it is helpful to classify the possible sources of stock market volatility. Recall first that prices, dividends, and returns are not independent but are linked by an accounting identity. If an asset's price is high today, then either its dividend must be high tomorrow, or its return must be low between today and tomorrow, or its price must be even higher tomorrow. If one excludes the possibility that an asset price can grow explosively forever in a "rational bubble", then it follows that an asset with a high price today must have some combination of high dividends over tile indefinite future and low returns over the indefinite future. Investors must recognize this fact in forming their expectations, so when an asset price is high investors expect some combination of high future dividends and low future returns. Movements in prices must then be associated with some combination of changing expectations ("news") about future dividends and changing expectations about future returns; the latter can in turn be broken into news about future riskless real interest rates and news about future excess returns on stocks over short-term debt. Until the early 1980s, most financial economists believed that there was very little predictable variation in stock returns and that dividend news was by far the most important factor driving stock market fluctuations. LeRoy and Porter (1981) and Shiller (1981) challenged this orthodoxy by pointing out that plausible measures of expected future dividends are far less volatile than real stock prices. Their work is related to stylized facts 6, 9, and 11. Later in the 1980s Campbell and Shiller (1988), Fama and French (1988a,b, 1989), Poterba and Summers (1988) and others showed that real stock returns are highly forecastable at long horizons. The variables that predict returns are ratios of stock prices to scale factors such as dividends, earnings, moving averages of earnings, or the book value of equity. When stock prices are high relative to these scale factors, subsequent long-horizon real stock returns tend to be low. This predictable variation in stock returns is not matched by any equivalent variation in long-term real interest rates, which are comparatively stable and do not seem to move with the stock market.
1236
J.Y. Campbell
in the late 1970s, for example, real interest rates were unusually low yet stock prices were depressed, implying high forecast stock returns; the 1980s saw much higher real interest rates along with buoyant stock prices, implying low forecast stock returns. Thus excess returns on stock over Treasury bills are just as forecastable as real returns on stock. This work is related to stylized facts 12 and 13. Campbell (1991) uses this evidence to show that the great bulk of stock market volatility is associated with changing forecasts of excess stock returns. Changing forecasts of dividend growth and real interest rates are much less important empirically. The stock market volatility puzzle is closely related to the equity premium puzzle. A complete model of stock market behavior must explain both the average level of stock prices and their movements over time. One strand of work on the equity premium puzzle makes this explicit by studying not the consumption covariance of measured stock returns, but the consumption covariance of returns on hypothetical assets whose dividends are determined by consumption. The same model is used to generate both the volatility of stock prices and the implied equity premium. This was the approach of Mehra and Prescott (1985), and many subsequent authors have followed their lead. Unfortunately, it is not easy to construct a general equilibrium model that fits all the stylized facts given above. The standard model of Mehra and Prescott (1985) gets variation in stock price-dividend ratios only from predictable variation in consumption growth which moves the expected dividend growth rate and the riskless real interest rate. The model is not consistent with the empirical evidence for predictable variation in excess stock returns. Bond market data pose a further challenge to this standard model of stock returns. In the model, stocks behave very much like long-term real bonds; both assets are driven by long-term movements in the riskless real interest rate. Thus parameter values that produce a large equity premium tend also to produce a large term premium on real bonds. While there is no direct evidence on real bond premia, nominal bond premia have historically been much smaller than equity premia. Since the data suggest that predictable variation in excess returns is an important source of stock market volatility, researchers have begun to develop models in which the quantity of stock market risk or the price of risk change through time. ARCH models and other econometric methods show that the conditional variance of stock returns is highly variable. If this conditional variance is an adequate proxy for the quantity of stock market risk, then perhaps it can explain the predictability of excess stock returns. There are several problems with this approach. First, changes in conditional variance are most dramatic in daily or monthly data and are much weaker at lower frequencies. There is some business-cycle variation in volatility, but it does not seem strong enough to explain large movements in aggregate stock prices [Bollerslev, Chou and Kroner (1992), Schwert (1989)]. Second, forecasts of excess stock returns do not move proportionally with estimates of conditional variance [Harvey (1989, 1991), Chou, Engle and Kane (1992)]. Finally, one would like to derive stock market volatility endogenously within a model rather than treating it as an exogenous variable. There is little evidence of cyclical variation in consumption or dividend volatility that could explain the variation in stock market volatility.
Ch. 19:
Asset Prices, Consumption, and the Business Cycle
1237
A more promising possibility is that the price of risk varies over time. Time-variation in the price of risk arises naturally in a model with a representative agent whose utility displays habit-formation. Campbell and Cochrane (1999), building on the work of Abel (1990), Constantinides (1990), and others, have proposed a simple asset pricing model of this sort. Campbell and Cochrane suggest that assets are priced as if there were a representative agent whose utility is a power function of the difference between consumption and "habit", where habit is a slow-moving nonlinear average of past aggregate consumption. This utility fi.mction makes the agent more risk-averse in bad times, when consumption is low relative to its past history, than in good times, when consumption is high relative to its past history. Stock market volatility is explained by a small amount of underlying consumption (dividend) risk, amplified by variable risk aversion; the equity premium is explained by high stock market volatility, together with a high average level of risk aversion. Time-variation in the price of risk can also arise from the interaction of heterogeneous agents. Constantinides and Duffle (l 996) develop a simple framework with many agents who have identical utility functions but heterogeneous streams of labor income; they show how changes in the cross-sectional distribution of income can generate any desired behavior of the market price of risk. Grossman and Zhou (1996) and Wang (1996) move in a somewhat different direction by exploring the interactions of agents who have different levels of risk aversion. Some aspects of asset market behavior could also be explained by irrational expectations of investors. If investors are excessively pessimistic about economic growth, for example, they will overprice short-term bills and underprice stocks; this would help to explain the equity premium and riskfree rate puzzles. If investors overestimate the persistence of variations in economic growth, they will overprice stocks when growth has been high and underprice them when growth has been low, producing time-variation in the price of risk [Barsky and DeLong (1993)]. This chapter has three objectives. First, it tries to summarize recent work on stock price behavior, much of which is highly technical, in a way that is accessible to a broader professional audience. Second, the chapter summarizes stock market data from other countries and asks which of the US stylized facts hold true more generally. The recent theoretical literature is used to guide the exploration of the international data. Third, the chapter systematically compares stock market data with bond market data. This is an important discipline because some popular models of stock prices are difficult to reconcile with the behavior of bond prices. The organization of the chapter is as follows. Section 2 introduces the international data and reviews stylized facts 1-9 to see which of them apply outside the USA. (Additional details are given in a Data Appendix available on the author's web page or by request from the author.) Section 3 discusses the equity premium puzzle, taking the volatility of stock returns as given. Section 4 discusses the stock market volatility puzzle; this section also reviews stylized facts 10-13 in the international data. Sections 3 and 4 drive one towards the conclusion that the price of risk is both high and time-varying. It must be high to explain the equity premium puzzle, and it
1238
J. Y Campbell
must be time-varying to explain the predictable variation in stock returns that seems to be responsible for the volatility o f stock returns. Section 5 discusses models which produce this result, including models with habit-formation in utility, heterogeneous investors, and irrational expectations. Section 6 draws some implications for other topics in macroeconomics, including the modelling of investment, labor supply, and the welfare costs o f economic fluctuations.
2. International asset market data
The stylized facts described in the previous section apply to postwar quarterly US data. Most empirical work on stock prices uses this data set, or a longer annual US time series originally put together by Shiller (1981). But data on stock prices, interest rates, and consumption are also available for many other countries. In this chapter I use an updated version o f the international developed-country data set in Campbell (1996a). The data set includes Morgan Stanley Capital International (MSCI) stock market data covering the period since 1970. ! combine the MSCI data with macroeconomic data on consumption, short- and long-term interest rates, and the price level from the International Financial Statistics (IFS) of the International Monetary Fund. For some countries the IFS data are only available quarterly over a shorter sample period, so I use the longest available sample for each country. Sample start dates range from 1970.1 to 1982.2, and sample end dates range from 1995.1 to 1996.4. I work with data from 11 countries: Australia, Canada, France, Germany, Italy, Japan, the Netherlands, Sweden, Switzerland, the United Kingdom, and the United States 2. For some purposes it is useful to have data over a much longer span of calendar time. I have been able to obtain annual data for Sweden over the period 1920-1994 and the U K over the period 1919-1994 to complement the US annual data for the period 1891-1995. The Swedish data come from Frennberg and Hansson (1992) and Hassler, Lundvik, Persson and S6derlind (1994), while the UK data come from Barclays de Zoete Wedd Securities (1995) and The Economist (1987) 3. In working with international stock market data, it is important to keep in mind that different national stock markets are o f very different sizes, both absolutely and in
2 The first version of this paper, following Campbell (1996a), also presented data for Spain. However Spain, unlike the other countries in the sample, underwent a major political change to democratic government during the sample period, and both asset returns and inflation show dramatic shifts fi'om the 1970s to the 1980s. It seems more conservative to consider Spain as an emerging market and exclude it from the developed-countrydata set. 3 1 acknowledge the invaluable assistance of Bjorn Hansson and Paul S6derlind with the Swedish data, and David Barr with the UK data. Full details about the construction of the quarterly and annual data are given in a Data Appendix available on the attthor's web page or by request fi'om the author.
1239
Ch. 19." Asset Prices, Consumption, and the Business Cycle
Table 1 MSCI market capitalization, 1993a Country
V/ (Bill. of US$)
--
vl
(%)
GDPi
v,
- -
VusMxcl
(%)
-
vi -
(%)
~f';4 Vi
AUL
117.9
41.55
4.65
1.85
CAN
167.3
30.62
6.60
2.63
FR
272.5
22.49
10.75
4.29
GER
280.7
16.83
11.07
4.41
ITA
86.8
9.45
3.42
1.37
JAP
1651.9
39.74
65.16
25.98
NTH
136.7
45.91
5.39
2.15
SWD
62.9
36.22
2.48
0.99
SWT
205.6
87.46
8.12
3.23
758.4
79.52
29.91
11.93
USA
UK MSCI
2535.3
37.25
100.00
39.88
USA
CRSP
4875.6
71.64
192.30
a vi is the stock index market capitalization in billions of 1993 US dollars. All stock index data are
from Morgan Stanley Capital International(MSCI), except for USA-CRSP which is from the Center for Research in Security Prices. Vi/GDP i is the index market capitalization as a percentage of 1993 GDP, Vi/VtjsMscI is the index market capitalization as a percentage of the market capitalization of the US MSCI index, and V i / ( ~ i Vi) is the percentage share of the index market capitalization in the total market capitalization of all the MSCI indexes. Abbreviations: AUL, Australia; CAN, Canada; FR, France; GER, Germany; 1TA, Italy; JPN, Japan; NTH, Netherlands; SWD, Sweden; SWT, Switzerland; UK, United Kingdom; USA, United States of America. proportion to national GDP's. Table 1 illustrates this by reporting several measures of stock market capitalization for the quarterly MSCI data. Column 1 gives the market capitalization for each country's MSCI index at the end of 1993, in billions of $US. Column 2 gives the market capitalization for each country as a fraction of its GDP. Column 3 gives the market capitalization for each country as a fraction of the US MSCI index capitalization. Column 4 gives the market capitalization for each country as a fraction of the value-weighted world MSCI index capitalization. Since the MSCI index for the United States is only a subset of the US market, the last row of the table gives the same statistics for the value-weighted index of New York Stock Exchange and American Stock Exchange stocks reported by the Center for Research in Security Prices (CRSP) at the University of Chicago. Table 1 shows that most countries' stock markets are dwarfed by the US market. Column 3, for example, shows that the Japanese MSCI index is worth only 65% of the US MSCI index, the U K MSCI index is worth only 30% of the US index, the French and German MSCI indexes are worth only 11% of the US index, and all
1240
J.Y. Campbell
other countries' indexes are worth less than 10% o f the US index. Column 4 shows that the U S A and Japan together account for 66% o f the world market capitalization, while the USA, Japan, the UK, France, and Germany together account for 86%. In interpreting these numbers one must keep in mind that the M S C I indexes do not cover the whole market in each country (the US M S C I index, for example, is worth about h a l f the US CRSP index), but they do give a guide to relative magnitudes across countries. Table 1 also shows that different countries' stock market values are very different as a fraction o f GDP. I f one thinks that total wealth-output ratios are likely to be fairly constant across countries, then this indicates that national stock markets are very different fractions o f total wealth in different countries. In highly capitalized countries such as the UK and Switzerland, the MSCI index accounts for about 80% o f GDP, whereas in Germany and Italy it accounts for less than 20% o f GDR The theoretical convention o f treating the stock market as a claim to total consumption, or as a proxy for the aggregate wealth o f an economy, makes much more sense in the highly capitalized countries 4. Table 2 reports summary statistics for international asset returns. For each country the table reports the mean, standard deviation, and first-order autocorrelation o f the real stock return and the real return on a short-term debt instrument 5. The first line o f Table 2 gives numbers for the standard postwar quarterly US data set summarized in the introduction. The next panel gives numbers for the 11-country quarterly MSCI data, and the bottom panel gives numbers for the long-term annual data sets. The table shows that the first four stylized facts given in the introduction are fairly robust across countries. (1) Stock markets have delivered average real returns o f 5% or better in almost every country and time period. The exceptions to this occur in short-term quarterly data, and are concentrated in markets that are particularly small relative to GDP (Italy), or that predominantly represent claims on natural resources (Australia and Canada). (2) Short-term debt has rarely delivered an average real return above 3%. The exceptions to this occur in two countries, Germany and the Netherlands, whose sample periods begin in the late 1970s and thus exclude much o f the surprise inflation o f the oil-shock period.
4 Stock ownership also tends to be much more concentrated in the countries with low capitalization. La Porta, Lopez-de-Silanes, Shleifer and Vishny (1997) have related these international patterns to differences in the protections afforded outside investors by different legal systems. 5 As explained in the Data Appendix, the best available short-term interest rate is sometimes a Treasury bill rate and sometimes another money market interest rate. Both means and standard deviations are given in almualized percentage points. To annualize the raw quarterly numbers, means are multiplied by 400 while standard deviations are multiplied by 200 (since standard deviations increase with the square root of the time interval in serially uncorrelated data).
Ch. 19." Asset Prices, Consumption, and the Business Cycle
1241
Table 2 International stock and bill returns a Country
Sample period
re
o(r~)
p(rc)
-~ rj
a(rf )
p(rj )
USA
1947.2-1996.4
7.569
15.453
0.104
0.794
1.761
0.501
AUL
1970.1 1996.3
2.633
23.459
0.008
1.820
2,604
0.636
CAN
1970.1-1996.3
4,518
16,721
0.119
2.738
1.932
0.674
FR
1973.2-1996.3
7.207
22.877
0,088
2.736
1.917
0.714
GER
1978.4-1996.3
8.135
20.326
0,066
3.338
1.161
0.322
ITA
1971.2-1995.3
0.514
27.244
0.071
2.064
2.957
0.681
JPN
1970.2--1996.3
5.831
21,881
0,017
1.538
2.347
0.493
NTH
1977.2-1996.2
12.721
15.719
0.027
3.705
1.542
SWD
1970.1-1995.1
7.948
23.867
0.053
1.520
2.966
SWT
1982.~1996,3
11.548
20.431
0.112
1.466
1.603
0.255
UK
1970.1-1996,3
7,236
21,555
0,103
1,081
3.067
0,474
USA
1970.1-1996.4
5.893
17.355
0.076
1.350
1,722
0.568
SWD
1920-1994
6.219
18.654
0.064
2.073
5.918
0,708
UK
1919-1994
7.314
22.675
-0.024
1.198
5.446
0.591
USA
1891 1995
6.697
18.634
0.025
1.955
8.919
0.338
-0.099 0.218
a ~ is the mean log real return on the stock market index, multiplied by 400 in quarterly data or 100 in annual data to express in annualized percentage points, tY(re) is the standard deviation of the log real return on the market index, multiplied by 200 in quarterly data or 100 in annual data to express in annualized percentage points, p(re) is the first-order autocorrelation of the log real return on the market index, rT, o(rf), and p(t).) are defined in the same way for the real return on a 3-month money market instrument. The money market instruments vary across countries and are described in detail in the Data Appendix. Abbreviations: AUL, Australia; CAN, Canada; FR, France; GER, Germany; ITA, Italy; JPN, Japan; NTH, Netherlands; SWD, Sweden; SWT, Switzerland; UK, United Kingdom; USA, United States of America.
(3) The annualized standard deviation o f stock returns ranges from 15% to 27%. It is striking that the market w i t h the highest volatility, Italy, is the smallest market relative to G D P and the one w i t h the lowest average return, (4) In quarterly data the annualized volatility o f real returns on short debt is around 3 % for the UK, Italy, and Sweden, around 2 . 5 % for Australia and Japan, and below 2 % for all other countries. Volatility is higher in l o n g - t e r m annual data because o f large swings in inflation in the interwar period, particularly in t 9 1 9 - 2 1 . M u c h o f the volatility in these real returns is probably due to unanticipated inflation and does not reflect volatility in the ex ante real interest rate.
1242
J Y. Campbell
These numbers show that high average stock returns, relative to the returns on shortterm debt, are not unique to the United States but characterize many other countries as well. Recently a number o f authors have suggested that average excess returns in the U S A may be overstated by sample selection or survivorship bias. i f economists study the U S A because it has had an unusually successful economy, then sample average US stock returns may overstate the true mean US stock return. Brown, Goetzmann and Ross (1995) present a formal model o f this effect. While survivorship bias m a y affect data from all the countries included in Table 2, it is reassuring that the stylized facts are so consistent across these countries 6. Table 3 turns to data on aggregate consumption and stock market dividends. The table is organized in the same way as Table 2. It illustrates the robustness o f two more o f the stylized facts given in the introduction. (5) In the postwar period the annualized standard deviation of real consumption growth is never above 3%. This is true even though data are used on total consumption, rather than nondurables and services consumption, for all countries other than the USA. Even in the longer annual data, which include the turbulent interwar period, consumption volatility slightly exceeds 3% only in the USA. (6) The volatility o f dividend growth is much greater than the volatility o f consumption growth, but generally less than the volatility o f stock returns. The exceptions to this occur in countries with highly seasonal dividend payments; these countries have large negative autocorrelations for quarterly dividend growth and much smaller volatility when dividend growth is measured over a full year rather than over a quarter. Table 4 reports the contemporaneous correlations among real consumption growth, real dividend growth, and stock returns. It turns out that these correlations are somewhat sensitive to the timing convention used for consumption. A timing convention is needed because the level o f consumption is a flow during a quarter rather than a point-in-time observation; that is, the consumption data are timeaveraged 7. If we think o f a given quarter's consumption data as measuring consumption at the beginning o f the quarter, then consumption growth for the quarter is next quarter's consumption divided by this quarter's consumption. If on the other hand
6 Goetzmalm and Jorion (1997) consider imernational stock-price data from earlier in the 20th Century and argue that the long-term average real growth rate of stock prices has been higher in the US than elsewhere. However they do not have data on dividend yields, which are an important component of total return and are likely to have been particularly important in Europe dtmng the troubled intei~ar period. 7 Tilne-averaging is one of a number of interrelated issues that arise in relating measured consumption data to the theoretical concept of consumption. Other issues include measurement error, seasonal adjustment, and the possibilitythat some goods classified as nondurable in the national income accounts are in fact durable. Grossman, Melino and Shiller (1987), Wheatley (1988), Miron (1986), and Heaton (1995) handle time-averaging, measurement error, seasonality, and dinability, respectively, in a much more careful way than is possible here, while Wilcox (1992) provides a detailed account of the sampling procedures used to constxuct US consumption data.
1243
Ch. 19." Asset Prices, Consumption, and the Business Cycle
Table 3 International consumption and dividends a Country
Sample period
Ac
o(Ac)
p(Ac)
Ad
~r(Ad)
p(Ad)
USA
1947.2-1996.4
1.921
1.085
0.221
2.225
28.794
-0.544
AUL
1970.1-1996.3
1.886
2.138
0.351
0.883
36.134
-0.451
CAN
1970.1 1996.3
1.853
2.083
0.113
-0.741
5.783
FR
1973.2 1996.3
1.600
2.121
--0.093
1.214
GER
1978.4 1996.3
1.592
2.478
-0.328
1.079
8.528
0.018
ITA
1971.2-1995.3
2.341
1.724
0.253
-4.919
19.635
0.294
JPN
1970.2-1996.3
3.384
2.347
-0.225
2.489
4.504
0.363
NTH
1977.2 1996.2
1.661
2.772
-0.265
4.007
4.958
0.277
SWD
1970.1-1995.1
0.705
1.920
0.305
1.861
13.595
0.335
SWT
1982.2-1996.3
0.376
2.246
-0.4t9
4.143
6.156
0.165
13.383
0.540 -0.159
UK
1970.1-1996.3
1.991
2.583
-0.017
0.681
7.125
0.335
USA
1970.1 1996.4
1.722
0.917
0.390
0.619
17.229
0.581 0.214
SWD
1920 1994
1.790
2.866
0.159
0.423
12.215
UK
1919-1994
1.443
2.898
0.281
1.844
7.966
USA
1891-1995
1.773
3.256
-0.117
1.485
14.207
0.225 -0.087
a Ac is the mean log real consumption growth rate, multiplied by 400 in quarterly data or 100 in annual data to express in annualized percentage points, cr(Ac) is the standard deviation of the log real consumption growth rate, multiplied by 200 in quarterly data or 100 in annual data to express in annualized percentage points, p(Ac) is the first-order autocorrelation of the log real consumption growth rate. Ad, a(Ad), and p(Ad) are defined in the same way for the real dividend growth rate. Consumption is nondurables and selwices consumption in the USA, and total consumption elsewhere. Abbreviations: AUL, Australia; CAN, Canada; FR, France; GER, Germany; ITA, Italy; JPN, Japan; NTH, Netherlands; SWD, Sweden; SWT, Switzerland; UK, United Kingdom; USA, United States of America. we think o f the c o n s u m p t i o n data as m e a s u r i n g c o n s u m p t i o n at the end o f the quarter, then c o n s u m p t i o n growth is this quarter's c o n s u m p t i o n divided by last quarter's consumption. Table 4 uses the former, " b e g i n n i n g - o f - q u a r t e r " timing convention because this p r o d u c e s a higher c o n t e m p o r a n e o u s correlation b e t w e e n c o n s u m p t i o n growth and stock returns. The t i m i n g convention has less effect on correlations w h e n the data are m e a s u r e d at l o n g e r horizons. Table 4 also shows h o w the correlations a m o n g real c o n s u m p t i o n growth, real dividend growth, and real stock returns v a r y w i t h the horizon. Each pairwise correlation a m o n g these series is calculated for h o r i z o n s o f 1, 4, 8, and 16 quarters in the quarterly data and for horizons o f 1, 2, 4, and 8 years in the l o n g - t e r m annual data. The table illustrates three m o r e stylized facts f r o m the introduction.
J.Y. Campbell
1244
%
I
I l l
II
II
[I
I I
I
', ~ '~ , .o ~" ~b o
m 0
I I
I I
II
I
I I
I
I
I
~
fa,
>~
I
N
0
~
;a4zaaza;a
d e m ~ : d ~ d ~ d o
NN~
~
a ca
Ch. 19: AssetPrices', Consumption, and the Business Cycle
1245
(7) Real consumption growth and dividend growth are generally weakly positively correlated in the quarterly data. In many countries the correlation increases strongly with the measurement horizon. However long-horizon correlations remain close to zero for Australia and Switzerland, and are substantially negative for Italy (with a very small stock market) and Japan (with anomalous dividend behavior). The correlations of consumption and dividend growth are positive and often quite large in the longer-term annual data sets. (8) The correlations between real consumption growth rates and stock returns are quite variable across countries. They tend to be somewhat higher in high-capitalization countries (with the notable exception of Switzerland), which is consistent with the view that stock returns proxy more accurately for wealth returns in these countries. Correlations typically increase with the measurement horizon out to 1 or 2 years, and are moderately positive in the longer-term annual data sets. (9) The correlations between real dividend growth rates and stock returns are small at a quarterly horizon but increase dramatically with the horizon. This pattern holds in every country. The correlations also increase strongly with the horizon in the longer-term annual data. After this preliminary look at the data, I now use some simple finance theory to interpret the stylized facts.
3. The equity premium puzzle 3.1. The stochastic discount factor To understand the equity premium puzzle, consider the intertemporal choice problem of an investor, indexed by k, who can trade freely in some asset i and can obtain a gross simple rate of return (1 +Ri, t+l) o n the asset held from time t to time t + 1. If the investor consumes Ck~ at time t and has time-separable utility with discount factor 6 and period utility U(Ckt), then her first-order condition is
g'((~t) = 6E~ [(1 +Ri, l+l)Ut(Ck,t+l)].
(1)
The left-hand side of Eqnation (1) is the marginal utility cost of consuming one real dollar less at time t; the right-hand side is the expected marginal utility benefit from investing the dollar in asset i at time t, selling it at time t + 1, and consuming the proceeds. The investor equates marginal cost and marginal benefit, so Equation (1) must describe the optimum. Dividing Equation (1) by U'(C~) yields
v'(G,,+,)]j
1 = Et (1 +Ri,,~,)6 ~
--E, [(1 +Ri,,+,)Ma,,+lJ,
(2)
where Mk,t.~l = 6U'(Ck, t+l)/U/(Ct) is the intertemporal marginal rate of substitution of the investor, also known as the stochastic discountjdctor. This way of writing the
1246
J..Y Campbell
model in discrete time is due originally to Grossman and Shiller (1981), while the continuous-time version of the model is due to Breeden (1979). Cochrane and Hansen (1992) and Hansen and Jagannathan (1991) have developed the implications of the discrete-time model in detail. The derivation just given for Equation (2) assumes the existence of an investor maximizing a time-separable utility function, but in fact the equation holds more generally. The existence of a positive stochastic discount factor is guaranteed by the absence of arbitrage in markets in which non-satiated investors can trade freely without transactions costs. In general there can be many such stochastic discount factors for example, different investors k whose marginal utilities follow different stochastic processes will have different M~, t+l - but each stochastic discount factor must satisfy Equation (2). It is common practice to drop the subscript k from this equation and simply write
1 = E, [(1 +&t+,lMi+~].
(3)
In complete markets the stochastic discount factor Mt+l is unique because investors can trade with one another to eliminate any idiosyncratic variation in their marginal utilities. To understand the implications of Equation (3) it is helpful to write the expectation of the product as the product of expectations plus the covariance,
E1[(1 +Ri,,~l)m~+l] = Et[(l + Ri,,+I)]E~[M,+I] + Covt[R~,l.~,M,+~].
(4)
Substituting into Equation (3) and rearranging gives 1 + E,[R~,,+I] -
1 - Covt[Ri, ¢+1,Mr+l] Et[Mt+l]
(5)
An asset with a high expected simple return must have a low covariance with the stochastic discount factor. Such an asset tends to have low retunas when investors have high marginal utility. It is risky in that it fails to deliver wealth precisely when wealth is most valuable to investors. Investors therefore demand a large risk premium to hold it. Equation (5) must hold for any asset, including a riskless asset whose gross simple return is 1 + Ry;t ~1. Since the simple riskless return has zero covariance with the stochastic discount factor (or any other random variable), it is just the reciprocal of the expectation of the stochastic discount factor: 1 1 +R/;,+t - Et[M,+I]"
(6)
This can be used to rewrite Equation (5) as 1 +Et[Ri,,+t] = (1 +RLt+I)(1 -Cov,[Ri,~+L,Mi+l]).
(7)
For simplicity I now follow Hansen and Singleton (1983) and assume that the joint conditional distribution of asset returns and the stochastic discount factor is lognormal
Ch. 19." Asset Prices, Consumption, and the Business Cycle
1247
and homoskedastic. While these assumptions are not literally realistic - stock returns in particular have fat-tailed distributions with variances that change over time - they do make it easier to discuss the main forces that should determine the equity premium. When a random variable X is conditionally lognormally distributed, it has the convenient property that log E t X
E~ l o g X + ½Vart logX,
(8)
where VartlogX = G [ ( l o g X - E t l o g X ) 2 ] . I f in addition X is conditionally homoskedastic, then Var, l o g X = E[(logX - E, l o g X ) 2] = Var(logX - Et logX). Thus with joint conditional lognormality and homoskedasticity of asset returns and consumption, I can take logs of Equation (3) and obtain 2 0 = Etri, t+l + Etmt+l + (1) [02 + O£, + 20,m].
(9)
Here rnt - log(Mr) and r , - - log(1 + Ri,), while 02 denotes the unconditional variance of log return innovations Var(r/, t+t - G r i , t+l), a 2 denotes the unconditional variance of innovations to the stochastic discount factor Var(mt~l Etmt+l), and G,, denotes the unconditional covariance of innovations Cov(ri, t+l - Elri, t v l , rntel - Etmt+l). Equation (9) has both time-series and cross-sectional implications. Consider first an asset with a riskless real return rt; ¢ ) 1. For this asset the return innovation variance c~2 and the covariance aim are both zero, so the riskless real interest rate obeys
rj;l+l = - E t m t + l
02
2
(10)
This equation is the log counterpart of Equation (6). Subtracting Equation (10) from Equation (9) yields an expression for the expected excess return on risky assets over the riskless rate:
o.2 Et[ri,/+1 - 9; tM] + ~ - - - o i ....
2
(ll)
The variance term on the left-hand side of Equation (11) is a Jensen's Inequality adjustment arising from the fact that we are describing expectations of log returns. This term would disappear if we rewrote the equation in terms of the log expectation of the ratio of gross simple returns: log G [(1 + Ri, t + I ) / ( 1 + Rf, ~+1)] = - a i m . The righthand side of Equation (11) says that the log risk premium is determined by the negative of the covariance of the asset with the stochastic discount factor. This equation is the log counterpart of Equation (7). The covariance O,m can be written as the product of the standard deviation of the asset return a,., the standard deviation of the stochastic discount factor (7,,,, and the
J Y. Campbell
1248
V~=7
>,~° ~
•~ ,.=
03 r.~
L) '~
:~
Z
q,
~
~P
•~ = o° f~
,.~
~'"
~o
~
II
rm ~ .
3
o,~o
2~=~
1000
TPR(1)
41.346 N/A >1000 >1000
14.634 -15.536 13.327 12.142 4.703
-9.021
13.440 23.970
-39.375 -11.201
>1000
20.705
-6.126
N/A
26.785
8.698
134.118 41.222 >1000 >1000 1, this second effect d o m i n a t e s and understated inflation m a k e s the riskfree rate p u z z l e even harder to explain.
Ch. 19." Asset Prices, Consumption, and the Business Cycle
1255
Table 7 International yield spreads and bond excess returns Country
Sample period
USA
1947.2-1996.4
AUL
1970.1-1996.3
a(s)
p(s)
er~
1.199
0.999
0.783
0.938
1.669
~
a
a(erb)
p(erb)
0.011
8.923
0.070
0.750
0.156
8.602
0.162
CAN
1970.1 1996.3
1.057
1.651
0.819
0.950
9.334
-0.009
FR GER
1973.2 1996.3 1978.4-1996.3
0.917 0.99l
1.547 1.502
0.733 0.869
1.440 0.899
8.158 7.434
0.298 0.117
ITA
197t.~1995.3
0.200
2.025
0.759
1.386
9.493
0.335
JPN NTH
1970.2-1996.3 1977.2-1996.2
0.593 1.212
1.488 1.789
0.843 0.574
1.687 1549
9.165 7.996
-0.058 0.032
SWD
1970.1-1995.1
0.930
2.046
0.724
0.212
7.575
0.244
SWT
1982.2 1996.3
0.471
1.655
0.755
1.071
6.572
0.268
UK USA
1970.1 1996.3 1970.1-1996.4
1.202 1.562
2.106 1.190
0.893 0.737
0.959 1.504
11.611 10.703
0.057 0.033
SWD UK
1920-1994 1919-1994
0.284 1.272
1.140 1.505
0.280 0.694
-0.075 0.318
6.974 8.812
0.185 -0.098
USA
1891 1995
0.720
1.550
0.592
0.172
6.499
0.153
a S is the mean of the log yield spread, the difference between the log yield on long-term bonds and the log 3-month money market return, expressed in annualized percentage points. ~7(s) is the standard deviation of the log yield spread and p(s) is its first-order autocorrelation, erh, a(ert,), and p(erb) are defined in the same way for the excess 3-month return on long-term bonds over money market instruments, where the bond return is calculated from the bond yield using the par-bond approximation given in Campbell, Lo and MacKinlay (1997), Chapter 10, equation (10.1.I9). Full details of this calculation are given in thc Data Appendix. Abbreviations: AUL, Australia; CAN, Canada; FR, France; GER, Germany; ITA, Italy; JPN, Japan; NTH, Netherlands; SWD, Sweden; SWT, Switzerland; UK, United Kingdom; USA, United States of America.
3.4. Bond returns and the equity premium and riskfree rate puzzles S o m e authors have argued that the riskfree interest rate is low because short-term g o v e r n m e n t debt is m o r e liquid than l o n g - t e r m financial assets. Short-term debt is " m o n e y l i k e " in that it facilitates transactions and can be traded at m i n i m a l cost. The liquidity advantage o f debt reduces its e q u i l i b r i u m return and increases the equity p r e m i u m [Bansal and C o l e m a n (1996), H e a t o n and Lucas (1996)]. The difficulty with this argument is that it implies that all l o n g - t e r m assets should have large excess returns over short-term debt. L o n g - t e r m g o v e r n m e n t bonds, for example, are not m o n e y l i k e and so the liquidity a r g u m e n t implies that they should offer a large t e r m p r e m i u m . But historically, the t e r m p r e m i u m has been m a n y times smaller than the equity p r e m i u m . This point is illustrated in Table 7, which reports two
1256
J g Campbell
alternative measures of the term premium. The first measure is the average log yield spread on long-term bonds over the short-term interest rate, while the second is the average quarterly excess log return on long bonds. In a long enough sample these two averages should coincide if there is no upward or downward drift in interest rates. The average yield spread is typically between 0.5% and 1.5%. A notable outlier is Italy, which has a negative average yield spread in this period. Average long bond returns are quite variable across countries, reflecting differences in inflationary experiences; however in no country does the average excess bond return exceed 1.7% per year. Thus both measures suggest that term premia are far smaller than equity premia. Table 8 develops this point further by repeating the calculations of Table 5, using bond returns rather than equity returns. The average excess log return on bonds over short debt, adjusted for Jensen's Inequality, is divided by the standard deviation of the excess bond return to calculate a bond Sharpe ratio which is a lower bound on the standard deviation of the stochastic discount factor. The Sharpe ratio for bonds is several times smaller than the Sharpe ratio for equities, indicating that term premia are small even after taking account of the lower volatility of bond returns. This finding is not consistent with a strong liquidity effect at the short end of the term structure, but it is consistent with a consumption-based asset pricing model if bond returns have a low correlation with consumption growth. Table 8 shows that sample consumption correlations often are lower for bonds, so that RRA(1) risk aversion estimates for bonds, which use these correlations, are often comparable to those for equities. A direct test of the liquidity story is to measure excess returns on stocks over long bonds, rather than over short debt. If the equity premium is due to a liquidity effect on short-term interest rates, then there should be no "equity-bond premium" puzzle. Table 9 carries out this exercise and finds that the equity-bond premium puzzle is just as severe as the standard equity premium puzzle 12.
3.5. Separating risk aversion and intertemporal substitution Epstein and Zin (1989, 1991) and Weil (1989) use the theoretical framework of Kreps and Porteus (1978) to develop a more flexible version of the basic power utility model. That model is restrictive in that it makes the elasticity of intertemporal substitution, % the reciprocal of the coefficient of relative risk aversion, 7. Yet it is not clear that these two concepts should be linked so tightly. Risk aversion describes the consumer's reluctance to substitute consumption across states of the world and is meaningful even
12 The excess return of equities over bonds must be measured with the appropriate correction for Jensen's Inequality. From Equation (16), the appropriate measure is the log excess return on equities over short-term debt, less the log excess return on bonds over short-term debt, plus one-halfthe variance of the log equity return, less one-half the variance of the log bond return.
1257
Ch, 19.• Asset Prices, Consumption, and the Business Cycle
~, ~
o
~,,
~
.
,
~
r¢3 t'4
V
V
,.n
~
~.
~
~.. V
•~
z
I
,.~
%
t-'q
~
t" ~
~
~
rz
t
0
t'-q
,,6 ~6 ,,6
•
"
~
~
~
~
~
~
~
~
~
~
~
r~
2
Z
JK Campbell
1258
¢S"~ ~
o O9 oo ~
V
V
~
~
1/~p. Of course, all these calculations are dependent on the assumption made at the beginning of this subsection, that the log dividend on stocks is a multiple )~ of log aggregate consumption. More general models, allowing separate variation in dividends and consumption, can in principle generate volatile stock returns without excessive variation in real interest rates. For example, we might modify Equation (30) to allow a second autonomous component of the dividend: det -'1c~ ~ at,
(41)
where Aat ~q has a similar structure to consumption growth, being forecast by an AR(1) state variable:
Aat~l - Yt + ~a,t+l,
(42)
Yt+l = (1 - 0)v + Oy, -~ ey,~+l.
(43)
This modification of the basic model would add a term v/(1 ---p) + (Yt v)/(1 -pO) to the formula for the log price-dividend ratio, Equation (37), and would add a term
JY. Campbell
1272
~a,t+l + p~y,t+l/(l - p O ) to the formula for the unexpected log stock return, (38). Cecchetti, Lain and Mark (1993) estimate a discrete-state Markov model allowing for this sort of separate variability in consumption and dividends. While such a model provides a more realistic description of dividends, it requires large predictable movements in dividends to explain stock market volatility. Unfortunately, as section 4.5 shows, there is little evidence for this.
4.4. Implications Jbr the equity premium puzzle I now return to the basic model in which the log dividend is a multiple of log aggregate consumption, and use the formulas derived in the previous subsection to gain a deeper understanding of the equity premium puzzle. The discussion of the puzzle in section 3 treated the covariance of stock returns with consumption as exogenous, but given a tight link between stock dividends and consumption the covariance can be derived from the stochastic properties of consumption itself. This is the approach of many papers including Abel (1994, 1999), Kandel and Stambaugh (1991), Mehra and Prescott (1985), and Rietz (1988). An advantage of this approach is that it clarifies the implications of Epstein-ZinWeil utility. The Epstein-Zin-Weil Euler equation is derived by imposing a budget constraint that links consumption and wealth, and it explains risk premia by the covariances of asset returns with both consumption growth and the return on the wealth portfolio. The stochastic properties of consumption, together with the budget constraint, can be used to substitute either consumption or wealth out of the EpsteinZin-Weil model. To understand this point, note that Equation (33) applies to the return on the wealth portfolio when ,~ = 1. Setting e = w and )~ = 1, Equation (33) becomes rw, t+~-Etrw, t+l
Act+l-EtAct~l +
1-
(Et+~-Et)ZpJAc~+l~/,
(44)
j=l
an equation derived by Restoy and Weil (1998) applying the approach of Campbell (1993). It follows that the covariance of any asset return with the wealth portfolio must satisfy
aiw- o~c+ ( 1 - ~ )
ai~,
(45)
where agz denotes the covariance of asset return i with revisions in expectations of future consumption growth: oc
aig =~ Coy (ri, t +~- E~ri, t +1, (Et+ l - Et) Z pJ Act+ l+j). j-1
The letter g is used here as a mnemonic for consumption growth.
(46)
Ch. 19." Asset Prices, Consumption, and the Business Cycle
1273
Substituting this expression into the formula for risk premia in the Epstein-Zin-Weil model, Equation (22), that formula simplifies to
Et[ri,t+l]-rj;t+l + ~- = ]/(Yic-~ Y-
Oig.
(47)
The risk premium on any asset is the coefficient of risk aversion 3/times the covariance of that asset with consumption growth, plus ( 7 - 1/~p) times the covariance of the asset with revisions in expected future consumption growth. The second term is zero if X = 1/% the power utility case, or if there are no revisions in expected future consumption growth 20. I now return to the assumption made in the previous subsection that expected consumption growth is an AR(1) process given by Equation (36). Under this assumption, (E,+I - Et) Z j=l
pJAct+L+j=
ez, t +1.
(48)
Equations (38), (47) and (48) imply that E,[r~,,t+l]-
rf, l+l + -~
y
(49) This expression nests many of the leading cases explored in the literature on the equity premium puzzle. To understand it, it is helpful to break the equity premium into two components, the premium on real consol bonds over the riskless interest rate, and the premium on equities over real consol bonds:
4 E,[rt,,,+ll-rt,t+l+T=7[-~ (1 P--@)
_}_(~/_~) [_@{1_~)20z21 " Et[re,,+l- r 1. or;kin, 1{R? } E,, { )
(4.10)
According to Equation (4.10), an unexpected one percent change in the ex post return to capital leads to a percentage change in entrepreneurial equity equal to the ratio of gross holdings of capital to equity. To the extent that entrepreneurs are leveraged, this ratio exceeds unity, implying a magnification effect of unexpected asset returns on entrepreneurial equity. The key point here is that unexpected movements in asset prices, which are likely the largest source of unexpected movements in gross returns, can have a substantial effect on firms' financial positions. In the general equilibrium, further, there is a kind of multiplier effect, as we shall see. An unanticipated rise in asset prices raises net worth more than proportionately, which stimulates investment and, in turn, raises asset prices even further. And so on. This phenomenon will become evident in the model simulations. We next obtain demand curves for household and entrepreneurial labor, found by equating marginal product with the wage for each case:
(1 - a ) ~
= x, N,
(1 -a)(1 - ~ ) ~
(4.11)
= x, wf,
(4.12)
where W~ is the real wage for household labor and Wf is the real wage for entrepreneurial labor. Combining Equations (4.1), (4.7), (4.8), and (4.12) and imposing the condition that entrepreneurial labor is fixed at unity, yields a difference equation for Nt+l:
(4.13) + (1 - a)(1
O)AtK~H~ l-")o.
Equation (4.13) and the supply curve tbr investment funds, Equation (4.5), are the two basic ingredients of the financial accelerator. The latter equation describes how
1360
B.S. Bernanke et al.
movements in net worth influence the cost of capital. The former characterizes the endogenous variation in net worth. Thus far we have determined wholesale output, investment and the evolution of capital, the price of capital, and the evolution of net worth, given the riskless real interest rate Rt+l, the household real wage Wt, and the relative price of wholesale goods I/X, To determine these prices and complete the model, we need to add the household, retail, and government sectors. 4.2. The complete log-linearized model
We now present the complete macroeconomic framework. Much of the derivation is standard and not central to the development of the financial accelerator. We therefore simply write the complete log-linearized model directly, and defer most of the details to Appendix B. As we have emphasized, the model is a DNK framework modified to allow for a financial accelerator. In the background, along with the entrepreneurs we have described are households and retailers. Households are infinitely-lived agents who consume, save, work, and hold monetary and nonmonetary assets. We assume that household utility is separable over time and over consumption, real money balances, and leisure. Momentary utility, further, is logarithmic in each of these arguments is. As is standard in the literature, to motivate sticky prices we modify the model to allow for monopolistic competition and (implicit) costs of adjusting nominal prices. It is inconvenient to assume that the entrepreneurs who purchase capital and produce output in this model are monopolistically competitive, since that assumption would complicate the analyses of the financial contract with lenders and of the evolution of net worth. To avoid this problem, we instead assume that the monopolistic competition occurs at the "retail" level. Specifically, we assume there exists a continuum of retailers (of measure one). Retailers buy output from entrepreneur-producers in a competitive market, then slightly differentiate the output they purchase (say, by painting it a unique color or adding a brand name) at no resource cost. Because the product is differentiated, each retailer has a bit of market power. Households and firms then purchase CES aggregates of these retail goods. It is these CES aggregates that are converted into consumption and investment goods, and whose price index defines the aggregate price level. Profits from retail activity are rebated lump-sum to households (i.e., households are the ultimate owners of retail outlets.) To introduce price inertia, we assume that a given retailer is free to change his price in a given period only with probability 1 - 0. The expected duration of any price change is 1@0- This device, following Calvo (1983), provides a simple way to incorporate staggered long-term nominal price setting. Because the probability of changing price is independent of history, the aggregation problem is greatly simplified. One extra
~5 In particular, householdatilityis givenby £ {~;~ 0[3~[ln(C~,k) + _~ln(Mt.JP, .-/~) + ~ In{1 l[,+i,)]}.
Ch. 21." The Financial Accelerator in a Quantitative Business Cycle Framework
1361
twist, following Bernanke and Woodford (1997), is that firms setting prices at t are assumed to do so prior to the realization of any aggregate uncertainty at time t. Let lower case variables denote percent deviations from the steady state, and let ratios of capital letters without time subscript denotes the steady state value of the respective ratio. Further, let ~ denote a collection of terms of second-order importance in the equation for any variable z, and let e[ be an i.i.d, disturbance to the equation for variable z. Finally, let Gt denote government consumption, :rt =-p~ - p t - i the rate of inflation from t - 1 to t, and r'/+1 ==- r~+~ + E { p t + l - P t } be the nominal interest rate. It is then convenient to express the complete log-linearized model in terms of four blocks of equations: (1) aggregate demand; (2) aggregate supply; (3) evolution of the state variables; and (4) monetary policy rule and shock processes. Appendix B provides details. (1) Aggregate d e m a n d C
1
G
Ce
y~ = ]7c, + ~ i t + ~ g t + --c~'yt + "
+ q~,
(4.14)
ct = -rt+L + Et {ct+l },
(4.15)
c~ = nt,l + " " +0~:~,
(4.16)
Et{r~÷I}
-Fz+I
-"-u[¥1t+l
r ) + t - ( 1 -- e ) @ t kl -
(qt +kt÷l)],
kt--i Xt+l) @ eqt~ 1 q ,
qt = cp(it - kt).
(4.17) (4.18) (4.19)
(2) Aggregate Supply yt = a, + a k t + (1 - a ) g 2 h ,
(4.20)
Yt- ht-xt -ct
(4.21)
=
~-Iht,
YL) : E t l{l~(-Xt)+ ~2Tt+l }.
(4.22)
(3) Evolution of State Variables kt+l = 6it + (1 - 6 ) k ,
yRK
t,
(4.23)
(4.24)
B.X Bernanke et al.
1362 (4) M o n e t a r y Policy R u l e a n d S h o c k P r o c e s s e s
r, - p r t 1 + gac~ I + el",
17 I
t~
(4.25)
& = pggt-i + ~ ,
(4.26)
aL = p,,at-i + g/,
(4.27)
with
(;
log Iz
~ P
D
# j)
e)dF(~o)R~Qt_IK/DK
)l
,
?O
6o dF(~o)R/',
O~'e = log(1-Ce+l/Ni+~ ) i T c~T;/N ' q~t" =
(Ri'lR-
N 1)K (r~"+q~-i +kt)+
lp(Rk/R) ~'(Rk/R) ' 1),,'
N
[2)(Y/X)
Yt-x~,
1- b (1 - cs) + a Y / ( X K ) '
( ~ ( I / K ) 1)t q) ~ ((D(I/K)
(1 - a)(1 -
(1~_) K" ~
(1 -- 0/~).
Equation (4.14) is the log-lineafized version of the resource constraint. The primary determinants of the variation in aggregate expenditures Yt are household consumption ct, investment it, and government consumption gL. Of lesser importance is variation in entrepreneurial consumption c~ 16. Finally, variation in resources devoted monitoring cost, embedded in the term ~ , also matters in principle. Under reasonable parametrizations, however, this factor has no perceptible impact on dynamics. Household consumption is governed by the consumption Euler relation, given by Equation (4.15). The unit coefficient on the real interest rate (i.e., the intertemporal elasticity of substitution) reflects the assumption of logarithmic utility over con.sumption. By enforcing the standard consumption Euler equation, we are effectively assuming that financial market frictions do not impede household behavior. Numerous authors have argued, however, that credit constraints at the household level influence a non-trivial portion of aggregate consumption spending. An interesting extension of
16 Note that each variable in the log-lmearizedresource constraint is weighted by the variable's share of output in the steady state. Under any reasonableparametrizationof the model, c~ has a relativelylow weight.
Ch. 21."
The Financial Accelerator in a Quantitatiee Business Cycle Framework
1363
this model would be to incorporate household borrowing and associated frictions. With some slight modification, the financial accelerator would then also apply to household spending, strengthening the overall effect. Since entrepreneurial consumption is a (small) fixed fraction of aggregate net worth (recall that entrepreneurs who retire simply consume their assets), it simply varies proportionately with aggregate net worth, as Equation (4.16) indicates. Equations (4.17), (4.18), and (4.19) characterize investment demand. They are the log-linearized versions of Equations (4.5), (4.4) and (4.3), respectively. Equation (4.17), in particular, characterizes the influence of net worth on investment. In /, the absence of capital market frictions, this relation collapses to Et{rf+~ } -rt+l = 0: Investment is pushed to the point where the expected return on capital, Et{r~+ 1 }, equals the opportunity cost of funds rt+117. With capital market frictions present, however, the cost of external funds depends on entrepreneurs' percentage equity holding, i.e., net worth relative to the gross value of capital, nt~l - (qr + ktf-l). A rise in this ratio reduces the cost of external funds, implying that investment will rise. While Equation (4.17) embeds the financial accelerator, Equations (4.18) and (4.19) are conventional (loglinearized) relations for the marginal product of capital and the link between asset prices and investment. Equations (4.20), (4.21) and (4.22) constitute the aggregate supply block. Equation (4.20) is the linearized version of the production function (4.1), after incorporating the assumption that the supply of entrepreneurial labor is fixed. Equation (4.21) characterizes labor market equilibrium. The left side is the marginal product of labor weighted by the marginal utility of consumption 18. In equilibrium, it varies proportionately with the markup of retail goods over wholesale goods (i.e., the inverse of the relative price of wholesale goods.) Equation (4.22) characterizes price adjustment, as implied by the staggered price setting formulation of Calvo (1983) that we described earlier [along with the modification suggested by Bernanke and Woodford (1997)]. This equation has the flavor of a traditional Phillips curve, once it is recognized that the markup xt varies inversely with the state of demand. With nominal price rigidities, the retail firms that hold their prices fixed over the period respond to increased demand by selling more. To accommodate the rise in sales they increase their purchases of wholesale goods from entrepreneurs, which bids up the relative wholesale price and bids down the markup. it is tbr this reason that - x t provides a measure of demand when prices are sticky. In turn, the sensitivity of inflation to demand depends on the degree of price inertia: The slope coefficient t¢ can be shown to be decreasing in 0, the probability an individual price stays fixed from period to period. One difference between Equation (4.22) and 17 In the absence of capital market frictions, the first-ordercondition from the entrepreneur'spartial equilibrium capital choice decision yields E{R)+ I } = Rt+ L. In this instance if E{R~'4 l} > R , j, the entrepreneurwould buy an infinite amount of capital, and if E{R~+1} < R~+l,he wouldbuy none. When E{Rt+ I } - R ~ 1, he is indifferentabout the scale of operation of his firm. i~ Given logarithmicpreferences,the marginal utility of consumption is simply -%.
1364
B.S. Bernanke et al.
a traditional expectations-augmented Phillips curve is that it involves expected future inflation as opposed to expected current inflation. This alteration reflects the forwardlooking nature of price setting 19 Equations (4.23) and (4.24) are transition equations for the two state variables, capital kt and net worth nt. The relation for capital, Equation (4.23), is standard, and is just the linearized version of Equation (4.2). The evolution of net worth depends primarily on the net return to entrepreneurs on their equity stake, given by the first term, and on the lagged value of net worth. Note again that a one percent rise in the return to capital relative to the riskless rate has a disproportionate impact on net worth due to the leverage effect described in the previous section. In particular, the impact of r) - r~ on nt+l is weighted by the coefficient y R K / N , which is the ratio of gross capital holdings to entrepreneurial net worth. How the financial accelerator augments the conventional D N K model should now be fairly transparent. Net worth affects investment through the arbitrage Equation (4.17). Equation (4.24) then characterizes the evolution of net worth. Thus, among other things, the financial accelerator adds another state variable to the model, enriching the dynamics. All the other equations of the model are conventional for the D N K framework [particularly King and Wohnan's (1996) version with adjustment costs of capital]. Equation (4.25) is the monetary policy rule 2°. Following conventional wisdom, we take the short-term nominal interest rate to be the instrument of monetary policy. We consider a simple rule, according to which the central bank adjusts the current nominal interest rate in response to the lagged inflation rate and the lagged interest rate. Rules o f this form do a reasonably good job of describing the variation of short term interest rates [see Clarida, Gali and Gertler (1997)]. We also considered variants that allow for responses to output as well as inflation, in the spirit of the Taylor (1993) rule. Obviously, the greater the extent to which monetary policy is able to stabilize output, the smaller is the role of the financial accelerator to amplify and propagate business cycles, as would be true for any kind o f propagation mechanism. With the financial accelerator mechanism present, however, smaller countercyclical movements in interest rates are required to dampen output fluctuations. Finally, Equations (4.26) and (4.27) impose that the exogenous disturbances to government spending and technology obey stationary autoregressive processes. We next consider two extensions of the model.
-~oc k t9 Iterating Equation (4.22) forward yields zct = ~,z¢=0/3 ~c(p,w ~ -Pt+k)- With forward-looking price setting, how fast prices adjust depends on the expected discounted stream of future demand. 2o The interest rate rule may be thought of as a money supply equation. The associated money demand equation is given by m, -Pt = ct - ( ~ ) r~l~. Note that under interest-rate targeting this relation simply determines the path of the nominal money stock. To implement its choice of the nominal interest rate~ the central bank adjusts the money stock to satisfy this equation.
Ch. 21:
The tqnancial Accelerator" in a Quantitatioe Business Cycle Framework
1365
4.2.1. Two extensions o f the baseline model
Two modifications that we consider are: (1) allowing for delays in investment; and (2) allowing for firms with differential access to credit. The first modification permits the model to generate the kind of hump-shaped output dynamics that are observed in the data. The second is meant to increase descriptive realism. 4.2.1.1. Inoestment delays. Disturbances to the economy typically appear to generate a
delayed and hump-shaped response of output. A classic example is the output response to a monetary policy shock [see, e.g., Christiano, Eichenbaum and Evans (1996) and Bernanke and Mihov (1998)]. It takes roughly two quarters before an orthogonalized innovation in the federal funds rate, for example, generates a significant movement in output. The peak of the output response occurs well after the peak in the funds rate deviation. Rotemberg and Woodford (1997) address this issue by assuming that consumption expenditures are determined two periods in advance (in a model in which non-durable consumption is the only type of private expenditure). We take an approach that is similar in spirit, but instead assume that it is investment expenditures rather than consumption expenditures that are determined in advance. We focus on investment for two reasons. First, the idea that investment expenditures take time to plan is highly plausible, as recently documented by Christiano and Todd (1996). Second, movements in consumption lead movements in investment over the cycle, as emphasized by Bernanke and Gertler (1995) and Christiano and Todd (1996). For example, Bernanke and Gertler (1995) show that in response to a monetary policy shock household spending responds fairly quickly, well in advance of business capital expenditures. Modifying the model to allow for investment delays is straightforward. Suppose that investment expenditure are chosenj periods in advance. Then the first-order condition relating the price of capital to investment, Equation (4.3), is modified to I
1
(4.28) Note that the link between asset prices and investment now holds only in expectation. With the time4o-plan feature, shocks to the economy have an immediate effect on asset prices, but a delayed effect on investment and output 21. To incorporate the investment delay in the model, we simply replace Equation (4.19) with the following log-linearized version of Equation (4.28): Et{qt+j - q)(it+j - kt+j)} - 0.
In our simulations, we take j = 1.
21 Asset prices move inunediately since the return to capital depends on the expected capital gain.
B.S. Bernanke et ai.
1366
4.2.1.2. Heterogeneous firms. The baseline model assumes that all firms are alike ex ante, except for initial net worth. In practice, o f course, there is considerable heterogeneity among firms along many dimensions, in particular in access to credit [see, e.g., the discussion in Gertler and Gilchrist (1994)]. To see how heterogeneity affects the results, we add to our model the assumption that there are two types o f firms, those that have easy access to credit, ceteris paribus, and those that (for various informational or incentive reasons, for example) have less access to credit. To accommodate two different types o f firms, we assume that there are two types o f intermediate goods (one produced by each type o f firm) which are combined into a single wholesale good via a CES aggregator. Production of the intermediate good is given by
Yit =A itKaI-[~tH it it t i~(1 J a £2),
i = 1,2.
(4.29)
Aggregate wholesale output is composed o f sectoral output according to (4.30)
= [ . Y ~ + (1 - . ) Y 2 ] ('/"~
We also assume that capital is sector-specific, and that there are costs of adjusting the capital stock within each sector: (4.31)
Ki, t , 1 - Kit = ()(Ii#K.)K. - 6K..
Let ji denote the number of periods in advance that investment expenditures must be chosen in sector i (note that the lag may differ across sectors): Then the link between asset prices and investment in each sector is given by
Note that the price of capital may differ across sectors, but that arbitrage requires that each sector generate the same expected return to capital k Et{ IRkk1,t+l - R2,t+I] [3CI/Cg+I}
=0,
where
~1P5
x,,t+~ + Q,,,+I(I - ,5) /Q,~.
and
Pit p~=a\
(Y1L) p-1 r, j '
Pzt Py
(l_a)(Y2t)P \ r, j
I
are the relative (wholesale) prices of goods produced in sectors t and 2 respectively.
Ch. 21:
The Financial Accelerator in a Quantitative Business Cycle Framework
1367
As we discuss in the next section, it is easy to parametrize the model so that firms in each sector face differential costs o f credit. Further, as we illustrate below, the financial accelerator can still be quite potent, even if only a portion o f firms face significant capital market frictions. Indeed, there may spillover effects from constrained to nonconstrained firms. it is straightforward to log-linearize these equations and append them to the general model. Modified will be the aggregate supply block, to allow for the two types of intermediate output, and the law o f motion for capital, to allow for two distinct types of capital.
5. Model simulations
In this section we present the results of some quantitative experiments to illustrate how the financial accelerator influences business cycle dynamics within the DNK framework. Specifically, we consider how credit-market imperfections amplify and propagate various shocks to the economy. We also examine the effects of allowing for delays in investment and of allowing for some firms to have better access to credit market than others. 5.1. M o d e l parametrization
We choose fairly standard values for the taste and technology parameters. We set the quarterly discount factor fi to 0.99 (which also pins down the steady state quarterly riskless rate, R = [3-1). We fix the labor supply elasticity, t/, at 3.0, in keeping with much o f the literature 22. As is also within convention, the capital share, a, is 0.35, and the household labor share, (1 - a)(1 - g2), is 0.64. The share of income accruing to entrepreneurs' labor is accordingly equal to 0.01. The quarterly depreciation rate for capital, 6, is assigned the usual value of 0.025. We take the steadystate share o f government expenditures in total output, G / Y , to be 0.2, the approximate historical average. The serial correlation parameters for the technology and government expenditure shocks, pa and pg, are assumed to be 1.0 and 0.95, respectively. Finally, the elasticity o f the price of capital with respect to the investment capital ratio, q), is taken to be 0.25. There is no firm consensus in the literature about what this parameter value should be 23. Reasonable assumptions about adjustment costs suggest that the value should lie within a range from 0.0 to 0.50.
22 in particular, we fix average hours worked relative to total hours available at a value that, in conjunction with logarithmic preferences over leisure, generates the desired labor supply elasticity. 23 King and Wolman (1996) use a value of 2.0, based on estimates fi-om aggregate data by Chirinko (1993). Because this value implies implausibly high adjustment costs, we do not use it.
1368
B.S. Bernanke et aL
The non-standard parameters of our model pertain to the interplay between real and financial factors within the entrepreneurial sector 24. Specifically, we choose parameters to imply the following three steady state outcomes: (1) a risk spread, R ~ - R , equal to two hundred basis points, approximately the historical average spread between the prime lending rate and the six-month Treasury bill rate; (2) an annualized business failure rate, F(N), of three percent, the approximate rate in the data; (3) a ratio of capital to net worth, ~, K of 2 (or equivalently, a leverage ratio of 0.5), the approximate value in the data. l b obtain these steady state values we choose the "death rate" of entrepreneurs, 1 - y, to be 0.0272 (quarterly), we take the idiosyncratic productivity variable, log(o)), to be log-normally distributed with variance equal to 0.28, and we set the fraction of realized payoffs lost in bankruptcy,/~, to 0.12. We note that our choice for/~ is within the reasonable set of estimates for bankruptcy costs 25. The final parameters to be selected are those related to the rate of price adjustment and to the policy rule. We let the probability a firm does not change its price within a given period, 0, equal to 0.75, implying that the average period between price adjustments is four quarters. In the policy rule, Equation (4.25), we set the autoregressive parameter, p, to 0.9 and the coefficient on inflation equal to 0.11 (implying a long-run rise in the nominal interest rate of one hundred and ten basis points in response to a permanent one hundred basis point increase in inflation.) These numbers are roughly in line with the evidence, allowing for the fact that there have been shifts in the actual feedback rule over time [see Clarida, Gali and Gertler (1997)]. 5.2. Results
In our experiments we consider four types of aggregate shocks: (1) a monetary policy shock, (2) a technology shock, (3) a government expenditure shock, and (4) a one° time, unanticipated transfer of wealth from households to entrepreneurs. We first study the response of the economy to these shocks in our model, excluding and including the financial accelerator. We then consider the implications of allowing for investment delays and heterogeneous firms. 5.2.1. Response to a monetary policy shock
The first experiment we consider is a monetary policy shock, specifically an unanticipated exogenous movement in the short-term interest rate. Analyzing the response of the model economy to a monetary policy disturbance provides a good way to evaluate our framework since a lengthy literature has produced a consensus of
24 Ore parameter choices here follow closely Fisher (1996) and Carlstrom and Fuerst (t997). 2s See the discussion of bankruptcy costs in Carlstrom and Fuerst (1997). They actually use a higher number than we do (0.20 versus 0.12).
Ch. 21."
The Financial Accelerator in a Quantitative Business Cycle I~)'amework
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Fig. 2. Impulse response to a funds rate shock. opinion about how the economy responds to this kind o f shock 26. Figure 2 summarizes this evidence, and also presents some new evidence on the behavior of several rate spread variables that proxy for premium for external funds, a key element o f our model. The results in Figure 2 are based on a five-variable quarterly VAR that includes four "standard" macroeconomic variables - the log o f real GDR the log o f the GDP deflator, the log o f a commodity price index, the federal funds rate -- along with two rate spread variables. To identify the policy shock, we order the funds rate after the price and output variables, based on the view that monetary policy can respond contemporaneously to these variables but can affect them only with a lag. We order tile spread variable after the funds rate based on the assumption that innovations in these variables do not contain any marginal information that is useful for setting current monetary policy. The two rate spread variables we consider are the difference between the six-month commercial paper rate and the six-month T-bill rate and the difference between the prime lending rate and the six-month T-bill rate.
26 See, for example, Ctmstiano, Eichenbaum and Evans (t996), Bernanke m~d Gertler (1995), Bernal~e and Mihov (1998), and Leeper, Sims and Zha (1996).
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Figure 2 illustrates the impulse responses of several variables to a negative innovation in the federal funds rate. As is typically found in the literature, output declines after about two quarters, and the price level declines after about six quarters. The output decline, further, persists well after the funds rate reverts to trend. Finally, each of the spread variables rises fairly quickly, leading the downturn in output 27. Figure 3 reports the impact of the same experiment, but this time using the model economy. As in all the subsequent figures, the time units on the graphs are to be interpreted as quarters. In each picture the hatched line designates the "baseline" impulse response, generated by fixing the external finance premium at its steady state level instead of allowing it to respond to changes in the capital-net worth ratio. In other words, the baseline simulations are based on a model with the same steady state as the complete model with imperfect credit markets, but in which the additional dynamics associated with the financial accelerator have been "turned off". The solid line in each picture indicates the response observed in the complete model, with the financial accelerator included. The figure shows the impact of an unanticipated 25 basis point (on an annual basis) decline in the nominal interest rate. Although the addition of credit-market frictions does not substantially affect the behavior of the nominal rate of interest, it does lead to a stronger response of real variables. In particular, with the financial accelerator included, the initial response of output to a given monetary impulse is about 50% greater, and the effect on investment is nearly twice as great. Further, the persistence of the real effects is substantially greater in the presence of the credit-market factors, e.g., relative to trend, output and investment in the model with credit-market imperfections after four quarters are about where they are in baseline model after only two quarters. The impact of the financial accelerator is mirrored in the behavior of the external finance premium, which is passive in the baseline model (by assumption) but declines sharply in the complete model, slowly reverting to trend. The unanticipated decline in the funds rate stimulates the demand for capital, which in turn raises investment and the price of capital. The unanticipated increase in asset prices raises net worth, forcing down the external finance premium, which in turn further stimulates investment. A kind of multiplier effect arises, since the burst in investment raises asset prices and net worth, further pushing up investment. Entrepreneurial net worth reverts to trend as firms leave the market, but the effect is slow enough to make the external finance premium persist below trend. This persistence in net worth and the external finance premium provides the additional source of dynamics. It is interesting to observe that the response of the spread in the model economy matches the VAR evidence reasonably well.
27 It is worth noting that the impulse response of the prime-rate spread is twice as large as the impulse response of the commercial-paperspread. Since commercial paper issuers are high quality firms, this result is consistent with our model's implication that lower-quality borrowers experience larger spread movementsin response to business cycle shocks.
1371
Ch. 21." The Financial Accelerator in a Quantitative Business Cycle Framework
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It is worth emphasizing that this experiment generates substantial output persistence without relying on an unusually high labor supply elasticity, as is required for the baseline model [see, e.g., the discussion in Chari, Kehoe and McGrattan (1996)]. The countercyclical movement in the premium for external funds (which is the essence of the financial accelerator) serves to flatten the marginal cost curve, as does making labor supply elastic in the baseline model. Overall, these results lend some supports to the claims of Bernanke and Gertler (1995), that credit-market effects can help explain both the strength of the economy's response to monetary policy and the tendency for policy effects to linger even after interest rates have returned to normal. The fact that the model economy replicates the VAR evidence reasonably well is particularly encouraging. The one major point of discrepancy is that the response of output to a monetary shock is delayed in the data, but occurs immediately in the model economy 28. We show shortly, however, that this problem can be fixed by allowing for investment delays.
2~ It is also true that the output response is large relative to the interest rate shock. This partly reflects the high degree of intertemporal substitution embedded in the household savings decision, It may also reflect unreasonably short investment delays.
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alternative shocks. All panels: time horizon in quarters.
5.2.2. Shock to technology, demand, and wealth
Figure 4 displays the effects on output of three alternative shocks: a technology shock, a demand shock (specifically a shock to government expenditures), and a redistribution of wealth between entrepreneurs and households. Once again, the hatched lines show impulse responses from the baseline model with the financial accelerator shut off, and the solid lines show the results from the full model. As the figure shows, the financial accelerator magnifies and propagates both the technology and demand shocks. Interestingly, the magnitude of the effects is about the same as for the monetary policy shock. Again, the central mechanism is the rise in asset prices associated with the investment boom, which raises net worth and thus reduces the external finance premium. The extra persistence comes about because net worth is slow to revert to trend. A positive shock to entrepreneurial wealth (more precisely, a redistribution fi:om households to entrepreneurs) has essentially no effect in the baseline model, but has both significant impact and propagation effects when credit-market frictions are present. The wealth shock portrayed is equal in magnitude to about 1% of the initial wealth of entrepreneurs and about 0.05% of the wealth of households. The transfer of wealth drives up the demand for investment goods, which raises the price of capital and thus entrepreneurs' wealth, initiating a positive feedback loop; thus, although the exogenous shock increases entrepreneurial net worth directly by only 1%, the total effect on entrepreneurs' wealth including the endogenous increase in asset prices exceeds 2%. Output rises by 1% at an annual rate, and substantial persistence is generated by the slow decay of entrepreneurial net worth. Thus the addition of credit-market effects raises the possibility that relatively small changes in entrepreneurial wealth could be an important source of cyclical fluctuations. This case is an interesting one, as it is reminiscent of(and motivated by) Fisher's (1933) "debt-deflation" argument, that redistributions between creditors and debtors arising from unanticipated price changes can have important real effects. Indeed, Fisher argued
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that this kind of mechanism accounted for the depth and protractedness of the Great Depression 29. The same kind of reasoning, further, helps explain why the recent spate of currency crises have had devastating real effects. To the extent loans from abroad are denominated in units of a foreign currency, an exchange rate collapse redistributes wealth from domestic borrowers to foreign lenders. 5.2.3. Investment delays and heterogeneous firms
We now suppose that investment expenditures must be planned one quarter in advance, as in Section 5.2, and consider the effect of a monetary shock. As Figure 5 illustrates, an expansionary monetary policy shock (again, an unanticipated 25 basis point decline in the funds rate) now generates a hump-shaped response of output, as in the data. This hump-shaped response is considerably more accentuated when the financial accelerator is allowed to operate. The initial response of output is still too strong, suggesting that it may be desirable to build in other types of lags. On the other hand, the persistence of the response of output is considerably greater than in the case without investment delays, and comes much closer to matching the data. Interestingly, there remains an immediate response of the external funds premium as the data suggest. The reason is that asset prices rise immediately, in anticipation of the investment boom. We next consider the model with heterogeneous firms. We choose parameters so that firms in sector 2 face a steady-state premium for external finance of 3% per year, while firms in sector l face a premium of only 1%. We set a = .5125 to generate an average steady-state premium of 2%. As a consequence of this assumption, roughly half of the economy's output is produced by credit-constrained firms, a breakdown which is in accord with the rough evidence summarized in Bernanke, Gertler and Gilctu'ist (1996). We set p = 0.9, implying that the goods produced in the two sectors are close substitutes. Assuming a high degree of substitutability biases the results against finding important aggregate effects of credit-market frictions in this setup; however, our results turned out to be not very sensitive to the choice o f p . With sector-specific adjustment costs, the effective marginal cost of adjusting the aggregate capital stock is dramatically increased owing to the additional curvature implied by the two sector model. To achieve the same degree of overall capital adjustment as in the one-sector model we lower the adjustment cost elasticity q) from 0.25 to 0.1. Finally, we allow for a one-period delay in the investment of sector-2 firms and a two period delay for sector-1 firms. This choice is based on the observation that credit-constrained firms tend to be smaller, and rims likely more flexible [see, e.g., Gertler and Gilchrist (1994)]. All other parameters are the same as in the baseline DNK model. Figure 6 shows the results of a shock to monetary policy in the model with heterogeneous firms. The top left panel shows the response of output (the solid line),
29 Bernanke and Gertler (1989, 1990) argue that the tinancial accelerator mechanismprovides a tormal rationale for Fisher's debt-deflationtheory of the Great Depression.
B.S. B e r n a n k e et al.
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one period investment delay, All panels: time horizon in quarters.
relative to the baseline case with the financial accelerator shut off (the hatched line). In response to an unanticipated fall in the funds rate, output rises by approximately the same amount as it did in the aggregative New Keynesian model with investment delays, both for the baseline model without credit-market frictions and for the complete model with differential access of firms to credit. One interesting difference is that the differential investment delays across sectors smooth out the hump-shaped response of output, adding to the overall persistence of the output response. Thus, the effect of credit-market frictions on the propagation of shocks is roughly the same in the onesector and two-sector versions of the model. The two-sector model also has cross-sectional implications, of course. The top and bottom panels on the right side of Figure 6 show the sectoral responses of output and investment. The solid line corresponds to the sector facing the relatively higher cost of external finance and the dotted line corresponds to the other sector. We find that, in response to an expansionary monetary policy shock, investment by firms with relatively poor access to external credit markets rises by nearly three times as much as the investment of firms with better access to credit. This "excess sensitivity" of the more constrained firms is consistent with evidence reported by Gertler and Gilchrist (1994), Kashyap, Lamont and Stein (1994), Oliner and Rudebusch (1994), Morgan ( 1998), and
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Fig. 6. Monetaryshock multisectormodel with investmentdelays. All panels: time horizon in quarters. Aggregate output: models with and without financial accelerator; other panels: model with financial accelerator. others. Although investment differs sharply across firrns in the simulation, changes in output are similar for the two types of firms. Differing output effects could be produced, for example, by introducing inventories or inputs to production that must be financed by borrowing. Our finding that constrained firms' investment spending reacts more strongly to monetary policy contrasts with that of Fisher (1996), who obtains an ambiguous result. We suspect that the main source of the difference in predictions is that, in our setting, borrowers' net worth is endogenous and is a key channel through which monetary policy affects credit availability. In Fisher's model, in contrast, borrowers' equity positions are exogenously fixed and are unaffected by changes in policy.
6. A highly selected review of the literature The theoretical and empirical literatures on credit-market imperfections are immense, Until recently, the great bulk of this research has been partial equilibrium in nature, e.g., theoretical analyses of equilibria in credit markets with asymmetric information
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and agency costs, or empirical studies of the effects of credit-market imperfections on various types of spending, including consumption, housing, business investment, and inventory investlnent. Some leading recent examples of the latter category are cited in the introduction; see, e.g., Bernanke, Gertler and Gilchrist (1996) tbr additional references. Other surveys of these literatures which the reader may find useful include Gertler (1988), Gertler and Hubbard (1988), Jaffee and Stiglitz (1990), Bernanke (1993), Calomiris (1993), Gertler and Gilchrist (1993), Kashyap and Stein (1994), Oliner and Rudebusch (1994), Bernanke and Gertler (1995), and Hubbard (1995). To keep our survey of relevant literature brief, we limit consideration to the more recent work that, like the present research, studies the implications of credit-market frictions for macroeconomic dynamics. Even within this limited field our review must necessarily be selective; we focus on the work that bears the closest relationship to the model we have presented. In particular, we do not discuss the burgeoning related literature on the role of financial markets in economic growth [see, e.g., Levine (1997) for a survey of this topic] or in economic development [see, e.g., Townsend (1995)]. Nor do we consider research focusing on the role of banks in business cycles, primarily because there has been little work on the "bank lending channel" and related effects in an explicitly dynamic context 3o. We do believe however that the incorporation of a banking sector into our model would be a highly worthwhile exercise. Indeed, given that commercial banks borrow to order to fund investments in information-intensive, risky projects, and in this way bear resemblance to the entrepreneurs in our model, one could envision a relatively straightforward that allows for agency frictions int tile intermediary sector. On the theoretical side, the two principal antecedents of the approach used in the present chapter are Bernanke and Gertler (1989) and Kiyotaki and Moore (1997). Bernanke and Gertler (1989) analyze an overlapping-generations model in which borrowers/firms with fixed-size investment projects to finance face the "costly state verification" problem of Townsend (1979) and Gale and Hellwig (1985) 31. As we discussed in detail in the presentation of our model above, the optimal contract in this setting has the features of a standard debt contract. As we noted earlier, the principal virtue of this setup, other than simplicity, is that it motivates an inverse relationship between the potential borrower's wealth and the expected agency costs of the lenderborrower relationship (here, the agency costs are equated with monitoring/bankruptcy costs). In particular, a potential borrower with high net worth needs to rely relatively little on external finance; he thus faces at most a small risk of bankruptcy and a small
3o Interestingrecent exceptions are Gersbach (t997) and Krishnamurthy (t997). Holmstrom and Tirole (1997) analyzethe role of bank collateral and monitoring in a static context. Severalpapers have studied the role of banks in the context of "limited participation" models, see for example Fisher (1996) and Cooley and Quadrini (1997).] 31 Williamson (1987) also incorporates the costly state verification assanaption into a modified real business cycle naodel.
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premium on external finance. A borrower with less resources of his own to invest, in contrast, faces a high bankruptcy risk and a high external finance premium. In the Bernanke-Gertler model, shocks to the economy are amplified and propagated by their effects on borrowers' cash flows. For example, an adverse productivity shock lowers current cash flows, reducing the ability of firms to finance investment projects from retained earnings. This decline in net worth raises the average external finance premium and the cost of new investments. Declining investment lowers economic activity and cash flows in subsequent periods, amplifying and propagating the effects of the initial shock. Bernanke and Gertler show that this effect can generate serially correlated movements in aggregate output, even though the exogenous shocks to the system are i.i.d. They also show that in their model the dynamics of the cycle are nonlinear; in particular, the weaker the initial financial condition of borrowers, the more powerful is the propagation effect through cash flows. A number of subsequent papers have shown that this basic analysis can be extended and deepened without affecting the qualitative results: For example, Gertler (1992) considers the case of multi-period financial contracts. Aghion and Bolton (1997) give an extensive analysis of the shortrun and long-run dynamic behavior of a closely-related model. And Aghion, Banerjee and Piketty (1997) show how the dynamics of this sort of model are affected when interest rate movements are endogenous (Bernanke and Gertler assume that the real interest rate is fixed by the availability of an alternative technology.) The model that we presented utilizes a number of the features of the Bernanke-Gertler model, notably the overlapping-generations assumption for entrepreneurs and the costly state verification model of intermediation. As in Bernanke and Gertler (1989), our model here implies a central role for the endogenous evolution of borrowers' net worth in macroeconomic dynamics. Other authors have developed dynamic macroeconomic models in which cash flows play a critical role in the propagation mechanism. Notably, Greenwald and Stiglitz (1993) construct a model in which, as in Bernanke and Gertler (1989), firms have access only to debt financing (equity finance is ruled out by assumption). Because bankruptcy is costly, firms are reluctant to become highly levered; their initial equity or net worth thus effectively constrains the quantity of funds that they can raise in capital markets. Greenwald and Stiglitz assume that there is a one-period lag between the use of variable inputs and the production of output. A firm that suffers a decline in cash flow is able to finance fewer inputs and less production. Lower production implies lower profits, which propagates the effects of the initial fall in cash flow. The Greenwald-Stiglitz model thus illustrates that financial factors may affect the level of inputs, such as employment or inventories, as well as the level of capital investment (as in Bernanke-Gertler). The basic intuition concerning how credit-market imperfections propagate the cycle is similar in the two models, however. The net worth of borrowers changes not only in response to variations in cash flow, but also (and often, more dramatically) to changes in the valuation of the real and financial assets that they hold. Indeed, changes in asset values are taken by Fisher (1933) and other classical writers on the subject to be the principal means by which
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financial forces propagate an economic decline. This element was added to the formal literature by Kiyotaki and Moore (1997), who develop a dynamic equilibrium model in which endogenous fluctuations in the market prices o f an asset (land, in their example) are the main source o f changes in borrowers' net worth and hence in spending and production 32. Kiyotaki and Moore analyze a stylized example in which land serves both as a factor o f production and as a source o f collateral for loans to producers, in this economy, a temporary shock (to productivity, for example) lowers the value o f land and hence o f producers' collateral. This leads in turn to tightened borrowing constraints, less production and spending, and finally to still further reductions in land values, which propagates the shock further through time 33. We consider the asset-price channel to be an important one, and it plays an important role in generating the significant quantitative effects we obtained in our calibration exercises 34. Turning from theoretical to empirical research, we note that there are very few examples o f fully articulated macro models including capital-market imperfections that have been estimated by classical methods (the major exception being some large macroeconometric forecasting models, as noted in the introduction). The quantitative research most closely related to the present chapter uses the calibration technique. Our work here is particularly influenced by Carlstrom and Fuerst (1997), which in turn draws from analyses by Fisher (1996), Fuerst (1995) and Gertler (1995), as well as from the theoretical model o f Bernanke and Gertler (1989) discussed above. As we do in the model presented in this chapter, Carlstrom and Fuerst (1997) study the optimal lending contract between financial intermediaries and entrepreneurs when verifying the return to entrepreneurs' projects is costly for the lender. They then embed the resulting representation o f credit markets in an otherwise conventional real business cycle model. They find that the endogenous evolution o f net worth plays an important role in the simulated dynamic responses o f the model to various types o f shock.
32 Suarez and Sussman (1997) present a dynamic model in which asset price declines, induced by "fire sales" by bankrupt firms, contribute to cyclical fluctuations. 33 In the model we presented earlier, entrepreneurs do not obtain insurance against aggregate shocks because their indirect utility functions are linear in wealth (due to the assumptions of risk neutrality and constant returns to scale), while households are risk-averse. Krishnamurthy (1997) points out that in more general settings entrepreneurs are likely to want to obtain this kind of insurance, which raises the question of why the posited credit-market effects should be empirically relevant. Krishnamurthy's answer is that the ability of lenders or other insurers to insure against large aggregate shocks depends in turn on the insurers' own net worth, which may be reduced during a severe recession. He goes on to develop a model with implications similar to that of Kiyotaki and Moore (1997), except that it is the net worth of lenders or insurers, rather than that of borrowers, that plays the crucial role. See Kiyotaki and Moore (1998) tbr a related argument. 34 Another potentially interesting chatmel, emphasized by Kiyotaki and Moorc (1998), involves the interdependency that arises from credit chains, where firms are simultaneously lending and borrowing. These authors show that small shocks can induce a kind of domino effect, due to the chain, that leads to big effects on the economy.
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An interesting finding of their research is that the model with credit-market frictions generates a hump-shaped output response, consistent with most empirical findings. Our model presented above has many features in comrnon with that of Carlstrom and Fuerst (1997). Putting aside some technical details, there are however two major differences between the two models. First, we consider a sticky-price setting in the Dynamic New Keynesian tradition, while Carlstrom and Fuerst restrict themselves to a model with flexible prices. Thus we are able to examine the interaction of credit-market frictions with shocks to monetary policy, or to other nominal variables. The second difference is more subtle but is also important: Carlstrom and Fuerst assume that the agency problem applies only to producers of investment goods, who produce capital directly from the output good. The output good is produced, using both capital and labor, by separate firms who do not face agency problems in external finance. As a result of these assumptions, in the Carlstrom-Fuerst model, changes in net worth affect the economy primarily by affecting the supply price of capital (when net worth is low, less capital is produced at any given price). In our model, in contrast, the agency problem applies to producers of final output, who own the economy's durable capital stock. Since borrowers own the economy's capital stock, changes in the price of capital directly affect their net worth; that is, our model more directly incorporates the asset price effects stressed by Kiyotaki and Moore (1997). As a result, we find that creditmarket frictions amplify shocks to the economy to a greater degree than do Carlstrom and Fuerst. On the other hand, a clear virtue of Carlstrom-Fuerst model is that the credit-mechanism helps able to explain the real world auto-correlation properties of output.
7. Directions ti)r future work In subsequent research we hope to consider several extensions to the work so far: First, as noted above, we have not addressed the role of banks in cyclical fluctuations, despite considerable attention to banking in the previous theoretical and empirical literatures. There are several ways to incorporate a nontrivial role for banks into our framework; one possibility is to allow the financial intermediaries which lend to entrepreneurs to face financial frictions in raising funds themselves. In this case, the net worth of the banking sector, as well as the net worth of entrepreneurs, will matter for the models' dynamics. Second, an important institutional fact is that debt contracts in low-inflation countries are almost always set in nominal terms, rather than in real terms as in this chapter. It would be relatively easy to incorporate nominal contracting into this model, in order to evaluate whether the redistributions among debtors and creditors associated with unanticipated changes in the price level are of quantitative significance. Doing so would enable us to critically assess recent arguments that deflation may pose a serious threat to the US economy.
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Third, we have restricted the analysis to a closed economy. It would be interesting to extend the analysis to the open economy. By doing so it would be possible to analyze how a currency crisis may induce financial distress that is transmitted to the real sector 35. As we discussed in Section 5, to the extent an exchange rate collapse redistributes wealth from domestic borrowers to domestic lenders (owing to the fact that loans are denominated in units o f foreign currency), the model o f our chapter predicts a contraction in real activity. Finally, in this chapter we have restricted the credit-market frictions to the investment sector. It would be interesting to study how the results might be affected if these frictions affect other components o f spending, such as consumption, inventory investment, and housing.
Appendix A. The optimal financial contract and the demand for capital In this appendix we provide a detailed analysis of the partial equilibrium costly-stateverification problem discussed in Section 3. We start with the case of no aggregate risk and show that under the assumptions made in the text, the optimal contract provides a monotonically increasing relationship between the capital/wealth ratio and the premium on external funds: QK/N = ~(RX/R) with ~p/(.) > 0. We also establish that the default probability N is a strictly increasing function o f the premium RX/R, implying that the optimal contract guarantees an interior solution and therefore does not involve quantity rationing of credit. This appendix also provides functional forms for the contract structure. In particular, for the case o f the log-normal distribution we provide exact analytical expressions for the payoff functions to the lender and entrepreneur. In the final section of this appendix we extend the analysis to the case of aggregate risk and show that the previously established results continue to hold.
A. L The partial equilibrium contracting problem Let profits per unit of capital equal coRk, where co ~ [0, ec) is an idiosyncratic shock with E(co) = 1. We assume F(x) = Pr[co < x] is a continuous probability distribution with F(0) = 0. We denote b y f ( c o ) the pdf o f o . Given an initial level o f net worth N, and a price of capital Q, the entrepreneur borrows QK - N, to invest K units o f capital in the project. The total return on capital is thus o)RkQK. We assume co is unknown to both the entrepreneur and the lender prior to the investment decision. After the investment decision is made, the lender can only observe co by paying the monitoring cost l~coR~QK, where 0 < ¢~ < 1. Let the required return on lending equal R, with R < R K,
35 See Mishkin (1997) for a discussion of how the financial accelerator mechanism may be useful ~br understanding the recent currency crises in Mexico and Southeast Asia.
Ch, 21." The Financial Accelerator in a Quantitative Business Cycle b)amework
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The optimal contract specifies a cutoffvalue N such that i f co ~> N, the borrower pays the lender the fixed amount NR KQK and keeps the equity (co - - ~ ) R K QK. Alternatively; if co < N, the borrower receives nothing, while the lender monitors the borrower and receives (1 - IJ)coRK QK in residual claims net o f monitoring costs, in equilibrium, the lender earns an expected return equal to the safe rate R implying [NPr(co ~> N ) + (1 -/OE(colco < N) Pr(co < N)]RKQK = R ( Q K - N ) . Given constant returns to scale, the cutoff N determines the division o f expected gross profits RXQK between borrower and lender. We define F(~5) as the expected gross share o f profits going to the lender: F(~) =
f0
cof(co) d o + N
f(co) dco, ,]co
and note that F'(~) = 1-F(~),
F'(N)
-f(N),
implying that the gross payment to the lender is strictly concave in the cutoff value N. We similarly define g G ( N ) as the expected monitoring costs:
14G (~) ==-p
f0~ col(co) do,
and note that
~ c ' (~) -: p~f(~). The net share o f profits going to the lender is F(~0) - t~G(N), and the share going to the entrepreneur is 1 - F(N), where by definition F(o--) satisfies 0 < F ( N ) < 1. The assumptions made above imply: F(bS)-pG(~)>0
for
N C ( 0 , oo)
and lim F ( N ) - p G ( N ) = 0, ~ 0
lim F(cd) - #G(bS) = l - ~. 75 .---* o c
We therefore assume that Rk(1 - #) < R, otherwise the firm could obtain unbounded profits under monitoring that occurs with probability one s6.
36 The bound on F(~5) can be easily seen 17oii1the Ihct that both F(N) = E(~@~ < W)Pr(w < (~).-~ NPr(co ~>N) and 1 F(N) = (E(~o!(o >~~) -N)Pr(~o/> N) are positive. The limits on F(~5) -/~G(~]) can be seen by recognizing that G(?5) = E(co[~o < ~)Pr(m < N) so that lim~o~ G(N) = E(~o) = 1.
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Let h(N) = (f(~o)/(1 - F ( N ) ) , the hazard rate. We assume that Nh(N) is increasing in N 37. There are two immediate implications from this assumption regarding the shape of the net payoff to the lender. First, differentiating F(N) - #G(N), there exists an ~* such that
F'(~5)--t~G'(N) = (1 - F ( N ) ) ( 1 -/~Nh(N)) > 0
for
N < o) ,
implying that the net payoff to the lender reaches a global maximum at N*. The second implication of this assumption is that
F'(~)G"(~)-r"(~)6'(co)
- d(--d@T0°)))(1- F ( e ) ) ) 2 > 0
for all
These two implications are used to guarantee a non-rationing outcome. The optimal contracting problem with non-stochastic monitoring may now be written as
F (N) )Rk QK
max(1 K,~O
subject to [F(N) - pG(o)]RI'QK = R(QK - N). It is easiest to analyse this problem by first explicitly defining the premium on external funds s = Rk/R and then, owing to constant returns to scale, normalizing by wealth and using k = Q K / N the capital/wealth ratio as the choice variable 3s. Defining 2 as the Lagrange multiplier on the constraint that lenders earn their required rate of return
37 Any monotonically increasing transformation of the normal distribution satisfies this condition. To see this, define the inverse transformation z = z(?5), z'(N) > 0, with z ~ N(0, 1). The hazard rate for the standard normal satisfies h(z) = O(z)/(t - qS(z)), implying
(1
~o0(z(co)) ~(z(~)))
Difl'erentiating Nh(N) we obtain
d(o~h((o))
h(z(N)) + Oh'(z(N)) z'(N) > O,
dN where the inequality follows from the fact that the hazard rate for the standard normal is positive and strictly increasing. 3s It is worth noting that the basic contract structure as well as the non-rationing outcome extends in a straightforward manner to the case of non-constant returns to capital, as long as monitoring costs remain proportional to capital returns.
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in expectation, the first-order conditions for an interior solution to this problem may be written: : r ' ( ~ - ~ [ r ' ( @ - ~ G ' ( ~ ) ] = 0, k " [(1 - F(o~)) + ,~(F(o---)- # 6 ( 0 ) ] ;t" [ F ( N ) -
yG(N)lsk
- (k -
s - )~ = 0,
1) = 0.
Since F ( ~ k~G(N) is increasing on (0,N*) and decreasing on (N*, oo), the lender would never choose N > N*. We first consider the case 0 < co < N* which implies an interior solution 39. As we will show below, a sufficient condition to guarantee an interior solution is 1
s < F ( ~ * ) - ~tG(~*) - s * . We will argue below that s / > s* cannot be an equilibrium. A s s u m i n g an interior solution, the EO.C. with respect to the cutoff-(5 implies we can write the Lagrange multiplier )~ as a function o f N:
Z(~) =
r,(~
F'(~) ~G'(~)
Taking derivatives we obtain ~,(~)
-
~ [r'(~)a"(@ [r'(~
- F"(~)G'(@] -
~G'(~] 2
>0
for
~C(0,~*),
where the inequality follows directly from the assumption that ~ h ( ~ ) is increasing. Taking limits we obtain lim 2 ( ~ )
1,
~/--~0
lim )~(~o)= +oo. ?5 --~ i5"
Now define X(@ p(~5) =_ (1 - F(?~) + 3,(F(~) - / ~ G ( ~ ) ) ' then the EO.C. imply that the cutoff ~ satisfies s = p(N)
(A. 1)
so that p ( N ) is the wedge between the expected rate o f return on capital and the safe return demanded by lenders. Again, computing derivatives we obtain 2~ ( ) 1 - C(~) p'(?~-) = p ( ~ ' ~. . ( 1 - F ( ~ ) + J ~ ( F ( ~ ) - ~ G ( ~ ) )
> 0
for
N 5 (0, N~),
and taking limits: lim p ( ~ ) - - 1, ~-~0
lim p ( ~ ) = .,-.,~3"
1 1 ( F ( N * ) - # G ( N * ) ) ~ s* < -1--. / 2
Thus, for s < s*, these conditions guarantee a one-to-one mapping between the optimal cutoff N and the premium on external fhnds s. By inverting Equation (A.1) we may 39 Obviously, 65 = 0 cannot be a solution if s > 1.
B.X Bernanke et al.
1384
express this relationship as N = ~(s), where N~(s) > 0 for s E (1,s*). Equation (A.1) thus establishes the monotonically increasing relationship between default probabilities and the premium on external funds. Now define T ( ~ ) -- 1 +
x(r(~)
- ~G(~))
1 - r(~
Then, given a cutoff N C (0, ~*) the EO.C. imply a unique capital/wealth (and hence leverage) ratio: k
kv(~.
(A.2)
Computing derivatives we obtain
~'(~) r'(~) ~'(~): ~ (~(~)-- 1)+ q~(~5) > 0 1- r ( ~ )
for
co E (0, ~*),
and taking limits: lim ~ ( N ) = 1, ~--+0
lim
tp(N) = +oc.
o) ---~ a~*
Combining Equation (A. 1) with Equation (A.2) we may express the capital/wealth ratio as an increasing function of the premium on external funds: k - ~p(s),
(A.3)
with
'q/(s) > 0 tbr s c (I,s*). Since lim~o~o, q-t(~o) - +oc and lim~o--+~o*p(~5) - s*, as s approaches s* from below, the capital stock becomes unbounded. In equilibrium this will lower the excess return s. Now consider the possibility that the lender sets o) - co*. The lender would only do so if the excess return s is greater than s*. In this case, the lender receives an expected excess return equal to
(c(~*)
~G(~*)) sk k =
S
--
S*
S*
k >0.
Since the expected excess return is strictly positive for all k, the lender is willing to lend out an arbitrary large amount, and both the borrower and lender can obtain unbounded profits. Again, such actions would drive down the rate o f return on capital
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in equilibrium, ensuring s < s* and guaranteeing an interior solution for the cutoff ~ (o, ~*). A.2. The l o g - n o r m a l d i s t r i b u t i o n
In this section, we provide analytical expressions for F(~--) and _F(N) - /~G(N), for the case where co is distributed log-normally 4°. Under the assumption that ln(co) ~ N(-½cr 2, cr2) we have E(co) = 1 and 1 -
E(co]co/> ~ ) -
4,(~ 1 -
-
a)
¢(z)
'
where @(.) is the c.d.f, of the standard normal and z is related to N through z - 0n(N) + 0.502)/o ". Using the fact that 1 - F ( N ) = (E(co]co ~> 05) - co) Pr(co ~> ~)), we obtain
r ( m ) - O(z
c0 + m[l - o(~)1
and r(co)-
~ G ( m ) = (l - ~ ) q , ( ~ -
,J) + co[1 - O(z)].
A.3. A g g r e g a t e r i s k
To accommodate the possibility o f aggregate risk, we modify the contracting framework in the following manner. Let profits per unit o f capital expenditures now equal rcoR k where co represents the idiosyncratic shock, r represents an aggregate shock to the profit rate, and E(co) = E ( r ) = 1. Since entrepreneurs are risk neutral, we assume that they bear all the aggregate risk associated with the contract. Again, letting Rk the ex ante premium on external funds, and k = Q K / N , capital per dollar of s = ~self-financing, the optimal contracting problem may be now be written: m a x E { ( 1 - F(zoD)risk ~ X [(F(N)
t~G(~5))risk - ( k - 1)1},
where ,l is the ex post value (after the realization of the aggregate shock r) of the Lagrange multiplier on the constraint that lenders earn their required return and E{ } refers to expectations taken over the distribution o f the aggregate shock ~. We wish to establish that with the addition of aggregate risk, the capital/wealth ratio k is a still an increasing function o f the ex ante premium on external funds. Define
40 Since the log-normal is a monotonic transformation of the normal, it satisfies the condition d(~h((~)))/d?~ > O.
B.S. Bernankeet al.
1386
F ( N ) -= I - F ( ~ ) + )~(F(co) - # G ( N ) ) . T h e first-order conditions for the contracting p r o b l e m m a y be written as
N - r ' ( N ) - z [ r ' ( ~ ) -- ~ c ' ( N ) ]
= 0,
k : E { F ( o ) ~s - ,t(N)} = 0, Z : (r(~
- ~G(~)
~s - (k - l) = 0.
A g a i n , under no rationing, the first-order condition with respect to ~) defines the f u n c t i o n 3,(N). This function is identical to )~(N) defined in the case o f no a g g r e g a t e risk. The constraint that lenders earn their required rate o f return defines an implicit function for the c u t o f f N = N(fi, s, k) 41 . C o m p u t i n g derivatives we obtain 0F
-(F(N)--- ~G(N))
Os
0.
To obtain a relationship o f the f o r m k = ~p(s), ~p'(s) > 0 we totally differentiate the first-order condition with respect to capital:
E ~D"(N)ds+~tsFt(N) Os-dS+o~dk
-)~'(~)
~-sdS+~dk
=0.
R e a r r a n g i n g gives
dk
E/(~sr'(N)--
OF + ~F(N)} X'(~o)) N
U s i n g the fact that F ' ( N ) --- ~ ' ( N ) ( F ( N ) - ~ O ( N ) )
41 As a technical matter, it is possible that the innovation in aggregate returns is sufficiently low that N(/~, s, k) > N*, in which case the lender would set N = N* and effectively absorb some of the aggregate risk. We rule out this possibility by assumption. An alternative interpretation is that we solve a contracting problem that is approximately correct and note that in our parametrized model aggregate shocks would have to be implausibly large before such distortions to the contract could be considered numerically relevant.
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we obtain = ~'(~)k
~,
implying that dk/ds simplifies to the expression d k _ E{fisF(~) - ~ ' ( ~ ) ~ ds
}
t -- OF
Since ON/Os < O, Oo)/Ok > 0, and U(N) > 0, the numerator and denominator of this expression are positive, thus establishing the positive relationship between the capital/wealth ratio k and the premium on external funds s. Appendix B. Household, retail and government sectors
We now describe the details of the household, retail, and govermnent sectors that, along with details of the entrepreneurial sector presented in Section 4, underlie the log-linearized macroeconomic framework. B.1. Households
Our household sector is reasonably conventional. There is a continuum of households of length unity. Each household works, consumes, holds money, and invests its savings in a financial intermediary that pays the riskless rate of return. Ct is household consumption, Mt/P~ is real money balances acquired at t and carried into t + 1, H/ is household labor supply, W~ is the real wage for household labor, Tt is lump sum taxes, Dt is deposits held at intermediaries (in real terms), and Ht is dividends received from ownership of retail firms. The household's objective is given by OG
max Et Z
[3k [ln(Ct+:~)+ ~ ln(Mt,/~/P~ k) + ~ ln( 1 Ht ~k)]-
(B. 1)
k-0
The individual household budget constraint is given by Ct = WtH: - Tt +17: + RtD~- Dt+l +
(M,-I - iV/:) P:
(B.2)
The household chooses C/, D~+I, Hi and Mt/Pr to maximize Equation (B. 1) subject to Equation (B.2). Solving the household's problem yields standard first-order conditions for consumption/saving, labor supply, and money holdings: 1
E f
1
B.S. Bernanke et al.
1388
W, 1
e
1
(B.4)
* Ct = b 1 - ~ '
Mt
-
~Ct ( R ; + I ~ I ) - I
Pt
\
,
(t3.5)
Rt+l
where R~ 1 is the gross nominal interest, i.e., n Pt~.l _ 1. it+ I -7_ Rt+ 1 Pt
Note that the first-order condition for M,/Pt implies that the demand for real money balances is positively related to consumption and inversely related to the net nominal interest rate. Finally, note that in equilibrium, household deposits at intermediaries equal total loanable funds supplied to entrepreneurs:
D l -- Bt. B.2. The retail sector and price setting
As is standard in the literature, to motivate sticky prices we modify the model to allow for monopolistic competition and (implicit) costs of adjusting nominal prices. As is discussed in the text, we assume that the monopolistic competition occurs at the "retail" level. Let Y,(z) be the quantity of output sold by retailer z, measured in units of wholesale goods, and let Pt(z) be the nominal price. Total final usable goods, Y{, are the following composite of individual retail goods:
=E/01 with e > 1. The corresponding price index is given by
Final output may then be either transformed into a single type of consumption good, invested, consumed by the government or used up in monitoring costs. In particular, the economy-wide resource constraint is given by
Y[=Ct+C[+L+Gt+/J
J0 ~odF(co)R~Q,~K~,
where C[ is enta'epreneurial consumption and # fo~)'o)dF(co)RfQ gate monitoring costs.
(B.8) 1I£t reflects aggre=
Ch. 21." The Financial Accelerator in a Quantitative Business Cycle Framework
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Given the index (B.6) that aggregates individual retail goods into final goods, the demand curve facing each retailer is given by r,(z) =
(P,(z) /
yi
(B9)
The retailer then chooses the sale price Pt(z), taking as given the demand curve and the price of wholesale goods, P~. To introduce price inertia, we assume that the retailer is free to change its price in a given period only with probability 1 - 0, following Calvo (1983). Let P[ denote the price set by retailers who are able to change prices at t, and let Yt*(z) denote the demand given this price. Retailer z chooses his price to maximize expected discounted profits, given by
o~ r p . pw -[ /a t_ ~ t + k * /~=o Ol'Et-I [l,t,/, Pt+k Yt+lc(z)~ ,
(B.10)
where the discount rate A,/, = fiCJ(Ct~/,) is the household (i.e., shareholder) intertemporal marginal rate of substitution, which the retailer takes as given, and where P ~ =-- PriNt is the nominal price of wholesale goods. Differentiating the objective with respect to P[ implies that the optimally set price satisfies
~OkE,
1 At,k \Pt+k/
kp.k -
p~+~j
:0.
(B.11)
k=0
Roughly speaking, the retailer sets his price so that in expectation discounted marginal revenue equals discounted marginal cost, given the constraint that the nominal price is fixed in period k with probability Ok. Given that the fraction 0 of retailers do not change their price in period t, the aggregate price evolves according to
Pt = [OP~_~ + (10)(P;)(I-~)] ~/(t c),
(B.12)
where P[ satisfies Equation (B.11). By combining Equations (B.11) and (B.12), and then log-linearizing, it is possible to obtain the Phillips curve in the text, Equation (4.22).
B.3. Government sector We now close the model by specifying the government budget constraint. We assume that government expenditures are financed by lump-sum taxes and money creation as follows:
Gt-
M,-M,~ Pt
4 Tt.
The government adjusts the mix of financing between money creation and lnmp-sum taxes to support the interest rate rule given by Equation (4.25).
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This, in conjunction with the characterization in Section 5 o f the entrepreneurial sector and the m o n e t a r y policy rule and shock processes, completes the description o f the model.
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Rotemberg, J.J., and M. Woodford (1997), "An optimization-based econometric framework for the evaluation of monetary policy", NBER Macroeconomics Annual, 297-345. Sharpe, S. (1994), "Financial market imperfections, firm leverage, and the cyclicality of employment", American Economic Review 84:1060~1074. Suarez, J., and O. Sussman (1997), "A stylized model of financially-driven bushless cycles", unpublished paper (CEMFI and Ben-Gurion University, September). Taylor, J.B. (1993), "Discretion versus rules in practice", Carnegie-Rochester Conference Series on Public Policy 39:195-214. Townsend, R.M. (1979), "Optimal contracts and competitive markets with costly state verification", Journal of Economic Theory 21:265-293. Townsend, R.M. (1995), "Fhlancial systems in northern Thai villages", Quarterly Journal of Economics 110:1011-1046. Whited, T, (1992), "Debt, liquidity constraints, and corporate investment: evidence from panel data", Journal of Finance 47:1425-1460. Williamson, S. (1987), "Financial intermediation, business failures, and real business cycles", Journal of Political Economy 95:1196-1216. Wojnilower, A. (1980), "The central role of credit crunches in recent 151ancial history", Brookings Papers on Economic Activity 1980(2):277-326. Zeldes, S.E (1989), "Consumption and liquidity constraints: an empirical investigation", Journal of Political Economy 97:305-346.
Chapter 22
POLITICAL ECONOMICS AND MACROECONOMIC POLICY* TORSTEN PERSSON Institute for International Economic Studies, Stockholm University, S-106 91 Stockholm, Sweden. E-mail:
[email protected]. GUIDO TABELLINI IGIER, Bocconi University, via Salasco 3/5, 20136 Milano, Italy. E-mail:
[email protected] Contents Abstract Keywords 1. I n t r o d u c t i o n
Part A. Monetary Policy 2. C r e d i b i l i t y o f m o n e t a r y p o l i c y 2.1. A simple positive model of monetary policy 2.2. Ex ante optimal monetary policy 2.3. Discretion and credibility 2.4. Reputation 2.5. Notes on the literature 3. Political cycles 3.1. Opportunistic governments 3.1.1. Moral hazard in monetary policy 3.1.2. The equilibrium 3.1.3. Adverse selection 3.2. Partisan governments 3.2.1. The model 3.2.2. Economic equilibrium 3.2.3. Political equilibrium 3.3. Notes on the literature
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* We are grateful to participants in the Handbook conference at the Federal Reserve Bank of New York, to our discussant Adam Posen and to Roel Beetsma, Jon Faust, Francesco Lippi, Ken Rogofl, Lars Svensson and Jolm Taylor for helpful comments. The research was supported by Harvard University, by a grant fi:om the Bank of Sweden Tercentenary Foundation and by a TMR Grant fi:om the Europema Commission. We are grateful to Christina Lrnnblad and Alessandra Startari for editorial assistance. Handbook of Macroeconomics, Volume 1, Edited by J.B. Taylor" and M. WoodJbrd © 1999 Elsevier Science B. I( All tights reserved 1397
1398 4. Institutions and incentives 4.1. Fixed exchange rates: simple rules and escape clauses 4.2. Central bank independence 4.3. Inflation targets and inflation contracts 4.4. Notes on the literature
Part B. Fiscal Policy 5. Credibility o f fiscal policy 5.1. The capital levy problem 5.1.1. The model 5.1.2. The e x a n w optimal policy 5.1.3. Equilibrium under discretion 5.1.4. Extensions 5.2. Multiple equilibria and confidence crises 5.3. Public debt management 5.4. Reputation and enforcement 5.5. Notes on the literature 6. Politics o f public debt 6.1. Political instability in a two-party system 6.1.1. Economic equilibrium 6.1.2. The political system 6.1.3. Equilibrium policy 6.1.4. Endogenous election outcomes 6.1.5. Discussion 6.2. Coalition governments 6.2.1. Equilibrium debt issue 6.2.2. A stronger budget process 6.3. Delayed stabilizations 6.4. Debt and intergenerationat politics 6.5. Notes on the literature
Part C. Politics and Growth 7. Fiscal policy and growth 7.1. Inequality and growth 7.2. Political instability and growth 7.3. Property rights and growth 7.4. Notes on the literature References
77. P e r s s o n a n d G. Tabellini
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Abstract
This chapter surveys the recent literature on the theory of macroeconomic policy. We study the effect of various incentive constraints on the policy making process, such as lack of credibility, political opportunism, political ideology, and divided government. The survey is organized in three parts. Part I deals with monetary policy in a simple Phillips curve model: it covers credibility issues, political business cycles, and optimal design of monetary institutions. Part II deals with fiscal policy in a dynamic general equilibrium set up: the main topics here are credibility of tax policy, and political determinants of budget deficits. Part II! studies economic growth in models with endogenous fiscal policy.
Keywords politics, monetary policy, fiscal policy, credibility, budget deficits J E L classification: E5, E6, H2, H3, O1
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1. Introduction
Traditional macroeconomic policy analysis asks the positive question of how the economy responds to alternative, but exogenous, policy actions or rules. Knowing these responses, the analyst can go on to the normative problem of policy advice. The best action or rule is selected, given a specific objective function. But as macroeconomists, we should also be able to shed light on a more ambitious set of questions. Why is it that we observe such different inflation rates across countries and time? Why did we not observe peace-time accumulations of government debt until the seventies, and why did they arise only in some countries? Why are growth rates so different in different parts of the world? To answer such questions, we need a positive theory, explaining why different countries choose different macroeconomic policies. Early steps towards such a theory were taken about twenty years ago; the credibility problem in macroeconomic policy was introduced by Kydland and Prescott (1977) and Calvo (1978), and the first models of electoral and partisan motivations in policymaking were suggested by Nordhaus (1975) and Hibbs (1977). The literature did not really take off until ten years later. But since then "political economy", or "political economics" as we prefer to call it, has been one of the most active fields in macroeconomics as well as in other branches of economics 1. With its emphasis on institutions as important determinants of policy, this literature has taken the normative analysis one step further, replacing the question: Which policies should be followed? with the question: What policymaking institutions produce better policy outcomes? In surveying this literature, we split the material into three parts: Part I deals with monetary policy, Part II with fiscal policy, and Part III with growth. Following the conventional approach in the literature, this division is based both on substance and on methodology. The monetary policy part relies on quadratic loss functions over macroeconomic outcomes and on models incorporating rational expectations, but assuming an ad hoc Phillips Curve. The fiscal policy and growth parts have better microfoundations: agents' preferences, technologies and endowments govern their economic and political interactions in simple, but complete, two-period general equilibrium models. Each part emphasizes the credibility and politics ofpolicymaking, and includes a normative evaluation of different institutions. The general approach of this line of research is to explain deviations in observed economic policies from a hypothetical social optimum by appealing to specific incentive constraints in the decision problem of optimizing policymakers. The positive analysis focuses on identifying the relevant incentive constraints, while the normative analysis focuses on institutional reforms which may relax them. Despite the separation into three parts, several common themes run throughout the chapter, reflecting similar incentive constraints. It is useful to summarize already here the nature of these incentive constraints, when they arise, and their positive and normative implications.
Many recent contributionshave been collectedin Persson and 'labellini (1994a).
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Desirable policies may suffer from lack o f credibility when policy decisions are taken sequentially over time (under "discretion") and the government lacks a nondistorting policy instrument, so that the socially optimal policy (the optimal policy in the absence of the incentive constraint) yields a second-best outcome. Lack of credibility has several positive implications, and arises both in monetary and in fiscal policy. When the government takes private expectations embodied in private economic decisions as given, it neglects the policy effects rumfing through expectation formation. This way, equilibrium average inflation or wealth taxes become too high. Moreover, in a Natural Rate world, monetary policy and inflation respond to all shocks, and not only to those over which the monetary authority has an information advantage, as the optimal policy should do. Losing control of private expectations also makes the governanen~ a prospective victim of confidence crises: runs on public debt, capital flight, or speculative attacks on the currency. All these events stem from the same fundamental problem: the government is forced to react to self-fulfilling private expectations. Finally, lack of credibility breaks a Modigliani-Miller theorem of government finance, in the same way as incentive constraints in the relationship between owners and managers break the Modigliani-Miller theorem of corporate finance. The composition of the outstanding public debt into nominal or real securities (i.e. indexed to the price level) affects the propensity of a govenmaent to rely on unexpected inflation as a source of government revenue. Similarly, the maturity composition o f government debt affects the likelihood of debt runs or the interest rate policies that future governments want to pursue. Thus, public debt management can relax future incentive constraints and thereby affect private sector expectations. Lack of credibility also has implications for institution design. First, it makes delegation to an independent policymaker desirable. Second, it makes it desirable to restrict the tasks of the policymaker. Rather than pursuing loosely defined social welfare, the central bank should target a specific variable, such as inflation, or the money supply, or the exchange rate. I f a sufficiently rich incentive mechanism - a complete contract - can be designed and enforced, the credibility problem can be eliminated completely. If state-contingent payments are not feasible, however, or if narrowly defined tasks are inappropriate, as in fiscal policy, incentive mechanisms are necessarily incomplete. But in order to gain credibility, strategic delegation of the decision-making authority to a policymaker with "distorted" preferences may still be desirable. This insight has been exploited in monetary policy, to advocate the benefit of an independent and "conservative" central bank. It also applies to the election of a conservative policymaker facing the task of selecting a wealth tax, or to the delegation of certain policy choices to a foreign government, as in the case of multilateral exchange rate arrangements, or currency boards 2. 2 International competition is another institutional device %r coping with credibility which is emphasized in the literature but not in this survey. Tax competition, or exchange rate competition, conhibute to overcoming a domestic credibility problem because they can reduce the ex-post incentives to unilaterally increase tax rates or inflation.
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A second incentive constraint is political opportunism, by which we mean that the incumbent government is prepared to introduce distorted policies to increase its chances of re-election. This incentive constraint typically applies when politicians value holding office p e r se and voters, although rational, are uninformed. We study the consequences of political opportunism in monetary policy only, but the empirical implications for fiscal policy have been spelled out in the literature. The main prediction is an electoral cycle in aggregate demand policies: the incumbent government has an incentive to stimulate the economy just before elections to appear more competent in the eyes of uninformed voters, thus boosting of the probability of re-election. This always leads to an electoral cycle in inflation which, depending on the information advantage of the government, could also increase output volatility at the time of elections. The normative implications tend to reinforce those of the credibility literature: central bank independence and monetary or inflation targets reduce the scope for electoral cycles in monetary policy. Other, deeper reforms, such as who should have the right to call the elections and at what time, remain to be investigated. Political ideology may shape policy formation if different parties pursue different "partisan" (i.e. ideological) platforms once in oNce, and if the election outcome is uncertain. Political polarization and political instability thus induce another incentive constraint, which also gives rise to an electoral cycle in aggregate demand, output or public spending. But here the cycle takes place after, rather than before, elections and reflects the winning party's desire to influence economic outcomes. In a dynamic context, this incentive constraint may generate "strategic myopia". The government in office realizes that it may be replaced by a policymaker with different ideological preferences. This gives an incentive to accumulate public debt or postpone investment, so as to influence the future behavior of the opponent. Political ideology also implies strategic manipulation of state variables to influence the voters; for instance, an extremist incumbent may restrain his own future behavior by appropriate institutional reforms to increase his own electability. The strategic manipulation of future opponents and voters are both stronger, the more unstable and polarized the political system. From a normative point of view, the benefits of delegation and targeting in monetary policy are further reinforced. More generally, there may be advantages of institutional checks and balances and institutions that moderate political conflict and policy extremism. The discussion, so far, applies to a single decision-maker facing static or dynamic incentive constraints. Often, however, decision-making power is dispersed among several political actors. This creates another incentive constraint, which we may call divided government. Examples include coalition governments, soft budget constraints on public enterprises or local governments, veto rights held by key individuals in government or by organized groups in society, or the lobbying activities of special interests. Divided government arises almost exclusively in fiscal policy. In a static context its central implication is over-spending, as every decision-maker fully internalizes the benefits of public spending but only a fraction of the cost: this is the so called "common pool" problem. In a dynamic context, myopic behavior emerges: each decision-maker has an incentive not only to over-spend, but also to spend
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sooner rather than later. Leaving tax revenues for tomorrow can be counter-productive, because they are partly appropriated by other decision-makers. Hence, models of divided government also predict debt accumulation and/or under-investment. In some circumstances, the dispersion of veto rights delays stabilization in an unsustainable fiscal situation. The most straightforward institutional remedy is to centralize power in the hands of a single decision-maker (a prime minister, or a president, or the Secretary of the Treasury). Alternatively, one might rely on two-stage budgeting, with a decision on aggregate items (total spending, or total borrowing) preceding the decision on how spending is allocated. Such budgetary solutions entail a trade-offbetween an allocative distortion (a lopsided spending result from centralized decision-making power) and an aggregate distortion (over-spending resulting from inadequate centralization). At a deeper political level, the incentive constraints induced by divided government and political ideology can be traded off. Political reforms that centralize power in the hands of single parties or individuals also exacerbate polarization between the majority and the opposition, and may thus imply that political instability becomes a more binding incentive constraint. The last incentive constraint considered in this chapter arises when there is income heterogeneity, so that tax policies are motivated by pressure .for redistribution. The positive implication is that the overall size of government is determined by the extent of inequality in pre-tax income or, in the case of social insurance policies, by inequality in risk. This, in turn, has implications for the link between inequality and measures of economic performance. But the redistributive motive is also an important force shaping the composition of spending or the structure of taxation. Public financial policies that redistribute along different dimensions become non-equivalent, because they are supported by different coalitions of voters. For instance, public debt and social security redistribute across generations in the same way; nevertheless in a political equilibrium they give rise to different allocations, because they redistribute between rich and poor in different ways. A similar non-equivalence result holds with regard to alternative instruments of geographic redistribution. As in the case of lacking credibility, an incentive constraint on policy formation breaks the Modigliani-Miller theorem of government finance. Some of the topics covered in this survey partly overlap with a companion survey, Persson and Tabellini (1999). There we cover the literature on public economics and public choice, dealing with static allocation issues in fiscal policy, rather than the intertemporal policy issues emphasized here. Neither do we cover the literature on monetary and fiscal policy in an international context, which is surveyed in Persson and Tabellini (1995). Each part starts with a separate introduction, in which we highlight a number of empirical regularities, motivating the sections to follow, and provide a more detailed road map. We comment on the original literature both as we go along and in separate "Notes on the Literature" at the end of each section.
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Part A. Monetary Policy The empirical evidence for the (democratic) OECD countries in the post-war period suggests the following stylized facts: (i) Inflation rates vary greatly across countries and time. But there is a common time pattern: in most countries inflation was low in the 1960s, but very high in the 1970s; it came down in the 1980s and 1990s in all countries, though at different speeds and to different extents 3. (ii) Inflation rates are correlated with real variables, such as growth or unemployment, in the short run. But there is little evidence o f a systematic correlation over longer periods. Across countries, average inflation and average growth tend to be negatively correlated or not correlated at all 4. (iii) There is little evidence o f systematic spillover effects between monetary and fiscal policy. Specifically, higher budget deficits are not systematically associated with higher inflation rates 5. (iv) Inflation increases shortly after elections; budget deficits tend to be larger during election years; there is also some (not very strong) evidence that monetary policy is more expansionary before elections. On the other hand, real variables such as growth or unemployment are not systematically correlated with election dates. (v) Output displays a temporary partisan cycle just after elections: newly appointed left-wing governments are associated with expansions, right-wing governments with recessions. This cycle tends to occur in the first half o f the inter-election period and is more pronounced in countries with two-party systems. Inflation displays a permanent partisan cycle: higher inflation is associated with left-wing governments 6 (vi) Average inflation rates and measures of central bank independence are negatively correlated; this holds up when controlling for other economic and institutional variables (even though the correlation is less robust). There is also some evidence that fixed exchange rates are associated with lower inflation. Real variables, on the other hand, have no systematic correlation with the monetary regime (although the variance o f the real exchange rate is lower under fixed than floating exchange rates) 7 These stylized facts will be taken as the starting point for Part I. Fact (i) clearly calls tbr a positive model of inflation. Fact (ii) is not well understood and the profession See, for instance, Bordo and Schwartz (1999). 4 Time-series evidence (for the USA) can be found in Stock and Watson (1999), whereas (broad) cross-country evidence can be found in Barro (1997) and in Fischer (1991). s See for instance Grilli et al. (1991). This fact no longer applies if one considers the interwar period or developing countries. In particular hyperinflations are typically associated with fiscal problems. 6 Statements (iv) and (v) are suggested by the comprehensive study by Alesina and Roubini (t997). 7 See Grilli et al. (1991), Cukierman (1992), Jonsson (1995), Eijffinger and de Haan (1996), Mussa ~1986), Baxter and Stockman (1989). The robusmess of these findings has been questioned by Posen (1993, 1995), however.
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is still searching for a satisfactory model of the joint determination of nominal and real variables. But it suggests that a plausible model would encompass the natural rate hypothesis that the Phillips curve is vertical and monetary policy is neutral in the long run, while preserving some scope for aggregate demand policies to affect output in the short run. Fact (iii) suggests that abstracting from fiscal policy may not be a bad first approximation. Facts (iv) and (v) indicate that political variables might be important ingredients in successful positive models of inflation and macroeconomic policy. Fact (vi) finally suggests that the institutional features of the monetary regime particularly the statutes regulating the central bank - should also play a role in a successful model. In Section 2 we formulate and discuss a model of macroeconomic policy and inflation which has been the workhorse in much of the recent literature. We illustrate how credibility problems in monetary policy may arise and how these may be fully or partly resolved by reputation. Section 3 extends the simple model with political institutions and incentives. We illustrate how political business cycles and partisan cycles, consistent with the stylized facts above, may come about. Designing nqonetary institutions to tackle the distortions created by credibility problems and political cycles is the topic of Section 4.
2. Credibility of monetary policy In this section, we first formulate and discuss a model of macroeconomic policy and inflation, in the spirit of Kydland and Prescott (1977), Fischer (1977) and Barro and Gordon (1983a), which has been the starting point for much of the recent literature. In subsection 2.1 we set up the model and make general comments. Subsection 2.2 derives a normative benchmark. In subsection 2.3 we emphasize how the credibility problems tied to the central banks' ability to temporarily boost the economy result in excessively high equilibrium inflation - the celebrated "inflation bias". Subsection 2.4 briefly illustrates how reputation may provide full or partial solutions to such credibility problems, drawing on the work by Barro and Gordon (1983b), Backus and Driffill (1985), Canzoneri (1985) and others that - in turn - borrow heavily from the literature on repeated games. 2.1. A simple positive model o f monetary policy
The demand side of our model economy is represented by :~: = m + v + # ,
(2.1)
where o~ is inflation, m is the money growth rate, v is a demand (or velocity) shock, and ?2 is a "control error" in monetary policy. Letting output enter the implicit money demand function underlying Equation (2.1) complicates the algebra, but does not yield
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important additional insights. The supply side of the model assumes that nominal wage setting (unilaterally by firms, unilaterally by labor unions, or bilaterally by bargaining between these actors) aims at implementing an exogenous, but stochastic, real wage growth target ~o 8. Letting er° denote rationally expected inflation, nominal wage growth w then becomes w = (o + :r e.
(2.2)
Employment (or output growth), x, satisfies x= y-(w-er)-e,
where 7 is a (potentially stochastic) parameter, and e is a supply shock. Combining this relation with Equation (2.2), we obtain an expectations-augmented short-run Phillips curve
x = 0 + (er
ere)_ e,
(2.3)
where 0 - 7 - ~o can be interpreted as the stochastic natural rate of employment (output growth). We assume that all shocks are i.i.d., orthogonal to each other, have (unconditionally) expected values of zero, well-defined variances ~7~,~ { , and so on. The timing of events is as follows: (0) rules of the monetary regime may be laid down at an institution design stage; (1) the value of 0 is observed both by the private sector and the policymaker; (2) er~ is formed, given the information about 0; (3) the values of v and e are observed; (4) the policymaker determines m; (5) /~ is realized together with er and x. The assumed timing captures the following concerns: Some shocks, related to the labor market, are commonly observable and can therefore be embodied in privatesector wage-setting decisions, here captured by expectations formation. Other shocks can only be embodied in policy. This distinction is best interpreted as reflecting the ease with which monetary policy decisions are made, relative to the laborious wage-setting process, but could also reflect a genuine information advantage of the policymaker (which is perhaps only plausible for financial sector shocks). O f course, it is this advantage that allows monetary policy to stabilize the economy. Finally, there is some unavoidable noise in the relation between policy and macroeconomic outcomes.
As is well-!~lown, the "surprise supply" formulation wc end up with below could also be derived from a model of price-setting finns, or from a Lucas-style "island model".
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Clearly, Equation (2.1) and the assumed information implies that rationally expected inflation is Jr° --E(ar ] 0 ) = E(m I 0),
(2.4)
where E is the expectations operator. Substituting Equations (2.1) and (2.4) into (2.3), we have x=O+m-E(m[
O)+v~-~
&
(2.5)
The model thus entails the usual neutrality result: only unanticipated aggregate demand policy affects real variables. But if policy responds to shocks, it can still stabilize employment. 2.2. Ex ante optimal monetary policy
We follow the rational expectations literature in thinking about policy as a rule. Suppose society has the quadratic loss function E[L(0r, x)] : ½E[(ar - yg*)2+ ~(X --
X*)2],
(2.6)
where a~* and x* are society's most preferred values for inflation and employment, and ,~ is the relative weight on fluctuations in these two variables. As the objective is quadratic in macroeconomic outcomes, which in turn are linear in the shocks, the optimal policy rule is of the form m - k + k ° O + k V v ~k%';
(2.7)
that is, policy potentially responds to all shocks observable to the policymaker. Suppose furthermore that the policymaker can make a binding commitment to the rule (2.7) at the institution design stage (0), i.e. before the observation of 0. Clearly, since E(v) = E(E) = 0, this implies private sector expectations: E(m [ O) = k + k°O.
(2.8)
By Equations (2.1), (2.5), (2.7) and (2.8), macroeconomic equilibrium under the rule is
Jc - k +k°O+ (k ~ + 1) v + U E + t~, x - O+(k~+ 1) v + g + ( k e - 1)e.
(2.9) (2.10)
What is the optimal rule? Substitute Equations (2.9) and (2.10) into (2.6), take expectations over all shocks, and set the derivatives of the resulting expression with regard to the intercept and the slope coefficients in Equation (2.7) equal to zero. The following results emerge:
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(i)
k - :~* and k ° = 0. The optimal rule provides an "anchor for inflationary expectations". Expectations are right where society wants them to be, namely at the preferred rate o f inflation: E(Jv [ 0) - zc*. The optimal rule is thus neither conditional on the observable shock to the natural rate, 0, nor on society' s output target, x*. Such conditionality would be embodied in expectations; it would therefore do nothing to stabilize employment, only add costly noise to inflation. (ii) k ~ = - 1 . Demand (velocity) shocks are fully stabilized. As policy also operates via aggregate demand, a complete stabilization o f demand shocks nullifies their effects on inflation as well as on employment. (iii) k e = ~ / ( i + 30. Supply shocks are stabilized according to the policymaker's tradeoff between inflation and employment fluctuations. The higher the weight on employment, the more these shocks are stabilized. The optimal state-contingent policy rule can thus be written as /l m = Yg* - v + ( 1 ~ 6 . Macroeconomic omcomes -- indexed by R - when the rule is ~bllowed are Jr j~ = ~* + ~ - ~ e q 1 xa = 0- ~e+/~.
/~,
(2.11) (2.12)
Results such as these have been - and continue to be - very influential for academic economists' thinking about policy. They suggest that delivering low inflation and stable employment is essentially a technical (not a strategic) problem: inflation can be kept low by clearly announcing a rule aiming at low average inflation. Demand shocks should be completely stabilized. The inflation and employment consequences o f supply shocks should be traded off according to society's preferences. Control errors are unavoidable, but can perhaps be reduced by better forecasting or operating procedures in monetary policy. Even though this picture is too rosy for a realistic positive model o f macroeconomic policy, it still provides a useful normative benchmark that we can use to evaluate the outcome in the positive models below. In the remainder o f the chapter, we simplify the stochastic structure by setting v = /~ = 0. Demand shocks, as we saw, present no problem for the policymaker in this class o f models, provided that they can be identified in time and that there are no other policy goals such as interest-rate smoothing. Control errors do present problems, but are unavoidable 9. With these simplifications, there is no meaningful
9 Abstracting from conUol errors is irmocuous as long as the public can monitor monetary policy perfectly and as long as policymaker competency and efforts are exogenous. Below, we comment on where control errors would matter. Moreover, in a richer (dynamic) setting with expectations entering the aggregate demand function, demand shocks and control errors may give rise to incentive problems similar to those discussed below.
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distinction in the model between m and st. For simplicity, we therefore assume that the policymaker sets .re directly. Why don't we eliminate the shocks to the natural rate 0, with a similar motivation? The answer is that such shocks do not affect the solution under commitment, whereas they do affect policy in an interesting way under alternative assumptions about the policymaking process. 2.3. Discretion and credibility
In reality, decisions on monetary policy are taken sequentially over time, rather than once and for all. Assuming ex ante commitment to a state-contingent policy rule rhymes badly with this practice. In our static model, reality is better captured by an alternative timing: policy is chosen under "discretion" when the policy instruments are set at stage (4) above, after wages have been set (37e formed) and shocks have been realized. This adds an ex post incentive compatibility condition to our positive model: policy has to be optimal ex post - when it is actually enacted. This additional credibility constraint makes the solution less advantageous for the policymaker (and society). The policymaker still sets sr (that is, m), seeking to minimize the loss in Equation (2.6). But all uncertainty has been resolved at the new decision stage, so the expectations operator is redundant. Consider how the loss is affected by a marginal expansion, for given :U and e. Using Equations (2.3) and (2.6), we have dL(yG x)
d~
-Ljr(zc, x)+L~(Jv, x)-~2 - ( z r - ~ * ) + ) ~ ( O + ( z C (lJ~
~)-~'-x*),
(2.13)
where a subscript denotes a partial derivative. By Equation (2.13), the benchmark policy rule is not incentive compatible under discretion. Suppose that wage setters believed in an announcement of that rule, implying that :ve - sT*. Using the optimal-rules outcome in Equations (2.1 1)-(2.12), and evaluating the derivative in Equation (2.13) at the point prescribed by the ex ante optimal policy rule, we get dL(~R'Xa)dz z~::z* = X(O x*). If preferred employment (output) exceeds tile natural rate (if x* > 0), ar~ expansioii reduces the loss, rendering the ex ante sub-optimal policy rule ex post inoptimal. Once wages have been set, the marginal inflation cost - the first term on the RHS of Equation (2.13) - is always smaller than the marginal employment benefit - the second term on the RHS 10. Thus, the ex post incentive-compatibility constraint is binding and the low-inflation rule is not credible.
l0 To make this more clear, consider the case when c - 0, such that tile optima| rule prescribes the policy sTR = ~*, implying xR = 0. Then, by Equation (2.13) the marginal inflation cost is acmalty zero (to first order), whereas the marginal employment benefit is positive (if x* > 0).
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A credible policy must simultaneously fulfill two conditions: (i) the policy is e x optimal, ~y dL = 0, given :re and e; (ii) expectations are rational, i.e. ~e = E(s~ I 0). In game-theoretic terms, those are the conditions for a Nash Equilibrium in a game with many atomistic private wage setters (desiring to minimize the deviation of the realized real wage w - ~e, from the targeted real wage co) moving before the policymaker 11. Condition (i) requires that the expression in Equation (2.13) equals zero. Taking expectations of that expression, condition (ii) can be expressed as E(zc ] 0) = ~* + 3,(x* - 0). Combining the two conditions, we get
post
a -D = st* + ,~(x* - 0) + ~ e , +A,
(2.14)
where the D superscript stands for discretion. The employment outcome remains as in Equation (2.12) except that /~ = 0 by assumption, if we assume x* - 0 > 0, the discretionary policy outcome in Equation (2.14) and the commitment outcome in Equations (2.11)-(2.12) illustrate the celebrated "inflation bias" result: equilibrium inflation is higher under discretion than under commitment to a rule, whereas employment is the same, independently of the policy regime. The bias is more pronounced the higher is ;, (the more valuable is employment on the margin) and the higher is x* relative to 0 (the higher is preferred employment relative to the natural rate); both factors contribute to a greater "temptation" for the policymaker to exploit his short-run ability to boost employment by expansionary policy once wages are fixed. Since the natural rate 0 is random, whereas the employment target x* presumably is constant (or at least more stable than 0), inflation is also more variable under discretion than under the rule. The inflation bias is due to two key assumptions. The first is the sequential timing of monetary policy decisions. The second is the assumption that the employment target is higher than the natural rate, that is: x* - 0 > 0. This assumption must reflect a lack of policy instruments: some distortion in the labor or product market keeps employment too low. The government does not remove this distortion; either because it does not have enough policy instruments or because the distortion is kept in place by some other incentive problem in the policy-making process. These assumptions capture important features of monetary policymaking in the real world. In this static model, the policy response to the supply shock e is not distorted: shocks are stabilized in the same way under discretion and commitment. This equivalence does not, however, carry over to a dynamic model where employment (but not the employment target) is serially correlated. In such a dynamic model, the future inflation bias depends on current employment (since the future equilibrium employmem depends on current employment). To reduce the future inflation bias, the
1 The equilibrium would also apply identically to a simultaneous game between the government and a single trade union. If the union moved before the government, the equilibrium might differ slightly, but the fundamental incentive problem would not be affected.
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policymaker thus responds more aggressively to supply shocks under discretion than under commitment. Moreover, the systematic inflation bias increases, as an ex post expansion today expands both current and future employment 12 The "distortion" in the policymaking process can be described as follows: under discretion, the policymaker (correctly) fails to internalize the mapping from actual policy to expected policy. He is not being foolish: he really cannot influence private sector expectations. This is what we mean when saying that a (low inflation) policy "lacks credibility". Yet, actual policy maps into expected policy in equilibrium when private agents have rational expectations. Under commitment, on the contrary, the policymaker internalizes this equilibrium mapping; indeed announcing the optimal policy rule brings rationally expected inflation down precisely to the preferred rate of inflation. The conclusions are pretty stark. First, a desirable policy rule does not become credible just by announcing it; is thus pointless to recommend a noncredible policy rule. Second, the inability to commit to a policy rule has obvious costs. Institutional reforms that give policymakers greater commitment ability can thus be desirable. This simple model of monetary policy credibility is often criticized with reference to the plausible objection that "real world policymakers are not trying to surprise the private sector with unexpected inflation". But this criticism misses the point of the analysis. The model does not predict that the policymaker tries to generate policy surprises in equilibrium. On the contrary, in equilibrium the policymaker would like to bring inflation down but refrains from doing so as his lack of credibility would turn any anti-inflationary policy into a recession, in other words, the model predicts an inertia of expectations to a suboptimally high inflation rate, and a difficulty in curbing these expectations down to the socially efficient rate. What the model does rely on, however, is an assumption that the policymaker would want to generate policy surprises outside o f equilibrium to a more favorable outcome. Is this a plausible positive model of inflation? Some observers, like McCallum (1996), apparently do not think so. A convincing rebuttal should address the question already posed by Taylor (1983), who - in his discussion of Barro and Gordon (1983b) - asked why society has not found ways around the credibility problem in monetary policy, when it has found ways around the credibility problem of granting property rights to patent holders. This question is best addressed in connection with a closer discussion of the institutions of monetary policymaking, so we come back to it in Section 4. What are the observable implications of the analysis so far? One implication is that a binding credibility problem would show up by the central bank reacting to variables that entered the private sector's information set (before policy is set), whereas the
12 Svensson (1997a) proves this result formally, drawing on earlier work by Lockwood et al. (1998) and Jonsson (1997). See also Obstfeld (1997b) for a related result in a dynamic model of seignorage. Beetsma and Bovenberg (1998) show that stabilizationbias mises also when monetary and fiscal policy are pursued by different authorities with diverging objectives.
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T. Persson and G. Tabellini
reaction function would not include such variables under commitment. Hence, the unconditional variance of inflation is higher under discretion. If the credibility problem is caused by a high )~, the model indeed predicts a positive correlation between average inflation and the variance of inflation, in conformity with international evidence. The discretionary model also suggests a plausible explanation of the secular trend in inflation experienced by the industrialized countries and mentioned in the introduction. The 1950s and 1960s were a period without serious supply shocks and with a low natural rate of unemployment (low variance of e, high realizations of 0), which made it easy to keep inflation low. Enter the 1970s with severe supply shocks (high realizations of E) pushing up the natural rate (to capture this in the model would require serial correlation in employment) and inflation; we may then interpret the rise in inflation as the result of policymakers maintaining their earlier high employment objectives (x* staying constant or falling by less than 0). The gradual decline in inflation from the mid-1980s and onward, despite continued high natural rates (in Europe), can be understood to derive from policymakers gradually adapting their employment ambitions to the structural problems in the labor market (x* drifting downwards over time) and from the institutional reforms in central banking arrangements in a number of countries in the recent decade. Naturally, learning from past policy mistakes is also likely to have played an important role. To date, time-series implications of this type have received too little attention in the credibility literature 13. Instead, the literature has focused on normative issues of institutional reform, and to some extent on explaining cross-sectional differences in macroeconomic outcomes by different institutions. 2.4. Reputation
One can criticize the simple model discussed so far for being static and failing to capture the repeated nature of policymaking. Specifically, the model rejects repeated interaction with the public and hence ignores reputational forces. A branch of the literature has studied reputational forces in detail. The main result is that a link from current observed policy to future expected policy can indeed discipline the policymaker and restore credibility. With repeated interaction, a policymaker operating under discretion faces an intertemporal trade-off: the future costs of higher expected inflation, caused by expansion today, may more than outweigh the current benefits of higher employment. To illustrate the idea, consider the model of subsection 2.3, repeated over an infinite horizon. The policymaker's intertemporal loss function, from the viewpoint of some arbitrary period s, can be written as E~.
[±
6' "L(JG xt)
,
(2.15)
[=S
1.~ See,however,the recentpapers by Parkin(1993), Barro and Broadbent(1997) and Broadhent(1996).
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where 6 is a discount factor. To simplify the algebra, we assume the static loss function to be linear, not quadratic, in employment: (2.16)
L(Tg, x) = ~2rl 2 _ /~.,x.
With the simpler loss function, the ex ante optimal policy rule is simply to have zero inflation all the time and to accept employment x = 0 - e (since ~* = 0 and employment volatility is not costly), while the static equilibrium under discretion has inflation equal to )~ and employment still at x = 0 - e. We now show that, even under discretion, reputation can indeed create strong enough incentives to enforce zero inflation. As an example, assume that wage setters set wages on the basis o f the following expectations: ~[=
0 iff ~ = ~ [ , 3, otherwise.
u= t-1 ..... t-T,
(2.17)
Equation (2.17) says that wage setters trust a policymaker who sticks to zero inflation in period t to continue with this same policy in the next period. But if they observe any other policy in period t, they lose this trust and instead expect the discretionary policy to be pursued for the next T periods. A policymaker confronted with such expectation formation, in effect, faces a non-linear incentive scheme: he is "rewarded" for sticking to the rule, but he is "punished" if deviating from it. Consider a policymaker that enjoys the trust of the public (i.e. :Vs~ = 0). When is the punishment strong enough to outweigh the immediate benefit of cheating on the rule? To answer formally, note that the optimal deviation (found by minimizing the static loss function, given e and COs ~ = 0) is simply ~. = 3,, thus implying employment x~. = )~ + Os - es. After some algebra, the current benefit from cheating can then be expressed as B = L(0, 0s -- e,) - L(,~, ,~ + 0~ - e,) = ~,~.~ 2
(2.18)
Due to the simpler loss function, the benefit is independent o f the realizations of 0 and e. The punishment comes from having to live with higher expected and actual inflation in the next T periods. Why higher actual inflation? As the expectations in Equation (2.17) are consistent with the static Nash Equilibrium outcome in subsection 2.3, it is indeed optimal for the policymaker to bear the punishment if it is ever imposed. In other words, the private sector's expectations will be fulfilled, both in and out o f equilibrium 14. Thus, the cost of a deviation is C=Es
6 t "(L(.,t, 0,-et)--L(O, Ot-e,))
~ Lt=s+
.... 6
)-Z2,
(2.19)
1
14 By this argument the analysis identifies a sequentially rational (subgame perfect) equilibrium. For other expectation formation schemes, in which expectations changed more drastically after a deviation, we would have to impose a separate incentive-compatibility constraint, namely that it is indeed optimal to carry out and bear the ptmishment after a deviation [see Persson and Tabellini (1990, ch. 3) on this point].
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which is clearly stationary if we assume that 0 is i.i.d, over time. Obviously, the policymaker finds it optimal to stick to the zero-inflation rule as long as B ~< C. Inspection of Equations (2.19) and (2.18) reveals that this is more likely the higher the discount factor c5 and the longer the horizon T for which inflationary expectations go up after a deviation. Many extensions of this basic framework are feasible; and some have been pursued in the literature. For instance, if we retained the quadratic loss function of the previous subsection, the benefit of cheating would be an increasing function of the actual realization of 0, while the cost would depend on the variance and the expected value of 0. As a result, even with reputation, equilibrium inflation would continue to depend on the actual realization of 0: a high value of 0 makes the incentivecompatibility condition more binding, as it increases the benefit B but not the cost C. The lowest sustainable inflation rate (defined by the condition that B = C) would be an increasing function of 0. Thus, reputation would reduce average inflation but would not change the main positive implications of the model of the previous section. Canzoneri (1985) studied a framework with shocks to inflation that are unobservable to private agents both ex ante and ex p o s t ; an example could be the /~ shocks in Equation (2.1) above. If observed inflation exceeds some threshold, such monitoring problems give rise to temporary outbreaks of actual and expected inflation, because the public cannot clearly infer whether high inflation is due to large shocks or to deliberate cheating. Backus and Driffill (1985), Barro (1986), Tabellini (1985, 1987) and Vickers (1986) studied reputational models where the private agents are uncertain about the policymakers "type" (as his )~ in the model above). They use the information embodied in current observations of policy to learn about this type, and the policymaker sets policy optimally with a view to this private learning process. Such models illustrate how a "dovish" policymaker (someone with a high )~ or without access to a commitment technology) can temporarily borrow the reputation of a "hawkish" policymaker (someone with a low )~ or with access to a commitment technology). They also illustrate how a hawkish policymaker may have to impose severe output costs on the economy to credibly establish a reputation. This differs from the equilibrium considered above, where the policymaker merely maintains a reputation he is lucky enough to have. Cukierman and Meltzer (1986) also studied credibility and private learning but in a richer dynamic setting, where parameters in the central bank's objective function vary stochastically over time. The central insight of the reputation literature is that ongoing interaction between a policymaker and private agents can mitigate the inflation bias and restores some credibility to monetary policy. Whether the problem is entirely removed is more controversial, however, and depends on details of the model and the expectations formation mechanism. Even though the insight is important, the reputation literature suffers from three weaknesses. As in the theory of repeated games, there is a multipleequilibrium problem, which strikes with particular force against a p o s i t i v e model of monetary policy. Moreover, the problem of how the players somehow magically
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coordinate on one of the many possible equilibria is worse when the ganle involves a large number of private agents rather than a few oligopolists. Finally, the normative implications are unclear. The existence of reputational equilibria with good outcomes is not helpful to a country where inflation is particularly high at a given moment in time. The lack of suggestions for policy improvements is another reason why researchers largely turned away from reputational models, towards an analysis of the policy incentives entailed in different monetary policy institutions Js 2.5. N o t e s on the literature
Textbook treatments of the general material in this section can be found in Persson and Tabellini (1990, Chs. 1-4), and in Cukierman (1992, Chs. 9-11, 16), both covering the literature up to around 1990. The literature on credibility in monetary policy starts with Kydland and Prescott (1977), who included a brief section with the basic insight of the static model in subsection 2.3. Barro and Gordon (1983a) formulated a linearquadratic version and pushed its use as a positive model of monetary policy. Calvo (1978) studied the credibility problem of monetary policy in a dynamic model, where the short-run temptation to inflate arises for public-finance reasons. Obstfeld (1997b) provides an insightful analysis of the credible policies in a dynamic seignorage model. Dynamic models of the employment motive to inflate were developed by Lockwood and Philippopoulus (1994), Lockwood et al. (1998), and Jonsson (1997). Parkin (1993) argues that the great inflation of the 1970s can be explained by an increase in the natural rate in the kind of model dealt with here. Ball (1996) points to indirect evidence that many disinflationary episodes in the 1980s lacked credibility. Barro and Gordon (1983b) started the theoretical literature on reputation in monetary policy, drawing on the work on trigger strategies in repeated games with complete information. Backus and Driffill (1985), Tabellini (1985, 1987) and Barro (1986) developed incomplete information models of reputation, emphasizing how a dovish policymaker can borrow a reputation from a super-hawkish policymaker who only cares about inflation and not at all about employment. Vickers (1986) instead emphasized how a policymaker who seriously wants to fight inflation may have to engage in costly recessionary policies in order to signal his true identity to an incompletely informed public. Reputation with imperfect monitoring of monetary policy was first studied by Canzoneri (1985). Grossman and Van Huyck (1986) and Horn and Persson (1988) studied reputational models dealing with the inflation tax and exchange rate policy, respectively. Rogoff (1987) includes an insightful discussion about the pros and cons of the reputational models of monetary policy.
15 Some interesting recent work, however, suggests an institutional interpretation of some of these reputational equilibria arguing that some institutional arguments are more conducive to reputation building than others; see Jensen (1997), al Nowaihi and Levine (1996) and Herrendorf(1996). The ideas are related to Schotter (1981) and to the view that international institutions may facilitate cooperation in hade policy [see Staiger (1995) tbr a survey].
1416 3o Political
T Persson and G. Tabellini
cycles
The empirical evidence for the democratic OECD countries during the post-war period suggests systematic pre-electoral expansionary policies - fact (iv) in the introduction as well a post-election partisan cycle in real variables and inflation - fact (v). These "facts" vary somewhat depending on the country and the time period considered, and their robustness has not been checked with the same standards as, say, in the modern macroeconometric literature attempting to identify innovations in monetary policy 16 But they are interesting enough to motivate this line of research. The empirical evidence also indicates that there is so-called "retrospective voting": the likelihood of election victory for the incumbent government or legislature depends largely on the state of the economy; as expected, a higher growth rate boosts the reelection probability of the incumbent iv. It is then tempting to "explain" fact (iv) the political business cycle - by opportunistic governments seeking re-election by taking advantage of the voters' irrationality. But how can we claim that the same individuals act in a rational and forward-looking way as economic agents, but become fools when casting their vote? One of the puzzles any rational theory o f political business cycles must address is thus how to reconcile retrospective voting with the evidence of systematic policy expansions before elections. This puzzle is addressed in subsection 3.1, under the assumption that voters are rational but imperfectly informed, and that 'the government is opportunistic and mainly motivated by seeking re-election. This section builds on work by Lohman (1996), Rogoff and Sibert (1988) and Persson and Tabellini (1990). The correlations between macroeconomic outcomes and the party in office are easier to explain, provided that we are willing to assume policymakers to be motivated by ideology (have preferences over outcomes) and, once in office, prepared to carry out their own agenda. These assumptions lead to a theory of "partisan" political business cycles, which is summarized in subsection 3.2, following the pioneering work by Alesina (1987). 3.1. Opportunistic gooernments
Throughout this section~ we discuss political business cycles in the simple monetary policy model of Section 2, as does most of the literature. But the ideas generally apply to aggregate demand management, including fiscal policy. We deal in turn with "moral
~ Faust and Irons (1999) criticize the literature on partisan cycles in the USA tot failing to control for simultaneity- and omitted-variable bias and argue that the support for a partisan cycle in output is much weaker than what a cursory inspection of the data would suggest. Mishra (1997) uses modern panel data estimation techniques trying to control for similar biases in a panel of 10 OECD countries. He finds strong support for a post-electoral partisan cycle and weaker support for a pre-electoral cycle. J; See, for instance, Fair (1978).
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hazard" and "adverse selection", where the labels refer to the informational asymmetry between voters and the elected policymaker. 3.1.1. Moral hazard in monetary policy
The model in this first subsection is adapted from Lohman (1996), whose work builds on that by Persson and Tabellini (1990) and Holmstrom (1982). Its main insight is that elections aggravate the credibility problem of monetary policy, because they raise the benefit of surprise inflation for the incumbent. Consider a version of the model in subsection 2.4. Voters are rational, have an infinite horizon and are all identical. Their preferences are summarized by a loss function defined over inflation and employment, identical to Equations (2.15) and (2.16) above - and are thus linear in employment. Political candidates have the same objectives, defined over output and inflation, as the voters. In addition, they enjoy being in office: their loss is reduced by K units each period they hold office. Candidates differ in their ability to solve policy problems. One candidate may be particularly able to deal with trade unions, another to deal with an oil-price shock, a third is better able to organize his administration. This competence is reflected in output growth (employment): a more competent candidate brings about higher growth, ceteris paribus. To capture this, we write the Phillips curve exactly as in Equation (2.3), except that we set 0 to zero; we thus consider only e shocks, but change their interpretation. Throughout this section, e captures the competence of the incumbent policymaker, not exogenous supply shocks. We assume that the competence of a specific policymaker follows a simple MA-process: e, = -~h - /~t-1, where ~/ is a mean zero, i.i.d, random variable, with distribution F(.) and density f ( . ) (in this formulation a positive realization of ~/ leads to high output). Competence is assumed to be random, as it depends on the salient policy problems, but partially lasting, as the salient policy problems change slowly and as competence may also depend on talent. Serially correlated competence is the basis of retrospective voting: as competence lasts over time, rational voters are more likely to re-elect an incumbent who brought about a high growth rate. In the very first period of this repeated game, we assume r/0 = 0. The timing in a given period t is as follows. The previous period's policy instrument and inflation & 1 are observed. Wages (and expected inflation) are determined. The policymaker sets the policy instrument for t. Competence is realized and output growtb xt is observed by everybody. Finally, if t is an election year - which happens every other year -~ elections are heldo Two remarks should be made about these assumptions. First, unlike in Section 2, the policymaker does not have any information advantage over private agents: when policy is set, the current competence shock ~/i is unknown to everyone, including the incumbent. The voters do not face an adverse selection problem in that the policymaker cannot deliberately "signal" his competence. This assumption distinguishes the model in Lohman (1996) from the earlier work by Rogoff and
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71 Persson and G. Tabellini
Sibert (1988), Rogoff (1990) and Persson and Tabellini (1990). The voters still face a moral hazard problem: through his monetary policy action, the incumbent can appear better than he really is. The voters understand these incentives, but can do nothing about them, as policy is unobservable. A model o f this kind was first studied by Holmstrom (1982) in a standard principal-agent set-up, where the agent has career concerns, subsection 3.1.3 discusses the alternative, and more complicated, setting when the policymaker is better informed about his own competence than the voters. Second, at the time o f the elections, voters only observe output growth and wages (expected inflation), but not inflation or policy. This assumption is not as bad as it may first appear. Inflation typically lags economic activity. A n d even though monetary policy instruments are immediately and costlessly observed, this information is meaningless unless the voters also observe other relevant information that the policymaker has about the state o f the economy. To properly understand an expansion o f the money supply six months before the elections, voters would have to know the policymaker's forecasts o f money demand and other relevant macroeconomic variables. Assuming that policy itself is unobservable is just a convenient shortcut to keep the voters signal-extraction problem as simple as possible is Finally, we make two other simplifying assumptions. Once voted out o f office, an incumbent can never be reappointed. The opponent in any election is drawn at random from the population and his pre-election competence is not known. Thus the expected competence o f any opponent is zero. 3.1.2.
The equilibrium
First, consider wage-setters. They have the same information as the policymaker and Call thus compute equilibrium policy and perfectly predict inflation. Hence, in equilibrium sr - Jv~ in every period. Next, consider voters. By observing output and knowing the previous period shock to competence, tk 1, they can correctly infer the current competence o f the incumbent by using Equation (2.3): tlt = xt - rlt i 19. The equilibrium voting rule is then immediate. Voters always prefer the policymaker with the highest expected competence. As the opponent has zero expected competence, the voters re-elect the incumbent with probability one i f and only i f xt > r/t--l, as in this c a s e t h > 0 (if xf --= rk 1, we can assume that the voters randomize, as they are indifferent). To an outside econometrician, who observes x~ but not t/l-l,
18 As Lohman (1996) observes, however, this assumption is not easily made consistent with a surprise supply formulation (like in Section 2) where employment (output growth) is determined by realized real wages in a one-sector setting. Lohman instead formulates her model as a Lucas island model where firms observe tile local inflation but not economy-wide inflation (the policy instrument). i9 Voters know that Jr = JU. Also, recall that in period 0 we have, by assumption, tl0 0. Hence in period 1: x I = t/l, and output fully reveals the policymaker's competence. Knowing r/l , in period 2, voters can intbr r/2 from x2 = t12+ th, and so on.
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this voting rule appears consistent with retrospective voting: the probability of reelection, Pr(~h i ~< x t ) - F ( x ~ ) , increases with output growth in the election period. Next, consider the policymaker's optimization problem. In @ e l e c t i o n years, he can do nothing to enhance future re-election probability, as competence shocks last only one period and are observed with the same lag. Hence, the equilibrium inflation rate minimizes the static loss in Equation (2.1 6) with respect to ~, subject to Equation (2.3) and taking yL"e as given. As in subsection 2.4, this yields 76 = X. O n - e l e c t i o n years entail different incentives: by raising output growth through unexpected inflation, the incumbent policymaker would increase his election probability. In equilibrium, wagesetters correctly anticipate these incentives, and raise expected inflation accordingly, so that output continues to grow at its natural rate. To formally derive these results, we first compute the equilibrium probability of re-election from the point of view of the incumbent. Recall that he is re-elected iff [xt > t/t_,], or - by Equation (2.3) and our definition of E - iff [tit > gete - Jrt I • When setting policy, the incumbent has not yet observed t/t. His perceived probability of reelection is 1 - Prob(r/t ~< xe _ ~ ) ~ 1 -- F(aVre - a~t), where F(.) is the cumulative distribution of t/. This probability is clearly an increasing function of unexpected inflation. Next, we need some additional notation. Let V R and V N be the expected equilibrium continuation values of reappointment and no reappointment, at the point when policy in an on-election year is chosen. Furthermore, let ~ be equilibrium inflation during on-election years, to be derived below. Simple algebra establishes that: VN _
~2 q_ 6~-g2
2(1 - 62) ,
K(1 + 6)
vR _ VN _
1
~2(1
(3.1)
F(0))'
where 1 F(O) is the equilibrium probability of re-election perceived by the incumbent in all . f u t u r e elections (he recognizes that future inflation surprises are not possible in equilibrium). Intuitively, the expected value of winning the elections - the difference V R - V N - depends on K, the benefits from holding office, but not on the equilibrium policies, ,~ and Yv, since those are the same irrespective of who wins. Note also that these continuation values do not depend on the policymaker's competence, as competence is not known when policy is set. We are now ready to formulate the problem of an incumbent during an on-election year. The incumbent takes expected inflation as given and chooses current inflation to minimize E[L t ]
[½yc 2 - )~(Jv - off) - K + 6(1 - - F ( s r ? - Jvt)) V ~ + 6F(¢c~ - Jrt) V N I .
(3.2) The first two terms in Equation (3.2) capture the expected loss in the current period. The last two terms capture the expected value of future losses, as determined by reappointment or not in the upcoming elections. Taking the first-order condition for a
Persson and G. Tabellini
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given ~e and then imposing the equilibrium condition Jr - :re yields the equilibrium inflation rate during on-election years: 6(1 + 6)f(O) = ~q-(~f(O)(VN - v R ) = "~ q - K 1 - 6 2 ( 1 - F(0))'
(3.3)
where the last equality follows from Equation (3.1). The LHS of Equation (3.3) is the marginal cost of inflation. The RHS is the marginal benefit: 3. is the usual benefit of higher output growth~ present at all times; the second term is tile additional on-election-year benefit; higher output growth increases the chance of re-election. This additional benefit of surprise inflation undermines credibility and makes policy more expansionary during on-election years. Thus, equilibrium inflation right after the election is higher, the more the policymaker benefits from holding office, as measured by K, and the more surprise inflation raises the probability of reappoinmlent, as measured by the density f(0). Finally, as the incentives to inflate before elections are perfectly understood by private agents, expected inflation is also higher, and equilibrium output growth is not affected. Thus, the equilibrium is consistent with stylized fact (iv) in the introduction. Elections aggravate the credibility problem, as the incumbent cares even more than usual about output growth. 3.1.3. A d v e r s e s e l e c t i o n
What happens when policy is instead chosen after the incumbent has observed the realization of current competence th, but the sequence of events is otherwise exactly as before? In this setting, studied by Rogoff and Sibert (1988), Rogoff (1990) and Persson and Tabellini (1990), the policymaker enjoys an information advantage over wage-setters, who do not know the realization of t/t when forming expectations. Output fluctuations can still reveal the policymaker's type, but in a less straightforward fashion: voters have to deal with an adverse selection problem, where output can be used as a deliberate signal of the incumbent's competence. To cope with this more intricate problem, we postulate that in each period tl can only take one of two values: ~ > 0 and tl < 0 with probabilities P and (1 - P ) , respectively. As before, ;'/is i.i.d, and has an expected value E(t/) = P ~ + (1 - P)~ = 0. We refer to an incumbent with a high (low) realization of t/as competent (incompetent). The opponent's competence is still unknown to everyone. In the moral hazard model, all incumbent types choose the same action, because e x a n t e they were all identical. Here, a more competent incumbent has stronger incentives to surprise with higher inflation. There are two reasons for this. First, a more competent incumbent cares more about winning the elections, since he knows that he can do a better job than his opponem. Second, a more competent incumbent also has a lower cost of signalling his competence through high output growth. Here, we only sketch the arguments needed to characterize the equilibrium A full derivation is provided by
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Persson and Tabellini (1990, Ch. 5). As a first step, compute the expected net value o f winning the elections:
(1 + 6 ) K V R - V N = A,r/+ 1 - 62(1 - P )
(3.4)
Comparing Equations (3. l) and (3.4), the net value of winning now depends on the competence o f the incumbent: a competent incumbent knows he is more likely to bring about higher future output growth than his opponent, and hence values office more. A incompetent incumbent realizes the converse - and is less eager to be re-elected 2°. The equilibrium inflation rate trades off this net value of winning against the short-run cost o f signalling. Both types want to appear competent and are prepared to artificially boost the economy through unexpected inflation to increase the chances of winning. But the competent type can signal at a lower cost: he needs to inflate less to produce any level o f output growth. As the value o f winning is also higher for the competent type, a "separating equilibrium" generally emerges: rational voters re-elect the incumbent only if output growth exceeds a minimum threshold. The threshold is so high that only a competent incumbent finds it optimal to reach it through unexpected inflation. The incompetent type instead prefers to keep inflation low, knowing he will not be re-elected. Recall that wage-setters have to form inflation expectations without knowing which incumbent type they face. expost, they will always be wrong, even though their ex ante inflation forecast is rational. If the incutnbent is incompetent, he chooses the short-run optimal inflation rate Uv = X in the model), which is lower than expected; hence, the economy goes through a recession. If the incumbent is competent, inflation is higher than expected and the economy booms. How do the conclusions o f this model compare with the stylized facts? Clearly, retrospective voting applies: voters reward pre-electoral booms with reappointment and punish pre-electoral recessions. Output is not systematically higher before elections; on average, inflation is higher just after the elections, but this cycle is weaker than in the moral hazard model, as only the competent type now raises equilibrium inflation. Overall, the predictions of this model are not inconsistent with the stylized facts. Which model is more satisfactory? The moral hazard model has more clear-cut predictions and makes less demanding assumptions about the rationality of the voters. Moreover, multiplicity of equilibria is an additional problem in the adverse selection model. With enough data, one could discriminate between the two models: output
2o We assume that K is sufficiently high that even an incompetent incmnbent values being re-elected. Note also that here the equilibrium probability of winning future elections coincides with P, the probability of a high realization of~t. That is, in equilibrium a competent incumbent is alwaysreappointed and an incompetent one is not. This is a feature of all separating equilibria, that will be discussed below; some equilibria may exist that are not separating, but we neglect them here. Persson m~d Tabellini (1990) contains a more general discussion of this issue.
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volatility before the elections and inflation volatility after the elections are higher only in the adverse selection model. Note that these two models also have different normative implications. With moral hazard, the political cycle is entirely wasteful, whereas it conveys valuable information to voters in the adverse selection model 21 . 3.2. Partisan gooernments
The prior section relied on two crucial assumptions. All voters are alike and policymakers are opportunistic: their main purpose is re-election to enjoy the rents from office. Elections serve only one purpose: to select the most competent policymaker. But voters are not alike, and policymakers are also motivated by their own "ideological" view of what ought to be done and which group o f voters to represent. Therefore, elections serve another goal: they resolve conflicts and aggregate preferences. The policy outcome then hinges on the partisan interests o f the elected government. In monetary policy, and more generally aggregate demand policies, one crucial concern is the relative weight assigned to stabilizing output. For left-wing governments output and employment may weigh more heavily than prices; if so, they will also pursue more expansionary aggregate demand policies than right-wing governments. Elections thus create uncertainty about economic policy. This uncertainty is greater in a two-party system with very polarized parties. It may create a post-electoral cycle in the policy instruments, and a resulting macroeconomic cycle. We now extend our simple monetary policy model to illustrate these ideas, showing how one can account for stylized fact (v) in the introduction. The ideas originate with the work o f Alesina (1987, 1988). 3.2.1. The model
Consider the same model as in the previous section, but suppose that individual voters differ in their relative evaluation o f output and inflation. The preferences o f voter i are still described by an intertemporal loss function like (2.15), but the static loss o f individual i has an idiosyncratic relative weight on output: Li(zc, x) = ~:vl 2
)~ix.
(3.5)
Two political candidates or parties, called D and R, have the same general loss function as the voters, with relative weights )LD > )~R. The D candidate thus cares more
21 Rogoff (1990) shows in a closely related adverse selection model of fiscal policy that society may actually be worse off if one tries to curtail pre-election signalling through, say, a balanced budget amendment (the loss of losing the information may more than outweigh the gain of eliminating the distortions associated with signalling). In a recent paper, however, al Nowaihi and Levine (1998) demonstrate that political cycles can be avoided and social welfare increased by delegating monetary policy to an independent central bmlk faced with an inflation contract of the type discussed in subsection 4.3 below.
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about output growth and less about inflation than the R candidate. The candidates' preferences are known by everybody, but the outcome of the election is uncertain. For simplicity, there are no competence or supply shocks: output growth is described by Equation (2.3), without any e so that x = 0 + ¢c - ¢ce. The timing of events is as follows: Wages are set at the beginning of each period. Elections are held every other period, just after wages are set for that period. Thus, wage contracts last through half the legislature and cmmot be conditioned on the election outcome. Finally, to capture the electoral uncertainty about policy, we assume that candidates can only set policy once in office. In other words, electoral promises are not binding and the policy must be ex post optimal, given the policymaker's pret~rences. 3.2.2. Economic equilibrium
Under these assumptions, voters are perfectly informed and the state of the economy does not reveM anything to them. Hence, policymaker I chooses the same inflation rate in office whether it is an on- or off-election period. Given the assumed timing, it is easy to verify that ¢d = )~I, I = D, R. In off-election periods, this inflation rate is perfectly anticipated by wage-setters, and output grows at the natural rate: x = 0. But just before the elections, wage-setters do not know which policymaker type will win. Suppose they assign probabilities P and (1 - P ) to the events that D and R win. During on-election periods, expected inflation is thus :ve = )~R + p()~o _ )~R). If party R wins, it sets 7c = XR < ¢ce and causes a recession in the first period of office: output is x = -P(3. D -tlR). If D wins, the opposite happens: actual inflation is higher than expected and a boom occurs: x = (1 - P ) ( ) ~ - 3.R). Thus, uncertain election outcomes may cause economic fluctuations. But this political output cycle occurs after the election and is due to different governments having different ideologies, in contrast to the previous model where the political output cycle is due to signalling and occurs beJore elections. interpreting these ideological differences along a left-right political dimension, we get a possible explanation for stylized fact (v). The model predicts that left-wing governments stimulate aggregate demand and cause higher inflation throughout their tenure, while the opposite happens under right-wing governnaents. An election victory of the left brings about a temporary boom just after the elections; victory of the right is instead tbllowed by a recession. These partisan effects are more pronounced under a more polarized political system (i.e. with large differences between tlD and )~R in the model), or more generally if the elections identify a clear winner, like in two-party systems. Alesina and Roubini (1997) argue that these predictions are consistent with the evidence for industrial countries. 3.2.3. Political equilibrium
The partisan model tbcuses on the role of party preterences in elections. Voters anticipate what each party would do if elected, and choose the party closest to their
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ideal point. Thus, the probability that one party or the other wins is entirely determined by fluctuations in the distribution of voters' preferences for the two parties. Moreover, as electoral promises are not binding and voters are rational and forward-looking, the policy platforms of the two candidates do not converge towards the median voter. In the model, voters face a trade-off. If R wins, inflation is lower but output is temporarily lower, while the opposite happens if D wins. How voters evaluate this trade-off depends on their relative weight parameter )~i. Computing the losses to a generic voter after an R and a D victory, respectively, and taking differences, it is easy to verify that voter i strictly pret~rs R to win if
,V < ½(1 + 6)(,~ R + X~)).
(3.6)
The probability (1 ~-P) that R wins is the probability that the relative weight of the median voter ~" satisfies inequality (3.6). Electoral uncertainty thus ultimately relies on the identity of the median voter being unknown, because of random shocks to the voters' preferences or to the participation rate. Ceteris paribus, right-wing governments enjoy an electoral advantage: because all policymakers suffer from an inflation bias, a high value of )~ is a political handicap 22. Inequality (3.6) implies that a voter whose ideological view is right in between R and D [that is, such that ,~i _ ½(3j~+ )j))] votes for the right-wing candidate. This suggests that an incumbent can act strategically to increase its chances of re-election. Specifically, a right-wing government can make its left-wing opponent less appealing to the voters by increasing the equilibrium inflation bias. This could be done by reducing wage indexation, by issuing nominal debt (to raise the benefits of surprise inflation), or by creating more monetary policy discretion, via a less disciplining exchange rate regime or weaker legislation regarding central bank independence, or even by current monetary policy if unemployment is serially correlated. These ideas have their roots in the literature on strategic public debt policy, further discussed in Section 6 below. On the normative side, electoral uncertainty and policy volatility are inefficient, and voters would be better off ex-ante by electing a middle-of-the-road government that enacted an intermediate policy. But in the assumed two-party system, there is no way of eliminating this unnecessary volatility. The stark result that there is no convergence to the median position, is weakened under two circumstances. One, studied by Alesina and Cukierwian (1988), is uncertainty about the policymaker type. Then each candidate has an incentive to appear more moderate, so as to raise the probability of winning the next election. The second, studied by Alesina (1987), is repeated interactions. Then the two candidates can sustain self-enforcing cooperative agreements: a deviation from a moderate policy would be punished by the opponent who also reverts to more extreme behavior once in office. Alternatively, cooperation could be enforced by the v o t e r s
22 This observation is related to the argument about the benefits of appointing a conservative central banker discussed in subsection 4.3 below.
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punishing a government that enacted extreme policies. Naturally, there is the same problem of multiple equilibria as in the reputational equilibria of subsection 2.4. Institutional checks and balances can also moderate policy extremism. In a presidential system, for instance, actual policies often result from a compromise between the legislature and the executive. The model of partisan policymakers suggests that the voters would take advantage of these institutional checks and balances to moderate the behavior of the majorities. Alesina and Rosenthal (1995) argue that the voters' attempt to moderate policy extremism can explain split ticket voting in Presidential systems (i.e., the same individuals voting for different parties in Presidential and Congressional elections) and the mid-term election cycle (the party who won the last general elections loses the interim election). 3.3. N o t e s on the litetz~ture
Alesina and Roubini (1997) present existing and new evidence on electoral cycles in OECD countries. They also survey the theoretical work on political cycles in aggregate demand policy. Alesina and Rosenthal (1995) focus on the United States in particular. The evidence for a partisan cycle is scrutinized by Faust and Irons (1999) (for the USA) and by Mishra (1997) (for a panel of OECD countries). Fair (1978), Fiorina (1981) and Lewis-Beck (1988) discuss the evidence on retrospective voting in the USA and elsewhere. The first models of political business cycles with opportunistic government are due to Nordhaus (1975) and Lindbeck (1976). The first theory of a partisan political cycle is due to Hibbs (1977). All these papers relied on the assumption that private agents are backward-looking, both in their economic and voting decisions. The model of an opportunistic govermnent and adverse selection with rational voters, summarized in subsection 3.1.3, was developed by Rogoff and Sibert (1988) in the case of fiscal policy, and adapted to monetary policy by Persson and Tabellini (1990). Rogoff (1990) generalized the fiscal policy results to two-dimensional signalling by the incumbent. Ito (1990) and Terrones (1989) considered political systems in which the election date is endogenous and chosen by the incumbent himself, after having observed his own competence. The moral hazard model studied in subsection 3.1.1 is very similar to a principalagent problem with career concerns developed by Holmstrom (1982). It was studied in the context of monetary policy by Lohman (1996) and, in a somewhat different set-up, by Milesi-Ferretti (1995b). Ferejohn (1986) and Barro (1973) study a more abstract moral hazard problem where an incumbent is disciplined by the voters through the implicit reward of reappointment. The model of partisan politics with rational voters is due to Alesina (1987, 1988). This model is extended by Alesina et al. (1993) and by Alesina and Rosenthal (1995) to allow for ideological parties who also differ in their competence. Milesi-Ferretti (1994) discusses how a right-wing incumbent might increase his popularity by reducing the extent of wage indexation; similar points with regard to nominal debt and the choice of
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an exchange rate regime were investigated by Milesi-Ferretti (1995a,b). Jonsson (1995) discusses strategic manipulation of monetary policy for political purposes when there is autoregression in employment. Uncertainty about the policymaker's ideological type is considered in Alesina and Cukierman (1988). The role of moderating elections, in theory and in the US data, is studied by Alesina and Rosenthal (1995).
4. Institutions and incentives
Theoretical work on institutions and incentives in monetary policy has developed over the last ten years. Below, we give a selective account of key ideas in that development. We do not follow the actual course of the literature over time, but we exploit what, in retrospect, appear to be the logical links between different ideas. The main issue is how the design of monetary institutions can remedy the incentive problems discussed in Sections 2 and 3. Even though we focus on lack of credibility, some results extend to the political distortions of Section 3. The ideas in this section rely on a common premise: institutions "matter". A constitutional or institution-design stage lays down some fundamental aspects of the rules of the game, which cannot be easily changed. Once an independent central bank has been set up, an international agreement over the exchange rate has been signed, or an inflation target has been explicitly assigned to the central bank, it has some such staying power, in the sense that changing the institution e x p o s t is costly or takes time. This premise is questioned by some critics [in particular by McCallum (t996) and Posen (1993)], who argue that some of the proposed institutional remedies discussed in this section "do not fix the dynamic inconsistency" that is at the core of this literature, they "merely relocate it". The criticism is correct, in that the institutions are assumed to enforce a policy which is e x p o s t suboptimal from society's (or the incumbent government) point of view. Hence, there is always a temptation to renege on the institution. But the staying power of institutions need not be very long to be effective. In the model that dominates the literature, what is needed is a high cost for changing the institution within the time horizon of existing nominal contracts. Beyond the contracting horizon, expectations would reflect any constitutional change, which removes the distinction between e x p o s t and e x a n t e optimality. As already remarked in subsection 2.4, the cost of suddenly changing the institution could also be a loss of reputation. By focusing political attention on specific issues and commitments, institutions alert private individuals if govermnents explicitly renege on their promises. To pick up the thread from Section 2, one purpose of successful monetary institutions is to make monetary policy a bit more like patent legislation. In our view, real-world monetary institutions do have such staying power. They can be changed, but the procedure for changing them often entails delays and negotiations between different parties or groups that were purposefully created when the institution was designed. We thus think that the premise of the literature is generally appropriate. But it would be more convincing to derive
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the institutional inertia as the result o f a well-specified non-cooperative strategic interaction between different actors, something the literature - so far - has failed to do 23. 4.1. Fixed exchange rates." simple rules and escape clauses
Pegging the value o f the exchange rate to gold or to some reserve currency has been a common device, particularly in smaller countries, to anchor inflationary expectations, discipline domestic price and wage setting, or prevent political interference in monetary policy. Such attempts have met with mixed success. A m o n g the industrialized countries during the post-war period, the Bretton Woods system and (part of) the European Exchange Rate Mechanism (ERM) were reasonably successful. But unilateral attempts o f some European countries to peg their exchange rates in the 1970s and 1980s often ended up in failure: with lack o f credibility generating a spiral of repeated devaluations, domestic wages and prices running ahead of foreign inflation. What can explain such differences? To shed light on this question, let us study a slight modification of the static model in Section 2. A small open economy is specialized in the production o f a single good which is also produced by the rest o f the world. The central bank controls 37 through the exchange rate, given a foreign inflation rate denoted 37*. The rest of the model, including the expectations-augmented Phillips curve (2.3), the rational-expectations assumption, the objective function o f the policy maker (2.6), and the timing o f events are as in subsection 2.2 or 2.3; except that we assume not only 0, but also 37* to be known when wages are set (7c° are formed). Note that 37* denotes both foreign and target inflation, as pegging the exchange rate to a low-inflation currency can be seen as an explicit or implicit attempt to target a low inflation rate. Under discretion, the model is formally identical to that in subsection 2.3 and thus generates the inflation and employment outcomes in Equations (2.12) and (2.14). As E(37) > 37*, the model is consistent with the idea o f a devaluation spiral, fuelled by low credibility among wage-setters and a devaluing exchange rate. Consider now the following institution. At stage (0), society commits to a simple rule o f holding the exchange rate fixed, or of letting it depreciate at a fixed rate k. There is commitment, in the sense that the rate o f depreciation k is chosen at the start of each period, and cannot be abandoned until one period later. The rule is simple, because it cannot incorporate any contingencies. In practice, simple commitments of this kind can be enforced by multilateral agreements such as the Bretton Woods system or the ERM, where the short-rnn interests of other countries are hurt if one country devalues. Policy commitments to complex contingent rules would require implausible assumptions on verifiability and foresight.
23 Jensen (1997) in tact studies a simple model related to the contracting solution to be studied in subsection 4.3 - where the government can renege on the initial institution at a continuous (nonlump sum) cost. In this setting institution design generally improves credibility, but cannot remove the credibility problem cmnpletely.
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What is the optimal rule? As the depreciation rate is known in advance of wage setting and expectation formation and is not contingent on the e shocks, it is neutral with respect to real variables. Hence, the optimal rule has k = 0. Under this simplicity constraint, a fixed exchange rate is thus the optimal commitment. This results in the following equilibrium outcome: ~s = jr., x s _ 0 - e, where the S superscript stands for simple rule. Is the simple rule better than discretion? It depends. The rule brings about lower average inflation, but employment is more variable. A formal comparison of the two regimes can be made by substituting Equations (2.12)-(2.14), and the previous expression for ~s and x s, into Equation (2.6) and taking expectations o f the difference in their payoffs. Recalling that E(O) = 0, this gives
E[L(~t)'xD)]-E[L(~S'xS)] = 2)'2- {E(x*)2 + o~ - -(1- ~ 2 ; ).
J
The first two "terms on the RHS capture the benefit of credibility under the simple rule the sum of the squared average inflation bias and its variance. The last term is the loss from not being able to stabilize employment. A simple rule is better than discretion if the gain o f credibility is larger than the loss o f stabilization policies. This trade-off between credibility and flexibility is a recurrent theme in the literature on institution design. The benefit o f the simple rule is further enhanced if, under discretion, monetary policy is also distorted by the electoral incentives discussed in Section 3. Another monetary regime, often advocated though harder to enforce, is a commitmerit to a k% money growth rule. Suppose we add a simple quantity-theory equation to our model, where money demand depends on output growth (or employment), so that + x = m + v. The policy instrument is m, like in Section 2. Under a simple money growth rule, velocity shocks v destabilize employment and prices. A simple exchange rate peg, on the other hand, automatically offsets velocity shocks. But a money supply rule might better stabilize supply shocks; as these destabilize both output and prices, the price response acts as an automatic output stabilizer. In the limit, if ~, = 1, a k% money rule mimics the optimal policy response to a supply shock 24. The assumption that an exchange rate peg, once announced, cannot be abandoned until next period, may be too stark. Multilateral exchange rate agreements often have escape ,clauses: European countries have temporarily left the ERM or realigned their central parities when exceptional circumstances made it difficult to keep the exchange rate within the band. An escape clause can be thought o f as follows. Define normal times as a range of possible realizations o f the unobservable supply shock: e C [eL(o), EU(o)]. Inside this interval, the central bank remains committed to the simple rule. During exceptional times, defined by the complementary event, an 24 A literature dating back to the 1970s has studied the choice between alternative rules in richer models - for surveys, see Genberg (t989) and Flood and Mussa (1994). Recent contributions to the comparison of exchange rate versus money based stabilizations of inflation are surveyed by Calvo and V6gh (1999).
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escape clause is invoked. The central bank abandons the simple rule and pursues a discretionary (ex p o s t optimal) policy, given inflationary expectations. At normal times, the exchange rate is fixed and output is destabilized by (small) supply shocks. There is also a p e s o problem: as the escape clause will be invoked with positive probability, expected inflation is always positive. Normal times with actual inflation at zero, thus has some unexpected deflation and employment below the natural rate. At exceptional times, on the other hand, the central bank abandons the rule and sets an ex p o s t optimal policy to stabilize (unusually large) supply shocks. But less inflation is now needed compared to the regime with pure discretion, because expected inflation is lower. Hence, a simple rule with an escape clause strikes a better balance between credibility and flexibility, by allowing for flexibility when it is most needed. Indeed, Flood and Isard (1989) have shown that a rule with an escape clause always dominates pure discretion and, if supply shocks are sufficiently volatile, it also dominates a simple rule. As Obstfeld (1997a) has stressed, however, escape-clause regimes can give rise to multiple equilibria. Intuitively, expected inflation depends on how often the escape clause is invoked. At the same time, the e x p o s t decision whether or not to invoke the escape clause depends on expected inflation. As higher inflationary expectations make it more tempting to abandon the rule, high inflationary expectations may become self-fulfilling. How can a regime with an escape clause be implemented? In a multilateral exchange rate regime where realignments have to be approved by an international body, the bounds would depend on the bargaining power of the devaluing (revaluing) country, which, in turn, would depend on the details of the institution (the prospective sanctions, the procedure for making the decisions, etc.). In a domestic context, we could suppose that at the institution design stage (before 0 is realized) society sets a pair of fixed costs [ct'(0), cU(0)] incurred whenever the escape clause is invoked. These costs would capture the public image loss for the central banker from not fulfilling his mandate, or the costs for the government of overriding a central bank committed to the simple rule. They would implicitly define bounds eL(0) and eu(0), that leave the central bank indifferent between sticking to the simple rule and bearing the cost of no stabilizing policies, or paying tile cost and invoking the escape clause, in neither of these interpretations it is reasonable to assume that the costs could be calibrated very carefully ex ante. For instance, costs may have to be state-dependent or symmetric; cL(O) = c j~, cU(O) = c ~j or c u = c1" = c. Such plausible constraints would prevent society from reaping the full value of the escape-clause regime, but still generally improve on the discretionary outcome. Flood and Marion (1997) point out that an important consideration behind the ex ante choice of c might be to prevent multiple equilibria. 4.2. Central b a n k independence
The first example of strategic delegation in monetary policy is the independent and conservative central banker, suggested by Rogoff (1985). To illustrate the idea in our simple model, we continue to make a formal distinction between society and the central bank. Society's true preferences take the form (2.6). At the institution design stage (0)
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o f the model, society appoints a central banker. The central banker is independent: once appointed, society can no longer interfere with his decisions. (Towards the end o f this subsection, we ask how reasonable this assumption really is.) Prospective central bankers have loss functions o f the form (2.6), but differ in their personal values of)L 25. The appointment thus boils down to the choice o f a parameter, say )~. The private sector observes )~B and forms its inflationary expectations accordingly. The appointed central banker sets monetary policy freely at stage (4), according to his own private preferences. As already discussed in subsection 2.3, this choice gives the equilibrium outcomes
XB ~(2, B, 0, e) - :v* + ,~B(x* -- 0) + 1 ~ - - ~ E, 1
x(,!, B, O, e) -- 0 - 1 + ~,R e. Note that the outcomes do not only depend on the realized shocks, but also on the bankers' preferences. These expressions illustrate a basic trade-off in the strategic delegation: a central banker more hawkish on inflation, i.e. someone with a lower 2,B, has more credibility in keeping inflation low, but is less willing to stabilize supply shocks. To formally study delegation, consider society's expected loss function, as a function of the central banker type: E[L(~B)] = 1E[(x()~ B, O, e ) - go*) 2 + ~ ( x ( ) f , O, e) -x*)21,
(4.1)
where the expectation is tal{en over 0 and E, for any 3~~. Next, insert the expressions for equilibrium inflation and employment into Equation (4.1) and take expectations. The derivative of the resulting expression with regard to At is dE[L(Jf)] d)~~
)~(x .2 + a0) + ( ) f - "~)(1 +a~)~B)3 '
(4.2)
The first term is the expected credibility loss of choosing a central banker with a higher ,~B. The second term measures the expected stabilization gain. The optimal appointment involves setting this expression equal to zero. Evaluating the derivative (4:2) at the extreme points implies that ~, > 3,~ > 0 26 Thus, by optimally choosing an independent central banker, society strikes a different compromise between credibility and flexibility than in the fixed exchange rate regime. 25 This suggests a heterogeneity in the population with regard to the relative weight placed on inflation versus employment, which ore formal model abstracts from. As discussed in Section 3, however, such heterogeneity can be formally introduced in the model without any difficulties. Alesina and Grilli (1992) indeed show that strategic delegation of the type to be discussed below would take place endogenously in a model where heterogeneous voters elect the central banker directly. 26 Equation (4.7) is a ~burth-order equation in ,~B, which is difficult to solve. But as the derivative is negative at )f = 0, positive for all 2~ > 2~, and the second-order condition is fulfilled for any ,~e in the interval (0, ,~), we kaaowthat the solution must be inside the interval (0,)~).
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But it is still a compromise: it is optimal to appoint a central banker who is more conservative on inflation than society itself (to address the inflation bias), but still not ultraconservative (to preserve some of the benefits of stabilization). Note also that fluctuations in the inflation bias arising from observable 0 shocks remain. If 3~8 could be chosen after the realization of 0, society would want to meet a more serious incentive problem - a smaller 0 - with a more hawkish central banker - a smaller XB. In practice, the extent of the incentive problem is serially correlated over time, so that making appointments at discrete points is probably a good way of dealing with this problem. Like in the escape-clause model, we could give society or government the option of overriding the central bank decision in exceptional circumstances. The override option could involve firing the central banker, introducing ad-hoc legislation or an explicit override clause under a prespecified procedure (the latter arrangement is indeed observed in the central bank legislation of many countries). An implicit escape clause mitigates the ex p o s t suboptimality of central bank behavior, inducing even a conservative central banker to stabilize extreme supply shocks to the same extent as society would do 27. This option should not be overemphasized, however; escape clauses can hardly be optimally designed ex ante. Moreover, as already noted in the introduction, if the government has an override option, why does it not use it all the time to get the policy it wants ex p o s t ? We may also note that having an independent central bank also protects society from the distortions introduced by the electoral business cycles discussed in Section 3. In this case, however, only independence is required, and no special emphasis on inflation relative to other macroeconomic goals. Waller (1989) was probably first in formulating a model of central bank independence under partisan politics 2s. Waller and Walsh (1996) study the optimal term length of central bankers in the context of partisan cycles, where society's objectives may change over time. The literal interpretation that society picks a central banker type is not very satisfactory: individual priorities or attitudes towards inflation and employment are often unknown and vaguely defined. Moreover, individual attitudes are probably less important than the general character and tradition of the institution itself. A better interpretation is that, at the constitutional stage, society drafts a central bank statute spelling out the "mission" of the institution. Thus, the parameter ,~ reflects the priority assigned to price stability relative to other macroeconomic goals. As instrument independence is a necessary condition for delegation to work, we should expect such a strategic setting of goals to work better if combined with institutional and legislative features, lending independence to the central bank and shielding it from short-run political pressures. In this interpretation, the model yields observable implications: countries or time periods in which the central bank statute gives priority to price stability and protects central bank independence should have lower average inflation and higher employmem 27 This is indeed proved by Lohman (1992). 28 Fratianni et al. (1997) formally analyze the role of central bank independence in the absence of a traditional credibility problem, but in the presence of explicit electoral incentives.
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(or output) volatility - since if )~B < )~, stabilization policies are pursued less vigorously. Moreover, electoral business cycles in inflation or output should be less pronounced with greater central bank independence. By now, a number o f studies have constructed measures o f central bank independence based on central bank statutes, also taking the priority given to the goal o f price stability into account 29. Crosscountry data for industrial countries show a strong negative correlation between those measures of central bank independence and inflation, but no correlation between output or employment volatility and central bank independence. Thus, central bank independence seems to be a free lunch: it reduces average inflation, at no real cost. Different interpretations o f this result have been suggested. Alesina and Gatti (1996) note that an independent central bank could reduce electorally induced output volatility, as would be predicted by the models of Section 3, and Lippi (1998) provides evidence that could support this proposition. Posen (1993, 1995) argues that the cross-country correlation between central bank independence and lower inflation is not causal, and suggests that both may be induced by society's underlying preferences for low and stable inflation. Finally, Rogoff (1985) also suggests another interpretation o f the model: the conservative central banker might be interpreted as a targeting scheme supported by a set of punishments and rewards. Having a conservative central banker is formally equivalent to having an additional term in inflation in his loss function, 0 ( B -- X)(J'g -- 3"g*) 2, where Z ~ > Z. The central banker thus has the same objective function as everybody else, but faces additional sanctions if actual inflation exceeds the target. In this simple model, a conservative central banker is thus equivalent to an inflation target 3o. This alternative interpretation has been picked up by a more recent literature, asking which targets are more efficient, and more generally how a targeting scheme should be designed to optimally shape the central bank ex-post incentives. 4.3. Inflation targei~ and inflation contracts'
Central banks have traditionally operated with intermediate targets, like money or the exchange rate. in the 1990s, several central banks started to target inflation: whereas some central banks imposed the procedure on themselves, the transition has been mandated by some governments 31. Such targeting schemes have recently been studied 29 See in particular Bade and Parkin (1988), Grilli et al. (1991), Alesina and Summers (1993), Cukierman (1992) and Eijffmger and Schaling (1993). 30 Rogoff (1985) compares an inflation target to other nominal targets, such as money and nominal income. He shows that strategic concerns of the type considercd here, can indeed overturn the ranldng of intermediate targets, based on parameter values and relative variance of shocks, in the traditional non-strategic literature on monetary targeting. 31 A substantial literature discusses real-world inflation targeting. See in particular Leiderman and Svensson (t995), Haldane (1995), McCallum (I996), Mishkin and Posen (1997) and Ahneida and Goodhart (1996). In practice, an inflation target means that the central bank is using its own inflation Jorecast as ml intermediate target; see Svensson (1997b) for instance
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from the point of view of the theory of optimal contracts. Society, or whoever is the principal of the central bank, presents its agent - the central b a n k with punisbments or rewards conditional on its performance. The question is what constitutes an optimal contract, and what kind of behavior it induces on the agent. We illustrate the basic ideas of this recent literature in our simple model of credibility. The optimal contract can easily be modified so as to implement the optimal monetary policy even in the presence of political distortions, but we do not pursue this extension. Much of the discussion in this subsection is based on results in Persson and Tabellini (1993) and Walsh (1995a). The central bank holds the same quadratic preferences as everybody in society. It operates under discretion, setting policy at stage (4). At the constitutional stage (0), the government formulates a publicly observable complete contract for the central bank which formulates state-contingent punishments (or rewards) conditional on realized inflation: P(2C; O, e) -po(O, e) +Pl (0, e) ~ + ½P2(O, e) at;2.
(4.3)
Our goal is to optimally set the terms pi(O, 0, i = 0, l, 2, that define the contract. We only include up to second-order terms in the contract, since that is sufficient for our purposes. Units are normalized so that, at stage (4), the central bank minimizes the sum of the loss function and its punishment with respect to inflation: L(zc, x)+ P(jr; 0, e). Going through the same steps as in subsection 2.3 (deriving the central bank optimum condition for inflation, given the contract and expected inflation, solving for rationally expected inflation, and combining the resulting expressions), we get the equilibrium condition ( l + p 2 ( 0 , e))jr
,~(1 + p2(0, e)) Jr* pj(O,e)+X(x*--O)+ l + • + p 2 ( O , e ) e .
(4.4)
The benchmark optimum in Equation (2.11) can be implemented by settingp2(0, e) = 0 and pl(O, e) = pl(O) = X(x* - 0). Since the constant po(O, e) does not afl?ct any of the central bank marginal incentives, it can be set freely - for instance, it can be set negative enough that the participation constraint is satisfied: the central bank leadership finds it attractive enough in expected terms to take on the job. Thus a remarkably simple linear performance contract - imposing a linear penalty on inflation - removes the inflation bias completely. The credibility-flexibility trade-off has disappeared: average inflation is brought down to the target, at no cost of output volatility. Once the simple contract has been formulated, the central bank has the right incentives to implement ex ante optimal policy. Note that the optimal contract is not conditional on e; this is because the marginal incentives to stabilize the economy are correct under discretion (in the terminology of Section 2, there is an inflation bias but no stabilization bias). But the slope of the penalty for inflation is conditional on 0; as the incentive to inflate the economy also varies linearly with 0. To see the intuition for this result, think about the punishment for inflation as a Pigovian corrective tax. As
T. Persson and Ca. Tabellini
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discussed in subsection 2.3, the distortion we want to address is that the central bank does not internalize the effect o f its policy on inflationary expectations, when acting expost. Since expected inflation E ( ~ I 0) is a linear projection o f Jr, a linear penalty for inflation makes the central bank correctly internalize the marginal cost o f its policy 32. To see this formally, substitute Equation (2.3) into the objective function (2.6) and calculate the equilibrium marginal cost o f expected inflation in state 0 as:
dE[L(~,x) l O] d~ e
= ,Vx* - O) =p~(O, e).
That there is no credibility-flexibility trade-off with an optimal contract contrasts with the previous subsection, where - under a quadratic inflation target - lower expected inflation was associated with distorted stabilization policy. A quadratic inflation target is thus not an optimal contract. The Rogoff (1985) targeting solution, discussed at the end o f the last section, is equivalent to an inflation contract with 1 B P2 = (X ~ - 2'), Pl = (2"B _ 2")st*, and P0 = ~(X - 2")(zc*)2. This clearly gives the central banker incorrect marginal incentives. Nevertheless, the optimal linear inflation contract can be reinterpreted as similar to an inflation target. As the intercept can be set freely, we can write the optimal contract as
P ( x ; O)
=~o + pL ( O)(x - zc*);
(4.5)
the central banker is punished linearly, but only for upward deviations from society's preferred inflation rate. Walsh (1995b) shows that the marginal penalty on inflation can be interpreted as resulting from an arrangement where the governor o f the central bank faces a probability o f being fired which increases linearly in inflation. Such an arrangement resembles the Price Targeting Agreement in force in New Zealand since 1990. Other looser interpretations would be to associate the penalty with altered central-bank legislation, a lower central-bank budget, or a loss o f prestige of the institution and the individuals heading it, for failing to deliver on a publicly assigned or self-imposed "mission". Naturally, it may be impossible to specify the penalty exactly as a linear function o f inflation. But to approximate an optimal incentive scheme, the punishment for upward deviations from an inflation target should not increase too rapidly with the size of the deviation. In fact, if the central bank is risk averse, the optimal contract entails a diminishing marginal penalty on inflation (to reintroduce linearity in the incentive scheme). Svensson (1997a) has proposed an alternative interpretation o f inflation targets, related to - but somewhat different from - the optimal performance contract interpretation. In his formulation the central bank is not assumed to have any generic
32 Indeed, tinearity of the optimal contract is preserved for any general loss ~unctions~ and not just for the quadratic one.
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preferences over macroeconomic outcomes; instead society can impose a specific quadratic objective function on the central bank o f the form in Equation (2.6). Suppose that society manages to assign a loss function with a lower goal for inflation, say avB(0) rather than ~*, to the central bank. Then the optimal central bank goal for inflation is ~ ( 0 ) = 0c* - ,a.(x* - 0). Pursuing this goal would eliminate the inflation bias, without giving up on stabilization policies. That is, the lower inflation goal is equivalent to our previous setting with a central bank minimizing L + P, where L is society's loss function and P is an inflation contract o f the form in Equation (4.3), with parameters p2 = 0, p~ = )~(x* - 0) and P0 = ½[)~(x* - 0) 2 - 2~*)~(x* - 0)]. This representation of an inflation target suggests an alternative explanation for the empirical observation discussed in the previous subsection. A lower zce is associated with lower inflation but not with higher output variability, as in the data. It is not without problems to associate this scheme with real-world institutions, however. Suppose that the optimal inflation rate for society, sT*, is about 2%, and that the average inflation bias, )~(x* - 0), is about 5% (not an outrageous number, given the recent monetary history of many European countries). The central bank should then be given an inflation goal, S~(0), o f - 3 % . But in equilibrium, tile central bank would not take any action to bring inflation below 2%, which may present it with some problems when explaining its policy to the public. A second, more important, problem relates to enforcement. How can we ensure that the central bank accepts to evaluate the costs and benefits o f the policy according to the imposed objective function, rather than according to society's preferences? A plausible answer is that the central bank is held accountable for its actions and that there is a performance based scheme o f rewards or punishments that makes the central bank behave in the desired fashion. But then we are back to the performance contract interpretation o f inflation targets explicitly suggested by Equation (4.5) 33 A natural question is whether to base the contract on inflation or on other measures of performance, such as money, the exchange rate, or nominal income. Persson and Tabellini (1993) show that if the central bank is risk neutral, if the constraints faced by the central bank (i.e. the behavioral equations o f the economy) are linear, as assumed so far, and if the marginal penalties under the contract can be contingent on 0, there is an equivalence result: alternative targets yield the same equilibrium. With relevant non-linearities, however, an inflation-based contract is simpler; to replicate the ex ante optimal policy with other measures o f performance, the contract must be contingent on a larger set of variables, such as shocks to money demand, or to the money multiplier. In this sense, an inflation target dominates targeting schemes based on other nominal variables: simplicity implies enhanced accountability and thus easier enforcement. Intuitively, the whole purpose of optimal contracts is to remove an inflation bias. This is most easily done by means o f a direct penalty on inflation, rather than in a
3~ The best assignment if society could really freely impose an objective f~nction on CB, would be to set x*(O) = 0, thereby eliminating the inflation bias completely.
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more rotmd about way, by targeting other variables that are only loosely related to inflation. What happens if the contract cannot be made state-contingent, so that P0, pl and p2 in Equation (4.3) each have to be constant across 0? This question and its answer are related to the problem in Herrendorf and Lockwood (1997), who study delegation in a model with observable shocks, and to the problem in Beetsma and Jensen (1998), who study delegation via an optimal contract when the central banker's preferences are tmcertain e x ante. To find the optimal incomplete contract in this case, we first plug the solution for Jr in Equation (4.4) with the slope coefficients constant, as well as the associated solution for x, namely x= 0-
1 +P2
1 +~+P2
E,
into the quadratic objective function. We then take expectations o f the resulting expression over 0 and e and maximize with regard to Pl and P2. After tedious but straightforward algebra, we can write the optimality conditions as ~. /!)1 -- ~x* --P2
,
(l +/92) 3 -- a2 P2 (1 + ~t,+p2) 3 02.
(4.6)
These conditions are both intuitive. It is easy to show that the first condition says E(3r) = 3:*: unconditionally expected inflation should coincide with society's preferred rate o f inflation. The second condition says that the coefficient on the quadratic term in the contract should be a positive hacreasing function o f the relative importance o f observable to unobservable shocks (the left-hand side is increasing in p2). Thus, when fluctuations in the observable incentives to inflate cannot be handled by a statecontingent linear punishment, the constrained optimum gives up a little bit on (firstbest) stabilization in order to diminish the costly fluctuations in Jr. Asp~ contains a term in Jr*, we can rewrite the optimal non-state contingent contract as
P(~c) - p o + P l ~ +p2(a: - ~.)2, with P2 given by Equation (4.6) and Pl - ( ~,x* +P2g~) • According to this expression, the central bank should be targeting society's preferred rate of inflation and face an extra reward for low inflation. It is perhaps not too far-fetched to interpret the inflation targeting schemes enacted in the 1990s in many countries as an instance o f this arrangement 34. The simple contracting model discussed here has been extended in several directions. I f some shocks are observable, but not verifiable and hence not contractible, the central :~ In the model of Beetsma and Jenscn (1998) with uncertain CB pre~brences, the optimal inflation target may instead be above society's target.
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bank can be required to report the value of these shocks. Persson and Tabellini (1993) show that the optimal contract is related both to the inflation outcome and to the central bank announcement; it is structured in such a way as to induce optimal behavior as well as truth telling. Policy announcements matter not because they convey information to the private sector (that already observes everything), but because they change central bank incentives, by providing a benchmark against which performance can be assessed e x p o s t 35. Walsh (1995a) shows that the optimal contract can also handle costly effort by the central bank. Dolado et al. (1994) as well as Persson and Tabellini (1996) extend the contract approach to the international policy coordination problems that arise when central banks fail to internalize the international externalities of their monetary policies, al Nowaihi and Levine (1998) show how delegation via inflation contracts may eliminate political monetary cycles. McCallum (1996) and others have argued that the contracting solution makes little sense, because it just replaces one commitment problem with another: who enforces the optimal contract? This question reintroduces the general question about institutional reforms raised at the beginning of this section, although it might apply more forcefully to a more ambitious incentive scheme such as the optimal contract. As in the case of the fixed-exchange rate regimes of subsection 4.1, enforcement is more likely if agents have heterogenous ex p o s t benefits of inflation and agents hurt by inflation are given a prominent role in the enforcement. Interestingly, Faust (1996) argues that a desire to balance redistributive interests for and against surprise inflation was a clear objective in the mind of the framers of the Federal Reserve. As stated before, we also do believe that changing institutions takes time. The public image of a policymaker who emphatically announces an inflation target, would be severely tarnished, if he explicitly abandoned it shortly afterwards. This is one of the main reasons why in the real world inflation targets can alter the ex p o s t incentives of policymakers. The emphasis of the contracting solution on accountability and transparency is helpful for thinking more clearly about these issues, and about the trade-offs that emerge if the reward scheme cannot be perfectly tailored to mimic the optimal contract. We cannot demand much more than that from simple theoretical models. But where the literature should go next is probably not to other variations of the objective function in the simple linear-quadratic problem. Instead it would be desirable to model the different steps and the incentives in the enforcement procedure as a well-defined extensive-form, non-cooperative game. 4.4. Notes on the literatuFe
The literature on institutions in monetary policy has been surveyed in textbook fbrm by Persson and Tabeltini (1990), Cukierman (1992) and Schaling (1995).
3s In the reputationat model of Cukierman and Liviatan (1991), by contrast, atmouncements matter because they convey information about the policymaker'stype.
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The formal theoretical literature on central bank independence starts with Rogoff (1985), whose analysis of the conservative central banker is the basis of the model in subsection 4.3, although the treatment of society's problem as a principal agent problem is suggested by Barro and Gordon (1983b) in an anticipatory footnote. Giavazzi and Pagano (1988) discuss the commitment ability in multilateral fixed exchange rate regimes, although their analysis is carried out in a richer dynamic framework than the simple model of subsection 4.1. Flood and Isard (1989) introduce the formal analysis of the rules with escape clauses. Lohman (1992) discusses the implementation of an escape clause, by costly government override, in a monetary policy model that also includes delegation to a Rogoff-type central banker. Obstfeld (1997a) applies an escape-clause model in his analysis of realignments within the ERM, emphasizing the possibility of multiple equilibria. Bordo and Kydland (1995) argue that the classical gold standard worked like a rule with escape clauses. Flood and Marion (1997) include an insightful discussion of escape-clause models and speculative attacks. The optimal contracting solution to the credibility problem, in subsection 4.3, was developed by Walsh (1995a) and by Persson and Tabellini (1993), and was further extended by Beetsma and Jensen (1998) and by Herrendorf and Lockwood (1997). Insightful recent general discussions about the appropriate institutional framework for monetary policy can be found in Fischer (1995), McCallum (1996) and Goodhart and Vinals (1994). Cukierman and Lippi (1998) study theoretically and empirically how the optimal central banking arrangement varies with the structure of labor markets. The early real-world experience with inflation targeting is surveyed in Leiderman and Svensson (1995). More recent surveys include Haldane (1995) and Mishkin and Posen (1996). A number of studies - including Bade and Parkin (1988), Alesina (1988), Grilli et al. (199 l), Cukierman (1992) and Eijffinger and Schaling (1993) - have developed empirical measures of central bank independence and studied their relation to inflation and other macroeconomic outcomes in a cross-section of countries during the last few decades. Capie et al. (1994) study historical evidence on inflation before and after major central bank reforms in twelve countries since the end of the 19th century. Jonsson (1997) uses pooled time-series and cross-section data from the OECD countries since the early 1960s and finds that the negative relation between central bank independence and inflation is robust to the control of a number of other institutional and economic variables. Posen (1993) criticizes this kind of finding and argues that it is caused by an omitted variable problem, the causal variable for both independence and inflation being the resistance against inflation in the financial community. A survey of empirical studies is found in Eijffinger and de ttaan (1996). Each subsection above refers to additional relevant studies on specific topics.
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Part B. Fiscal Policy This part o f the chapter focuses mainly on intertemporal aspects of fiscal policy, such as government debt issue and taxation o f wealth. A companion piece [Persson and Tabellini (1999)] surveys the research on static "public finance" problems. The main stylized facts regarding the intertemporal aspects o f post-war fiscal policy in the industrialized countries include: (i) Tax rates on capital vary considerably across countries and fluctuate over time, with an upward trend. In many countries, estimates of effective tax rates on capital are quite high and often higher than tax rates on consumption or labor 36. (ii) Many countries have accumulated large debts, even in peace time. For most countries, debt accumulation in the post-war period started in the early 1970s. The cross-sectional pattern o f deficits is far from homogeneous; some countries have been endemically in deficit and built up massive debts, whereas others have not 37 (iii) Large deficits and debts have been more common in countries with proportional rather than majoritarian and presidential electoral systems, in countries with coalition governments and frequent government turnovers, and in countries with lenient rather than stringent government budget processes 3s. It is difficult to account for these regularities by the theory of optimal taxation or, more generally, any theory that assumes policy to be set by a benevolent social planner. According to Chamley (1986), the optimal capital tax should decline over time, asymptotically approaching zero, as the long-run elasticity o f investment is very high compared to that of other tax bases. Similarly, Barro's (1979) tax-smoothing model o f deficits can successfully explain war-time deficits, but not the persistent accumulation o f debt that has occurred in many industrial countries since the 1970s. Moreover, the correlations between policies and political institutions suggest that political and institutional factors play an important role in shaping fiscal policy. In this second part o f the chapter, we survey some recent literature that speaks to these stylized facts on the basis o f positive models o f fiscal policy. As in monetary policy, these recent contributions try to explain departures from socially optimal outcomes by various incentive constraints in the policy formation process. In Section 5 we discuss credibility again, abstracting from politics and individual heterogeneity. In Section 6 we add politics to our basic model o f fiscal policy and discuss alternative explanations for large government borrowing. 3~ Mendoza et al. (1996), building on earlier work by Mendoza et al. (1994), compute effective tax rates for a sample of 14 industrial countries, during the period 1965-1991. For the most recent six-year period, the average capital tax rate for these countries was close to 40%, higher than both the average labor tax rate and the average consumption tax rate. Furthemmre, the average tax rate on capital was higher than that on labor and consumption during every five-year period since 1965, and kept rising over time. 37 See ibr instance Elmendorf and Mankiw (1999) and Alesina and Perotti (1995b). 3s See von Hagen and Harden (1995), Alesina and Perotti (1995b), Grilli et al. (1991), Roubffli and Sachs (1989).
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5. Credibility of fiscal policy We first discuss the ex p o s t incentive compatibility constraints that imply a lack of credibility for desirable tax policies. Many insights parallel those in monetary policy. But by adding microeconomic foundations, we can now make more meaningful welfare statements. And by adding an explicitly dynamic setting, we can investigate how state variables link policy decisions over time. As in monetary policy, sequential (or discretionary) decision-making and a lack of policy instruments may imply that the government lacks credibility and loses control of private sector expectations. The economy gets trapped in a third-best equilibrium, where the government relies excessively on a highly distorting policy instrument. The most obvious example is the "capital levy problem". But credibility problems are not confined to capital taxation: they are the norm rather than the exception in a dynamic economy. These issue are discussed in subsection 5.1. Subsection 5.2 treats another consequence of lack of credibility: the possibility of multiple equilibria and confidence crises, features often observed in countries with high punic debts. In a dynamic economy current policy credibility depends on previous policy decisions; for instance, it depends on the size and denomination of the outstanding public debt; this new dimension is discussed in subsection 5.3. Finally, as in monetary policy, reputation can mitigate the adverse effects of the ex p o s t incentive constraint and institutions can be designed to relax it. These remedies are briefly discussed in subsection 5.4. 5.1. The capital l e w problem
According to the standard theory of optimal taxation, capital should be taxed at a much lower rate than labor or consumption. Moreover, the tax rate on capital income should generally decrease over time and approach zero asymptotically. The reason is that the elasticity of investment tends to be higher than those of labor supply and consumption, and it is even higher over longer horizons, as there are more opportunities for intertemporal substitution. This prescription sharply contrasts with stylized fact (i) above. Lack of credibility offers a reason why even a benevolent government can end up with such a suboptimal tax structure 39. 5.1.1. The m o d e l
Consider a two-period closed economy, t -- 1,2, with one storable commodity. A representative consumer has preferences defined over consumption in both periods, ca, and leisure in the second period, x, represented by u - U ( c l ) + c 2 + V(x).
(5.1)
In the first period, the consumer either consumes his exogenous and untaxed endowment, e, or invests a non-negative amount in a linear storage technology with 39 The next two subsections draw oil Persson and Tabellini (1990, ch. 6).
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unitary gross returns. In the second period, he devotes his unitary time endowment to labor l, or leisure time x, and consumes all his income and wealth after having paid taxes. His budget constraints are cl + k = e,
(5.2)
c2 = (1 - 0) k + (1 - r) l,
(5.3)
where k is the investment in the storage technology, 0 and r are the capital and labor income tax rates, and the real wage is unity. Finally, the government must finance a given amount o f second-period per-capita public consumption, g. Thus, the government budget constraint is (5.4)
g = rl + Ok.
Taxes are only paid in the second period, and lump-sum (i.e. non-distorting) taxes are not available. We follow the public-finance tradition o f treating the set o f available Ramsey taxes as exogenous; but ultimately, the non-availability of (personalized) lump-sum taxes must be due to some heterogeneity that can only be imperfectly observed by the government. What is the optimal tax structure in this economy? And what is the equilibrium tax structure if the government lacks credibility? We address both questions in turn. 5.1.2. The ex ante optimal policy
To derive a normative benchmark, we assume that at the start of period 1 - before any private decision is made - the government commits to a tax structure (0, r) for period 2. The decision is observed by the private sector, and cannot be changed. There is no uncertainty, and period-2 public consumption, g, is known already in period 1. We first describe how the private sector responds to the tax rates. The private sector first-order conditions are: U c ( e - k ) >~ 1 - 0 ;
Vx(l-l) = l-r,
(5.5)
where the equality in the first condition applies at an interior optimum with positive investment. Each tax rate thus drives a wedge between the relevant marginal rates of transformation and substitution. Optimal policy seeks to minimize the resulting distortions. Inverting these two expressions, we obtain the private sector savings function k = Max[O,K(1 - 0)], where K(1 - O) ~- e - Ucl(1 - 0), and labor supply function l = L(1 - r) _--_ 1 - vxl(1 - r). The partial derivatives Ko and Lr are both negative. By the separability and quasi-linearity o f the utility function, each tax base depends on its own tax rate only. For future reference, it is useful to define the
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elasticities of these two tax bases with respect to their own net of tax returns, as ek(0) and el(O, respectively 4°. The optimal tax structure maximizes consumer welfare, subject to the private sector and government budget constraint (5.2)-(5.4), and the private sector first-order conditions (5.5). Solving this optimization problem yields the following version of the Ramsey Rule41: 0
r
(5.6)
1 - 0 ek(O) = ~ e l ( r ) .
Equation (5.6) implicitly defines the ex a n t e optimal tax structure. What are its general properties? First, optimal tax rates are higher on the more inelastic tax base. Second, it is always optimal to tax both bases, as long as both elasticities are finite and strictly positive. Finally, both tax rates move in the same direction if the revenue requirements change; higher public consumption drives up both tax rates, in proportion to their elasticities. If, as empirically plausible, labor supply is much more inelastic than investment, the optimal tax rate on labor is much higher than that on capital. As taxes are distorting, the economy reaches a second best - not a first best. 5.1.3. E q u i l i b r i u m u n d e r d i s c r e t i o n
Suppose instead that the policy decision is taken at the start of period 2, after period-1 investment decisions have been made. This timing is much more plausible, as a sovereign country can change its tax structure at any time, under a normal legislative procedure. Under this timing, however, every tax structure promised in period 1 is not credible. A credible tax structure must be optimal e x p o s t ; from the vantage point of period 2. More precisely, a credible equilibrimn tax structure satisfies three requirements. (i) Individual economic decisions are optimal, given the expected policies and the decisions of all other individuals in the economy. (ii) The tax structure is e x p o s t optimal, given outstanding aggregate capital and individual equilibrium responses to the tax structure. (iii) Individual expectations are fulfilled and markets clear in every period. Let us consider each of these requirements. (i) Optimal individual behavior is still summarized by the functions K and L and by the corresponding elasticities. But the investment function and the corresponding elasticity are now defined over the expected, not the actual, capital tax rate, as the tax structure is decided in period 2, after the investment decision. Thus, k = K(1 0 e) and ei~(0e). We call this elasticity the ex a n t e elasticity of investment, since it is defined over 0 e rather than 0. 4o These elasticities are, respectively: (1 0) ek(O) -
K
dK d(1 - 0)
U,~ KUcc > 0,
el(r) ~
(1 r) dL L d(1 v)
41 See Persson and Tabellini (1990, ch. 6), for a derivation.
V~
LV~ >0.
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(ii) The ex p o s t optimal tax structure also continues to be described by the Ramsey Rule (5.6), but with one important proviso. The investment elasticity that enters Equation (5.6) is the ex p o s t elasticity, that is the elasticity with respect to the actual tax rate 0, since that is what the government is choosing. By the argument at point (i), this e x p o s t elasticity is zero: k depends on 0 e, not on 0. Equation (5.6) then implies that for any given capital stock k the ex p o s t optimal capital tax rate, 0", must satisfy 0* - Min[1, g / k l .
(5.7)
The optimal labor tax rate r follows from the govenmaent budget constraint. In particular, r - 0 if 0* = g / k < 1. This result is very intuitive. When tax policy is chosen, the supply of capital is completely inelastic at k, whereas the supply of labor continues to have a positive elasticity, as it is chosen by the private sector after observing tax policy. Hence, the government finds it ex p o s t optimal to set either a fully expropriating capital tax rate of 1, or a tax rate sufficiently high to finance all of public consumption with capital taxes, driving labor taxes to 0. (iii) Rational individuals correctly anticipate government policy. Hence, 0 e = 0* and k = K(1 - 0"). Combining this last result with Equation (5.7), the equilibrium tax rate is defined by 0* = M i n [ 1 , g / K ( 1 - 0")]. We illustrate the possible equilibria in Figure 1. The solid curve is the ex a n t e revenue function for different values of 0. Tax revenues first grow with the tax rate, but at a decreasing rate, since the tax base shrinks as 0 rises. Once we reach the "top of the Laffer Curve", tax revenue begins to shrink, as the reduction in the tax base more than offsets the higher tax rate. l f g is sufficiently high (higher than point G) only one equilibrium exists, in which 0* = 1 and k = 0 (point C in the diagram). Irrespective of private expectations, the government fully expropriates any outstanding capital stock. Anticipating this, nobody invests. It is easy to verify that all three requirements for an equilibrium are fulfilled. Private individuals optimize and have correct expectations about policy. And the government also optimizes, for even with no capital outstanding, 0 = 1 is (weakly) optimal, as confirmed by Equation (5.7). This equilibrium is disastrous: there is a prohibitive tax on capital, but still a large tax on labor which is the only available tax base. Yet, the government can do nothing to change the outcome. No promise to tax capital at a rate lower than 1 would be believed, because it would not be ex p o s t optimal for the government to fulfill it. If g is below point G in Figure 1, this disastrous outcome continues to exist together with two other equilibria. Suppose that government spending corresponds to the horizontal line in Figure 1. Then points A and B are also equilibrium outcomes. At point A, every consumer expects 0 e = 0 a and invests K(1 - 0a). Hence, the government can just finance g by setting 0 exactly at 0 A, while keeping the labor tax equal to 0. Thus, the government is at an ex p o s t optimum. The same argument establishes that point B is also an equilibrium.
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oK(1 -o) G
C 0
0A
0B
l
0
Fig. 1.
These equilibria are clearly Pareto ranked: A is better than B which is better than C. They are all worse than the e x a n t e optimal tax structure, since they tax capital too heavily and labor too lightly (except at point C where both bases are taxed too heavily). If the government is unable to commit, the economy is trapped in a third-best, or worse, allocation. 5.1.4. E x t e n s i o n s
Results similar to those above, apply to the taxation o f other forms o f wealth, in particular to public debt and real money balances; in the case of money, naturally, the tax takes the form of inflation. The logic is always the same. Once an investment decision has been made, the tax base is fixed and it becomes ex p o s t optimal to tax it as much as needed, or as much as possible. Moreover, credibility problems are not confined to wealth taxes, but are generic in a dynamic economy with sequential policy decisions. The reason is that the e x p o s t and e x a n t e elasticity o f tax bases generally differ from each other. In general this difference is not as stark as with wealth taxes, where the ex p o s t elasticity is zero. In the case o f other tax bases than wealth, we can no longer conclude that the optimal tax rate is always higher e x p o s t than e x ante. To gain some intuition for why, consider an increase in a labor tax rate in a given period t. If the tax increase is u n a n t i c i p a t e d , the household substitutes from labor into leisure in the current period. But if the tax increase was a n t i c i p a t e d in period t - 1, some intertemporal substitution has already taken place: the household works less in period t, but has already worked more in period t - 1. We cannot generally tell whether an anticipated or an unanticipated tax hike is more distorting, however. Intertemporal substitution increases the distortion at time t, the period of higher taxes, as the tax base is more elastic. But this greater distortion is offset by a larger tax base in period t 1, when the household is working more in
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anticipation of higher future taxes. In general, therefore, we can say that optimal tax rates are different, but not whether they are higher ex ante or e x post 42. We close this discussion with two remarks. First, characterizing the equilibrium with sequential government decisions is relatively easy in a two-period economy, and doable in a finite-horizon economy. But it becomes very difficult in an infinite-horizon economy 43. Second, so far we have considered a representative consumer economy in which the government lacks a non-distorting tax and has incentives to raise revenues in less distorting ways. Lump-sum taxation may, however, not be enough to avoid lack of credibility. If the goverlmaent also has distributive goals, but not enough lump-sum taxes and transfers to reach its desired income distribution, the optimal tax policy may still lack credibility despite the availability of (non-personalized) lump-sum taxation. What matters ultimately is thus a scarcity of policy instruments relative to objectives. 5.2. Multiple equilibria and confidence crises'
When discussing reputational equilibria in monetary policy, we argued that multiple equilibria indicated an incomplete theory. Here, multiplicity of equilibria instead reflects an indeterminacy in the economy, and helps explain the occurrence of sudden speculative attacks or capital flights that have plagued many economies. Absent a commitment technology, policy is driven by private expectations rather than the other way around. Equilibria under discretion thus become intrinsically fragile, as investors face a difficult coordination problem. The ex post optimal policy depends on aggregate investment. But aggregate investment depends on the simultaneous decisions of many atomistic individuals, which in turn depend on expectations about policy. Thus, there is a strategic complementarity. A single investor expecting nobody else to invest also finds it optimal not to invest: he realizes that aggregate capital will be small, and hence full expropriation is inevitable. Thus, individual expectations are self-fulfilling and, as they are not nailed down by any economic fundamentals, can fluctuate widely. The resulting policy uncertainty is yet another drawback of a discretionary policy environment. These problems arise in many policy decisions. Consider public-debt repayment in a two-period economy, and suppose that in the second period debt can be partially defaulted or taxed away, at a cost proportional to the size of the default. Calvo (1988) shows that we then get multiple equilibria, in a good equilibrium, every investor expects the debt to be fully repaid and demands a low interest rate. To avoid the cost of default, the government indeed services the outstanding debt. In a bad equilibrium, every investor expects partial default and demands a higher interest rate. The cost of servicing this debt is now higher, and with distorting taxes the government prefers a partial default; hence, default expectations are self-fulfilling. The equilibrium with default is Pareto inferior, as the net amount serviced is the same, but default costs are borne. 42 For a further &scussion, see Persson and Tabellini (1990, ch. 8). 43 See also the survey by Krusell et al. (1997).
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Another example, studied by Velasco (1994) and Giavazzi and Pagano (1990), concerns exchange-rate crises in a high public debt economy. By assumption, the cost o f outright default is prohibitive, but the outstanding debt could be monetized away. In a good equilibrium, investors expect the exchange rate peg to be viable and the domestic interest rate equals the foreign interest rate; at this low interest rate, it is optimal to service the outstanding public debt by tax revenue alone. In a bad equilibrium, investors expect the peg to collapse. They demand a higher interest rate, which raises the cost o f servicing the debt through tax revenue; at the higher interest rate, it becomes optimal to fulfill the expectations, the peg is abandoned and the debt is partially monetized through higher inflation 44. Related coordination problems arise in s e q u e n t i a l (as opposed to simultaneous) investment decisions. Alesina et al. (1990) and Cole and Kehoe (1996a,b) study an infinite-horizon economy with a large public debt. Like in Calvo (1988), default is costly, but the cost is assumed to be a lump sum cost. In the good equilibrium, the debt is rolled over forever at low interest rates, and distorting taxes are raised to pay interest on the debt. In the bad equilibrium, there is a debt run, as nobody wants to buy the outstanding debt for fear that - next period - investors will refuse to roll it over. Faced with such a situation, it is indeed e x p o s t optimal for the government to default on the debt, rather than repaying it all at once. Thus the investors' fears are indeed rational and self-fulfilling. Here, the coordination problem thus concerns investment decisions at different points in time. 5.3. P u b l i c d e b t m a n a g e m e n t
The papers discussed in the previous subsection have implications for debt management policies, as the occurrence of a confidence crisis depends on the maturity structure or currency denomination o f outstanding debt. For instance, tile debt-run equilibrium discussed by Alesina et al. (1990) disappears if the outstanding debt has a long enough maturity, whereas it is more likely with a short-maturity debt that must be rolled over every period. Similarly, the results in Giavazzi and Pagano (1990) suggest that issuing foreign currency debt can reduce the risk o f capital flight, as investors are already protected against depreciation. More generally, public debt management policies alter the future incentives of the monetary and fiscal authorities in many subtle ways, even if the ex a n t e and ex p o s t elasticities o f all tax bases are the same. This point was first noted in the seminal paper by Lucas and Stokey (1983) with regard to the maturity structure o f public debt. They start from the observation that fiscal policy typically alters real interest rates. The resulting wealth effect can benefit or harm the government, depending on the composition o f its balance sheet. With a lot of long-term debt, a higher long-term 44 A high cost of servicing the debt is not the only reason why an exchange rate peg may not be credible~ in a related argument, Bensaid and Jeanne (1997) show that multiple equilibria can arise if raising the interest rate to det?nd an exchange-rate peg is too costly lbr the government.
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real interest rate depreciates the outstanding debt and acts like a non-distorting capital levy. Alternatively, if it has long-term assets and short-term liabilities, the government benefits from a policy that reduces the short-term real interest rate. Under sequential decision making, the government's ex a n t e optimal policy may not be credible: the government may have an incentive to deviate from it e x p o s t , in order to change the value o f its outstanding assets and liabilities. Conversely, these incentives give an additional role for public debt management policies: if the maturity and contingency structure o f the debt is rich enough, it can be revised over time so as to maintain credibility o f the e x a n t e optimal tax policy under sequential decision making, even if ex a n t e and e x p o s t elasticities of relevant tax bases differ from each other 45. Naturally, these results only hold if the economy is closed or large enough to affect intertemporal world prices. Not only the maturity structure o f the public debt shapes policy incentives. Its composition into nominal and indexed debt plays a similar role, as the real value of the former, but not the latter, depends on the price level 46. Based on this observation, Persson et al. (1987) show that the capital-levy incentive for the government to dilute the real value o f its outstanding nominal liabilities - such as the money stock - can be relaxed if the govermnent holds claims on the private sector, denominated in nominal terms, if the nominal claims and liabilities are balanced, the e x a n t e Ramsey solution may be sequentially sustained. But nominally denominated liabilities can also offer valuable insurance against unanticipated fluctuations in government spending, if the government does not have access to contingent debt. Calvo and Guidotti (1990) study the choice between nominal and indexed debt as a trade-off between credibility and flexibility. The upshot is thus that the structure of the public debt becomes a strategic variable that can be manipulated by a government to relax incentive constraints which it will meet in the future. As a result, the "government capital structure" again becomes nonneutral, even if a Modigliani-Miller theorem about the irrelevance of the govenmaent financial structure would apply in the absence o f these incentive constraints. In this section, we have only considered governments that continue to make decisions in the future with full certainty. But the idea of using public financial policies strategically to influence future fiscal policy decisions, obviously extends to the case which is more relevant for real-world democracies (dictatorships), where elections (coups and revolutions) shift the identity and policy preferences o f governments over time. Strategic public financial policies have indeed received attention in the literature on the politics of public debt that we survey in Section 6.
45 "Rich enough" generally means that there are as many goverrmlent debt instruments as there are policy instruments. ,16 Public debt denominated in foreign currency is similar to indexed debt in this regard, but will not be considered here.
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5.4. R e p u t a t i o n a n d e n J b r c e m e n t
As in monetary policy, repeated interaction creates incentives to maintain a reputation, which may mitigate the capital-levy problem. Suppose that future expected capital tax rates depend on the current tax structure. Even though existing capital is taken as given by the government, it still perceives future investment to respond to current tax rates, through expected future tax rates, and this discourages overtaxation. Chari and Kehoe (1990) have studied this reputation mechanism in an infinitely repeated version of the simple two-period model of subsection 5.1. The equilibrium with reputation comes arbitrarily close to the ex a n t e optimal Ramsey rule, under appropriate assumptions about the government discount factor and the length of the punishment period. Kotlikoff et al. (1988) show that a related enforcement mechanism may be available in an overlapping-generations economy. A misbehaving government is not deterred by investors' expectations, but by the threat that future generations of tax payers will withdraw their intergenerational transfers to a generation that breaks "the social contract" by overtaxing capital. Naturally, multiplicity of equilibria remains in both models. When we consider default on public debt, however, reputational equilibria encounter additional difficulties. Suppose that a defaulting government is "punished" by savers, who refuse to buy public debt in the future. The punishment thus consists of not being able to smooth tax distortions overtime, in the face of fluctuating public spending or tax bases. Is this sufficiently strong to deter default? Bulow and Rogoff (1989) argue that it is not. Suppose that a defaulting government can never borrow again, but can nevertheless still invest budget surpluses in assets earning the market rate of return (for instance, by accumulating reserves of a foreign asset). Then, a simple arbitrage argument implies that the government is always better off defaulting rather than repaying its debt 47. Thus, simple reputation models cannot explain public debt repayment. There must be other reasons why governments honor their debts: either reputational spillovers across policy instruments, or other costs in a default, such as distress in the banking system, arbitrary redistributions, or sanctions credibly enforced by the international community. In Part I, we discussed various institutional reforms that might raise the credibility of desirable policies. In the case of fiscal policy, such reforms are less effective, however, as the tasks of a sovereign legislature cannot be narrowly defined. Nevertheless, some institutional devices could mitigate the capitaMevy problem. Political delegation to a conservative policymaker is one way. International tax competition is another. As discussed in a companion survey [Persson and Tabellini (1995)], capital controls or international tax agreements that limit tax competition exacerbate the domestic credibility problems, and could thus be counterproductive. 47 Bulow and Rogoff (1989) develop their argument in the case of sovereign loans that finance consumption or investment, with no tax distortions, for arbitrary concave utility and production function. But their result generalizes to a model with tax distortions.
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5.5. Notes' on the literature
Much of this section is based on Persson and Tabellini (1990, chs. 6-8). There is a large game-theoretic literature on dynamic games with sequential decision-making. What started this line of research are again the papers by Kydland and Prescott (1977) and Calvo (1978). The book by Basar and Olsder (1982) provides a game-theoretic analysis of these problems in an abstract setting. The "capital levy problem" has a long history in economics. Eichengreen (1990) provides a historical account. It has been formally analyzed (although with numerical solutions) in a two-period economy by Fischer (1980). An early treatment of surprise inflation to tax real money balances is Auernheimer (1974), but Calvo (1978) is the classic here. A large literature deals with speculative attacks and multiple equilibria. In this section we have only focused on multiple equilibria that arise when policy is endogenous and there is a credibility problem. Confidence crises on public debt have been studied by many authors; in particular by Calvo (1988), Alesina et al. (1990), Cole and Kehoe (1996a,b) and Giavazzi and Pagano (1990). Multiple equilibria with discretionary monetary policy have also been extensively treated in the literature, in particular by Obstfeld (1997a), Bensaid and Jeanne (1997), Chari et al. (1996) and Velasco (1994). Reputation and capital taxation is discussed by Kotlikoff et al. (1988), Chari and Kehoe (1990) and, more recently, by Benhabib and Rustichini (1996), while Grossman and Van Huyck (1988) and Chari and Kehoe (1993) applied reputation to a model of public debt repayment. The idea that reputation can fail in the case of sovereign debt repayment is due to Bulow and Rogoff (1989), whereas Chari and Kehoe (1993) show that enforcement problems on both sides of the market can restore a role for reputation. Reputational spillovers across contracts are discussed by Cole and Kehoe (1994). Political delegation and capital levies are modeled in Persson and Tabellini (1994c) and discussed by North and Weingast (1989) in a fascinating historical context. The literature on international tax competition and credibility is surveyed by Persson and Tabellini (1995). The credibility of optimal tax structures in a general intertemporal context and without capital has been studied by Lucas and Stokey (1983). Their seminal paper discusses both debt management and the credibility of tax policy. Subsequently, Persson and Svensson (1984) and Rogers (1987) reinterpret and clarify some of the general issues concerning the credibility of optimal intertemporal taxation. The debt management implications of the Lucas and Stokey paper are also generalized and interpreted, by Chari et al. (1992) and by Persson and Svensson (1986). Persson et al. (1987) extend the Lucas and Stokey result to a monetary economy, whereas M. Persson et al. (1997) show that the temptation to generate surprise inflation may be much stronger than the theoretical literature suggests, once the full set of nominal rigidities in public expenditure and tax programs are taken into account. Rogers (1987) discusses strategic debt management and credible tax policy in an economy with endogenous
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government consumption, while Rogers (1986) considers distributive goals. Missale and Blanchard (1994) study how the maturity structure required to make a low-inflation policy incentive compatible varies with the level of debt. Calvo and Guidotti (1990) study the credibility-flexibility trade-off in the optimal decomposition of public debt into indexed and non-indexed securities. Finally, Missale et al. (1997) as well as Drudi and Prati (1997) have studied public debt management as a signal of the government resolution to enact stabilization policies.
6. Politics of public debt As noted in the introduction to Part II, many industrial countries have accumulated large debts in peace time. Moreover, debt and deficits appear to be correlated with specific political and institutional features. The goal of this section is to survey the literature that addresses these issues. We begin with the idea that deficits may be a by-product of political instability. Section 5 emphasized that governments can manipulate their debt structure to resolve their own future credibility problems. Subsection 6.1 takes up this thread, showing how the debt level itself can be used strategically to bind the hands of succeeding governments with different political preferences, in a way first suggested by Alesina and Tabellini (1990) and Persson and Svensson (1989). This idea typically applies to political systems with two parties and a government that clearly represents the view of a cohesive political majority. The debt level can also be used to enhance the incumbent government's re-election probability, in a way first suggested by Aghion and Bolton (1990) and also discussed in Section 3. We construct a simple two-period example that incorporates both of these mechanisms. The remainder of the section then looks at political systems with more dispersed political powers, as in the case of coalition govermnents or powerful political interest groups. In subsection 6.2, we discuss why such a situation may be particularly prone to generate deficits. The argument is a dynamic version of the common-pool problem formulated by Levhari and Mirman (1980) - in the context of natural resources and applied to government debt by Velasco (1999). In subsection 6.3 we follow the approach of Alesina and Drazen (1991), showing how the struggle between powerful groups, about who will bear the cost of necessary cuts in spending, may lead to a war of attrition delaying the elimination of existing deficits. In both these subsections, we reduce the full-blown dynamic models found in the literature to simple two-period examples. In subsection 6.4, finally, we discuss briefly how the politics of intergenerational redistribution may trigger government deficits, as suggested by Cukierman and Meltzer (1989), Tabellini (1991) and others.
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6.1. Political instability in a two-party system 6.1.1. Economic equilibrium
Consider a two-period economy without capital, but otherwise similar to that of subsection 5.1. A continuum of individuals have identical preferences over consumption and leisure. First we describe their preferences over private economic outcomes and their private economic behavior, for a given economic policy. Individual preferences over public policy and different parties are described later. Preferences over private economic outcome are given by the utility function: (6.1)
U = C 1 + C 2 + V ( X l ) + V(x2).
Every consumer faces the same constraints. Leisure and labor in period t, xt and lt, must sum to unity. Budget constraints are c2=(1
cl+b=(1-rl)ll,
rz)12+Rb,
where Tt is a labor tax rate, R is the gross interest rate, and b is the holding of public debt - the only available form of saving. By the absence of discounting and the linearities in the utility function, an interior equilibrium f o r b requires R = 1. Recognizing this, we can write the equilibrium consolidated budget constraint as Cl +C2 = (1 - ' g l ) l l
+ ( 1 - T 2 ) I 2.
Solving the consumer problem, leads to labor supply functions L(1 - rt) identical to those of subsection 5.1. Public spending only takes place in period 2. Let g denote total per capita public consumption. Using R = 1, the government budget constraints are - b = rill,
b+g-
T212.
It is useful to re-express private utility as an indirect utility function defined over the policy variables b and g. Private equilibrium utility is only a function of the two tax rates T~ and r2. From the govermment budget constraints, these tax rates can be expressed as functions of b and g. Thus we can rewrite Equation (6.1) as J ( b , g ) - Max[c1 + c2 + V(xl) + V(x2)]. This indirect utility function has intuitive properties. First, Jg < 0, is the private marginal cost of government spending which is increasing in g: Jgg < 0. Second, Jb is the private marginal cost of government debt. The symmetry of labor supply implies > O as Jt, ~
1 b ~< -~g.
(6.2)
That is, when tax rates are equal over time, tax distortions are optimally smoothed out (orb = 0). But if more (less) than half the revenue necessary to finance g is raised in
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period 1, so that b < - ½ g (> -½g), private utility could be enhanced by higher (lower) debt issue. Finally, as taxes are distortionary and as higher b adds to the government's tax bill in period 2, the cross-derivative Jbg is negative 48.
6.1.2. The political system Individuals belong to two different groups, which we label d and r, o f given sizes s and (1 - s ) . The two groups are identified with the supporters of two political parties: D and R. Individuals and parties differ in their preferred allocation of public spending over two types o f public consumption: gd and gr. The two types of public consumption each require one unit o f output, but they provide different utilities to the two parties and their individual supporters. For simplicity we assume that individuals belonging to group d (r) only care about gd (g,.) and that each party only cares about the utility o f its own supporters. If elected, party I thus maximizes the utility function
u1 = J(b, g) + H(gi).
(6.3)
Thus, party I correctly internalizes the welfare effects of economic policy on private economic outcomes, according to the indirect utility function J defined over debt and total spending, and evaluates the benefits o f public consumption for its constituency according to the (concave) H function, defined over gi. Political parties are "outcome motivated" rather than "office motivated". It is easy, however, to amend the model with a separate benefit o f holding office, as in Section 3. Finally, we assume that relative group size s is a random variable, the realization o f which determines the election outcome. We define P = Pr(s ~< 0.5) as the probability, from the viewpoint of period 1, that party R wins. This electoral uncertainty can be due to a random participation rate, or to uncertainty about the relative popularity of parties on other policy dimensions. Below we suggest an explicit model for P, but for now we take it as exogenous.
6.1.3. Equilibrium policy Events in the model unfold as follows: (1) One o f the parties holds office in period 1; this party sets debt (tax) policy b. (2) Economic decisions in period 1 are made. (3) The elected party takes office and sets public spending. (4) Economic decisions in period 2 are made. As before, we consider a sequentially rational equilibrium, and we characterize it by backward induction.
48 Note that our formulation of the model rules out credibility problems of the type discussed in Section 5. The asstuned preferences imply that labor supply fimctions depend on the current after-tax wage only, so that there is no difference between ex ante and ex post elasticities. Also, incentives for debt repudiation do not arise, because the government is a creditor and has no opportunity to manipulate the equilibrium interest rate.
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Optimal private decisions at stages (2) and (4) are already subsumed in the indirect utility function. Suppose party I holds office in period 2. It chooses g so as to maximize its objective in Equation (6.3), given the outstanding debt level b. The first-order condition for good i is Jg(b, g) + Hg(g i) = O.
(6.4)
Thus party I spends on good i only (good j # i has only costs and no benefits) and equates the marginal cost of supplying good i to its marginal benefit (to group i). Clearly, this condition defines a reaction function gi = G(b) which is the same for both parties. Since higher debt implies higher period-2 tax distortions, any government type is less willing to spend on public goods if it inherits a higher public debt; hence: Gb < 0. We can look at the period-1 incentives to issue debt at stage (1). The identity of that government does not matter for the results, but to fix ideas we suppose that party D is the incumbent. Its expected payoff, given the expected election outcome, depends on debt policy according to the incentive constraint imposed by equilibrium policy choices in period 2: E(uD (b)) - J (b, G( b)) + (1 - P ) H ( G ( b ) ] . Optimal debt policy thus has to satisfy & + [Jg + (1 - P ) Hg]@, : & - P H g G b : O,
(6.5)
where the second equality follows once we impose condition (6.4). Condition (6.5) has an intuitive interpretation. To strengthen the intuition, first consider the special case in which party R stands no chance at winning - that is, P - 0 for any b. Then Equation (6.5) reduces to Jh = 0. In words, a government that is certain of re-election chooses the efficient debt policy, smoothing completely over time the tax distortions from the financing of its preferred public good. When re-election is not certain, however, other incentives come into play. The larger is the probability that the opponent will win, the more party D deviates from the efficient debt policy, as is evident from the second term. As this term is positive, party D sets Jt~ < 0 whenever P > 0. A positive probability of losing the election leads to excessive debt issue - or more precisely to an insufficient surplus today [recall Equation (6.2)]. Whereas the incumbent government fully internalizes the benefits of borrowing associated with tax smoothing, it does not fully internalize the cost of lower public spending in the future, because these costs are borne only if the government is re-elected. Thus, the over-issue of debt is larger the slimmer is the re-election probability. To express the intuition in an alternative way: it is optimal for the party-D government to tie the hands of a prospective party-R government, as that party will spend on a good not valued by the natural constituency. This strategic motive, creating
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facts for a successor with different preferences, was first stressed by Persson and Svensson (1989) and Alesina and Tabellini (1990). 6.1.4. Endogenous election outcomes As mentioned already in Section 3, governments also manipulate state variables to increase their chances of re-election. We now modify our model to show how this incentive applies to public debt, illustrating an idea first stressed by Aghion and Bolton (1990). Consider the same model, but suppose that parties and individuals also differ along a second - not explicitly modeled - dimension capturing aspects of public policy that do not directly affect the economy. Specifically, we assume that individual utility depends on the identity of the party holding office, in addition to the public good it provides. But we allow individuals belonging to the same group to have different preferences over policymakers in this second dimension. Thus, we postulate the following overall preferences for individual j in group i, for i = D, R: u ij = J ( b , g ) + H ( g i) + ( U +/3)K o,
(6.6)
where H(.) is the same concave function as in Equation (6.3), and the dummy variable K z) equals 1 if party D holds office in period 2, and 0 if party R holds office. The parameter aJ is distributed around a mean value of 0 in the population of each group, according to the symmetric and unimodal distribution function F(-). In period 1 the precise value of/3 is not known, but only its expected value E(/3). The aJ parameter thus measures an idiosyncratic "ideological" (and exogenous) bias for party D, and to the extent that/3 is positive, party D enjoys a popularity advantage. That is, individuals evaluate public consumption according to their group affiliation, and each party cares about its natural constituency. But voters also trade off the economic benefits obtained from their party against other (exogenous or noneconomic) aspects of public policy, according to the parameters a and [3. These "non~ economic" determinants of political preferences are not related to group affiliations in any precise way. This specification of political preferences implies that group affiliation does not completely determine how individuals vote, so that the vote share of each party is endogenous. Finally, we assume that the relative size of the two groups, given by s, is now a fixed parameter, not a random variable. The timing of events is as before, except that just before the date of elections the realization of aggregate popularity,/3, becomes known. What determines the election outcome? At the time of elections, debt policy b is given by previous decisions. Consider voter j in group d. She votes for party R if and only if J ( b , g ) + H(G(b)) + a j +/3 > J(b,g), or if aJ > - ( H ( G ( b ) ) + [3). Thus, unless party D is generically unpopular ~3 < 0), only group-d individuals with a strong idiosyncratic ideological bias against party D vote for party R. Next, consider voter j in group r. She votes for party R if and only i f J ( b , g ) + aJ +/3 > J ( b , g ) + H(G(b)),
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or if aJ > H ( G ( b ) ) - / 3 . Not surprisingly, a group-r voter is more likely to support party R, since she draws economic benefits from its election. Combining these conditions and using the law of large numbers, we get the total vote share for party R: SR(b,/3) = s F ( - H ( G(b)) - [3) + (1 - s) F ( H ( G(b)) - [3),
where fi is a random variable; everything else is known or chosen by the incumbent government. Thus, before knowing the realization of/3, the probability that R wins is P(b)
-
p[[se(b,/3) >~ 0.51.
We want to know how this probability depends on public debt. As a preliminary step, note that dSR db - HgGh[(1 - s))C(H(G(b)) - [3) - s f l ( - H ( G ( b ) ) -/3)], where f is the derivative (density) of F. As HgG~ is negative, the sign hinges on the expression in square brackets. Consider first the case/3 = 0. By symmetry of F, we see that the vote share of party R goes up for any/3 if s > (1 - s ) . Intuitively, higher b leads to lower furore spending, which increases party R's advantage among voters in group d, but it reduces it among voters in group r. if group d is larger, the 1 Then, by former effect prevails. Consider next the case in which s = (1 - s) = g. symmetry and unimodality of F, the vote share for R goes up as b increases if and only if/3 < 0. Again the voters in group d are more important, not because the whole group is larger, but because at the margin the voters in group d are more mobile when party D is generally unpopular. It follows from this discussion that Pb > 0 is more likely the larger is s and the smaller is E(/3). That is, from the point of view of a party-D incumbent, issuing more debt reduces the probability of re-election (Pb > 0) if its economic policies benefit a large group of voters (s is large) or if it is unpopular among all the voters (/3 < 0). It is now easy to characterize the equilibrium debt issued by a party-D government Going through the same steps as in the previous subsection, the optimality condition for public debt - the analog of (6.5) is & - P ( b ) Hg Gb - P b H ( G ( b ) ) - O.
(6.7)
The first two terms on the left-hand side of Equation (6.7) are identical to those in Equation (6.5) and have the same meaning. The government trades off the efficiency considerations of public debt (captured by Jb) and the strategic effects on the future spending decisions of its opponent (captured by P H x G v ). The last term captures the effect of debt on the re-election probability. If issuing debt enhances the re-election
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chances for party D, so that Pb < 0, this effect adds to the incentives to issue debt, but when Pb > 0 it pulls in the opposite direction. From the previous discussion we know that Pb < 0 is more likely when s is small and when E([3) > 0. Intuitively, a party-D government whose spending policies benefit only a small "minority" - one for which s is small - enhances it re-election chances by constraining its own future spending, that is by issuing more debt, since this makes him more attractive to swing voters in the larger group r. Similarly, a party-D government whose non-economic policies are generically popular finds it more beneficial to go after swing voters in the opposition party's natural constituency, group r. 6.1.5. Discussion
What happens if the disagreement between the two parties is not as extreme as we assumed, so that both parties always spend on both goods, g~ and gr, although the preferred composition of public spending differs across parties? The answer depends on the shape of the utility function: more debt forces future spending cuts, but which public good is cut the most depends on preferences. If lower total spending is associated with a more similar mix of the public goods by the two parties, Tabellini and Alesina (1990) show that more instability (a lower probability of re-election) still leads to larger equilibrium debt 49. The model thus yields the empirical prediction that political polarization (i.e. sharp disagreement between the majority and the opposition) and political instability (i.e., frequent government turnovers) lead to larger debt accumulation. The simple idea that political instability causes government to behave myopically can be applied in more general models. Adding government spending in period 1 does not change the argument in any respect. Similarly, the results go through if policies are chosen directly by the voters, rather than by the government, as long as there is a probability that the current majority will be replaced by a future majority with different preferences. In fact, the prediction is more general and really applies to any intertemporal aspect of public policy, such as the choice of public investment [Glazer (1989) and Part Ill below], or the implementation of tax reforms [Cukierman et al. (1992)]. If" political disagreement concerns the overall size of public spending, rather than its composition, the result that public debt policy is economically inefficient continues to apply. But-now the direction of the inefficiency depends on which government is in office. Persson and Svensson (1989) show that a conservative government facing a more liberal opposition has an incentive to borrow, to force future spending cuts if the liberal is elected; but a liberal government has the opposite incentives and underissues debt (runs an excessively large surplus). Hence the empirical prediction that on average left-wing governments are more disciplined than their opponents, because they are more willing to raise tax revenue. ~t9 Tabellini and Alesina (1990) tbrmulate this condition in a precise way, referring to thc concavity index of the function H.
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As we saw in the introduction to this part, the general idea that govenmlent turnover is positively associated with debt issue is consistent with the stylized facts. Some of the models' specific predictions regarding public debt issue have been taken to the data by Ozler and Tabellini (1991) for developing countries and by Lambertini (1996) for industrial countries, with supportive results in the first paper but not in the second one
50 ,
Stretching the model somewhat, it also predicts that minority governments would be more prone to issue debt, as the two strategic effects pull in this direction for a government with a small natural constituency (a small s tends to raise P and to make Pb negative) 51. For a government with popular candidates, the two effects pull in opposite directions, though. The specific positive implications concerning the effect o f debt on re-election probabilities are not necessarily robust, but depend on the assumptions about voters' preferences in Equation (6.6). But the general idea, that public financial policies can also be used to manipulate the relative popularity of the two parties, is sound and has many other applications besides public debt. Clearly, these determinants of economic policy would be even more important if parties were also opportunistic, i.e., also cared about staying in office p e r se. Finally, note that all of these predictions are confined to a two-party system, and in particular to a political system in which a government, once elected, behaves as a single decision-maker. We now turn to coalition governments.
6.2. Coalition governments
To see why coalition governments may issue debt, consider a two-period, two-group, two-party model, silnilar to that in the previous section. As tax distortions are not central to the argument here, we assunae taxes to be exogenous and lump-sum. Furthermore, we abstract from elections and popularity and instead assume that the two parties share office, both in period 1 and period 2. Public spending occurs in each period. As before, the two groups have sharply different preferences over the composition o f public consumption. We can write the utility of a typical group-i individual as u i = cl ~ c2 + H ( g { ) + H(g~) = 2 ( y -- r) + H(g{) + H ( g '2),
where y and r are exogenous per capita incomes and per capita taxes assumed to be equal over time.
50 Petterson (1997) test the Persson-Svensson and Aleshla-Tabellini models of strategic debt issue on panel data from Swedish municipalities. He finds support for the former model but not for the latter. 51 Questioning the stylized fact cited in the Introduction to Part II, Edin and Ohlsson (1991) argue that minority governments, rather than coalition govermnents, are associated with larger debt issue.
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To simplify further, let us assume that s = ½, so groups (or parties) d and r are of equal size. The government budget constraints are g,--(g~+g~):r+b,
g2
(g~+g~):r-b.
It is easy to see that in this setting the optimal cooperative policy (giving equal weight to the two groups) would set b = 0, and g~ = gI T f o r i = d, r a n d t = 1,2, sincethat would smooth the benefits of government spending optimally across groups and time. This is not the equilibrium outcome, though, if groups do not cooperate. In each period, the coalition partners simultaneously and non-cooperatively propose a spending level for their constituency. Period-2 debt is always honored. I f jointly feasible, these proposals are implemented; if infeasible, each group gets a share of the feasible spending level in proportion to its proposal. More precisely, using p(g~) to denote the proposal of group i in period t we assume that 52
gl
f p(g~)
if
] @
~2r
f p(gi2)
if
(p(gl)+p(gi/)) g£ for i = d, r, it follows from Equation (6.8) that b > 0. This result is an instance of the familiar common pool argument: as the property rights to future income are not well defined, each of the parties only internalizes a fraction of the cost of current spending and debt issue. The result is a collective irrationality, which departs radically from the cooperative solution. Naturally, with N > 2 groups the problem becomes even worse, because now each party only internalizes I / N of the future costs of debt issue. This model can be generalized in several directions. Velasco (1999) studies a genuine multi-period model. This gives richer debt dynamics, including the possibility of delayed endogenous stabilizations. Chari and Cole (1993) study a two-period model which combines ideas from this and the previous subsection. Legislators facing a free-rider problem that drives spending too high try to constrain future spending and avoid collective irrationality by issuing more debt. Lizzeri (1996) applies a related idea to a very different model of redistribution, originally formulated by Myerson (1993). He considers a two-period economy where elections are held every period. Candidates can make binding promises before elections, over how to redistribute the available resources across voters and over time. Rational voters reward myopic behavior, however, favoring a candidate who promises to distribute all resources today. The reason is that resources left for the future can be taken away by the opponent if the first-period incumbent is not re-elected 53.
53 Tile commonpool problem has also been extensivelystudied in a static context. Persson and 'Ihbellini (1999) smvey that literature.
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6.2.2. A stronger budget process
The over-issue o f debt is obviously caused by a flawed government budget process, where each party o f the coalition (each group) is given decision-making authority over part of the budget, but nobody is given decision-making authority over the aggregate outcome. Which institutional reforms could address this problem? A natural idea is to centralize decision-making authority completely to one of the parties (or perhaps to reform the electoral system, to make majority governments, rather than coalition governments, more likely). I f the same party fully controlled all spending decisions, it would indeed appropriately internalize the cost o f overspending and o f debt issue. Such centralization o f decision-making power could be abused, however. In the model o f subsection 6.1, party I would spend all the revenue evenly over time on its own group, if it had the power to do so. The allocation o f spending across time would thus be fine, but the allocation across groups would be terrible. Moreover, in such a world, electoral uncertainty would re-introduce the incentives for debt issue considered in that section. This problem could be mitigated by institutional "checks and balances", for instance by splitting agenda-setting power between the two groups, giving, say, party D agenda-setting power over the budget size and party R agenda-setting power over its allocation 54. It turns out that a simple institution can implement the socially optimal allocation in the model. The solution is to split the decision in stages. First public debt is chosen. Then the allocation o f g t across different types o f public goods is sequentially determined, first in period 1 and then in period 2, with a separate budget constraint for each period. Suppose that the allocation o f spending is made according to Equation (6.8), except that (r + b) replaces 2 r in the expression for first-period spending on the RHS of Equation (6.8). It is easy to see that both groups now agree to a balanced budget (b = 0), as any other choice would be inefficient for both of them. Since there is unanimity, any mechanism for choosing b would give the same result. Interestingly, the empirical evidence in yon Hagen (1992), von Hagen and Harden (1995) and Alesina et al. (1996) suggests that certain features of the budget process makes it less likely that countries run into public debt problems. One o f the indicators that make up the index of budget stringency in their work is precisely whether the budget process entails a decision on the overall budget, before the decision on its allocation 5s.
54 Fhe effects of some of these checks and balances are investigated in a difterent set up by T. Persson et al. (1997). s5 Hallerberg and yon Hagen (1997) argue that countries with majoritarian electoral systems (and which thus are more likely to have one-party governments) have chosen to centralize power to the finance minister in the budget process, whereas coantries with proportional electoral systems (more likely to have coalitions and minority governments) instead have tried to limit their deficits by adopting formal budget targets.
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Ch. 22." Political Economics and Macroeconomic Policy 6. 3. D e l a y e d stabilizations
In this section we do not focus on why budget deficits arise, but on why it may take time to get rid of them once they have arisen. Following Alesina and Drazen (1991), we illustrate the possibility o f delayed stabilizations when two parties in a coalition government, or two powerful interest groups, both have an incentive to let the other party bear the brunt o f the necessary adjustment. Alesina and Drazen's continuoustime model built on the biological war-of-attrition model o f Riley (1980) and on the public-goods model o f Bliss and Nalebuff (1984). We adapt their analysis to our simple two-period setting. In the model of the previous section, assume that aggregate government spending has got stuck at a level higher than aggregate tax revenue. In particular, assume that gd + gr = g = r +/3, with/3 > 0. As before, tax revenue is exogenously fixed at the same level in each period. We study two possible outcomes: (i) Stabilization is delayed, in which c a s e g ~ + g ~ " = gl = r + / 3 , b = /3, a n d g ~ + g ~ = g2 = r - j 3 . (ii) Stabilization occurs in period 1, in which case aggregate overspending is cut by [3 so that gl = r = g2 and hence b = 0. The allocation o f spending cuts across the two groups in case (ii) depends on how stabilization came about. We return to this question below. We are interested in the probability that stabilization is delayed, and what factors make delay more likely. To simplify the algebra, we assume that the utility o f group i is linear in gi. We assume that the costs o f debt policy enter additively in the utility function. They can be thought o f as either a suboptimal spending allocation over time, or other costs associated with debt issue - perhaps part of the deficit is financed by a distortionary inflation tax. We thus write utility o f group i as u i = 2 ( y - z') + g{ + g i9 - lcib.
(6.10)
The parameter t¢i measures the cost to group i of postponing the stabilization. A crucial assumption is that this cost is private information to group i. G r o u p j only knows that K"i is distributed on the interval [0, ?(] according to the distribution function F(lfi). The corresponding parameter tcJ has the same distribution, but the realizations o f ~ci and tcJ are independent. All political action takes place at the beginning o f period 1, when each party, simul. taneously and non-cooperatively, makes a proposal p/ of whether to stabilize (pl = s) or not (pI = n). If both parties propose n, the stabilization is delayed. But i f at least one party proposes s, stabilization takes place. If only one party "gives in" and proposes s, that party bears the main burden of the necessary cutbacks. Specifically, we assume: gi(n,n)=½(r+/3),
g ~ ( n , n ) = ½(r -/3),
g~(s, n) = g[(n, s) = ~i r - a , g~(n,s)=g~(s,n)=½"r+a, g~(s, s) = gr, '
i=d,r,
t = 1,2, t=l,2~ t=1,2,
i=d,r,
(6.11)
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where gi(pt),pD) denotes how spending on group i depends on the two proposals, and where a > 0 measures the advantage of not giving in. Implicit in Equation (6.11) is the idea that the political process gives veto rights to some party or interest group. Thus, this model applies to countries ruled by coalition governments, or more generally to a situation where the executive is weak and faces effective opposition by organized interests in the legislature or outside of Parliament. Consider one of the parties, say party D. It compares expected utility when proposing n, denoted by E[u d I pd = n], and when proposing s, denoted by E[u d ] pd _ s]. Let q = Pr[p" = s] be the probability that party R proposes s (q is determined in equilibrium). Then, Equations (6.10)-(6.11) and some algebra imply E[ ud I S = n ] - E [ ud [ S = s] = a - ( l
q)tedb.
(6.12)
Thus, it is more advantageous to propose n if the gains from not giving in are large (a is large), if the costs of deficit finance for group d is low (k d is low), and if the probability that party R proposes s is high (q is high). Clearly, party D says no whenever ted is below some critical number K. But, since party R faces an identical decision problem, it also proposes n whenever te" < K. Thus it must be the case that (1 - q ) = F ( K ) . Using that and setting the expression in (6.12) equal to zero, we can implicitly define the equilibrium value of K by: X F ( K ) = all3.
The LHS of this expression is increasing in K. Therefore, K = K ( a , fi), with Ka > 0 and Kf~ < 0. We can now answer the main questions, namely how often we would observe a delayed stabilization and what factors make equilibrium delay more likely. Delayed stabilization requires that both groups propose n. As teJ and te" are independently distributed, the unconditional probability o f observing delay is (1 - q)(1 - q) -- F ( K ( a , f i ) ) F ( K ( a , fi)). The likelihood of delay is thus increasing in a, the gain from winning the war of attrition when the other party gives in first. If we interpret a as a measure of cohesion in the political system, this result thus says that delayed stabilizations and prolonged deficits are more likely in polarized political systems. Note that if a = 0, there is never any delay; postponing adjustment only implies losses for each party. The likelihood of delay is also decreasing in fi, the initial fiscal problem. The model is consistent with the general idea that a worse fiscal crisis makes adjustment more likely; here we get that result because the expected cost of waiting becomes individually larger with a higher ft. Thus, the model supports the general idea that financial crises and times of economic distress resulting from budgetary instability are catalysts of reform, and
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should not be feared too much [Drazen and Grilli (1993)]. The mechanism causing delay in the model, namely a conflict over how to distribute the losses from cutbacks in government programs, also rhymes well with casual observation. Finally, the model can be used to study the consequences of financial aid to developing countries and conditionality [Casella and Eichengreen (1995)]. To be effective, external financial aid should not ease the pain of an unsustainable situation (in terms of our model, it should not reduce fi), for this would simply delay the stabilization. Effective financial aid should instead be conditional on a stabilization taking place and shrink over time if the stabilization is postponed, to increase the incentives to give in early for the rivaling parties. 6.4. Debt and intergenerational politics
The models in this section all focus on how debt redistributes tax distortions, or benefits of government spending, over time. But they ignore another role of debt: redistribution across generations. They also all assume any outstanding debt to be honored by the government that inherits it. But as we have seen in Section 5, this requires a strong form of commitment. Reputational or institutional forces facilitate commitments, but then they should really be part of the argument; such forces may also not go all the way. In conventional representative-agent macroeconomics, debt issue and pay-as-yougo social security are identical policies. Several authors have addressed the political determinants of such policies in a median-voter setting without altruism - see Browning (1975) for an early contribution, Boadway and Wildasin (1989), and Cooley and Soares (1999). In these papers, future social-security policies are honored by assumption (at least in the next period); i.e. commitment is assumed. Working agents not too far from retirement favor introducing pay-as-you-go social security, as this allows them to free ride on younger agents. Old-age agents are, of course, also in favor. Therefore a majority of voters typically favors social security and equilibrium policy depends, in a predictable way, on age-earning profiles and the population growth rate. Cukierman and Meltzer (1989) analyze budget deficits in a similar way, but introduce inter-generational altruism. The degree of altruism varies across households: some households leave positive bequests, but others are bequest-constrained. Nonconstrained voters, who can undo any intergenerational redistribution, are only concerned with the general equilibrium effects of the policy, and not on how it redistributes across generations. But a budget deficit is favored by the bequestconstrained voters, because it allows them something they cannot do privately redistribute resources towards themselves. In a median voter equilibrium, the size of the budget deficit depends of the efficiency effects and the number of bequest-constrained voters. Even though these contributions introduce important aspects of politics, they still hinge on the commitment assumption. At any moment social security strictly benefits
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only a minority (the retired) but imposes a cost on a majority (the workers). A similar problem exists for debt. Why then does the majority not repeal the policy? Reputational concerns may help, if honoring the current program enhances the probability that it will be honored in the future. But as we have already discussed in Section 5, this argument is not without problems. Tabellini (1990, 1991) suggests one should allow intra-generational heterogeneity in income, when thinking about these questions. Pure intergenerational policies rarely exist, at least when generations are altruistically linked. Social security programs thus redistribute not only from kids to parents, but also from rich to poor. Similarly, public debt default would have both intergenerational and intragenerational effects (as the rich are likely to hold more debt). A policy redistributing across generations may therefore be upheld in equilibrium, without ex ante commitments, by a coalition of voters that contains members of different generations who belong to similar income groups. But the coalitions that form ex p o s t to support existing social security and outstanding debt are different. Social security is supported by the old and the kids of poor parents, whereas debt is supported by the old and the kids of rich parents. These two intergenerational policies are thus not equal under heterogeneity and lack of commitment. As in Section 5, incentive constraints in policymaking violate the Modigliani-Miller theorem of government finance. Majority voting is not the only way of thinking about how the policy preferences of different generations get aggregated in the political process. In many societies, different age-groups - the old, in particular - have well-organized interest groups that lobby and take other political action to support policies benefitting their members. Rotemberg (1990) discusses the repayment of government debt as the outcome of bargaining between living generations. Grossman and Helpman (1996) formulate a dynamic model of intergenerational redistribution where policy commitments are again not feasible. In the model, pressure groups of living generations make contributions to the government conditional on the support given to their members. The model has multiple expectational equilibria, which remind of the equilibria in capital taxation studied in Section 5. But it is the expectations of the current goverm'nent - rather than the expectations of private agents - about the policy of the next government that introduce the self-fulfilling property. One can easily end up in a very bad equilibrium, where the pressure groups get engaged in a very stiff and costly competition for policy favors and Where capital formation suffers.
6.5. N o t e s on the literature
A huge literature deals with the politics on government deficits. Here we only refer to the more recent contributions, that typically study general equilibrium models with rational voters and politicians. A broader survey of the public choice literature is Mueller (1989). Much of the modern macroeconomic literature on public debt is surveyed in Alesina and Perotti (1995a).
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The idea that political instability induces a govermnent to use public debt strategically, to influence the future policies of its opponent, was first independently studied by Alesina and Tabellini (1990) and Persson and Svensson (1989). The model of subsection 6.1 is related to Alesina and Tabellini (1990), while Persson and Svensson (1989) studied a model where parties disagree on the overall size (as opposed to the composition) of public spending. Since then, many other papers have applied this idea to intertemporal fiscal policy. In particular, Tabellini and Alesina (1990) provide a generalization of these results, Alesina and Tabellini (1989) study capital flight and external borrowing, Tabellini (1990) looks at these models in the context of international policy coordination, Glazer (1989) applies the same idea to the choice of duration in public investment, Cukierman et al. (1992) analyze tax reforms from this point of view and provide empirical evidence that political instability is associated with more inefficient tax systems, and Roubini and Sachs (1989), Grilli et al. (1991), Ozler and Tabellini (1991) and Lambertini (1996) analyze the empirical evidence. Finally, the result that public debt policies also affect the re-election probability was first studied in this context by Aghion and Bolton (1990). Modeling the voters' preferences as entailing a trade-off between economic and non-economic dimensions, as we do in subsection 6.1, is a common strategy in some of this literature - see in particular Lindbeck and Weibull (1987). The dynamic "common pool" problem has a long history. It has been studied in industrial organization, where it refers to dynamic games among oligopolists facing an exhaustible resource, such as an oil field or a fishery [Levhari and Mirman (1980), Benhabib and Radner (1992)]. In fiscal policy, it was studied by Tabellini (1987) in a dynamic game of monetary and fiscal policy coordination, and by Velasco (1999) in a setting more similar to that of this model. This idea is also at the core of the more empirically oriented literature on budgetary procedures, such as Alesina and Perotti (1995a), von Hagen and Harden (1995), and Hallerberg and yon Hagen (1997). There is also an interesting (mainly empirical) line of research, that has investigated the effects of various restrictions on government borrowing. Most of this literature has studied the variety of institutional arrangements in US states. See for instance Bohn and Inman (1996), Poterba (1994), and Eichengreen and yon Hagen (1996). The model of delayed stabilizations is due to Alesina and Drazen (1991), who in turn have elaborated on earlier ideas by Riley (1980) and Bliss and Nalebuff (1984). Since then, the model has been extended in several directions, among others, by Drazen and Grilli (1993), Casella and Eichengreen (1995) and Alesina and Perotti (1995b). Finally, a large literature deals with intergenerational redistribution. Besides the papers quoted in the previous subsection, a separate line of research has investigated the sustainability of social-security systems in reputational models [Kotlikoff eta!. (1988), Boldrin and Rustichini (1996)].
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Part C. Politics and Growth Distorted fiscal policies, such as those emerging from the political equilibria in Part II, are likely to affect economic performance. It is therefore natural to ask whether political factors and political institutions are correlated with long-run economic growth. Here, too, there are some stylized facts. Most notably, after controlling for the conventional determinants o f growth: (i) Inequality in the distribution o f income or wealth is significantly and negatively correlated with subsequent growth in cross-country data. On the other hand, the evidence on the effect o f growth on the distribution o f income (the Kuznets curve) is quite mixed, both in cross section and time series data 56. (ii) Political instability, as measured by more frequent regime changes, or political unrest and violence, is significantly and negatively correlated with growth in cross-country data 57. (iii) Better protection of property rights is positively and significantly correlated with the growth. Whereas political rights and the incidence o f democracy are strongly correlated with the level o f income, there are no robust findings regarding the effect o f democracy on economic growth. 58 A recent literature has tried to explain these regularities in a setting where both economic growth and fiscal policies are endogenous. Section 7 surveys this literature.
7. Fiscal policy and growth Subsection 7.1 illustrates how income inequality can produce a negative effect on investment and growth, because it provides stronger incentives for redistributive policies that hurt growth-promoting investment. This idea was suggested by Alesina and Rodrik (1994) and Persson and Tabellini (1994b). As in these papers - and a great deal of subsequent work - we rely on a simple median-voter model inspired by Roberts (1977) and Meltzer and Richards (1981). Subsection 7.2 then illustrates how political instability can hurt growth, by inducing the incumbent government to follow more myopic policies, as in the work by Svensson (1996) and Devereux and Wen (1996). The argument here is closely related to that on strategic debt policy in subsection 6.1. Finally, subsection 7.3 briefly discusses how poor protection o f property rights may hurt investment and growth, as in Tornell and Velasco (1992)
56 This finding was first obtained by Atesina and Rodrik (1994) and Persson and Tabellmi (1994b). For a recent and comprehensive survey of the empirical evidence on inequality and growth, see Perotti (1996). 57 On this point see Alesina et al. (t996) and Barro (1991). 58 On the relation be~ieen property rights and growth see Knack and Keefer (1995). A survey of the voluminous literature on the links fi-om democracy to growth can be found in Przeworski and Limongi (1993).
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and Benhabib and Rustichini (1996). The underlying ideas are closely related to the dynamic common-pool problem discussed in subsection 6.2. 7.1. I n e q u a l i t y
and growth
Consider again a two-period economy inhabited by a continuum of heterogenous agents. Everyone has the same quasi-linear preferences over private consumption in periods 1 and 2 and over government (per capita) consumption in period 2. The utility of consumer i is:
u' = u(c~)+ c~ +H(g)
(7.1)
The budget constraints are C i1
e i - r - k i,
(7.2)
C2i = (1 - O) A ( 1 ) k i,
where k i is private investment, r and 0 lump-sum and capital taxes, and A ( I ) the gross return to private capital, which is increasing in public investment 1. We abstract from credibility problems; the government can commit to these policy instruments before private capital accumulation. Finally, e i is the endowment of agent i. These endowments are distributed in the population with mean e and a distribution function for the idiosyncratic part F ( e i - e). To proxy empirical income distributions, we assume that F is skewed to the right: the median value o f e i - e, labeled e" - e and defined by F ( e " - e) ½, is negative. Assuming a balanced budget in every period, the government budget constraint in per capita terms is: I = "r,
(7.3)
g = OA(l)k,
(7.4)
where k denotes per capita (average) capital. Following the approach of subsection 5.1, we can derive equilibrium private investment from Equations (7.1)-(7.3) as k i = e - I - UcI(A(I)(1
- 0)) + ( e i - e) =~ K ( O , I )
+ ( e i - e),
where the common investment function satisfies K0 < 0 and K1 > 0. It is again convenient to express the utility from private consumption as an indirect utility function defined over the policy variables: ji(o,[,
e i) --~
Max[U(ci0 + c~]
=U(e-I-K(O,I))+(I = J(O,I)
O)A(I)K(O,I)+A(I)(t-O)(e
i
e)
~ A ( I ) (1 - O)(e i - e).
(7.5) By the envelope theorem, the direct welIhre cost of the capital tax Jo = - A ( I ) K is negative. Moreover, the welfare effect of public investment, .11 = -U~ + (1 - O ) A t K , is
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monotonically decreasing in I (by Ucc < 0 and AH < 0). Substituting Equation (7.5) into (7.1) and using (7.3), we obtain individual-/policy preferences over the two policy instruments 0 and I: u i = j i ( o , I, e i) + H ( O A ( I ) K ( O , I)).
These policy preferences are linear in the idiosyncratic variable e i. They therefore fulfill a monotonicity (single-crossing) condition, such that the preferred policy of the agent with endowment e m will be a Condorcet winner, even though the policy space is two-dimensional. If we imagine that policy decisions are taken at the begilming of period 1 by direct democracy, the winning proposal is thus the policy preferred by this decisive voter. I f the second-order conditions are fulfilled 59, the equilibrium values for I and 0 thus satisfy dl + It~,O(KAI + A K D + (em -- e)(1 - O)AI = O, Jo + H g A ( K + OKo) - (e" - e ) A = O.
(7.6)
To understand these conditions, first assume that the distribution is symmetric, so that e m = e. Then the third terms in both conditions are zero, and Equation (7.6) characterizes the optimal policy for the average agent, which by quasi-linear preferences - would be chosen by a utilitarian planner. The first condition says that it is optimal to provide more public investment than would maximize private indirect utility (i.e. Jr < 0) due to the beneficial effects on the future tax base and hence on public spending (if public debt were allowed this result would be different). The second condition equates the average private marginal cost of raising revenue (Jo < 0) with the marginal benefit it generates via public consumption. But if e m < e, redistributive effects come into play. The decisive voter's capital falls short of average capital by exactly (e m - e). This implies that I is smaller and 0 is higher than in the hypothetical planning solution. The reason is that the decisive w,ter does not benefit from public investment as much as the average capital holder, and he also does not suffer as much from capital taxes. To see this formally, notice that the third term in the first equation of (7.6) is negative and the third term in the second equation is positive. By the second-order conditions, ! has to be lower and 0 has to be higher than in the social planner's solution. We thus see that inequality hampers growth via two different channels. The growth rate from period 1 to period 2, given by [ A ( 1 ) K ( O , I ) / e ] - l, is increasing in I (both directly and indirectly) and decreasing in 0. Furthermore, the higher is inequality, as measured by the distance between median and average income, the lower is growth as equilibrium public investment is smaller and capital taxation - as well as government consumption - is higher. ~') As hi all optimal taxation problems, this assumption is not necessarily innocuous, but can involve restrictive assumptions on underlying fimctional forms.
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Alesina and Rodrik (1994) and Persson and Tabellini (1994b) developed this kind of reduced-form prediction in related but explicitly dynamic models. Whereas Persson and Tabellini (as we have done) focused on the size distribution of income, Alesina and Rodrik focused on the functional distribution of income between labor and capital. Both papers also took the reduced-form prediction to the data - here Alesina and Rodrik too look at the size distribution of income. And they indeed found a strong negative effect of inequality on growth in a cross section of post-war data from a broad sample of countries 60. These papers stimulated a body of subsequent work scrutinizing both the empirical and the theoretical argument. Whereas the reduced-form relation from inequality to growth indeed seems empirically robust, the structural links implied by the theory have not generally found support in later empirical work 61. Thus, it has been hard to identify both the implied link from inequality to redistribution and the link from redistribution to growth, as emphasized in the recent surveys by Perotti (1996) and Benabou (1996). The model in this section suggests that these links could be pretty subtle, however (with opposite effects of inequality on government consumption and investment, for example, and ambiguous effects on total government spending). Moreover, the failure to find a robust link from tax rates and redistribution to economic growth is a problem for conventional growth theory, not just for political theories of growth. The literature has also searched for other reasons why inequality and growth may be inversely related. Perotti (1996) stresses that one link may run via political instability or via other, non-political, channels such as education. Benabou covers a whole range of recent theoretical work showing that the links between income distribution, policy and growth may run in different directions. For instance, redistribution may promote growth when agents are credit constrained, or when it promotes education.
7.2. Political instability and growth We now modify the previous model as follows. First, every private agent has the same first-period endowment: that is, e i = e and the average investment function K(O,I) applies for everyone. Instead, as in subsection 6.1, agents belong to two different groups, d and r, and public spending is of either of two types: gJ (benefitting only group d) or g" (benefitting only group r). Second, and again following subsection 6.1, policy is not set by majority rule but by an incumbent government D that acts so as to maximize the utility of group-d agents. The incumbent may be replaced by an alternative government R in the future.
r,0 Perssonand Tabellini (1994b) also round a similar relation in a small historical panel of industrialized countries with data going back to the late 19th century. ~l Later empirical work based on better data has also questioned an empirical finding by Persson and Tabellini (1994b) that was interpreted as giving indirect support for the theory-,namely that the relation between inequality and growth was only present in democracies and not in dictatorships.
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For simplicity, we take the re-election probability (1 - P ) as exogenous. It is natural to interpret P as a measure o f political instability. Third, to introduce a meaningful policy choice in period 2, policies are chosen sequentially. Thus, public investment I is chosen in period 1, before private capital, and the capital tax rate 0 is chosen in period 2. To avoid the capital-levy problem discussed in Section 5, we assume that in period 2 the private sector can still avoid some of the tax, though at a cost, by reallocating some o f its accumulated capital to a non-taxed asset with a lower return. We could think o f this as tax avoidance, or capital flight. A convenient formulation, following Persson and Tabellini (1992), is to rewrite the period-2 budget constraint as c2 = (1 - O)A(I)(k - f ) + f - M ( f ) , where M ( f ) is a concave and increasing function o f the amount f shielded from taxation and where we have recognized that everybody makes the same savings decision. It is easy to show that average savings are still given by the function K(O, I) and that tax avoidance is given by the function F ( O , I ) with Fo > 0 and FI < 0 62. The government's tax base can thus be written as a function K ( O , I ) = A ( I ) K ( O , I ) - F(O,I). The ex ante properties o f this function (that is from the viewpoint of period 1) are the same as before: decreasing in 0 and increasing in I. in period 2, when K and I are given from previous decisions, the ex post tax base K 2 ( 0 , I ) is still decreasing in 0 but with a smaller slope (intertemporal substitution possibilities are eliminated). The bottom line after these modifications is similar to the previous section: we can write the ex ante indirect utility of an agent in group i as u i = J(O, I) + H ( g i) - J (0, I) + H(OK(O, I)).
(7.7)
We can also define ex post indirect utility (for given K and I) as j2(O, I) + H ( O K --2 (O,D). Both J(O,I) and j2(0, I) have the same qualitative properties as the corresponding function in subsection 7.1. Any government holding power in period 2 spends all revenue on the public good favored by its own constituency. The expost optimal tax rate is given by the condition: +H
(K 2 +
= 0,
(7.8)
which has the same interpretation as the second condition in Equation (7.6). Thus, both prospective governments will set the same tax rate. Condition (7.8) implicitly defines the optimal tax rate as a function o f past public investment O(I), with slope o, =
4 + --2 ° Jgo + HggKo0
(i? The first--order condition for optimal tax avoidance is for the consumer to set A(I)(1 Mr(f) = 0. When this condition is inverted, we get the desired tax avoidance function.
O)
1 -I
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Unless H is very concave, Ol > O, as the numerator is positive and the denominator is negative (by the second-order condition). Public investment enlarges the tax base and this drives up the optimal tax rate. The incumbent party-D government in period 1 chooses I so as to maximize
E ( S ) : PJ(O(1),I) + (1
P)[J(O(I),I) + H(O(1)K(O(1),I))]
= J(O(I), I) + (1 - P)[H(O(I)K(O(1), 1-))]. We can rewrite the first-order condition to this problem with Equation (7.8), recognizing that J~ = Jo and g2 = ~ at the equilibrium tax rate. Some additional algebra gives
Jl +Hg[OKI + O(Ko --K2o)Ol] PHg[OKI + 0I(K + OKo)] = O.
(7.9)
Suppose first that D is certain to be re-elected: P = 0. Then the optimal choice o f / b o i l s down to the familiar weighting of private welfare (the first term) against government revenue (the second term), where the latter are fully internalized as the government is certain to remain in office. The resulting condition is the same as the second condition in Equation (7.6) of the previous subsection, adjusted for the different timing of tax policy and for the lack of heterogeneity. But when re-election is uncertain, P > 0, future government revenue is less valuable and policy myopia sets in. As the third term in Equation (7.9) is negative, a higher probability P of losing office makes public investment less attractive and reduces it in equilibrium. Higher instability not only draws down public investment, but reduces growth in this model. Second-period income, c2 + g = A(I)K(O, I ) - M(F(O, I)), unambiguously goes down as I falls. The direct negative effects of lower public investment and the indirect negative effects of higher waste due to more tax avoidance always outweigh the positive effects of the smaller equilibrium capital tax. Much of the informal discussion of why political instability is harmful for growth seems to suggest a direct effect of uncertainty or unpredictability on private investment. We know, however, that uncertainty in returns has ambiguous effects on private investment. Here a different mechanism is at work: political instability induces more myopic fiscal policies, which in turn cause lower public investment and growth. This is related to Svensson (1998), who shows that political instability may make a forwar& looking government abstain fi'om improvements in the legal system that enforce private property rights. He also finds empirical support for this idea. Political instability [as measured by Alesina et al. (1996)] indeed reduces the protection of private property rights [as measured by the same index as in Knack and Keefer (1995)] in a wide crosscountry sample. And controlling for property-rights protection, political instability drops out of a cross-country investment regression. The theoretical paper by Devereux and Wen (1996) emphasizes a somewhat different mechanism: political instability induces incumbent governments to leave smaller assets to their successors, thereby forcing theln to tax capital at a higher rate; the expectation of higher taxes drives down private investment, which leaves a smaller tax base for the successor government.
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7. 3. Property rights and growth
As mentioned in the introduction, the data support the idea that poor enforcement of property rights is harmful for investment and growth. This idea is also derived from some recent theoretical work. Benhabib and Rustichini (1996) study a growth model where two groups try to redistribute consumption towards themselves at the expense of the economy's capital stock. They show how such incentives may arise both at low and high levels of income, and how they may be exacerbated by greater inequality in the two groups' incomes. Their model abstracts from the political mechanism and the channels of redistribution, however. Tornell and Velasco (1992) focus on redistribution through the fiscal policy process in a linear (Ak) growth model. Their argument, as Benhabib and Rustichini's, is another instance of the common pool problem discussed in subsection 6.3. The common pool is now a part of the economy capital stock rather than the government tax base, but the incentive to over-exploit this common pool is the same. Because the redistribution is supposed to take place via the governlnent policy process, the poorly enforced property rights are closely related to weak government. Tornell (1995) studies a related model, but allows for endogenous property rights. in particular, property rights can be created and destroyed at a cost. He shows that the economy can go through a cycle with low property-rights protection at low and high levels of income. I f so, this pattern is perfectly foreseen and leads to gradually falling growth rates at intermediate levels of income. Lane and Tornell (1996) show that an exogenous positive shock due to productivity or the terms of trade may actually reduce the growth rate in an economy with powerful interest groups and poorly defined property rights. The mechanism is again a coordination failure between the interest groups, whereby the initial increase in the incentives to invest is more than outweighed by an increase in redistributive transfers. Svensson (1996) produces a related result, where the incentives of the interest groups to hold back on their demand for transfers vary negatively with government income. 7.4, Notes" on the literature
Beyond the papers cited in the text, early contributions to the theory of income distribution," investment and growth were made by Perotti (1993), who studied human capital accumulation, and tax-financed subsidies in the presence of borrowing constraints, by Bertola (1993) who studied tax policy and the functional distribution of income, by Glomm and Ravikumar (1992) who studied private versus public provision of education, and by Saint-Paul and Verdier (1993) who also studied redistributive policies that finance public education in a setting with wealth-constrained individuals. Perotti (1996) and Benabou (1996) provide additional references to recent empirical work. Finally, Caballero and Hammoar (1996) focus on the rents created by factor specificity and how the distribution of those rents affects the incentives to invest. As stated in the text, few theoretical models spell out the mechanisms whereby political
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instability is harmful for growth. As emphasized by Benabou (1996), there is thus scope for new work to provide better theoretical underpinnings for the empirical findings. Sharper theory is also needed to sort out the empirical channels whereby politics interacts with growth. This is not going to be easy, however, given the strong empirical correlations between inequality, instability and lacking enforcement of property rights. We want to end with a methodological note. In this section, as in the previous one, we have relied exclusively on simple two-period examples. This avoids a major difficulty: a full-fledged treatment o f the dynamic interactions between collectively chosen policy decisions and income distribution rapidly becomes analytically complex. As a result, the dynamic models studied in the literature have often relied on simplifying assumptions: dynamic links are assumed away in the model's economic structure, voting only takes place at an initial point in time rather than sequentially over time, or agents are assumed to be myopic and ignore some o f the dynamic implications of their actions. The clearest formulation of a general solution concept for dynamic political models with heterogenous agents is made in Krusell and Rios-Rull (1996). This paper also makes a contribution by showing how the endogenous build-up of vested interests, as agents acquire monopoly skills in operating new technologies, can lead to a growth cycle: the political majority at different points in time will shift between less and more growth-promoting policies. Krusell et al. (1997) survey parts of the literature on politics and growth from a methodological angle. They also show how to go from their proposed solution concept to quantitative (numerical) applications.
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Persson, T., and L.E.O. Svensson (1984), "Time consistent fiscal policy and government cash flow", Journal of Monetary Economics 14:365 374. Persson, T., and L.E.O. Svensson (1986), "International borrowing and time-consistent fiscal policy", Scandinavian Journal of Economics 88:273-295. Persson, T., and L.E.O. Svensson (1989), "Why a stubborn conservative would run a deficit: policy with time-inconsistency preferences", Quarterly Jomnal of Economics 104:325-345. Persson, T., and G. Tabellini (1990), Macroeconomic Policy, Credibility and Politics (Harwood Academic Publishers, Chur). Persson, T., and G. Tabellini (1992), "The politics of 1992: fiscal policy and European integration", Review of Economic Studies 59:689~01. Persson, T., and G. Tabellini (1993), "Designing institutions for monetary stability", Carnegie-Rochester Conference Series on Public Policy 39:53-89. Persson, T., and G. Tabellini, eds (1994a), Monetary and Fiscal Policy. vol. 1, Credibility; vol. II, Politics (MIT Press, Cambridge, MA). Persson, T., and G. Tabellini (1994b), "Is inequality harmful for growth?", Americml Economic Review 84:600-621. Persson, T., and G. Tabellini (1994c), "Representative democracy and capital taxation", Journal of Public Economics 55:53 70. Persson, T., and G. Tabellini (1995), Double-edged incentives: institutions and policy coordination, in: G. Grossman and K. Rogoff, eds., Handbook of International Economics, vol. III (North-Holland, Amsterdam) 1973-2030. Persson, T., and G. Tabellini (1996), "Monetal7 cohabitation in Europe", American Economic Review, Papers and Proceedings 86:111--I 16. Persson, T., and G. Tabellini (1999), "Political economics and public finance", in: A. Averbach and M. Feldstein, eds., Handbook of PuNic Economics (Elsevier Science, Amsterdam) forthcoming. Pcrsson, T., G. Roland and G. Tabellini (1997), "Separation of powers and political accountability", Quarterly Journal of Economics 112:1163-1202. Petterson, R (1997), "An empirical investigation of the strategic use of debt", mimeograph (Uppsala University). Posen, A. (1993), "Why central bank independence does not cause low inflation: there is no institutional fix for politics", min~eograph (Harvard University). Posen, A. (i 995), "Declarations are not enough: financial sector services of central bank independence", in: B.S. Bernanke and J.J. Rotemberg, eds., NBER Macroeconomics Annual 1995 (MIT Press, Cambridge, MA) 253-274. Poterba, J.M. (1994), "State responses to fiscal crises: natural experiments for studying the effects of budget institutions", Journal of Political Economy 102:799-821. Przeworski, A., and E Limongi (1993), "Political regimes and economic growth", Journal of Economic Perspectives 7:51-70. Riley, J. (1980), "Strong evolutionary equilibrmrn and the war of attrition ~', Journal of Theoretical Biology 82:383-400. Roberts, K. (1977), "Voting over income tax schedules", Journal of Public Economics 8:329-340. Rogers, C. (1986), "The effects of distributive goals on the time inconsistency of optimal taxes", Journal of Monetary Economics 17:251 ~70. Rogers, C. (1987), "Expenditure taxes, income taxes~ and time-inconsistency", Journal of Public Economics 32:215-230. Rogoff, K. (t985), "The optimal degree of commitment to an intermediate monetary target", Quarterly Journal of Economics 100:1169-1 t90. Rogoft, K. (1987), "A reputational constraint on monetary policy", Carnegie-Rochester Conference Series on Public Policy 24:115-t65. Rogoff, K. (1990), "Equilibrium political budget cycles", American Economic Review 80:21 36.
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Rogoft, K., and A. Sibert (1988), "Elections and macroeconomic policy cycles", Review of Economic Studies 55:1-16. Rotemberg, J.J. (1990), "Constituencies with finite lives and the valuation of government bonds", mimeograph (MIT). Roubini, N., and J. Sachs (1989), "Political and economic determinants of budget deficits in the industrial democracies", European Economic Review 33:903-933. Saint-Paul, G., and T. Verdier (1993), "Education, democracy and growth", Journal of Development Economics 42:399-407. Schaling, E. (1995), Institutions and Monetary Policy: Credibility, Flexibility, and Central Bank Independence (Edward Elgar Publishers, Aldershot). Schotter, A. (1981), The Economic Theory of Social Institutions (Cambridge University Press, Cambridge). Staiger, R. (1995), "International rules and institutions for cooperative trade policy", in: G. Grossman and K. Rogoff, eds., Handbook of International Economics, vol. III (North-Holland, Amsterdam) 1495-1551. Stock, J.H., and M.W Watson (1999), "Business cycle fluctuations in US macroeconomic time series", ch. 1, this Handbook. Svensson, J. (1996), "Collusion and interest groups: foreigaa aid and rent dissipation", mimeograph (The World Bank). Svensson, J. (1998), "Investment, property rights and political instability: theory and evidence", European Economic Review 42:1317-1341. Svensson, L.E.O. (1997a), "Optimal inflation targets, 'conservative' central bankers and linear inflation contracts", American Economic Review 87:98-114. Svensson, L.E.O. (1997b), "Inflation forecast targeting: implementing and monitoring inflation targets", European Economic Review 41:1111-1146. Tabellini, G. (1985), "Accommodative monetary policy and central bank reputation", Giornale Dcgli Economisti 44:389-425. Tabellini, G. (1987), Money, debt and deficits in a dynamic game, Journal of Economic Dynamics and Control 10:427-442. Tabellini, G. (1990), "A positive theory of social security", Working Paper No. 3272 (NBER). Tabellini, G. (1991), "The politics of intergenerational redistribution", Journal of Political Economy 99:335-357. Tabellini, G., and A. Alesina (1990), "Voting on the budget deficit", American Economic Review 80:37-39. Taylor, J.B. (1983), "Rules, discretion and reputation in a model of monetary policy: Comments", Journal of Monetary Economics 12:123-125. Terrones, M. (1989), "Macroeconomic policy choices under alternative electoral structures", mimeograph (University of California at Berkeley). "lbrnell, A. (1995), '~Economic growth and decline with endogenous property rights", mimeograph (Harvard University). Tornell, A., and A. Velasco (1992), "The tragedy of the commons and economic growth: why does capital flow from poor to rich countries", Journal of Political Economy 100:1208-!231. Velasco, A. (1994), "Are balance of payment crises rational?", Working Paper (New York University). Velasco, A. (1999), "A model of endogenous fiscal deficit and delayed fiscal reforms", in: J. Poterba and J. von Hagen, eds., Fiscal Institutions and Fiscal Performance (University of Chicago Press~ Chicago, IL) 37-58. Vickers, J. (1986), "Signalling in a model of monetary policy with incomplete information", Oxford Economic Papers 38:443 55. yon Hagen, J. (t 992), "Budgeting procedures and fiscal performance in the European communities", Economic papers No. 96 (European Commission).
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von Hagen, J., and I. Harden (1995), "National budget processes and fiscal performance", European Economy, Reports and Studies 3. Waller, C. (1989), "Monetary policy games and central bank politics", Journal of Money, Credit and Banking 21:422-431. Waller, C., and C.E. Walsh (1996), "Central bank independence, economic behavior, and optimal term limits", American Economic Review 96:1139-1 t 53. Walsh, C.E. (1995a), "Optimal contracts for central bankers", American Economic Review 85:150-167. Walsh, C.E. (t995b), "Is New Zealand's Reserve bank act of 1989 an optimal central bank contract?", Journal of Money Credit and Banking 27:1179-1191.
Chapter 23
ISSUES
IN THE
DESIGN
OF MONETARY
POLICY
RULES *
BENNETT T. McCALLUM Carnegie Mellon University and National Bureau of Economic Research
Contents Abstract Keywords 1. Introduction 2. Concepts and distinctions 3. Special difficulties 4. Choice o f target variable 5. Choice o f instrument variable 6. Issues concerning research procedures 7. Interactions with fiscal policy 8. Concluding remarks References
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The author is indebted to Peter B. Clark, 'lodd Clark, Charles Evans, Robert Flood, Marvin Goodfriend, Charles Goodhart, An(hew Haldane, Robert Hetzel, Lars Joining, Allan Meltzer, Edward Nelson, Christopher Sims, Lars Svensson, John Taylor, John Whittaker, and especially Michael Woodford for helpful suggestions and criticisms. Handbook qf Macroeconomics, Volume 1, Edited by AB. laylor and M. WoodJbrd © 1999 Elsevier Science B.V. All rights reserved
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Abstract
This chapter begins with a number of important preliminary issues including the distinction between rules and discretion in monetary policy; the feasibility of committed rule-like behavior by an independent central bank; and optimal control vs. robusmess strategies for conducting research. It then takes up the choice among alternative target variables - with the most prominent contenders including price level, nominal income, and hybrid (inflation plus output gap) variables - together with the issue of growth-rate vs. growing-level target path specifications. One conclusion is that im'tation and nominal income growth targets, but not the hybrid target, would have induced fairly similar policy responses in the US economy over 1960-1995. With regard to instrument choice, the chapter argues that both nominal interest rate and monetary base measures are feasible; this discussion emphasizes the basic conceptual distinction between nominal indeterminacy and solution multiplicity. Accordingly, root-mean-square-error performance measures are estimated for interest rate and base instruments (with nominal income target) in the context of a VAR model. Other topics emphasized in the chapter include the operationality of policy-rule specifications; stochastic vs. historical simulation procedures; interactions between monetary and fiscal policies; and the recently-developed fiscal theory of the price level.
Keywords JEL classification: E52, E58
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1. Introduction The topic o f rules for the conduct o f monetary policy has a long and distinguished history in macroeconomic analysis, with notable contributions having been made by Thornton (1802), Bagehot (1873), Wicksell (1907), Fisher (1920, 1926), Simons (1936), M. Friedman (1948, 1960), and others 1. A major reorientation in the focus of the discussion was provided as recently as 1983, however. In particular, Barro and Gordon (1983a) built upon the insights of Kydland and Prescott (1977) in a manner that put an end to the previously widespread notion that policy rules necessarily involve fixed settings for the monetary authority's instrument variable. This step served to separate the "rules vs. discretion" dichotomy from the issue o f "activist vs. nonactivist" policy behavior and thus opened the door to possible interest in policy rules on the part o f actual monetary policymakers - i.e., central bankers. In fact there has been a great increase in apparent interest in rules by policymakers during recent years - say, 1990-1996. Evidence in support o f that claim is provided by several studies conducted at the Federal Reserve's Board o f Governors of the rule introduced by John Taylor (1993b), such as Brayton et al. (1997) and Orphanides et al. (1998), as well as by discussions of this rule in speeches by members o f the Board [e.g., Blinder (1996)]. In the United Kingdom, interest by the Bank o f England in Taylor's rule as well as an alternative due to McCallum (1988, 1993a) is clearly indicated in an article by Stuart (1996) that attracted considerable attention in the British press. Numerous analytical studies of these rules 2 have been conducted by central bank economists from a number of countries 3. To some extent this upsurge in interest is related to the arrival o f inflation targeting as a leading candidate for the provision o f a practical guideline for monetary policy, significant applications having been introduced during 1990-1993 in Canada, New Zealand, Finland, Sweden, and the United Kingdom 4. There are, to put it mildly, numerous issues concerning monetary policy rules on which professional agreement is far from complete, even among academics that is, even neglecting the split between academic and central-bank views, which itself has probably diminished in recent years. The main purpose o f this chapter is to survey the most critical of these issues. The first to be discussed, which concerns the fundamental nature of policy rules and an independent central bank's capacity to
1 For other early rule proposals, see Laidler (1996) and Humphrey (1992). Also see Jonung (1979) for an interesting discussion of the Swedish experience of the 1930s. 2 Including proposals of Meltzer (1984, 1987), Hall (1984), Hall and Mankiw (1994), Feldstein and Stock (1994), and Gavin and Stockman (1990). 3 An incomplete list of notable studies would include those mentioned above plus Hess, Small and Brayton (1993), Clark (1994), Croushore and Stark (1995), Dueker (1993), Dueker and Fischer (1995), Estrella and Mishkha (1997), Judd and Motley (1991, 1992), Haldane and Salmon (1995), King (1996), and Jefferson (1997). Many more have been added since this chapter was written, most featuring Taylor's rule. 4 There is a sizable and growing litcrature on inflation targeting that will be mentioned below.
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behave in accordance with a rule - i.e., the commitment problem - is reviewed in Section 2. Next, Section 3 takes up some special difficulties that bedevil all attempts to design good policy rules and also to study ones previously proposed, namely, the lack of agreement (especially among academics) concerning models of monetary policy effects - and the associated social costs of inflation and unemployment - plus the existence of ongoing changes in economic structure relevant to monetary policymaking (e.g., improvements in payments technology). Two major substantive areas of rule design, the specification of target and instrument variables, are then taken up in Sections 4 and 5. In the first of these, the choice among basic target variables - such as exchange rate, price level, or nominal income measures - is considered along with the desirability of specifying target paths in trendstationary or difference-stationary form (i.e., levels vs. growth rates). In the second, the classic dispute between advocates of interest-rate and monetary-base (or bank reserve) instruments is reviewed, brief discussions being given of the rather extreme views that one or the other is actually infeasible as an instrument. The following pair of sections, 6 and 7, take up a number of analytical issues involving the study of candidate rule specifications. Among these are the design of simulation exercises; issues involving operationality (i.e., feasibility of specified instruments and information sets); and the interaction of monetary and fiscal policy rules. Finally, a brief conclusion is included as Section 8. Since the author has been writing on the subject of monetary rules for well over a decade, it would be futile to pretend that the chapter's discussion will be entirely "balanced" or "unbiased". What is intended, rather, is that important alternative points of view are mentioned and presented with reasonable accuracy even where agreement is lacking. Another recent overview is provided by Clarida, Gali and Gertler (1999).
2. Concepts and distinctions The crucial point that a policy rule can be activist has already been mentioned. Of course this is a matter of definition; thus the use of a terminological system that does not permit rules to be activist i.e., to involve policy instrument settings that are conditional on the state of the economy - cannot be ruled out on strictly logical grounds. But since the publication of Barro and Gordon (1983a), standard usage in the profession has been virtually unanimous in permitting activist rules and in basing the "rules vs. discretion" distinction on the manner in which (typically activist) instrument settings are determined. Roughly speaking, discretion implies period-byperiod reoptimization on the part of the monetary authority whereas a rule calls for period-by-period implementation of a contingency formula that has been selected to be generally applicable for an indefinitely large number of decision periods. The foregoing distinction is satisfying and straightforward to apply in the context of the simple "workhorse" model that features a surprise Phillips curve as utilized by Kydland and Prescott (1977), Barro and Gordon (1983a,b), and a host of subsequent
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writers. When it comes to practical application to the behavior o f actual central banks, however, the distinction is not so easily drawn. Suppose that a particular central bank, which presumably cares about both inflation and unemployment outcomes, is observed regularly to be more stimulative when recent unemployment is high and/or current macroeconomic shocks threaten to increase unemployment. How does one decide whether this central bank's behavior should be classified as discretionary or rule-based but activist? Within a simple model one can calculate the settings implied by each type of behavior, or simply observe whether inflation exceeds its target value on average (i.e., whether the discretionary inflation bias is present). But such steps are not possible for an actual central bank, because there will typically not be any clear-cut agreement concerning the nature and magnitude o f shocks that have occurred in specific historical periods or even (in many cases) agreement as to the prevailing target inflation rate expressed in precise quantitative terms - even for analysis within the central bank itself. Taylor (1993b) explicitly addressed the problem of distinguishing "rule-like" from discretionary behavior in practice, recognizing that no actual central bank would be likely to follow literally a simple formula for its instrument settings but contending that the distinction could be of importance nevertheless 5. The key, Taylor suggested, is that rule-like behavior is systematic in the sense of"methodical, according to a plan, and not casual or at random". Clearly, being systematic is a necessary condition for rule-like behavior, but even those central bankers who defend discretionary behavior do not think of it as unsystematic. Accordingly, McCallum (1993b) argues that being systematic is not sufficient and points out that discretionary behavior in the workhorse model can, even with the inclusion o f random shock terms, be accurately represented by systematic application o f a simple formula. The needed additional criterion, McCallum suggests, is that the monetary authority "must also design the systematic response pattern [so as] to take account o f the private sector's expectational behavior" (p. 217), i.e., to optimize once, not each period. Taking such account is basically what Barro and Gordon (1983a) specified in their characterization, within the workhorse model with rational expectations, o f policy according to a rule. There is then no attempt to exploit temporarily given inflationary expectations for brief output gains 6. Qualitative knowledge of the policymaking process o f an actual central bank may then be sufficient in some cases to determine whether or not policy responses are designed to try to exploit temporarily given expectations.
5 Taylor, like Judd and Motley (1992), envisions the genuine possibility that central bard~ policy committees would enrich their considerations by referring to the instrument settings suggested by a numerical rule, e.g., taking them as a starting point for their policy deliberations. 6 It may be asked why a one-time optimization will not involve the exploitation of expectations that happen to exist at the time. But my meaning of systematic implies that the same actions are specified each time the same conditions are faced, so the response pattern cannot be different for the "first" or "first few" periods. Basically, the optimization calculation must be made fi:om the perspective of a dynamic stochastic steady state.
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It is interesting to note, parenthetically, that although Milton Friedman has never embraced the concept o f activist rules, in one o f his most carefully considered arguments on b e h a l f o f nondiscretionary monetary policy the crucial advantage o f a rule is said to be that decisions are made in the form o f a policy applicable to many distinct cases, not on a case-by-case basis, with such a form o f policymaking having favorable effects on expectations. In particular, Friedman (1962) suggests that monetary policymaking is in important ways analogous to freedom-of-speech issues, in the sense that adopting a rule that applies in general will on average lead to different and preferable - outcomes than those generated by decision making on a case-by-case basis. After presenting the analogy and remarldng on "our good fortune o f having lived in a society that did adopt the self-denying ordinance o f not considering each case o f [contested] speech separately" (1962, p. 241), Friedman contends that: Exactly the same considerations apply in tile monetary area. if each case is considered on its [individual] merits, the wrong decision is likely to be made in a large fi'action of cases because the decision-makers are ... not taking into account the cumulative consequences of the policy as a whole. On the other hand, if a general rule is adopted for a group of cases as a bundle, the existence of that rule has favorable effects on people's attitudes ... and expectations that would not follow even from the discretionary adoption of precisely the same [actions] on a series of separate occasions. ]~ Friedman (1962, p. 241) Thus we see that the logic o f Friedman's argument is basically the same as that identified by Barro and Gordon (1983a) and is entirely compatible with "activism," i.e., conditioning clauses in the rule 7. A controversial issue is whether it is feasible for an independent central bank to behave in a rule-like fashion. The most straightforward point o f view- is that expressed b y Taylor (1983, 1993b), McCallum (1995b, 1997b), Kydland and Prescott (1977), and Prescott (1977), namely, that an independent central bank is perfectly free to choose its instrument settings as it sees fit. Since it will generate superior outcomes on average i f it does so in a rule-like manner, and is presumably capable o f understanding that, the well-managed central bank will in fact behave in such a maimer. This requires it to adopt instrument settings that are different, however, from those that would appear optimal i f it were making a fresh optimization calculation each period (i.e., not considering the cases as a group). Thus many authors have suggested that, since there is no tangible "commitment technology" to guarantee that future choices will be made similarly, independent central banks are inevitably destined to behave in a discretionary fashion, making a fresh optimization calculation each period. One o f the strongest explicit statements o f this position has been made by Chari, Kehoe and Prescott (1989, p. 303), as follows: "We should emphasize that in no sense can societies choose between commitment [and] time-consistent [i.e., discretionary] equilibria. Commitment technologies are like teclmologies for making shoes in an A r r o w - D e b r e u
"1 An example of a conditioning clause in the fieedom-of-speech example would be one pertaining to cases of false alarms shouted in "crowded theaters".
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model - they are either available or not". But while this form o f language is rather extreme, the position taken is probably more representative o f academic thought over (say) 1984-1994 than is the pragmatic Taylor-McCallum position. That is, most analyses o f the consequences o f various issues simply presume, often without explicit justification, that central bank behavior will be o f the uncommitted discretionary type ~. In many cases it is contended that there is a necessary tradeoff between commitment and flexibility, which the Taylor-McCallum position denies. The justification typically given, explicitly or implicitly, for tile assumption o f (suboptimal) discretionary behavior is that although rule-like behavior is superior on average, it remains true that within each period prevailing expectations are "given" so each extra bit o f inflation or monetary ease will add output or reduce unemployment, implying that the discretionary choice would typically be superior from the perspective of that single period. Furthermore, the public understands this feature o f policy choice, according to the usual position, so individuals will expect the central bank to behave discretionarily, thereby making the discretionary action preferable (from the singleperiod perspective). But to conclude that the central bank will therefore consistently choose the discretionary outcome is analytically to adopt a particular equilibrium concept - see Chart, Kehoe and Prescott (1989). The solution concept preferred by Taylor, McCallum, Lucas (1976, 1980), and Prescott (1977) is simply rational expectations in a competitive model with a monetary authority that behaves as a Stackelberg leader vis-a-vis the private sector 9. To the present writer the latter concept seems more plausible 10, but the key point here is that neither o f the two modes of central bank behavior - rule-like or discretionary - has as yet been firmly established as empirically relevant or theoretically appropriate. Also, it would seem to be indisputable that there is nothing tangible to prevent a central bank from behaving in a rule-like
A particularly strildng example of tile importance of this assumption is provided by Svensson (1996), who argues that in the workhorse model, extended to inchide persistence of output or unemployment in the surprise Phillips relationship, price-level targeting will lead to less inflation variability (as well as less price-level variability) than will inflation targeting. This dramatic result depends, however, upon the presence of discretionary behavior on the part of the monetary authority. It does not obtain if the central bank is behaving in a rule-like fashion. Svensson (1996) recognizes this point but his discussion emphasizes the discretionary case. This exposition does not explicitly refer to thc reputational models pioneered by Barro and Gordon (1983b), the reason being that the author finds these models implausible. Of course the argunlent here advanced relies upon reputational effects, but does not utilize the type of equilibria featured in the reputation literature. i0 Empirically it is unlike the usual position consistent with tile "free lunch" finding that increased CB independence provides improved inflation performance without increased output employment variability. On this finding, see Fischer (1995) or Debelle and Fischer (1995, p. 201). It should be noted, incidentally, that my hypothesis is quite different from that of Mervyn King (1996), who suggests that CBs do not aim for output in excess of the natural rate value (as they do in the worldlorse model). The latter implies, since inflation and output desires are reflected in separate terms in King's loss function, that actual CBs would not want to keep output above the natural rate value even if they could do so without generating any inflationary tendency.
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fashion 11 so that there is no necessary (i.e., inescapable) tradeoff between "flexibility and commitment", as has often been suggested ~2. This position does not deny that central banks are constantly faced with the temptation to adopt the discretionary policy action for the current period; it just denies that succumbing to this temptation is inevitable. In practice, adoption o f rule-like decision making procedures is one mechanism for combating these temptations.
3. Special difficulties To economists who do not specialize in monetary or macroeconomic issues, it may seem surprising or perhaps a matter for professional embarrassment that a large volume o f debate can be sustained on the subject o f monetary policy rules. Surely, the argument would go, it should not be terribly difficult to conduct an optimal control exercise using some reasonably good macroeconometric model and thereby discover what an o p t i m a l monetary policy rule would be. This would have to be done for a number o f different economies, o f course, but the problems involved are in principle almost negligible and in practice are easily surmountable. Admittedly, the model would have to be one that is structural - policy invariant - so as not to be subject to the Lucas critique (1976), but that necessity has been well understood for many years by now 13 In fact, however, such an argument fails entirely to recognize one basic and fundamental difficulty that underlies a large fraction o f the issues concerning monetary policy rules. This difficulty stems from the lack o f professional agreement concerning the appropriate specification o f a model suitable for the analysis o f monetary policy issues. There are various aspects o f such a model that different researchers would emphasize. Many would suggest that money demand theory is quite undeveloped and inadequate for policy analysis. The viewpoint taken in McCallum (1997a), by contrast, contends that it is the dynamic connection between monetary policy actions and real aggregative responses that is the main source o f difficulty 14. Others, including
1t In the workhorse model, policy settings of both the committed and discretionary type may be expressed as resulting from policy feedback equation of the form or, = a o + a l E ~ 1 ~ +a2u~, with different coefficient values. Here E t l¢gt represents prevailing expectations and u~ is a current macroeconomic shock. There is nothing tangible to prevent a~ choices that represent conmaitment. t2 The absence of any inescapable tradeoffis implicit in the central bank contracting approach pioneered by Walsh (1995) and Persson and Tabellini (1993). 13 Taylor (1979) conducted an optimal policy exercise in the context of a dynamic macro model with rational expectations almost 20 years ago. 14 In this reference, the argument is stated as follows. It is not just that the economics profession does not have a well-tested quantitative model of the quarter-to-quarter dynamics, the situation is much worse than that: we do not even have any basic agreement about the qualitative nature of the mechanism. This point can be made by mentioning some of the leading theoretical categories, which include: rcal business cycle models; monetary misperception models; semi-classical price adjustment models; models with overlapping nominal contracts of the Taylor variety or the Fischer variety or the Calvo Rotemberg
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King (1993) and Fuhrer (1997) would point to weaknesses in modeling investment or consumption behavior, and o f course empirical understanding o f exchange rates and other open-economy influences is widely regarded as highly unsatisfactory. But whatever the particular model component that is singled out for special criticism, it seems extremely hard to avoid the conclusion that agreement upon macroeconomic model specification is predominantly absent - and that different models carry highly different alleged implications for monetary policy. The upshot, clearly, is that in practice one cannot simply conduct an optimal control exercise with an "appropriate" model. That approach simply collapses in response to the question "What is the appropriate model?" In light of this mundane but fundamental difficulty, the research strategy recommended by several writers including Blanchard and Fischer (1989, p. 582), McCallum (1988, 1997a), and to some extent Brunner (1980) - is to search for a policy rule that possesses "robustness" in the sense o f yielding reasonably desirable outcomes in policy simulation experiments in a wide variety o f models. In effect, the same type o f approach is collectively utilized by the various teams o f researchers participating in the Brookings projects directed by Ralph Bryant [Bryant et al. 1988, 1993)] ts. It is worth mentioning briefly that the research strategy based on robustness may serve to some extent as a protection against failures o f the Lucas-critique type. That critique is best thought o f not as a methodological imperative regarding model building strategies, but as a reminder o f the need to use policy-invariant relations in sinmlation studies and especially as a source o f striking examples in which policy invariance is implausible. The construction o f a policy-invariant model faces a major difficulty, however, in the above-mentioned absence o f professional agreement about model specification. Thus it would seem sensible to consider a variety o f models in the hope that one will be reasonably well specified - and therefore immune to the critique - and search for a rule that will perform satisfactorily in all o f them 16. O f course, there is no need for such a project to be carried out by a single researcher; furthermore, attempts to make each contending model policy invariant would enhance the effectiveness
type; models with nominal contracts set as in the recent work of Fuhrer and Moore; NAIRU models; Lucas supply function models; MPS-style markup pricing models; and so on. Not only do we have all of these basic modeling approaches, but to be made operational each of them has to be combined with some measure of capacity output - a step that itself involves competing approaches - and with several critical assumptions regarding the nature of different types of unobservable shocks and the timeseries processes generating them. Thus there are dozens or perhaps hundreds of competing specifications regarding the precise nature of the connection between monetary policy actions and their real short-term consequences. And there is little empirical basis for much narrowing of the range of contenders. 15 For the optimal-design point of view, see Fair and Howrey (1996). 16 From the perspective of the robustness approach, there is something to be said in favor of expressing "satisfactorily" in terms of nominal variables - even though individuals are concerned ultimately with real magnitudes because the relationship between monetary policy instruments and nominal variables may be less subject to Lucas-critique difficulties than is the case with real variables. An argument to this effect is attempted in McCallum (1990b, pp. 21-22).
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o f the overall project. Thus there is no necessary conflict between a robustnessoriented strategy and studies by individual researchers that involve construction o f single models [e.g., Ireland (1997), Rotemberg and Woodford (1997)]. The lack of professional agreement over model specification also makes it difficult to reach any firm conclusions about the proper goals o f monetary policy, as is discussed at the end o f this section, before the related but more pragmatic issue o f target variables is taken up. Other issues that are of greater technical interest but less fundamental importance - for example, issues concerning operationality and the simulation techniques appropriate for investigating a rule's properties - will be considered below, in Section 6. In any discussion of monetary policy, but especially in ones involving the design o f rules, it is useful to adopt a terminology regarding goals, objectives, targets, instruments, etc., that clearly reflects basic conceptual distinctions and at the same time is reasonably orthodox (or at least non-idiosyncratic). With those criteria in mind, we shall below use the word goals" to refer to the ultimate but typically nonoperational objectives of the monetary authority, and the term target to refer to an operational variable that takes precedence in the actual conduct of policy. The leading contenders for a central bank's target variable would be some comprehensive price index, nominal GDP or some other measure of nominal spending, a monetary aggregate, or a foreign exchange rate - with growth rates rather than (growing) levels perhaps pertaining in the case o f the first three. The choice among target variables will be considered in some detail in Section 4. At the opposite end o f the scale from goals are instrument variables, i.e., the variables that central banks actually manipulate more or less directly on a daily or weekly basis in their attempts to achieve specified targets. For most central banks, some short-term interest rate would be regarded as the instrument variable, but some analysts continue to promote the monetary base (or some other controllable narrow aggregate) in that capacity. It must be said that a term such as "operating target" would probably be nearer to standard for central bank economists or even policy-oriented academics, and there is a sense - to be described momentarily - in which it is more accurate than "instrument variable". But in an article such as the present one it would seem desirable to employ a terminology that promotes a clear distinction between target and instrument variables. Thus we seek to avoid ambiguous usage such as "interest rate targeting" to refer to a central bank's weekly instrument (or operating target) settings, rather than its policy-governing target variable. The sense in which "operating target" would be preferable to "instrument" is as follows. Many actual central banks choose not to manipulate their interest rate instruments in a literally direct fashion but rather to conduct open-market operations only once a day with quantities chosen so as to be expected to yield a market-influenced interest rate that lies within (or close to) some rather narrow band. The USA's Federal Reserve, for example, typically enters the Federal Funds market only once a day (normally around 10:30-10:45 a.m.) so the end-of-day or daily average value of the Federal Funds rate (FF rate) can depart from the open-market desk's "target value" by
Ch. 23.. Issues" in the Design of Monetary Policy Rules"
1493
20-30 basis points on any given day. Thus writers such as Cook and Hahn (1989) or Rudebusch (1995) will distinguish between "actual" and "target" values at the daily level. But the Fed keeps the FF rate within a few basis points o f its operating target on average over periods as short as a week. Thus there is little harm, in a study such as the present one, in using the term instrument variable and pretending that the Fed controls its interest instrument directly. There is, it should be said, a significant amount of debate over the feasibility of a central bank's using one variable or another as its instrument (even in our sense). Those issues will be taken up in Section 5. In our terminology, then, a policy rule might be thought o f as a formula that specifies instrument settings that are designed to keep a target variable close to its specified target path. If rt and xt were the instrument and target variables, then, the simplest prototype rule might be o f the form r, = rt-i +)~(x~ 1 xi-l),
X < 0,
(3.1)
which specifies that the instrument setting should be decreased if xt fell short o f its target value x T in the previous period. Somewhat more realistic examples involving more variables and other timing patterns will be considered below. Some writers have taken the position that the specification o f a policy rule is complete when a target variable has been selected and a target path (or perhaps a tolerance range) has been designated. Hall and Mankiw (1994, p. 79), for example, recommend that the central bank behave so as to keep each period's externallygenerated forecast o f future nominal income equal to a value given by a selected target path, but beyond that "we see no need to tel! it how to go about achieving the peg." Also, Svensson (1997a) distinguishes between "instrument rules" and "target rules" and expresses a preference for the latter, which specify target values but not instrument settings 17. The position taken in the present chapter, however, is that a monetary policy rule is by definition a formula that specifies instrument settings, with the choice of a target variable and path constituting only one ingredient. For some particular target choices it might be the case that the problem o f designing instrument settings would be extremely simple or uninteresting, but in general such will not be the case. McCallum's series o f rule studies (1988, 1993a, 1995a), for example, was undertaken partly in response to a claim by Axilrod (1985) - who was at the time a principal monetary policy advisor at the Fed's Board of Governors - that the achievement of nominal GNP targets was technically infeasible. From this practical perspective, the investigation o f a rule expressed in terms of a feasible instrmnent variable becomes
J7 As a related matter, Svensson has suggested that behavior conforming to a rule of the form (3.1) should not be referred to as involving a x t target; that terminology should be reserved (he suggests) to cases in which the central bank's instrument is set so as to make Etxt~/= xt*+j. But a rule such as (3.1) with 3.(x~i - E~xt~:i) on the right-hand side leads to equivalent behavior in the limit as )~---,oo,and so is a compatible but more general formulation.
1494
B.T. McCallum
an essential portion of the selection of a desirable target. For there is little point in designating a particular target if in fact it is not achievable. Svensson's (1997a) preference for what he terms target rules is not based on any lack of interest in the instrument-target relationship, but stems (apparently) from a point of view that does not recognize the difficulty emphasized above, namely, the absence of a satisfactory model of the economy. Thus Svensson presumes that any change in knowledge about the economy's workings will typically require some change in an instrument rule, whereas "with new information about structural relationships ... a target rule implies automatic revisions of the reaction function" [Svensson (1997a), pp. 1136-1137]. Indeed, if the central bank were conducting policy by conducting optimal control exercises each period with a single model, it would be true that changes in the latter would typically entail changes in the implied instrument rule. But under the presumption presented above, that it would be unwise to design a rule optimally on the basis of any single model, Svensson's conclusion does not follow. Instead, if an instrument rule has been designed so as to work reasonably well in a wide variety of models, then new information about the economy's structure is unlikely to entail any change in rule specification even when the rule designates instrument settings. Terminologically, moreover, it seems best to distinguish between the choice of policy rules and policy targets. The selection of a target variable is an extremely important aspect of systematic policy-making and may involve sophisticated analysis, as in the work of Svensson. But nevertheless a target is just that, a target. A rule, by contrast, is a formula that can be handed to a central banker for implementation without any particular knowledge of the analysts' views about model specification or objectives, in any event, in what follows it will typically be presumed that the term monetary policy rule refers to a formula or guide such as Equation (3.1) for period-by-period setting of instrument values in response to specified conditions. In evaluating candidate formulas such as Equation (3. l), it would clearly be desirable to have at hand an established specification of the appropriate ultimate goals of monetary policy. In that regard there exist important issues, such as whether a CB should keep actual or expected inflation close to some normative value, what that normative value is, and precisely how variability of output - or is it output relative to capacity (measured how?) or consumption? - should be weighed in relation to the inflation criterion. Now, in optimizing models that are specified at the level of individuais' tastes and technology, such as Ireland (1997) and Rotemberg and Woodford (1997), the answers to such questions are unambiguous and implicit in the solution to the optimal control problem. But again the fundamental difficulty mentioned above intrudes in a crucial manner, for these answers will depend nonnegligibly upon the specification of the model at hand 18. Consequently, the marked
is One rather prominent issue is whether there exists some externality that makcsthe appropriateoutput reference value greater than the natural-rate value that is relevant for price and wage behavior. Another crucial issue concerns the validity or invMidityof strict natural-rate hypothesis, i.e., the proposition that
Ch. 23:
Issues in the Design of Monetary Policy Rules
1495
absence o f professional agreement regarding model specification implies that there can be (at least at present) no consensus as to the CB goals that are appropriate from the perspective o f an economy's individuals. In practice, nevertheless, there seems to be a substantial anaount o f agreement about actual (not ideal) CB objectives; namely, that many CBs strive to keep expected inflation close to zero (allowing for measurement error) and to keep output close to a capacity or natural-rate value that is itself a variable that grows with the capital stock, the labor force, and technical progress 19. Although it cannot be established that these objectives are optimal, it would seem to this writer that they probably provide a fairly good specification o f appropriate CB macroeconomic goals.
4. Choice of target variable After a long dose o f preliminaries, let us now finally turn to substantive issues in the design o f a monetary rule. In this section we shall be concerned with the choice o f a target variable - both its idemity and the question o f whether its path should be specified in growth-rate or level form. For the reasons just outlined, our discussion will be pragmatic rather than theoretical in nature. In recent years, the most fashionable target variable for the monetary authority has been a nation's inflation rate - in other words, a comprehensive price-level variable with its target path set in growth-rate terms. A great deal has been written about inflation targeting in policy-oriented publications, and substantial scholarly efforts have been contributed by A l m e i d a and Goodhart (1996), Bernanke and Mishkin (1997), Goodhart and Vinals (1994), McCallum (1997a), and others, as well as the individual authors represented in books edited by Leiderman and Svensson (1995) and Haldane (1995). Other leading target-variable choices are aggregate spending magnitudes such as nominal GNP or G D P - often in growth rate form - and a "hybrid" variable that sums inflation and real output measured relative to some sort o f trend or reference value 2°. A l l o f these choices presume, however, that the economy in question does not have its monetary policy dedicated to an exchange rate target, so a brief prior discussion o f exchange rate policy should be appropriate.
output cammt be kept above its natural-rate value permanently by any monetary policy strategy, even one that features a permanently increasing (or decreasing) rate of inflation [Lucas (i972)]. J9 This variable capacity value may, however, exceed the natural-rate value, as mentioned in footnotes 10 and 18, and as is typically assumed in the CB credibility literature. 2o The magnitude of inflation rates depends upon the length of a single time period whereas the percentage (or fractional) deviation of output from its reference path does not. The usual convention with this hybrid variable is to add percentage inflation rates measured lbr annual periods to percentage output deviations. It would be equivalent to use inflation over a quarter plus one-fom'th of the relative output deviation. Use of fractional units for both variables would also be equivalent, with appropriate adjustments in the response coefficient. This last convention will be utilized below.
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B. T. McCallum
Perhaps the most basic of all monetary policy choices is whether or not to adopt a fixed exchange rate. The principal considerations involved in this choice are those recognized in the optimal currency area literature began by Mundell (1961) and extended by M c K i n n o n (1963) and Kenen (1969). Basically, these all boil down to the question of whether the lnicroeconomic (i.e., resource allocation) advantages of an extended area with a single medium of exchange outweigh the macroeconomic (i.e., stabilization policy) disadvantages of being unable to tailor monetary policy to local conditions 2j. Some analysts [e.g., Bruno (1993), Fischer (1986)] have contended that there are some macroeconomic advantages of a fixed exchange rate22 but the arguments seem actually to be based on political or public-relations considerations, not economic costs and benefits 23. Thus in the case o f small economies for which large fractions of their market exchanges are international in character, and which tend frequently to experience the same macroeconomic shocks as their neighbors and trading partners, it is clearly advantageous to forgo the flexibility of an independent monetary policy by keeping a fixed exchange rate (and common currency) with a specified currency or basket of currencies 24. And at the other extreme, the macroeconomic advantages o f a floating exchange rate would seem to be clearly dominant for pairs of nations such as the USA, Japan, and the prospective European monetary union. The main point of the previous paragraph is that the advantages that might lead a nation to choose to have a fixed exchange rate, and thus to dedicate its monetary policy actions to that criterion, are basically either microeconomic or political in nature. Thus the type of considerations involved are quite different than those that are involved in the selection among macroeconomic target variables such as inflation, nominal spending growth, or the above-mentioned hybrid variable. Because of the scope of the present chapter, we shall henceforth focus our attention on the latter type of choice 25.
21 If a set of countries is to have permanently fixed exchange rates, it would seem that from a purely economic perspective there are extra benefits (reduced transaction costs) with no extra costs of having a common currency. (No ongoing costs, that is; there may obviouslybe significantchangeover costs, as in the EMU example.) As for rates that are fixed, but not permanently,the European experiences of 1992 and 1993 support Friedman's (1953) classic argmnent that such an arrangement is undesirable because of the self;destructive speculativeimpulses that are encomaged. 22 From the monetary-policyperspective, a moving peg or narrow bm~dfalls into the same category as a fixed exchmlge rate, since it entails the dedication of monetary policy to its maintenance. 23 This statement is applicable to much of the literature relating to the planned European monetary union, of course. 24 A relatively clear-cut example is provided by Luxembourg, which has had a monetary union with Belgium since 1921 (except for an intenuption during World War II), Belgian francs serving as a legal tender in both nations, Luxembourgalso issues franc notes and coins, but has kept these interchangeable -with their Belgian counterparts. 25 It should be recognized, however, that it would be possible to consider a target that consists of a weighted average of (say) exchange rate changes and inflation. This example couid alternatively be thought of as an inflation target with an unusual specificationof the price index to be utilized.
Ch. 23: Issues in the Design of Monetary Policy Rules
1497
In the literature on this subject, which is large, the most popular approach is to determine how well the various targets would perform in terms of yielding desirable values of postulated social and/or policy-maker objective fimctions, with these pertaining primarily to root-mean-square (RMS) deviations from desired values of variables such as inflation or real GDP relative to capacity 26. Such studies may be conducted with theoretical or estimated models, but in either case need to take account of the various types of macroeconomic shocks that may be relevant - need to take account, that is, of the variance, covariance, and autocovariance magnitudes of the shock processes. Some of the leading examples of theoretical studies are those of Bean (1983), West (1986), Aizenman and Frenkel (1986), Henderson and McKibbin (1993), Frankel and Chinn (1995), Ratti (1997), and Ireland (1998), while welllcnown simulation studies with estimated models have been conducted by Taylor (1979, 1993a), Feldstein and Stock (1994), Haldane and Salmon (1995), and the individual authors in Bryant et al. (1988, 1993). In some of these studies it is pretended, for the sake of the issue at hand, that the selected target variables are kept precisely on their target path; the Bean, West, Aizemnan-Frenkel, Frankel-Chinn, Ratti, and (in part) Henderson-McKibbin studies are of that type. Others, however, focus on RMS deviations in simulations with policy rules expressed in terms of instrument variables. Proponents of the first approach would argue, presumably, that they prefer to keep the issue of whether a variable can be controlled separate from the evaluation of its effects if well-controlled. Those who disagree would point out that there is little need to know such properties tbr variables that in fact can be controlled only very poorly. Indeed, they might argue that unless controllability is taken into account, the issue is simply that of specifying an appropriate social objective function; i.e., that "targeting" is not the matter under investigation. In this regard it is worth keeping in mind the point emphasized above, namely, that there is in fact no professional agreement on the appropriate specification of a dynamic macroeconomic model. This implies not only an absence of agreelnent on the "true" social objective function, but also the absence of agreement on a matter as basic as the listing of relevant macroeconomic shocks. Keynesians and real-businesscycle analysts, for example, would disagree sharply as to the very nature of the relevant shock processes. For the candidate target variables mentioned above, other than the hybrid variable, an important question is whether it is preferable to specify a growth-rate target or one of the growing-levels type, i.e., whetber the target should be specified in a differencestationary or trend-stationary manner. This issue is often discussed under the heading of "inflation vs. price-level targeting," but similar considerations would apply if the target variable were nominal GDP, some other measure of nominal spending, or even
~' These are the two valiables that are most closely related to the utility t~mctions of individuals m explicit optimizing models such as those of Ireland (1997) or Rotemberg and Woodtbrd (1997).
1498
B.T. McCallum
a money-stock variable 27. Specifically, the weakness o f the growth-rate choice is that it will - by treating past target misses as bygones - introduce a random walk (or more general unit root) component into the time-series processes for all nominal variables, including the price level. Thus there will exist a possibility that the price level would drift arbitrarily far away from any given value (or predetermined path) as time passes, implying considerable uncertainty as to values that will obtain in the distant future. By contrast, the main disadvantage with a levels-type target path is that the target variable will be forced back toward the preset path after any disturbance that has driven it away, even if the effect o f the disturbance is itself o f a permanent nature. Since any such action entails general macroeconomic stimulus or restraint, this type o f targeting procedure would tend to induce extra cyclical variability in demand conditions, which may imply extra variability in real output i f price-level stickiness prevails. Furthermore, variability in output and other real aggregative variables is probably more costly in terms o f human welfare than is an equal amount o f variability in the price level about a constant or slowly-growing path. Also, although it is not entirely clear that fully permanent shocks are predominant, most time-series analysis seems to suggest that the effects o f shocks are typically quite long lasting - indeed, are virtually indistinguishable from permanent. Consequently, it would seem desirable not to drive nominal variables back to preset paths - or at least not to do so quickly and frequently. Thus, it seems preferable to adopt a nominal target o f the growth-rate type, rather than the growing-levels type 28. One reason for the foregoing conclusion is that very few transactions are based on planning horizons as distant as 50 years. A more representative long-lasting arrangement might be more like 20 years in duration. But price-level uncertainty 20 years into the future might not be very large even i f the (log o f the) price level included a unit root component. Suppose that the log price level were to behave as a pure random walk relative to a preset target path (say, a zero-inflation path). Then i f it is assumed that the random, unpredictable component at the quarterly frequency has a standard deviation o f 0.0045 (which is approximately the standard deviation o f one-step ahead forecast errors for the U S A over 1954-1991) 29, it follows that a 95% confidence interval for the (log) price level 20 years ahead would be only about 8% (plus or minus) 3°. This, it seems to the writer, represents a rather small amount o f price level
27 Here and below the language will often be stated in terms of nominal variables such as nominal GDP or a price index when it is the natural logarithm of that variable that is actually meant. 28 For alternative argmnents that reach this conclusion, which is taken for granted by Feldstein and Stock (1994), see Fischer (1995) and Fillion and Tetlow (1994). The opposing position is taken by Hall and Mankiw (1994) and Svensson (1996) [but see footnote 8 above]. 29 Thus it is being tentatively assumed that the control error, if inflation targeting were adopted, would have a mean of zero and a variance equal to that of the currently-prevailing one-step-ahead forecast error, which might be taken as an approximation of the minimum feasible control error variance. 3o I am taking the control error to be serially lmcorrelated. Then the 80-period ahead error would have variance (80) (0.00452) -0.00162 whose square root is 0.040. Thus two standard deviations equals 0.08
Ch. 23." Issues in the Design of Monetary Policy Rules
1499
uncertainty - at least in comparison with the magnitudes that prevailed over the 1960s, 1970s, and 1980s, because of non-zero and uncertain trend rates. The foregoing argument seems moderately persuasive to the present writer, but it is clearly not compelling and the conclusion is certainly not accepted by all analysts. Furthermore, even if it were accepted, it might be possible to obtain the benefits of trend stationarity by adopting a target that is a weighted average of ones o f the growth-rate and growing-level types 31. Accordingly, in the simulations reported below, consideration will be given to growth-rate, growing level, and weighted average types. Now let us consider some points regarding the comparative merits of three leading target-variable possibilities. Because they seem at present to command the most support, we will discuss (i) the inflation rate, (ii) the growth rate o f nominal GDP, and (iii) the above-mentioned hybrid variable. As some notation will be useful, henceforth let xt, Yt, and Pt denote logs of nominal GDP, real GDP, and the price level (as represented by the deflator so that xt = Yt +Pt), with time periods referring to quarteryears. Then the three contending target variables in their simplest form are Apt, Act, and ht - A p t + 0.253~t, where yt - y t -j~t with )Tt denoting the reference value of real GDR In choosing among these three contenders, a straightforward approach would be to select the target variable that corresponds most closely to the central bank's views about social objectives that are influenced by monetary policy. From that perspective, it would appear that the hybrid variable ht might be the most appropriate of the three, a point o f view taken implicitly by Blinder (1996), with Axt arguably ranking second 32 But among actual central banks that have adopted formal numerical targets, virtually all have (as o f early 1997) opted for inflation targets. So apparently the straightforward approach is not the only one that needs to be considered. There are undoubtedly several reasons for this tendency for actual central banks to choose Apt over the others as their formal target, but three o f these seem justifiable and in any event deserve to be mentioned. First, it is believed by a large number of policymakers and a large number o f scholars that monetary policy has, from a
so a 95% confidence interval will have width roughly ±0.08 or ±8 percent. If the control error is serially correlated, then the relative effect of the unit root term will depend on the autocorrelation pattern but is likely to be more serious. 31 If used in a rule of form (3.1), this sort of weighted-average target would be equivalent to a pure growing-levels target with both "proportional" and "derivative" feedback. 32 The case for nominal income targeting is that it should, from a long-term perspective, provide almost as good inflation control as direct inflation targeting, since average real outpnt growth will be virtually independent of monetary policy and reasonably ~brecastable, while probably providing somewhat better automatic stabilization of real variables. About the latter advantage one cannot be certain, because of the absence of professional understanding mentioned in footnote 14. The basic logic of nominal income targeting applies, moreover, to other aggregative measures of nominal spending, not just to nominal GDP or GNP per se. The sharp criticism of nominal income targeting recently expressed by Ball (1997) is, it is argued below, fundamentally misguided.
1500
B.T. McCallum
long-rml perspective, no substantial effect on fit = Y t - ) S t 33. In other words, while monetary policy may have significant effects on output relative to capacity, these are only temporary. Therefore, so the argument goes, central banks should concentrate their attention on the Apt variable that their policy actions affect strongly on a longrun basis 34. Second, measurement of)Tt and therefore )~t is difficult and controversial, even in comparison to measurement o f Aps. We have described Yt as a capacity, trend, or reference value, but that does not define the appropriate variable even in conceptual terms, much less in operationally measurable terms 35. in particular, errors in measuring )Tt are likely to be much larger than errors in measuring the long-term average value o f Ayt, which is all that is necessary for correct design o f a Axt target. Thus the ht target is more demanding o f knowledge concerning the economy than is either o f the other contenders under discussion. The third reason is related to the other two, especially the first. It is that communication with the public is thought by practitioners to be much easier when only the inflation variable is involved. Typical citizens have an understanding o f the concept o f inflation, so the argument goes, but not o f the national income accounting concepts xt andyt, much less the reference value)Tt. In addition, it must be mentioned that in practice actual inflation targets are typically based on yearly average inflation rates, and with those values forecasted to prevail 1-2 years into the future 36. Since inflation forecasts are in practice based in part on recent levels or growth o f real output, the three target variables under consideration may be fairly closely related to each other. Furthermore, inflation targets are usually accompanied by provisions stating that the occurrence o f "supply shocks" - such as crop failures, terms-of-trade changes, or indirect tax-rate changes - will entail temporary modification o f the current inflation target measures. Thus, for example, the New Zealand legislation includes several such escape clauses - termed "caveats" that are built into the Reserve Bank's targeting procedures 37. Because o f considerations such as these, it would probably be unrealistic (and unreasonable) to expect that a truly compelling argument could be made for any one 33 This proposition, often termed the "natural rate hypotlaesis", is subscribed to by a large fraction of macroeconomic researchers. 34 This position is explicitly expressed by McCallum (1997a) and by Reserve Bank of New Zealand (1993). 35 In recent years there has been a tendency, most marked in media discussions but also present in professional literature, to speak as if "natural rate" and "NAIRU" conccpts and theories were equivalent. To the present writer that is far from being the case. The strict version of the natural rate hypothesis, due to Lucas (1972), is the proposition that there is no monetary policy that will keep output permanently high in relation to its natural rate (i.e., market clearing) value. By contrast, the NAIRU (non-acceleratinginflation rate of unemployment) approach posits a stable relationship between tmemployment (or output relative to its reference value) and the "acceleration" magnitude, i.e., the change in the inflation rate. But the latter implies that permanent acceptance of a positive acceleration magnitude (i.e., increasing inflation) will result in a permanent increase in output relative to its reference value, in stark contradiction to the natural rate hypothesis. 36 Of course the same sort of averaging could be applied to the Axt and h~ variables. 37 On this subject, see Reserve Bank of New Zealand (1993).
Ch. 23: Issues in the Design of Monetary Policy Rules'
1501
0.06 l
o.o4.1
t
0.02 -
0.00 -0.02.
-004
~ 60
_ 65
[--
~ 70
_ 75
80
~ 85
DLXGAP ....... DLPGAP . . . . .
90
95
ZERO I
Fig. 1. Gap measures for inflation and nominal GDP targets, 196~1995. of the candidate target measures. Consequently, it should be of interest to compare actual past values of the three leading measures with those values that would have been called for if corresponding targets had been in place. For the purpose of this exercise, it will be assumed that the desired value of Apt is 0.005, which amounts to approximately two percent inflation on an annual basis. Also, for simplicity it will be assumed that 37t values are given by deterministic trends obtained by regression ofyt on time for the sample period under consideration. This last assumption is unsatisfactory, of course - as will be discussed again - but should suffice for the limited purpose at hand of making comparisons. Let us first consider the time period 1960.1-1995.4, with United States GDP data used for xt and with Yt based on GDP in 1992 fixed-weight prices (i.e., using the fixedweight rather than the chain-weight deflator). Over this period, the 37t trend variable is given by the expression fit = 7.520749 + 0.006881t (with t = 1 in 1947.1). Therefore, Aft = 0.006881 is assumed and the target value for Axt is 0.011881, with 0.005 being the target value for both Apt and h , For each of the three variables we calculate the gap between actually observed values and these retrospective, hypothetical target values. These gaps are denoted Ap(gap)t - Apt - 0.005, Ax(gap)t = A& - 0.011881, and h(gap)t = Apt + 0.25yt- 0.005. Their values for the first two variables (over 1960.1-1995.4) are plotted in Figure 1 and those for the second and third are plotted in Figure 2. In Figure 1 we see that the Ap~ and Axt targets both suggest that monetary policy was excessively expansive most of the time between 1965 and 1989. The Ax(gap) measure is considerably more variable from quarter to quarter than the Ap(gap) measure, basically because Ayt is more variable than Apt. Averaging over the whole period, the two measures give the same signals simply because the A& target value was calculated
1502
B.T. McCallum 0.06
0.04
0.02
0,00
-0.02.
-0.0460
65 [
70
75
80
85
DLXGAP ....... HGAP . . . . .
90
95
ZERO]
Fig. 2. Gap measures for hybrid and nominal GDP targets, 1960-1995.
so as to yield the desired inflation rate given the realized average growth rate of output over the sample period, Of course, actual policymakers could not know this rate in advance, when choosing their target value for Axt. Thus desired inflation would tend to differ from the average realized value to the extent that average output growth is forecast incorrectly. The magnitude of this error would not be large, however, when averaged over long spans of time. By and large, a striking feature of Figure 1 is that the two target variables do not give greatly different signals when averaged over periods as short as 2-3 years. Nevertheless, there are a few quarters when the Axt variable suggests that policy should be loosened whereas the Apt variable suggests the opposite, and this situation prevails for over a year during 1990-1991. Those analysts who favor Axt targeting believe, of course, that keeping Axt values steady would result in smaller fluctuations in Yt than would a policy of keeping Ap~ values steady. Whether such is the case in fact will depend upon the precise nature of the economy's short-term, dynamic Phillips relation, a point emphasized in McCallum (1988, 1997a) 3s. Figure 2 compares gap values for ht and Axt targets. In this case there is much more divergence in signals, with the hybrid measure calling for more monetary expansion over lengthy periods during the early 1960s and 1990s, and tighter monetary policy during much of the 1970s, in. comparison with the zk~ct measure. (Of course both measures signal that policy was too inflationary from 1965-1989, as before.) These features of the plots in Figure 2 are basically a consequence of the fact that a linear trend line for yt implies negative residuals in the early 1960s and 1990s and many
3~ See fbotnote 14 above.
Ch. 23:
1503
Issues in the Design of Monetaly Policy Rules
0.06. 0.04. 0.02-
-0.02-
8'5' '86 '87 '88 I
DLXGAP85
89
90
91
92
93
..... HGAP85 . . . . .
94
95
ZERO]
Fig. 3. Gap measures for hybrid and nominal GDP targets, 1985 1995. positive residuals during the 1970s, which it does because o f the sustained period o f rapid growth in real G D P from 1960 to 1973. To emphasize this last point, Figure 3 gives results for the same type o f exercise but with the sample period limited to 1985.1-1995.4. Here it will be noted that the h(gap)t values are quite different from those for 1985-1995 in Figure 2, solely because the y~ trend line is estimated differently and yields a significantly different residual pattern 39. Now there are no major discrepancies that persist as long as in Figure 2, although the two measures give quite different policy signals over most o f 1990 and 1992, the Axt target calling for a relatively more expansionary monetary stance in the former year and a more restrictive stance in the latter year. The sizable difference between the h(gap)t figures shown in Figures 2 and 3 illustrates the main weakness o f the hybrid target variable, namely, its sensitivity to alternative calculations o f y t reference values. Proponents o f the hybrid variable might argue that more sophisticated measures o f f t should be used, and it is certainly true that our linear trends are not conceptually attractive. But neither are, say, HodrickPrescott (HP) filtered series, for reasons emphasized by Cogley and Nason (1995) plus a recognition o f what the HP filter would imply about US GNP for the period 1929-1939 4°. Other measures exist, but have attracted little professional support. In
39 It also has a reduced slope, which changes the definition of Ax(gap) to Axt 0.010336. 40 If the HP filter were applied to US real GNP over a period including 1929-1939, the HP "trend" series would turn down fairly sharply during the early 1930s. If this series were used as one's measme of trend or capacity output, it would then be concluded that the Great Depression was not very serious i.e., that output was low over 1932 1938 largely because capacity was low. But measured unemployment figures suggest strongly that this conclusion would be misleading.
B.T. McCallum
1504
0.06 . 0'04 t 0.024 0.00-
--7~, ~
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
-0,02-
'6's ....
7'0 ....
7'6 ....
6'0 ....
6'2 ....
9'0 ....
9's
DLXFGAP ....... DLPFGAP ..... ZERO] Fig. 4. Gap measures for inflation and nominal GDP values forecast 4 quarters ahead, 1960-1995. sum, there is no widely accepted and conceptually sound measure for f~, but use o f the hybrid target variable requires such a measure and its value is rather sensitive to the particular measure adopted. One weakness o f the indicators presented in Figures 1-3 is that they pertain to currently-measured values of the target gaps whereas in practice actual central banks focus upon gaps expected to prevail several months in the future. Also, Svensson (1997a) has argued rather convincingly that "inflation forecast targeting" has several attractive features. Consequently, indicators o f expected future gaps were obtained by regressing gap values on information variables observed 4 to 7 quarters in the past. The variables used in these regressions are Axt, Apt, Ab, and Rt (four lagged values o f each), where bt is the log of the monetary base and Rt is the 3-month Treasury bill interest rate. Also one lagged value o f fit was included; a second lagged value would create perfect collinearity among the regressors. Values o f these forecasted future gaps are presented in Figures 4 and 5, where the measures should be interpreted as giving policy signals one quarter in advance of the dates shown. Clearly, the values are smoothed greatly for zXxt and Apt, relative to the previous graphs, but the overall messages remain the same: that there is apparently little basis for choice between Axt and Apt while the ha indicator appears to give signals that are quite different. Recently, Ball (1997) has put forth, in rather strong language, some striking propositions regarding target variables 41. Among these are claims to the effect that efficient monetary policy 42 consists o f a special case o f a Taylor rule that is equivalent
41 Some of these have been noted favorably by Svensson (1997a,b). 42 The paper's concept of"efficient monetary policy" is one that focuses on the variances of inllation and output (relative to capacity) while assmning tmrealistically that the central bank has full contemporaneous
Ch. 23:
1505
Issues in the Design of Monetary Policy Rules
0.06 . 0.04 t 002
,,,
',
,:
",
" ~ , ' "~" i
0.00-"
;';
", , ,"~' ',', "\l L';, -^""
b'
,J -'V
-0.02
i , ,615 ....
7~0 ....
I --DLXFGAP
7~5 ....
810 ....
8~5 ~
90
95
....... HFGAP ..... ZERO]
Fig. 5. Gap measures for hybrid and nominal GDP values forecast 4 quarters ahead, 1961~1995. to a partial-adjustment variant of inflation targeting (even when output variance is important); that efficient monetary policy requires much stronger responses to output fluctuations than is implied by historical practice or Taylor's (1993b) suggested weights; and that nominal income targeting would be "disastrous" as it would give rise to non-trend-stationary behavior o f output and inflation processes. These results are shown to hold, however, only in a single theoretical model, with no attempt being made to determine their robustness. In fact, the last one depends sensitively upon details of the utilized model that are not justified either theoretically or empirically. The model's Phillips curve, in particular, has a superficial similarity in appearance to the Calvo Rotemberg specification as exposited by Roberts (1995), but differs by being backward rather than forward-looking. If a forward-looking version were utilized, the implied coefficient relating inflation to current output would have the opposite sign and Ball's instability result would be overturned, as it would be with several other prominent Phillips curve specifications,
5. Choice of i n s t r u m e n t variable In this section we consider the choice o f a variable to serve as the instrument through which a central bank's policy rule will be implemented. It is well known that, although a substantial number o f academic economists have favored use o f a monetary base or
knowledge of all variables (oil this, see Section 6 below)• Thus it simply assumes away thc first-order problem of designing an operational rule that will generate the desired mean value tbr :r~ while avoiding explosions.
1506
B. Z McCaHum
reserve aggregate instrument, almost all actual central banks utilize some short-term interest rate in that capacity. Before turning to a review o f their relative desirability, however, it will be appropriate to consider the sheer feasibility o f interest rate and monetary base instruments, since there are a few scholars who have contended that one or the other would be infeasible in some sense. In this category the most well-known argument is that of Sargent and Wallace (1975). That paper put forth the claim that, in a model in which all private agents are free of money illusion and form their expectations rationally, the economy's price level would be indeterminate if the central bank were to use an interest rate as its instrument. Specifically, the Sargent-Wallace (1975) paper included a result suggesting that if the interest rate Rt were set each period by means of a policy feedback rule that specifies Rt as a linear function o f data from previous periods, then all nominal variables would be formally indeterminate. Sargent (1979, p. 362) summarized this conclusion as follows: "There is no interest rate rule that is associated with a determinate price level. ''43 Subsequently, however, McCallum (1981, 1986, p. 148) showed that the SargentWallace claim was actually incorrect in such a model; instead, all nominal variables are fully determinate provided that the policy rule utilized for the interest rate instrument involves some nominal variable, as suggested previously by Parkin (1978) and in the classic static discussion of Patinkin (1961). The problem with the alleged proof o f Sargent and Wallace is that it showed that the model at hand imposed no terminal condition on the price level, but did not consider the possibility of an initial condition. In the present context it is important to distinguish between two quite different types of price-level behavior that have been referred to in the literature as involving "indeterminacy". Both involve aberrational price level behavior, but they are nevertheless very different both analytically and economically. Consequently, McCallum (1986, p. 137) proposed that they be referred to by terms that would recognize the distinction and thereby add precision to the discussion. The proposed terms are "nominal indeterminacy" and "solution multiplicity (or nonuniqueness)" 44, The former refers to a situation in which the model at hand fails for all nominal variables (i.e., variables measured in monetary units) to pin down their values. Thus money stock values and values o f (say) nominal income, as well as the price level, would not be defined by the model's conditions. Paths o f all real variables are nevertheless typically well defined. In terms of real-world behavior, such a situation could conceivably obtain
43 Sargent and Wallace (1982) advanced arguments quite different from those of their 1975 paper, and attributed this difference to their use in (1982) of a model with agents who solve explicit dynamic optimization problems, in contrast to the linear IS-LM model with a Lucas supply function in (1975). in fact, however, the main relevant difference is that the 1982 analysis is based on a model in which monetary and nonmonetary assets cannot be distinguished and hldeterminacy does not actually prevail in any case. On this, see McCallum (1986, pp. 144-154). An important recent contribution is Benassy (1999). 44 Actually,McCallam (1986) proposed "indeterminacy~ for the tormer, but the addition of the adjective is clearly desirable.
Ch. 23:
Issues in the Design of Monetary Policy Rules
1507
if the monetary authority failed entirely to provide a nominal anchor 45. This type of phenomenon has been discussed by Gurley and Shaw (1960), Patinkin (1949, 1961), Sargent (1979, pp. 360-363), Sargent and Wallace (1975), McCallum (1981, 1986), and Canzoneri, Henderson and Rogoff (1983), among others. Solution multiplicity, by contrast, refers to aberrational behavior usually described as involving "bubbles" or "sunspots" that affect the price level. In these situations it is typically the case that the path of the money stock - or some other nominal instrument controlled by the monetary authority - is perfectly well specified. Nevertheless, more than one path for the price level - often an infinity of such paths - will satisfy all the conditions of the model. In terms of real world behavior, arbitrary yet selfjustifying expectations is the source of this type of aberration. It has been discussed by a vast number of writers including Taylor (1977), Sargent and Wallace (1973), McCallum (1983), Brock (1975), Black (1974), Obstfcld and Rogoff (1983), and Flood and Hodrick (1990). Nominal indeterminacy is a static concept that concerns the distinction between real and nominal variables whereas solution multiplicity is an inherently dynamic concept involving expectations. An important application of this distinction is to the "indeterminacy" results of Brock (1975, pp. 144-147) and Woodford (1990, pp. 1119-1122). These results pertain to cases in which (base) money is manipulated by the central bank and involve non-uniqueness of rational expectations equilibria when the imposed money growth rates are low, close to the Chicago Rule rate that satiates agents with the transaction-facilitating services of money. But since these equilibria involve wellspecified paths of nominal money holdings, the non-uniqueness is clearly not of the nominal indeterminacy type. Instead, it is of the solution multiplicity type, involving price level bubbles or sunspots. Such theoretical multiplicities may or may not be of practical significance 46, but in any event are not examples of "price level indeterminacy" in the sense of Gurley and Shaw (1960), Patinkin (1949, 1961), S argent (1979, pp. 360-363), or Sargent and Wallace (1975). To some readers, this fact may diminish the force o f Woodford's (1990, 1994) argument in favor of an interest rate instrument. Let us now return to the issue of instrument feasibility, switching to the extreme opposite side of the debate. In a recent article, Goodhart (1994) has argued not just that monetary base control by a modern central bank is undesirable, but that it is essentially infeasible. In particular, Goodhart states that "virtually every [academic?] monetary economist believes that the CB can control the monetary base . . . " so that if the CB does not do so, then "it must be because it has chosen some alternative
45 And the system lacked sufficient inertia or money illusion to make the nominal paths determinate requirements that are actually almost inconceivable. 46 It is unclear whether there is any compelling evidence in support of tile notion that macroeconomic bubbles or stalspots are empirically relevant [Flood and Hochick (1990)]. In any event, it is a plausible hypothesis that, in cases with an infinity of solutions, there is a single bubble-free or fundamentals solution that obtains in practice.
1508
B.T. McCallum
operational guide for its open market operations" (p. 1424). But, he asserts, "almost all those who have worked in a CB believe that this view is totally mistaken; in particular it ignores the implications o f several o f the crucial institutional features o f a m o d e r n commercial b a n k i n g system, notably the n e e d for unchallengeable convertibility, at par, b e t w e e n currency and deposits, and secondly that commercial b a n k reserves at the CB receive a zero, or below-market, rate o f interest" [Goodhart (1994), p. 1424]. T h e n as the discussion proceeds it b e c o m e s clear that Goodhart is h i m s e l f taking a position that is predominantly, if n o t entirely, supportive o f the opinions o f those who have worked in a CB. Thus he asserts, o n his own account, that "if the CB tried to r u n a system o f m o n e t a r y base control, it would fail" (p. 1425). A n d he goes on to outline the putative flaws in logic or factual knowledge that invalidate the cited views o f academic economists (pp. 1424-1426). In fact, however, although Goodhart's discussion is apparently i n t e n d e d to be c o n c e r n e d with feasibility, the actual a r g u m e n t a t i o n presented pertains to desirability. Specifically, the m a i n analytical points are those made in the first three complete paragraphs o f p. 1425, which argue that tight base control would lead in practice to overnight interest rates that at the end o f most days would equal either the CB's penal rate or a value "near zero ''47. H a v i n g developed that point, Goodhart concludes as follows: "Some economists might prefer such a staccato pattern o f interest rates, b u t it would not seem sensible to practitioners" (p. 1425). But clearly this is an a r g u m e n t that pertains to the desirability, not the feasibility, o f tight base control 48 H a v i n g concluded, then, that neither interest rate nor m o n e t a r y base i n s t r u m e n t s are infeasible 49, we turn to the task o f considering their relative desirability 5°. In that
47 If required-reserve averaging is practiced, then the statements referred to pertain only to days near the end of reserve maintenance periods. 48 More extensive but still inconclusive arguments are presented by Whittaker and Theunissen (1987) and Okina (1993). The latter presumes lagged reserve requirements, an arrangement that is inappropriate with a base instrument [McCallum (1985)]. 49 A different objection to use of a base instrument is that central batiks do not literally control the stun of currency and reserves, since currency is demand determined and only the non-borrowed component of total reserves is directly controlled, since banks can use the discount window to add to or subtaact from reserve holdings. But there are three flaws with this position. First, since the base can be read from the CB's own balance sheet, it can observe it frequently and make whatever adjustments are needed to keep the magnitude closer to its target. Second, the CB could, if it chose, close the discount window. Third, it would be possible to consider the non-borrowed base as the instrument under discussion. s0 Brief mention should be made of a study by Howitt (1992), who finds that an interest rate peg would lead to dynamic instability in a model that includes a sticky-price Phillips curve and a generalized adaptive form of dynamic "learning behavior" rather than rational expectations. Whether or not one finds the latter feature appealing, Howitt's results do not pertain to the issue at hand since the type of "pegging" that he is concerned with involves keeping Rt at some preset value indefinitely, not varying Rt period by period in an instrument capacity. Several writers have shown that, under rational expectations, nominal indeterminacy does not prevail with an interest rate peg. Canzoneri, Henderson and Rogoff (1983) and McCallum (1986) have established this in models of the IS-LM-AS type under the assumption that the peg is a limiting version of a money supply rule designed to reduce interest rate fluctuations.
Ch. 23." Issues in the Design of Monetary Policy Rules
1509
regard, m o s t proponents o f a base instrument do not deny that such a r e g i m e w o u l d involve substantially m o r e variability o f short-term interest rates than is e x p e r i e n c e d under today's typical procedures, w h i c h involve interest-rate instruments and shortterm interest rate smoothing 51. B a s e proponents w o u l d contend, however, that with a base instrument it m a y be possible to design simple p o l i c y rules that are m o r e effective f r o m a m a c r o e c o n o m i c perspective than are c o m p a r a b l e rules with interestrate instruments 52, 53. In order to illustrate the plausibility o f that contention, let us consider s o m e counterfactual historical simulations o f the general type u s e d by M c C a l l u m (1988, 1993a, 1995a) with quarterly U S data. In order to keep the m o d e l specification from biasing the results, the m a c r o e c o n o m e t r i c m o d e l in these simulations will be an unconstrained V A R w i t h four lags included for each o f the four variables Ayt, Apt, Abt, and Rt 54 H e r e Rt is the t h r e e - m o n t h treasury bill rate, bt is the log o f the St. Louis Fed adjusted m o n e t a r y base, and G N P data is utilized for Yt and Pt. The estimation and s i m u l a t i o n p e r i o d is 1954.1-1991.4. We have seen above that there has not b e e n a large discrepancy, historically, between signals p r o v i d e d by Ax~ and Apt targets, when the target values are gauged so as to imply the s a m e average inflation rate. Accordingly, let us concentrate our attention on rules for Abt and Rt designed to keep xt close to three target paths, all o f w h i c h provide e x p e c t e d Axe, values o f 0.01125 ( i . e , approximately 4.5 n o m i n a l G N P growth per year,
Woodford (1990, 1994) and Sims (1994) extend tlfis type of result to a "pure peg" and conduct their analysis in general equilibrium models with explicit optimization on the part of individual agents. 51 The concept of interest rate smoothing that I have in mind is keeping R~ close to Rt 1, but there is no major conflict here with concepts such as a tendency to minimize E(Rt-Et iRt)2 [Goodfriend (1987)]. 52 The reason why design of a simple interest rate rule may be more difficult stems fxom the ambiguity of nominal interest rates as indicators of monetary tightness or ease. High interest rates, that is, are associated with tight monetary policy from a short-run or point-in-time perspective, but with loose monetary policy from a long-ran (i.e., maintained) perspective. This means that the interest rate effects of an open market action are in opposite directions ~?omshort-term and long-term perspectives. Accordingly, the design of a policy rule for the control of target variables would seem to be more complex and dynamically delicate if an interest rate is the instrument variable than if a nominal quantity variable serves in that capacity. 53 One objection to use of a base instrument lbr the USA is that much of the currency component of the base - which is by far the larger component - is believed to be held outside the comatry. Recently, Jefferson (1997) has indicated that use of only that portion held in the country [as estimated by Porter and Judson (1996)] alters the estimated relationship between the base and nominal GDR and yields improved base-rule simulation results for the period 1984-1995. 54 The use of an unconstrained VAR is undesirable because such a model is almost certainly not policy invariant. However, the small "structural models" used in McCallum (1988) are biased in favor of the base instrument because the real monetary base (and no interest rate) appears as an explanatory variable in these models' common aggregate demand relation. In Hess, Small and Brayton (1993), by contrasi, the small macro model discussed on pp. 1 4 ~ t might be considered to be biased in favor of an interest rate instrument. The author hopes to conduct simulations with a more appropriate model in the near future.
1510
B. Z M c C a l l u m
designed to yield 2.0 percent inflation). These three paths will be of the growth-rate, growing level, and weighted average types. For the monetary base instrument, the rule to be considered is
Abt = 0 . 0 1 1 2 5 - ~ ( x t
1 - b t 1 - x t 17+bt 17)-t-/~(x] 1 - x t 1),
(5.1)
where ,~ > 0 is a policy adjustment parameter and the target variable x; can be defined in various ways 55. To yield a growing-levels target, we would have x 21 = xt11 + 0.01125 whereas a growth-rate version would use instead x23 = xt 1 + 0.01125. Besides these, we will consider x[ 2 = 0.2x] l + 0.8x)"3, where the weights are chosen semi-arbitrarily but so as to give more importance to the growth-rate target. According to the policy rule (5.1), monetary base growth is set in each quarter so as to equal the target value for nominal GNP growth minus average base velocity growth over the past four years 56, plus a cyclical correction term that reacts to past target misses. Note that x~31-&l =(xt2+0.01125)-x*l
.... 0.01125
A&.I
and that x;21 x,-1 = 0.2(x~ll
x , q ) + 0.8(0.01125-zZv, 1)
= 0.2(Xtll-Xt 1)+ 0"8(z~Xt 1 --/~Ct 1) so that use of x22 is equivalent to having a growing-levels target but using derivative as well as proportional feedback, in the terminology o f Phillips (1954). So as to obtain some indication of robustness to rule specification, a range of ;. values from 0 to 1 will be examined. For the interest instrument rule, no velocity growth term is needed so the comparable rule can be expressed as Rt = Rt-I -
100~.(x2
1 - xt-I).
(5.2)
Thus, the value of the interest rate instrument is lowered relative to the previous quarter when target spending x; exceeds the actual level in the previous quarter. The - 1 0 0 factor is inserted so as to make the same range o f )~ values as in Equation (5.1)
55 This is the type of rule studied in McCallmn (1988, 1993a, 1995a). 56 The velocity connection term serves implicitly as a forecast of the average growth rate of base velocity over the indefinite future, i.e., the long-lasting component of velocity growth that is due to institutional change (not growth due to cyclical effects, which are accounted for in the third telan). More sophisticated methods of forecasting the permanent component of both velocity growth and real output growth would be used in practice by actual central banks.
Ch. 23." Issues in the Design of Monetary Policy Rules
1511
Table 1 RMS errors with base/interest instruments, rules (5.1) and (5.2), VAR Model, US Data 1954.1-1991.4 ~ = 0.00
3.=0.25
Ni 1
0.0503 1.153
0.0235 expl a
0.0376 expl
expl expl
x~2
0.0133 0.2415
0.0ll3 expl
0.0184 expl
expl expl
x~3
0.0097 0.0184
0.0112 expl
0.0188 expl
expl expl
x~ I
0.0503 1.153
0.0284 0.0619
0.0232 0.0381
0.0201 0.0254
x~2
0.0133 0.2415
0.0109 0.0155
0.0106 0.0123
0.0114 0.0147
x~3
0.0097 0.0184
0.0100 0.0105
0.0105 0.0107
0.0118 0.0142
RMS error relative to:
~ = 0.50
,~= 1.00
Panel A: x~ 1 target
Panel B: x2 2 target
Panel C: x~ 3 target
x~J
0.0503 1.153
0.0418 0.3321
0.0361 0.t825
0.0292 0.0959
x~'2
0.0133 0.2415
0.0123 0.0680
0.0117 0.0378
0.0116 0.0217
x~3
0.0097 0.0184
0.0099 0.0104
0.0102 0.0100
0.0111 0.0123
a expl, explosive oscillations.
a p p r o p r i a t e a g a i n 57. T h e s a m e trio o f x~ definitions is e m p l o y e d as with the b a s e instrument. Table 1 r e p o r t s results o f c o u n t e r f a c t u a l h i s t o r i c a l s i m u l a t i o n s e a c h u s i n g rule (5.1) or (5.2) w i t h V A R e q u a t i o n s for Ayt, Apt, a n d e i t h e r Rt or A b , In these, e s t i m a t e d r e s i d u a l s for Aye, Ap~, a n d e i t h e r Rt or Abt are f e d into the s y s t e m as e s t i m a t e s o f s h o c k s that o c c u r r e d historically, w i t h the s i m u l a t i o n s b e g i n n i n g w i t h initial c o n d i t i o n s
57 The factor 100 is needed because R/ is expressed in tern~ls of percentage points whereas Ab~ is in logarithmic (i.e., fractional) units. Comparability is not complete, however, because R t is measured as percentage points on a per annum basis. Use of -400 as the scale factor would, however~ result m dynamically unstable behavior for most 3~values over 0.25.
B.T. McCallum
1512
as o f 1954.1 and running for 152 periods 5s. The table's entries are RMS errors, i.e., deviations o f xt from target values x~, with the top figure in each pair pertaining to the Abt instrument and the bottom figure to the Rt instrument. The three panels A, B, and C refer to simulations with the three target values (x2 l, x~ 2, x~3), and for each simulation the RMS error performance is reported relative to each o f the three target paths. Thus, we are able to see if performance relative to alternative criteria is sensitive to the target utilized, for each o f the targets. Comparing the three panels we see that when tile levels target is used (with only proportional feedback) performance is very bad with the Rt instrument, explosive fluctuations in xt resulting with ,~ = 0.25, 0.5, and 1.0. Even with the base instrument, the levels target does not perform too well and leads to instability when ;~ = 1.0. With = 0.25, somewhat better performance relative to the xj'1 target path obtains than when x~ 2 or x~3 is the target, but the difference is not large. Panel C, by contrast, shows that when the pure growth rate target xt 3 is adopted, successful stabilization o f x~ is achieved for all )~ values with both instruments. Performance relative to the growing levels path x; 1 is much better in Panel B with the x; 2 target, however, and brings about very little deterioration in performance relative to the pure growth rate criterion (i.e., the x; 3 path). Accordingly, the weighted average criterion xt 2 seems quite attractive, as was noted for Japan in McCallum (1993a). Equivalently, application o f a limited amount o f proportional as well as derivative feedback is evidently desirable 59 As for the comparison between monetary base and interest rate instruments, the results in Table 1 are distinctly more favorable to the former. In only one o f 30 separate comparisons 6° is the R M S error value smaller with the Rt instrument 61. And, more significantly, the number o f cases in which explosive oscillations result is larger with the interest instrument. These cases, should be noted, all involve the growing-levels target, xt ~. Some proponents o f an interest instrument might argue that it is important that Rt be adjusted relative to a reference level, rather than to the previous quarter's value. Following the practice o f Taylor (1993b), therefore, let us also consider performance o f a rule o f the following type:
R t = 10010.029 + (Pt 1 --Pt 5)] - 100~(xt-1 -xt-1).
(5.3)
s8 Stochastic simulations, with shocks generated randomly, have been conducted by Judd and Motley (t992) in a related study mentioned below in Section 6. 59 Judd and Morley's (1992) findings with regard to the use of some proportional control are less encouraging, evidently because their mixture is more heavily weighted toward proportional control. Also, they do not consider performance relative to the x*lt path when x*2~ is the target utilized. 60 Note that the first-colurrm cases are the same with the three different targets, since with ~ - 0 there is no feedback from target misses. (,I Michael Wood~brd has emphasized to me that there is no inherent interest in comparing base and interest instruments with equal values of k; that we want to compare entire families. These comments are correct. But Table 1 attempts to do that by scaling the 3, values - recall that the factor -100 has been inserted in Equation (5.2) - so that instrument instability occurs for about the same value of (scaled))~.
1513
Ch. 23: Issues' in the Design o f Monetary Policy Rules
Table 2 RMS errors with level-style interest instruments, rule (5.3), VAR Model, US Data 1954.1-1991.4 = 0.00
3,= 0.25
x~ x~,2 x~3
0.3825 0.0809 0.0118
0.1541 0.0326 0.0104
x~l x~2 x~3
0.3825 0.0809 0.01 t 8
0.2996 0.0630 0.0111
RMS error relative to:
2~- 0.50
2 - 1.00
Panel A: x~ 1 target
0.0915 0.0208 0.0108
0.0551 0.0169 0.0143
0.24l 6 0.0507 0.0110
0,1702 0.0366 0.0129
Panel B: x; z target
Panel C: x~ 3 target
x~t x~2 x~3
0.3825 0.0809 0.0118
0.3687 0.0780 0.0118
0.3559 0.0754 0.0120
0.3328 0.0711 0.0153
Here the (p~_j pt 5) term uses the past year's inflation rate as a forecast o f the next quarter's so as to make the rule one that sets a real interest rate in relation to the (annualized) target value o f 0.029, which is designed to be consistent with a long-run real interest rate o f 2.9 percent. The latter follows Taylor's (1993b, p. 202) suggestion of using the sample average rate o f growth o f real output. The feedback term is as before. Results are presented in Table 2 for cases using rule (5.3) that are exactly analogous to those in Table 1. |t will be seen that the performance is better than with interest instrument rule (5.2) for all 12 comparisons when x~ 1 is the target, i.e., when a levels target is utilized. A m o n g the 18 remaining comparisons, however, rule (5.3) outperforms (5.2) in only a single case. So, it is unclear whether the levels form o f interest instrument rule is superior to the form that calls for adjustment of R~ relative to the previous quarter's value. In comparison to the base instrument, rule (5.3) avoids the explosive outcome in the case in which 3, = 1 and the levels target x~ 1 is used, and also does better relative to the x23 path in two more cases (with the levels target). But for all cases in which the growth rate target x~ 3 or the weighted average target x/" is used, the R M S error is larger with rule (5.3) than with (5.1) - and is substantially larger when the criterion path is either x~ 1 or x~2. It must be emphasized that the foregoing is just a single illustration, not a study purporting to be conclusive - especially since the model used is o f the VAR t y p e
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B.T.. M c C a l l u m
Nevertheless, the apparent superiority o f the base instrument gives rise to the question o f why it is that, in actual practice, almost all central banks utilize operating procedures that are akin to use o f an interest rate instrument. It is almost certainly the case that use o f a base instrument would entail more short-term interest rate variability, but it is unclear that this would have any substantial social costs 62. One hypothesis is that interest rate instruments and interest rate smoothing are practiced because financial communities dislike interest variability and many central banks cater to the wishes o f financial institutions with which they have to work in the course o f their central-banking duties. The extent o f interest-instrument preference by CBs suggests, however, that there are additional reasons. Accordingly, Goodfriend (1991) and Poole (199l) have made interesting efforts to understand the Fed's attachment to an interest rate instrument. Despite their contribution o f various insights, however, the question remains unanswered 63. M y own thoughts on the subject suggest two intelligible reasons for a CB to prefer a R~ instrument, one having to do with beliefs concerning possible instrument instability and the other involving the CB's role as a lender o f last resort. Regarding the former, consider a grossly simplified base money demand function that includes lagged as well as current interest rates: bz = ao + a l R t + (x2Rt ] + th,
6It < O.
(5.4)
Here the absence o f price level and income/transaction variables reflects the presumption that their movements are slow in comparison to those of bt and Rt 64. N o w suppose that the CB were to manage bf exogenously 65. Then Rt will behave as R~ -- [30 + [3 t Rt 1 + [32 rh + [~3
(bt determinants),
(5.5)
where/31 = - a 2 / a l . Thus, if a2 < 0, there will be oscillations in Rt. More importantly, if la2t > lal I, then the system will be explosive. B e l i e f that market demand for the monetary base is such that la21 > la~ I represents the actual state of affairs would then lead one to believe that use o f a base instrument would be disastrous, as suggested by Goodhart. And, in fact, there is some reason to
(,2 Between 19'75 and 1987 the Swiss National Bank used procedures that were akin to use of a base instrument. [See Rich (1987, pp. 11-13).] Short-term interest rate variability in Switzerland was much greater than in other economies, but macroeconomic performance was excellent. (In 1987 there were two major institutional changes, involving new required-reserve structures and a new clearing system, that seriously disrupted monetary control and resulted in altered operating procedures.) 63 It is possible that Goodhart's (t 994) belief, that a base instrument would be infeasible, is shared by many central bankers. But why? One possible reason is developed in the next two paragraphs. 64 This simplification should not be misleading for the purposes at hand, although it would be ~5tal for many other issues. In Equation (5.4), th is a stochastic disturbance term. 65 Here l do not literally mean exogenous, but rather that bt is varied for macroeconomic reasons, not so as to s m o o t h R t values.
Ch. 23: Issues in the Design of Monetary Policy Rules
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think that such beliefs might be held by central bankers. In particular, econometric estimates o f base money demand functions (direct or indirect) sometimes indicate that la2l > la~l in fact. Central bank analysts would be aware o f these estimates. My own belief is that it is not true that fa2 ] > ]ctl [ holds in reality, for time periods of one month or longer, so that the posited CB attitude is unjustified. 66 But it could be prevalent, nevertheless, even if my belief is correct. A second intelligible reason for CB interest instrument preference concerns the lender-of-last-resort (LLR) role. That role is to prevent financial crises that involve sharply increased demands for base money [Schwartz (1986), Goodfriend and King (1988)]. To prevent such crises, the CB needs to supply base money abundantly in times o f stress [Bagehot (1873)]. This is usually conceived o f as occurring by the route o f discount-window lending. But Goodfriend and King pointed out that a policy involving interest rate smoothing i.e., not allowing R: to change much relative to Rt t - would amomatically provide base money in times o f high demand 67. Then if a CB is going to practice R~ smoothing it is quite natural for it to use a R~ instrument 6s. This last discussion leads one to consider the possibility o f using an interest rate instrument - and smoothing its movements at a high frequency (e.g., weekly) so as to keep monetary base values close to target levels implied by a policy rule such as (5.1). The motivation, of course, is the notion that quarterly base rules seem to function better macroeconomically than interest rules. The preliminary investigation in McCallum (1995a) attempts to study this question while accounting realistically and in quantitative terms for shock variances and market responses in the US economy. The results suggest that the federal funds rate could be manipulated weekly to approximate monetary base values that are designed to hit desired quarterly-average nominal GNP targets, with considerable smoothing o f the funds rate on a weekly basis (only about twice as much weekly variability as now obtains).
6. Issues concerning research procedures In this section consideration will be given to a number o f issues concerning procedures used in investigations of the properties o f monetary policy rules. One set of issues has to do with the operationality of various rule specifications while another set focuses
G6 In part my belief stems from the fact that for base demand in period t the value ofR t 1 is an irrelevant bygone, so Rt 1 does not belong in a properly specified demand function. There are reasons, involving omission of expectational variables, why econometric studies would nevertheless tend to find strong R~ ~ effects. On this, see McCallum (1985, pp. 583 585). 67 As would a practice of keeping R~ from rising above some preset penal rate. 68 Goodfriend (1991, p. 15) and Poole (1991, pp. 37-39) observe, however, that this is not a stricl logical necessity. Also, many actual CBs apparently do not accept the Goodfriend-King argument that the LLR role can be fulfilled by Rt smoothing without discount-window lending.
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B. Z McCallum
on the types of simulations used to generate model outcomes. Regarding the latter, a weakness of the simulation results reported above in Section 5, and also those in McCallum (1988, 1993a, 1995a), is that they are based on simulation exercises with a single set of shock values, i.e., shocks estimated to have occurred historically. As explained by Taylor (1988) and Bryant et al. (1993), there are several advantages to be obtained by using true stochastic simulations with a large number of shock realizations generated by random selection from (multivariate) distributions that have covariance properties like those of the historical shock estimates. The studies of Judd and Motley (1991, 1992) for example, improve upon those of McCallum (1988) by conducting "experiments" each of which consists of 500 stochastic simulations with a given model, policy rule, and policy parameter values, rather than a single simulation with the historical residuals used as shocks. One obvious advantage of stochastic simulations over historical counterfactuals is that they avoid the possibility that the historical residuals happen to possess some particular quirk that makes performance unrepresentative for the shock moments being utilized. Another advantage is that sample-mean values of shocks may not equal zero, as they must by construction in the case of historical residuals. This feature is especially important in considering the consequences of rules that feature difference stationarity (rather than trend-stationarity) of nominal variables. The residual values used as shocks in the simulations in Tables 1 and 2, for example, sum to zero for each equation's shock tenn. Thus the extent of a tendency for xt (say) to drift away from a levels target path such as xt 1 is understated by the results in those tables 69. Bryant et al. (1993, pp. 373-375) suggest that, in addition, stochastic simulations are helpful from a robustness perspective. Perhaps the most ambitious project undertaken to date on the characteristics of alternative monetary policy rules is the Brookings-sponsored study reported in Bryant et al. (1993). In this study, which is a follow-up to Bryant et al. (1988), eight prominent modeling groups (or individuals) reported on policy rule simulation exercises conducted with the following multicountry models: GEM, INTERMOD, MSG, MX3, MULTIMOD, MPS, LIVERPOOL, and TAYLOR. These studies were designed to explore the macroeconomic consequences of adopting different target variables for monetary policy, with contenders including nominal GDP (in levels form) and the hybrid variable discussed above in Section 4, as well as monetary aggregates and the exchange 'rate. Most impressively, the conference organizers took pains to arrange for the various modeling groups all to consider the same range of policy alternatives, thereby creating the possibility of obtaining results that would gain m credibility as a consequence of being relatively robust to model specification. At the strategic level of research design, therefore, this Brookings project possessed the potential for contributing greatly to knowledge concerning the design of monetary
69 Understated, but not entirely absent; thne plots of xt hldicate the absence of any path-restoring behavior except toward the end of the 152-quartersimulation (and sample) period.
Ch. 23: lssues in the Design of Monetary Policy Rules
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and fiscal policy rules (even in the face of potential weaknesses of the models' specifications). It is argued in McCallum (1993b, 1994), however, that this potential was significantly undermined by the particular generic form of policy rule specified for use by all the modeling groups. The alleged problem is that the rule form permits rule specifications that are not operational and, in addition, suggests performance measures that can be seriously misleading. The rule form in question, which has also been used in several other studies, may be written as Rt - Rbt
=/l(zt
- z~),
(6.1)
where Rt is an interest rate instrument and zt is a target variable such as nominal GDP. Here the "b" superscripts designate baseline reference paths for the variables, baseline paths that may be defined differently by different investigators. Also, the performance of various targets is evaluated by measures such as E[(zt - - Z bt ~~2 l J, which pertain to target variable(s) for the rule and perhaps also other criterion variables. In terms of operationality there are two problems with this rule form (6.1)7o. The more obvious is that it is unrealistic to pretend that monetary policymakers can respond to the true value of current-period realizations of zt for several leading specifications of the latter. It is reasonable to assume that contemporaneous observations are available for interest rates, exchange rates, or other asset-market prices. It would be unreasonable, however, to make such an assumption for nominal or real GDP (or GNP) or the price level. One could make arguments pro and con in the case of monetary aggregates such as M1 or M2, but in the case of national-income values, data are not produced promptly enough for actual central bankers to respond to movements without an appreciable lag. Ignoring that lag, as is done throughout the Bryant et al. (1993) studies, clearly makes it possible for the simulated performance to be significantly better than could be obtained in reality. Furthermore, simulations that ignore this lag also intend to understate the danger of instrument-induced instability, a bias that is quite important because instrument instability is one of the most serious dangers to be avoided in the design of a policy rule. The second and less obvious way in which rules like (6.1) are not operational involves the baseline values R ) and z ). ttere the problem is that an actual policymaker could not implement any rule of form (6.1) without knowledge of these reference paths. But by definition these paths may be related to each other by the model being investigated, so the policy rule is model-specific and therefore of reduced interest to a practical policymaker. In terms of misleading performance measures, the problem is that the instrumem variable under consideration may be one that can be used to smooth out fluctua~ tions in zt but not to control the long-term growth o f z , Then by using fluctuations in z,
70 It should be noted favorablythat the instrument variable is operational and realistic.
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B. 717.McCallurn
relative to the baseline path z b in a performance measure like E [ ( z t - - z b ) 2 ] , the investigator may conclude that Rt is a desirable instrument when in fact it is highly unsuitable 71. Another type of nonoperationality involves the specification of instrument variables that would, in actual practice, be infeasible in this capacity. Broad monetary aggregates such as M2 or M3 would seem clearly to fall into this category and, under typical current institutional arrangements, probably the same applies to variants of M1. Studies that pretend that such variables are feasible instrument have declined in frequency in recent years, as the practice of specifying an interest instrument has gained in popularity [e.g., Taylor (1993a), Bryant et al. (1993), Fuhrer and Moore (1995)]. Objections based on the operationality criterion have been directed at rules that use nominal GDP or GNP targets, even when these rules refer only to values lagged by at least one quarter. The point is that national income statistics are not produced often enough or quickly enough, and are significantly revised after their first release. But this criticism seems misguided since the essence of nominal income targeting is to utilize some rather comprehensive measure of aggregate (nominal) spending; the variable does not need to be GDP or GNP p e r se. Other measures could readily be developed on the basis of price and quantity indices that are reported more often and more promptly -in the USA, for example, one could in principle use the product of the CPI and the Fed's industrial production index (both of which are published monthly). It might even be possible to develop a monthly measure that is more attractive conceptually than GDP, by making the price index more closely tailored to public perceptions of inflation and/or by using a quantity measure that treats government activity more appropriately.
7. Interactions with fiscal policy The relationship between monetary and fiscal policy has been quite an active topic recently, possibly in part as a response to the magnitude and duration of fiscal deficits experienced in many developed countries and/or to controversies concerning proposed fiscal rules for the planned European monetary union. It is obviously impossible to discuss in this chapter all of the many ramifications of monetary/fiscal policy interactions, but it seems important to recognize some recent arguments which suggest that it is necessary, or at least desirable, for the monetary authority to take account of fiscal policy behavior when designing its monetary policy rule 72. Such a recommendation is implicitly critical of the policy rules discussed in previous sections and runs counter to the spirit of much current central-bank thinking, as expressed for example in the practice of inflation targeting. Consequently, three strands of literature will be considered. :1 Some examples are described in McCallum (1994). 72 Among these contributions are papers by Alesina and Tabellini (1987), Debelle and Fischer (1995), Leeper (1991), Sims (1994, 1995), and Woodford (1994, 1995).
Ch. 23: Issues in the Design of Monetary Policy Rules
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An early paper on the subject that has received a great deal of attention is the Sargent and Wallace (1981) piece entitled "Some Unpleasant Monetarist Arithmetic". As many readers will be aware, that paper's principal contention was that an economy's monetary authority cannot prevent inflation by its own control of base money creation if an uncooperative or irresponsible fiscal authority behaves so as to generate a continuing stream of primary fiscal deficits 73. Whether the central bank has control over inflation is viewed as depending upon, in the words of Sargent and Wallace (1981, p. 7), "which authority moves first, the monetary authority or the fiscal authority. In other words, who imposes discipline on whom?" Having posed the problem in that way, the Sargent-Wallace paper then goes on to suggest that it might well be the fiscal authority that dominates the outcome. In fact, however, the paper's analysis proceeds by simply assuming that the fiscal authority dominates, an assumption that is implicit in the procedure of conducting analysis with an exogenously given path of primary deficits. Proceeding in that fashion, the Sargent-Wallace paper seems to show that even a determined central bank could be forced by a fiscal authority to create base money along a path that is inflationary when a non-inflationary path is intended. It is argued by McCallum (1990a, pp. 984-985), however, that this suggestion is unwarranted. It is of course true that fiscal authorities may be able to bring political pressure to bear on central banks in ways that are difficult to resist. But the SargentWallace analysis is not developed along political lines; instead it seems to invite the reader to conclude that a politically independent central bank could be dominated in some technical sense by a stubborn fiscal authority. My basis for disputing this is that an independent central bank is technically able to control its own path of base money creation, but fiscal authorities cannot directly control their own primary deficit magnitudes. The reason is that deficits are measures of spending in excess of tax collections, so if a fiscal authority embarks on a tax and spending plan that is inconsistent with the central bank's (perhaps non-inflationary) creation of base money, it is the fiscal authority that will have to yield. Why? Simply because in this circumstance, it will not have the purchasing power to carry out its planned actions 74. In other words, the fiscal authority does not actually have control over the instrument variable - the deficit - that it is presumed to control in the Sargent-Wallace experiment. Thus a truly determined and independent monetary authority can always have its way, technically speaking, in monetary versus fiscal conflicts. This simple point is one tha~ seems to the author to be of great importance in the design of central bank institutions. The point is also intimately related to a quite recently developed body of theorizing that takes a strongly "fiscalist" stance, leading examples of-which include Woodford
73 The result pertains to primary deficits, i.e., deficits exclusive of interest payments, but not to deficits measured in the conventional interest-inclusive way. 74 This is directly implied by the government's budget constraint which limits purchases to revenue raised by taxes, net bond sales, and base money creation. In this regard it should be recognized that the government cannot compel pfivatc agents to buy its bonds (i.e., lend to it), since such would represent taxation.
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(1994, 1995), Sims (1994, 1995), and Leeper (1991). Perhaps the most dramatic theme in this literature is the presentation o f a "fiscal theory o f the price level" [Woodford (1995, pp. 5-13), Sims (1994)]. For an introductory exposition and analysis, let us consider the simplest case, which involves a Sidrauski-BrockT5 model with constant output y and utility function u(ct, mr)+ [3u(ct+l, m r + t ) + . . , with u ( c , m ) = (1 - a ) - I A l c 1-~ + (1 - rl) IA2ml-rl, where a, , / > 0 and fi = 1/(1 + p ) with p > 0. Also we assume t / < 1, in order to facilitate presentation o f the fiscalist theory, not the counter-argument outlined subsequently. In this setup, the households' firstorder conditions include mt+l _ A R 1/8 Pt+l t , 1 P, 1
l + R, - / 3 P, '
A =
R, > 0
(7.1)
(7.2)
for all t = l, 2 . . . . . Here Pt is the money price o f output, Mt is nominal money at the start o f period t, mt = M t / P , ca is consumption during t, and R¢ is the rate o f interest on government bonds, the household's budget constraint being Pt(Y
vt) - Ptct + Mt+l - M t + (1 + Rt)-I Bt+l _ Bt '
(7.3)
where vt is lump-sum taxes and Bt is the nominal stock o f bonds at the end o f t. In per-household terms, the government budget constraint with zero purchases is - P t v t = Mt+j - M r + (1 + Rt) 1Bt+l - B~,
(7.4)
so vt is the per-household value o f the fiscal surplus. If the government chooses time paths for M t and vt (or Bt), then Equations (7.1)-(7.4) give equilibrium values for ct, Pt, Rt, and Bt (or vt) provided that two transversality conditions are satisfied, these requiring that [3tMt/Pt and [3tB/pt approach zero as t---+ oo. Note that Equations (7.3) and (7.4) imply ct = y , the constancy o f which is utilized in formulations (7.1) and (7.2). Following the fiscalist argument v6, now suppose that the value o f Mr is kept constant at M and that vt = v > 0 for all t = 1, 2 . . . . . Then the price level is determined as follows. The GBR can be written as
b._, = (1 +RO
[b,-v~] = B1 b , - l
(7.5)
implying that bt = B,/P~ will explode as t ~ o c , since 1/fi > l, unless it is the case that B1/P1 = o/(1 -/~), which would induce bt to remain constant at the level bt = v / ( l [3) 75 That is, a model in which infinite-lived households with time-separablc preferences makc their decisions in a optimizing fashion and interact with each other and the government (monetary authority and fiscal authority) on competitive markets. Woodford's (1995) version of the model, and ours, does not include capital goods but that feature of the setup is not relevant to the issues at hand. 76 I am indebted to Michael Woodford for special efforts to explain the argumcnt to me, bm lie is certainly not responsible for the point of view expressed here.
Ck. 23: Issues in the Design of MonetalT Policy Rules
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thereafter. Therefore, so the theory says, PI = B1 (l -/3)/v is determined by the fiscal surplus magnitude v and the initial stock of nominal debt B1. At the same time, Equations (7.1) and (7.2) imply a difference equation relating Pt+~ to Pt in an unambiguously explosive fashion, starting from P1, provided that PI exceeds a critical value Pc. That explosion in Pt makes M / P t approach zero and so, with bt constant, both transversality conditions are satisfied although Bt is exploding. Thus the fiscal theory of the price level asserts that with a constant money stock and constant fiscal surplus, the price level explodes as time passes, starting from a level that is directly related to the size of the pre-existing nominal bond stock and to the magnitude of the maintained surplus. No other path could be an equilibrium because it would imply an exploding bt, which would violate a transversality condition. The foregoing is an ingenious argument but, in the opinion of the writer, is open to a crucial objection. It is that there is another equilibrium - typically ignored by fiscalist writers that does not rely upon explosive-bubble behavior of the price level. This more fundamental "monetarist" equilibrium features Pt+l = P t - MPl/'t/A, i.e., a constant price level, together with values Bt+l = 0 for all t = 1, 2 , . . . . With these paths for Pt and Bt it is clear that Equations (7.1)-(7.3) and both transversality conditions are satisfied. It might be objected that this solution does not satisfy the budget constraint (7.4) for the values of vt = v specified by the fiscalist writers, but it has been argued above that the fiscal surplus is actually not a variable that can legitimately be specified as exogenous 77. What the monetarist solution says is that if the fiscal authority tried to keep vt = v as in the fiscalist solution, then households would refuse to purchase the bonds that are required to be sold by the fiscal authority. It would be necessary to distinguish between bonds supplied in (7.4) and bonds demanded in (7.3), with Bt = 0 in the latter. If there were an initial stock of bonds outstanding, B I ~ 0, then they would be retired in period 1 with a resulting real primary surplus of B1/P1. In sum, a formally correct and arguably more plausible solution than the fiscalist candidate is one in which the price level remains constant, with a magnitude that is proportional to the money stock. At the same time, the stock of bonds offered for sale by the fiscal authority may be explosive bm if so these bonds will not be purchased by optimizing households. The fiscal authority's realized surplus will then be zero after the initial period leaving us with a traditional non-fiscalist result 78. There are, of course, several other cases and more complex models featured in the recent fiscalist literature~ indeed, a rather bewildering variety. But it would appear to the present writer that the sta'iking fiscalist outcomes typically result from emphasizing the possibility of bubble
77 This is also the basis for the argument hi a recem paper by Buiter (1998), which reaches conclusion,s predominantly compatible with those presented here. 78 Note that it is not being claimed that this is the only solution, but merely that it is a solution (and one that might be thought likely to prevail by analysts who are skeptical of the empirical importance of macroeconomic bubbles).
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B.T. McCallum
solutions while ignoring the existence of a non-bubble or fundamentals solution that would deliver an entirely traditional policy message. 79, 8o The third strand of the monetary-fiscal interaction literature to be discussed is represented by papers by Alesina and Tabellini (19 87) and Debelle and Fischer (1995). In the former, the workhorse Barro-Gordon model is extended by assuming that real government purchases are controlled by a fiscal authority (FA) that may have different objectives - concerning the level of these purchases as well as inflation and output than those of the central bank (CB). The FA's revenues come from non-lump-sum (distorting) taxes and money growth, government debt being excluded from the m o d e l In this setting, Alesina and Tabellini derive outcomes pertaining to both discretionary and rule-like behavior by the CB 81. Their most striking result is that when preferences of the CB and the FA are sufficiently different 82, equilibrium outcomes with monetary policy commitment can be inferior 83 to those obtained under discretion. This result is with independent behavior by the CB and FA, so the message is that monetary-fiscal policy cooperation is needed. In a more recent paper, Debelle and Fischer (1995) have modified the AlesinaTabellini framework by also including a social objective function, one that can be different from those of the CB and FA. Only the latter cares, in their setup, about the level of government purchases. In this model, Debelle and Fischer conduct analysis always assuming discretionary behavior by the CB but under different assumptions regarding the Stackelberg leadership positions of the CB and FA. A major aim of the analysis is to determine the optimal value, in terms of society's preferences, of the "conservativeness" of the CB, i.e., the relative importance that it assigns to ilfftation. It is not optimal, they find, for the CB's preferences to match those of society - i.e.,
79 Dotscy (1996) shows that a reahstic specificationof parameter values gives rise to a more traditional policy message than one promoted in the fiscalist literature, for an issue concerning the responsiveness of the CB to fiscal variables under the assumption that the fiscal anthority's policy rule tends to prevent debt explosions. 8o One other feature of the recent fiscalist literature is its contention that pegging the nominal interest rate at a low value will result in a correspondinglylow inflation rate and in no indeterminacyproblem, implying that such a policy would be preferable to the maintenance of a low growth rate of the (base) money supply. The analyticalkey to this argument is that explosive price level (bubble) solutions, which are possible with a low money stock growth rate, would be precluded by a constant interest rate in models with a well-behaved (possibly constmat) real rate of interest - see, e.g., Equation (7.2) above. It has been established above, however, that when money growth is exogenous, the possible aberration reflects multiple (bubble) solutions, not nominal indeterminacy.But the empirical relevance of bubble solutions for macroeconomicvariables is dubious, this writer would contend, and if such solutions are not relevant then the theoretical disadvantage for the low money growth policy is itself irrelevant. 81 In the absence of debt, the FA has no incentive for dynamic inconsistency, i.e., no commitment problem. 82 The CB is assumed to assign at least as much weight to the inflation rate (relative to each of the other goal variables) as does the FA. 83 Inferior in terms of both authorities' prelbrences; the private sector is assumed to care only about real wages.
Ch. 23." Issues in the Design of iVlonetary Policy Rules
/523
the private sector. And they find that it is undesirable socially for the FA to dominate (in a Stackelberg sense) the CB, requiring the CB bank to finance FA deficits 84 An objection to this last strand of analysis stems from its reliance on the presumption that an economy's CB and FA will have preferences that differ from each other's and from social (i.e., household) preferences. While such might be the case in some nations, one would expect that in democratic societies, CBs and FAs will be aware of and tend to reflect the basic preferences of the population. That tendency might be combatted by various devices, but it seems likely that (e.g.) attempts to appoint CB governors with tastes more anti-inflationary than society's would often result in ex-post surprises regarding these tastes. Also, one might expect that fiscal or monetary legislation would be overturned fairly promptly if it were to yield results that are truly inconsistent with the preferences of the society's voters. In any event, it would seem that designing institutions nnder the presumption that CB and/or FA preferences differ from those of the society at large is unlikely to be fruitful.
8. Concluding remarks This final section will consist of a brief and perhaps opinionated recapitulation of conclusions obtained for the main topics of discussion. First, in actual practice the defining characteristics of rule-like behavior are that the central bank conducts policy in a systematic fashion, and while doing so systematically abstains from attempts to exploit existing expectations for temporary gains in output. Central banks can behave in this committed manner if they choose; there are dynamic-inconsistency pressures on them to act in a more discretionary fashion, but there is nothing tangible to prevent committed behavior. Indeed, the adoption o f a monetary policy rule is one technique for overcoming discretionary pressures. In terms of research strategy, the chapter's discussion has promoted the robustness approach - i.e., searching for a rule that works reasonably well in a variety of models rather than the more straightforward approach of deriving an optimal rule relative to a particular model, No strong claims are made in this regard, however, and the value of the optimal design approach is recognized. The importance of operationality of any proposed rule is also emphasized, as well as the merits of stochastic simulations as opposed to simpler historical counterfactual simulations. Regarding the choice of a target variable, the chapter suggests that in practice the difference between an inflation target and one that aims for nominal spending growth, at a rate designed to yield the same target inflation rate on average, is unlikely to be large. More dissimilar is the hybrid target variable that adds together inflation and output relative to capacity. This hybrid variable is probably more closely related to
~4 Of course, it is argued above that tile FA will not be able to dominate if the CB has independence (i.e., can choose its own base money creation rates),
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actual central bank objectives, but the absence o f any reliable and agreed-upon method o f measuring capacity or trend output creates a major drawback for this variable. Also, it is argued that the magnitude o f future price-level uncertainty, introduced by the unit root component that results from a growth-rate type of target, is probably rather small. Thus growth-rate targets appear somewhat more desirable than growing-level targets as the latter requires stringent actions to drive any nominal target variable back toward its predetermined path after shocks have led to target misses. Turning to the choice o f an instrument variable, the chapter presents a small bit o f evidence designed to illustrate why it is that a number o f academic economists are inclined to prefer quantity instruments, such as the monetary base, rather than short-term interest rates. The exposition includes arguments against some literature claims that either short-term nominal interest rates or the monetary base are infeasible as instruments. In this discussion, particular emphasis is given to the distinction between two quite different types o f abberational price level behavior, namely, nominal indeterminacy and multiple solutions. The former has to do with the distinction between real and nominal variables while the latter concerns self-fulfilling dynamic expectational phenomena - i.e., bubbles. Also, the former pertains to all nominal variables whereas the latter involves real variables. Finally, with regard to prominent fiscalist positions two points are made. First, the recently developed fiscal theory o f price-level determination typically leads to a solution that is not unique; there also exists a less exotic bubble-free solution that has a much more traditional (indeed, monetarist) flavor. This conclusion stems from recognition that central banks can dominate in any conflicts with fiscal authorities. Also, there are some results in the literature that suggest that monetary/fiscal cooperation is important, but these depend upon the assumption that central banks and fiscal authorities have fundamentally different objective fimctions. It is doubtful whether such an assumption can play a fruitful role in the design o f desirable central bank institutions and behavior patterns.
References
Aizenman, J., and J.A. Frenkel (1986), "Targeting rules for monetary policy", Economics Letters 21:183-187. Alesina, A., and G. Tabellini (1987), "Rules and discretion with noncordinated monetary and fiscal policies", Economic Inquiry 25:619 630. Almeida, A, and C.A.E. Goodhart (1996~ "Does the adoption of inflation targets affect central bank behavior?", Working Paper (London School of Economics, July). Axihod, S.H. (1985), "Comment on 'On consequences and criticisms of monetary targeting'", Journal of Money, Credit and Banking 17:598-602. Bagehot, W. (1873), Lombard Street: A Description of the Money Market (ES. King, London). Ball, L. (1997), "Efficient rules for monetary policy", Working Paper No. 5952 (NBER). Barro, RJ., and D.B. Gordon (1983a), "A positive theory of monetary policy in a natnral rate model", Jom'nal of Political Economy 91:58%610.
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Chapter 24
I N F L A T I O N STABILIZATION A N D B O P C R I S E S IN DEVELOPING
COUNTRIES
*
GUILLERMO A. CALVO
University of Maryland CARLOS A. VEGH**
UCLA
Contents Abstract Keywords 1. Introduction 2. Understanding chronic inflation 2.1. 2.2. 2.3. 2.4. 2.5. 2.6.
Inflation as an optimal tax Shocks and accommodation Multiple equilibria The "provinces" efl~ct Delayed stabilization In conclusion
3. Evidence on the real effects of stabilization in chronic-inflation countries
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3.1. Exchange-rate-based stabilization: empirical regularities 3.1.1. Stabilization time profiles 3.1.2. Panel regressions 3.1.3. Do exchange-rate-based stabilizations sow the seeds of their own destruction? 3.2. Money-based stabilization: empirical regularities 3.3. Recession now versus recession later 3.4. A word of caution
1550 1553 1554 1557 1559
4. Exchange-rate-based stabilization I: inflation inertia and lack of credibility
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4.1. Inflation inertia
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" We are grateful to Francesco Daveri, David Gould, Amartya Lahiri, Carmen Reinhart, Sergio Rodriguez, Jorge Roldos, Julio Santaella, John Taylor, Aaron Tornell, Martin Uribe, Sara Wong, Mike Woodford, Carlos Zarazaga, participants at the conference on "Recent Developments i~ Macroecononomics", organized by the Federal Reserve Bank of New York (February 1997), and, especially, Ratna Sahay and Miguel Savastano for insightful comments and discussions. ** Corresponding author. Department of Economics, UCLA, 405 Hilgard Avenue, Los Angeles~ CA 90095-1477. E-lnaih
[email protected]. Website: http://vegh.sscnet.ucla.edu.
Handbook of Macroeconomics, Volume 1, Edited by ~B. Taylor and M, Wood~fbrd © 1999 Elseuier Science B.V. All rights reserved 1531
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4,2. Lack of credibility 1569 5. Exchange-rate-based stabilization ll: durable goods, credit, and wealth effects 1573 5.1. Durable goods 1573 5,2. Credit market segmentation 1575 5,3. Supply-sideeffects 1577 5,4. Fiscalpolicy 1580 5,5. And the winner is ... 1581 6. Money-based stabilization 1582 6,1. A simple model 1582 6,2. Extensions to other money-basedregimes 1587 6,3. Money anchor versus exchange-rate anchor 1588 7. Balance-of-payments crises 1590 7,1. Liquidity 1591 7~2. The Krugman model 1592 7,3. Krugman model: critique and extensions 1595 7.3.1. Bonds 1595 7.3.2. Sterilization 1595 7.3.3. lnterest rate policy 1596 7,4. The current account approach 1597 7.5. Financial considerations 1599 7.5.1. Volatilityof monetary aggregates 1599 7.5.2. Short-matmity debt 1601 7.5.3. Domestic debt and credibility 1603 7.5.4. Credibility,the demand for money and fiscal deficits 1603 8. Concluding remarks 1604 References 1607
Ch. 24." Inflation Stabilization and BOP Crises in Developing Countries
1533
Abstract High and persistent inflation has been one of the distinguishing macroeconomic characteristics of many developing countries since the end of World War II. Countries afflicted by chronic inflation, however, have not taken their fate lightly and have engaged in repeated stabilization attempts. More often than not, stabilization plans have failed. The end of stabilizations - particularly those which rely on a pegged exchange rate - has often involved dramatic balance-of-payments crises. As stabilization plans come and go, a large literature has developed trying to document the main empirical regularities and to understand the key issues involved. This chapter undertakes a critical review and evaluation of the literature related to inflation stabilization policies and balance-of-payments crises in developing countries. The chapter begins by trying to rationalize the existence of chronic inflation in a world of rational agents. It then offers an empirical analysis of the main stylized facts associated with stopping chronic inflation. It is shown that the real effects of disinflation depend on the nominal anchor which is used. Exchange-rate-based stabilizations lead to an initial output and consumption boom - which is particularly evident in the behavior of durable goods - real exchange rate appreciation, and current account deficits. The contractionary costs typically associated with disinflation emerge only later in the program. In contrast, in money-based stabilizations, the contraction occurs in the beginning of the program. The chapter then proceeds to review several explanations for these puzzling phenomena, emphasizing the real effects of lack of credibility, inflation inertia, and consumption cycles generated by durable goods purchases. The chapter also documents the fact that most exchange-rate-based stabilizations end up in balance-of-payments crises. The Mexican crisis of December 1994 brought back to life some of the key questions: Do exchange-rate-based stabilizations sow the seeds of their own destruction by unleashing "unsustainable" real exchange rate appreciations and current account deficits? Or are credibility problems and self-fulfilling prophecies at the root of these crises? The remainder of the chapter is devoted to analyzing the main ideas behind this unfolding literature.
Keywords JEL classification: E52, E63, F41
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G.A. Caluo and C.A. V~gh
1. Introduction
High and persistent inflation has been one of the distinguishing macroeconomic characteristics of many developing countries - particularly in Latin America - since the end of World War II. Pazos (1972) coined the term "chronic inflation" to refer to this phenomenon. In his view, chronic inflation is quite a different creature from the much more spectacular hyperinftations studied by Cagan (1956). First, unlike hyperinflations whose duration is measured in terms of months, chronic inflation may last for decades. Second, countries learn how to live with high and persistent inflation by creating various indexation mechanisms which, in turn, tend to perpetuate the inflationary process. As a result, inflation does not have an inherent propensity to accelerate and, if it does, soon reaches a new plateau. Countries afflicted by chronic inflation, however, do not take their fate lightly. Quite to the contrary, in the last four decades they have engaged in repeated stabilization attempts which, more often than not, have failed. The end of stabilizations - in particular those which rely on a pegged exchange rate - has often involved dramatic balance-of-payments crises with costly devaluations and losses of international reserves. With increasingly open capital markets, some of these crises now send shock waves throughout the world, as vividly illustrated by the Mexican crisis of December 1994. In the last ten years, however, countries such as Chile, Israel, and Argentina have succeeded in reducing inflation close to international levels. Still, most developing countries continue to struggle through stabilization attempts, and some former socialist economies have also begun to face similar cycles of inflation and stabilization. The currency crises that hit South East Asia during the second half of 1997 were also a startling reminder that no region is immune to boom-bust cycles which were once thought as being mainly a Latin American disease. Over the course of the last four decades, a myriad of major stabilization plans went by, leaving behind a rich legacy of issues and puzzles. In retrospect, the stabilization plans implemented in the late 1970s in the Southern Cone countries - Argentina, Chile, and Uruguay - proved to be a turning point. Designed by US-trained technocrats, these plans were in some sense the first ones to openly recognize the constraints imposed on monetary policy by open financial markets. Trying to make the most of such constraints, policymakers decided to abandon the "closed-economy" monetary policies of the past - aimed primarily at controlling the money supply - and switch to "open-economy" policies based on setting a declining rate of devaluation which would quickly bring domestic inflation in line with tradable-goods inflation (given by world inflation plus the rate of devaluation). To the consternation of policymakers, however, the inflation rate failed to converge to tradable-goods inflation, which resulted in a large real appreciation of the domestic currency. More puzzling still, in spite of the real appreciation, real economic activity - particularly private consumption -- expanded in the early years of the programs. Later in the programs, a recession set in, eve1~before the programs collapsed. In the mid-1980s, major programs in Argentina, Brazil, and Israel brought back to
Ch. 24:
Inflation Stabilization and BOP Crises in Developing Countries
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life some o f the same, and still mostly unresolved, issues. In spite o f the use o f wage and price controls to supplement an exchange rate peg, real appreciation remained an integral part o f the picture. More puzzling, however, was the reemergence o f the pattern of an initial b o o m and a later recession. The Israeli recession was viewed as particularly hard to rationalize because o f its occurrence in a fiscally sound and largely successful stabilization program. Based on these new programs - and a reexamination of older programs going back to the 1960s - Kiguel and Liviatan (1992) and V6gh (1992) argued that the outcome observed in the Southern-Cone stabilizations is a pattern common to most stabilization plans which have relied on the exchange rate as opposed to a monetary aggregate - as the main nominal anchor. Specifically, the beginning o f an exchange-rate-based stabilization is characterized by an economic boom and sustained real appreciation. Later in the programs - and often aggravated by the collapse o f the program - a contraction takes hold. In contrast, the scanty evidence on money-based stabilization in chronic-inflation countries lends support to the notion that, as in low-inflation countries, the recession takes place at the beginning o f the program [Calvo and V6gh (1994b)]. Hence, it would appear that under money-based stabilization, the costs (in terms o f output losses) would be paid up-front, whereas, under exchange-rate-based stabilization, these costs would be postponed until a later date. The intriguing idea that choosing between the two nominal anchors may imply choosing not t f b u t w h e n to bear the costs o f disinflation has been dubbed the "recession-now-versus-recession-later" hypothesis. The twin puzzles o f the b o o m - r e c e s s i o n cycle in exchange-rate-based stabilizations and the recession-now-versus-recession-later hypothesis have been the driving force behind recent developments in the area o f inflation stabilization in developing countries. An emerging empirical literature has attempted to document these phenomena in a systematic way, while an extensive theoretical literature has advanced various hypotheses - such as inflation inertia and lack o f credibility - to explain the real effects of disinflation. A critical review and evaluation o f this literature constitutes the core of this chapter i. A third puzzle is the fact that most exchange-rate-based stabilizations end up in balance-of-payments (BOP) crises. The literature, however, has had precious little to say so far about the possible links between the dynamics o f exchange-rate-based stabilizations and BOP crises. The Mexican crisis o f December 1994 which put an end to an exchange-rate-based stabilization plan initiated seven years earlier - brought back to life some o f the key questions: Do exchange-rate-based stabilizations sow the Not suprisingly, most of the literature has been respired by the experiences of chronic inflation countries, which constitute a rich laboratory for the discussion of inflation and stabilization in developing countries. To focus the discussion, we follow this tradition and confine our discussion on inflation and stabilization mostly to chronic inflation countries. We will thus ignore some rare episodes of fullblown hyperinfations (like Bolivia in the mid-1980s) - which have more in common with Cagan's classic hyperinflations [see V6gh (1992)]. We will also mostly ignore the inflationary experience of the transition economies, as the dramatic transformation from plan to market raises some special issues [see, for example, De Melo, Denizer and Gelb (1995), and Sahay and V6gh (1996)].
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G.A. Calvo and C.A~ V~gh
seeds of their own destruction by unleashing "unsustainable" real appreciations and current account deficits? Or are credibility problems and self-fulfilling prophecies at the root of these crises? The remainder of the chapter is devoted to analyzing the main ideas behind this unfolding literature. O f course, the potential for BOP crises is a more general issue, which goes back to Krugman's (1979) seminal contribution, and applies to any pegged exchange rate system. Hence, while many of the issues to be discussed have broader relevance, we focus on factors which may be of particular importance for developing countries. The chapter proceeds as follows. Section 2 focuses on how to explain the existence of chronic inflation in a world of rational economic agents. Section 3 examines the main empirical regularities of inflation stabilization in chronic-inflation countries. Section 4 begins the theoretical discussion on exchange-rate-based stabilization by focusing on two key thctors: inflation inertia and lack of credibility. Section 5 continues the analysis of exchange-rate-based stabilization by highlighting the role of consumer durables, credit market segmentation, supply-side effects, and fiscal policy. Section 6 examines money-based stabilization. Section 7 discusses the causes and mechanics of balance-of-payments crises. Section 8 concludes.
2. Understanding chronic inflation For the purposes of this chapter, the rate of inflation in period t is defined as the proportional rate of growth of the price level (usually the consumer price index) from period t - l to period t. An essential ingredient in the definition of inflation is the "price level", that is to say, the relative price of goods in terms of money. Therefore, one cannot have inflation without money, and one cannot have inflation without goods. During high inflation - unless something very unusual is happening to the demand tot money or to the demand t0r or supply of goods - the supply of money also grows at a high rate. Hence, although inflation is a phenomenon that results from the interaction of monetary and real phenomena, monetary factors are likely to dominate. The situation, however, is not symmetric: it does not follow from the above observations that real phenomena, like output or domestic absorption, are largely independent of money. This would be true only under very special circumstances~ including (i) no nominal rigidities, and (ii) no effects of changes in nominal interest rates on consumption (see below). As the ensuing analysis will reveal, the channel from money to output is particularly relevant during stabilization programs. The empirical evidence is quite clear about the following two points: inflation is closely tracked by money supply, and inflation - particularly, changes in the rate of inflation - affects real variables. The latter represents a formidable challenge faced by stabilization programs. As will be argued below, however, the real effects of either inflation or stopping inflation are not necessarily rooted in fundamentals but may, to a large extent, be due to factors - like policy credibility - which suitable institutional/political arrangements may help to modify.
Ch. 24: lnflation Stabilization and BOP Crises in Developing Countries
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Under ideal circumstances, stopping inflation may be a socially painless process. Those circumstances, however, require appropriate fiscal adjustment. One serious difficulty in that respect is that there is more than one way to effect a fiscal adjustment, and each o f these ways has different implications for various groups in society. Consequently, it is not easy to reach wide consensus on any particular policy. This has two important consequences: (i) delayed stabilization, and (ii) adoption o f incomplete stabilization programs. Point (i) rationalizes inflation persistence, while point (ii) explains the prevalence of short-lived stabilization programs. But what sets inflation in motion in the first place? And, in particular, how can the phenomenon of high and persistent inflation be explained in a world of rational economic agents? 2 Although it would seem fair to say that the profession is still struggling to provide an answer to these questions and is far from reaching a consensus, the existing literature provides several useful insights. 2.1. Inflation as an optimal tax
One explanation, due to Phelps (1973), is that in a world o f distorting taxes, governments may find it optimal to depart from Friedman's (1969) celebrated optimum quantity of money rule, which calls for setting the nominal interest rate to zero. Phelps's (1973) result is quite intuitive. It follows from the observation that at Friedman's optimum quantity o f money rule, the marginal cost of the inflation tax (i.e., the nominal interest rate) is, by definition, nil. Thus, at the margin, increasing fiscal revenue thi'ough money creation has no cost. In contrast, the marginal benefit o f lowering any distorting tax is unambiguously positive. Therefore, starting from a zero nominal interest rate, it is welfare-improving to increase the inflation tax and lower any other distorting tax used to collect revenue. Thus, Phelps's result calls for a positive inflation tax 3. A key assumption in Phelps (1973) and the ensuing literature is that there is no fundamental difference between the inflation tax and other "conventional" taxes. It has long been recognized, however, that the costs of collection, enforcement, and evasion associated with the inflation tax are negligible compared to those o f other taxes. As Keynes (1924, p. 46) put it, inflationary finance "is the form o f taxation which the public finds hardest to evade and even the weakest Government can enforce, when it can enforce nothing else". An inefficient tax system may make it optimal to resort to 2 An alternative explanation tbr the existence of chronic inflation is simply that policymakers in these countries are systematically ignorant or incompetent. We find this explanation both implausible as a description of the real world and maintercsting from a theoretical point of view (given that we do not have good theories of "ignorance" or "incompetence"). Hence, the basic premise of this section is that chronic inflation is a phenomenon in search of a "rational" explanation. 3 A large literature has developed which analyzes the robustness of Phelps' (1973) findings [see the critical survey by Woodford (1990)]. Modeling money as an intermediate input, Kimbrough (1986) shows an interesting case in which Friedman's rule holds even though all available taxes arc distorting. Kimbrough's result, however, holds only under rather restrictive assumptions [see Woodford (1990), Guidotti and V6gh (1993), and Correia and Teles (t996)].
1538
G.A. Calvo and C.A. V~gh
the inflation tax even in cases in which Friedman's optimum quantity of money rule would otherwise be optimal [see Aizenman (1987) and V6gh (1989)]. The above arguments - valid as they may be as normative propositions - appear rather insufficient to rationalize chronic high inflation in developing countries. First, high inflation is a phenomenon that the society is typically trying to get rid of and, thus, could hardly be expected to be optimal in accord with Phelps's (1973) prescriptions. Second, while the evidence does show a long-run relationship between fiscal deficits and inflation [see, for example, Fischer, Sahay and V6gh (1997)], crosscountry econometric studies for developing countries have not found support for the main empirical implication of Phelps's (1973) hypothesis that there should be a positive correlation between the inflation tax and other conventional taxes [see Edwards and Tabellini (1991)]. In fact, the inflation tax appears to act more as a residual source of government revenue. Third, empirical estimates show that inflation is often larger than the level that maximizes revenue from inflation [see, for example, Easterly and Schmidt-Hebbel (1994)] 4. This implies that lower inflation and higher revenues from inflation could be simultaneously achieved - a glaring contradiction of Phelps's (1973) prescription. In sum, although the optimal taxation approach could explain perhaps the persistence of low levels of inflation, it would seem that other factors are needed to explain the actual pattern of inflation observed in chronic inflation countries. 2.2. Shocks and accommodation
While fiscal deficits may constitute the original sin that gives rise to inflation, the persistence of inflation may involve policy accommodation which transforms temporary domestic or external shocks into permanent increases in the inflation rate [see, in particular, Bruno and Fischer (1986) and Bruno (1993, Chapter 3)]. For example, consider a shock which calls for a real appreciation of the domestic currency. Authorities may dislike real appreciation because, say, it might be detrimental to exports. Therefore, incipient real appreciation would lead authorities to devalue. Since conditions after the shock require a more appreciated equilibrium real exchange rate, such a policy reaction cannot provide a definitive solution to the authorities' problem. After the first devaluation, domestic prices will rise to regain lost ground and attempt, once again, to climb a little higher (in order to generate the equilibrium real appreciation). Thus, another devaluation will eventually follow - and, of course~ prices will continue rising, setting in motion an inflationary process quite unrelated to fiscal revenue considerations/t la Phelps 5. 4 Although measuring the seigniorage-maximizinginflation rate is not without problems [see Easterty~ Mauro and Schmidt-Hebbel(1995)]. 5 Empirical evidence on the inflationary consequences of real exchange rate targeting in Brazil, Chile, and Colombiamay be found in Calvo, Reinhart and V6gh (1995). At a theoretical level,the inflationary conseqnences of real exchange rate targeting have been analyzed by Adams and Gros (1986), Lizondo
Ch. 24: Inflation Stabilization and BOP Crises in Deoeloping Countries
1539
More generally, monetary accommodation is typically reflected in the fact that key nominal variables - the rate of devaluation, the rate of monetary growth, and nominal wage growth - are linked to past inflation through accommodative policy rules and institutional arrangements such as backward-looking wage indexation. A greater degree of accommodation will be reflected in more inflation inertia. Bruno (1993) shows how nominal variables linked to past inflation may generate an autoregressive process for the inflation rate. Under these circumstances, temporary shocks to the inflation rate lead to permanent increases in the inflation rate. Bruno and Melnick (1994) further show that the higher is the degree of monetary accommodation, the higher is the new inflation plateau. While the process of shocks and accommodation captures some important elements of chronic inflation processes, it is less clear whether it can be argued that inflation is unduly high, in the sense of not being socially optimal. Presumably, policymakers accommodate shocks because not doing so would bring about undesirable consequences. In fact, one can show simple examples in which, in response to temporary shocks, it may be optimal to keep constant the real exchange rate by generating higher inflation [see Calvo, Reinhart and V6gh (1995)]. In the same vein, it is often argued that not accommodating expected inflation by printing money could bring about a severe liquidity crunch and thus lower output. Hence, this view leaves unresolved the issue of why society would periodically wish to get rid of inflation. 2.3.
Multiple equilibria
A more clear-cut case of socially suboptimal inflation is multiple equilibria. An example that we find particularly relevant [Calvo (1992)] is one in which there is a stock of public debt denominated in domestic currency, D. Let the one-period nominal interest rate be denoted by i. Then, next period's full service of the debt (i.e., principal plus interest) will be (1 + i)D. Let us choose units of measurement so that the present price level equals 1, and indicate the one-period expected inflation rate by ~e. Thus, if, say, the equilibrium real interest rate is zero, we have that i = sr e. Therefore, if actual inflation is zero, the real burden of servicing domestic debt would be (1 + ~°)D. This could very well be a large number. On the other hand, if the government fulfills the private sector's expectations and sets actual inflation equal to expected inflation, the real burden of the debt is just D. Thus, the temptation not to stop inflation in its tracks may be irresistible. A numerical example may help bringing the above point home. Suppose that the stock of debt is just 20 percent of GDP, and consider the case of Brazil (in the late 1980s) where the monthly rate of inflation was about 30 percent. If inflation is stopped but the private sector expected it to continue at previous levels, the nominal interest rate will remain at 30 percent per month. Therefore, just interest on the debt will (1991), Montiel and Ostry (1991), Calvo, Reinhart and V6gh (1995), Uribe (1995), and Lahiri (1997) See also Heymaimand Leijonhufvud (1995) for a more general analysis of these issues.
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G.A. Calvo and C.A. Vdgh
amount to 6 percent of GDP per month. This sizable cost of stopping inflation may, quite plausibly, lead authorities to relent by either keeping inflation at the original high levels, or adopting a very gradual stabilization program. 2.4. The "provinces" eJfect
Another explanation is what one might call the "provinces effect." Provinces, municipalities, state enterprises, etc., are entities that, at best, attempt to maximize social welfare by controlling a small set of levers. In particular, for these institutions, inflation is a p u n i c good, generated by total government expenditure, to which their individual expenditure adds an insignificant amount. Therefore, in choosing "provincial" expenditure, each entity will overlook the adverse welfare consequences of inflation on all other entities. Consequently, like with any other public good, too much inflation (i.e., too little price stability) will be generated 6. While this approach provides an attractive rationale for the existence of inflation, it still needs to explain cross-sectional variation in inflation outcomes. In other words, why should this effect be more relevant in, say, Argentina than in the USA? 2.5. Delayed stabilization
We now come to a more recent explanation for the persistence of high inflation; namely, the "war of attrition". This is an extremely useful idea formally developed by Alesina and Drazen (1991) 7. Suppose that inflation is unduly high for any of the reasons discussed above. Thus, policymakers would know that inflation could be brought under control if institutions were changed, or some appropriate transfers were put in place. So, why do they not act upon this knowledge and stop inflation in its tracks? Alesina and Drazen's (1991) explanation is that, since there is more than one way to get out of the inflation quagmire, and each way has different welfare implications across groups, it may be optimal for each group to wait for another group to give in. Eventually, the most "anxious" group will give in, adjustment will take place, and inflation will stop. In the meantime, inflation will remain high. Note, however, that Alesina and Drazen's (1991) model per se does not rationalize the advent of high inflation. Thus, Alesina and Drazen's model would need to be appended with some inflation-causing factor, or factors, in order to be able to track empirical evidence. An interestingapplication of the Alesina-Drazen tramework is the fbrmalizatlon of the idea that, in practice, things must get worse before they get better, in other words, oftentimes societies need to go through a truly devastating hyperinflationary ¢~ See Aizemnan (1992), Velasco (1993), Sanguinetti (1994), Mondino, Sturzenegger and Tommasi (1996), Zarazaga (1996), and Jones, Sanguinetti and Tomrnasi (1997). 7 Of course, the perception of inflation as the outcome of an unresolved distributive struggle is not new, and goes back to Hirsclmaan (1963) [see tteymann and Leijonhufvud (1995) fbr a detailed discussion]. It should also be noted that these last two factors - the "provinces" effect and delayed stabilization are part of a large, and growing, literature on the polical economy of reform [see Tommasi and Velasco (t996) for a survey].
Ch. 24: Inflation Stabilization and BOP Crises in Developing Countries
1541
outburst before a political consensus for a stabilization emerges. In the war-of-attrition framework just described, Drazen and Grilli (1993) show how a higher rate of inflation may be welfare-improving by bringing forward the expected time of resolution. The earlier resolution of the war of attrition may thus more than offset the short-term costs of higher inflation. 2.6. In conclusion
Based on the analysis thus far, we believe there is no single explanation for the phenomenon of chronic inflation. In fact, we would argue that, when taken together and in the proper dynamic sequence, the five factors discussed above probably explain the key features of processes of chronic inflation. At a fundamental level, governmems with inefficient tax-systems will always find it optimal to resort to some inflation (inflation as an optimal tax). The "provinces effect" is likely to add another - socially suboptimal - layer to the optimal public finance level of inflation. Once inflation has emerged, the economy as a whole naturally develops various indexation mechanisms (including accommodative policy rules) aimed at minimizing, for a given inflation rate, the real effects of inflation. Heavy indexation of the economy makes relative prices less responsive to various shocks, which sets the stage for temporary shocks to have permanent effects on the rate of inflation (the "shocks and accommodation" view). At this stage, the inflationary process will probably bear little relation to its original cause (the fiscal deficit), fueling the perception that putting the fiscal house in order may, after all, not help in dealing with the inflation problem. By now, the government's incentives to tackle the problem seriously are greatly diminished. After inflation has become entrenched in the public's mind, it may be too costly for the government not to validate the public's expectations (multiplicity of equilibria). In addition, and even if the government finally managed to credibly commit to a low level of inflation, political battles over the distribution of the fiscal adjustment needed to implement a stabilization may prolong chronic inflation (delayed stabilization). In the end, things may indeed need to get worse - by, say, having a hyperinflationary outburst - before they get better.
3o Evidence on the real effects of stabilization in chronic-inflation countries It is perhaps fair to say that until recently the dominant opinion in the professioit was that stopping inflation would bring about a sharp fall in output and domestic absorption. In fact, the notion that disinflation is contractionary is so entrenched m the literature that the question asked has typically been n o t / f b u t by how much outpul would fall in response to an anti-inflationary program. The best-known manifestation of this approach is the so-called "sacrifice ratio," or cumulative percent output loss per percentage point reduction in inflation. Okun (1978, p. 348), summarizing the findings of several papers on the USA, awaes that "the cost of a 1 point reductio~ in the basic inflation rate is 10 percem of a year's GNP, with a range of 6 percent
1542
G.A. Calc~oand C.A. V~gh
to 18 percent." Fischer (1986b) estimates a sacrifice ratio of 5 to 6 - at the lower end of the Okun range - for the USA for the period 1979-1986. Based on a review of fourteen episodes in eight countries, Gordon (1982) concludes that, by and large, contractionary policies - especially "cold turkey" policies - aimed at bringing down inflation have entailed large output costs. More recently, Ball (1994) examined 28 disinflation episodes in nine OECD countries using quarterly data and found that, with one exception, disinflation is always costly, with the sacrifice ratio ranging from 2.9 for Germany to 0.8 for France and the United Kingdom. The conventional view about the output costs of disinflation has also been taken to apply to open economies, indeed, in traditional open-economy models, disinflation is expected to cause an initial recession regardless of the nominal anchor which is used (the exchange rate or the money supply), as argued by Fischer (1986a). Therefore, the choice of the nominal anchor is based on a comparison of the sacrifice ratio involved in the two alternative strategies. By examining the sacrifice ratio under different parameter configurations, Fischer (1986a) concludes that the exchange rate should be the preferred nominal anchor. A similar conclusion is reached by Chadha, Masson and Meredith (1992). Based on simulations using MULTIMOD (a large-scale, multi-region macroeconometric model), they conclude that, for the United Kingdom, the sacrifice ratio is cut almost in half under an exchange-rate anchor compared to a money anchor. The intuition behind the view that "disinflation is always and everywhere contractionary" owes much to the unemployment-inflation trade-off, Phillips-curve literature. Particularly influential has been the staggered-contracting approach pioneered by Fischer (1977) and Taylor (1979, 1980). In these models, wage contracts are preset for a number of periods. Hence, credibility of the policy is not enough to generate a costless disinflation. Only a fully-credible gradual disinflation, which would take into account the structure of labor contracts, could reduce inflation with no output cost. For the case of the USA, Taylor (1983) concludes that it would take tbur years to disinflate from a rate of wage increase of 10 percent per year to 3 percent without creating unemployment. The conventional view has not gone unchallenged. In an influential paper, Sargent (1982) has argued that inflation was stopped virtually overnight with little or no output costs in the hyperinflations which developed in Austria, Germany, Poland, and Hungary in the aftermath of World War I. Based on this evidence, he argues that disinflation need not be contractionary if it is accompanied by a credible change in regime, which drastically alters the public's perceptions about future government policies. However, even if Sargent's (1982) conclusions regarding the output costs of stopping hyperinflation were accepted, such hyperinflations are seen as extreme episodes whose lessons are not necessarily applicable to much more mundane, garden~ variety inflations 8.
8 Notice that tile averagemonthly rate of inflation in these tbur episodes in the twelvemonths preceding stabilization ranged fiom a low of 33.3% in Hungary to a high of 455.1% in Gemaany[see V6gh (1992),
Ch. 24: Inflation Stabilization and BOP Crises in Deueloping Countries
1543
Perhaps a more fundamental challenge to the conventional view began to emerge in the late 1970s when major stabilization plans were implemented in the SouthernCone countries of Latin America (Argentina, Chile, and Uruguay). The cornerstone of these programs was the announcement of a predetermined path for the exchange rate, which involved setting a declining rate of devaluation 9. Contrary to Phillips-curve based predictions, the resulting decline in inflation was accompanied by a boom in consumption and no signs of higher unemployment. Moreover, the expansion took place in spite of a sharp appreciation of the real exchange rate. The contractionary costs associated with disinflation appeared only later in the programs, often before the programs finally collapsed. As it turned out, the puzzling phenomenon of an initial expansion followed by a later recession observed during the Southern-Cone "tablitas" appears to be a common pattern of exchange-rate-based stabilizations [see Kiguel and Liviatan (1992) and V6gh (1992)]. In sharp contrast, money-based stabilizations - which are much less common in chronic-inflation countries - have typically led to an initial recession, as the conventional view would have it. The remainder of this section takes a detailed look at some of the empirical evidence on these issues.
3.1. Exchange-rate-based stabilization." empirical regularities Table 1 lists twelve major exchange-rate-based stabilizations in chronic inflation countries in the last 35 years. These programs - which took place in Argentina, Brazil, Chile, Israel, Mexico, and Uruguay - have been studied in great detail and constitute the main motivation behind much of the literature in the area 10, 11. Based Table 2]. Garber (1982) and Wicker (1986) have both taken issue wit1 Sargent's (1982) conclusions. See also V~gh (1992) and Bruno (1993, Chapter 1). 9 In popular parlance, the announced schedule would be referred to as the "tablita" (Spanish for "little table"). In Chile, the exchange rate was eventually fixed. 10 Case studies include but are certainly not limited to the following. On the Argentine plans, see De Pablo (1974), Fernandez (1985), Canavese and Di Tdla (t988), Heymann (199l), and Dornbusch (1995). On the Brazilian plans, see Kafka (1967), Modiano (1988), and Cardoso (1991). On Chile, sec Corbo (1985) and Edwards and Cox Edwards (1991). On the Israeli plan, see Bruno (1993) and Bufman and Leiderman (1995). On Mexico, see Dornbuschand Werner(1994) and Santaella and Vela (1996). On the Uruguayan plans, see Finch (1979), Hanson and de Melo (1985), Viana (1990), and Talvi (1995). See also Foxlcy (1980), Diaz-Alejandro (1981), Ramos (1986), Corbo, De Melo and Tybout (1986), Kiguel and Liviatan (1989), Edwards (1991), and Ag6nor and Montiel (1996, Chapter 8). 11 The literature has often distinguished between "orthodox" programs (which do not rely on prices and/or wages controls) and "heterodox" programs (which do, and thus have "multiple nominal anchors") Of the programs listed in Table l, five were "orthodox" plans (the three "tablitas", the Argentine 1991 Convertibility plan, and the Uruguayan 1990 plan); the rest were "heterodox" plans. Except tbr tile behavior of inflation and domestic real interest rates (see below), the response of key macroeconomics variables to major stabilizationplans has been very similar, regardless of whether the plans were orthodox or heterodox. Hence, for the purposes of our analysis,not much will be made of this distinction.It should be noted, however, that the policy debate over the desirabilityof price and wage controls has been intensc: see, for instance, Dornbusch and Simonsen (1987), Dornbusch, Sturzenegger and Wolf (1990), Bruno (1993), Leidernlan (1993), and Meltzer (1994).
1544
G.A. C a l v o a n d C.A. V~gh
o
o
~
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~
~.~
o~ N ~..~ ~
~,
~
o
'
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~.~ .~
tg3 o
% ©
o o
o ~o
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~o
0.
(4.1 3)
et
The consumer's preferences are now given by: .f~/0 [v(cT) + u(c~)] exp(-fit)dt.
(4.14)
51 Note that, formally, lack of credibility is modeled as a temporary stabilization~ which explains the label "temporariness hypothesis", often used in the literature. 52 It should be noted, however, that the basic results of Section 4.1 hold true even under non-separability of real money balances (say, under the cash-in-advance specification explored below). Since we studied a permanent reduction in the devaluation rate, it would still be the case that consumption of traded goods remains unchanged under a cash-in-advance specification. s3 We adopt a cash-in-advance, flexible-prices specification to illustrate the essential mechanisms behind lack-of-credibility in the simplest possible model. The same results would obtain under a money-in-theo utility-function specification provided that the cross-derivative between consumption and real money balances is positive [see Calvo (1986)]. s4 For the derivation of the cash-in-advance constraint in continuous time, see Feenstra (1985)
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G.A. Catvo and C.A. V&gh
After substituting Equation (4.13) into (4.2), we obtain a lifetime constraint that involves only c~ and c~ as choice variables (and whose corresponding Lagrange multiplier will be denoted by ~). Maximization of Equation (4.14) subject to this lifetime budget constraint yields
v'(clF) = ~(1 + air),
(4.15)
u'(c~) = ~(1 + air).
(4.16)
el
The term involving the nominal interest rate i, 1 + ai, has a straightforward interpretation. Under the present assumptions, individuals must hold a stock of cash before making purchases. This means that, in addition to the market price of the good (unity for the tradable good and 1/e for the non-tradable good), the cost of the good is augmented by the opportunity cost of holding the needed real money balances. The eIfective price of consumption is thus 1 + ai for tradable goods and (1 + ai)/e for non-tradables. For the present discussion, we can simplify the supply side even further and assume that the domestic supplies of tradables and nontradables are fixed at y:r and yN, respectively. Then, by Equations (4.15) and (4.16), and home goods-market equilibrium (i.e., c~ = yN), it follows that
et
.'(cy)
u,(yN).
(4.17)
Hence, in equilibrium, the real exchange rate and consumption of tradable goods move in opposite direction, in other words, any shock that causes consumption of tradable goods to increase will also entail a real exchange rate appreciation (i.e., a fall in et). Consider now the effects of a non-credible stabilization program as described above (Figure 6). Since the representative individual expects a policy reversal at time T, it implies that he/she will expect the nominal interest rate i to be low from 0 to T, and high afterwards. Thus, by Equation (4.15), consumption of tradables will be high between 0 and T and low afterwards. Given that the present discounted value of c'r must satisfy the resource constraint (4.4), the path of consumption of tradable goods must look like that in Panel B of Figure 6. Intuitively, since the consumer expects the good to be cheaper between 0 and T than after T, he/she substitutes consumption away from the future (when consumption is expected to be relatively expensive) and towards the present (when consumption is cheaper). The current account deteriorates on impact and worsens throughout the stabilization as debt service increases (or net interest income falls), as illustrated in Panel C of Figure 6. Unlike tradable goods whose supply is rendered perfectly elastic by the rest of the world - non-tradable goods are in fixed supply. Hence, the excess demand for non-tradable goods between 0 and T will have to be met by a rise in their relative price (i.e., a fall in et), as follows ti-om Equation (4.17) (Panel D of Figure 6).
1571
Ch. 24." Inflation Stabilization and BOP Crises in Deueloping Countries B. Consumption of traded goods
A. Rate of devaluation
A
CT '~
H~ r
Li ~i
¸
rko+y T
i
L
0
T
time
time
D. Real exchange rate
C. Current account e
0
T
time
0
T
time
Fig. 6. Temporary stabilization. At the beginning of the program there is thus a boom in the consumption of tradables and a real appreciation, which is eventually followed by a contraction in the consumption of tradables and a real depreciation 55. Thus, this model displays two basic stylized facts that have accompanied exchange-rate-based stabilization programs, as argued in Section 3. It is also noteworthy that, unlike the previous explanation based on inflation inertia, this model does not rely on an initial fall in real interest rates. Hence, it could also explain the stylized facts even in programs in which only nominal, but not necessarily real, interest rates fall in the early stages 56. By introducing price stickiness into this model, Calvo and V~gh (1993) have shown that a temporary stabilization may account for other key stylized facts discussed in Section 3: (i) the joint occurrence of an output boom and a real exchange rate ss The real effects at time T will occur regardless of whether the program is actually abandonedor not, provided that if it is not abandoned, the program becomes fully credible at T. Formally,it can be shown that permanentchanges in the rate of devaluationare everywhere superneuh-al. 56 An interesting extension of the basic model is to assume that T is a stochastic variable, as in Calvo and Drazen (1998), which leads to richer dynamicpatterns for consumption.In particular, they show thal in the absence of state-contingentassets, consumptionrises on impact and continues to increase as long as the policy is in effect. See also Lahiri (1996a,b), Mendoza and Uribe (1996), and Venegas-Martinez (1997). Fm-thervariations of the basic model include Obstfeld (1985), who studies a gradual, tablita-type stabilization, and Talvi (1997), who analyzes tile endogenous impact of higher consumption on fiscal revenues.
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G.A. Calvo and C.A. VSgk
appreciation in the early stages of the program; (ii) a recession in the non-tradable goods sector (i.e., a fall in output below its full-employment level) which may take place before the program is discontinued; and (iii) inflation remaining above the rate o f devaluation until the time at which the program is expected to be discontinued 57. Hence, in this case, inflation persistence is not due to some ad-hoc backward-looking mechanism but rather to lack of policy credibility. The model thus suggests that the fact that inflation remains high is not prima-facie evidence o f stickiness in the rate of inflation 58. It should be noted that in the exercise illustrated in Figure 6, lack of credibility is socially costly, because a central planner would set consumption o f tradables constant and equal to rko + y rr, instead o f setting a path displaying the boom-bust pattern shown in Panel B of Figure 6. Hence, even though consumption rises as a noncredible exchange-rate-based stabilization program is put into effect, the stabilization still proves to be a socially costly process. This conclusion, though, depends critically on the fact that, in cash-in-advance models (with no labor-leisure choice), there are no benefits associated with a reduction in inflation (i.e., the real equilibriurn is independent of permanent changes in the inflation rate). In contrast, in transactioncosts models, lower inflation is beneficial because it frees time for productive activities. In such a set-up, a temporary stabilization may be welfare-improving if the benefits (in terms of freed resources) o f temporarily lower inflation more than offset the intertemporal distortion caused by a non-constant path o f the nominal interest rate [see Reinhart and V6gh (1995a)]. Hence, policymakers may still find it optimal to implement stabilizations plans that may not be fully credible, provided they command a "reasonable" level of credibility. Lack o f credibility thus provides a rich framework to explain the main stylized facts observed in exchange-rate-based disinflations. The most common criticism o f this type o f model is that it relies critically on intertemporal consumption substitution, which is believed to be small or not significantly different from zero. Reinhart and V6gh (1995a) have examined the empirical relevance o f the "temporariness" hypothesis, by estimating the intertemporal elasticity o f substitution for five chronic-inflation countries (Argentina, Brazil, Israel, Mexico, and Uruguay). Using these estimates, they compute the predicted increases in consumption for seven major stabilization plans
5'7 In this model, the domestic real interest rate falls on impact. As discussed in Section 3, howeve,, real interest rates have typically increased on impact in heterodox programs. This often reflects tight credit policy in the early stages of the programs. For instance, the Israeli 1985 plan had an explicit target tbr bank credit, which was to be achieved by a combination of higher reserves requirements and a higher discount rate [Barkai (1990)]. The idea is for money to act as an additional nominal anchor in the early stages of the plan. This could be modeled by assuming that the stock of money is predetermined at each point in time due to the presence of capital controls [Calvo and V~gh (1993)]. Ag6nor (1994) incorporates fiscal considerations into a model with imperfect capital mobility to address this issue, 58 Within this fiamework, Ghezzi (1996) has analyzed the important but still little understood question of when to abandon an initial peg and switch to a more flexible exchange rate regime (a common occurrence in practice, as argued in Section 3).
Ch. 24." Inflation Stabilization and BOP Crises in Developing Countries
1573
(the three Southern Cone tablitas, the Argentine 1985 Austral plan, the Brazilian 1986 Cruzado plan, the Israeli 1985 plan, and the Mexican 1987 plan) and compare them to the actual increases. They conclude that, in spite of low (but statistically significant) elasticities of substitution - ranging from 0.19 to 0.53 - this mechanism has a good explanatory power in four out of the seven episodes. It is the case, however, that nominal interest rates must fall substantially for this mechanism to be quantitatively important, which explains why the model appears to perform poorly for the SouthernCone tablitas 59. If anything, however, the estimates provided by Reinhart and V6gh (1995a) should probably be viewed as a lower bound for the importance of the "temporariness" hypothesis. The reason is that the model does not incorporate durable goods which, as argued in Section 3, appear to play a central role in the initial consumption boom. The presence of durable goods is likely to increase the quantitative importance of intertemporal substitution for two reasons. First, the introduction of durable goods might yield higher intertemporal elasticities of substitution, as found by Fauvel and Sampson (1991) for Canada. Second, in addition to intertemporal consumption substitution, durable goods introduce the possibility of intertemporal p r i c e substitution because goods can be stored [Calvo (1988)].
5. Exchange-rate-based stabilization lI: durable goods, credit, and wealth effects The explanations discussed in the previous section rely on what we view as two key characteristics of chronic inflation processes: inflation persistence and lack of credibility. There are other elements, however, which may have played an important role in stabilization plans in chronic inflation countries. We first discuss the role of durable goods consumption and credit market segmentation. We then turn to a discussion of wealth effects, which may result from either supply-side responses or fiscal policy. 5.1. Durable goods
As shown in Section 3, the consumption boom that characterizes exchange-rate-based stabilization programs has been particularly evident in the behavior of durable goods. This pattern of durable goods consumption has inspired an alternative explanation for the boom-bust cycle put forward by De Gregorio, Guidotti and V6gh (1998) (henceforth DGV). This hypothesis, which is unrelated to inflation inertia or lack 59 It is worth pointing out that trying to explain all of the observed consumption booms may bc misleading, as other factors such as lower international interest rates - may account for part of the boom.
1574
G.A. Calvo and C.A. V~gh
ci BI
IA!B ]
-4
-3
I
0,
DAD
-2
-1
0
1
time
Fig. 7. Consumption of durable goods.
of credibility, is capable of generating a boom-bust cycle even in a fully credible program. Suppose that there are transactions costs associated with the purchase of durable goods. This implies that individuals buy durable goods only at discrete intervals of time. in the aggregate, however, sales of durable goods are smooth over time since different individuals purchase durable goods at different points in time 6°. This is illustrated in Figure 7. There are four consumers (whose purchases of durable goods are represented by the squares labeled A, B, C, and D) who buy durable goods at different points in time (i.e., every four periods). Hence, before time 0, aggregate sales o f durables goods are constant. Consider now a stabilization plan implemented at time 0. Furthermore, suppose that there is a wealth effect associated with the stabilization (more on this below). Then, some consumers will be inclined to anticipate their purchase o f durable goods and perhaps buy a more expensive durable good. In other words, next year's new Honda becomes today's new Mercedes. In terms o f Figure 7, consumers B and C (who, in the absence of the stabilization plan, would have replaced the durable good at time t = 1 and t = 2, respectively) decide to buy the durable good at t = 0 (the picture abstracts from "size" effects). Consumer D, who just replaced his/her durable good at t = -1, also anticipates his/her purchase but to t = 1. In this simple example, there are no purchases of durables at t = 3 and t = 4, due to the initial bunching o f purchases at t = 0 and t = 1. The initial boom (in period 0) is thus followed by a bust in periods 2 and 3. Hence, this model is capable of accounting for the boom-bust cycle without resorting to inflation inertia or lack o f credibility 61. A key difference between this story and the previous two (inflation inertia and lack of credibility) lies in the policy implications. Under the temporariness (i.e., lack of credibility) hypothesis, the boom-bust cycle is a clear indication that policymakers have not done enough at the outset to convince the public that the program is 6o In the absence of transaction costs and given fliat durable goods depreciate over time consumers would find it optimal to buy in each period the amount of durable goods that they are planning to consume during that period. Buying a greater amount would imply a loss for next period. Technically, it is assumed that consumers follow (S,s) rules and choose optimally the trigger points. 61 Furthemore, if idiosyncratic shocks were introduced into the pictm'e, aggregate purchases of durable goods would eventually return to the pattern prevailing before the plan was implemelated.
Ch. 24: Inflation Stabilization and BOP Crises in Developing Countries
1575
sustainable over time. Hence, one would expect policymakers to worry when the initial boom emerges, and perhaps consider measures aimed at enhancing the program's credibility. In the same vein, inflation inertia (due to backward-looking indexation) also reflects some unresolved institutional problems which clearly endanger the whole stabilization strategy [as in the Chilean tablita; see Edwards and Cox Edwards (1991)]. In such a case, policymakers should try to cut the link between current and past inflation. In sharp contrast, the boom-bust cycle emphasized by DGV (1998) is a direct consequence of the policymakers' ability to implement a fully credible stabilization plan. The eventual consumption bust is the natural counterpart of the initial "bunching" in consumption, and any policy measures aimed at counteracting it are likely to be suboptimal. In DGV (1998), the wealth effect formally comes about because the fall in inflation leads to an increase in real money balances which, in turn, frees time spent in transacting to be used in productive activities. This channel is consistent with models (to be examined below) that emphasize supply-side effects of disinflation. The durablegoods consumption cycle described above, however, is independent of how this wealth effect comes about, and would also hold under alternative scenarios which may not involve, strictly speaking, a wealth effect. One such scenario, which we find particularly attractive and examine next, relies on the existence of credit market constraints. 5.2. Credit market segmentation
A boom in domestic absorption, which lies at the heart of the initial expansion and real exchange rate appreciation, can only happen if domestic residents are able to borrow from the rest of the world, or lower their holdings of foreign assets (i.e., capital repatriation). The examples examined so far rely on the fiction of a representative individual. There is thus no room for some individuals to borrow abroad and lend at home, while the rest engage in higher domestic borrowing and spending. Developing countries, however, are typically characterized by large segments of the population which do not have direct access to international borrowing and lending 62 A relevant scenario with two types of borrowers is one in which type l, say, has perfect access to international capital markets (like in the above examples), and type lI can only borrow at home. In addition, type-II individuals borrow in terms of domestic currency and are constrained to loan contracts displaying a constant nominal interest rate or a constant string of nominal installments. These are, admittedly, very special loans but their simplicity may make them cost-effective for medium-ticket durable consumption loans (i.e., television sets). In this setup, lower inflation/devaluation may induce a consumption boom, even though the program is fully credible. To see this, consider the realistic case in which borrowers pay back their debts in the form of a constant stream of nominal installments. ('~ See, lbr instance, Rojas-Suarez and Weisbrod (1995) who show that domestic bank lending is mote prevalent ha developingthan in developedcountries.
1576
G.A. Calvo and C.A. VOgh
6050if)
Ill
40-
/
E
~ i = 0.50 \ \
C
30-
\ \ \ \
I1)
\ \
20-
\\
10
\ --.
i = 0.20
"x l'l-I~ IiTH]
Y~ il i i i ii1~
0
..........
i illtlt
ii H i H lii
5
i = 0.03 ii H ii i I i iii
H i j ii i i i i i i i i i i H i i i i H i H i~ i i i i i ii i i Iii
10
i i1'1'1 i"i i
15
20 time
Fig. 8. Real instaUments for various nominal interest rates (percent per year, r = 0.03).
Thus, abstracting from credibility and country-risk problems, and asstmaing that the real (and nominal) international interest rate is r, the domestic nominal interest rate, i, will be equal to r + e. We now assume, for simplicity, that loans are given in perpetuity and that the rate of devaluation is expected to be constant. Hence, an individual who borrows a sum S will have to pay an installment equal to iS in perpetuity. Furthermore, normalizing the present price level, P0, to unity, and assuming a constant real exchange rate, we get that domestic inflation will also be equal to e. The real value of the installments is then given by (r-~e) S P~
(r+e) S exp(et) '
t~>0,
where t = 0 is the time at which the loan is granted. Consequently, the higher is the rate of devaluation, the higher will be the nominal interest rate, i, and thus the higher will be the real value of the first few installments. When inflation is high, the real value of the first few installments could be exorbitantly large, deterring credit. Figure 8 illustrates the effects of a lower inflation rate on the time path of real payments. In the three cases depicted, r = 0.03. The rate of devaluation takes three different values: 0, 0.17, and 0.47, so that i = 0.03, 0.20, and 0.50, respectively. The figure shows how the rate of inflation/devaluation can dramatically affect the time path of real payments. When i - 0.03, the path of real installments is flat. When i = 0.50, real installments in the early periods are the highest. Naturally, changes in the inflation
Ch. 24: Inflation Stabilization and BOP Crises in Deoeloping Countries
1577
(devaluation) rate do not affect the present discounted value of real installments as o f time 0, which equals S. Formally, note that
,f0 ~
i S exp(-rt) dt = S, exp(et)
so that changes in e affect real payments, but not the value o f the integral. Therefore, a substantially lower rate o f devaluation may make credit affordable to type-II individuals. The ensuing consumption boom puts upward pressure on retailing a highly labor-intensive activity - contributing to further real appreciation of the currency. Notice that the boom so generated may be socially desirable because it signifies an improvement in the credit market. Furthermore, if the newly available credit is directed towards durable goods consumption - as is likely to be the case purchases will fall later on during the program along the lines o f DGV (1998), contributing to an eventual downturn in economic activity. Hence, this type of scenario should be quite successful in explaining several stylized facts. Existence o f credit segmentation may also help to rationalize these phenomena even in the case in which there are no loan-contract constraints on type-II individuals. This would be so, for example, if type-I individuals take the implementation of the stabilization plan as a signal that the government is starting to "get its house in order". High inflation reflects the existence of tensions among policy objectives. Hence, until a stabilization program is implemented, foreign investors and type-! individuals may feel that placing their funds in the country in question exposes them to some kind of surprise taxation (particularly, if the funds are placed in highly visible domestic banks) 63. Thus, by assuaging the investors' fears, a stabilization program - which enjoys some but not necessarily complete credibility - may bring about a lowering of interest rates for type-II individuals, stimulating expenditure 64. 5.3. Supply-side effects'
All the explanations examined so far are based on demand-side considerations. This is perhaps only natural considering that much of the literature was inspired by the Southern-Cone tablitas of the late 1970s where, to most casual observers, the most striking fact was the increase in consumers' demand for goods (particularly durable goods). In more recent programs - such as Mexico 1987 and Argentina's 1991 Convertibility plan - it has been argued that monetary stabilization may have played an important role in unleashing supply-side responses in labor and investment [see 63 Domestic banks play a key role in making funds available to type-iI individuals, because their comparative advantage stems f?om their better knowledge of the local mmket. 64 Again, if some of the higher consumption falls on durable goods, a boom-bust pattern may emerge along the lines of DGV (1998). Moreover, there is, in principle, no reason in this example for social welfare to be negatively affected by the rise in consumption.
1578
G.A. Caluo and C.A. F~gh
Rebelo (1993), Roldos (1995, 1997), Uribe (1997a), and Lahiri (1996a, 1996b)] 6s. While the evidence presented in Section 3 casts some doubts on the general empirical relevance o f the investment channel, supply-side effects may well have contributed to the initial boom in some instances and thus deserve attention 66. The role o f capital accumulation in generating a steady rise in the relative price of non-tradables (i.e., a real exchange rate appreciation) is emphasized by Rebelo (1993) in the Portuguese context. I f reforms increase the economy's steady-state capital stock, then as the capital-labor ratio rises, the price o f the capital-intensive good (the tradable good) falls. Roldos (1995) and Uribe (1997a) present models in which domestic money is needed to buy (or install) capital goods, in the spirit o f Stockman (1981). As a result, inflation drives a wedge between the real return o f foreign assets and that o f domestic assets, which implies that the domestic capital stock is a decreasing function of the inflation rate. A reduction in the inflation rate thus leads to a higher desired capital stock, and hence to an expansion in aggregate demand and investment. Since the supply o f non-traded goods is assumed to be relatively inelastic in the short-run, the expansion in aggregate demand leads to an increase in the relative price o f non-traded goods (i.e., a real appreciation) and a trade account deficit. A somewhat unsatisfactory aspect o f some o f these models is that they rely on some features - gestation lags, adjustment costs, and particularly the assumption that the investment good be a "cash good" - which do not have a clear economic interpretation. In particular, there is no evidence that would seem to tie investment to the level o f cash transactions. From a qualitative point o f view, however, this assumption is not necessary for this type o f model to generate the effects just described, as made clear by Lahiri (1996a). In his model, the nominal interest rate introduces a distortion between consumption and leisure [as in Roldos (1997)]. When inflation falls, labor supply increases. This, in turn, leads to a rise in the desired capital stock and, hence, in investment. Rebelo and V6gh (1995), however, argue that the assumption that investment be in some way related to cash transactions is critical for the q u a n t i t a t i o e performance o f a broad class o f models 67. A more fundamental problem o f supply-side based models is that, given that the driving force behind such models are wealth effects, they cannot explain the late
o5 It should be noted that these programs were also accompanied by important structural reforms. As stressed in Section 3, it would be important - though far from trivial - to disentangle the effects of these reforms from those of the exchange rate-based stabilization per se. Clearly, we would not want to ascribe to monetary stabilization supply-side effects which may be due to real reforms. 66 There is little systematic evidence on labor supply responses in exchange rate-based stabilization. For some evidence on Mexico and Argentina, see Roldos (1995). 67 Similar results would obtain if money were used as a factor of production [see Uribe (i 997b)]. This channel could be rationalized by assuming - following the credit channel literature - that firms do not have access to capital markets and must resort to bank credit to finance the need for short-term working capital [see Bernanke and Gertler (1995) and, in the context of stabilization policies, the discussion below on Edwards and V6gh (1997)]. Bank-intermediated capital has been used to improve the quantitative predictions of some monetary models; see, for instance, Chaff, Jones and Manuelli (1995).
Ch. 24." Inflation Stabilization and BOP Crises in Developing Countries
1579
contraction observed in many programs. To this end, supply-side considerations must be supplemented by either lack of credibility or some nominal rigidity 68. To illustrate how supply-side effects may be combined with temporary stabilization to replicate some of the stylized facts of exchange-rate-based stabilizations, we proceed to analyze a simple model which incorporates a consumption-leisure choice in the same cash-inadvance specification presented in Section 4. Consider a one-good economy in which the representative household maximizes
f
(5.1)
o~ , ( c~ , gt ) exp(-fit) dt,
where g~ denotes leisure, subject to the lifetime constraint (which already incorporates the cash-in-advance constraint mt a C Tt ) 69.. ( 1 - g t + vt) e x p ( - r t ) d t =
bo+mo+
f0
cT(l +ai~) e x p ( - r t ) d t .
(5.2)
First-order conditions imply that (assuming fi = r): Ucv(cT, gt) = ~(1 + air),
(5.3)
uc~(cT,g,) (5.4)
ue(ctr,gt) - 1 + air,
where ~ is the Lagrange multiplier associated with constraint (5.2). Note how the nominal interest rate introduces a wedge between consumption and leisure, as Equation (5.4) makes clear. Taking into account the government's intertemporal budget constraint, it is easy to show that /co +
(1 - gt) exp(-rt) dt -
f0
cll exp(-rt) dr.
(5.5)
Two important observations, which illustrate some of the points noted above, follow easily from Equations (5.3), (5.4) and (5.5). First, a permanent reduction in the rate of devaluation, and thus in i, would cause a once-and-for all increase in consumption and output. Hence, this would explain the initial expansionary effects, but not the eventual contraction, observed in exchange-rate-based stabilizations. Second, if the utility function were separable (i.e., Ucle(') = 0), then a temporary (i.e., non-credible) stabilization of the type studied in Section 4.2 would lead to a consumption cycle similar to that illustrated in Panel B of Figure 6, but to a p e r m a n e n t increase in output 6s Sec Rcbeto and V6gh (1995), Lahiri (1996a,b), Mendoza and Uribc (1996), and Edwards and Vdgh (1997). (,9 The function u(.) is assumed to be sta-ictlyincreasing and strictly concave, and goods are assumed to be normal. The household's time endowment is taken to be one. Production is given by 1 - g.
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G.A. Calvo and C.A. V~gh
(i.e., a permanent fall in leisure). Hence, the output cycle cannot be rationalized with a separable utility function. Suppose now that the cross-derivative is negative; that is, UcTe(.) < 0. Then it follows from Equations (5.3) and (5.4) that at time T, consumption falls and leisure increases (i.e., work effort decreases). This piece of information, together with Equation (5.5), implies that at time 0 both consumption and labor effort rise. Hence, such a specification of preferences would lead to a boom-bust cycle in both consumption and output. An extension of this simple model - which would generate the boom-recession cycle in output even with separable preferences - is to introduce a costly banking system and assume that firms need bank credit to pay the wage bill [Edwards and V6gh (1997)]. In such a framework, a fall in consumption at time T leads to a fall in demand deposits and, hence, to a reduction in the supply of bank credit. The resulting "credit crunch" leads to higher lending rates, a lower level of bank credit, and a recession. More generally, the idea that the banking system may amplify both booms and busts through changes in bank credit appears quite attractive to explain the issues at hand, from both a theoretical and a quantitative point of view. 5.4~ Fiscal policy
The elimination of large public sector deficits is clearly a necessary condition for a lasting reduction in inflation. It is thus not surprising that programs in which the fiscal adjustment was either absent or short-lived got quickly off track, the best° known examples being the Argentine 1978 tablita and 1985 Austral plan, and the Brazilian 1986 Cruzado plano In successful plans (like the Israeli 1985 plan and the Argentine 1991 Convertibility plan), however, the fiscal adjustment has often been quite important. Such adjustment typically involves some combination of tax increases and cuts in government spending. While this is consistent with the initial fall in public consumption shown in the stabilization time profile (Figure 1, Panel D), the panel regressions reported in column (5) of Table 2 indicate that the coefficient on the "early" dummy is not significant. Still, there is an important branch of the literature which has focused on the expansionary effects of the fiscal policies that often accompany major exchange-ratebased stabilizations. In Helpman and Razin (1987), the reduction in the inflation tax generates a wealth effect due to the lack of Ricardian equivalence. In Drazen and Helpman (1988), the wealth effect comes through the expectation of a future reduction in government spending. Rebelo (1997) considers a scenario in which, in the absence of reforms, government expenditure increases, thus raising the present value of the resources needed to finance that spending. By bringing the fiscal situation in order, a stabilization leads to a wealth effect that may produce a boom even though taxes increase in the short run 7°. 70 See also Giavazzi aald Pagano (1990) and Bertola and Drazen (1993), who analyze the possibly expansionary role of fiscal policy in the stabilizations of Denmark in 1982 and Ireland in 1987.
Ch. 24:
Inflation Stabilization and BOP Crises in Developing Countries
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Rebelo and V6gh (1995) examine the effects of reductions in public consumption and increases in taxes in a two-sector, general equilibrium model. A fall in government consumption of tradable goods leads to a consumption boom and a real appreciation, but investment falls and the current account improves. A reduction in public consumption of non-tradables leads to a counterthctual real depreciation. Hence, cuts in fiscal expenditures seem to have limited power in explaining the stylized facts of exchange-rate-based stabilization. On the other hand, tax increases are recessionary. Finally, as with supply-side effects, fiscal-based explanations would not be able to generate an eventual recession, unless of course the policy is reversed.
5.5. A n d the w i n n e r is . . .
In the end, we would want to have a sense of whether a "winner" emerges among all the competing theories aimed at explaining the empirical regularities associated with exchange-rate-based stabilization which have been examined in the last two sections. To focus on essentials, the above models have abstracted from features which, while "realistic", would have diverted attention away from the key channels. While this is the logical route to follow, it makes a comparison across models difficult since not all channels are operating simultaneously. To remedy this, Rebelo and V6gh (1995) have evaluated, both qualitatively and quantitatively, all the hypotheses examined in the last two sections (except for the one related to durable goods) in a single, two-sector model with a labor-leisure choice and capital accumulation. They conclude that, qualitatively, the only two hypotheses that may explain a boom-recession cycle are lack of credibility and price or wage stickiness (inflation inertia). (In their model, an initial wealth effect stemming from supply-side etfects helps the inflation-inertia hypothesis in generating an initial consumption boom.) This is, of course, consistent with the evaluation that follows from the simpler models analyzed above. Quantitatively, however, Rebelo and V6gh (1995) find that supply-side effects seem critical to account for any sizeable fraction of the observed outcomes. Still, baseline parametrizations fall short of explaining the observed consumption booms and real appreciations. While there are configurations of the technology that are consistent with the data, there is still little information to assess whether these configurations are empirically plausible. Hence, further work on the structure of the supply-side and on the differential response of the tradable and non-tradable goods sector - which would allow us to build more refined quantitative models - would be particularly usefuk Finally, it is worth stressing the importance of disentangling the effects of stabilization from other reforms. The reason is that we may be asking models to explain "too much" in quantitative terms. In other words, the poor quantitative performance of a broad class of models found by Rebelo and V6gh (1995) may be due not to a lack of "good" models but rather to the fact that we may be trying to explain all of the observed consumption booms and real appreciation as a result of exchange-rate-based stabilizations.
G.A. Calvo and C.A. Vdgh
1582
6. Money-based stabilization The use of a money anchor to bring down chronic inflation has been much less common than the use of an exchange-rate anchor. Available evidence, however, suggests that these stabilizations have led to an initial recession, higher real interest rates, and real exchange rate appreciation (Section 3). As discussed earlier, the monetary regimes prevailing in these plans have borne little resemblance to the textbook case of a "pure" money anchor (i.e., a clean floating exchange rate), and have ranged from dirty floating to dual exchange rate systems (with a pegged commercial rate). Nonetheless, a common feature of such regimes is that money has been, albeit to varying degrees, the predominant nominal anchor. Therefore, to fix ideas, we will focus on the textbook case of a pure money anchor. We will then argue that, qualitatively, deviations from this benchmark would not alter the basic results.
6.1. A simple model From an analytical point of view, the two key elements needed to reproduce the stylized facts illustrated in Section 3 are (i) an interest-rate elastic money demand and (ii) sticky prices. We will introduce these two critical elements in the simplest possible way 71. We generate an interest-rate elastic money demand by introducing money in the utility function. We will therefore keep the utility function postulated in Equation (4.1), but assume that it takes a log-specification72: /o ~ [log(etT) + log(c~) + log(mt)] exp(-/3t) dt.
(6.1)
The household maximizes Equation (6. l) subject to (4.2). The first-order conditions imply that (again, assuming that fi = r)
c~ = etc~, 1
-
~.i,,
(6.2)
(6.3)
mt
where 2~ is the Lagrangean multiplier associated with lifetime constraint (4.2). On the supply side, we follow Calvo's (1983) staggered-prices formulation a continuous-time version of the overlapping-contracts models A la Fischer (1977) and Taylor (1979, 1980) - whereby the price level is sticky (i.e., it is a predetermined 71 In the absence of sticky prices, there would be no difference between money-based and exchange rate-based stabilization. The reason is that, under money-based stabilization, the real money supply could change at any point in time fllrough changes in the price level. 72 This model is a simplified version of Calvo and V6gh (1994c). See also Dornbusch (t980) and Fischer (1986a, 1988).
Ch. 24: Inflation Stabilization and BOP Crises"in Developing Countries
1583
variable at each instant in time), output o f home goods is demand-determined, and the rate of change in inflation is a negative function of excess aggregate demand: _
2c, - - i f (
CN
t -Y
-N
),
~ > 0.
(6.4)
Equation (6.4) can be derived by assuming that finns set prices in a non-synchronous manner taking into account the future path o f aggregate demand and the average price level prevailing in the economy [see Calvo (1983)]. At any point in time, only a small subset of firms can change their price. The price level is therefore a predetermined variable. If excess demand develops at some point in time, a small subset of firms will change their price and inflation rises. The subset o f firms that will change their price diminishes over time, which implies that inflation o f home goods falls over time. Hence, the change in the rate of inflation is negatively related to excess demand in the non-traded goods sector 73. As in the previous section, the interest parity condition implies that it = r + ft. Output of non-tradable goods is demand determined so that c N = yN for all t. The resource constraint continues to be given by Equation (4.4). To solve the model, we proceed in two stages, in the first stage, we show that the path of real money balances, mt (= Mt/EtPT*), is governed by an unstable differential equation. Note that - # , - et,
(6.5)
mt
where/~t(--- ~lJMt) denotes the rate of growth of the money supply, which is the policy instrument in a money-based stabilization. Substituting into Equation (6.5) the interest parity condition and first-order condition (6.3), we have that rht
1 - ~t + r - =--.
mt
(6.6)
,~,mt
Around the steady state, Equation (6.6) is an unstable differential equation 74. Hence, following an unanticipated and permanent reduction in/~t, mt adjusts instantaneously to its higher steady-state value. Hence, from Equation (6.3), it and thus ~t also adjust instantaneously to their lower steady-state values. 73 Note that in this formulation, the price level of home goods (,oN) is sticky (i.e., it is a predermined variable) but the inflation rate of non-tradable goods (~) is fully flexible (i.e., it is a forward-looking variable). It is also worth stressing that the formulation embedded in Equation (6.4) is not inconsistent with the one postulated in (4.8), where the level of the inflation rate of home goods depends positively on excess aggregate demand. The reason is that, in equilibrium, the staggered-prices formulation given by Equation (6.4) may still generate a Phillips-curve relation in which inflation is above its steady-state value when excess aggregate demand develops. 74 Notice that, as before, ~ is invariant to changes in ~t~.
t584
G.A. Cairo and C.A. V~gh
fi:=O !I
I
I ii
~H,I
A /
B/
gL
/
//
/
./ fi=O
/C
L
V
nss
n
Fig. 9. Money-based stabilization: dynamic system. Intuitively, if et fell on impact below ~t~, then mt would be increasing over time, which necessitates of a lower i (and lower e) to equilibrate the money market, which further increases mr, and so on. Thus, for mf not to diverge, the rate of depreciation, and thus the nominal interest rate, must adjust instantaneously. In the second stage, we form a dynamic system in real money balances in terms of home goods and the rate of inflation. To that effect, let us define real money balances in terms o f home goods; that is, nt = M / P N. Then, ht
- ~t, - st,.
(6.7)
/'/t
The second dynamic equation follows fiom Equation (6.4), taking into account Equation (6.2) and the fact that, from the definition o f mr and nz, et = nt/mt: ~, = ~@N _ n , c ] ) . mt
(6.8)
Equations (6.7) and (6.8) constitute a system o f differential equations in n and Jc, for given c T, m¢, and the policy variable gt. Around the steady state, the system is saddlepath stable, as it should be since n is the only predetermined variable (Figure 9 depicts the corresponding phase diagram)75. J5 Thc deteirninant associated with the linear approximation aroand the steady state is -~nssC~s/mss < O, which indicates that there is one positive and one negative root.
Ch. 24." Inflation Stabilization and BOP Crises in Developing Countries
1585
Suppose that initially (i.e., for t < 0), the public expects the rate of money growth to remain constant forever at #H. This initial steady state is characterized by C~lss = rko +yT, cN = •N, ess
-
fiN rko + yT '
(6.9) (6.10) (6.11)
&~ = /~n,
(6.12)
iss = r + #n, ~N nss r + #H'
(6.13)
d = F~ rss
(6.15)
(6.14)
where, as before, the domestic real interest rate, r °, is defined as i - ar. In terms of Figure 9, the initial steady state is at point A. Suppose now that, at time 0, policymakers announce a permanent and unanticipated reduction in the money growth rate from b~u to #L. The new steady state becomes point B where real money balances in terms of home goods are higher and inflation is lower. On impact, the system jumps from point A to point C and then travels along the saddle path towards its new steady state, point B. The path of the main variables is illustrated in Figure 10. Real money balances (in terms of home goods) increase gradually over time (Panel B). On impact, inflation falls below its new steady-state value and then increases over time (Panel C). The path of the real exchange rate (Panel E) follows from the fact that ~t/e~ = et - &. The real exchange rate must fall (i.e., appreciate) on impact to allow for a subsequent real exchange rate depreciation. The initial fall in the real exchange rate is effected through a fall in the nominal exchange rate, given that the price level of home goods is a predetermined variable. The path of consumption of home goods (Panel D) can be derived from Equation (6.2) and the path of the real exchange rate. Since consumption of traded goods does not change - and continues to be equal to permanent income of traded goods - consumption of home goods falls on impact as the relative price of home goods (i.e., the inverse of the real exchange rate) increases. It then increases as home goods become cheaper over time. The path of the domestic real interest rate (Panel F) follows from the definition r d = it - art. The domestic real interest rate increases on impact - as the inflation rate of home goods falls below the nominal interest rate - and then falls towards its unchanged steady state. What is the driving force behind these results? It is best to think about the equilibrium condition in the money market, which is given by: nl -
(6.16) it We think of the left-hand side of Equation (6.16) as the real money supply in terms of non-tradable goods and of the right-hand side as real money demand. Upon the
1586
G.A. Caluo and C.A. V@h B. Real money balances
A. Rate of monetary growth n
! /
/-
/
rlss
O
/~!
time
0
time
D. Consumption of home goods
C. Inflation rate cN~ ~N
g H
j_-
//
//
/
[ 0
time
0
E. Real exchange rate
time
F. Domestic real interest rate
e
ess' ,
f--
j_--
_-- . . . . . r
O
time
- - 4
--
O
7:~:
=
time
Fig. 10. Money-basedstabilization: time paths.
announcement of a lower rate of money growth, expected inflation and thus the nominat interest rate fall. For a given c N this increases real money demand in terms of home goods. Real money supply, n( = M/PN), however, cannot change on impact because neither Mt (a policy variable) nor pN (a predetermined variable) change. Hence, the fall in the nominal interest rate generates an incipient excess demand for real money balances. To equilibrate the money market, consumption of home goods (and thus output) needs to fall. For consumption of home goods to fall, home goods must become more expensive (i.e., the real exchange rate must fall). Since consumption of home goods must return to its initial steady-state, the domestic real interest rate must increase to induce a rising path of consumption of home goods.
Ch. 24.. Inflation Stabilization and BOP Crises in Developing Countries'
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This simple model thus reproduces the main stylized facts associated with moneybased stabilization illustrated in Section 3: an initial recession, a real exchange rate appreciation, and higher domestic real interest rates. The model does not exhibit, however, inflation persistence. To generate that result, we would need to introduce either inflation inertia or lack of credibility, along the lines of Section 4 [see Calvo and V6gh (1994c)]. The model also predicts no change in the trade and current account balances. As a first approximation, unchanged external accounts are not really at odds with the facts, as argued in Section 3. To generate an alternative prediction, we would need to get rid of the separability between c N and c T, which would considerably complicate the solution method because the system would cease to be block-recursive. 6.2. Extensions to other money-based regimes
Would the basic results change if we deviated from the extreme case of a pure money anchor (i.e., a clean floating)? The answer is no. Consider first a dirty floating, whereby the monetary authorities intervene in foreign exchange markets to influence the nominal exchange rate. In the example just analyzed, policymakers might want, on impact, to buy foreign exchange (i.e., accumulate international reserves) in exchange for domestic money to prevent the nominal exchange rate from appreciating too much. In terms of the model, the effects of intervention could be captured in a very simple way by assuming that, on impact, policymakers increase the nominal money supply so as to prevent the nominal exchange rate - and thus the real exchange rate - from appreciating (while still reducing the rate of growth to /~L)76. Since m(= M / E P r*) jumps immediately to its higher steady-state value, it follows that a higher M0 implies a higher E0 (relative to the case in which the nominal money supply is not changed on impact). In other words, the larger the initial increase in the level of the money supply, the smaller the initial nominal and real appreciation. In terms of Figure 9, this implies that, depending on how much the money supply increases, the system would jump on impact to a point along the saddle path between points C and B and then proceed towards point B. Qualitatively speaking, then, the impact efI~cts would be the same. Quantitatively, the initial real appreciation and thus the initial recession would be lessened. An extreme case of the "intervention" policy just described is a situation in which the initial level of the money supply is increased as much as needed for tile nominal exchange rate not to change on impact. In this case, the system would jump immediately to its new steady state (Point B in Figure 9). Neither the nominal nor the real exchange rate would change and the initial recession would be avoided altogether. This case is typically ruled out as implausible on the basis that, in practice, a large initial increase in the stock of money would likely be interpreted as an increase in the rate of growth of money, which would severely affect the credibility of the whole '16 Of course, this is not, strictly speaking, intervention since there is no accmnulation of reserves (I.e.. money is introduced through a "helicopter" drop).
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G.A. Caloo and C.A. FOgh
program. Still, it helps rationalizing the monetary authorities' incentives to intervene in foreign exchange markets. From a theoretical point of view, if policymakers can manipulate at will the initial money stock, then to generate a recession it would be necessary to introduce inflation inertia, along the lines analyzed in Section 3. Consider now the case in which there are capital controls. From a monetary point o f view, capital controls give policymakers the ability to have further control over the money supply (if they did not have it to begin with). In the case of a floating rate (or dirty floating), then it should make little difference. In fact, adding capital controls to the model above - by, say, assuming that the private sector's stock of net foreign assets is given and cannot change - would not change anything since the restriction would not be binding (recall that the current account is zero throughout the adjustment). Mixed regimes - such as dual exchange rates with a predetermined commercial rate - should also lead to an initial recession 77. The key is that the initial nominal money supply will still be a policy instrument (unlike a predetermined exchange rate regime in which the initial nominal money supply adjusts endogenously to satisfy real money demand). Hence, any disinflationary policy which leads to a reduction in expected inflation and thus to an increase in real money demand - will lead to a "liquidity crunch" and an initial recession. In sum, the effects o f disinflation in any monetary regime which involves significant capital controls should be qualitatively similar to those of a textbook money-based stabilization 78. 6.3. Money anchor versus exchange-rate anchor
As noted earlier, a money anchor is much less common than an exchange-rate anchor in stabilization programs in chronic-inflation countries. Although far from being a panacea for stopping inflation, policymakers' revealed preference for an exchange-rate anchor may be rationalized on a number of grounds. First, the behavior o f money velocity may be quite difficult to predict in the transition from high to low inflation, especially in chronic-inflation countries where the distinction between monies and quasi-monies is particularly blurred. Therefore, as a practical matter, it may be quite difficult to gauge how "tight" a given monetary rule is likely to be, and whether a "stable" relationship will hold in the aftermath o f disinflation. In contrast, using the exchange rate has the intrinsic advantage tha~, given the endogeneity o f the money supply, there is no need in principle to have any infolmation about money demand and velocity. 77 Models of dual exchange rates using tile samc type of framework emphasized thIoughout this chapter may be found in Obstfeld (1986a), Guidotti and V6gh (1992), and Calvo, Reinhart and V6gh (1995). 78 As noted in Section 3, there may be regimes with a clean floating which do not necessarily have a monetary aggregate as the main nominal mlchor [see Masson, Savastano and Sharma (1997) for a taxonomy of monetary regimes]. These regimes, however, have been rare in major stabilization programs. Still, V~gh (1997) shows an example in which nominal and real interest rate rules are equivalent to a money-based reghne.
Ch. 24: Inflation Stabilization and BOP Crises in Developing Countries'
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A second, and related, issue is that prolonged periods of high inflation lead to a high degree of dollarization of the economy 79. In such a situation, the "relevant" money supply (i.e., the one which affects inflation and real activity) is likely to include (the domestic-currency value of) foreign currency holdings and deposits. Since this component cannot be controlled by policymakers, a reduction in the domestic component of the money supply may have little effect on total liquidity, and, hence, on inflation. In effect, policy simulations of money-based disinflation for the case of Uruguay [Hoffmaister and V6gh (1996)] suggest that reducing the rate of growth of either M1 or M2 (which do not include foreign currency deposits) results in an extremely slow disinflation compared to using the exchange rate. In sharp contrast, if policymakers c o u l d (which, of course, they cannot) control M3 (M2 plus foreign currency deposits), then the speed of disinflation would be roughly the same as that achieved with an exchange-rate anchor. A third issue is that, by the simple virtue of being a price rather than a quantity, the exchange rate provides a much clearer signal to the public of the govermnent's intentions and actual actions than a money supply target. Thus, if the public's inflationary expectations are influenced to a large extent by the ability to easily track and continuously monitor the nominal anchor, the exchange rate has a natural advantage. Based on the considerations just discussed, it should not come as a surprise that, by and far, disinflation programs in chronic-inflation countries have relied on the exchange rate as the main nominal anchor (with the August 1990 Peruvian program being the most notable exception). Revealed preferences, therefore, would seem to support the view - with which we would certainly agree - that the exchange rate should be viewed as the more suitable nominal anchor in chronic-inflation countries. This is also consistent with Uribe's (1994) findings on the welfare costs of money-based versus exchange-rate-based stabilization. By performing different simulations of Calvo and V6gh's (1994c) model, he argues that exchange-rate-based stabilization is generally less costly, in terms of welfare, than money-based stabilization. An important caveat against the use of an exchange-rate anchor is in situations of very little credibility. For instance, in a countW in which a series of failed exchangerate-based stabilizations has led the public to identify the initial boom and current account deficit as a signal of an unsustainable stabilization effort, it would probably be wise to try to switch strategies and opt for a money anchor. The main reason is that theory suggests [see Calvo and V~gh (1994c)] that the effects of imperfect credibility differ drastically under each regime: lack of credibility is more disruptive under an exchange-rate anchor because it reduces the benefits (inflation falls by less) at the same time that it increases the size of the real dislocations (the boom-bust cycle becomes more pronounced). In contrast, in money-based stabilization, lack of credibility reduces
"19 See Calvo and V6gh (1992) and Savastano(1996).
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G.A. Calvo and C.A. V~gh
both the benefits (in terms of lower inflation) but also the initial recession. Hence, if the public is perceived as being highly skeptical, a money anchor may be less risky 8°.
7. Balance-of-payments crises As argued in Section 3, most exchange-rate-based stabilization programs end in balance-of-payments (BOP) crises (recall Table 1). These programs typically unleash dynamics - consumption booms, sustained real appreciation, current account deficits which call into question their sustainability 81. This, in turn, fuels speculation o f a possible abandonment o f the exchange-rate anchor. Once the survival of the program has been called into question, financial factors - such as a large stock o f shortterm debt - often aggravate the situation and may induce self-fulfilling crises. Whether balance-of-payment crises are ultimately caused by worsening fundamentals or self-fulfilling elements is a matter o f ongoing debate 82. But even if the ultimate demise o f the peg responds to some self-fulfilling event, it is still the case that fundamentals go a long way in determining the potential vulnerability of the system [Obstfeld and Rogoff (1995)]. Naturally, the potential for balance-of-payments crises is a more general issue and applies to any pegged exchange rate system, whether the peg is part of an explicit fifflation stabilization program or not (as most recently exemplified by the South East Asian crises of the second half o f 1997). However, even when the peg was not instituted as part o f a program, crises tend to occur as the economy enters a recession, following a prolonged boom in economic activity, credit expansions, real exchange rate appreciation, and current account deficits [Kaminsky and Reinhart (1995)] ~3. These are, of course, essentially the same dynamics as those generated by exchange-rate-based stabilizations (recall Figures 1 and 2). We suspect this is no coincidence, since it may be argued that pegged exchange rates keep inflation down (mainly by linking inflation of tradable goods to world inflation) at the expense o f an appreciating currency. We would thus suspect that some of the mechanisms discussed in Sections 4 and 5 may help in explaining the dynamics leading to balance-of-payment crises in general. This area has enjoyed a renaissance o f sorts in the aftermath o f the Mexican crisis. Researchers have gone back to gh'ugman's (1979) seminal paper on the mechanics of balance-of-payments crises and refined it in several important ways. Hence, after a brief discussion o f liquidity considerations, we take Krugwnan's (1979) model as the starting 80 Another argLmlent for a money anchor is given in Tornell and Velasco (1995), who ague thai a money anchor might provide more fiscal discipline. 81 Naturally, a fiscal disequilibrium will only reinforce the sense of tmsustainability. 82 See Krugman (1996) and the comments therein by Kehoe and Obstfeld 83 See also Bordo and Schwartz (1996), Dornbusch, Goldfajn and Valdes (1995), Eichengreen, Rose and Wyplosz (1995, 1996), Frankel and Rose (1996), Obstfeld (1995), and Sachs, Tornell and Velasco (1996). For an early analysis of devaluation crises, see Harberger (1981).
Ch. 24: Inflation Stabilization and BOP Crises in Developing Countries'
1591
point o f this section. We then discuss the notion of current account sustainability. Finally, we examine the role o f financial factors and lack o f credibility in precipitating balance-of-payment crises.
7.1. Liquidity Balance-of-payments crises take different forms. A common characteristic is that the government finds itself unable to comply with financial obligations. A n example is when the government is committed to keeping a fixed exchange rate (against, say, the US dollar), and the public wishes to exchange domestic money for dollars in an amount that exceeds the international reserves available for this operation. As a result, the government has to abandon its exchange-rate policy. However, the loss of reserves may occur for other reasons. For instance, reserves may be lost if the country has shortterm liabilities, bonds, that cannot be rolled over in the capital market, and exceed the level o f available international reserves 84. A BOP crisis does not necessarily involve insolvency, i.e., the country's inability to pay. As a general rule, countries undergoing BOP crises have ample resources to meet their financial obligations. In practice, the problem is that the country does not have enough financial assets that can be swiftly activated to meet its financial obligations. Thus, at the core o f a BOP crisis, there is typically a mismatch between the "liquidity" o f financial obligations and that of government financial assets. This mismatch is associated with another dominant characteristic of BOP crises, namely, they take place within a relatively short period of time (normally within a month), a fact that contributes to dramatize the event 85. The word "liquidity" in the above paragraph is just a signpost, not a definition. A good definition o f liquidity is highly elusive. We will discuss the concept in the context of a special environment. Let p(t, v) be the output price o f a given asset at time t, if the asset was placed on the market at time v ~< t. We say that the asset is perfectly liquid ifp(t, t) = p(t, v) for all t and v (and all states o f nature). In other words, an asset is perfectly liquid if there is no advantage to the seller in announcing his/her intention to sell in advance o f the actual transaction. Otherwise, ifp(t, t) < p(t, v), we say that the asset displays some illiquidity. The asset's degree of liquidity could be measured by
~(t, v)
p(t, t) p(t, v)"
Some simple models assume only two types o f assets, namely (i) perfectly liquid assets, and (ii) assets for which g(t, v) = 0 for all v < t; that is, assets that would have no 84 This was a key ingredient in the December 1994 balance of payments crisis in Mexico. See, for instance, Sachs, Tornell and Vetasco (1995) and Calvo and Mendoza (1996). ~5 This should not be interpreted to mean thai the ftmdamental reasons behind a balance of payments crisis are so short-lived - just the symptoms are.
G.A. Calvo and C.A. V~gh
1592
market value if they had to be liquidated in no time's notice 86. In this case, a BOP crisis would take place if the liabilities that the government is called upon to service at time t exceed the stock of liquid assets. In the models to be discussed here the liquidity properties of an asset are postulated, not explained.
7.2. The Krugman model This is an elegant model that captures the essential features mentioned above. We will present a version along the lines of the utility-based models used in previous sections of this chapter [see, for example, Calvo (1987) and Obstfeld (1986b)]. For present purposes, it is enough to assume that all goods are fully tradable, and that the representative individual is endowed with a constant flow of tradable goods per unit of time. Hence, using the same notation, lifetime utility is given by j0 °~ Iv(c/) + z(mt)] exp(-[Jt) dt.
(7.1)
As in Section 4, let the country be fully integrated in goods and capital markets and thus face a constant international price of the tradable good and a constant world real interest rate, r, which equals the subjective discount rate. The consumer's intertemporal budget constraint is thus given by Equation (4.2) (abstracting from the terms that relate to non-traded goods). The first-order conditions are therefore (4.5) and (4.7). Therefore, as before, Equation (4.5) implies that, along a perfect foresight equilibrium path, consumption is constant. The exchange rate is assumed to be fixed if there are enough reserves to sustain the value of the domestic currency (i.e., if reserves are above or at their "critical" level, which we assume to be zero). The exchange rate is sustained by intervening in the foreign exchange market. Thus, the fixed rate is abandoned once the public wants to turn domestic into foreign currency in an amount that exceeds the stock of liquid assets set aside for this operation. In Krugman (1979), these assets are identified with (international) reserves, R. While the fixed exchange rate regime lasts, perfect capital mobility implies that the domestic nominal interest rate equals the international one; that is, it = r. After the fixed rate is abandoned, the exchange rate is allowed to float, and exchange rate intervention is stopped. Hence, again denoting by et the rate of devaluation/inflation, perfect capital mobility implies that it = r + et. We assume that the central bank transfers net profits to the fiscal budget, which implies that the central bank's capital is constant. Hence, from the central bank's balance sheet, it follows that
X/It - E t k t + NbA~, 86 Lucas's (1990) cash-in-advancemodel has this characteristic.
(7.2)
Ch. 24: Inflation Stabilization and BOP Crises in Developing Countries
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where M is high-powered money, E is the nominal exchange rate (i.e., the price o f foreign exchange in terms o f domestic currency), R denotes reserves denominated in foreign exchange, and NDA stands for net domestic assets (i.e., domestic credit)87. The government's only source of expenditures are lump-sump transfers to households. It finances an exogenously given level of transfers, r, with central bank credit and proceeds from international reserves (which we assume earn the international interest rate, r). Thus, (7.3)
E t T = N b A I + rE~Rt.
Since during the fixed-rate period, it = r and hence, by Equation (4.7), the demand for money is constant (implying 3)/t = 0), we have: Rt = - ( r - rRt).
(7.4)
In other words, under fixed exchange rates the loss of international reserves equals the budget deficit (given by government transfers minus interest revenues from international reserves) 8s After fixed rates are abandoned, Rt = Rt - 0, and hence, by Equations (7.2) and (7.3), hh + elmt = T.
(7.5)
Assuming, for simplicity, that the individual initially holds no foreign assets or liabilities, it follows from first-order condition (4.5) and the lifetime constraint that crt = f r o + yT for all t. Hence, combining first-order conditions (4.5) and (4.7) and solving for mr, we get the familiar demand-for-money expression: mi - L(i, rRo +yT),
Li < 0,
Lrt~0+yv> 0.
For simplicity, we will tbcus on steady states (i.e., rh~ (7.5) and (7.6), we have that eL(r ~ e, f r o + S )
= r.
(7.6) 0). Thus, by Equations
(7,7)
The left-hand side of Equation (7.7) corresponds to revenue from the creation of money at steady state, while the right-hand side is the amount to be financed by these means. Clearly, Equation (7.7) will in general display multiple equilibria because the demand for money is negatively sloped with respect to e. However, since equilibrium 87 Equation (7.2) implicitly assLmaes with no loss of generality that the central bank does not monetize nominal capital gains on international reserves. Typically the central bank creates a fictitious non-monetary liability instead. ~8 It is assumed that the initial fiscal deficit is positive; i.e., r -- rRo > O.
G.A. Caluo and C.A. Vdgh
1594 IR R
AIR
i
0
\
T T* time
Fig. 11. Krugmat~ crisis.
multiplicity is not a key theme in Krugman (1979), we will assume that the economy settles down on the lowest rate o f devaluation consistent with Equation (7.7), which will be indicated by e*. Clearly, if r > 0, then after the currency peg is abandoned, the economy jumps to a higher inflation plateau, and stays there forever. It follows from expression (7.6) that at "switch point," i.e., the point in time T at which the currency peg is abandoned, the demandJbr money" collapses. This is a key feature of the model. Figure 11 depicts the central characteristics o f an equilibrium path for international reserves assuming that the government runs a fiscal deficit (i.e., ~ - r R o > 0) and that the nominal exchange rate is a continuous function o f time (this assumption will be rationalized later). From 0 to T reserves are driven by Equation (7.4). The system is abandoned at time T - and not when reserves reach zero because, as pointed out above, at switch time the demand for money takes a sudden dip equal to L(r, rRo + S ) - L ( r + e, fro + S ) = AR. Since the exchange rate is assumed not to jump at time T, it follows that the government suffers a loss of reserves equal to AR at time T. Clearly, switch point T is uniquely determined. Thus, the model is able to capture some of the main characteristics of a BOP crises outlined above. To close we will now briefly discuss the continuity of the exchange rate path E. In the first place, we will constrain E to be piece-wise continuous and everywhere righthand differentiable. These are technical assumptions which help to make sure that the problem is well-defined in a mathematical sense, and that irrelevant nonuniqueness situations are ruled out. Notice that jumps in E are not ruled out. Suppose that, contrary to our assumption above, E jumps at t ~> T, and let M[ be the left liminf of M at t. I f M t > 0, then the representative individual suffers a capital loss on account of his/her money holdings at time t. Thus, assuming that the demand for money goes to zero as the nominal interest rate diverges to plus infinity, a plausible regularity condition, it follows that it will never be optimal to undergo that kind of capital loss, which implies that M S = 0. Thus, if t > T, there will be an excess supply o f money at t, which is inconsistent with equilibrium. Suppose now that t = T, and,
Ch. 24:
Inflation Stabilization and BOP Crises in Developing Countries
1595
hence, the jump takes place exactly at switch point. Since M t- = 0, then the BOP crisis would have occurred before time T, which is a contradiction. This proves that E is continuous everywhere as assumed above. Finally, it is worth stressing that, since the interest rate on international reserves is equal to the international interest rate, the current account will be zero at all times. Notice, however, that external balance equilibrium does not prevent the occurrence of a BOP crisis. This is worth keeping in mind when we discuss the current account approach below. 7.3.
Krugman model: critique and extensions
We now extend the above model in several useful directions. 7.3.1. Bonds
Domestic debt (outside the central bank) may be introduced and thus account for an element that has played a prominent role recently. Thus, Equation (7.3) would become: E~r - N b A t + rEiRt - itD~ + L)t,
(7.8)
where D stands for instant-maturity government debt outside the central bank (in nominal terms). Actually, bond issuance could completely finance the deficit and, thus, NDAt = 0. Under those circumstances, no reserves would be lost during the fixed rates period. However, domestic debt D would increase without bound and, at some point, no more debt could be placed in the market becanse, otherwise, the government would not satisfy its intertemporal budget constraint. This is an interesting example because it is not unusual for governments to try to mask the fiscal disequilibrium in this manner. International reserves, which are closely watched by the private sector, would in this fashion be insulated from fiscal disequilibrium (prior to the BOP crisis). 7.3.2. Sterilization
The Krugman model assumes that the mo~etary authority makes no attempt at sterilizing the effects of reserve accumulation. Money supply is not a target. Thus, the model assumes that at switch time the monetary authority will not interfere with the run against domestic money and allow money supply to fall. In practice, money is not simply cash but includes bank deposits. Therefore, a fall in the money stock is normally associated with a cut in bank credit. This is a cause of trouble especially if the event is not fully anticipated 89. Of course, if bank credit is easily substitutable ~9 Under perfect foresight, everybody knows the exact timing of the BOP crisis. However, the model is easily and realistically extended to the case in which, say, the demand for money has a stochastic component and hence, there is always an element of surprise in the timing of the crisis [see Flood and Garber (1984)].
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G.A. Caluo and C.A. VOgh
for other type of credit, the bank credit crunch would cause no major disruption. But in LDCs this is not the case. Consequently, the central bank is induced to intervene through open market operations to provide the bank credit that would disappear as a result of the collapse in money demand at switch time. Flood, Garber and Kramer (1996) argue that there are several important instances in which central banks have attempted to fully sterilize the collapse in money demand. Interestingly, they show that this policy, if anticipated, would lead to a BOP crisis happening immediately, i.e., at time 0. There would be no fixed exchange rate period like the interval [0, T) in the Krugman model. The proof is straightforward. For money to remain constant (i.e., full sterilization) at time T, after-crisis inflation should equal inflation before crisis (which is zero). But this would imply that there is no crisis mid the exchange rate is constant forever. However, Equation (7.4) implies that sooner or later international reserves will be driven down to zero, and a crisis will take place, a contradiction. Thus, the only possibility left is for the crisis to take place at t - 0. In other words, the fixed-exchange-rate regime collapses upon the announcement. To have a more vivid picture of this instantaneous crisis, let us assume that at the time of the announcement real monetary balances fall short of total reserves (implying that an attack against domestic currency cannot be successful unless it triggers an expansion of domestic credit). The government's announcement is followed by an immediate attack on the domestic currency. Since authorities try to stabilize the stock of money, they intervene increasing domestic credit. Given that the demand for money has collapsed, the additional liquidity infusion only results in a loss of international reserves. This will continue until reserves are depleted. At that point authorities lose control of the exchange rate. Since there are no reserves, the exchange rate is the adjustment variable. Hence, the currency will devalue (the price level will rise) until real monetary balances are consistent with the equilibrium expected rate of devaluation/inflation. Anticipated sterilization although inconsistent with fixed rates under the above assumptions could, however, be sustained under other set of plausible assumptions. F'ood, Garber and Kramer (1996) and Kumhof (1997) show that fixed-rates-cumsterilization is consistent with a situation in which government bonds are imperfect substitute with international bonds. Calvo (1996b) shows that the same holds if it is costly to move in and out of money. 7.3.3. Interest rate policy
Another important aspect of reality which is not captured in Krugman's (1979) model is the possibility of the central bank actively defending the currency by raising shortterm interest rates. Sweden, for instance, raised short-term interest rates to around 500 percent per year in September 1992 to stave off a speculative attack [see, for instance, l~ugman (1996)]. More recently, both Hong Kong and Brazil sharply raised interest rates to defend their currencies in the aftermath of the South East Asian currency crisis. While not always successful, higher interest rates often buy time for
Ch. 24: inflation Stabilization and BOP Crises in Deoeloping Countries
1597
the government to try to uphold the system's credibility by adopting more fundamental measures. Lahiri and V6gh (1997) model interest rate policy by assuming that the government controls the interest rate on highly liquid government debt - along the lines of Calvo and V6gh (1995) - and show that by announcing a policy of higher interest rates in the event o f a crisis, the crisis may be postponed until international reserves actually reach zero (i.e., at a point like T* in Figure 11). At that point, the central bank is forced to float but there is no run (i.e., the money supply remains constant). This result of "crisis with no run" might also explain situations in which centTal banks abandon a peg with no dramatic loss of international reserves. 7.4. The current account approach
This approach has become popular after Mexico's 1994 BOP crisis since some observers have claimed that the crisis originated in the fact that Mexico was spending "beyond its means". In other words, Mexico's current account deficit was "too large." (It is worth recalling that in Krugman's model a BOP crisis could take place even though the current account deficit is nil to the extent that a payments crisis involves a liquidity shortage, irrespective of the country's overall solvency.) More generally and as shown in Section 3 - exchange-rate-based stabilizations typically lead to large current account deficits. Whether or not such imbalances are sustainable is thus a critical question when it comes to evaluate the reasons behind these programs' collapse. The sustainability literature is based on the budget-constraint equation for the conntry as a whole 9o. To illustrate, let us denote b y f and CAD net international debt and current account deficit (both as a share o f GDP), respectively. Then, ]; : CAm,
- 72;,
(7.9)
where t/is the rate o f growth o f output. Sustainability analysis focuses on steady states. Thus, settingj; = 0, the steady-state - sustainable - current account deficit satisfies CADss = r/fs~,
(7.10)
where, as in earlier sections, the subscript "ss" denotes "steady state". This equation establishes a relationship between steady-state debt and current account deficit. In the absence of growth (i.e., r/ = 0), then the sustainable current account deficit is necessarily equal to zero. In contrast, with positive growth a sustainable current accoum deficit is possible. This analysis is unable to give us a definite answer on C~4Dss until we pin down J;s. Recent experience shows that the capital market is reluctant to keep lending to LDCs exhibiting levels o f indebtedness that exceed 80 percent o f GDP [Williamson 90 For an elaboration, see Milesi-Ferretti and Razin (1996)~
G.A. Calvo and C.A. Vdgh
1598
(1993)]. Hence, this additional piece of information allows us to write the sustainability condition (7.10) as follows: CADss r/ when Hi >/-/.1, consumption goods which are relatively more price inelastic (have low e,.) should be taxed relatively heavily. To summarize, with additive separability, the general result is that tax rates depend on income elasticities, with necessities taxed more than luxuries. Moreover, the familiar
EV.. Chari and P..J. Kehoe
1682
intuition from partial equilibrium that goods with low price elasticities should be taxed heavily does not necessarily apply in a general equilibrium setting.
1.3. Uniform commodity taxation Here we set up and prove the classic result on uniform commodity taxation. This result specifies a set of conditions under which taxing all goods at the same rate is optimal. [See Atkinson and Stiglitz (1972).] Consider a utility function of the form
U(c, l) - W(G(c), l)
(1.24)
where c = ( c i , . . . , cn) and G is homothetic. Proposition 3. I f utility satisfies' condition (1.24) that is', utility is weakly separable across consumption goods and is homothetic in consumption then Ui/Uj = Fi/Fj for i = 1.... , n. That is, optimal commodity taxation is uniform in the sense that the Ramsey taxes satisfy "ci = ~- for i = 1 , . . . , n. Proof: Substituting the firm's first-order conditions (1.13) into the consumer's first-
order condition, we have that
u~ l+ri-
U1Fi
Thus ~ - rj if and only if ~ / F / - Uj/~. Note that a utility function which satisfies condition (1.24) satisfies
cj
cj
'~
J
-'~
for all
i, k.
(1.25)
J
To see this, notice that from homotheticity, it follows that
Ui(ac, l) Uk(ac, l)
Ui(c, l) gk(c, l)
or
[ Ui(c, 1) ] Ui(ac, l) = [ Uk(c,l)J Ul,(ac, l). Differentiating Equation (1.26) with respect to c~ and evaluating it at a gives (1.25).
(1.26) =
1
Ch. 26." Optimal Fiscal and Monetary Policy
1683
Consider next the first-order condition for ci from the Ramsey problem, namely,
where, again, ~ is the multiplier on the implementability constraint and 7 is the multiplier on the resource constraint. From Equation (1.25), we have that there is some constant A such that ~ / c / U / j = A ~ for all i. Using this fact and the form of utility function, we can rewrite Equation (1.27) as (1 + 3") WLGi + ,~ [AWl Gi + lW12Gi] ~ ~Fi.
(1.28)
Since Equation (1.28) holds for all i and j, Gi/Fi ~ Gj/Fj for all i a n d j and Ui _ WLG i _ W1Gi _ Uj
[] Note that the Ramsey allocations can be decentralized in many ways. For example, taxes on goods can all be set to an arbitrary constant, including zero, and remaining revenues raised by taxing labor income. Consider some generalizations of this proposition. Suppose that the utility function is homothetic and separable over a subgroup of goods, in the sense that the utility function can be written as
U ( c l , . . . , c¢,,~(ck+l . . . . . c,),l) with ~b homothetic. Then it is easy to show that the Ramsey taxes Tk+L = ... - r~. Next, if there is some untaxed income, then we need to modify Proposition 3. Suppose that we add to the model an endowment of good 1, Yl, which is not taxed. Then the implementability constraint becomes
Uici + U1l = Ulyl.
Z i
Then even if U satisfies U(0(Cl .... , c,0, l) with 0 homothetic, it is not true that optimal taxes are uniform (because of the extra terms Uljyl from the derivatives of Utyl). If we add the assumption that U is additively separable across c l , . . . , co, then the Ramsey taxes for goods 2 through n will be uniform, but not equal to the tax on good 1. Next, suppose that the tax system is incomplete in the sense that the government is restricted to setting the tax on good 1 to some fixed number, say, TI = 0. Then the Ramsey problem now must include the constraint U~ _ F1 in addition to the resource constraint and the implementability constraint. Then even if U satisfies condition (1.24), optimal commodity taxes on goods 2 through n are not
EE Chari and PJ. Kehoe
1684
necessarily uniform. Finally, in order to connect this result on uniform commodity taxation to some of the later results, suppose that the utility function is defined over an infinite sequence of consumption and labor goods as U(cl, c2 . . . . ,11,12,...). The assumption that the utility is of the form V(q~(Cl. . . . . ct .... ),11,12,...) with homothetic and separable between consumption and all labor goods 11,/2.... , together with the assumption that the utility function is additively separable across time with constant discount factor/3, restricts the utility function to the form ~ C 1 c7
]
I
1.4. Intermediate goods' Here we establish the classic intermediate-goods result for a simple example. (This example turns out to be useful when we study monetary economies.) Recall the standard result in public finance that under a wide variety of circumstances, an optimal tax system maintains aggregate production efficiency. [See Diamond and Mirrlees (1971).] In the context of an economy with multiple production sectors, transactions between firms can be taxed. Taxing such transactions distorts the relations between the marginal rate of transformation in one sector and the marginal rate of transformation in another sector and yields aggregate production inefficiency. In such a setup, the standard result on aggregate production efficiency immediately implies that taxing intermediate goods is not optimal. Consider an economy with three final goods .... private consumption x, government consumption g, and labor l - and an intermediate good z. The utility function is U(x, l)~ The technology set for producing the final consumption good using labor ll and the intermediate good is described by
f ( x , z , ll) 1; and for t = 0, W equals the right-hand side o f Equation (2.37) evaluated at t = 0 minus ~ ~ U~o(Rkok i i Here 3,i is the Lagrange multiplier on the ~i + Rbobo). implementability constraint for the consumer o f type i. The Ramsey problem is, then, to maximize O(3
~_~ fit W(CII, CZt, 11;, lat, "~'1,/~2) t-O subject to the resource constraint (2.34). The first-order conditions for this problem imply that
W~f--fiW~.~+l(1-6+Fkt~l)
for
i=1,2
and
t=0,1,2 .....
(2.38)
In a steady state, W , is a constant, and thus 1 = [3(1 - 6 + F~),
(2.39)
which as before implies that the steady-state tax on capital income is zero. This resait is due to Judd (1985). I Notice in (2.35) tile initial assets arc denoted k~ and b~, while in (2.8) they are denoted k I and b i. Throughout the chapter hi deterministic environments initial assets have a subscript 0, while in stochastic environments initial assets have a subscript -1. This unfortunate inconsistency stems from the traditiov, of using kt ~t to denote the capital choise in period t.
1695
Ch. 26." Optimal Fiscal and Monetary Policy
This result also holds when type-1 consumers are workers who supply labor, cannot save or borrow, and hold no initial capital, while type-2 consumers are capitalists who own all the capital but supply no labor. Then we replace Equation (2.35) for type-1 consumers with
U~tclt + Ul~llt = 0
for all t.
(2.40)
Notice that in the solution to the Ramsey problem, Equation (2.38) continues to hold for the capitalists, and thus the steady-state tax on capital income is zero. Notice also that this result shows that even if the Ramsey planner puts zero weight on the capitalists, taxing capital in the long run is still not optimal. The reason is that the cumulative distortion o f the capital taxes on intertemporal margins makes even the workers prefer the static distortion o f marginal rates that comes from labor income taxes. Now suppose that the tax system does not allow tax rates on either capital income or labor income to differ across consumer types. These restrictions on the tax system imply extra constraints on the allocations that can be achieved in a competitive equilibrium. Consider first the restriction that tax rates on capital income do not differ across consumers. To derive the restrictions that this adds to the Ramsey problem, consider the consumers' intertemporal first-order conditions, which can be written as U~t - fi [1 + (1 Uc(t+ 1
Ot+l)(Fktq
1 -
6)].
(2.41)
Since the right-hand side of Equation (2.41) does not vary with i, the restriction U]t =-U2'2t Uct+l
(2.42)
holds in any competitive equilibrium. Thus Equation (2.42) is an extra restriction that must be added to the Ramsey problem. Let/~ denote the Lagrange multiplier on (2.42). Defining
ui + J' where xt - (cmczt,ll~,12t,Zi,Z2), we can use the same argument as before, with V replacing W, to conclude that the steady-state tax on capital income is zero. Consider next the restriction that tax rates on labor income do not vary across consumers. Consider the consumers' first-order conditions for labor supply, which can be written as -
Uict Flit
1 -
Tt.
(2.43)
V.V. Chari and P..J Kehoe
L696
Since the right-hand side of Equation (2.43) does not vary with i, the restriction v,',
_ e,,,
Uclt U~t
(2.44)
F/2I
holds in any competitive equilibrium and thus must be added to the Ramsey problem. We proceed as before and, with no confusion, define
{ U/~U;2
Fm ~
(2.45)
where vt is the Lagrange multiplier on (2.44). A first-order condition lbr the Ramsey problem is
-~V/,+t + V+t, - / 3 G t , + l
[Fk,+~ + (l
-
O)].
In a steady state, this reduces to
vc! Clearly, unless Vk - 0, the steady-state tax on capital income is not zero. Inspection of Equation (2.45) shows that Vk = 0 if and only if Filt/F12t does not depend on k. Recall that the production function is separable between k and (11,I2) if Fm/F12t does not depend on k. Such separable production functions can be written in the form F(k, ll,/2) = F(k, H(ll,/2)) for some function H. [For some related discussion, see Stiglitz (1987).] This analysis of fiscal policy with restrictions suggests that other restrictions on tax rates may lead to nonzero taxation of capital income in a steady state even in a representative agent model. Consider an economy with identical consumers, and consider another restriction on the tax system, namely, that tax rates are equal for all periods. Suppose, for example, that taxes on capital income are restricted to being equal for all periods l?om period 1 onward, while labor tax rates are unrestricted. Using the consumer's first-order conditions, we see that G/
G,+I
-- /3 [1 q- (1 -- 0t+l)(~'kt+l
(2.46)
- ~)]
together with the restriction that 0t~ 1 = 01 for all t > 1, implies the following restriction across allocations: fiU~.f+~
1 F~-1,t+i~L-~5- L~-~c i - 1 F~,j--~
for all
t > 1.
(2.47)
The appropriate Ramsey problem, then, has constraints of the torm (2.47), as well as the imptementability constraint and the resource constraint. We leave it to the reader
Ch. 26:
Optimal Fiscal and Monetary Policy
1697
(as a difficult exercise) to show that, under suitable conditions, the optimal tax on capital income is positive, even in the steady state. The intuition is that with no such restrictions, it is optimal to front-load the capital income taxes by initially making them large and positive and eventually setting them to zero. When taxes are constant, it is optimal to try to balance these two opposing forces and make them somewhat positive tiu'oughout. The discussion of the extra constraints on the Ramsey problem implied by restrictions on the tax system suggests the following observation. Zero capital income taxation in the steady state is optimal if the extra constraints do not depend on the capital stock and is not optimal if these constraints depend on the capital stock (and, of course, are binding). Another possible restriction is that there is some upper bound on tax rates. Suppose, for example, that capital tax rates are at most 100 percent. Then in addition to satisfying the analogs of conditions (2.7) and (2.8), an allocation must satisl}¢ an extra condition to be part of a competitive equilibrium. Rewrite the analog of Equation (2.19) as Ucz - - ~ U c t ~ l ( ] .@ ( l - Ot.l l )(Fkl+l - c~)).
(2.48)
Then if an allocation satisfies Fk~+~ >~ 6 and
0t+ 1
(2.49)
~ 1, Equation (2.48) implies that
U~ >~ fiU~t+L.
(2.50)
Thus we can simply impose (2.50) as an extra constraint. With this constraint, for suitable restrictions on the utility function, the optimal policy is to set the tax rate to its upper bound for a finite number of periods. After that, the tax takes on an intermediate value for one period and is zero thereafter. 2.2.2. In a non-steady state
in the preceding subsection, we showed that in a variety of circumstances, in a steady state, the optimal tax on capital income is zero. Sometimes one can establish a much stronger result, namely, that optimal capital income taxes are close to zero after only a few periods. [See Chamley (1986), for example.] In this subsection, we show that for a commonly used class of utility functions, it is not optimal to distort the capital accumulation decision in period 1 or thereafter. The class of utility functions we consider are of ~/he fbrm cl-O U(c, l) = l-.S a + V(l).
(2.5l)
One might conjecture that if utility functions of this fbrm have the property that optimal capital income taxes are exactly zero after period 1, then for utility functions that are in
1698
V..g Chari a n d P..£ K e h o e
some sense close to these, keeping capital income tax rates close to zero after period 1 is also optimal. To motivate our result, we write the consumer's first-order condition for capital as qt+ 1 ( 1 -- 6 + F k t + 1 ) -- 1 = qt+ 10t v 1 ( F k t + 1 -- (~),
(2.52)
where qz+l - flUct+/Uc: is the Arrow-Debreu price of a unit of consumption in period t + 1 in units of consumption in period t. Now, in an undistorted equilibrium, the consumer's first-order condition has the same left-hand side as (2.52), but the righthand side equals zero. Thus the right-hand side of (2.52) measures the size of the wedge between the distorted and undistorted first-order conditions for capital accumulation in period t. We then have Proposition 7. For utility functions o f the form (2.51), it is not optimal to distort the capital accumulation decision at period 1 or thereafter. Namely, the optimal tax rate on capital income received in period t is zero f o r t ~ 2. Equivalently, qt+lOt+l(F~t+l-6) = 0 Jbr all
t ~> 1.
(2.53)
Proof: For t >~ 1, the first-order conditions for the Ramsey problem imply that Wct+ l . .
1 =/3~O
- 6 + Fk~+i),
(2.54)
where W is given in Equation (2.25). For t ~> 1, the consumer's first-order conditions for capital imply that Uct+l
1 =/3~
[1 + (1 - O,-,q)(Fk~+l - 6)1.
(2.55)
Now, for any utility function of the tbrm (2.51), we can easily show that
W.+l Uct+l We, U.
(2.56)
Substituting Equation (2.56) into (2.54) and subtracting the resulting equation from (2.55) gives the result. E] Proposition 7 implies that the tax rate on capital income received in period t is zero for t ~> 2 and is typically different from zero in period 1. In period 0, of course, the tax rate is fixed by assumption. This result is much stronger than the standard Chamley result, which refers to steady states, and the logic behind this result is actually more connected to the uniform tax results than to the rest of the Chamley-type results. To see this, suppose that the tax
Ch. 26." Optimal Fiscal and Monetary Policy
1699
system allows the government to levy only proportional taxes on consumption and labor income. For this tax system, the analog of the restriction o f the initial tax on capital income is that the initial consumption tax is given. Then with a utility function of the form (2.51), consumption taxes are constant in all periods except period 0. In a continuous-time version o f the deterministic model with instantaneous preferences given by Equation (2.51), Chamley (1986) shows that the tax rate on capital income is constant for a finite length o f time and is zero thereafter. The reason for Chamley's different result is that he imposes an exogenous upper bound on the tax rate on capital income. If we impose such an upper bound, the Ramsey problem must be amended to include an extra constraint to capture the restrictions imposed by this upper bound. (See the example in Subsection 2.2.1.) In the deterministic version of the model, with preferences given by Equation (2.51), the tax rate is constant at this upper bound for a finite number of periods, there is one period o f transition, and the tax rate is zero thereafter. In the stochastic version of the model, constraints o f this kind can also be imposed. One can derive an upper bound endogenously. Consider the following scenario. At the end of each period t, consumers can rent capital to firms for use in period t + 1 and pay taxes on the rental income from capital in period t + 1. Or consumers can choose to hide the capital, say, in their basements. If they hide it, the capital depreciates and is not available for use in t + 1. Thus, if they hide it, there is no capital income, and consumers pay zero capital taxes. 2.3. Cyclical properties 2.3.1. D e b t taxation as a shock absorber
In this subsection, we illustrate how state-contingent returns on debt can be used as a shock absorber in implementing optimal fiscal policy. One interpretation of state-contingent returns on debt is that the government issues debt with a non-statecontingent return and uses taxes or partial defaults to make the return state-contingent. We show that under reasonable assumptions, during periods o f high government expenditures such as wartime, the government partially defaults on debt, and during periods o f low government expenditures such as peacetime, it does not. Many o f the insights here are developed in Lucas and Stokey (1983) and Chaff et al. (1991). We illustrate this shock-absorber role in a version o f our model o f fiscal policy with no capital. Specifically, we assume that F ( k , 1,z) = zl, where z is a technology shock. The resource constraint is c(s t) + g ( s t ) ~" z ( s ' ) l(s')
and the consumer's first-order condition for labor supply is
ul(st) - I1 r(s')] z(~) gc(s t)
(2.57)
V.E Chari and P.J Kehoe
1700
The first-order condition tbr debt is
(2.58)
Uc(s t) = ~ [3~(St+l) Vc(st+l)Rb(xt+l)/[A(st). st+~
For convenience, let H(s t) - Uc(s t) c(s ~) + Ul(s t) l(st). Notice that the resource constraint and the consumer's first-order condition imply H(s t) = Uc(st)[v(st)z(s t) l(s t) g(st)]. Thus H(s t) is the value of the (primary) government surplus at s t in units of current marginal utility. The implementability constraint reduces to
~_~ fig(st) H(st) = U~(so) R0 b t.
(2.59)
t,S t
Expression (2.17) reduces to
(2.60) t=r+l
s t
Now imagine that the government promises a non-state-contingent (gross) rate of return on government debt R(s t 1) and then levies a state-contingent tax v(s t) on the gross return on government debt. That is, R and v satisfy
Rh(s ~) = [1 - V(s~)]/~(s~~ 1, there exist .functions ~, 7, and ~ such that the Ramsey consumption allocations, labor allocations, and labor tax rates can be written as
c(s') ' C'(gt,zD,
l(s') = 7(g,z,),
c(s') = ~(gt,z,).
Moreover, if b ~ = O, then c(so), l(so), and ~C(so) are given by these same functions. Proof: For t /> 1, substituting from the resource constraint for l(s t) into (2.65) gives one equation o f the form F ( c , g , z ; ) O = 0. Solving this gives the Ramsey consumption allocation as a function o f the current levels o f government consumption, the technology shock, and the multiplier. From the resource constraint and from Equation (2.57), we know that the labor allocation and the labor tax rate are a function of these same variables. For t = 0, the same procedure gives allocations and the labor tax rate in period 0 as a function of go, z0, and 5~. We can solve for )~ by substituting
V.V Chari and P.J. Kehoe
1702
the allocations into the implementability constraint (2.59). Clearly, for b-1 = 0, the first-order conditions for t = 0 are the same as the first-order conditions for t ~> 1. [] Proposition 8 says that the allocations and the labor tax rate depend only on the current realizations of the shocks and not separately on the entire history o f realizations. This proposition implies that labor tax rates inherit the stochastic properties of the underlying shocks. For example, if government consumption is i.i.d. and the technology shock is constant, then tax rates are i.i.d. (This result does not hold in general with capital.) If government consumption is persistent, then so are the tax rates. This result of standard neoclassical theory sharply contrasts with claims in the literature that optimal taxation requires labor tax rates to follow a random walk. [See Barro (1979), Mankiw (1987), and our discussion in the following subsection, 2.3.2.] To understand the nature of the Ramsey outcomes, we consider several examples. In all o f them, we let technology shocks be constant, so z(st) = 1 for all s t. We begin with a deterministic example that illustrates how Ramsey policies smooth distortions over time. E x a m p l e 1. Consider an economy that alternates between wartime and peacetime. Specifically, let gt = G for t even and gt = 0 for t odd. Let the initial indebtedness R l b 1 = 0. We will show that the government runs a deficit in wartime and then pays off the debt in the ensuing peacetime. Consider the first-order condition for the Ramsey problem in peacetime. Using the resource constraint, we have that (1 + )L)[U,.(O) + Ul(O)] + ,~c[U~.,..(O) + 2 U~.I(O)+ Ua(O)] - 0, where the partial derivatives are evaluated at gr = 0. By strict concavity, the second bracketed term is negative. Since the multiplier ~ is positive, the first term is positive. From Equation (2.57), we have that U~. + Uz -- rUc. Thus r(0) > 0. When we use Proposition 8, Equation (2.59) implies that H ( G ) +/3H(0) = 0, which can be rewrittetJ as
Uc( G)[ T( G) l(g ) - G] + [3U,,( O)['~( O) l(O)] - O. That is, the discoumed value of the government surplus is zero over the two-period cycle o f government consumption. Since the government runs a surplus in peacetime, it must run a deficit in wartime. Here the government sells debt b(G) - G -- r(G) l(G) in wartime and retires debt in the next peacetime. The gross return on the debt from wartime to peacetime is R ( G ) = Uc(G)/[3U~(O), and with our normalization, the tax rate on debt is always zero. E x a m p l e 2. Consider an economy that has recurrent wars with long periods of peace in between. Specifically let gt = G for t = 0, T, 2T, ..., and let gt - 0 otherwise. Let
1703
Ch. 26." Optimal Fiscal and Monetary Policy
the initial indebtedness R-lb-x = over each T-period cycle, that is,
0.
Again, by Proposition 8, the budget is balanced
G ( G ) [ T ( G ) l(G) - G] + fiU~(O)[v(O) l(O)] + . . . +/3 ~ 1U~(O)[r(O) l(O)] = O. Here, as in Example 1, the government runs a deficit in wartime and a constant surplus in peacetime. The war debt is slowly retired during the following T - 1 periods of peace. The government enters the next wartime with zero debt and restarts the cycle. Specifically, the government issues debt of level G - v(G) l(G) in wartime. In the first period of peacetime, the government sells
G(G) fiu.(o) ---
[G
r(G) I(G)].- r(0) l(0)
units of debt. In the second period, it sells
G(G)_ [G - ¢(G) I(G)]- -rS-°~l--(-°) r(0), l(0),
fi2 Uc(O)
and so on. Clearly, the debt is decreasing during peacetime. E x a m p l e 3. Here we will illustrate the shock-absorbing nature of optimal debt taxes. Let government spending follow a two-state Markov process with a symmetric transition matrix with positive persistence. The two states are g: = G and gt = 0. Let Jr=Prob{gt~l=GIg,-G}=Prob{g,+l=01g:
0} > 31
Therefbre, the probability of staying at the same state is greater than the probability of switching states. Let go =- G, and let the initial indebtedness R 1b 1 be positive. The government's period t budget constraint is
b(s t) = [1 - v(st)] R(s t-l) b(s: 1) + g ( s ' ) - T(s') l(s').
(2.66)
From Proposition 8, the allocations and the labor tax rates depend only on the current realization gt for t ~> 1. Under the Markov assumption, Equations (2.60) and (2.63) imply that the end-of-period debt b(s t) and the interest rate R(s t) depend only on the current realization gt. From Equation (2.66), we know that the tax rate on debt depends on the current and the previous realizations. Let b(g:), R(g:), and v(g~-i ,g~) denote the end-of-period debt, the gross interest rate, and the tax rate on debt, For a large class of economies, we can prove the following proposition: Proposition 9. Suppose that in the solution to the Ramsey problem, tt(0) > H(G) > O; that is, the value of government surpluses is larger in peacetime than in wartime, the
1704
V.Y Chari and P..Z Kehoe
government's debt is always positive, the marginal utility of consumption is greater in wartime U~(G) than in peacetime Uc(O), and both b(G) and b(O) are positive. Then v(0, G) > v(G, G) > 0 > v(O, 0) > v(G, 0).
(2.67)
That is, the debt tax rates' are most extreme in periods of' transition: they are highest in transitions from peacetime to wartime and lowest in transitions from wartime to peacetime. Furthermore, debt is taxed in wartime and subsidized in peacetime. R e m a r k : It is possible to show that the assumptions in this proposition are satisfied for a large class of economies if the initial debt is sufficiently large. Proof: Let V(G) and V(0) denote the expected present value of govermnent surpluses
when the economy is in state G and state 0, respectively. These surpluses are given by the left-hand side of Equation (2.61) multiplied by the marginal utility of consumption in that state, which can be written recursively as V(G) = H(G) + fi[jr V(G) + (1 - Jr) V(0)],
(2.68)
V(0) = H(0) +/3[¢cV(0) + (1 - Jr) V(G)].
(2.69)
Solving these, we obtain Jr)H(O)+(I-/3Jr)H(G) ~ D /3(1 - ¢v)H(G) + (1 -/3jr)H(O) V(0) = , D V(G) -
fi(1
(2.70) (2.71)
where D = (1 -/3go) 2 -/32(1 -Jr)2 > 0. From Equation (2.60), we obtain
/3[:rV(G) + (1 - Jr) V(0)] , U~.(G) /3[jrV(O) + (1 sD V(G)] b(0) = , uc(0) b(G) =
(2.72) (2.73)
and from Equation (2.63), we obtain gc(c) R(G) . . . . . . . . . . . . . . . . . . . , /3[~Uc(G) + (1 - :r) Uc(O)] ~
uc(o) R(0) =/3[jrUe(0) + (1 --Jr) U~.(G)]"
(2.74) (2.75)
Combining these, we obtain expressions for the befbre-tax obligations of the government: JrV(G) + (1 - aT) V(0) R(G) b(G) = JrUc(G) + (1 - :v) Uc(O)' R(O) b(O) --
Jr V(0) + (1 - Jr) V(G) Jr U~:(0) + (1 -- Jr) Uc(G)
(2.*76) (2./7)
Ch. 26.. OptimalFiscal and Monetary Policy
1705
Since H(G) < H(0), Equations (2.70) and (2.71) imply that V(G) < V(0). Using this result, :w > ½, and U~(0) < U~(G), we can see that Equations (2.76) and (2.77) imply that
R(G) b(G) < R(O) b(O).
(2.78)
We can rewrite Equation (2.61) as
V(&)
[1 - v(gt-a,gt)] R(&-I) b(&-l) - Uc(gt)"
(2.79)
The right-hand side of Equation (2.79) depends only on the cm'rent state; thus (2.78) implies that v(0, G) > v(G, G) and v(0, 0) > v(G, 0). To establish Equation (2.67), we need only show that v(G, G) > 0 > v(0, 0). But this follows from (2.64) and (2.'79), using V(G) < V(0) and Uc(0) < Uc(G). [] The intuition for these results is as follows. The Ramsey policy smooths labor tax rates across states. This smoothing implies that the government runs a smaller surplus in wartime than in peacetime. With persistence in the shocks, the expected present value of surpluses starting from tile next period is smaller if the economy is currently in wartime than if it is in peacetime. The end-of-period debt is, of course, just the expected present value of these surpluses. [See Equation (2.60).] Thus the end-of'period debt is smaller if tile economy is in wartime than if it is in peacetime, so
D(G) < b(O). As was shown in (2.78), R(G)b(G) < R(O)b(O). Thai is, the obligations of the government if there was war in the preceding period are smaller than if there was peace. Suppose the economy is currently in wartime, so gt = G. The current deficit and end-of-period debt are the same regardless of the history. Thus, if the inherited debt obligations are larger, the only way to meet the government budget constraint is to tax debt at a higher rate. So a transition from peacetime to wartime results in higher debt taxes than does a continuation of wartime. Similar intuition applies for the comparisons of transitions from wartime to peacetime with continuations of peacetime. 2.3.2. Tax-smoothing and incomplete markets Here we develop Barro's (1979) result on tax-smoothing and compare it to the work of Marcet et al. (1996) on optimal taxation with incomplete markets. In a wellknown paper, Barro (1979) analyzes a reduced-form model of optimal taxation. Ithis theoretical development, there is no uncertainty and the government chooses a sequence of tax rates ~t on income to maximize
t=Z-~o(1 + r ) "
1706
EV. Chari and P.J. Kehoe
where Yt is income in period t and r is an exogenously given interest rate, subject to budget constraints of the form bt = (1 + r ) b t
I + g t - "6Yt,
where g~ is government spending, b-t is given, and an appropriate boundedness condition on debt is imposed. These constraints are equivalent to the present value budget constraint Z "rty: _ gt t=0 (1 +r)t l=0 ( l + r ) t + b °
(2.80)
Barro shows that in this deterministic setup, optimal tax rates are constant. Barro goes on to assert that the analog of this result with uncertainty is that optimal taxes are a random walk. In an environment with uncertainty, the properties of optimal policy depend on the structure of asset markets. If asset markets are complete, the analogous present value budget constraint is
r(sgy(s') t~S t
1 +.(s,)
g(s') -
l,s t
i-+r( -Z +b°
With this asset structure, optimal tax rates are clearly constant across both time and states of nature. If asset markets are incomplete, then the analysis is much more complicated and depends on precise details of the incompleteness. Suppose, for example, that the only asset available to the government is non-state-contingent debt. The sequence of budget constraints for the government can be written as
b(s') = (l + ,) b(s' t) + g(s ~) _ r(~)y(s,) together with appropriate boundedness conditions on debt. Substituting the first-order conditions to the government's problem into the budget constraints and doing some manipulations yields
~ [ 3 ' '~(~' t s ) f--F
S t
U r ( s I ) y ( s t)
T(St)y(st)]
.... (1 +~)b(: ~).
U~(s")y(s9
(2.82)
The restriction that debt is not state-contingent is equivalent to the requirement that the left-hand side of Equation (2.82) is the same for any two states in period r in the sense that for all s r l,
t--r
u~(s~)y(s') [g(s~) - ~(s')y(~')l U~(s")y(s")
St
U~(s')y(s') I = r
s'
(2.83)
[g(,,)
Ur(s ~'/ ) y ( s
r(st)y(st)j F/
)
>
where s ~ = (s: ~,s.) and s"' - (s" 1,s~,) tbr all s,.,s.,. Analyzing an economy with incomplete markets requires imposing, in addition to (2.81), an infinite number of
Ch. 26:
Optimal Fiscal and Monetary Policy
1707
constraints of the form (2.83). This problem has not yet been solved. An open question is whether optimal tax rates in such an environment follow a random walk. In our general equilibrium setup, restrictions on government policy also impose extra constraints. Suppose that neither capital tax rates nor the return on debt can be made state-contingent. Then the additional restrictions that the allocation must satisfy so that we can construct a competitive equilibrium are given as follows. Substituting Equations (2.17) and (2.18) into the consumer's budget constraint yields, after some simplification,
t=v
(2.84)
xr
- {1 + [1 - O(s ~ l)][Fl~(s")- c5]} k(s '-1)
:Ro(s r l)b(s'
1),
where 0(s r 1) satisfies (2.85) Sr
The requirement that the debt be non-state-contingent is, then, simply the requirement that the left-hand side of Equation (2.84) with O(s ~ -l) substituted from (2.85) be the same for all st. Furthermore, we need to impose bounds on the absolute value of the debt to ensure that the problem is well posed. We then have that if an allocation satisfies these requirements, together with the resource constraint (2.7) and the implementability constraint (2.8), a competitive equilibrium can be constructed which satisfies the restriction that neither the capital tax rate nor the return on debt be state-contingent. Clearly, computing equilibria with non-state-contingent capital taxes and return on debt is a difficult exercise. Marcet et al. (1996) analyze an economy with incomplete markets but without capital. When government consumption is serially uncorrelated,, they find that the persistence properties of tax rates are a weighted average of a random walk and a serially uncorrelated process. They also find that the allocations are close to the complete markets allocations. They argue that their results partially affirm Barro's (1979) assertion. In Section 3, we consider a model in which debt is nominal and non-state-contingent. There we show that inflation can be used to make the real returns state.-contingent and that the Ramsey allocations are identical to those in an economy with real statecontingent debt. This result is reminiscent of our result that even if debt returns are not state-contingent, as long as capital tax rates are state-contingent, the Ramsey allocations are identical to those in an economy in which all instruments are statecontingent. This feature suggests that for actual economies, judging the extent of market incompleteness can be tricky.
1708
EV. Chari and P.J. Kehoe
2.3.3. A quantitative illustration
Here we consider a standard real business cycle model and use it to develop the quantitative features of optimal fiscal policy. We follow the development in Chari et al. (1994). In quantitative stochastic growth models, preferences are usually specified to be of the form el(c, l) -
[c 1 ~(L - l)y]v' ~p
where L is the endowment of labor. This class of preferences has been widely used in the literature [Kydland and Prescott (1982), Christiano and Eichenbaum (1992), Backus et al. (1992)]. The production technology is usually given by F ( k , l,z, t) = UZ(ePt+~l) 1 a.
Notice that the production technology has two kinds of labor-augmenting technological change. The variable p captures deterministic growth in this change. The variable z is a technology shock that follows a symmetric two-state Markov chain with states zt and zh and transition probabilities Prob(zt~l = zi I zt = zi) = ~ for i = l, h. Government consumption is given by gt = ge pt, where again p is the deterministic growth rate and g follows a symmetric two-state Markov chain with states gf and gh and transition probabilities Prob(gt+t = gi i gt = gi) = ~ for i = l,h. Notice that without shocks to technology or government consumption, the economy has a balanced growth path along which private consumption, capital, and government consumption grow at rate p and labor is constant. Zhu (1992) shows that in economies of this form, setting capital income tax rates to be identically zero is not optimal. We ask whether capital tax rates are quantitatively quite different from zero. Recall from the proof of Proposition 5 that certain policies are uniquely determined by the theory, while others are not. Specifically, the labor tax rate is determined, while the state-by-state capital tax rate and return on debt are not. From Equation (2.19), however, we know that the value of revenues fi'om capital income taxation in period t + 1 in terms of the period-t good is uniquely determined. To turn this variabie into a tax rate, consider the ratio of the value of these revenues to the value of capital income, namely;
O~(s ,) = )2 q(s~'t) O(s~l)[F/,(s~) 6] q(s'+l)[Fk(s t+l) - 6] ~
(2.86)
where q(s t*l ) = [3[.1(stt i ] s t) U~.(st~l)/Uc(s i) is the price of a unit of consumption at state s t+l in units of consumption at s t. We refer to Oe(s ~) as the ex ante tax rate on capital income.
Ch. 26:
Optimal Fiscal and Monetary Policy
1709
Table 1 Parameter values for two models" Model
Parameters and values
Baseline model
Preferences
y - 0.80
Technology
a = 0.34
~p- 0 6 = 0.08
fi - 0.97 p = 0.016
Gover,tment consumption
g/= 350
g h - 402
¢ = 0.95
Technology shock
z l - 0.04
z h = 0.04
~ = 0.91
L = 5475
Markov chains for
High risk aversion model
Preferences
q~= -8
a Source: Chari et al. (1994). Next, in defining the last variable that is uniquely determined by the theory, it is useful to proceed as follows. Imagine that the government promises a non-statecontingent rate of return on government debt ?(s t ~) and levies a state-contingent tax v(s ~) on interest payments from government debt. That is, ? and v satisfy
Rh(s t) = 1 + ?(s ~ L)[1 - v(st)],
(2.87)
and ~ q ( s t ) v ( s t) = 0, where q(s t) is the price of a unit of consumption at state s ¢ in units of consumption at state s t-l. Thus ?(s t 1 ) is the equilibrium rate of return on a unit purchased in period t - 1 at s t 1, which yields a non-state-contingentreturn ?(s t` l) at all states s t. It is clear from (2.21) that the theory pins down Rl,(s t) k(s f 1) ~ Rb(S t) b(s t 1). Given our definition of v, it is also clear that the theory pins down the sum of the tax revenues from capital income and the interest on debt, which is given by
O(s t) [Ft(s t) - 6]/~(s ~ 1)+ v(s')~(s' ')b(s'-l).
(2.88)
We transform these revenues into a rate by dividing by the income from capital and debt to obtain the tax rate on private assets, given by
rl(st)= O(s')[l~'k(st)
6]k(st ~)+ v(st)~(s t L)b(s' ~) [Fk(s t) - 6] k(s t 1) + ?(s t l)b(s, 1)
(2.89)
We consider two parametrizations of this model. (See Table 1.) Our baseline model has ~p = 0 and thus has logarithmic preferences. Our high risk aversion model has ~p = - 8 . The remaining parameters of preferences and the parameters tbr technology are those used by Chari et al. (1994). We choose the three parameters of the Markov chain for government consumption to match three statistics of the postwar US data:
ggChari and R J K e h o e
1710 Table 2 Properties of the fiscal policy modelsa
Percentage in models
Income tax rates
Labor Mean
Baseline
High risk aversion
23.87
20.69
Standard deviation
0.10
0.04
Autocorrelation
0.80
0.85
Capital
Mean
0.00
0.06
Standard deviation
0.00
4.06
Autocorrelation
0.83
Private assets
Mean
1.10
0.88
Standard deviation
53.86
78.56
Autocorrelation
-0.01
0.02
a All statistics are based on 400 simulated observations. The means and standard deviations are in percentage terms. For the US economy,the tax rates are constructed as described by Chari et al. (1994). For the baseline model, the capital tax rate is zero; thus, its autocorrelationis not defined. the average value of the ratio of government consumption to output, the variance of the detrended log of government consumption, and the serial autocorrelation of the detrended log of government consumption. We construct the Markov chain tbr the technology parameters by setting the mean of the technology shock equal to zero, and we use Prescott's (1986) statistics on the variance and serial correlation of the technology shock to determine the other two parameters. For each setting of the parameter values, we simulate the Ramsey equilibrium for our economy, starting from the steady state of the deterministic versions of our models. In Table 2, we report some of the resulting properties of the fiscal variables in our models. In the baseline model, the tax rate on labor income fluctuates very little. For example, i f the labor tax rate were approximately normally distributed, then 95 percent of the time, the tax rate would fluctuate between 23.67 percent and 24.07 percent. The tax on capital income is zero. This is to be expected because with ~p = 0, the utility function is separable between consumption and leisure and is homothetic in consumption, and the utility function thus satisfies the conditions discussed in Subsection 2.2.2. In the baseline model, the tax on private assets has a large standard deviation. Intuitively, we know that the tax on private asset income acts as a shock absorber. The optimal tax rate on labor does not respond much to shocks to the economy. The government smooths
Ch. 26:
Optimal Fiscal and Monetary Policy
1711
labor tax rates by appropriately adjusting the tax on private assets in response to shocks. This variability of the tax on private assets does not distort capital accumulation, since what matters for the capital accumulation decision is the ex ante tax rate on capital income. This can be seen by manipulating the first-order condition for capital accumulation. In Table 2, we also report some properties of the fiscal policy variables for the high risk aversion model. Here, too, the tax rate on labor income fluctuates very little. The tax rate on capital income has a mean o f - 0 . 0 6 percent and a standard deviation of 4.06 percent so that the tax rate is close to zero. We find this feature interesting because it suggests that, for the class of utility functions commonly used in the literature, not taxing capital income is optimal. Here, as in the baseline model, we find that the standard deviation of the tax rate on the income from private assets is large. 2.4. Other environments' 2.4.1. Endogenous growth models' Thus far, we have considered fiscal policy in models in which the growth rate of the economy is exogenously given. We turn now to models in which this growth rate is determined by the decisions of agents. Our discussion is restricted to a version of the model described in Lucas (1990). Analysis of optimal policy in this model leads to a remarkable result: Along a balanced growth path, all taxes are zero. Bull (1992) and Jones et al. (1997) discuss extensions to a larger class of models. Consider a deterministic, infinite-horizon model in which the technology for producing goods is given by a constant returns to scale production function F(kl, h~lj~), where kt denotes the physical capital stock in period t, ht denotes the human capital stock in period t, and lli denotes labor input to goods production in period t. Human capital investment in period t is given by htG(12t), where 12t denotes labor input into human capital accumulation and G is an increasing concave function. The resource constraints for this economy are ct + g + kt+l = F(kl, htllt) + (1 - Ok) kt
(2.90)
hx+L = htG(lzt) + (1 - 6h) h,~
(2.91)
and
where et is private consumption, g is exogenously given government consumption, and 6/, and Oh are depreciation rates on physical and human capital, respectively. The consumer's preferences are given by oo
~
[3' c'] ° v(lt, + let)~(1 - a),
t-O
where v is a decreasing convex function. Government consumption is financed by proportional taxes on the income from labor and capital in the goods production sector
1712
EV. Chari and RJ Kehoe
and by debt. Let rt and 0t denote the tax rates on the income from labor and capital. Government debt has a one-period maturity. Let bt+l denote the number of units of debt issued in period t and Rbtbt denote the payoff in period t. The consumer's budget constraint is ct + k~+j + bt+l ~< (1 - rt) wthtllt + Rekt + Rbtbt,
(2.92)
Rkt - 1 + ( 1 - Ot)(rt - c5) is the gross return on capital after taxes and depreciation and 1"1 and wt are the before-tax returns on capital and labor. Note that human capital accumulation is a nonmarket activity. The consumer's problem is to choose sequences of consumption, labor, physical and human capital, and debt holdings to maximize utility subject to (2.91) and (2.92). We assume that consumer debt holdings are bounded above and below by some arbitrarily large constants. Competitive pricir~ ensures that the returns to factor inputs equal thei,~ marginal pre~ducts, nameIy, tha~ where
rl = f k ( k . h~l~),
(2.93)
wt = Ft(kt, hfllt).
(2,94)
We let xt = (ct, lit, 12t, kt, kt, bt) denote an allocation for consumers in period t and let x = (st) denote an allocation for all t. The government's budget constraint is b,+ l = Rbtb~ + g - rtwthtll~ - Ot(r~ - (3)k,
(2.95)
We let zct = (rt, 0t) denote the goverrmaent policy at period t and let s~ ~- (zc~) denote the infinite sequence of policies. '1"he initial stock of debt, b 1, and the initial stock of capital, k-l, are given. A competitive equilibrimn is defined in the usual way. We have the following proposition. Proposition lO. The consumption allocation, the labor allocation, the physical and human capital allocations, the capital tax rate, and the return on debt in period 0 in a competitive equilibrium satisfy (2.90), (2.91), and O(3 "~ [3 [ ct
Uct = Ao,
(2.96)
t-0
where
A0 -- C:~.0{[I + (1 -00)(~0 - 6)1 l,o +R~0b0}
U~o [l~0 + 1 - 6h + (~(l~0)] G'(12o)
j
Furthermore, given any allocations and period-O policies' that satisfy (2.90), (2.91Z (2.96), and
Ul,
[3U/~.!
hLG'(12~) - ht+l G'(lzt+l) [ 1 -
C~h -I-
G(12, l )] +
[3U~z+l ll~+l ht+~ '
(2.97)
we can construct policies, prices, and debt holdings whick, together wztk the given allocations and period-O policies, constitute a competitive equilibrium.
Ch. 26:
Optimal tqscal and Monetary Policy
1713
Proof: The procedure we use to derive the implementability constraint is to express the consumer budget constraint in period-0 form with the prices substituted out. Recall that in the model with exogenous growth, this procedul"e implied that the capital stock from period 1 onward did not appear in the implementability constraint. It turns out that when human capital is accumulable, human capital does not appear in the implementability constraint from period 1 onward either. The consumer's first-order conditions imply that (2.98) (2.99)
-[YU1, = )~t(1 - rt)wtht, -ill U# -= ~tthtG' (12,),
(2.100)
-ktt + ktt ~1 [1 - Oh + G(121+l)] + )~t+l (1
(2./01)
t)+O wt+lllt+l - O.
Multiplying Equation (2.101) by ht~l, substituting for /tt~ and gt+~ from (2.99) and (2.100), and using Equation (2.91), we obtain --
2t(1 ---Tt)wlhl+L '~t+l(1-- Tt+l)w~+lht+2 + G'(lzt) G'(12,+1)
+ "~t+l (1 -- Z)+I ) W t + 1 l t t . l l h t t
1 - O.
(2.102) From Equation (2.102) and a standard transversality condition, we know that ~,o )to(1 - Z'O)Wohl Z )~t+l(l - "gt~i) wt+tllt+lht, 1 = t =o G'(12o)
(2.103)
Similarly, we can show that ~l+lRk,.+lk~+l = 2okt + Z t-o
,~tkt.
(2.104)
t=l
Next, we multiply the consumer budget constraint (2.92) by ~.t and sum from period 0 onward. When we use (2.103) and (2.104), (2.96) follows. To derive (2.97), we substitute (2.99) into (2.102). We leave it to the reader to prove the converse. [] The Ramsey problem is to maximize consumer utility subject to conditions (2.90), (2.91), (2.96), and (2.97). Recall that human capital accumulation occurs outside the market and cannot be taxed. In any competitive equilibrium, the Euler equation for human capital accumulation is undistorted. Therefore, there is no tax instrument that can be used to make the Euler equation for human capital accumulation hold for arbitrary allocations. In contrast, for arbitrary allocations, the Euler equation for physical capital can be made to hold by choosing the tax on capital income appropriately. This incompleteness of the tax system implies that the undistorted Euler equation for human capital accumulation is a constraint on the set of competitive allocations. We have the following proposition.
1714
V.V. Chari and P..J Kekoe
Proposition 11. Suppose that the Ramsey allocations converge to a balanced growth path. In such a balanced growth path, all taxes are zero. Proof." We prove that along a balanced growth path, the first-order conditions for the Ramsey problem are the same as those for a planner who has access to lump-sum taxes. (This, of course, does not mean that the government can achieve the lump-sum tax allocations, because there are distortions along the transition path.) Let W(ct, lit + 12t; )0 = U ( c , lit + 12t) + ~ctUct, where ~ is the Lagrange multiplier on (2.96). For our specified utility function, W(ct, lit + 12t; ~) = [1 + ~(1 - o')] U(ct, lit + [2t). The Ramsey problem is to maximize t
[3 W(cf, lit + [2t; ~.) - )~Ao subject to (2.90), (2.91), and (2.97). Consider a relaxed problem in which we drop condition (2.97). Since the objective function in this rewritten problem from period 1 onward is proportional to that of a social planner who has access to lump-sum taxes, the solutions to the two problems are the same along a balanced growth path. This solution also satisfies condition (2.97). Thus, along a balanced growth path, the Ramsey problem has the same solution as the lump-sum tax problem. The solutions to these last two problems differ along the transition paths only because the two problems imply different allocations for period 0 and therefore for the capital stocks for the beginning of period 1. [] The reader may be concerned that this result depends on the ratio of government consumption to output going to zero. To see that this concern is not warranted, consider an extension of the model described above. Consider an environment in which the government chooses the path of government consumption optimally. To see this, suppose that the period utility function is given by U(cl, li + 12) + V(g), where V is some increasing function of government consumption. The government problem in this setup is to choose both tax rates and government consumption to maximize the consumer utility. We can solve this problem in two parts. In the first part, government consumption is taken as exogenous and tax rates are chosen optimally. In the second part, government consumption is chosen optimally. The proof described above obviously goes through for extensions of this kind. For V(g) - a g I °/(1 -(f)~ it is easy to show that along a balanced growth path, govermnent consumption is a constant fraction of output. 2.4.2. Open economy models' So far, we have considered models of a closed economy. We turn now to considering issues that arise in an open economy. The elasticity of capital supply is likely to be
Ch. 26." Optimal Fiscal and Monetary Policy
1715
much greater in an open economy than in a closed economy because in the open economy capital is mobile and can flow to the country with the highest rate o f return. We consider a small open economy that takes the rates o f return on saving in the rest o f the world as given. In so doing, we abstract from the interesting strategic issues that arise when more than one authority sets taxes, and we abstract from general equilibrium linkages between an economy's fiscal policy and world prices. In an open economy, in addition to the standard taxes a government can levy on its citizens, a government can tax foreign owners o f factors that are located in its country. To allow this possibility, we allow there to be source-based taxes as well as residence-based taxes. Source-based taxes are taxes that governments levy on income generated in their country at the income's source, regardless o f ownership. Residencebased taxes are taxes that governments levy on the income o f their residents regardless o f the income's source. We show that source-based taxes on capital income are zero in all periods and that, with a restriction that ensures that the economy has a steady state, residence-based taxes on capital income are zero in all periods as well. This result is much stronger than the corresponding result for closed economies. [See Razin and Sadka (1995) for some closely related work.] Consider a model with both source-based and residence-based taxation. We model source-based taxes as those levied on a firm and residence-based taxes as those levied on consumers. Let r[ denote the world rental rate on capital absent any domestically levied taxes. The firm's problem is to solve
m a x f ( k t , l t ) - (1 + 02~)r[lq- (1 + rj~)writ, where 0fi and Tji are the source-based tax rates on capital and labor. The first-order conditions are Ot~r,*
Fk, - r ,*,
(2.105)
"Cj~wt = Fit - wt.
(2.106)
Consumers solve O 1. The consumer's first-order conditions imply that U~(st)/U2(s t) = R(st); thus in any equilibrium, the following constraint must hold:
gl(s t) >~ g2(st).
(3.6)
This feature of the competitive equilibrium constrains the set of Ramsey allocations. Consider now the policy problem faced by the government. As before, we assume that there is an institution or a commitment technology through which the government can bind itself to a particular sequence of policies once and for all in period 0, and we model this technology by having the government choose a policy ~ = (r(s0) at the beginning of time and then having consumers choose their allocations. Since the government needs to predict how consumer allocations and prices will respond to its policies, consumer allocations and prices are described by rules that associate allocations with government policies. Formally, allocation rules and price functions are sequences of functions x(jr) = (x(s t t :r)) and q(jr) = (/)(s t ] ~ ) , R ( s t [ ~)) that map policies Jr into allocations and prices. A Ramsey equilibrium is a policy Jr, an allocation rule x(.), and a price system q(.) that satisfy the following: (i) the policy Jr maximizes
}-~'[Y~(s9 g(cx(st l m, c2(s' l m, l(st l jr)) I~S r
subject to (3.5), with allocations given by x(jr), and (ii) ~br every Jr', the allocation x ( ~ ' ) and the price system q(~t), together with the policy Jr', constitute a competitive equilibrium. As is well known, if the initial stock of nominal assets held by consumers is positive, then welfare is maximized in the Ramsey problem by increasing the initial price level to infinity. If the initial stock is negative, then welfare is maximized by setting the initial price level so low that the government raises all the revenue it needs without levying any distorting taxes. To make the problem interesting, we set the initial sum of nominal assets of consumers M 1 + R I B 1 to zero. For convenience, let Ui(sO for i = 1,2, 3 denote the marginal utilities at state s t. Using standard techniques [for example, from Lucas and Stokey (1983), Chari et al. (1991), and Section 1], we can establish the implementability constraint: Proposition 14. The consumption and labor allocations in a competitive equilibrium satisfy conditions (3.1), (3.6), and the implementability constraint
Z/{tg(st) [c,(s~) U~ (s~)+ c2(s~)U~(st)+/(s t)U3(st)] = O, l
S t
(3.7)
1724
V.V. Chari and P.J. Kehoe
Furthermore, allocations that satisfy (3.1), (3, 6), and (3.7) can be decentralized as a competitive equilibrium. The Ramsey problem is to maximize consumer utility subject to conditions (3.1), (3.6), and (3.7). Consider utility functions of the form (3.8)
U(cI, c2, l) ~- V(w(c1, c2), [),
where w is homothetic. We then have Proposition 15. For utility functions of the .]'brm (3.8), the Ramsey equilibrium has R(s t) = 1 .for all st. Proof: Consider for a moment the Ramsey allocation problem with constraint (3.6) dropped. We will show that under (3.8), constraint (3.6) is satisfied. Let Z denote the Lagrange multiplier on (3.7) and fitkt(s t) y(s t) denote the Lagrange multiplier on (3.1). The first-order conditions for ci(s t) :for i - 1,2 in this problem are (l +Z) Ui(s ~) +Z
cj(s t) Uji(s t) + l(s t) U3i(s t) = y(st).
(3.9)
U =
Recall from Section ] that a utility function which satisfies (3.8) also satisfies
v'2 c:(s') ~l(s') @, C:(s9 ~2(s t) Z_., j=l
V 1(S t)
Z_,
j=l
(3.10)
U2(s t)
Next, dividing Equation (3.9) by Ui and noting that U3i/Ui have that
+ ,ts r v-7~f ~
= VI2/VI
for i
=- 1 , 2 ,
we
(3.1 l)
Using Equation (3.10), we have that the left-hand side of (3.11) has the same value for i - 1 and for i = 2. Therefore, Ul(st)/U2(s t) = 1. Since the solution to the less-constrained problem satisfies (3.6), it is also a solution to the Ramsey allocation problem. From the consumer's first-order condition, we have that UI (st)/U2 (s t) = R(st) and thus that R(s t) = 1. [] Now let us relate our results to Phelps' (1973) arguments for taxing liquidity services. Phelps (1973, p. 82) argues that "if, as is often maintained, the demand for money is highly interest-inelastic, then liquidity is an attractive candidate for heavy taxation at least from the standpoint of monetary and fiscal efficiency". Our results suggest that the commction between the interest elasticity of money demand and the desirability of taxing liquidity services is, at best, tenuous.
Ch. 26: Optimal Fiscal and Monetary Policy
1725
To see this, suppose that the utility function is of the form clj ~
U ( c l , c2, l)
~
c~ ~
+~
+ V(1).
(3.12)
Then the consumer's first-order condition UE/U2 = R becomes m o -
-
(c - m) a
- R,
(3.13)
where m is real money balances and c - cl + c2. The implied interest elasticity of money demand r/is given by 1
R 1/°
r/= ~ - R ~ / - r
1"
(3.14)
Evaluating this elasticity at R = 1 gives r/ = 1/2a, and thus the elasticity of money demand can range from zero to infinity. Nevertheless, all preferences in this class satisfy our homotheticity and separability conditions; hence the Friedman rule is optimal. Phelps' partial equilibrium intuition does not hold up for reasons we saw in Section 1. As we noted there, in general equilibrium, it is not necessarily true that inelastically demanded commodities should be taxed heavily. The homotheticity and separability conditions are equivalent to the requirement that the consumption elasticity of money demand is unity. To see this, consider a standard money demand specification: log m = a0 + ai log c + f ( R ) , w h e r e f ( R ) is some invertible function of the interest rate. If al - 1, so the consumption elasticity of money demand is unity, this formulation implies that m/c = e a°+jO~), or that there is some function h such that h(m/c) = R. The consumer's first-order condition is U1/U2 = R. Thus UI/U2 must be homogeneous of degree 0 in m and c if the consumption elasticity of money demand is unity. This formulation immediately implies the homotheticity and separability conditions. Note two points about the generality of the result. First, restricting w to be homogeneous of degree 1 does not reduce the generality of the result, since we can write w(.) = g ( f ( . ) ) , where g is monotone and f is homogeneous of degree 1, and simply reinterpret V accordingly. Second, the proof can be easily extended to economies with more general prodnction technologies, including those with capital accumulation. To see how, consider modifying the resource constraint (3.1) to f (Cl(Sl), C2(St),g(xt), l(st), k(s'), k(sl-l)) = O,
(3.15)
where k is the capital stock a n d f is a constant returns to scale function, and modifying the consumer's and the government's budget constraints appropriately. Let capital
1726
Vii
Chari and PJ. Kehoe
income net of depreciation be taxed at rate O(s~), and let capital be a credit good, although the result holds if capital is a cash good. For this economy, combining the consumer's and the firm's first-order conditions gives
U1 (s ~) _ R(s,fl(s'). Thus the optimality of the Friedman rule requires that Ul(st)/U2(s The constraint requiring that R(s t)/> 1 now implies that
~) = ft(st)/J2(st).
g~(s') ./i(s') u2(s,--5 >~ A(s'~'
(3.16)
and the implementability constraint (3.7) now reads t
s,
(3.17)
= vc(s0) {[l - 0(s0)] [./i(s0) - 6)]} k
~,
where k_ 1 is the initial capital stock. Since the tax on initial capital O(so) acts like a lump-sum tax, setting it as high as possible is optimal. To make the problem interesting, we follow the standard procedure of fixing it exogenously. The Ramsey allocation problem is to choose allocations to maximize utility subject to conditions (3.15), (3.16), and (3.17). For preferences of the form (3.8), the analog of Equation (3.11) has the right-hand side multiplied by f(s') for i = 1,2. This analog implies that U1(st)/U2 (s t) = fl (st)/f2 (st), and thus the Friedman rule holds. We now develop the connection between the optimality of the Friedman rule and the uniform taxation result, in this economy, the tax on labor income implicitly taxes consumption of the cash good and the credit good at the same rate. In Section l, we showed that if the utility function is separable in leisure and the subutility function over consumption goods is homothetic, then the optimal policy is to tax all consumption goods at the same rate. If R(s t) > 1, the cash good is effectively taxed at a higher rate than the credit good, since cash goods must be paid for immediately, but credit goods are paid for with a one-period lag. Thus, with such preferences, efficiency requires that R(s t) = 1 and therefore that monetary policy follow the Friedman rule. To make this intuition precise, consider a real barter economy with the same preferences (3.2) and resource constraint (3.1) as the monetary economy and with commodity taxes on the two consumption goods. Consider a period-0 representation of the budget constraints. The consumer's budget constraint is
~ q(s t) {[1 + rl(s~)] ci (s t) + [1 + T2(st)] C2(st)} ~ ~ q(s ~) l(st), t
(3.18)
St
and the government's budget constraint is
~ q(st)g(st)= ~ Z q(s~)[ T'(st)c''(s~) + T2(st)c2(s~)] ' t
St
•
(3.19)
St
where q(s t) is the price of goods in period t and at state sq A Ramsey equilibrium for this economy is defined in the obvious fashion. The Ramsey allocation problem for
Ch. 26." Optimal Fiscal and Monetary Policy
1727
this barter economy is similar to that in the monetary economy, except that the barter economy has no constraint (3.6). The consumer's first-order conditions imply that Ul(s t)
1 -b Tl(S t)
U2(s9
1 + r2(sg
Thus Ramsey taxes satisfy Tt(s t) = r2(s ~) if and only if in the Ramsey allocation problem of maximizing Equation (3.2) subject to (3.1) and (3.7), the solution has Ui(sZ)/Uz(s t) = 1. Recall from Proposition 3 in Section 1 that for utility functions of the form (3.8), the Ramsey equilibrium has ~q(s t) = r2(s t) for all s t. Thus, with homotheticity and separability in the period utility function, the optimal taxes on the two consumption goods are equal at each state. Notice that this proposition does not imply that commodity taxes are equal across states. [That is, Ti(s t) may not equal Tj(sr) for t ~ r and for i,j = 1,2.] We have shown that if the conditions for uniform commodity taxation are satisfied in the barter economy, then in the associated monetary economy, the Friedman rule is optimal. Of course, since the allocations in the monetary economy must satisfy condition (3.6) while those in the barter economy need not, there are situations in which uniform commodity taxation is not optimal in the barter economy but in which the Friedman rule is optimal in the monetary economy. To see this, consider the following. Example. Let preferences have the form 1 oi
1 o2
U(Cl, c2, l) - icl~ al + ~_-U~ c2 + V(l).
(3.20)
The first-order conditions for the Ramsey problem in the barter economy imply that
Ul(s t) U2(s t)
cl(s t) a~ -
c2(st)-~
1 +).(1 -
a2)
1 + )~(1 - 01)"
(3.21)
Clearly, Ul(s t) >~ U2(s ~) if and only if CVl ~ o 2. For cases in which al = 02, these preferences satisfy condition (3.6), and both uniform commodity taxation and the Friedman rule are optimal. If as > a2, then neither uniform commodity taxation nor the Friedman rule is optimal. What is optimal is to tax good 1 at a higher rate than good 2. In the barter economy, this higher taxation is accomplished by setting rl (s t) > r2 (s t), while in the monetary economy, it is accomplished by setting R(st) > 1. More interestingly, when a~ < a2, uniform commodity taxation is not optimal, but the Friedman rule is. To see this, note that when a~ < {72, the solution in the monetary economy that ignores the constraint Ul(s t) >~ U2(s t) violates this constraint. Thus this constraint must bind at the optimum, and in the monetary economy, U1 (s t) = Ue(st). Thus, in the barter economy, taxing good 1 at a lower rate than good 2 is optimal, and this is accomplished by setting rl (st) < r2(s~). In the monetary economy, taxing
v.v. Chari and P..L Kehoe
1728
good 1 at a lower rate than good 2 is not feasible, since R(s t) ~> 1, and the best feasible solution is to set R(s t) = 1. in this subsection, we have focused on the Lucas and Stokey (1983) cash-credit version of the cash-in-advance model. It turns out that in the simpler cash-in-advance model without credit goods, the inflation rate and the labor tax rate are indeterminate. The first-order conditions for a deterministic version of that model are the cash-in= advance constraint, the budget constraint, and
Ult _ Rt U2i 1 - Tt'
1 Ult _ R~p: [3 U2t Pt+l
where the period utility function is U(ct, lt) and Rt is the nominal interest rate from period t to period t + 1. Here, only the products R / ( 1 - vt) and Rtp/pt+~ are pinned down by the allocations. Thus the nominal interest rate, the tax rate, and the inflation rate are not separately determined. The Ramsey allocation can be decentralized in a variety of ways. In particular, trivially, both the Friedman rule and arbitrarily high rates of inflation are optimal.
3.1.2. Money-in-the-utility-fimction In this section, we prove that the Friedman rule is optimal for a money-in-the-ntilityfunction economy under homotheticity and separability conditions similar to those above. Consider the tbllowing monetary economy. In this economy, labor is transformed into consumption goods according to c(s ¢) + g(s t) = l(st).
(3.22)
(We use the same notation here as in the last subsection.) The pretbrences of the representative consumer are given by
Z ~_~ffl~(st) U(M(st)/P(St)' c(st)' l(st))' t
(3.23)
S t
where the utility function has the usual monotonicity and concavity properties and satisfies the Inada conditions. In period t, the consumer's budget constraint is
p(s t) c(s,)+ M ( s t ) + B(s ~) = M(st-l) + R(s t a) B(s ~ 1) +p(s~)[ 1 _ T(st)] l(st). (3.24) The holdings of real debt B(s~)/p(s ~) are bounded below by some arbitrarily large constant, and the holdings of money are bounded below by zero. Let M l and
Ch. 26: OptimalFiscal and Monetary Policy
1729
R_IB 1 denote the initial asset holdings of the consumer. The budget constraint of the government is given by B(s t) = R(s t 1)B(st 1)+p(st)g(st ) _ [M(s t) _ M ( s t
1)] _p(st)[1
_ r(st)ll(sZ). (3.25) A Ramsey equilibrium for this economy is defined in the obvious fashion. We set the initial stock of assets to zero for reasons similar to those given in the preceding section. Let m(s t) = M(st)/p(s t) denote the real balances in the Ramsey equilibrium. Using logic similar to that in Proposition 14, we can show that the consumption and labor allocations and the real money balances in the Ramsey equilibrium solve the Ramsey allocation problem max
Z Z f
(3.26)
ff t~(s~) U (m(s~)' c(st)' l(s~) )
S t
subject to the resource constraint (3.22) and the implementability constraint
~ [Y [m(s~) U~(s') + c(s') U2(s~)+ l(s ~) U3(s ~)]
- o.
(3.27)
These two constraints, (3.22) and (3.27), completely characterize the set of competitive equilibrium allocations. We are interested in finding conditions under which the Friedman rule is optimal. Now the consumer's first-order conditions imply that Ut(s')
U2(s9
_ 1
1
R(st)
(3.28)
Thus, for the Friedman rule to hold, namely, for R(s f) = 1, it must be true that Ui (s t) _ O.
U2(s t)
(3.29)
Since the marginal utility of consumption goods is finite, condition (3.29) will hold only if Ul(s t) = 0, that is, if the marginal utility of real money balances is zero. Intuitively, we can say that under the Friedman rule, satiating the economy with real money balances is optimal. We are interested in economies for which preferences are not satiated with any finite level of money balances and for which the marginal utility of real money balances converges to zero as the level of real money balances converges to infinity. That is, for each c and l, l i m m ~ Ul(m,c,l) = 0 and l i m m ~ U2(m,c,l) > 0. Intuitively, in such economies, the Friedman rule holds exactly only if the value of real money balances is infinite, and for such economies, the Ramsey allocation problem has no solution. To get around this technicality, we consider an economy in which the level of real money balances is exogenously bounded by a constant. We will say that the
V.V.Chari and P..J Kehoe
1730
Friedman rule is optimal if, as this bound on real money balances increases, the associated nominal interest rates in the Ramsey equilibrium converge to one. With this in mind, we modify the Ramsey allocation problem to include the constraint
m(s t) ~ 1, we have that 02(ac, ]tm) = ak-102(C , m). Differentiating with respect to a and evaluating at a = 1, we have that c012 + m022 = (k - 1)02, and thus CO12 q- toO22
02
~> 0.
(3.49)
Since 3. ~> 0, U2 < 0, and y > 0, conditions (3.48) and (3.49) contradict each other. [] Note that this proof does not go through if q~(c, m) is homogeneous of degree less than 1. Using the dual approach, however, Correia and Teles (1996) prove that the Friedman rule is optimal for this shopping-time economy when 0(c, m) is homogeneous of any degree. 3.2. From monetary to real
In this subsection, we examine the relationship between the optimality of the Friedman rule and the intermediate-goods result developed in Section 1. The relationship is the following. First, if the homotheticity and separability conditions hold, then in the three monetary models we have studied, the optimality of the Friedman rule follows from the intermediate-goods result. Second, if these conditions do not hold, then in all three economies, the optimality of the Friedman rule and the intermediate-goods result are not connected. To establish these results, we proceed as follows. We begin by setting up the notation for a simple real intermediate-goods economy and review the intermediategoods result for that economy. We then show that when our homotheticity and separability conditions hold, the cash-credit goods and the money-in-the-utilityfunction economies can be reinterpreted as real economies with intermediate goods. For these two monetary economies, we establish that the optimality of the Friedman rule in the monetary economy follows from the intermediate-goods result in the reinterpreted real economy. It is easy to establish a similar result for the shoppingtime economy. This proves the first result. Next, we consider monetary economies which do not satisfy our conditions. We establish our second result with a couple of examples. We start with an example in which the monetary economy can be reinterpreted as a real intermediate-goods economy but in which the Friedman rule does not hold in the monetary economy. We then give an example of a monetary economy in which the Friedman rule does hold, but this economy cannot be reinterpreted as a real intermediate-goods economy.
t734
EV. Chari and P.J. Kehoe
The cash-credit economy can be reinterpreted as a real production economy with intermediate goods. Under our homotheticity and separability assumptions, the period utility is U(w(cl~, c2t), 4) and the resource constraint is cll + c2l +gt = 4.
(3.50)
Since the gross nominal interest rate cannot be less than unity, the allocations in the monetary economy must satisfy
wl(cl,, c2~) >>.w2(c1~, c2~).
(3.51)
The reinterpreted economy is an infinite sequence of real static economies. In each period, the economy has two intermediate goods zlt and z2t, a final private consumption good xt, labor 4, and government consumption gt. The intermediate goods zlt and z2t in the real economy correspond to the final consumption goods c~t and c2t in the monetary economy. The period utility function is U(xt, 4). The technology set for producing the final good xt is given by f l ( x , , z l , , z z t , 4) = x , - - w ( z l , , z 2 , ) 141 see also Romer and Romer shock pitfalls 134 136 plausibility 100-104 assessment strategies 114-123 problems t43-145 interpretations 71-73 non-recursive approaches 127-134 output effects 1129 recm'siveness assumption 78-127 see also recursiveness assumption responses to 1368 monetary regimes 153, 168, 178, 202, 204, 211,216, 220 nmney 44, 1011 1013, 1020-1029, 1031-1033, 1035, 1036, 1040, 1041 money anchor 1588 money-based stabilization 1535, 1543, 1554, 1558, 1582 money demand 50, 598, 1603, 1736 consumption elasticity of 1725 interest elasticity of 1736 money growth rate 1738 money-in-the-utility-function model 1720, 1728
money supply 1536 money velocity 1588 see also M1 velocity monopolies 695 monopolistic competition 1033-1036, 1041, 1042 monotonicity 830 Morgan Stanley Capital International (MSCI) 1238 MSV (minimal state variable) solutions 488, 493, 502 and learning 503
locally (in)deternfinate 490 non-MSV solutions 493 multiple competitive equilibria 1679 multiple equilibria 1539, 1603 multiple REE, see under R E E multiple solutions 487, 1506, 1524 multiple steady states 460 multiple strongly E-stable solutions 501 multiplicity of steady states 658, 662 multivariate models 502 with time t dating 505 mutation 522 Muth model 465, 484, 525 myopia 1653, 1654 Nash bargain, generalized 1189 National Account 751,752 national accounting identities 1628 National Bureau of Economic Research (NBER) 6,8 national income 1617 national saving 1628, 1629, 1637, 1639, 1641, I652, 1659-1662 natural experiments 822 natural rate 1176 nalnral resources 639 negative income tax experiments 1148 neoclassical exogenous growth model 243,261, 673 neoclassical growth model 245, 246, 252, 259, 269, 272, 276, 639, 695, 697, 701, 1140 basis for RBC model 942 neoclassical theory of investment 817 net convergence effect 692, 693 net present value rule 835 net worth and the demand for capital 1352 neural networks 465, 524 neurons 524 noise case of small 513 intrinsic 507 noise traders 1290 noisy k-cycle 5/3 noisy steady states 483, 509 nominal anchor 207, 211, 215, 216, 1535, 1542, 1557 nominal income targeting 1505 non-durables 746 non-nested models 840 non-random attrition 787 non-Ricardian policy 418
1-43
Subject Index
non-Ricardian regime 418 non-separability of consumption and leisure 759 non-state-contingent nominal claims 1722 Non-Accelerating Inflation Rate of Unemployment (NAIRU) 46 nonlinear models 468 nonlinearity 828, 839 nonparametric techniques 532 numerical algorithms 320, 324, 326, 328, 348, 358, 378 numerical solutions 318, 326, 352, 805 obsolescence 848 OECD 685, 718, 719, 1174 OECD adult equivalence scale 757 oil prices, effects of 1089 one-sector model 639 one-step-ahead forward-looking reduced form 506 open economy 1714 open market operations 1722 openness 703 operationality 1486, 1523 opportunism 851,858 opportunity costs 854 optimal control 1490 optimal debt policy 1639, 1659, 1660, 1662 optimal fiscal policy 1686 optimal investment path 834 optimal national saving 1617 optimal tax theory 1692 optimal trajectory 650 optimal wedges 1692 optimum quantity of money rule 1537 option to wait 832, 834 ordinary differential equation (ODE) approximation 468, 478 orthogonality conditions 785 out-of-sanrple forecasting 840 out-of-steady-state behavior 649 output 1687 output levels 206 output variability 208, 211 overconfidence 1319-1323, 1325, 1326, 1328 overhead labor 1065 overidenfifying restrictions 768 overlapping contracts models 495, 1582 overlapping generations model 390, 395, 397, 398, 427, 458, 546, 549, 576-594, 660, 1634, 1635, 1645 1647
overparanletrization 473 overreaction 1319 1322 overtaking 650 overvaluation 1563
panel data 275, 283-287, 295, 781 Pareto weights 55%564, 796 partial adjustment model 821,838 participation 574, 601, 1218 path dependence of adaptive learning dynamics 455 peacetime 1699 Penn World Table 674, 680 pent-up demand 841 perceived law of motion (PLM) 466, 472, 490, 511 perceptron 524 perfect competition 831 perfect foresight 650 perfect insulation 846 perfect-insurance hypothesis 796 periodic or chaotic dynamics 646 see also cycles permanent-income hypothesis 749, 1641, 1662 permanent shocks 216-219 perpetual inventory method 680 persistence 870 882, 891, 893, 900, 902, 904, 1142, 1162, I166, 1739 of business cycles, see persistence under business cycles of fluctuations 527 of inflation 1537 peso problem 1252 pessimism 1295 Phillips cm've 46, 1056, 1363, 1542 planner's problem in RBC model 997, 1002 policy 455 affecting labor markets 672 distorting investment 695 impeding efficient production 672 policy accommodation 1538 policy ftmction 320-381 political rights 671,689 political stability 671,688, 692 Ponzi scheme 1650 population aging 1625, 1640 population growth 941 endogenous 639 power utility 1249
1-44 precautionary saving 744, 770, 1253, 1288, 1653 preference parameters 550, 555, 556, 558, 567, 601, 605 preferences 546-550, 552, 553, 556-558, 564, 565, 567, 572, 582, 593, 601, 604, 605, 607, 608, 610, 614, 616, 617, 623 additive 594 conditional 778 fimctional forms 550 Gorman polar 766, 783 heterogeneity 545, 552, 558-565, 567, 593, 594, 609, 621,623 homogeneity 553 556, 577 of representative agent in RBC model 942 quadratic 762, 770 present-value model of stock prices 1264 log-linear approximation 1265 present-value neutrality 573 price elasticity 1681 price functions 1723 price puzzle 97-100 price rules 1688 price-cost margin 1053 s e e also markup price-dividend ratio 1265, 1266, 1276 prices 42 of maclfinery 696 of raw materials 1082 pricing, equilibrium 555, 602, 845 primal approach 1676 primary budget 1619 principal-agent problems 1345 principles of optimal taxation 1676 private and public saving 1629 private information 574-576, 849 production costs, non-convex 897, 911 production economy 1686 production efficiency 1684, 1735 production function 548-550, 578, 579, 581, 583-586, 588, 590, 591,594 non-Cobb-Douglas 1064 production possibilities surface 401 production smoothing 876, 877, 884, 895, 1085 production to order 887 production to stock 887 productivity 552, 553, 566, 583, 602, 1057 cyclical 938, 1094 deterministic growth of 943 general 1192, 1193
Subject I n d e x
growth of 942 shocks 930, 943, 965, 972 amplification of 963 modeled as first-order autoregressive process 963 persistence of (serial correlation) 952, 963 RBC model's response to 964 remeasurement of 982 slowdown 664 profit function 830 profits 1057 cyclical 1100 projection facility (PF) 480 propagation of business cycles 865 propensity to constune 762 property rights 852, 856 proportional costs 825 proportional taxes 1687 prospect theol2¢ 1308 1313 protection of specific investments 1154 "provinces" effect 1540 proxies for capital utilization 1080 prudence 771 PSID 783 public consumption 1581 public debt 1601, 1603 public finance 1676 public saving 1629, 1641 putty-clay models 847, 848 q-theory
817 Tobin's q averageq 817,818 "flexible q" 818 marginal q 818 fragility of 828 quadratic adjustment cost model 823, 838 Quandt Likelihood Ratio (QLR) 34 quantitative perfunnance 1578, 1581 quantitative theory 671-673, 695-719 see also dynamic stochastic general equilibrinm models quasi-magical thinking 1329, 1330 see also
Ramsey allocation problem 649, 1679, 1691, 1692, 1713, 1719, 1723, 1729 Ramsey equilibrium 1678, 1688, 1723, 1'729, 1732 Ramsey growth model 1651, 1652 Ramsey prices 1679
1-45
Subject Index
random walk 767, 1316, 1319, 1702, 1706, 1738, 1742 geometric 825 range of inaction 826 rate of arrival of shocks 1193 rate of discount 1193 rate of return 566, 577, 582, 595, 606, 610 ratio models of habit 1284 rational bubbles 499, 1266 rational expectations 453 transition to 454 rational learning 461 rationalizability 464 rationing 857 RBC models, see real business cycle Reagan, R, 1641 rea~ balance model 489, 496 real business cycle (RBC) 394, 402, 413,427, 428, 437, 442, 505, 843, 928, 1296 amplification of productivity shocks in 958, 967 as basic neoclassical model 942 baseline model 1143, 1709, 1736 failures 1144 calibration 953-955,959 competitive equilibrium 999 concave planning problem 1002 contingent rules 1000 criticisms 961 depreciation rate of capital 944 discount factor 942 modified 945 endowments in 943 cxtensions 994 firm's problem 1001 government spending and taxes in 974 high risk aversion model 1709 high-substitution version calibration 985, 987 decision rules for 985 ingredients of 984 probability of technical regress 989, 990 role of capacity utilization in 985 role of indivisible labor in 985 sensitivity to measurement of output 992 sensitivity to parameters 990, 991 simulation of 986 household's problem 1000 importance of consumption smoothing in 967
Inada conditions on production function 996 interest rate effects 973 internal propagation in 967 labor demand for 956 supply of 956 Lagrangian for 946 lifetime utility 996 market clearing 1001 production function in 943 RBC model as basic neoclassical model 942 simulations of 957 solution certainty equivalence 952 dynamic programming 951 linear approximations 949 loglinear approximations 952 rational expectations 951 steady state of 947 transtbrmation to eliminate growth 944 transitional dynamics of 948 transversality condition for 946 wage effect in 973 wealth effects in 971 with nominal rigidities 974 real exchange rate 1547 real interest rate 1220, 1233, 1276, 1286 measurement of 939 real marginal cost 1053 real shocks 1174 real wage 1296 reallocation of workers 1160, 1183, 1199 recession now versus recession later 1535, 1557 recursive algorithm 468, 475, 479, 486 recursive least squares 467 recursive least squares learning 494 recursive utility 557 recursiveness assumption 68, 73, 78 127 benchmark identification schemes 83 -85 F F policy shock 87, 88 influence of federal funds futmes data 104--108 NBR policy shock 88 NBR/TR policy shock 89 problems 97 results 85 robustness 96, 97 sample period sensitivity 108 1i4
1-46 recursiveness assumption (cont'd) relation with VARs 78-83 REE (rational expectations equilibria) 452 cycles 458 multiple 454, 467 reduced order lhnited information 529 unique 484 reflecting barriers 828 regime switching 426 regression tree 289 regular models 490 regulation barrier 832 relative price of inves~lent to consumption 696 698, 700, 701 reluctance to invest 828, 832 renegotiation 1153, 1t55 renewable/nonrenewable resources 655,656 rental prices 588, 590, 592 of capital 1000 reorganization 1160, 1161 representative agent 556, 557, 560, 561, 563, 587, 601, 838, 1249, 1259, 1268 in RBC model altered preferences in indivisivle labor 977 altruistic links 943 preferences of 942 representative household 643 representativeness heuristic 1319, 1322, 1327 reproduction 522 research and development (R&D) 664, 672, 692, 695, 708, 709, 715-7!9 residence-based taxation 1715 restricted perceptions equilibrium 529 restrictions in job separation 1222 restrictions on government policy t707 retailers 869 retirements 839 returns to scale 639 decreasing 656 increasing 652, 653,664, 828, 830, 1066 social 460, 509, 521 Ricardian equivalence 418, 1617, 1640 1659, 1661 Ricardian regime 418 Ricardo, D. 1640 risk 546, 547, 552, 554-558, 563 567, 569, 572, 575,593,606 risk adjustment 555, 557, 558 risk aversion 547, 552, 556 -558, 564-566, 606, 771
Subject Ndex risk premium 1246, 1247, 1250 risk price 1236, 1280 risk-sharing in indivisible labor version of RBC model 977 riskfree rate puzzle 1235, 1252 robustness approach 1491, 1523 Romer and Romer shock 137-142 rnte-like behavior i487, 1522 rule-of-thumb decision procedure 524 rules I52-154, 156, 158, 160, 166, 168, 184, 200, 208, 219, 220 rules vs. discretion 1485 Rybczinski theorem 404 (S, s) model 801,802, 831,910, 911 sacrifice ratio 1541 saddle point 405, 649 saddle point stability 490 Sargent and Wallace model 489 saving 641 private 1628, 1629, 1632--1634, 1637, 1641, 1648 'saving lot a rainy day' equation 764 scale effects 672, 715, 716, 718, 719 school attainment 691 school enrolhnent 681,684 post-secondary 683 primary 683 secondary 68l.-683 schooling 576 578, 581 592 sclerosis 856 scrapping 844, 847, 855, 856 endogenous 844 search and matching approach 1173, 1183 search efficiency 1162 search equilibrium 1186 search externalities 506 seasonal adjustment 1242 seasonal variations in work volulne 1149 second-best solutions 849 secondary job loss 1163 sector-specific external effects 402 sectoral shifts hypothesis 1221 securities market 1722 seignorage model 460, 471, 509, 525, 530, 1741 selection criterion 468 selection device 454 self-fulfilling fluctuations 506 separability 556, 602, 603, 607, 608, 612, 613, 617, 1725, 1728, 1733
Subject lndex
tests 611 separation rate 1151 Sharpe ratio 1249 shock absorber 1699, 1710, 1739 shock propagation 1203 shocks and accommodation 1539 shopping-time model 1720, 1732 shopping-time monetary economy 1732 short-term bonds 1280 shurt-tenn maturity debt 1603 o-convergence 659 Sims Zba model 128-134 empirical results 131-134 skill-biased technology shock 1215, 1216, 1218 skills 546, 547, 569, 576-579, 581,582, 584, 586-588, 590-594, 623 slow adaption 480 slow speed of adjustment 8"77,894 small durables 798 small open economy 1715 small sample 820 small versus large finns t373 smooth pasting conditions 827 Social Security 1619, 1622, 1624, 1626, 1635 Solow residual 930, 1140, 1141 as productivity measure 962 in growth accounting 962 mismeasurement 962 solvency conditions 575 specificity 851,852, 856 spectral analysis 11 SSE, see stationary sunspot equilibria stability conditions 454 stabilization 1534, 1562 stabilization goals 153 stabilization time profiles 1547 stable equilibrium point 481 stable roots 393 staggered contracts model 1012, 1013, 1024, 1027, 1030, 1032, 1039 staggered price and wage setting 1012, 1013, 1027, 1030, 103t, 1033, 1035-1037, 1040 staggered price setting 397, 422, 423, 1129, t363 staggered-prices formulation t582 standardized employment deficit 1621 state-contingent claims 555, 602 state-contingent returns on debt 1687, 1699 state-dependent pricing 1031, 1032 state dynamics 477
1-47 state prices 1294 stationary distribution of RBC model 999 stationary sunspot equilibria (SSE) 408, 517 e-SSE 517 near deterministic solutions 520 steady states 468, 507, 525, 549-551,576, 592, 598, 639 of RBC model 944 sterilization 1595 sticky price models 503, 1113 stochastic approximation 468, 475, 476 stochastic discount factor 1234, 1245 log-normal 1246 stochastic growth model 546 577, 592 stochastic simulations 1516, 1523 stock market 1310, 1312, 1313, 1315, 1316, 1320-1328, 1331, 1333 stock market volatility puzzle 1235, 1236, 1268, 1276, 1280 stock prices 43 stock return 1233, 1240 stockout costs 884, 885 Stolper-Samuelson theorem 404 Stone price index 783 storage technologies 574, 575 strategic complementarity 1129 strategic delays 858 strong rationality 464 structural model 462 structural shifts 530 structalres 840 subgame perfection 1679 subjective discount factor 548, 552, 561, 593, 595, 609, 616 subsistence wage 657 substitutes 577, 590, 591,613,616 sm~ costs 858 sunspot equilibria 454, 515 sunspot paths 662 sunspot solutions 495 see also learning sunspot solutions sunspots 489, 515 supply of capital 846 supply price of labor 1192, 1193 supply shocks 1129 supply-side responses 1577 surplus 853 surplus consumption ratio 1286 survivorship bias 1242 sustainability 1597
1-48 T-mapping 467, 471,512 Tanzi effect 1741 target points 826 target variables 1492, 1523 tariff 672, 695, 703-707 taste shift 778 tax see also labor tax rate; capital taxation distortionary 165l, 1652, 1654 on capital income 1686 on employment 1220 on international trade 703 policy 672, 708 rate 1441 on private assets 1709 reforms 822 smoothing 1655, 1659, 1662, 1705 intertelnporal 1617 source-based 1715 system 1679 Taylor expansion 1265 Taylor rule 1364 technological change 1708 technological embodiment 848 technological progress 641, 1207, 1213 disembodied 1207, 1208 endogenous 639 Harrod-neutral, Hicks-neutral 944 labor-augmenting 944 purely labor-augmenting 650 techimlogical regress, probability of in RBC models 930 technology adoption 672, 708 technology shocks 1141, 1142, 1736 temporariness hypothesis 1569, 1572 temporary shocks 216 temporary work 1165 term premimn 1255 term structure of interest rates 1270 termination costs 708 thick-market externality 1161 threshold externalities 527 thresholds 258-262, 276, 289 time-additive utility function 661 time aggregation 881 time-consistent behavior 1488 time dependency 799 time-dependent pricing 1031, 1032 time-inconsistent behavior 1653 time preference 547, 588 time preference rate 1253
Subject Index
time series 264, 272, 287, 288 time series volatility 756 time to build 832, 850 time-vary/ng aggregate elasticity 841 timing assumption 469 Tobin's q 817, 1296 see also q-theory total factor productivity (TFP) 42, 673, 678, 687, 688, 702 trade deficit 1630, 1658, 1659 trade policy 672, 692, 694, 702 training 577, 582-584, 586-592, 653 transition rates 1166 transversality conditions 392, 393,400, 650 Treasury bills 1233 trend-stationary models 764 trend-stationary process 10, 211, 1497 trigger points 830 tuition costs 583, 588, 590 twin deficits 1630 two-stage least squares estimation 1261 tmcertainty 545-547, 556, 558, 564, 566, 567, 569, 572, 574, 575, 593, 605, 606, 620, 621,623,744, 1627, 1653 underinvestment 852, 854 underreaction 1319-1322 unemployment 546, 569-571, 578, 579, 1143, 1150, 1158, 1161, I162, 1173, 1174, 1194, 1214 experiences of OECD countries 1213 natural level 1157 rise in 1182 serial correlation 1163 unemployment compensation 1217 unemployment income 1214 unemployment inflow and outflow rates 1181 unemployment rates 1176 unemployment spell duration hazard 1184 tmemployment-skill profile 1216 unified budget 1619 uniform commodity taxation 1676, 1726 union bargaining 1098 uniqueness of equilibrium in RBC model 1002 unit root 11 United Kingdom 45 tmivariate models 488, 497 unstable equilibrium point 481 utility function 548-550, 556-558, 560, 594, 596, 597, 599-601,606, 607, 610
1-49
Subject Index
momentary in RBC model 944 offsetting income and substitution effects 944 utility recursion 557 utilization of capital 1079 vacancies 41, 1194 vacancy chain 1200 vacancy dmation hazard 1184 value function 319-327, 329, 335, 336, 340, 345, 351-355, 357-359, 365,368, 378 value matching 827 variable costs 828 variety, taste for 705 vector autorcgression (VAR) 73,438 definition 73 vintage capital models 847, 848 volatility employment 1157 inventories 869, 870 monetary aggregates 1599 vote share 1455 wage bargaining 1130 wage contract 1173, 1186 wage inequality 1182, 1214, 1218, 1219
wages 42, 547, 550-553, 556, 566-569, 572, 577-579, 581,587, 593, 595-601,603-607, 611, 612, 616, 617, 619, 621, 623, 1181, 1629, 1637 see also earnings cyclical 939 equilibrium 556 fixed 1157 marginal 1069 rigidity 1055 war of attrition 1540 wars 1619, 1642, 1656, 1661-1663, 1699 wealth distribution 556, 561,567, 572, 593 wealth-output ratios 1240 wealth shock 1372 welfare costs of macroeconomic fluctuations 1297 welfare theorems, role in RBC analysis 1001 wholesalers 869 within-period responscs 599 women 550, 552, 607, 615, 620, 623 worker flows 1180 into unemployment 1164 worker turnover 1176 works in progress inventories 887 yield spread
1256, 1280
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