Handbook of Macroeconomics, Volume 1C

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 j ournal 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 lA PART 1

�

EMPIRICAL AND HISTORICAL P ERFORMANCE

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 .T. CHRISTIANO, MARTIN EICHENBAUM and CHARLES L. EVANS Chapter 3 Monetary Policy Regimes and Economic Performance: The H istorical 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

�

METHODS OF DYNAMIC ANALYSIS

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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Contents of the Handbook

viii

PART

3 -MODELS OF ECONOMIC GROWTH

Chapter 9 Neoclassical Growth Theory ROBERT M. SOLOW Chapter 10 Explaining Cross-Country Income Differences ELLEN R. McGRATTAN and JAMES A. SCHMITZ, Jr.

VOLUME IB PART

4

-

CONSUMP TION AND INVESTMENT

Chapter 1 1 Consumption ORAZlO P. ATTANASIO Chapter 12 Aggregate Investment �CARDO J. CABALLERO Chapter 13 Inventories VALE�E A. RAMEY and KENNETH D. WEST PART

5 -MODELS OF ECONOMIC FLUCTUATIONS

Chapter 14 Resuscitating Real Business Cycles ROBERT G. KING AND SERGlO T. REBELO Chapter 15 Staggered Price and Wage Setting in Macroeconomics JOHN B. TAYLOR Chapter 1 6 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, Employment Fluctuations and Unemployment DALE T. MORTENSEN and CHRISTOPHER A. PISSA�DES

Contents of the Handbook

VOLUME lC PART 6 -FINANCIAL MARKETS AND THE M ACROECONOMY 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 GILCHRIST PART

7

-

MONETARY AND FISCAL POLICY

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 CA RLOS A. VE GH Chapter 25 Government Debt DOUGLAS W ELMENDORF AND N. GREGORY MANKIW Chapter 26 Optimal Fiscal and Monetary Policy VV CHARI and PATRICK J. KEHOE

IX

PREFACE TO THE HANDBOOK

Purpose

The Handbook ofMacroeconomics 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 1 970's and 1 980'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 1 980'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 1 990'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.

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Xll

Preface

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 of macroeconomics 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 Performance of the aggregate economy, to provide factual background for the 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 cross­ country 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 ofMathematical Economics, The Handbook ofEconometrics, 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 i11 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

ASSET PRICES, CONSUMPTION, AND 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 premium 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 premiun1 and riskfrcc rate puzzles 3.5. Separating risk aversion and intertemporal substitution

4. The dynamics of asset returns and consumption 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. Cyclical variation in the price of risk 5. 1 . Habit formation

5 .2. Models with heterogeneous agents

1 232 1 232 1233 1238 1 245 1 245 1 249 1 252 1 25 5 1256 1 260 1 260 1 264 1 268 1 272 1 275 1 277 1 280 1 284 1 284 1 290

This chapter draws heavily on Jolm 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 Siidcrlind for providing data. *

Handbook of Macroeconomics, Volume 1, lidited by JB. Taylor and M. Woodford © 1999 Elsevier Science B. V. All rights reserved 1 231

1 232

5.3. Irrational expectations

6. Some implications for macroeconomics References

J. Y Campbell

1 293 1 296 1 298

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 habit­ formation 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: G 12

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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 i s high. I n quarterly US data over the period 1 947.2 to 1 996.4, 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 1 5 .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.

1 234

J. Y Campbell

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 0.5 1 at a 4-year horizon. ( 1 0) 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 price­ dividend ratio forecasts less than 5% of the variation of real consumption growth at horizons of 1 to 4 years. ( 1 1 ) 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. ( 1 2) The real interest rate has some positive serial correlation; its first-order autocor­ relation 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 l % of the variation of the real interest rate at horizons of l to 4 years. ( 1 3) Excess returns on US stock over Treasury bills are highly forecastable. The log price-dividend ratio forecasts 1 8% of the variance of the excess return at a 1 -year horizon, 34% at a 2-year horizon, and 5 1 % 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 ( 1 985) 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 consumption­ based asset pricing model of the type studied by Hansen and Singleton ( 1 983), 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 ( 1 982), Hansen and Jagannathan ( 1 99 1 ), and Cochrane and Hansen ( 1 992) 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 (9)

•

•

1 For excellent recent surveys, see Cochrane and Hansen ( 1 992) or Kocherlakota ( 1 996 ) .

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 ( 1 99 1 ), 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 ( 1 989). 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 the 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 1 980s, 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 ( 1 9 8 1 ) and Shiller ( 1 9 8 1 ) 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 1 1 . Later in the 1 980s Campbell and Shiller ( 1 988), Fama and French ( 1 988a,b, 1 989), Poterba and Summers ( 1 988) 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.

1 236

J. Y. Campbell

In the late 1 970s, for example, real interest rates were unusually low yet stock prices were depressed, implying high forecast stock returns; the 1 980s 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 1 2 and 1 3 . Campbell ( 1 99 1 ) 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 ( 1 985), 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 ( 1 992), Schwert ( 1 989)] . Second, forecasts of excess stock returns do not move proportionally with estimates of conditional variance [Harvey ( 1 989, 1 99 1 ), Chou, Engle and Kane ( 1 992)]. 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 ( 1 999), building on the work of Abel ( 1 990), Constantinides ( 1 990), 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 function 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 heteroge­ neous agents. Constantinides and Duffie ( 1 996) 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 ( 1 996) and Wang ( 1 996) 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 ( 1 993)]. 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 1 0- 1 3 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 of 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 of 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 ( 1 98 1) . But data on stock prices, interest rates, and consumption are also available for many other countries. In this chapter I use an updated version of the international developed-country data set in Campbell ( 1 996a). The data set includes Morgan Stanley Capital International (MSCI) stock market data covering the period since 1 970. I 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 1 970. 1 to 1 982.2, and sample end dates range from 1 995 . 1 to 1 996.4. I work with data from 1 1 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 1 920-1994 and the UK over the period 1 9 1 9-1 994 to complement the US annual data for the period 1 89 1- 1 995. The Swedish data come from Frennberg and Hansson ( 1 992) and Hassler, Lundvik, Persson and Soderlind ( 1 994), while the UK data come from Barclays de Zoete Wedd Securities ( 1 995) and The Economist ( 1 987) 3 . In working with international stock market data, it is important to keep in mind that different national stock markets are of 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-country data set. 3 I acknowledge the invaluable assistance of Bjorn Hansson and Paul Siiderlind 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 author's web page or by request fi·om the author.

Ch. 19:

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Asset Prices, Consumption, and the Business Cycle

Table 1 MSCl market capitalization, 1993 a Country

v,

(%) ___!J_ GDP;

__ vi_ (%)

___!J_ (%)

1 1 7.9 167.3

41.55 30.62 22.49

4.65 6.60

1.85 2.63

10.75 1 1.07

4.29 4.41 1 .37 25.98 2. 15

(Bill. of US$) AUL CAN FR GER

272.5 280.7 86.8

16.83 9.45 39.74

VusMscJ

2:.:; V;

ITA JAP NTH

165 1.9 136.7

45.9 1

3.42 65. 16 5.39

SWD SWT

62.9 205.6

36.22 87.46

2.48 8.12

0.99 3.23

758.4 2535.3 4875.6

79.52 37.25

29.91 100.00 192.30

39.88

UK

USA - MSCI USA - CRSP

7 1.64

1 1.93

a

V; 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. V;IGDP; is the index market capitalization as a percentage of 1993 GDP, V;IV usMsct is the index market capitalization as a percentage of the market capitalization of the US MSCI index, and V/(2:.:; V;) 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; ITA, 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. Colunm 1 gives the market capitalization for each country's MSCI index at the end of 1 993, 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. Colunm 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. Colunm 3, for example, shows that the Japanese MSCI index is worth only 65% of the US MSCI index, the UK MSCI index is worth only 3 0% of the US index, the French and German MSCI indexes are worth only 1 1 % of the US index, and all

1240

JY Campbell

other countries' indexes are worth less than 10% of the U S index. Column 4 shows that the USA and Japan together account for 66% of 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 MSCI indexes do not cover the whole market in each country (the US MSCI index, for example, is worth about half 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 of GDP. If 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 of total wealth in different countries. In highly capitalized countries such as the UK and Switzerland, the MSCI index accounts for about 80% of GDP, whereas in Germany and Italy it accounts for less than 20% of GDP. The theoretical convention of treating the stock market as a claim to total consumption, or as a proxy for the aggregate wealth of 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 of the real stock return and the real return on a short-term debt instrument 5. The first line of Table 2 gives numbers for the standard postwar quarterly US data set summarized in the introduction. The next panel gives numbers for the 1 1-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 of 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 of the surprise inflation of 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 ( 1 997) 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-tern1 interest rate is sometimes a Treasury bill rate and sometimes another money market interest rate. Both means and standard deviations are given in atmualized percentage points. To annualize the raw quarterly munbers, means are multiplied by 400 wlrile standard deviations are multiplied by 200 (since standard deviations increase with the square root of the time interval in serially uncorrelated data).

Ch. 19:

1241

Asset Prices, Consumption, and the Business Cycle

Table 2 International stock and bill returns" Country

Sample period

r:

a(re)

p(re)

If

a(r1)

p( rf)

USA

1947.2-1996.4

7.569

15.453

0. 104

0.794

1.761

0.501

AUL CAN

1970.1-1996.3 1970. 1-1996.3

1.820

2.604

1973.2-1996.3 1978.4-1996.3

23.459 16.72 1 22.877

0.008

FR GER

2.633 4.518 7.207

0 . 1 19 0.088

2.738 2.736

1.932 1.917

0.636 0.674 0.714

ITA JPN NTH

20.326 27.244

3.338 2.064

5.831 12.721

2 1.881 15.719

0.066 0.071 0.017 0.027

1.161 2.957 2.347

SWD SWT

1971.2-1995.3 1970.2 1996.3 1977.2 1996.2 1970.1-1995. 1 1982.2-1996.3

8. 135 0.5 14

1.520

UK USA

1970.1-1996.3 1970.1-1996.4

1.466 1.081 1.350

1.603 3.067

-0.099 0.218 0.255 0.474

1.722

0.568

SWD

1920-1994 1919-1994 1891-1995

0.708 0.591 0.338

UK USA

1.538 3.705

1.542 2.966

1 1.548 7.236

23.867 20.431 2 1.555

5.893

17.355

0.053 -0. 1 12 0. 103 0.076

6.2 19 7.314 6.697

18.654 22.675

0.064 -0.024

2.073 1. 198

5.918 5.446

18.634

0.025

1.955

8.919

7.948

0.322 0.681 0.493

a r;; 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. a(re) is the standard deviation of the log real return on the market index, multiplied by 200 in quarterly data or I 00 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. r;, a(rr), and p(r1) 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 of stock returns ranges from 15% to 27%. It is striking that the market with the highest volatility, Italy, is the smallest market relative to GDP and the one with the lowest average return. (4) In quarterly data the annualized volatility of 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 long-term annual data because of large swings in inflation in the interwar period, particularly in 1 9 1 9-2 1 . Much of the volatility in these real returns is probably due to unanticipated inflation and does not reflect volatility in the ex ante real interest rate.

1 242

J Y. Campbell

These numbers show that high average stock returns, relative to the returns on short­ term debt, are not unique to the United States but characterize many other countries as well. Recently a number of authors have suggested that average excess returns in the USA may be overstated by sample selection or survivorship bias. If economists study the U SA 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 ( 1 995) present a formal model of this effect. While survivorship bias may 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 of two more of 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 of dividend growth is much greater than the volatility of consump­ tion growth, but generally less than the volatility of 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 of consumption is a flow during a quarter rather than a point-in-time observation; that is, the consumption data are time­ averaged 7. If we think of a given quarter's consumption data as measuring consumption at the beginning of the quarter, then consumption growth for the quarter is next quarter's consumption divided by this quarter's consumption. If on the other hand

" Goetzmmm and Jorion (1997) consider international 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 arc an important component of total return and are likely to have been particularly important in Europe during the troubled interwar period. 7 Time-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 possibility that some goods classified as nondurable in the national income accounts are in fact durable. Grossman, Melino and Shiller ( 1987), Wheatley (1988), Miron ( 1 986), and Heaton (1995) handle time-averaging, measurement error, seasonality, and durability, respectively, in a much more careful way than is possible here, while Wilcox (1992) provides a detailed account of the sampling procedures used to construct US consumption data.

Ch. 19:

1243

Asset Prices, Consumption, and the Business Cycle Table

3

International consumption and dividends a Country

Sample period

/';.c

a(/';.c)

p(/';.c)

t;.d

a(M)

p(M)

USA

1 947.2-1996.4

1 .921

1.085

0.22 1

2.225

28.794

-0.544

AUL

1 970. 1-1996.3 1970. 1-1996.3 1 973.2-1996.3

1.886 1 .853 1 .600

-0.35 1 0. 1 1 3

36. 134 5.783

1.592 2.341 3.384

--0.093 -0.328

0.883 -0.741 - 1 .2 1 4

1978.4-1996.3 1971.2-1995.3 1 970.2-1996.3

2.138 2.083 2.121 2.478

1 .079

1.724 2.347

0.253 -0.225

1 977.2-1996.2 1 970. 1-1995 . 1

1 .661 0.705

-0.265 -0.305

8.528 1 9.635 4.504 4.958

0.376 1 .991

-0.41 9

1 .86 1 4.143

13.595 6. 1 56

0.335 0.165

UK

1982.2--1996.3 1 970. 1-1996.3

2.772 1 .920 2.246

-4.919 -2.489 4.007

-0.451 0.540 -0.159 0.018 0.294 0.363 0.277

USA

1970.1-1996.4

1 .722

2.583 0.91 7

-0.01 7 0.390

0.68 1 0.619

7.125 17.229

0.335 -0.58 1

SWD

1 920-1994 1919-1994

1.790 1.443

0.2 1 4

1891-1995

1 .773

0. 1 59 0.28 1 -0. 1 17

1 2.2 1 5

USA

2.866 2.898 3.256

0.423

UK

1.844 1 .485

7.966 14.207

0.225 -0.087

CAN FR GER ITA JPN NTH SWD SWT

13.383

/';.c 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. a(/';.c) is the standard deviation of the log real consumption growth rate, multiplied by 200 in quarterly data or 1 00 in annual data to express in annualized percentage points. p(/';.c) is the first-order autocorrelation of the log real consumption growth rate. /';.d, a(/';.d), and p(/';.d) arc defined in the same way for the real dividend growth rate. Consumption is nondurables and services consumption in the USA, and total consumption elsewhere. Abbreviations: AUL, Australia; CAN, Canada; FR, France; GER, Germany; ITA, Italy; JPN, Japan; a

NTH, Netherlands; SWD, Sweden; SWT, Switzerland; UK, United Kingdom; USA, United States of America.

we think of the consumption data as measuring consumption at the end of the quarter, then consumption growth is this quarter's consumption divided by last quarter's consumption. Table 4 uses the former, "beginning-of-quarter" timing convention because this produces a higher contemporaneous correlation between consumption growth and stock returns. The timing convention has less effect on correlations when the data are measured at longer horizons. Table 4 also shows how the correlations among real consumption growth, real dividend growth, and real stock returns vary with the horizon. Each pairwise correlation among these series is calculated for horizons of 1 , 4, 8, and 1 6 quarters in the quarterly data and for horizons of 1 , 2 , 4, and 8 years in the long-term annual data. The table illustrates three more stylized facts from the introduction.

�

N """ """

Table 4

Horizon effects on correlations of real consumption growth, dividend growth, and stock returns a Country

Sample period

p(!l..c, re)

p(!l..c,M) 4

8

16

1

4

p(!l..d, re) 8

16

0.055

0.134

0.210

0.258

0.217

0.329

0.267

0.042

1970.2�1996.2

�0.065

�0.043

0.118

�0.047

0.172

0.288

0.268

1970.2�1996.2

�0.042

�0.014

0.073

0.099

0.143

0.305

0.254

FR

1973.2�1996.2

0.109

0.177

0.349

0.422

�0.058

0.083

GER

1978.4-1996.2

0.001

0.113

0.318

0.417

0.037

ITA

1971.2�1995.2

0.139

�0.064

�0.193

�0.250

JPN

1970.2�1996.2

�0.026

�0.123

�0.184

USA

1947.3�1996.3

AUL CAN

1

4

8

16

0.041

0.065

0.223

0.513

0.523

0.095

�0.002

0.197

0.383

0.109

�0.031

0.164

0.381

0.398

�0.064

�0.033

0.055

0.140

0.093

0.108

�0.119

�0.062

�0.141

0.050

0.297

0.414

0.452

�0.018

0.004

0.010

�0.110

0.070

0.295

0.382

0.724

�0.255

0.101

0.353

0.351

0.153

0.056

0.134

0.150

0.338 0.563

NTH

1977.2�1996.1

0.057

0.128

0.246

0.276

0.018

0.126

0.111

0.057

0.096

0.232

0.345

SWD

1970.2�1994.4

0.022

0.101

0.171

0.181

0.011

0.064

�0.004

�0.041

0.021

�0.024

0.134

0.523

SWT

1982.2�1996.2

�0.070

�0.169

�0.063

�0.035

�0.138

�0.108

�0.209

�0.378

0.072

0.237

0.433

0.564

UK

1970.2�1996.2

0.034

0.092

0.085

0.247

0.126

0.182

0.330

0.420

�0.132

0.004

0.269

0.645

USA

1970.2�1996.3

�0.030

0.124

0.261

0.451

0.258

0.330

0.306

0.131

0.032

�0.044

0.002

0.393

SWD

1920-1993

0.288

0.387

0.362

0.141

0.213

0.312

0.450

0.172

0.236

0.434

0.685

0.682

UK

1920-1993

0.065

0.321

0.515

0.425

0.426

0.465

0.455

0.389

0.159

0.441

0.599

0.782

USA

1891�1994

0.181

0.153

0.202

0.109

0.454

0.496

0.399

0.154

0.477

0.504

0.680

0.786

a The table gives the contemporaneous cross-correlations of real consumption growth /l..c, real dividend growth !l..d, and the stock index return re, where these variables are measured at horizons of 1, 4, 8, or 16 quarters in quarterly data and 1, 2, 4, or 8 years in annual data. The timing convention used for consumption is that consumption measured in a given period corresponds to beginning-of-period consumption, so log consumption growth for the period is the log of next period's consumption divided by this period's consumption. 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.

� �

�

�c(\} :::::

Ch. 19:

Asset Prices, 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 + R;, 1 + 1 ) on the asset held from time t to time t + 1 . If the investor consumes Ckt at time t and has time-separable utility with discount factor 15 and period utility U(Ck1), then her first-order condition is

(I ) The left-hand side o f Equation ( 1 ) i s the marginal utility cost o f 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'(Ckt) yields

[

_

]

U'(Ck , t+ 1 ) - Et [(l + R;, t+ l ) Mk , t + l J- , U' (C,a ) 15U'(Ck , t +d!U'(C1) is the intertemporal marginal rate

l - E1 (l + Ri, t+J ) o

___

(2)

where Mk , n! = of substitution of the investor, also known as the stochastic discount factor. This way of writing the

J Y Campbell

1 246

model in discrete time is due originally to Grossman and Shiller ( 1 98 1), while the continuous-time version of the model is due to Breeden ( 1 979). Cochrane and Hansen ( 1 992) and Hansen and Jagannathan ( 1 99 1 ) 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 Mk, 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 (3) In complete markets the stochastic discount factor M1+ 1 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,

E, [( 1 + R;, t+J ) Mt+J ] Et [( l + Ri, t+J )]Et [Mt+J] + Covt[R ;, r , Mt+l ]. +I

=

(4)

Substituting into Equation (3) and rearranging gives

l + Et [R, , t +l ]

=

1 - Cov, [Ri , t+l , Mt+J ]

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 returns 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 + R;; 1 1 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

+ Rf, t + l =

1

Et[Mt;J

·

(6)

This can be used to rewrite Equation (5) as 1

+ E1[R;, t+I ]

=

(1

+ RJ, t + I )( l - Cov1 [R;, r + I , Mt+l]) .

(7)

For simplicity I now follow Hansen and Singleton ( 1 983) 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 E1X = E1 log X + � Var, logX ,

(8)

where Var, log X E1 [(logX - E1 logX)2] . If in addition X is conditionally homoskedastic, then Var1 log X = E[(log X - E, logX)2 ] Var(logX - E1 logX). Thus with joint conditional lognormality and homoskedasticity of asset returns and consumption, I can take logs of Equation (3) and obtain =

(9) Here m1 = log(Mt) and rit = log( I + R it), while a? denotes the unconditional variance of log return innovations Var(ri t+ 1 - E1ri , t+ 1 ), a� denotes the unconditional variance of innovations to the stochastic discount factor Var( m11 1 E1m1+ 1 ), and aim denotes the unconditional covariance of innovations Cov(ri, t+ i - E,r;, 1 , 1 , mn.1 - E1m1+1 ). Equation (9) has both time-series and cross-sectional implications. Consider first an asset with a riskless real return r1; t+ 1 For this asset the return innovation variance a} and the covariance O;in are both zero, so the riskless real interest rate obeys ,

-

•

( 1 0) This equation is the log counterpart of Equation (6). Subtracting Equation ( 1 0) from Equation (9) yields an expression for the expected excess return on risky assets over the riskless rate: (1 1) The variance term on the left-hand side of Equation ( 1 1 ) 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 E1[(1 + R;, t + l )/( l + Rr, 1 1 1 )] = -aim· The right­ hand side of Equation ( 1 1 ) 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 aim can be written as the product of the standard deviation of the asset return a;, the standard deviation of the stochastic discount factor am, and the

Table 5 The equity premium puzzle

-

N � 00

a

Country

Sample period

aere

a(ere)

a(m)

a(t..c)

USA

1 947.2-1 996.3

7.852

1 5.2 ! 8

5 1 .597

1 .084

0. 1 93

3.185

246.556

47.600

AUL

1 970. 1-1 996.2

3.531

23.194

1 5.221

2.142

0. 1 56

7.725

45.704

7. 1 07

CAN

1 970. 1-1 996.2

3.040

1 6.673

1 8.233

2.034

0. 1 5 9

5.387

56.434

FR

1 973.2-1 996.2

7.122

22.844

3 1 . 1 75

2.130

-0.047

-2.295

p(er" !J.c)

Cov(ere, /J.c)

RRA(1 )

RRA(2)

8.965

< 0

1 4.634 1 3.327

GER

1 978.4-1 996.2

6.774

20.373

33.25 1

2.495

0.039

1.974

343. 1 33

ITA

1971 .2-1 995.2

2.166

27.346

7.920

1 .684

0.002

0.088

2465.323

4.703

JPN

1 970.2-1996.2

6.831

2 1 .603

3 1 .621

2.353

0.1 00

5.093

1 34. 1 1 8

1 3.440

NTH

1 977.2- 1 996.1

9.943

1 5.632

63.607

2.654

0.023

0.946

1 050.925

23.970

SWD

1970.1-1 994.4

9.343

23.541

39.688

1 .9 1 7

0.003

0. 1 29

72 1 5. 1 76

20.705

SWT

1 982.2-1 996.2

1 2.393

20.466

60.553

2.261

-0.129

-5.978

UK

1 970. 1-1 996.2

8.306

2 1 .589

38.473

2.589

0.095

5.3 1 4

1 5 6.308

1 4.858

USA

1 970. 1-1 996.3

5.8 1 7

1 6.995

34.228

0.9 1 9

0.248

3.875

1 50. 1 36

37.255

SWD UK

1 920-1993

6.000

18.906

3 1 .737

2.862

0. 1 69

9. 1 4 1

65.642

1 1 .091

1 9 1 9-1993

8.677

2 1 .706

39.974

2.820

0.355

2 1 .738

39.914

1 4. 1 74

USA

1 891-1 994

6.258

18.534

33.767

3.257

0.497

30.001

20.861

1 0.366

< 0

26.785

a

aere is the average excess log return on stock over a money market instrument, plus one half the variance of this excess return: aere = re - r1 + a2 (re - r1 )12. It is multiplied by 400 in quarterly data and 1 00 in annual data to express in annualized percentage points. a(ere) and a(!J.c) are the standard deviations of the excess log return ere = re - r1 and consumption growth /J.c, respectively, multiplied by 200 in quarterly data and 1 00 in annual data to express in annualized percentage points. a(m) = 1 00aerela(ere) is calculated from equation ( 1 2) as a lower bound on the standard deviation of the log stochastic discount factor, expressed in annualized percentage points. p(er0 /J.c) is the correlation of ere and /J.c. Cov(er"' !J.c) is the product a(ere)a(!J.c)p(er, !J.c). RRA( l ) is 1 00aere1Cov(er" ' !J.c), a measure of risk aversion calculated from equation ( 1 6) using the empirical covariance of excess stock returns with consumption growth. RRA(2) is 1 OOaerel a( ere )a(!J.c) , a measure of risk aversion calculated using the empirical standard deviations of excess stock returns and consumption growth, but assuming perfect correlation between these series. 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.

,..., �

� �I:J-

"' ::::::

Ch. 19:

Asset Prices, Consumption, and the Business Cycle

1 249

correlation between the asset return and the stochastic discount factor Pim · Since Pim ;? - 1 , -O;m :( O; Om . Substituting into Equation ( 1 1 ), ( 1 2) This inequality was first derived by Shiller ( 1 982); a multi-asset version was derived by Hansen and Jagannathan ( 1 99 1 ) and developed further by Cochrane and Hansen ( 1 992). The right-hand side of Equation ( 1 2) is the excess return on an asset, adjusted for Jensen's Inequality, divided by the standard deviation of the asset's return - a logarithmic Sharpe ratio for the asset. Equation ( 1 2) says that the standard deviation of the log stochastic discount factor must be greater than this Sharpe ratio for all assets i, that is, it must be greater than the maximum possible Sharpe ratio obtainable in asset markets. Table 5 uses Equation ( 1 2) to illustrate the equity premium puzzle. For each data set the first column of the table reports the average excess return on stock over short­ term debt, adjusted for Jensen's Inequality by adding one-half the sample variance of the excess log return to get a sample estimate of the numerator in Equation ( 1 2). This adjusted average excess return is multiplied by 400 to express it in annualized percentage points. The second column of the table gives the annualized standard deviation of the excess log stock return, a sample estimate of the denominator in Equation ( 12). This standard deviation was reported earlier in Table 2. The third column gives the ratio of the first two columns, multiplied by 1 00; this is a sample estimate of the lower bound on the standard deviation of the log stochastic discount factor, expressed in annualized percentage points. In the postwar US data the estimated lower bound is a standard deviation greater than 50% a year; in the other quarterly data sets it is below 1 0% for Italy, between 1 5% and 20% for Australia and Canada, and above 3 0% for all the other countries. In the long-run annual data sets the lower bound on the standard deviation exceeds 3 0% for all three countries. 3.2. Consumption-based asset pricing with power utility

To understand why these numbers are disturbing, I now follow Mehra and Prescott ( 1 985) and other classic papers on the equity premium puzzle and assume that there is a representative agent who maximizes a time-separable power utility function defined over aggregate consumption C1 :

c�-y - 1

...._ ' u( ct ) = _t'-:._ 1-y

(13)

where y i s the coefficient o f relative risk aversion. This utility function has several important properties. First, it is scale-invariant; with constant return distributions, risk premia do not change over time as aggregate wealth and the scale of the

J. Y Campbell

1250

economy increase. Related to this, if different investors in the economy have different wealth levels but the same power utility function, then they can be aggregated into a single representative investor with the same utility function as the individual investors. A possibly less desirable property of power utility is that the elasticity of intertemporal substitution, which I write as 1/J, is the reciprocal of the coefficient of relative risk aversion y. Epstein and Zin ( 1 989, 1 99 1 ) and Weil ( 1 989) have proposed a more general utility specification that preserves the scale-invariance of power utility but breaks the tight link between the coefficient of relative risk aversion and the elasticity of intertemporal substitution. I discuss this form of utility in section 3.4 below. Power utility implies that marginal utility U ' (C1) = c;r, and the stochastic discount factor Mt+l = b(Ct+1/C1tY. The assumption made previously that the stochastic discount factor is conditionally lognormal will be implied by the assumption that aggregate consumption is conditionally lognormal [Hansen and Singleton ( 1 983)]. Making this assumption for expositional convenience, the log stochastic discount factor is m1+ 1 = log(b) - y�ct+ 1 , where c1 = log(C1), and Equation (9) becomes ( 1 4) Here aJ denotes Var(ct+ 1 - E1ct+ 1 ), the unconditional variance of log consumption innovations, and O;c denotes Cov(r; t+ I - E1r;, 1_1 1 , ct+ 1 - E1ct+ 1), the unconditional covariance of innovations. Equation ( 1 0) now becomes ,

Tj', t +l

= - log () + yE1�Ct+ 1

-

y2 ac2

__

2

.

( 1 5)

This equation says that the riskless real rate is linear in expected consumption growth, with slope coefficient equal to the coefficient of relative risk aversion. The conditional variance of consumption growth has a negative effect on the riskless rate which can be interpreted as a precautionary savings effect. Equation ( 1 1) becomes ( 1 6) The log risk premium on any asset is the coefficient of relative risk aversion times the covariance of the asset return with consumption growth. Intuitively, an asset with a high consumption covariance tends to have low returns when consumption is low, that is, when the marginal utility of consumption is high. Such an asset is risky and commands a large risk premium. Table 5 uses Equation ( 1 6) to illustrate the equity premium puzzle. As already discussed, the first column of the table reports a sample estimate of the left-hand

Ch.

19:

Asset Prices, Consumption, and the Business Cycle

1 25 1

side of Equation ( 1 6), multiplied by 400 to express it in annualized percentage points, The second column reports the annualized standard deviation of the excess log stock return (given earlier in Table 2), the fourth column reports the annualized standard deviation of consumption growth (given earlier in Table 3), the fifth column reports the correlation between the excess log stock return and consumption growth, and the sixth colunm gives the product of these three variables which is the annualized covariance O;c between the log stock return and consumption growth. Finally, the table gives two colunms with implied risk aversion coefficients. The column headed RRA( l) uses Equation ( 1 6) directly, dividing the adjusted average excess return by the estimated covariance to get estimated risk aversion 8 . The column headed RRA(2) sets the correlation of stock returns and consumption growth equal to one before calculating risk aversion. While this is of course a counterfactual exercise, it is a valuable diagnostic because it indicates the extent to which the equity premium puzzle arises from the smoothness of consumption rather than the low correlation between consumption and stock returns. The correlation is hard to measure accurately because it is easily distorted by short-term measurement errors in consumption, and Table 4 indicates that the sample correlation is quite sensitive to the measurement horizon. By setting the correlation to one, the RRA(2) column indicates the extent to which the equity premium puzzle is robust to such issues. A correlation of one is also implicitly assumed in the volatility bound for the stochastic discount factor, Equation ( 1 2), and in many calibration exercises such as Mehra and Prescott ( 1 985), Campbell and Cochrane ( 1 999), or Abel ( 1 999). Table 5 shows that the equity premium puzzle is a robust phenomenon in international data. The coefficients of relative risk aversion in the RRA(l) column are generally extremely large. They are usually many times greater than 1 0, the maximum level considered plausible by Mehra and Prescott ( 1 985). In a few cases the risk aversion coefficients are negative because the estimated covariance of stock returns with consumption growth is negative, but in these cases the covariance is extremely close to zero. Even when one ignores the low correlation between stock returns and consumption growth and gives the model its best chance by setting the correlation to one, the RRA(2) colunm still has risk aversion coefficients above 1 0 in most cases. Thus the fact shown in Table 4, that for some countries the correlation of stock returns and consumption increases with the horizon, is unable by itself to resolve the equity premium puzzle. The risk aversion estimates in Table 5 are of course point estimates and are subject to sampling error. N o standard errors are reported for these estimates. However authors such as Cecchetti, Lam and Mark ( 1 993) and Kocherlakota ( 1 996), studying the long-

R The calculation is done correctly, in natural units, even though the table reports average excess returns and covariances in percentage point tmits. Equivalently, the ratio of the quantities given in the table is multiplied by I 00.

1 252

J Y Campbell

run annual US data, have found small enough standard errors that they can rej ect risk aversion coefficients below about 8 at conventional significance levels. Of course, the validity of these tests depends on the characteristics of the data set in which they are used. Rietz ( 1 988) has argued that there may be a peso problem in these data. A peso problem arises when there is a small positive probability of an important event, and investors take this probability into account when setting market prices. If the event does not occur in a particular sample period, investors will appear irrational in the sample and economists will mis-estimate their preferences. While it may seem unlikely that this could be an important problem in 1 00 years of annual data, Rietz ( 1 988) argues that an economic catastrophe that destroys almost all stock-market value can be extremely unlikely and yet have a major depressing effect on stock prices. One difficulty with this argument is that it requires not only a potential catastrophe, but one which affects stock market investors more seriously than investors in short-term debt instruments. Many countries that have experienced catastrophes, such as Russia or Germany, have seen very low returns on short-term government debt as well as on equity. A peso problem that affects both asset returns equally will affect estimates of the average levels of returns but not estimates of the equity premium 9 . The maj or example of a disaster for stockholders that did not negatively affect bondholders is the Great Depression of the early 1 930s, but of course this is included in the long-run annual data for Sweden, the UK, and the USA, all of which display an equity premium puzzle. Also, the consistency of the results across countries requires investors in all countries to be concerned about catastrophes. If the potential catastrophes are uncorrelated across countries, then it becomes less likely that the data set includes no catastrophes; thus the argument seems to require a potential international catastrophe that affects all countries simultaneously.

3.3. The riskf'ree rate puzzle

One response to the equity premium puzzle is to consider larger values for the coefficient of relative risk aversion y. Kandel and Stambaugh ( 1 99 1 ) have advocated

9

This point is relevant for the stndy of Goetzmann and Jorion ( 1 997). These authors measure average growth rates of real stock prices, as a proxy for real stock returns, but they do not look at real returns on short-term debt. They find low real stock-price growth rates in many countries in the early 20th Century; in some cases these may have been accompanied by low returns to holders of short-term debt. Note also that stock-price growth rates are a poor proxy for total stock returns in periods where investors expect low growth rates, since dividend yields will tend to be higher in such periods.

Ch. 19:

Asset Prices, Consumption, and the Business Cycle

1 253

this 10 . However this leads to a second puzzle. Equation ( 1 5) implies that the unconditional mean riskless interest rate is ( 1 7) where g is the mean growth rate of consumption. Since g is positive, as shown in Table 3 , high values of y imply high values of yg. Ignoring the term -y2 a'/;12 for the moment, this can be reconciled with low average short-term real interest rates, shown in Table 2, only if the discount factor c) is close to or even greater than one, corresponding to a low or even negative rate of time preference. This is the riskfree rate puzzle emphasized by Weil ( 1 989). Intuitively, the riskfree rate puzzle is that if investors are risk-averse then with power utility they must also be extremely unwilling to substitute intertemporally. Given positive average consumption growth, a low riskless interest rate and a high rate of time preference, such investors would have a strong desire to borrow from the future to reduce their average consumption growth rate. A low riskless interest rate is possible in equilibrium only if investors have a low or negative rate of time preference that reduces their desire to borrow 1 1 . Of course, if the risk aversion coefficient y is high enough then the negative quadratic term - y2a'/;12 in Equation ( 1 7) dominates the linear term and pushes the riskless interest rate down again. The quadratic term reflects precautionary savings; risk-averse agents with uncertain consumption streams have a precautionary desire to save, which can work against their desire to borrow. But a reasonable rate of time preference is obtained only as a knife-edge case. Table 6 illustrates the riskfree rate puzzle in international data. The table first shows the average riskfree rate from Table 2 and the mean consumption growth rate and standard deviation of consumption growth from Table 3 . These moments and the risk aversion coefficients calculated in Table 5 are substituted into Equation ( 1 7), and the equation is solved for an implied time preference rate. The time preference rate is reported in percentage points per year; it can be interpreted as the riskless real interest rate that would prevail if consumption were known to be constant forever at its current level, with no growth and no volatility. Risk aversion coefficients in the RRA(2) range imply negative time preference rates in every country except Switzerland, whereas larger risk aversion coefficients in the RRA( l ) range imply time preference rates that are often positive but always implausible and vary wildly across countries. 10 One might think that introspection would be sufficient to rule out very large values of y, but Kandel and Stambaugh ( 1 99 1 ) point out that introspection can deliver very different estimates of risk aversion depending on the size of the gamble considered. This suggests that introspection can be misleading or that some more general model of utility is needed. 11 As Abel ( 1 999) and Kocherlakota (1 996) point out, negative time preference is consistent with finite utility in a time-separable model provided that consumption is growing, and marginal utility shrinking, sufficiently rapidly. The question is whether negative time preference is plausible.

J. Y. Campbell

1 254 Table 6 The riskfree rate puzzle Country

Sample period

rf

L'l.c

a(L'l.c)

USA

1 947.2-1996.3

0.794

1 .908

1 .084

AUL

1970.1-1 996.2

1 .820

1 .854

2 . 142

a

TPR(1 )

RRA(2) TPR(2)

246.556

- 1 12.474

47.600

-76.71 0

45.704

-34.995

7. 1 07

- 1 0 . 1 96

8.965

- 1 3 .066

RRA(l)

CAN

1970. 1-1 996.2

2.738

1 . 948

2.034

FR

1973.2-1996.2

2.736

1 .5 8 1

2 . 130

1 000

SWD

1970.1-1 994.4

1 .520

0.750

1 .9 1 7

SWT

1982.2-1 996.2

1 .466

0.414

2.261

UK

1970. 1-1 996.2

1 .081

2.025

USA

1 970. 1-1 996.3

1 .350

SWD

1920-1993

UK

1 9 1 9-1993

USA

1 891-1994

56.434

-41 .346 N/A

1 4.634

- 1 5.536

> 1 000

1 3.327

-12. 142

4.703

-9.021

1 3.440

-39.375

> 1 000

23.970

-1 1 .201

> 1 000

> 1 000

20.705

-6. 1 26

1 000 1 34. 1 1 8

> 1 000 41 .222

a r; is the mean money market return from Table 2, in annualized percentage points. L'l.c and a(L'l.c)

are the mean and standard deviation of consumption growth from Table 3, in annualized percentage points. RRA(1 ) and RRA(2) are the risk aversion coefficients from Table 5 . TPR(I) = r; - RRA ( I)L'l.c +

RRA ( l ? a2 (L'l.c)/200, and TPR(2) r; - RRA(2)L'l.c + RRA(2)2a2(L'l.c)/200. From Equation ( 1 7), these time preference rates give the real interest rate, in annualized percentage points, that would prevail if consumption growth had zero mean and zero standard deviation and risk aversion were RRA(l ) or RRA(2), respectively. 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. =

An interesting issue is how mismeasurement of average inflation might affect these calculations. There is a growing consensus that in recent years conventional price indices have overstated true inflation by failing to fully capture the effects of quality improvements, consumer substitution to cheaper retail outlets, and price declines in newly introduced goods. If inflation is overstated by, say, 1 %, the real interest rate is understated by 1%, which by itself might help to explain the riskfree rate puzzle. Unfortunately the real growth rate of consumption is also understated by 1 %, which worsens the riskfree rate puzzle. When y > 1 , this second effect dominates and understated inflation makes the riskfree rate puzzle even harder to explain.

Ch. 19:

Asset Prices, Consumption, and the Business Cycle

1 255

Table 7 International yield spreads and bond excess returns a Country

Sample period

USA

1 947.2- 1996.4

AUL

1 970. 1 - 1 996.3

s

a(s)

p(s)

erh

1 . 1 99

0.999

0.783

0.0 1 1

8.923

0,070

0.938

1 .669

0.750

0. 1 56

8.602

0. 1 62

a(erh)

p(erb)

CAN

1 970. 1 - 1 996.3

1 .057

1 .6 5 1

0.8 1 9

0.950

9.334

-0.009

FR

1 973.2-1996.3

0.91 7

1 .547

0.733

1 .440

8 . 1 58

0.298

GER

1 978.4-- 1 996.3

0.99 1

1 .502

0.869

0.899

7.434

0. 1 17

ITA

1 9 7 1 .2- 1 995.3

-0.200

2.025

0.759

- 1 .386

9.493

0.335

JPN

1 970.2- 1 996.3

0.593

1 .488

0.843

1 .687

9. 1 65

-0.058

NTH

1 977.2-1996.2

1.2 1 2

1 .789

0.574

1 .549

7.996

0.032

SWD

1 970. 1 - 1 995. 1

0.930

2.046

0.724

-0. 2 1 2

7.575

0.244

SWT

1 982.2-1 996.3

0.471

1 .655

0.755

1 .07 1

6.572

0.268

UK

1 970. 1 - 1 996.3

1 . 202

2 . 1 06

0.893

0.959

1 1 .6 1 1

-0.057

USA

1 970. 1 - 1 996.4

1 .562

1 . 1 90

0.737

1 .504

1 0.703

0.033

SWD

1 920-1994

0.284

1 . 1 40

0.280

-0.075

6.974

-0. 1 85

UK

1 9 1 9- 1994

1 .272

1 .505

0.694

0.3 1 8

8.8 1 2

-0.098

USA

1 89 1 - 1 995

0.720

1 .550

0.592

0. 1 72

6.499

0 . 1 53

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. a(�) is the standard deviation of the log yield spread and p(s) is its first-order autocorrelation. er1, a(erh), 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 1 0, equation (10. 1 . 1 9). Full details of this calculation are given 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.

3.4. Bond returns and the equity premium and riskfree rate puzzles

Some authors have argued that the riskfree interest rate is low because short-term government debt is more liquid than long-term financial assets. Short-term debt is "moneylike" in that it facilitates transactions and can be traded at minimal cost. The liquidity advantage of debt reduces its equilibrium return and increases the equity premium [Bansal and Coleman ( 1 996), Heaton and Lucas ( 1 996)] . The difficulty with this argument is that it implies that all long-term assets should have large excess returns over short-term debt. Long-term government bonds, for example, are not moneylike and so the liquidity argument implies that they should offer a large term premium. But historically, the term premium has been many times smaller than the equity premium. This point is illustrated in Table 7, which reports two

1256

J. Y 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( l ) 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 j ust as severe as the standard equity premium puzzle 12. 3.5. Separating risk aversion and intertemporal substitution

Epstein and Zin ( 1 989, 1991) and Weil ( 1 989) use the theoretical framework of Kreps and Porteus ( 1 978) 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, 1/J, the reciprocal of the coefficient of relative risk aversion, y. 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 ( 1 6 ), 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-half the variance of the log equity return, less one-half the variance of the log bond return.

Table 8 The bond premium puzzle

......

:-?

RRA( l )

RRA(2)

a(erb)

o(m)

a(/lc)

0.320

8.924

3.591

1 .084

0.066

0.642

1 970. 1-1996.2

0.227

8.5 1 0

2.669

2. 142

0.076

1 .384

1 6.410

1 .246

1 970.1-1 996.2

1 .232

9.344

1 3 . 1 89

2.034

0.097

1 .853

66.521

6.485

1 973.2-1996.2

1 .569

8. 143

1 9.268

2 . 1 30

0.036

0.628

249. 8 1 1

9.045

1 978.400-1996.200

1 .017

7.455

1 3.636

2.495

0. 1 17

2 . 1 77

46.707

5.465

Country

Sample period

aerb

USA

1947.2-1996 3

AUL CAN FR GER

�

a

p(erb, 1lc)

Cov(erb, /lc)

49.949

3.3 1 3

ITA

1971.2- 1 995.2

- 1 . 157

9.479

- 1 2 .208

1 . 684

0.032

0.506

---------� Demand for Capital // -+------�""·""- · -·-·-· - · - · -

6

7

8

9

10

11

12

Capital Stock

Fig. I . Effect of an increase in net worth.

debt and expand the size of his firm. He is constrained from raising the size of the firm indefinitely by the fact that expected default costs also rise as the ratio of borrowing to net worth increases. An equivalent way of expressing Equation (3.8) is (3 .9) For an entrepreneur who is not fully self-financed, in equilibrium the return to capital will be equated to the marginal cost of external finance. Thus Equation (3.9) expresses the equilibrium condition that the ratio s of the cost of external finance to the safe rate - which we have called the discounted return to capital but may be equally well interpreted as the external finance premium - depends inversely on the share of the finn's capital investment that is financed by the entrepreneur's own net worth. Figure 1 illustrates this relationship using the actual contract calibrated for model analysis in the next section. Firm j 's demand for capital is on the horizontal axis and the cost of funds normalized by the safe rate of return is on the vertical axis. For capital stocks which can be financed entirely by the entrepreneur's net worth, in this case K < 4.6, the firm faces a cost of funds equal to the risk free rate. As capital acquisitions rise into the range where external finance is necessary, the cost­ of-funds curve becomes upward sloping, reflecting the increase in expected default costs associated with the higher ratio of debt to net worth. While the supply of funds curve is upward sloping, owing to constant returns to scale, the demand for capital i.s horizontal at an expected return 2 percentage points above the risk free rate .

Ch. 21:

The Financial Accelerator in a Quantitative Business Cycle Framework

1 355

Point E, where the firm's marginal cost of funds equals the expected return to capital yields the optimal choice of the capital stock K = 9.2. For this contract, the leverage ratio is 50%. It is easy to illustrate how a shift in the firm's financial position affects its demand for capital. A 1 5% increase in net worth, Ni�l ' for example, causes the rightward shift in the cost-of-funds curve depicted by the hatched line in Figure 1 . At the old level of capital demand, the premium for external finance declines: The rise in net worth relative to the capital stock reduces the expected default probability, everything else equal. As a consequence, the firm is able to expand capacity to point E' . Similarly, a decline in net worth reduces the firm's effective demand for capital. In the next section we incorporate this firm-level relation into a general equilibrium framework. Before proceeding, however, we note that, in general, when the firm's demand for capital depends on its financial position, aggregation becomes difficult. The reason is that, in general, the total demand for capital will depend on the distribution of wealth across firms. Here, however, the assumption of constant returns to scale throughout induces a proportional relation between net worth and capital demand at the firm level; further, the factor of proportionality is independent of firm-specific factors. Thus it is straightforward to aggregate Equation (3 . 8) to derive a relationship between the total demand for capital and the total stock of entrepreneurial net worth.

4. General equilibrium

We now embed the partial equilibrium contracting problem between the lender and the entrepreneur within a dynamic general equilibrium model. Among other things, this will permit us to endogenize the safe interest rate, the return to capital, and the relative price of capital, all of which were taken as given in the partial equilibrium . We proceed in several steps. First we characterize aggregate behavior for the entrepreneurial sector. From this exercise we obtain aggregate demand curves for labor and capital, given the real wage and the riskless interest rate. The market demand for capital is a key component of the model since it reflects the impact of financial market imperfections. We also derive how the aggregate stock of entrepreneunal net worth, an important state variable determining the demand for capital, evolves over time. We next place our "non-standard" entrepreneurial sector within a conventional Dynamic New Keynesian framework. To do so, we add to the model both households and retailers, the latter being included only in order to introduce price inertia in a tractable manner. We also add a government sector that conducts fiscal and monetary policies. Since much of the model is standard, we simply write the log-linearized framework used for computations and defer a more detailed derivation to Appendix B. Expressing the model in a log-linearized form makes the way in which the financial accelerator influences business cycle dynamics reasonably transparent.

B.S. Bernanke et al.

1356

4. 1. The entrepreneurial sector

Recall that entrepreneurs purchase capital in each period for use in the subsequent period. Capital is used in combination with hired labor to produce (wholesale) output. We assume that production is constant returns to scale, which allows us to write the production function as an aggregate relationship. We specify the aggregate production function relevant to any given period t as (4. 1 ) where Y1 is aggregate output o f wholesale goods, K1 i s the aggregate amount of capital purchased by entrepreneurs in period t 1 , L 1 is labor input, and A1 is an exogenous technology parameter. Let I1 denote aggregate investment expenditures. The aggregate capital stock evolves according to -

(4.2) where i5 is the depreciation rate. We assume that there are increasing marginal adjustment costs in the production of capital, which we capture by assuming that aggregate investment expenditures of I1 yield a gross output of new capital goods cfJ(I/K1) K1, where cJJO is increasing and concave and R, 1 , the entrepreneur would buy an infinite amount of capital, and if E { R7+ 1 } < Rl+ he would buy none. When E{RJ+ 1 } = R,_,_ b he is indifferent about the scale of operation of his firm. 1 � Given logarithmic preferences, the marginal utility of consumption is simply --c, .

1,

1 364

B.S. Bemanke 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 forward­ looking nature of price setting 1 9 . Equations (4.23) and (4.24) are transition equations for the two state variables, capital k1 and net worth n1 • 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� - r1 on n1+ is weighted by the coefficient yRKIN, which is the ratio of gross capital 1 holdings to entrepreneurial net worth. How the financial accelerator augments the conventional DNK model should now be fairly transparent. Net worth affects investment through the arbitrage Equation (4. 1 7). 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 DNK framework [particularly King and Wolman's ( 1 996) version with adjustment costs of capital]. Equation (4.25) is the monetary policy rule 20 . 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 of this form do a reasonably good job of describing the variation of short term interest rates [see Clarida, Gali and Gertler ( 1 997)]. We also considered variants that allow for responses to output as well as inflation, in the spirit of the Taylor ( 1 993) 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 of 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.

1 9 Iterating Equation (4.22) forward yields n:, = L'.,'f:"� o fY K(p;�k -·Pt+k) - With forward-looking price setting, how fast prices adjust depends on the expected discounted stream of future demand. 20 The interest rate rule may be thought of as a money supply equation. The associated money demand equation is given by m1 - p1 = c1 - ( -f, ) r;', • Note that under interest-rate targeting this relation simply 1 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:

4.2. 1.

The Financial Accelerator in a Quantitative Business Cycle Framework

1 365

Two extensions of 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. Investment 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 ( 1 996) and Bernanke and Mihov ( 1 998)] . 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 ( 1 997) 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 (1 996). Second, movements in consumption lead movements in investment over the cycle, as emphasized by Bernanke and Gertler ( 1 995) and Christiano and Todd ( 1 996). For example, Bernanke and Gertler ( 1 995) 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 chosen j periods in advance. Then the first-order condition relating the price of capital to investment, Equation (4.3), is modified to

(4.28) Note that the link between asset prices and investment now holds only in expectation. With the time-to-plan feature, shocks to the economy have an immediate effect on asset prices, but a delayed effect on investment and output 2 1 . To incorporate the investment delay in the model, we simply replace Equation (4. 1 9) with the following log-linearized version of Equation (4.28):

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 a/.

1 366

Heterogeneous firms. The baseline model assumes that all firms are alike ex ante, except for initial net worth. In practice, of 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 ( 1 994)]. To see how heterogeneity affects the results, we add to our model the assumption that there are two types of 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 of firms, we assume that there are two types of intermediate goods (one produced by each type of firm) which are combined into a single wholesale good via a CES aggregator. Production of the intermediate good is given by 4.2. 1 . 2.

v

1 zt

= A·zlKtat H1Q1 (He ) < w ,

implying that the net payoff to the lender reaches a global maximum at w* . The second implication of this assumption is that

r'(w)G" (w) - T" (w)G' (w) =

d(wh(w)) dw

( l -F(w)f > 0 for all

W.

These two implications are used to guarantee a non-rationing outcome. The optimal contracting problem with non-stochastic monitoring may now be written as

max(l - T(w))R" QK K, W

subject to

[T(w) - f.lG(w)] R" QK = R(QK - N).

It is easiest to analyse this problem by first explicitly defining the premium on external funds s = R"IR and then, owing to constant returns to scale, normalizing by wealth and using k = QKIN the capital/wealth ratio as the choice variable Defining A as the Lagrange multiplier on the constraint that lenders earn their required rate of return

38.

37

Any monotonically increasing transformation of the normal distribution satisfies this condition. To see this, define the inverse transformation z z(w), z' (w) > 0, with z - N(O, I). The hazard rate for the standard normal satisfies h(z) = ifl(z)/(1 - o.

1 386

B.S. Bernanke et al.

Y(w)

= I - r(w) + Jc(F(w) - p,G(w)). The first-order conditions for the contracting

problem may be written as

w : r' (w) - Jc [r '(w) -- p,G' (w)] k : E {Y(w) us - Jc(W)}

= 0,

A : (F(W) - p,G(W)) us -

(k- l)

=

o,

=

0.

Again, under no rationing, the first-order condition with respect to w defines the function Jc(W). This function is identical to Jc(W) defined in the case of no aggregate risk. The constraint that lenders earn their required rate of return defines an implicit function for the cutoff w = w(u, s, k) 4 1 . Computing derivatives we obtain ( r (W) -· - p, G(W) )=::-'--_,_=-==': (r'(W) - p,G'(w)) s

aw

"CC: -c:':-

as

0


0·

To obtain a relationship of the form = 1/J(s), 1/J' (s) > 0 we totally differentiate the first-order condition with respect to capital:

k

{

E uf'(w) ds + usY' (ill)

Rearranging gives

dk

{ {

(a-a; a-a; )

E (usY'(W) -- Jc'(w))

ds

_

ds +

ow

---

as

_

E (A'(w) - usY' (W))

dk

+ u l{w)

a} w

}

- Jc' (ill)

(a-a; a; ) } ds +

c-

dk

=

0.

ak

Using the fact that Y ' (w)

=

Jc' (w) (r(w) - p,G(w))

4 1 As a technical matter, it is possible that the innovation in aggregate returns is sufficiently low that w(p,, s, k) > w* , in which case the lender would set w = w* 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 co!Tect 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.

Ch. 21:

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1 3 87

we obtain

A. '(w) - Y'(w) us = A.'(w) [ 1 - ( T(w) - p,G(w)) us] = A-'(w)k- 1 , implying that dk/ds simplifies to the expression dk ds

E

{ usY(w) - A.'(w) �} { '( ) �;} E A w

Since awl as < 0, awlok > 0, and A' (w) > 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 government sectors that, along with details of the entrepreneurial sector presented in Section 4, underlie the log-linearized macroeconomic framework. B. l.

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. C1 is household consumption, M/P1 is real money balances acquired at t and carried into t + 1 , H, is household labor supply, � is the real wage for household labor, T1 is lump sum taxes, D1 is deposits held at intermediaries (in real terms), and fit is dividends received from ownership of retail firms. The household's objective is given by

(8 . 1 ) The individual household budget constraint is given by

Ct = Wt H, - T, + llr + RrDr - Dt+ 1 +

(Mt-1 - M1) . P,

(8 .2)

The household chooses C" D1+ 1 , H1 and M/P, to maximize Equation (8 . 1 ) subject to Equation (B.2). Solving the household's problem yields standard first-order conditions for consumption/saving, labor supply, and money holdings: (8 .3)

B.S. Bernanke et al.

1 388

= 1 ' Ct ( R�+� - ) - ' = Pt R 1

Wt C1

s1

1

(B.4)

H1 '

M,

t+l

1

(B.5)

where R7+ 1 is the gross nominal interest, i.e., . zt+1

_ =

Pn1 Rt+l -Pt n

-

1.

Note that the first-order condition for M/P1 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: Dt = B t . 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 Y1(z) be the quantity of output sold by retailer z , measured in units of wholesale goods, and let P1(z) be the nominal price. Total final usable goods, Y{, are the following composite of individual retail goods:

Y{

= [1

1

l

Yt(z)lE- 1 )/E dz

EI(E- 1 )

(B.6)

with E > 1 . The corresponding price index is given by

P1

=

[1

I

P1(z)< 1

]

c) dz

I /( 1 E)

(B.7)

Final output may then be either transformed into a single type of consumption good, invested, consumed by the govemment or used up in monitoring costs. In particular, the economy-wide resource constraint is given by

(B. S ) where q is entrepreneurial consumption and gate monitoring costs.

fl .f;"' w dF(w) R7Q1 1 K1 reflects aggre­

The Financial Accelerator in a Quantitative Business Cycle Framework

Ch. 21:

1 3 89

Given the index (B.6) that aggregates individual retail goods into final goods, the demand curve facing each retailer is given by

Y1 (z) =

( p��) y-c Y{.

(B.9)

The retailer then chooses the sale price P1(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 - 8, following Calvo ( 1 983). Let P;' denote the price set by retailers who are able to change prices at t, and let �*(z) denote the demand given this price. Retailer z chooses his p1ice to maximize expected discounted profits, given by

[

oc

L ekEl- I

At,k

k-0

-

]

p * pw l t+k * (z) pt+k yt+k

(B. l O)

'

where the discount rate A1 ,k = f3C/(Ct+k ) is the household (i.e., shareholder) intertemporal marginal rate of substitution, which the retailer takes as given, and where P;' = P/Xr is the nominal price of wholesale goods. Differentiating the objective with respect to Pt' implies that the optimally set price satisfies CXJ

L ekEt- 1

k-0

{ ( )-c Pt* Al,k Pt+k

[- - (--=-) E ]}

p1* �+* k (z) Pt+k

E

pw t+ k 1 Pl+k

-

=

0.

(B. l l )

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 e". Given that the fraction 8 of retailers do not change their price in period t, the aggregate price evolves according to (B. l 2) where P1* satisfies Equation (B. l l). By combining Equations (B. l l) and (B. l 2), 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 =

Mt - Mt- 1

PI

+ TI ·

The government adjusts the mix of financing between money creation and lump-sum taxes to support the interest rate rule given by Equation (4.25).

1 390

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This, in conjunction with the characterization in Section 5 of the entrepreneurial sector and the monetary policy rule and shock processes, completes the description of the model.

References Aghion, P., and P. Bolton ( 1997), "A theory oftrick1e-down growth and development with debt overhang", Review of Economic Studies 64: 1 5 1- 1 72. Aghion, P., A. Banerjee and T. Piketty ( 1997), "Dualism and macroeconomic volatility", unpublished paper (University College, MIT, and CEPREMAP, November). Akerlof, G. ( 1970), "The market for lemons: quality uncertainty and the market mechanism", Quarterly Journal of Economics 85:488-500. Bacchetta, P., and S. Gerlach ( 1 997), "Consumption and credit constraints: some international evidence", Journal of Monetary Economics 40:207-238. Bernanke, B.S. ( 1 983), "Nonmonetary effects of the financial crisis in the propagation of the great depression", American Economic Review 73:257-276. Bernankc, B.S. ( 1 993), "Credit in the macroeconomy", Quarterly Review, Federal Reserve Bank of New York 1 8:50-70. Bcrnanke, B.S., and M. Gertler ( 1 989), "Agency costs, net worth, and business fluctuations", American Economic Review 79: 1 4 --3 1 . Bemanke, B.S., and M . Gertler ( 1 990), "Financial fragility and economic performance", Quarterly Journal of Economics 1 05 : 87- 1 1 4. Bernanke, B.S., and M. Gertler ( 1995), "Inside the black box: the credit channel of monetary policy transmission", Journal of Economic Perspectives 9:27-48. Bernanke, B.S., and C. Lawn ( 1 992), "The credit crunch", Brookings Papers on Economic Activity 1 992(2):205-239. Bernanke, B.S., and I. Mihov ( 1998), "Measuring monetary policy", Quarterly Journal of Economics 1 13 : 869-902. Bernanke, B.S., and M. Woodford ( 1 997), "Inflation targets and monetary policy", Journal of Money, Credit and Banking 29:653-684. Bernankc, B.S., M. Gertler and S. Gilchrist ( 1996), "The financial accelerator and the flight to quality", Review of Economics and Statistics 78: 1-- 1 5 . Blinder, A.S., and L.J. Maccini ( 1 99 1 ), "Taking stock: a critical assessment o f recent research on inventories", Journal of Economic Perspectives 5 :73-96. Brayton, F., A. Levin, R. Tryon and J.C. Williams ( 1 997), "The evolution of macro models at the Federal Reserve Board", Board of Governors, Finance and Economics Discussion Series No. 29, May 1 997. Calomiris, C.W ( 1993), "Financial factors in the Great Depression", Journal of Economic Perspectives 7 : 61-86. Calvo, G.A. ( 1983), "Staggered prices in a utility-maximizing framework", Journal of Monetary Economics 1 2 : 383-398. Cantor, R. ( 1 990), "Effects of leverage on corporate investment and hiring decisions", Quarterly Review, Federal Reserve Bank of New York 1 5 : 3 1--4 1 . Carlstrom, C., and T. Fuerst ( 1 997), "Agency costs, net worth, and business fluctuations: a computable general equilib1ium analysis", American Economic Review 87:893-9 1 0. Carpenter, R.E., S.M. Fazzari and B.C. Petersen ( 1 994), "Inventory (dis)investment, internal finance fluctuations and the business cycle", Brookings Papers on Economic Activity 1 994(2):75-138. Carroll, C.D. ( 1 997), "Buffer-stock saving and the life cycle/permanent income hypothesis", Quarterly Journal of Economics 1 12 : 1-55.

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Chari, VV, P.J. Kehoe and E.R. McGrattan ( 1 996), "Sticky price models of the business cycle: can the contract multiplier solve the persistence problem?", Staff Report 2 1 7 (Federal Reserve Bank of Miuneapolis). Chirinko, R.S. ( 1 993), "Business fixed investment spending: a critical survey of modelling strategies, empirical results, and policy implications", Journal of Economic Literature 3 1 : 1 875-1 9 1 1 . Christiano, L.J., and R. Todd ( 1996), "Time to plan and aggregate fluctuations", Federal Reserve Bank of Minneapolis Quarterly Review, Winter, 1 4-27. Christiano, L.J., M. Eichenbaum and C.L. Evans ( 1 996), "The effects of monetary policy shocks: evidence from the flow of funds", Review of Economics and Statistics 78: 1 6-34. Clarida, R., J. Gali and M. Gertler ( 1 997), "Monetary policy rules and macreconomic stability: evidence and some theory", unpublished paper (New York University, March). Cooley, T.F., and V. Quadrini ( 1 997), "Monetary policy and the financial decisions of firms", unpublished paper ( University of Rochester, December). Cummins, J.G., K.A. Hassett and R.G. Hubbard ( 1 994), "A reconsideration of investment behavior using tax refonns as natural experiments", Brookings Papers on Economic Activity 1 994(2) : 1 -74. Deaton, A. ( 1 99 1 ), "Saving and liquidity constraints", Econometrica 59: 1 2 2 1 - 1 248. Eberly, J.C. ( 1 994), "Adjustment of consumers' durable stocks: evidence from automobile purchases", Journal of Political Economy 1 02:403-436. Eckstein, 0., and A. Sinai ( 1 986), "The mechanisms of the business cycle in the postwar era", in: R.J. Gordon, ed., The American Business Cycle: Continuity and Change (University of Chicago Press for NBER, Chicago, IL). Engelhardt, G. ( 1996), "Consumption, down payments, and liquidity constraints", Journal of Money, Credit and Banking 28:255-76 1 . Fazzari, S.M., R.G. Hubbard and B.C. Petersen ( 1988), "Financing constraints and corporate investment", Brookings Papers on Economic Activity 1 988( 1 ) : 1 4 1-195. Fisher, I. ( 1 933), "The debt-deflation theory of great depressions", Econometrica 1 :337-357. Fisher, J.D.M. ( 1 996), "Credit market imperfections and the heterogeneous response of firms to monetary shocks", Working Paper WP-96-23 (Federal Reserve Bank of Chicago, December). Fuerst, T. ( 1 995), "Money and financial interactions in the business cycle", Journal of Money, Credit and Banking 27: 1321-1338. Gale, D., and M. Hellwig ( 1 985), "Incentive-compatible debt contracts: the one-period problem", Review of Economic Studies 52:647-664. Gcrsbach, H. ( 1997), "Financial intermediation, capital spillovers, and business fluctuations", unpublished paper (Alfred-Weber-Institut, University of Heidelberg, November). Gertler, M. ( 1 988), "Financial structure and aggregate economic activity: an overview", Journal of Money, Credit and Banking 20(3):559-588. Gertler, M. (1 992), "Financial capacity and output fluctuations in an economy with multiperiod financial relationships", Review of Economic Studies 59:455-472. Gertler, M. ( 1 995), "Comment on 'Money and financial interactions in the business cycle"', Journal of Money, Credit and Banking 27: 1 342--1 3 5 3 . Gertler, M . , and S. Gilchrist ( 1993), "The role o f credit market imperfections i n the monetary transmission mechanism: arguments and evidence", Scandinavian Journal of Economics 95:43-64. Gertler, M., and S. Gilchrist ( 1994), "Monetary policy, business cycles, and the behavior of small manufacturing firms", Quarterly Journal of Economics 59:309-340. Gertler, M., and R.G. Hubbard ( 1988), "Financial factors in business fluctuations", in: Financial Market Volatility (Federal Reserve Bank of Kansas City) 33-72. Gilchrist, S., and C.P. Himmelberg ( 1995), "Evidence on the role of cash flow for investment", Journal of Monetary Economics 36:541-572. Goodfiiend, M., and R.G. King ( 1 997), "The new neoclassical synthesis", NBER Macroeconomics Annual, 23 1-282. Gourinchas, P.-O., and J. Parker (1 995), "Consumption over the lifecycle", mimeograph (MIT).

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Greenwald, B., and J. Stiglitz ( 1993), "Financial market imperfections and business cycles", Quarterly Journal of Economics 1 08 :77-1 1 4 . Gross, D . ( 1 994), "The investment and financing decisions o f liquidity-constrained firms", unpublished paper (MIT). Hassett, K.A., and R.G. Hubbard ( 1 996), "Tax policy and investment", Working Paper No. 5683 (NBER, July). Holmstrom, B., and .T. Tirole ( 1 997), "Financial intermediation, loanable funds, and the real sector", Quarterly Journal of Economics 1 1 3 : 663-692. Hoshi, T., A.K. Kashyap and D. Scharfstein ( 1 99 1 ), "Corporate structure, liquidity, and investment: evidence from Japanese industrial groups", Quarterly Journal of Economics 1 06:33-60. Hubbard, R.G. ( 1 995), "Is there a "credit channel" for monetary policy?", Review 77 (Federal Reserve Bank of St. Louis, May/June) 63-77. Hubbard, R.G., A.K. Kashyap and T. Whited ( 1 995), "Internal finance and firn1 investment", Journal of Money, Credit and Banking 27:683-701 . Jaffee, D.M., and J. Stiglitz ( 1 990), "Credit rationing", in: B.M. Friedman and F.H. Hahn, Handbook of Monetary Economics (North-Holland, Amsterdam). Jappelli, T. ( 1 990), "Who is credit-constrained in the U.S. economy?", Quarterly Journal of Economics 1 05 : 2 1 9-234. Jensen, M., and W. Meckling ( 1 976), "Theory of the firm: managerial behavior, agency costs, and capital stmcture", Journal of Financial Economics 3 :305-360. Kaplan, S.N., and L. Zingales ( 1 997), "Do investment-cash flow sensitivities provide useful measures of financing constraints?", Quarterly Journal of Economics 1 12 : 1 59-2 1 6. Kashyap, A.K., and J.C. Stein ( 1 994), "Monetary policy and bank lending", in: N.G. Mankiw, ed., Monetary Policy (University of Chicago Press for NBER, Chicago, IL) 22 1-262. Kashyap, A.K., O.A. Lamont and J.C. Stein ( 1 994), "Credit conditions and the cyclical behavior of inventories", Quarterly Journal of Economics I 09:565-592. Kaufman, H. ( 1986), "Debt: the threat to economic and financial stability", in: Debt, Stability, and Public Policy (Federal Reserve Bank of Kansas City) 1 5-26. King, R.G., and A.L. Wolman ( 1 996), "Inflation targeting in a St. Louis model of the 2 1 st century", Working Paper No. 5507 (NBER, March). Kiyotaki, N., and J. Moore ( 1 997), "Credit cycles", Journal of Political Economy 1 05 :2 1 1 -248. Kiyotaki, N., and J. Moore (1 998), "Credit chains", unpublished paper (London School of Economics). Krishnamurthy, A ( 1997), "Collateral constraints and the credit channel", unpublished paper (MIT). Leeper, E.M., C.A. Sims and T. Zha ( 1996), "What does monetary policy do?'', Brookings Papers on Economic Activity 1 996(2): 1-63. Levine, R. (1 997), "Financial development and economic growth: views and agenda", Journal of Economic Literature 35:688-726. Ludvigson, S. ( 1997), "Consumption and credit: a model of time-varying liquidity constraints", unpublished paper (Federal Reserve Bank of New York, October). Manger, R.P. ( 1 987), "A life-cycle consumption model with liquidity constraints: theory and empirical results", Econometrica 55:533-558. Mishkin, F.S. ( 1 997), "The causes and propagation of financial instability: lessons tor policymakers", in: C. Hakkio, ed., Maintaining Financial Stability in a Global Economy (Federal Reserve Bank of Kansas City). Modigliani, F., and M. Miller (1958), "The cost of capital, corporation finance, and the theory of investment", American Economic Review 48:26 1 -297. Morgan, D. (1 998), "The lending view of monetary policy and bank loan commitments", Journal of Money, Credit and Banking 30: 1 02- 1 1 8 . Oliner, S.D., and G.D. Rndebusch ( 1 994), "Is there a broad credit channel for monetary policy?", unpublished paper (Board of Governors of the Federal Reserve System).

Ch. 21:

The Financial Accelerator in a Quantitative Business Cycle f 0, the discretionary policy outcome in Equation (2. 1 4) and the commitment outcome in Equations (2. 1 1 )-(2. 1 2) illustrate the celebrated "inflation bias" result: equilibrilUll 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 A (the more valuable is employment on the margin) and the higher is x* relative to 8 (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 8 is random, whereas the employment target x* presumably is constant (or at least more stable than 8), 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* 8 > 0. This asslUllption 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 employment depends on current employment). To reduce the future inflation bias, the -

-

11 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 1 2 . The "distortion" i n the policymaking process can b e 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 non­ credible 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 of equilibrium to a more favorable outcome. Is this a plausible positive model of inflation? Some observers, like McCallum ( 1 996), apparently do not think so. A convincing rebuttal should address the question already posed by Taylor ( 1 983), who - in his discussion of Barro and Gordon ( 1 983b) - 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

1 2 Svensson ( l997a) proves this result formally, drawing on earlier work by Lockwood el al. ( 1 998) and Jonsson ( 1 997). See also Obstfeld ( 1 997b) for a related result in a dynamic model of seignorage. Beetsma and Bovenberg ( 1 998) show that stabilization bias arises also when monetary and fiscal policy are pursued by different authorities with diverging objectives.

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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 A, 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 1 950s and 1 960s were a period without serious supply shocks and with a low natural rate of unemployment (low variance of E, high realizations of 8), which made it easy to keep inflation low. Enter the 1 970s 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 8). The gradual decline in inflation from the mid- 1 980s 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 1 3 . Instead, the literature has focused on normative issues o f 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 rej ects 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

Es

[�

]

(/ sL(nr , Xr) ,

(2. 1 5 )

l.l See, however, the recent papers b y Parkin ( 1 993), Barro and Broadbent ( 1 997) and Broadbent ( 1 996).

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where D is a discount factor. To simplifY the algebra, we assume the static loss function to be linear, not quadratic, in employment:

L(n, x) = �n2 - A.x.

(2. 1 6)

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 = () - E (since n * = 0 and employment volatility is not costly), while the static equilibrium under discretion has inflation equal to A and employment still at X = e - 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 of the following expectations:

n,e _-

{A 0

iff nu = n;, otherwise.

u = t - l , . . . , t -- T,

(2 . 1 7)

Equation (2. 1 7) 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. Jr5c = 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 nse = 0) is simply ns = A, thus implying employment xs = A + Bs - £5 . After some algebra, the current benefit from cheating can then be expressed as (2. 1 8) Due to the simpler loss function, the benefit is independent of the realizations of 8 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. 1 7) 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 of equilibrium 1 4. Thus, the cost of a deviation is

c = Es.

[

T

1 "' � 0 -s(L(A' t�s+ l

l

( 1 - iV)

et - EI ) -- L(O' eI - Et )) = 15 ---),_2 ( 1 - D) '

(2. 1 9)

1 4 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 e 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. 1 9) and (2. 1 8) reveals that this is more likely the higher the discount factor (5 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 e, while the cost would depend on the variance and the expected value of e. As a result, even with reputation, equilibrium inflation would continue to depend on the actual realization of e: a high value of e makes the incentive­ compatibility 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 e. Thus, reputation would reduce average inflation but would not change the main positive implications of the model of the previous section. Canzoneri ( 1 985) studied a framework with shocks to inflation that are unobservable to private agents both ex ante and ex post; an example could be the f.l 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 ( 1 985), Barro ( 1 986), Tabellini ( 1 985, 1 987) and Vickers ( 1 986) studied reputational models where the private agents are uncertain about the policymakers "type" (as his A 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 A or without access to a commitment technology) can temporarily borrow the reputation of a "hawkish" policymaker (someone with a low A 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 ( 1 986) 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 multiple­ equilibrium problem, which strikes with particular force against a positive 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 game 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 1 5. 2.5. Notes o n the literature

Textbook treatments of the general material in this section can be found in Persson and Tabellini ( 1 990, Chs. 1-4), and in Cukierman ( 1 992, Chs. 9-1 1 , 1 6), both covering the literature up to around 1 990. The literature on credibility in monetary policy starts with Kydland and Prescott ( 1 977), who included a brief section with the basic insight of the static model in subsection 2.3. B arro and Gordon ( l 983a) formulated a linear­ quadratic version and pushed its use as a positive model of monetary policy. Calvo ( 1 978) studied the credibility problem of monetary policy in a dynamic model, where the short-run temptation to inflate arises for public-finance reasons. Obstfeld ( 1 997b) 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 ( 1 994), Lockwood et al. ( 1 998), and Jonsson ( 1 997). Parkin ( 1 993) argues that the great inflation of the 1 970s can be explained by an increase in the natural rate in the kind of model dealt with here. Ball ( 1 996) points to indirect evidence that many disinflationary episodes in the 1 980s lacked credibility. Barro and Gordon ( l983b) 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 ( 1 985), Tabellini ( 1 985, 1 987) and Barro ( 1 986) 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 ( 1 986) 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 ( 1 985). Grossman and Van Huyck ( 1 986) and Horn and Persson ( 1 988) studied reputational models dealing with the inflation tax and exchange rate policy, respectively. Rogoff ( 1 987) 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 ( 1 997), al Nowaihi and Levine ( 1 996) and Herrendorf ( 1 996). The ideas arc related to Schottcr ( 1 9 8 1 ) and to the view that international institutions may facilitate cooperation in trade policy [see Staiger ( 1 995) for a survey].

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3. Political 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 1 6 . But they are interesting enough t o motivate this line o f 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 re­ election probability of the incumbent 17. 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 of 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 ( 1 996), Rogoff and Sibert ( 1 988) and Persson and Tabellini ( 1 990). 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 ( 1 987). 3. 1. Opportunistic governments 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 tum with "moral

!(, Faust and Irons ( 1999) criticize the literature on partisan cycles in the USA for 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 ( 1 997) uses modern panel data estimation techniques trying to control for similar biases in a panel of 1 0 OECD countries. He finds strong support for a post-electoral pa1iisan cycle and weaker support for a pre··electoral cycle. 17 See, for instance, Fair ( 1 978).

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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 ( 1 996), whose work builds on that by Persson and Tabellini ( 1 990) and Holmstrom ( 1 982). 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. 1 5) and (2. 1 6) 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 8 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 -rj1 fJH , where of a specific policymaker follows a simple MA-process: £1 rJ is a mean zero, i .i .d. random variable, with distribution F(-) and density JO (in this formulation a positive realization of rJ 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 fJo = 0. The timing in a given period t is as follows. The previous period's policy instrument and inflation JT1_ 1 are observed. Wages (and expected inflation) are determined. The policymaker sets the policy instrument for t. Competence is realized and output growth x1 is observed by everybody. Finally, if t is an election year - which happens every other year - elections are held. 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 rj1 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 ( 1 996) from the earlier work by Rogoff and =

-

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Sibert ( 1 988), Rogoff ( 1 990) and Persson and Tabellini ( 1 990). 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 of this kind was first studied by Holmstrom ( 1 982) 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 of 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. And 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 of the economy. To properly understand an expansion of the money supply six months before the elections, voters would have to know the policymaker's forecasts of 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 1 8 . Finally, we make two other simplifying assumptions. Once voted out of 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 of any opponent is zero. 3.1.2. The equilibrium

First, consider wage-setters. They have the same information as the policymaker and can thus compute equilibrium policy and perfectly predict inflation. Hence, in equilibrium :rr = :;re in every period. Next, consider voters. By observing output and knowing the previous period shock to competence, 1]1_ 1 , they can correctly infer the current competence of the incumbent by using Equation (2.3): 1]1 = x1 - 1Jt- l 1 9. 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 if and only if x1 > 111-1 , as in this case 1}1 > 0 (if x1 = 1Jr-- I , we can assume that the voters randomize, as they are indifferent). To an outside econometrician, who observes x1 but not 11t- I , 18

As Lohman ( 1 996) observes, however, this asswnption 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 fhe local inflation but not economy-wide inflation (the policy instrument). 19 Voters know that n = ne Also, recall that in period 0 we have, by asswnption, '1/o 0. Hence in period 1 : x 1 = ry 1 , and output fully reveals the policymaker's competence. Knowing ry 1 , in period 2, voters can infer ry2 from x2 = ry2 + ry 1 , and so on. =

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this voting rule appears consistent with retrospective voting: the probability of re­ election, Pr(1Jt- I ::;; x1) = F(xt), increases with output growth in the election period. Next, consider the policymaker's optimization problem. In off-election 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 :rr , subject to Equation (2.3) and taking :n;e as given. As in subsection 2.4, this yields :rr1 A. On-election years entail different incentives: by raising output growth through unexpected inflation, the incumbent policymaker would increase his election probability. In equilibrium, wage­ setters 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 [x1 > 1]1 _ J ], or - by Equation (2.3) and our definition of f - iff [1]1 > n1e - n1 ] . When setting policy, the incumbent has not yet observed 1]1 • His perceived probability of re­ election is 1 - Prob(171 ::;; :rr1e - :rr1 ) = 1 - F(:rr1e - :rr1 ), where F(-) is the cumulative distribution of 1]. This probability is clearly an increasing function of unexpected inflation. Next, we need some additional notation. Let V11 and VN 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 fc be equilibrium inflation during on-election years, to be derived below. Simple algebra establishes that: =

K(l + AR. The D candidate thus cares more 2 1 Rogoff (1 990) 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 ( 1 998) demonstrate that political cycles can be avoided and social welfare increased by delegating monetary policy to an independent central bank 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 f so that X = e + :n; - :n;e , 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 cannot 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 preferences. 3.2.2. Economic equilibrium Under these assumptions, voters are perfectly informed and the state of the economy does not reveal 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 verity that n1 }/ , 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 :n;e = A,R + P(J.cD - A,R). If party R wins, it sets :n; = AR < :n;c and causes a recession in the first period of office: output is x -P(J.cD - J.cR). If D wins, the opposite happens: actual inflation is higher than expected and a boom occurs: x = ( 1 - P)(J.cD - J.cR). Thus, uncertain election outcomes may cause economic fluctuations. But thi s 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 before 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 governments. An election victory of the left brings about a temporary boom just after the elections; victory of the right is instead followed by a recession. These partisan effects are more pronounced under a more polarized political system (i.e. with large differences between J.cD and J.cR in the model), or more generally if the elections identify a clear winner, like in two-party systems. Alesina and Roubini ( 1 997) argue that these predictions are consistent with the evidence for industrial countries. =

=

3.2. 3. Political equilibrium The partisan model focuses on the role of party preferences in elections. Voters anticipate what each party would do if elected, and choose the party closest to their

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T Persson and G. Tabellini

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 prefers R to win if (3 . 6) The probability (1 - P) that R wins is the probability that the relative weight of the median voter Am 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 = !(A.11 + ).D)] 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 Cukierrrian ( 1 988), 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 voters

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 maj orities. Alesina and Rosenthal ( 1 995) 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. Notes on the literature Alesina and Roubini ( 1 997) 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 ( 1 995) focus on the United States in particular. The evidence for a partisan cycle is scrutinized by Faust and Irons ( 1 999) (for the USA) and by Mishra ( 1 997) (for a panel of OECD countries). Fair ( 1 978), Fiorina ( 1 9 8 1 ) and Lewis-Beck ( 1 988) discuss the evidence on retrospective voting i n the USA and elsewhere. The first models of political business cycles with opportunistic government are due to Nordhaus ( 1 975) and Lindbeck (1 976). The first theory of a partisan political cycle is due to Hibbs ( 1 977). 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 government and adverse selection with rational voters, summarized in subsection 3 . 1 .3, was developed by Rogoff and Sibert ( 1 988) in the case of fiscal policy, and adapted to monetary policy by Persson and Tabellini ( 1 990). Rogoff ( 1 990) generalized the fiscal policy results to two-dimensional signalling by the incumbent. Ito ( 1 990) and Terrones ( 1 9 89) 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 principal­ agent problem with career concerns developed by Holmstrom ( 1 982). It was studied in the context of monetary policy by Lohman ( 1 996) and, in a somewhat different set-up, by Milesi-Ferretti ( 1 995b). Ferejohn ( 1 986) and Barro ( 1 973) 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 ( 1 987, 1 988). This model is extended by Alesina et al. ( 1 993) and by Alesina and Rosenthal ( 1 995) to allow for ideological parties who also differ in their competence. Milesi-Ferretti ( 1 994) 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 ( 1 995a,b). Jonsson ( 1 995) 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 ( 1 988). The role of moderating elections, in theory and in the US data, is studied by Alesina and Rosenthal ( 1 995).

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 ex post is costly or takes time. This premise is questioned by some critics [in particular by McCallum ( 1 996) and Posen ( 1 993)], 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 ex post suboptimal from society's (or the incumbent gov­ ernment) 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 ex post and ex ante 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 governments 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 of a well-specified non-cooperative strategic inter­ action 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 of 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. Among 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 of some European countries to peg their exchange rates in the 1 970s and 1 980s often ended up in failure: with lack of 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 of a single good which is also produced by the rest of the world. The central bank controls :rr through the exchange rate, given a foreign inflation rate denoted :rr* . The rest of the model, including the expectations-augmented Phillips curve (2.3), the rational-expectations assumption, the objective function of the policy maker (2.6), and the timing of events are as in subsection 2.2 or 2.3; except that we assume not only 8, but also :rr * to be known when wages are set (:rrc are formed). Note that :rr* 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. 1 2) and (2. 1 4). As E(:rr) > :rr* , the model is consistent with the idea of 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 of holding the exchange rate fixed, or of letting it depreciate at a fixed rate k. There is commitment, in the sense that the rate of 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-run 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 ( 1 997) in fact 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 (non­ lump sum) cost. ln this setting institution design generally improves credibility, but cannot remove the credibility problem completely.

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T Persson and G. Tabellini

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: J£:8 = JC * , XS = e - 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. 1 2)-(2. 14), and the previous expression for n8 and x8 , into Equation (2.6) and taking expectations of the difference in their payoffs. Recalling that E( e) = 0, this gives

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 of credibility is larger than the loss of stabilization policies. This trade-off between credibility and flexibility is a recurrent theme in the literature on institution design. The benefit of 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, i s a commit­ ment 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 n + x = m + v. The policy instrument is m, like in Section 2. Under a simple money growth rule, velocity shocks u 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 A = 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 of as follows. Define normal times as a range of possible realizations of the unobservable supply shock: E E [eL (e), (e)]. Inside th:s interval, the central bank remains committed to the simple rule. During exceptional times, defined by the complementary event, an

Eu

24 A literature dating back to the 1 970s has studied the choice between altemative rules in richer models - for surveys, see Genberg ( 1 989) and Flood and Mussa ( 1 994). Recent contributions to the comparison of exchange rate versus money based stabilizations of inflation are surveyed by Calvo and vegh ( 1 999).

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escape clause is invoked. The central bank abandons the simple rule and pursues a discretionary (ex post 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 peso 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 post 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 ( 1 989) 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 ( 1 997a) 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 ex post 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 tum, 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 8 is realized) society sets a pair of fixed costs [cL(8), cu (8)] 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( 8) and Eu ( 8), that leave the central bank indif­ ferent between sticking to the simple rule and bearing the cost of no stabilizing policies, or paying the 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( 8) = d", cu ( 8) = cu or cu = cL = 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 ( 1 997) point out that an important consideration behind the ex ante choice of c might be to prevent multiple equilibria. 4.2. Central bank independence The first example of strategic delegation in monetary policy is the independent and conservative central banker, suggested by Rogoff ( 1 985). 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)

T. Persson and G. Tabellini

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of 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 of this subsection, we ask how reasonable this assumption really is.) Prospective central bankers have loss functions of the form (2.6), but differ in their personal values of A 25 . The appointment thus boils down to the choice of a parameter, say AB. The private sector observes AB 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

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 del­ egation: a central banker more hawkish on inflation, i.e. someone with a lower As, 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: (4. 1 ) where the expectation i s taken over e and E , for any AB. 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 AB is dE[L(A8 )]

oR

*2 �� = A (x + Oo ) + (AB - A)(l

OE

+ AB)} ·

(4.2)

The first term is the expected credibility loss of choosing a central banker with a higher A8. 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 A > AB > 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 our formal model abstracts from. As discussed in Section 3, however, such heterogeneity can he formally introduced in the model without any difficulties. Alesina and Grilli ( 1 992) 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 fourth-order equation in J..B , which is difficult to solve. But as the derivative is negative at )./1 = 0, positive for all }..'1 > i\., and the second-order condition is fulfilled for any i\.B in the interval (0, i\.), we know that the solution must be inside the interval (0, i\.).

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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 fluc­ tuations in the inflation bias arising from observable 8 shocks remain. If A 8 could be chosen after the realization of 8, society would want to meet a more serious incentive problem - a smaller 8 - with a more hawkish central banker - a smaller AB. 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 post suboptimality of central banlc 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 post? 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 ( 1 989) was probably first in formulating a model of central bank independence under partisan politics 2 8 . Waller and Walsh ( 1 996) 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 ofthe institution itself. A better inter­ pretation is that, at the constitutional stage, society drafts a central bank statute spelling out the "mission" of the institution. Thus, the parameter AB 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 employment 27

This is indeed proved by Lohman (1 992). Fratianni et a!. ( 1 997) formally analyze the role of central bank independence in the absence of a traditional credibility problem, but in the presence of explicit electoral incentives. 28

T Persson and G. Tabellini

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(or output) volatility - since if ).,8 < A, 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 of studies have constructed measures of central bank independence based on central bank statutes, also taking the priority given to the goal of price stability into account 29. Cross­ country 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 of this result have been suggested. Alesina and Gatti ( 1 996) note that an independent central bank could reduce electorally induced output volatility, as would be predicted by the models of Section 3 , and Lippi ( 1 998) provides evidence that could support this proposition. Posen ( 1 993, 1 995) 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 ( 1 985) also suggests another interpretation of 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, (XB X)(JT - ;r * )2 , where XB > X · 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 30. 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 target, and inflation contracts Central banks have traditionally operated with intermediate targets, like money or the exchange rate. In the 1 990s, several central banks started to target inflation: whereas some central banks imposed the procedure on themselves, the transition has been mandated by some governments 3 1 . Such targeting schemes have recently been studied 29 See in particular Bade and Parkin ( 1 988), Grilli et al. (J 991 ), Ales ina and Summers ( 1 993 ), Cukierman

( 1 992) and Eijffmger and Schaling ( 1 993). Rogoff ( 1985) compares an inflation target to other nominal targets, such as money and nominal income. He shows that strategic concerns of the type considered here, can indeed overturn the ranking 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. Sec in particular Leiderman and Svensson ( 1 995), Haldane (1 995), McCallum ( 1 996), Mishkin and Posen ( 1 997) and Almeida and Goodhart ( 1 996). In practice, an inflation target means that the central bank is using its own inflation forecast as an intermediate target; see Svensson ( 1 997b) for instance.

30

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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 bank - with punishments 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 ( 1 993) and Walsh ( 1 995a). 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 in:flation: P(n ; 8, E) = Po( 8, E) + P I ( fJ, E) Jt + �P2 ( 8, E) n2 .

(4.3)

Our goal is to optimally set the terms p;(8, E), i = 0, 1 , 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(n, x) + P(:rr ; e, 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 (4.4) The benchmark optimum in Equation (2. 1 1 ) can be implemented by setting p2 (8, E) = 0 and p 1 (8, E) = p1 (fJ) = .A(x* - 8). Since the constant p0(fJ, f) does not affect 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 f; 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 in:flation is conditional on 8; as the incentive to inflate the economy also varies linearly with 8. To see the intuition for this result, think about the punishment for inflation as a Pigovian corrective tax. As

T. Persson and G. Tabellini

1 434

discussed in subsection 2.3, the distortion we want to address is that the central bank does not internalize the effect of its policy on inflationary expectations, when acting ex post. Since expected inflation E(n I 8) is a linear projection of Jr, a linear penalty for inflation makes the central bank correctly internalize the marginal cost of its policy 3 2 . To see this formally, substitute Equation (2.3) into the objective function (2.6) and calculate the equilibrium marginal cost of expected inflation in state 8 as:

dE[L(n, x) I & = (x * _ = ] Jc &) Pt ( & dne

'

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 ( 1 985) targeting solution, discussed at the end of the last section, is equivalent to an inflation contract with P2 = ( X8 - X), P I = ( X8 - X) JT *, and po = 1 (X8 - X)(n*)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 (n; 8) =Po +pt (8)(n - n*);

(4. 5)

the central banker is punished linearly, but only for upward deviations from society's preferred inflation rate. Walsh ( 1 995b) shows that the marginal penalty on inflation can be interpreted as resulting from an arrangement where the governor of the central bank faces a probability of being fired which increases linearly in inflation. Such an arrangement resembles the Price Targeting Agreement in force in New Zealand since 1 990. Other looser interpretations would be to associate the penalty with altered central-bank legislation, a lower central-bank budget, or a loss of 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 of 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 banlc is risk averse, the optimal contract entails a diminishing marginal penalty on inflation (to reintroduce linearity in the incentive scheme). Svensson ( 1 997a) has proposed an alternative interpretation of 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 9

Indeed, linearity of the optimal contract is preserved for any general loss functions, and not JUS( 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 of the form in Equation (2.6). Suppose that society manages to assign a loss function with a lower goal for inflation, say :reB ( 8) rather than :rc* , to the central banlc Then the optimal central bank goal for inflation is :rr;B ( 8) = :rc * - A,(x* - 8). 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 of the form in Equation (4.3), with parameters A-(x* - 8) and P o = HA-(x* - 8)2 - 2:rc* A-(x* - 8)] . This representation 0, P1 P2 of an inflation target suggests an alternative explanation for the empirical observation discussed in the previous subsection. A lower :reB 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, :rc*, is about 2%, and that the average inflation bias, A-(x* - 8), 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, :rcB(8), of -3%. But in equilibrium, the 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 of 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 of rewards or punishments that makes the central bank behave in the desired fashion. But then we are back to the performance contract interpretation of 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 ( 1 993) show that if the central bank is risk neutral, if the constraints faced by the central bank (i.e. the behavioral equations of the economy) are linear, as assumed so far, and if the marginal penalties under the contract can be contingent on 8, 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 of 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 of a direct penalty on inflation, rather than in a =

=

33 The best assignment if society could really freely impose an objective function on Cl:l, would be to set x*(8) = 8, thereby e liminating the inflation bias completely.

T Persson and G. Tabellini

1 43 6

more round 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, P1 and p2 in Equation (4.3) each have to be constant across 8? This question and its answer are related to the problem in Herrendorf and Lockwood ( 1 997), who study delegation in a model with observable shocks, and to the problem in Beetsma and Jensen ( 1 998), who study delegation via an optimal contract when the central banker's preferences are tmcertain ex 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 = A-

1 + pz

1

+ A + P2 E ,

into the quadratic objective function. We then take expectations of the resulting expression over A and E and maximize with regard to p 1 and p2 . After tedious but straightforward algebra, we can write the optimality conditions as ( 1 + Pz P pz ___-::-"'-_ -- _-=( l + .A. + pz )3

(4.6)

These conditions are both intuitive. It is easy to show that the first condition says E(n) = ;r* : unconditionally expected inflation should coincide with society's preferred rate of inflation. The second condition says that the coefficient on the quadratic term in the contract should be a positive increasing function of the relative importance of observable to unobservable shocks (the left-hand side is increasing in pz ). Thus, when fluctuations in the observable incentives to inflate cannot be handled by a state­ contingent linear punishment, the constrained optimum gives up a little bit on (first­ best) stabilization in order to diminish the costly fluctuations in Jr. As p1 contains a term in ;r*, we can rewrite the optimal non-state contingent contract P(n) = Po + P 1 n + pz (n - n *i ,

with p2 given by Equation (4.6) and p 1 = (h' +p2 n'). 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 1 990s in many countries as an instance of this arrangement 3 4. The simple contracting model discussed here has been extended in several directions. lf some shocks are observable, but not verifiable and hence not contractible, the central In the model of Beetsma and Jensen ( 1 99g) with uncertain CB preferences, 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 ( 1 993) 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 ex post 35. Walsh ( 1 995a) shows that the optimal contract can also handle costly effort by the central bank. Dolado et al. ( 1 994) as well as Persson and Tabellini ( 1 996) 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 ( 1 998) show how delegation via inflation contracts may eliminate political monetary cycles. McCallum ( 1 996) 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 post benefits of inflation and agents hurt by inflation are given a prominent role in the enforcement. Interestingly, Faust ( 1 996) 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 post 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 literature The literature on institutions in monetary policy has been surveyed in textbook forn1 by Persson and Tabellini ( 1 990), Cukierman ( 1 992) and Schaling ( 1 995). In the reputational model of Cukiennan and Liviatan ( 1 99 1 ), by contrast, announcements matter because they convey information about the policymaker's type.

35

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The formal theoretical literature on central bank independence starts with Rogoff ( 1 985), 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 ( 1 983b) in an anticipatory footnote. Giavazzi and Pagano ( 1 988) 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 ( 1 98 9) introduce the formal analysis of the rules with escape clauses. Lohman ( 1 992) 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 ( 1 997a) applies an escape-clause model in his analysis of realignments within the ERM, emphasizing the possibility of multiple equilibria. Bordo and Kydland ( 1 995) argue that the classical gold standard worked like a rule with escape clauses. Flood and Marion ( 1 997) 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 ( 1 995a) and by Persson and Tabellini ( 1 993), and was further extended by Beetsma and Jensen ( 1 998) and by Herrendorf and Lockwood ( 1 997). Insightful recent general discussions about the appropriate institutional framework for monetary policy can be found in Fischer (1 995), McCallum ( 1 996) and Goodhart and Vinals ( 1 994). Cukierman and Lippi ( 1 998) 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 ( 1 995). More recent surveys include Haldane ( 1 995) and Mishkin and Posen ( 1 996). A number of studies - including Bade and Parkin ( 1 988), Alesina ( 1 988), Grilli et al. ( 1 99 1 ), Cukierman ( 1 992) and Eijffinger and Schaling ( 1 993) - 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. ( 1 994) study historical evidence on inflation before and after major central bank reforms in twelve countries since the end of the 1 9th century. Jonsson (1 997) uses pooled time-series and cross-section data from the OECD countries since the early 1 960s 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 ( 1 993) 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 Haan ( 1 996). Each subsection above refers to additional relevant studies on specific topics.

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Part B. Fiscal Policy

This part of the chapter focuses mainly on intertemporal aspects of fiscal policy, such as government debt issue and taxation of wealth. A companion piece [Persson and Tabellini ( 1 999)] surveys the research on static "public finance" problems. The main stylized facts regarding the intertemporal aspects of 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 1 970s. The cross-sectional pattern of 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 maj oritarian and presidential electoral systems, in countries with coalition governments and frequent government turnovers, and in countries with lenient rather than stringent government budget processes 38. 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 Charnley ( 1 986), the optimal capital tax should decline over time, asymptotically approaching zero, as the long-run elasticity of investment is very high compared to that of other tax bases. Similarly, Barro's ( 1 979) tax-smoothing model of deficits can successfully explain war-time deficits, but not the persistent accumulation of debt that has occurred in many industrial countries since the 1 970s. 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 of the chapter, we survey some recent literature that speaks to these stylized facts on the basis of positive models of 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 of fiscal policy and discuss alternative explanations for large government borrowing. 36 Mendoza et a!. ( 1 996), building on earlier work by Mendoza et a!. ( 1 994), compute effective tax rates for a sample of 1 4 industrial countries, during the period 1 965- 1 99 1 . 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. Furthem1ore, the average tax rate on capital was higher than that on labor and consumption during every five-year period since 1 965, and kept rising over time. 37 See for instance Elmendorf and Mankiw (1 999) and Alesina and Perotti ( 1 995b ). Jx See von Hagen and Harden (1 995), Alcsina and Perotti ( 1 995b), Grilli et a!. ( 1 99 1), Roubini and Sachs ( 1 989).

T Persson and G. Tabellini

1440 5. Credibility of fiscal policy

We first discuss the ex post 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 public 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 post incentive constraint and institutions can be designed to relax it. These remedies are briefly discussed in subsection 5.4. 5. 1 . The capital levy 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 model

Consider a two-period closed economy, t = 1 , 2, with one storable commodity. A representative consumer has preferences defined over consumption in both periods, c1, and leisure in the second period, x, represented by

u = U(c t ) + c2 + 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 on Persson and Tabellini ( 1 990, 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

c 1 + k = e, c2 = (1 - 8) k + ( 1 - r) l,

(5.2) (5.3)

where k is the investment in the storage technology, 8 and T are the capital and labor income tax rates, and the real wage is unity. Finally, the government must finance a given amount of second-period per-capita public consumption, g. Thus, the government budget constraint is g

= r l + fJk.

(5.4)

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 of treating the set of 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 I -- before any private decision is made - the government commits to a tax structure (8, 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:

Uc (e - k) � 1 - &;

Vx ( l - l)

= 1 -- 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( l - 8)], where K( l - 8) = e - U; 1 ( 1 - 8), and labor supply function l = L(l - r) = 1 - Vx 1 ( 1 - r). The partial derivatives Ko and Lr are both negative. By the separability and quasi-linearity of 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( 8) and Et( r), respectively 40 . 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 Rule 4 1 :

e

r (5.6) E, ( r). E" (e) = 1-r Equation (5.6) implicitly defirles the ex ante 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.

1-e

5. 1.3. Equilibrium under discretion

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 ex post; from the vantage point of period 2. More precisely, a credible equilibrium 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 ex post 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 ( l ee) and E�c( ee). We call this elasticity the ex ante elasticity of investment, since it is defined over ee rather than e -

0

40 These elasticities are, respectively: fJ

' (8)

41

=

( 1 - 8)

df(

--- -··---

K

d(l - 8)

=

u,

---

K Ucc

> 0'

c1(r)

=

(1 - r)

dL

d(l - r)

- - - -----

See Persson and Tabellini ( 1 990, ch. 6), for a derivation.

L

= - - > 0.

Vx

L V...,

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(ii) The ex post 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 post elasticity, that is the elasticity with respect to the actual tax rate e, since that is what the government is choosing. By the argument at point (i), this ex post elasticity is zero: k depends on ee, not on e. Equation (5 .6) then implies that for any given capital stock k the ex post optimal capital tax rate, e*, must satisfy e * = Min[ l , g/k].

(5.7)

The optimal labor tax rate r follows from the government budget constraint. In particular, r = 0 if e* = 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 post optimal to set either a fully expropriating capital tax rate of I , 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, ee = e* and k = K ( l - e*). Combining this last result with Equation (5 .7), the equilibrium tax rate is defined by e* = Min[ 1 , g/K(1 - e*)]. We illustrate the possible equilibria in Figure 1. The solid curve is the ex ante revenue function for different values of e. Tax revenues first grow with the tax rate, but at a decreasing rate, since the tax base slu·inks as e 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. If g is sufficiently high (higher than point G) only one equilibrium exists, in which 8* = 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, e = I 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 post 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 ee = eA and invests K( 1 eA). Hence, the government can just finance g by setting 8 exactly at (JA, while keeping the labor tax equal to 0. Thus, the government is at an ex post optimum. The same argument establishes that point B is also an equilibrium. -

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8 K( l - 8) G A

B

c

0

L--------�-+

()

Fig. 1 .

These equilibria are clearly Pareto ranked: A i s better than B which i s better than C. They are all worse than the ex ante 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. Extensions

Results similar to those above, apply to the taxation of other forms of 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 post 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 ex post and ex ante elasticity of tax bases generally differ from each other. In general this difference is not as stark as with wealth taxes, where the ex post elasticity is zero. In the case of other tax bases than wealth, we can no longer conclude that the optimal tax rate is always higher ex post than ex 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 unanticipated, the household substitutes from labor into leisure in the current period. But if the tax increase was anticipated 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 2 rates are different, but not whether they are higher ex ante or ex post 4 . 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 economy43 . 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 government 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 ( 1 988) 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 43

For a further dl.scussion, see Persson and Tabellini ( 1990, ch. 8). See also the survey by Krusell et al. ( 1 997).

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Another example, studied by Velasco ( 1 994) and Giavazzi and Pagano ( 1 990), concerns exchange-rate crises in a high public debt economy. By assumption, the cost of 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 of 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 sequential (as opposed to simultaneous) investment decisions. Alesina et al. ( 1 990) and Cole and Kehoe ( 1 996a,b) study an infinite-horizon economy with a large public debt. Like in Calvo ( 1 988), 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 ex post 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. Public debt management

The papers discussed in the previous subsection have implications for debt man­ agement policies, as the occurrence of a confidence crisis depends on the maturity structure or currency denomination of outstanding debt. For instance, the debt-run equilibrium discussed by Alesina et al. ( 1 990) 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 ( 1 990) suggest that issuing foreign currency debt can reduce the risk of 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 ante and ex post elasticities of all tax bases are the same. This point was first noted in the seminal paper by Lucas and Stokey ( 1 983) with regard to the maturity structure of 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 of 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. ln a related argument, Bensaid and Jeanne ( 1997) show that multiple equilibria can arise if raising the interest rate to defend an exchange-rate peg is too costly for 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 ante optimal policy may not be credible: the government may have an incentive to deviate from it ex post, in order to change the value of its outstanding assets and liabilities. Conversely, these incentives give an additional role for public debt management policies: if the maturity and contingency structure of the debt is rich enough, it can be revised over time so as to maintain credibility of the ex ante optimal tax policy under sequential decision making, even if ex ante and ex post 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 of 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. ( 1 987) show that the capital-levy incentive for the government to dilute the real value of its outstanding nominal liabilities - such as the money stock - can be relaxed if the government holds claims on the private sector, denominated in nominal terms. If the nominal claims and liabilities are balanced, the ex ante 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 ( 1 990) 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 non­ neutral, even if a Modigliani-Miller theorem about the irrelevance of the government financial structure would apply in the absence of 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 of 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 government debt instruments as there are policy instruments. 46 Public debt denominated in foreign currency is similar to indexed debt in this regard, but will not be considered here.

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Reputation and enforcement

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 ( 1 990) 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 ante optimal Ramsey rule, under appropriate assumptions about the government discount factor and the length of the punishment period. Kotlikoff et al. ( 1 988) 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 ( 1 989) 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 cam10t be narrowly defined. Nevertheless, some institutional devices could mitigate the capital-levy problem. Political delegation to a conservative policymaker is one way. International tax competition is another. As discussed in a companion survey [Persson and Tabellini ( 1 995)], 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 ( 1 990, 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 ( 1 977) and Calvo ( 1 978). The book by Basar and Olsder ( 1 982) provides a game-theoretic analysis of these problems in an abstract setting. The "capital levy problem" has a long history in economics. Eichengreen ( 1 990) provides a historical account. It has been formally analyzed (although with numerical solutions) in a two-period economy by Fischer ( 1 9 80). An early treatment of surprise inflation to tax real money balances is Auernheimer ( 1 974), but Calvo ( 1 978) 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 ( 1 98 8), Alesina et al. ( 1 990), Cole and Kehoe ( 1 9 96a,b) and Giavazzi and Pagano ( 1 990). Multiple equilibria with discretionary monetary policy have also been extensively treated in the literature, in particular by Obstfeld ( 1 997a), Bensaid and Jeanne ( 1 997), Chari et al. ( 1 996) and Velasco ( 1 994). Reputation and capital taxation is discussed by Kotlikoff et al. ( 1 988), Chari and Kehoe ( 1 990) and, more recently, by Benhabib and Rustichini ( 1 996), while Grossman and Van Huyck ( 1 988) and Chari and Kehoe ( 1 993) 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 ( 1 989), whereas Chari and Kehoe ( 1 993) 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 ( 1 994). Political delegation and capital levies are modeled in Persson and Tabellini ( 1994c) and discussed by North and Weingast ( 1 989) in a fascinating historical context. The literature on international tax competition and credibility is surveyed by Persson and Tabellini ( 1 995). The credibility of optimal tax structures in a general intertemporal context and without capital has been studied by Lucas and Stokey ( 1 983). Their seminal paper discusses both debt management and the credibility of tax policy. Subsequently, Persson and Svensson ( 1 9 84) and Rogers ( 1 987) 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. ( 1 992) and by Persson and Svensson ( 1 986). Persson et al. ( 1 987) extend the Lucas and Stokey result to a monetary economy, whereas M. Persson et al. ( 1 997) 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 ( 1 987) discusses strategic debt management and credible tax policy in an economy with endogenous

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government consumption, while Rogers ( 1 986) considers distributive goals. Missale and Blanchard ( 1 994) study how the maturity structure required to make a low-inflation policy incentive compatible varies with the level of debt. Calvo and Guidotti ( 1 990) study the credibility-flexibility trade-off in the optimal decomposition of public debt into indexed and non-indexed securities. Finally, Missale et al. ( 1 997) as well as Drudi and Prati ( 1 997) 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 ( 1 990) and Persson and Svensson ( 1 989). 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 ( 1 990) 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 ( 1 980) - in the context of natural resources and applied to government debt by Velasco ( 1 999). In subsection 6.3 we follow the approach of Alesina and Drazen ( 1 99 1 ), 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 ( 1 989), Tabellini ( 1 99 1 ) 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 ) Every consumer faces the same constraints. Leisure and labor i n period t , must sum to unity. Budget constraints are

x1

and

/1 ,

where 7:1 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 for b requires R = 1 . Recognizing this, we can write the equilibrium consolidated budget constraint as

Solving the consumer problem, leads to labor supply functions L ( l r1) 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 -

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 r1 and r2 • From the government 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[c 1 + c2 + V(x1) + 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 (6.2) That is, when tax rates an� equal over time, tax distortions are optimally smoothed out (J& = 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 < -�g (> - �g), 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, of 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 of public consumption: gd and g,.. The two types of public consumption each require one unit of 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 of its own supporters. If elected, party l thus maximizes the utility function

J

=

J(b, g) + H(g;).

(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 of public consumption for its constituency according to the (concave) H function, defined over g;. Political parties are "outcome motivated" rather than "office motivated". It is easy, however, to amend the model with a separate benefit of holding office, as in Section 3 . Finally, we assume that relative group size s i s a random variable, the realization of 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 of 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 assmned preferences imply that labor supply functions 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 (6.4) Thus party I spends on good i only (good } * 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- ! 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(uJJ (b)) = J(b, G(b)) + ( 1 - P) H(G(b)]. Optimal debt policy thus has to satisfy (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 Jh < 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 ( 1 989) and Alesina and Tabellini ( 1 990). 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 ( 1 990). 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: �

uii = J(b, g) + H(i) + (ai + f3) K D ,

�

(6.6)

where H(-) is the same concave function as in Equation (6.3), and the dummy variable KJJ equals 1 if party D holds office in period 2, and 0 if party R holds office. The parameter ai 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 f3 is not known, but only its expected value E(/3). The ai parameter thus measures an idiosyncratic "ideological" (and exogenous) bias for party D, and to the extent that f3 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 non­ economic) 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)) + ai + f3 > J(b, g), or if ai > �(H(G(b)) + ()) . 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 if J(b,g) + ai + f3 > J(b, g) + H(G(b)),

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or if ai > 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) = sF (-H(G(b)) - {3) + ( 1 - s) F(H( G(b)) - {3), where f3 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) = Pr [SR(b, {3) ): 0.5]. (i We want to know how this probability depends on public debt. As a preliminary step, note that dSR

db = Hg Gb[( l - s)f( H(G(b)) - {3) - sf(-H( G(b)) - {3)], where f is the derivative (density) of F. As Hg Gb is negative, the sign hinges on the expression in square brackets. Consider first the case f3 = 0. By symmetry of F, we see that the vote share of party R goes up for any f3 if s > (1 - s). Intuitively, higher b leads to lower future 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 former effect prevails. Consider next the case in which s = ( 1 - s) = � - Then, by symmetry and unimodality of F, the vote share for R goes up as b increases if and only if f3 < 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 P6 > 0 is more likely the larger is s and the smaller is E(f3). That is, from the point of view of a party-D incumbent, issuing more debt reduces the probability of re-election (Ph > 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

(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 PHg G6). 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 Pz, < 0, this effect adds to the incentives to issue debt, but when P6 > 0 it pulls in the opposite direction. From the previous discussion we know that ?6 < 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, gd 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 ( 1 990) 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 maj ority 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 ( 1 989) and Part Ill below], or the implementation of tax reforms [Cukierman et a!. ( 1 992)] . 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 ( 1 989) 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 under­ issues 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. Tabellini and Alesina ( 1 990) formulate this condition in index of the function H.

49

a

precise way, referring to the concavity

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As we saw in the introduction to this part, the general idea that government 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 Ozier and Tabellini ( 1 99 1 ) for developing countries and by Lambertini ( 1 996) for industrial countries, with supportive results in the first paper but not in the second one 5°. 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) 5 1 . For a government with popular candidates, the two effects pull in opposite directions, though. The specific positive implications concerning the effect of 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 per 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, similar to that in the previous section. As tax distortions are not central to the argument here, we assume 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 I and period 2. Public spending occurs in each period. As before, the two groups have sharply different preferences over the composition of public consumption. We can write the utility of a typical group-i individual as

where y and r are exogenous per capita incomes and per capita taxes assumed to be equal over time.

50 Petterson ( 1 997) test the Persson-Svensson and Alesina-Tabellini models of strategic debt issue on panel data from Swedish municipalities. He finds suppoti for the fom1er model but not for the latter. 5 1 Questioning the stylized fact cited in the Introduction to Part II, Edin and Ohlsson ( 1 99 1 ) argue that minmity governments, rather than coalition governments, are associated with larger debt issue.

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To simplify further, let us assume that s = ! , so groups (or parties) equal size. The government budget constraints are

d

and

r are of

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; = ! r for i = d, r and t = 1 , 2, since that 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. If 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 5 2

i

g1 1

g2

= =

{ {

p(g\ )' if (p(g\) + p(g{)) � 2 r, p(g · + 1 ) . 2 r otherwise , p(g\ ) p(g{ ) p(g;) if (p(gD + p(gi )) � r - b, , p(g2 ) . ( r - b) otherwise. 2+ {

(6.8)

p(g ) p(g )

Clearly, this model implicitly assumes a weak budget process, where each of the coalition partners is given responsibility for one separate part of the government budget, and none of them has responsibility for the overall budget constraint. We can also interpret the model as referring to a very weak government where spending ministers are in the hands of powerful interest groups. Given the relation between proposals and outcomes in Equation (6.8), there is a unique Nash equilibrium in period 2: each party proposes that the whole remaining pool of government resources, r - b, be allocated to its own group. Bidding for the whole pie in period 2, by setting p(gD = ( r - b), is costless. Such a proposal is a dominant strategy, as any lower proposal reduces the share of group i. Equilibrium spending thus satisfies

(6.9)

6.2. 1 . Equilibrium debt issue In period 1 the situation is different, because insisting on high spending eats up future resources. This cost is not high enough, though, to prevent equilibrium over-issue of

52 We also assume that no group can bid for more than the total available resources. Thus, p(g\ ) � 2 r and p(g]_) � r - b for i = r , d.

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debt. To see this, consider how debt links spending in periods 1 and 2. Given future equilibrium spending in Equation (6.9) and the budget constraints (6.7), we can write the objective of party I in period 1 as

d

=

2(y - r) + H(g\ ) + H[r -- (g( + g{ )/2] .

When contemplating its spending proposal and taking party J 's proposal as given, party I thus does not internalize more than half the cost of current spending. The optimal proposal satisfies

As the proposals of both parties are identical, they are clearly feasible: the second expression in parentheses is positive, satisfying the feasibility constraint in Equa­ tion (6.9). They are thus implemented and the equilibrium spending profile for group i satisfies

As g( > 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 liN of the future costs of debt issue. This model can be generalized in several directions. Velasco ( 1 999) studies a genuine multi-period model. This gives richer debt dynamics, including the possibility of delayed endogenous stabilizations. Chari and Cole ( 1 993) 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 ( 1 996) applies a related idea to a very different model of redistribution, originally formulated by Myerson ( 1 993). 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 . 03 The common pool problem has also been extensively studied in a static context. Persson and Tabcllini ( 1999) smvey that literature.

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stronger budget process

The over-issue of debt is obviously caused by a flawed government budget process, where each party of 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). If the same party fully controlled all spending decisions, it would indeed appropriately internalize the cost of overspending and of debt issue. Such centralization of decision-making power could be abused, however. In the model of 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 of 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 of g1 across different types of 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 of 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 von Hagen ( 1 992), von Hagen and Harden ( 1 995) and Ales ina et al . ( 1 996) suggests that certain features of the budget process makes it less likely that countries run into public debt problems. One of 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 5 5 .

5 4 The effects o f some o f these checks and balances are investigated i n a different set u p by T. Persson

et al. ( 1997). 55 Hallcrberg and von Hagen ( 1 997) 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 cotmtries with proportional electoral systems (more likely to have coalitions and minority governments) instead have tried to limit their deficits by adopting fonnal budget targets.

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6.3. Delayed 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 ( 1 99 1), we illustrate the possibility of 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 of the necessary adjustment. Alesina and Drazen's continuous­ time model built on the biological war-of-attrition model of Riley ( 1 980) and on the public-goods model of Bliss and Nalebuff ( 1 984). 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 f3 > 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 case gf + g]' = g1 = r + {3, b = {3, and gf + g2 = g2 = r - {3 . (ii) Stabilization occurs in period 1 , in which case aggregate overspending is cut by f3 so that g1 = r = g2 and hence b = 0. The allocation of 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 of group i is linear in g; . We assume that the costs of debt policy enter additively in the utility function. They can be thought of 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 of group i as (6. 1 0) The parameter K; measures the cost to group i of postponing the stabilization. A crucial assumption is that this cost is private information to group i. Group j only knows that Ki is distributed on the interval [0, K'] according to the distribution function F(Ki) . The corresponding parameter K.i has the same distribution, but the realizations of Ki and KJ are independent. All political action takes place at the beginning of period 1 , when each party, simul taneously and non-cooperatively, makes a proposal p1 of whether to stabilize (p1 = s) or not (p1 = n). If both parties propose n, the stabilization is delayed. But if 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: g\ (n, n)

=

�( r -f- {3),

gf (s, n) = g; (n, s) =

gi (n, n) =

! r - a, gf (n, s) = g; (s, n) = ! r + a, g; (s, s) = ! r, i = d, r, t =

�( r - {3), t = 1 , 2, t = 1 , 2,

l , 2,

i = d, r, (6. 1 1 )

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T. Persson and G. Tabellini

where gi(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. 1 1) 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[ud I pd = n], and when proposing s, denoted by E[ud I pd = s]. Let q = Pr [p' = s] be the probability that party R proposes s (q is determined in equilibrium). Then, Equations (6. 1 0)-(6. 1 1) and some algebra imply

E [ud I p" = n] - E [ u" I p" = s] = a - ( 1 - q) Kd b.

(6. 1 2)

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 (kd is low), and if the probability that party R proposes s is high (q is high). Clearly, party D says no whenever K" is below some critical number K. But, since party R faces an identical decision problem, it also proposes n whenever K' < K. Thus it must be the case that ( 1 - q) = F(K). Using that and setting the expression in (6. 1 2) equal to zero, we can implicitly define the equilibrium value of K by:

KF(K) = a!(3. The LHS of this expression is increasing in K. Therefore, K = K ( a, (3), with Ka > 0 and Kr1 < 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 Kd and K' are independently distributed, the unconditional probability of observing delay is

( 1 - q)(l - q) = F(K( a, {3)) F(K(a , (3 )). 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 {3, 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 (3. Thus, the model supports the general idea that financial crises and times of economic distress resulting from budgetary instability are catalysts of reforn1, and

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should not be feared too much [Drazen and Grilli ( 1 993)]. 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 ( 1 995)] . To be effective, external financial aid should not ease the pain of an unsustainable situation (in terms of our model, it should not reduce /3), 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-you­ go social security are identical policies. Several authors have addressed the political determinants of such policies in a median-voter setting without altruism - see Browning ( 1 975) for an early contribution, Boadway and Wildasin ( 1 989), and Cooley and Soares ( 1 999). 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 ( 1 989) 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. Non­ constrained 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 bequest­ constrained 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, 1 99 1 ) 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 post 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 ( 1 990) discusses the repayment of government debt as the outcome of bargaining between living generations. Grossman and Helpman ( 1 996) 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 government - 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.

Notes 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 equilibrimn models with rational voters and politicians. A broader survey of the public choice literature is Mueller ( 1 989). Much of the modern macroeconomic literature on public debt is surveyed in Alesina and Perotti ( 1 995a).

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The idea that political instability induces a government to use public debt strategically, to influence the future policies of its opponent, was first independently studied by Alesina and Tabellini ( 1 990) and Persson and Svensson ( 1 989). The model of subsection 6. 1 is related to Alesina and Tabellini ( 1 990), 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 ( 1 990) provide a generalization of these results, Alesina and Tabellini ( 1 989) study capital flight and external borrowing, Tabellini ( 1 990) looks at these models in the context of international policy coordination, Glazer ( 1 989) applies the same idea to the choice of duration in public investment, Cukierman et al. ( 1 992) 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 ( 1 989), Grilli et al. ( 1 99 1 ), Ozier and Tabellini ( 1 99 1 ) and Lambertini ( 1 996) 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 ( 1 990). 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 ( 1 987). 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 ( 1 980), Benhabib and Radner ( 1 992)] . In fiscal policy, it was studied by Tabellini ( 1 987) in a dynamic game of monetary and fiscal policy coordination, and by Velasco ( 1 999) 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 ( 1 995a), von Hagen and Harden ( 1 995), and Hallerberg and von Hagen ( 1 997). 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 ( 1 996), Poterba ( 1 994), and Eichengreen and von Hagen ( 1 996). The model of delayed stabilizations is due to Alesina and Drazen ( 1 99 1), who in turn have elaborated on earlier ideas by Riley ( 1 980) and Bliss and Nalebuff ( l 984). Since then, the model has been extended in several directions, among others, by Drazen and Grilli ( 1 993), Casella and Eichengreen ( 1 995) and Alesina and Perotti ( 1 995b). 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 et al. ( 1 988), Boldrin and Rustichini ( 1 996)] .

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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 of growth: (i) Inequality in the distribution of income or wealth is significantly and negatively correlated with subsequent growth in cross-country data. On the other hand, the evidence on the effect of growth on the distribution of 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 of democracy are strongly correlated with the level of income, there are no robust findings regarding the effect of 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 ( 1 994) and Persson and Tabellini ( 1 994b). As in these papers - and a great deal of subsequent work - we rely on a simple median-voter model inspired by Roberts ( 1 977) and Meltzer and Richards ( 1 98 1 ). 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 ( 1 996) and Devereux and Wen ( 1 996). 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 of property rights may hurt investment and growth, as in Tomell and Velasco ( 1 992) 56 This finding was first obtained by Alesina and Rodrik ( 1 994) and Persson and Tabellini ( l 994b). For a recent and comprehensive survey of the empirical evidence on inequality and growth, see Perotti ( 1 996). 57 On this point see Alesina et a!. ( 1 996) and Barro ( 1 99 1 ). 58 On the relation between property rights and growth see Knack and Keefer ( 1 995). A survey of the voluminous literature on the links fi·om democracy to growth can be found in Przeworsk:i and Limongi ( 1 993),

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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. Inequality 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:

(7. 1 ) The budget constraints are

(7.2) where ki is private investment, r and e lump-sum and capital taxes, and A(I) the gross return to private capital, which is increasing in public investment l . We abstract from credibility problems; the government can commit to these policy instruments before private capital accumulation. Finally, ei 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' - e). To proxy empirical income distributions, we assume that F is skewed to the right: the median value of ei - e, labeled e111 - e and defined by F(e111 - e) = �' is negative. Assuming a balanced budget in every period, the government budget constraint in per capita terms is: l

=

T,

(7.3) (7.4)

g = 8A(I) k,

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' = e - l - u; 1 (A(/ )(1 -- 8)) + (ei - e) = K( O , I) + (ei - e),

where the common investment function satisfies K0 < 0 and K1 > 0. lt is again convenient to express the utility from private consumption as an indirect utility function defined over the policy variables:

Ji ( O , I, ei ) = Max[ U(c\ ) + c� ] = U(e - I- K(O, I)) + ( I - O)A(I) K( O , I) + A(/) ( l - O)(ei - e) = J( O , l) + A(/) ( 1 - O )(e' - e). By the envelope theorem, the direct welfare cost of the capital tax negative. Moreover, the welfare effect of public investment, .1] = U -

c

J0

=

+ (1

(7.5)

A(l) K is 8) - A1K, is

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T Persson and G. Tabellini

monotonically decreasing in I (by Ucc < 0 and A11 < 0). Substituting Equation (7.5) into (7 . 1 ) and using (7 .3), we obtain individual-i policy preferences over the two policy instruments 8 and I:

u; = J'(B, I, e') + H(8A(I) K(8, I)). These policy preferences are linear in the idiosyncratic variable e; . They therefore fulfill a monotonicity (single-crossing) condition, such that the preferred policy of the agent with endowment em will be a Condorcet winner, even though the policy space is two-dimensional. If we imagine that policy decisions are taken at the begitming of period 1 by direct democracy, the winning proposal is thus the policy preferred by this decisive voter. If the second-order conditions are fulfilled 59, the equilibrium values for I and 8 thus satisfY J1

+ Hg 8(KAI + AK1) + (em - e)( l - 8)A1

Je + HgA(K + 8Ke) - (em - e)A = 0.

=

0,

(7.6)

To understand these conditions, first assume that the distribution is symmetric, so that em = 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. J1 < 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 (Je < 0) with the marginal benefit it generates via public consumption . But if em < e, redistributive effects come into play. The decisive voter's capital falls short of average capital by exactly (em - e). This implies that I is smaller and 8 is higher than in the hypothetical planning solution. The reason is that the decisive V 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(J) K( H, I) - M(F(8, 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 ( 1 998), who shows that political instability may make a forward­ looking government abstain from 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. (1 996)] indeed reduces the protection of private property rights [as measured by the same index as in Knack and Keefer ( 1 995)] in a wide cross­ country 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 them 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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1 472

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 ( 1 996) 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 ( 1 992) 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 government policy process, the poorly enforced property rights are closely related to weak government. Tornell ( 1 995) 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. If so, this pattern is perfectly foreseen and leads to gradually falling growth rates at intermediate levels of income. Lane and Tornell (1 996) 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 ( 1 996) 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 ( 1 993), who studied human capital accumulation, and tax-financed subsidies in the presence of borrowing constraints, by Bertola ( 1 993) who studied tax policy and the functional distribution of income, by Glomm and Ravikumar ( 1 992) who studied private versus public provision of education, and by Saint-Paul and Verdier ( 1 993) who also studied redistributive policies that finance public education in a setting with wealth-constrained individuals. Perotti ( 1 996) and Benabou ( 1 996) provide additional references to recent empirical work. Finally, Caballero and Hammour ( 1 996) 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 ( 1 996), 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 of 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 of 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. ( 1 997) 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.

References

Aghion, P., and P. Bolton ( 1 990), "Government domestic debt and the risk of a default: a political­ economic model of a strategic role of debt", in: R. Dornbusch and M. Draghi, eds., Public Debt Management: Theory and History (Cambridge University Press, Cambridge) 3 1 5-345. a! Nowaihi, A., and P Levine (1 996), "Independent but accolrntable: Walsh contracts and the credibility problem", Discussion Paper No. 1 387 (CEPR). a! Nowaihi, A., and P. Levine ( 1 998), "Can political monetary cycles be avoided?", Journal of Monetary Economics 42:525-545. Alesina, A. ( 1 987), "Macroeconomic policy in a two-party system as a repeated game", Quarterly Journal of Economics 1 02:65 1-678. Alcsina, A. ( 1988), "Credibility and policy convergence in a two-party system with rational voters", American Economic Review 78:496-805. Alesina, A., and A. Cukierman ( 1988), "The politics of ambiguity", Quarterly Journal of Economics 105:829-850. Alesina, A., and A. Drazen (1991), "Why are stabilizations delayed?", American Economic Review 8 1 : 1 1 70-1 1 88. Alesina, A., and R. Gatti ( 1 996), "Independent central banks: low inflation at no cost?", American Economic Review Papers and Proceedings 8 5 : 1 96-200. Alesina, A., and V Grilli ( 1 992), "The European central bank: reshaping monetary politics in Europe", in: M. Canzoneri, V Grilli and P Masson, eds., Establishing a Central Bank. Issues in Europe and Lessons from US (Cambridge University Press, Cambridge) 49-77.

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Alesina, A., and R. Perotti ( 1 995a), "Budget deficits and budget institutions", Working Paper No. 5556 (NBER). Alesina, A., and R. Perotti (1 995b), "The political economy of budget deficits", IMF Staff Papers March: 1-37. Alesina, A., and D. Rodrik ( 1 994), "Distributive politics and economic growth", Quarterly Journal of Economics 1 09:465-490. Alesina, A., and H. Rosenthal ( 1 995), Partisan Politics Divided Government and the Economy (Cambridge University Press, Cambridge). Alesina, A., and N. Roubini ( 1 997), Political Cycles and the Macroeconomy (MIT Press, Cambridge, MA). Alesina, A., and L.H. Summers (1 993), "Central bank independence and macroeconomic performance: some comparative evidence", Journal of Money, Credit and Banking 25: 1 5 1 -62. Alesina, A., and G. Tabellini (1 989), "External debt, capital flight and political risk", Journal of International Economics 27: 1 99-220. Alesina, A., and G. Tabellini (1 990), "A positive theory of fiscal deficits and government debt", Review of Economic Studies 57:403-414. Alesina, A., A. Prati and G. Tabellini ( 1990), "Public confidence and debt management: a model and a case study of Italy", in: R. Dornbusch and M. Draghi, eds., Public Debt Management: Theory and History (Cambridge University Press, Cambridge) 94-- 1 1 8. Alesina, A., J. Londregan and H. Rosenthal ( 1 993), "A model of the political economy of the United States", American Political Science Review 87: 1 2-33. Alesina, A., S. Ozier, N. Roubini and P. Swage! ( 1 996), "Political instability and economic growth", Journal of Economic Growth 1 : 1 89-212. Almeida, A., and C.A.E. Goodhart ( 1996), "Does the adoption of inflation target affect central bank behavior?", Working Paper (London School of Economics, July). Auernheimer, L. ( 1974), "The honest government's guide to the revenue from the creation of money", Journal of Political Economy 82:598-606. Backus, D., and J. Driffil\ (1 985), "Inflation and reputation", American Economic Review 75:530-538. Bade, R., and M . Parkin (1988), Central Bank laws and inflation: a comparative analysis, mimeograph (University of Western Ontario). Ball, L. ( 1996), "Disinflation and the NA!RU", Working Paper No. 5520 (NBER, July). Barro, R.J. ( 1973), "Inflationary finance under discretion and rules", Canadian Journal of Economics 1 6: 1-25. Barro, R.J. (1979), "On the determination of public debt", Journal of Political Economy 87:940 -47. Barro, R.J. (1986), "Reputation in a model on monetary policy with incomplete inforn1ation", Journal of Monetary Economics 1 7: 1-20. Barro, R.J. (1991), "Economic growth in a cross section of countries", Quarterly Journal of Economics 1 06:407-443. Barro, R.J. (1 997), Determinants of Economic Growth (MIT Press, Cambridge). Barro, R.J., and B. Broadbent ( 1997), "Central bank preferences and macroeconomic equilibrium", Journal of Monetary Economics 39: 1 7-43 . Barro, R.J., and D. B. Gordon (1 983a), "A positive theory of monetary policy in a natural rate model", Journal of Political Economy 9 1 :589-61 0 . Barro, R.J., and D.B. Gordon ( 1983b), Rules, discretion and reputation i n a model o f monetary policy, Journal of Monetary Economics 1 2 : 1 0 1 -1 2 1 . Basar, T., and G. Olsder ( 1982), Dynamic Noncooperative Game Theory (Academic Press, London). Baxter, M., and A.C. Stockman ( 1 989), "Business cycles and the exchange rate regime: some international evidence", Journal of Monetary Economics 23:377-400. Beetsma, R., and L. Bovenberg ( 1 998), "The interaction of ftscal and monetary policy in a monetary union: credibility and flexibility", in: A. Razin and E. Sadka, eds., Globalization: Public Economics Perspectives (Cambridge University Press, Cambridge).

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Beetsma, R., and H. Jensen ( 1998), "Inflation targets and contracts with uncertain central bank preferences", Journal of Money, Credit and Banking 30:384-403. Benabou, R. ( 1996), "Inequality and growth", in: B.S. Bernanke and J.J. Rotcmbcrg, eds., NBER Macroeconomics Annual 1 996 (MIT Press, Cambridge). Benhabib, J., and R. Radner ( 1992), "The joint exploitation of a productive asset: a game-theoretic approach", Economic Theory 2 : 1 55-190. Benhabib, J., and A. Rustichini ( 1 996), "Social conflict and growth", Journal of Economic Growth

1 : 1 25-1 39.

Bensaid, B., and 0. Jeanne ( 1997), "The instability of fixed exchange rate systems when raising the nominal interest rate is costly", European Economic Review 4 1 : 1461-1 478. Bertola, G. ( 1993), "Factor shares and savings in endogenous growth", American Economic Review

83: 1 1 84-1 198. Bliss, C., and B. Nalebuff ( 1 984), "Dragon-slaying and ballroom dancing: the private supply of a public good", Journal of Public Economics 25: 1-12. Boadway, R., and D. Wildasin ( 1 989), "A median voter model of social security", International Economic Review 30:307--328. Bohn, H., and R. Inman ( 1 996), "Balanced budget rules and public deficits: evidence from the U S states", Carnegie-Rochester Conference Series on Public Policy 45: I 3-76. Boldrin, M., and A. Rustichini ( 1996), "Equilibria with social security" (Universidad Carlos III de Madrid). Bordo, M.D., and F. E. Kydland ( 1 995), "The gold standard as a rule: an essay in exploration", Explorations in Economic History 32:423-464. Bordo, M.D., and A.J. Schwartz ( 1 999), "Monetary policy regimes and economic perfonnancc: the historical record", ch. 3, this Handbook. Broadbent, B. ( I 996), "Monetary policy regimes and the cost of discretion", mimeograph (Harvard University). Browning, E. ( 1 975), "Why the social insurance budget is too large in a democracy?", Economic Inquiry

22:373-388.

Bulow, J. , and K. Rogoff ( 1989), "Sovereign debt: is to forgive to forget?", American Economic Review

79:43-50.

Caballero, R.J., and M.L. Hammour ( 1996), "The macroeoconomics of specificity", Working Paper No. 5757 (NBER). Calvo, G.A. ( 1 978), "On the time consistency of optimal policy in a monetary economy", Econometrica

46: 1 4 1 1-1428. Calvo, G.A. ( 1 988), "Servicing the public debt: the role of expectations", American Economic Review

78:647-661 . Calvo, G.A., and P.E. Guidotti ( 1 990), "Indexation and maturity of government bonds: an exploratory model", in: R. Dornbusch and M. Draghi, eds., Public Debt Management. l11eory and History (Cambridge University Press, Cambridge) 52-82. Calvo, G.A., and C.A. Vegh ( 1 999), "Inflation stabilization and BOP crises in developing countries", ch. 24, this Handbook. Canzoneri, M.B. ( 1 985), "Monetary policy games and the role of private information", American Economic Review 75: 1056-1070. Capic, F., T.C. Mills and G.E. Wood (1 994), "Central bank independence and inflation performance: an exploratory data analysis", in: P Siklos, ed., Vatieties of Monetary Reforms: Lessons and Experiences on the Road to Monetary U nion (Kluwer Academic Publishers, Dordrecht). Casella, A., and B. Eichengreen ( 1 995), "Can foreign aid accelerate stabilization?", Discussion Paper No. 961 (CEPR). Charnley, C. ( 1986), "Optimal taxation of capital income in general equilibrium with infinite lives", Econometrica 54:607-622.

1 476

T Persson and G. Tabellini

Chari, V.V, and H.L. Cole ( 1 993), "Why are representative democracies fiscally irresponsible?", Staff Report No. 1 63 (Federal Reserve Bank of Minneapolis). Chari, VV, and P.J. Kehoe ( 1 990), "Sustainable plans", Journal of Political Economy 98:61 7-636. Chari, VV, and P.J. Kehoe ( 1 993), "Sustainable plans and mutual default", Review of Economic Studies 60: 1 75-196. Chari, VV, L.J. Christiano and P.J. Kehoe ( 1 992), "Optimal fiscal and monetary policy: some recent results", in: A. Cukierman, Z. Hercowitz and L. Leiderman, eds., Political Economy, Growth and Business Cycles (MIT Press, Cambridge) 283-305. Chari, VV, L.J. Christiano and M. Eichenbaum ( 1 996), "Expectation traps and discretion", mimeograph (Northwestern University). Cole, H.L., and P.J. Kehoe ( 1994), "Reputation spillover across relationships with enduring and transient benefits: reviving reputation models of debt", Working Paper No. 534 (Federal Reserve Bank of Minneapolis). Cole, H.L., and T.J. Kehoe ( 1 996a), "Self-fulfilling debt crises and capital flight", mimeograph (Federal Reserve Bank of Minneapolis). Cole, H.L., and T.J. Kehoe ( 1996b), "Self-fulfilling debt crises", Staff Report No. 2 1 1 (Federal Reserve Bank of Minneapolis). Cooley, T.F., and J. Soares ( 1 999), "A positive theory of social security based on reputation", Journal of Political Economy 1 07 : 1 35-160. Cukierman, A. ( 1992), Central Bank Strategy, Credibility and Independence - Theory and Evidence (MIT Press, Cambridge, MA). Cukierman, A., and F. Lippi ( 1 998), "Central bank independence, centralization of wage bargaining, inflation and unemployment - theory and evidence", mimeograph (Bank of Italy). Cukierman, A., and N. Liviatan ( 1 99 1 ), "Optimal accommodation by strong policymakers under incomplete information", Journal of Monetary Economics 27:99-127. Cukierman, A., and A.H. Meltzer ( 1986), "A theory of ambiguity, credibility and inflation under discretion and asymmetric information", Econometrica 54: 1 099·-1 1 28. Cnkiemmn, A., and A.H. Meltzer ( 1989), "A political theory of government debt and deficits in a Neo-Ricardian framework", American Economic Review 79: 7 1 3-748. Cuk:ierman, A., S. Edwards and G. Tabellini ( 1 992), "Seignorage and political instability", American Economic Review 82:537-555. Devereux, M., and J.F. Wen (1 996), "Political uncertainty, capital taxation and growth", mimeograph (University of British Cohunbia). Dolado, .T., M. Griffiths and J. Padilla ( 1994), "Delegations in international monetary policy games", European Economic Review 3 8 : 1057-1069. Drazen, A., and V Grilli ( 1 993), "The benefit of crisis for economic refonn", American Economic Review 83:598-607. Drudi, F., and A. Prati ( 1 997), "An incomplete inforn1ation model of the optimal maturity structure of public debt"; Working Paper (IMf} Edin, D.A., and H. Ohlsson ( 1991), "Political determinants of budget deficits: coalition effects versus minority effects", European Economic Review 3 5 : 1 597-1603. Eichengreen, B. ( 1 990), "The capital levy in theory and practice", in: R . Dornbusch and M. Draghi, eds., Public Debt Management: Theory and History (Cambridge University Press, Cambridge) 1 91-220. Eichengreen, B., and J. von Hagen ( 1 996), "Federalism, fiscal restraints and European monetary union", American Economic Review Papers and Proceedings 86: 1 35- 1 38. Eijffinger, S., and J. de Haan ( 1996), "The political economy of central bank independence", Special Papers in International Economics, No. 19 (Princeton University), Eijffinger, S., and E. Schaling ( 1 993), "Central bank independence in twelve industrial countries", Banca Nazionale de Lavoro 1 84: 1-4 1 . Elmendorf, D.W, and N.G. Mankiw ( 1 999), "Government debt", ch. 25, this Handbook.

Ch. 22:

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1477

Fair, R. ( 1 978), "The effect of economic events on votes for president", The Review of Economics and Statistics 60: 159-73. Faust, J. ( 1 996), "Whom can we trust to run the Fed? Theoretical support for the founders' views", Journal of Monetary Economics 37:267-283. Faust, J., and J. Irons ( 1 999), "Money, politics and the post-war business cycle", Journal of Monetary Economics 43:61-89. Ferejohn, J. ( 1986), "Incumbent performance and electoral control", Public Choice 50:5-26. Fiorina, M. (198 1 ), Retrospective Voting in American National Elections (Yale University Press, New Haven, CT). Fischer, S. ( 1977), Long-term contracts, rational expectations and the optimal money supply rule, Journal of Political Economy 85 : 1 63-190. Fischer, S. ( 1 980), "Dynamic inconsistency, cooperation, and the benevolent dissembling government", Journal of Economic Dynamics and Control 2:93-107. Fischer, S. ( 1 99 1 ), "Growth, macroeconomics and development", in: O.J. Blanchard and S. Fischer, eds., NBER Macroeconomics Annual 1 99 1 (MIT Press, Cambridge, MA) 3 29-364. Fischer, S. ( 1 995), "The unending search for monetary salvation", in: B.S. Bernanke and J.J. Rotemberg, eds., NBER Macroeconomics Annual 1 995 (MIT Press, Cambridge, MA) 275--286. Flood, R.P., and P. lsard ( 1 989), "Monetary policy strategies", IMF Staff Papers 36:612-32. Flood, R.P., and N. Marion ( 1 997), "Perspectives on the recent currency crisis literature", mimeograph (IMF). Flood, R.P., and M. Mussa ( 1 994), "Issues concerning nominal anchors for monetary policy", Working Paper No. 4850 (NBER). Fratianni, M., J. von Hagen and C. Waller ( 1 997), "Central banking as a principal agent problem", Economic Inquiry 35:378-393. Genberg, H. ( 1 989), "Exchange rate management and macroeconomic policy: a national perspective", Scandinavian Journal of Economics 9 1 : 439-469. Giavazzi, F., and M. Pagano ( 1 988), "The advantage of tying one's hands: EMS discipline and central bank credibility", European Economic Review 32:1055-1075. Giavazzi, F., and M. Pagano ( 1990), "Confidence crises and public debt management", in: R. Dornbusch and M. Draghi, eds., Public Debt Management: Theory and History (Cambridge University Press, Cambridge) 1 25-143. Glazer, A. ( 1989), "Politics and the choice of durability", American Economic Review 79: 1 207-1214. Glomm, G., and B. Ravikumar (1 992), "Public versus private investment in human capital endogenous growth and income inequality", Journal of Political Economy 1 00:8 1 3-834. Goodhart, C.E.A., and J. Vinals ( 1994), "Strategy and tactics of monetary policy", in: J.C. Fuhrer, cd., Goals, Guidelines and Constraints Facing Monetary Policymakers (Federal Reserve Bank of Boston)

1 39-187.

Grilli, V , D. Masciandaro and G. Tabellini ( 1 99 1), "Political and monetary institutions and public financial policies in the industrial countries", Economic Policy ! 3 :342-392. Grossman, G.M., and E. Helpman (1 996), "Intergenerational redistribution", mimeograph (Princeton University). Grossman, H.J., and J.B. Van Huyck (1 986), Inflation, seignorage and reputation, Journal of Monetary Economics 1 8 :20-32. Grossman, H.J., and J.B. Van Huyck (1 988), "Sovereign debt as a contingent claim: excusable default, repudiation, and reputation", American Economic Review 78: 1 988-1997. Haldane, A.G., ed. (1 995), Targeting Inflation, A conference of central banks on the usc of inflation targets, organized by the Bank of England (Bank of England). Hallerberg, M., and J. von Hagen ( 1 997), "Electoral institutions, cabinet negotiations, and budget deficits within the European union", Discussion Paper No. 1 555 (CEPR). Herrendorf, B. (1 996), "Inflation targeting as a way of precommitment", mimeograph (University of Warwick).

1478

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Herrendorf, B., and B. Lockwood ( 1 997), "Rogoff's 'conservative' central banker restored", Journal of Money, Credit and Banking 29:476-495. Hibbs, D. ( 1 977), "Political parties and macroeconomic policy", American Political Science Review 7 1 : 1467-1478. Holmstrom, B. ( 1982), "Managerial incentive problems - a dynamic perspective", in: Essays in Economics and Management in Honor of Lars Wahlbeck (Swedish School of Economics, Helsinki). Horn, H., and T. Persson ( 1 988), "Exchange rate policy, wage formation and credibility", European Economic Review 32: 1 621-1 636. Ito, T. ( 1 990), "The timing of elections and political business cycles in Japan", Journal of Asian Economics 1 : 1 35-146. Jensen, H. (1997), "Credibility of optimal monetary delegation", American Economic Review 87: 9 1 1-920. Jonsson, G. ( 1 995), "Institutions and macroeconomic outcomes - The empirical evidence", Swedish Economic Policy Review 2 : 1 8 1 -2 12. Jonsson, G. (1 997), "Monetary politics and unemployment persistence", Journal of Monetary Economics 39:303-325. Knack, S., and P. Keefer ( 1 995), "Institutions and economic performance: cross-country tests using alternative institutional measures", Economics and Politics 7:207-227. Kotlikoff, L., T. Persson and L.E.O. Svensson ( 1 988), "Social contracts as assets: a possible solution to the time-consistency problem", American Economic Review 78:662-677. Krusell, P., and V. Rios-Rull ( 1 996), "Vested interests in a positive theory of stagnation and growth", Review of Economic Studies 63 :60 1 -63 1 . Krusell, P., V Quadrini and V. Rios-Rull ( 1 997), "Politico-economic equilibrium and economic growth", Journal of Economic Dynamics and Control 2 1 :243-272. Kydland, EE., and E.C. Prescott ( 1977), "Rules rather than discretion: the inconsistency of optimal plans", Journal of Political Economy 85:473-490. Lambertini, L. ( 1 996), "Are budget deficits used strategically?", mimeograph (UCLA). Lane, P., and A. Tornell ( 1 996), Power, growth and the voracity effect, Journal of Economic Growth 1 :2 1 3-24 1 . Leiderman, L., and L. E.O. Svensson, eds ( 1995), Inflation Targets (CEPR, London). Levhari, D., and L. Mirman ( 1980), "The great fish war: an example using the Cournot-Nash solution", Bell .Toumal of Economics 1 1 :322-334. Lewis-Beck, M. ( 1 988), Economics and Elections: The Major Western Democracies (University of Michigan Press, Ann Arbor, MI). Lindbeck, A. (1 976), "Stabilization policies in open economies with endogenous politicians", American Economic Review Papers and Proceedings 66: 1 - 1 9. Lindbeck, A., and J. Wcibull ( 1987), "Balanced budget redistribution as the outcome of political competition", Public Choice 52:272-297. Lippi, F. ( 1998), "On central bank independence and the stability of policy targets", Scandinavian Journal of Economics 1 00:495-5 1 2 . Lizzeri, A . ( 1 996), "Budget deficits and redistributive politics", mimeograph (Princeton University). Lockwood, B., and A. Philippopoulus ( 1994), "Insider power unemployment and multiple inflation equilibria", Economica 6 1 :5 9 -77. Lockwood, B., M. Miller and L. Zhang ( 1 998), "Designing monetary policy when unemployment persists", Economica 65:327-345. Lohman, S. (1 992), "The optimal degree of commitment: credibility and flexibility", American Economic Review 82:273-286. Lohman, S. ( 1 996), "Democracy and inflation", mimeograph (UCLA). Lucas, R.E., and N.L. Stukey ( 1983), "Optimal fiscal and monetary policy in an economy without capital", Journal of Monetary Economics 12:55-94.

Ch. 22:

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McCallum, B.T. ( 1 996), "Crucial issues concerning central bank independence", Working Paper No. 5597 (NBER). Meltzer, A.H., and S. Richards ( 1 98 1), "A rational theory of the size of government", Journal of Political Economy 89:9 1 4-927. Mendoza, E . , A. Razin and L. Tesar ( 1994), "Effective tax rates in macroeconomics: cross-country estimates of tax rates on factor incomes and consumption", Journal of Monetary Economics 34: 297-323. Mendoza, E., G.-M. Milesi-Ferrctti and P. Asea ( 1996), "On the ineffectiveness of tax policy in altering long-run growth: Harberger's superneutrality conjecture", Discussion Paper No. 1 378 (CEPR). Milesi-Ferretti, G.-M. ( 1 994), "Wage indexation and time consistency", Journal of Money, Credit and Banking 26:941-950. Milesi-Ferretti, G.-M. ( 1 995a), "Do good or do well? Public debt management in a two-party economy", Economics and Politics 7:58-74. Milesi-Ferretti, G.-M. ( 1 995b), "The disadvantage of tying their hands: on the political economy of policy commitments", Economic Journal 1 05 : 1 381-1402. Mishkin, F.S., and A. Posen (1 996), "Experiences with inflation targeting as a strategy for the conduct of monetary policy", mimeograph (Federal Reserve Bank of New York). Mishkin, F.S., and A. Posen (1 997), "Inflation targeting: lessons from four conntries", Federal Reserve Bank of New York Economic Policy Review 3:9-1 1 0 . Mishra, D . (1 997), "An unbiased reexamination o f political cycle in OECD countries", mimeograph (University of Maryland). Missale, A., and O.J. Blanchard (1 994), "The debt burden and debt maturity", American Economic Review 84:309-3 1 9. Missale, A., F. Giavazzi and P. Benigno ( 1 997), "Managing the public debt in fiscal stabilizations: theory and practice", Working Paper (IGIER). Mueller, D. ( 1 989), Public Choice II (Cambridge University Press, Cambridge). Mussa, M . (1 986), "Nominal exchange rate regimes and the behavior of real exchange rates", Carnegie­ Rochester Conference Series on Public Policy 25: 1 1 7-2 1 4 . Myerson, R . ( 1993), "Incentives to cultivate favored minorities under alternative electoral systems", American Political Science Review 87:856-869. Nordhaus, W. ( 1 975), "The political business cycle", Review of Economic Studies 42: 1 69-190. North, D., and B. Weingast ( 1989), "Constitutions and commitment: the evolution of institutions governing public choice in seventeenth-century England", Journal of Economic History 69:803-832. Obstfeld, M. (1 997a), "Destabilizing effects of exchange rate escape clauses", Journal of International Economics 43 : 6 1--77. Obstfeld, M. ( 1997b), "Dynamic seigniorage theory: an exploration", Macroeconomic Dynamics 1 : 588-6 14. Ozier, S., and G. Tabellini ( 1 99 1 ), "External debt and political instability", Working Paper No. 3772 (NBER). Parkin, M. ( 1 993), "Inflation in North America", in: K. Shigehara, ed., Price Stabilization in the 1 990s (Macmillan, London) 47-93. Perotti, R. ( 1 993), "Political equilibrium, income distribution and growth", Review of Economic Studies 60:755- -776. Perotti, R. ( 1 996), ''Growth, income distribution and democracy: what the data say", Journal of Economic Growth 1 : 149-1 88. Persson, M., T. Persson and L.E.O. Svensson ( 1 987), "Time consistency of fiscal and monetary policy", Econometrica 5 5 : 1 4 1 9-143 1 . Persson, M., T. Persson and L.E.O. Svensson ( 1 997), "Debt, cash flow and inflation incentives: a Swedish example", in: M. King and G. Calvo, eds., The Debt Burden and it Consequences for Monetary Policy (MacMillan, London) 28-62.

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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 ( 1 986), "International borrowing and time-consistent fiscal policy", Scandinavian Journal of Economics 88:273-295 . Persson, T. , and L.E.O. Svensson ( 1 989), "Why a stubborn conservative would run a deficit: policy with time-inconsistency preferences", Quarterly Journal of Economics 1 04:325-345 . Persson, T., and G. Tabellini (1 990), Macroeconomic Policy, Credibility and Politics (Harwood Academic Publishers, Chur). Persson, T., and G. Tabellini ( 1992), "The politics of 1 992: fiscal policy and European integration", Review of Economic Studies 59:689-701 . Persson, T. , and G. Tabellini ( 1 993), "Designing institutions for monetary stability", Carnegie-Rochester Conference Series on Public Policy 39:53-89. Persson, T., and G. Tabellini, eds ( 1 994a), 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?", American Economic Review 84:600-621 . Persson, T., and G. Tabellini ( 1 994c), "Representative democracy and capital taxation", Journal of Public Economics 55:53-70. Persson, T., and G. Tabellini ( 1 995), Double-edged incentives: institutions and policy coordination, in: G. Grossman and K. Rogoff, eds., Handbook of International Economics, vol. III (North-Holland, Amsterdam) 1 973-2030. Persson, T., and G. Tabellini ( 1996), "Monetary cohabitation in Europe", American Economic Review, Papers and Proceedings 86: 1 1 1 --1 1 6. Persson, T., and G. Tabellini (1 999), "Political economics and public finance", in: A. Averbach and M. Feldstein, eds., Handbook of Public Economics (Elsevier Science, Amsterdam) forthcoming. Persson, T., G. Roland and G. Tabellini ( 1 997), "Separation of powers and political accountability", Quarterly Journal of Economics 1 1 2 : 1 1 63-1202. Petterson, P ( 1 997), "An empirical investigation of the strategic use of debt", mimeograph (Uppsala University). Posen, A. ( 1 993), "Why central bank independence does not cause low inflation: there is no institutional fix for politics", min1eograph (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 1 995 (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 1 02 :799-821 . Przcworski, A., and F. Limongi ( 1 993), "Political regimes and economic growth", Journal of Economic Perspectives 7:5 1 �70. Riley, J. (1 980), "Strong evolutionary equilibrium and the war of attrition", Journal of Jheoretical Biology 82:383-400. Roberts, K. (1 977), "Voting over income tax schedules", Journal of Public Economics 8:329-340. Rogers, C. ( 1 986), "The effects of distributive goals on the time inconsistency of optimal taxes", Journal of Monetary Economics 1 7:25 1 --270. Rogers, C. (1 987), "Expenditure taxes, income taxes, and time-inconsistency", Journal of Public Economics 32:2 1 5-230. Rogoff, K. ( 1 985), "The optimal degree of commitment to an intermediate monetary target", Quarterly Journal of Economics I 00: 1 1 69-1 1 90. Rogoff; K. ( 1987), "A reputational constraint on monetary policy", Carnegie-Rochester Conference Series on Public Policy 24: 1 15-165. Rogoff, K . (1 990), "Equilibrium political budget cycles", American Eronomic Review 80:21-36.

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Rogoff, K., and A. Sibert ( 1 988), "Elections and macroeconomic policy cycles", Review of Economic Studies 5 5 : 1-16. Rotemberg, J.J. (1 990), "Constituencies with finite lives and the valuation of government bonds", mimeograph (MIT). Roubini, N., and .T. 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 ( 1 993), "Education, democracy and growth", Journal o f Development Economics 42:399-407. Scha1ing, E. (1 995), Institutions and Monetary Policy: Credibility, Flexibility, and Central Bank Independence (Edward Elgar Publishers, Aldershot). Schotter, A. ( 1 98 1), 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) 1495-1 5 5 1 . Stock, J.H., and M.W. Watson (1 999), "Business cycle fluctuations in US macroeconomic time se1ies", ch. 1 , this Handbook. Svensson, J. (1 996), "Collusion and interest groups: foreign aid and rent dissipation", mimeograph (The World Bank). Svensson, J. (1 998), "Investment, property rights and political instability: theory and evidence", European Economic Review 42: 1 3 17-1341. Svensson, L.E.O. (1 997a), "Optimal inflation targets, 'conservative' central bankers and linear inflation contracts", American Economic Review 87:98- 1 14. Svensson, L.E.O. (1997b), "Inflation forecast targeting: implementing and monitoring inflation targets", European Economic Review 4 1 : 1 1 1 1-1 1 46. Tabellini, G. ( 1985), "Accommodative monetary policy and central bank reputation", Giomalc Dcgli Economisti 44:389-425. Tabellini, G. (1 987), Money, debt and deficits in a dynamic game, Journal of Economic Dynamics and Control 1 0:427-442. Tabellini, G. (1 990), "A positive theory of social security", Working Paper No. 3272 (NBER). Tabellini, G. ( 1 991 ) "The politics of intergenerational redistribution", Journal of Political Economy 99:335-357. Tabellini, G., and A. Alcsina ( 1 990), "Voting on the budget deficit", American Economic Review 80:37-39. Taylor, J.B. (1 983), "Rules, discretion and reputation in a model of monetary policy: Comments", Journal of Monetary Economics 1 2 : 1 23-125. Terrones, M. ( 1989), "Macroeconomic policy choices under alternative electoral structures", mimeograph (University of California at Berkeley). Tornell, A. (1 995), "Economic growth and decline with endogenous property 1ights", mimeograph (Harvard University). Tornell, A., and A. Velasco (1 992), "The tragedy of the commons and economic growth: why docs capital flow from poor to rich countries", Journal of Political Economy 1 00 : 1 208-123 1 . Velasco, A . ( 1994), "Are balance of payment crises rational?", Working Paper (New York University} Velasco, A. (1 999), "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. (1 986), "Signalling in a model of monetary policy with incomplete infonnation", Oxford Economic Papers 38:443-55. von Hagen, J. (1 992), "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 ( 1 995), "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 2 1 :422-43 1 . Waller, C., and C.E. Walsh (1 996), "Central bank independence, economic behavior, and optimal term limits", American Economic Review 96: 1 1 39-1 1 53 . Walsh, C.E. ( 1995a), "Optimal contracts for central bankers", American Economic Review 85: 1 50-167. Walsh, C.E. ( 1995b), "Is New Zealand's Reserve bank act of 1 989 an optimal central bank contract?", Journal of Money Credit and Banking 27: 1 179-1 1 9 1 .

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 of target variable 5. Choice of instrument variable 6. Issues concerning research procedures 7. Interactions with fiscal policy 8. Concluding remarks References

1484 1484 1485 1486 1490 1495 1 505 1515 1518 1 523 1 524

The author is indebted to Peter B. Clark, Todd Clark, Charles Evans, Robert Flood, Marvin Goodfriend, Charles Goodhart, Andrew Haldane, Robert Hetzel, Lars Jommg, Allan Meltzer, Edward Nelson, Christopher Sims, Lars Svensson, John Taylor, John Whittaker, and especially Michael Woodford for helpful suggestions and CJiticisms. Handbook of Macroeconomics, Volume I, Hdited by JB. Taylor and M. Woodford © 1999 Elsevier Science B. V. All rights reserved 1483

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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. robustness 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 inflation and nominal income growth targets, but not the hybrid target, would have induced fairly similar policy responses in the US economy over 1 960- 1 995. 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

Jl!.L classification:

E52, E58

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1 . Introduction

The topic of rules for the conduct of monetary policy has a long and distinguished history in macroeconomic analysis, with notable contributions having been made by Thornton ( 1 802), Bagehot ( 1 873), Wicksell ( 1 907), Fisher ( 1 920, 1 926), Simons ( 1 93 6), M. Friedman ( 1 948, 1 960), and others 1 . A major reorientation in the focus of the discussion was provided as recently as 1 983, however. In particular, Barra and Gordon ( 1 983a) built upon the insights of Kydland and Prescott ( 1 977) 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 of "activist vs. non­ activist" policy behavior and thus opened the door to possible interest in policy rules on the part of 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, 1 990- 1 996. Evidence in support of that claim is provided by several studies conducted at the Federal Reserve's Board of Governors of the rule introduced by John Taylor ( 1 993b), such as Brayton et al. ( 1 997) and Orphanides et al. ( 1 998), as well as by discussions of this rule in speeches by members of the Board [e.g., Blinder ( 1 996)] . In the United Kingdom, interest by the Bank of England in Taylor's rule as well as an alternative due to McCallum ( 1 988, 1 993a) is clearly indicated in an article by Stuart ( 1 996) 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 conntries 3 . To some extent this upsurge in interest is related to the arrival of inflation targeting as a leading candidate for the provision of a practical guideline for monetary policy, significant applications having been introduced during 1 990- 1 993 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 of 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, sec Laidler ( 1 996) and Humphrey ( 1 992). Also sec Jonung ( 1979) for an interesting discussion of the Swedish experience of the 1 930s. 2 Including proposals of Meltzer (1 984, 1 987), Hall ( 1 984), Hall and Mankiw ( 1994), Feldstein and Stock ( 1 994), and Gavin and Stockman ( 1 990). 3 An incomplete list of notable studies would include those mentioned above plus Hess, Small and Brayton ( 1993), Clark ( 1994), Croushore and Stark ( 1 995), Dueker ( 1 993), Dueker and Fischer ( 1 995), Estrella and Mishkin ( 1997), Judd and Motley ( 1 9 9 1 , 1 992), Haldane and Salmon ( 1 995), King ( 1 996), and Jefferson ( 1 997). Many more have been added since this chapter was written, most featuring Taylor's rule. 4 There is a sizable and growing literature 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 trend­ stationary 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 o n the subject o f 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 ( 1 999). 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 ( 1 983a), 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-by­ period 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 ( 1 977), Barro and Gordon ( 1 983a,b), and a host of subsequent

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writers. When it comes to practical application to the behavior of 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 of 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 ( 1 993b) 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 ( 1 993b) argues that being systematic is not sufficient and points out that discretionary behavior in the workhorse model can, even with the inclusion of random shock terms, be accurately represented by systematic application of 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 of the private sector's expectational behavior" (p. 2 1 7), i.e., to optimize once, not each period. Taking such account is basically what Barro and Gordon ( 1 983a) specified in their characterization, within the workhorse model with rational expectations, of 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 of 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 banlc 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 from 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 of activist rules, in one of his most carefully considered arguments on behalf of nondiscretionary monetary policy the crucial advantage of a rule is said to be that decisions are made in the form of a policy applicable to many distinct cases, not on a case-by-case basis, with such a form of policymaking having favorable effects on expectations. In particular, Friedman ( 1 962) 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 remarking on "our good fortune of having lived in a society that did adopt the self-denying ordinance of not considering each case of [contested] speech separately" ( 1 962, p. 24 1), Friedman contends that: Exactly the same considerations apply in the monetary area. If each case is considered on its [individual] merits, the wrong decision is likely to be made in a large fraction 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 M Friedman (1962, p. 241) separate occasions.

Thus we see that the logic of Friedman's argument is basically the same as that identified by Barro and Gordon ( 1 983a) and is entirely compatible with "activism," i.e., conditioning clauses in the rule 7 . A controversial issue i s whether it i s feasible for an independent central bank to behave in a rule-like fashion. The most straightforward point of view is that expressed by Taylor ( 1 983, 1 993b), McCallum ( 1 995b, 1 997b), Kydland and Prescott ( 1 977), and Prescott ( 1 977), 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 if it does so in a rule-like manner, and is presumably capable of understanding that, the well-managed central bank will in fact behave in such a manner. This requires it to adopt instrument settings that are different, however, from those that would appear optimal if 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 of the strongest explicit statements of this position has been made by Chari, Kehoe and Prescott ( 1 989, 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 technologies for making shoes in an Arrow-Debreu

7 An example of a conditioning clause in the freedom-of-speech example would be one petiaining to cases of false alam1s shouted in "crowded theaters".

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model - they are either available or not". But while this form of language is rather extreme, the position taken is probably more representative of academic thought over (say) 1 984- 1 994 than is the pragmatic Taylor-McCallum position. That is, most analyses of the consequences of various issues simply presume, often without explicit justification, that central bank behavior will be of the uncommitted discretionary type 8 . In many cases it i s contended that there i s a necessary tradeoff between commitment and flexibility, which the Taylor-McCallum position denies. The justification typically given, explicitly or implicitly, for the assumption of (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 of 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 of 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 single­ period perspective). But to conclude that the central bank will therefore consistently choose the discretionary outcome is analytically to adopt a particular equilibrium concept - see Chari, Kehoe and Prescott ( 1 989). The solution concept preferred by Taylor, McCallum, Lucas ( 1 976, 1 980), and Prescott ( 1 977) 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 1 0 , but the key point here is that neither of 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

B A particularly striking example of the importance of this assumption is provided by Svensson ( 1 996), who argues that in the workhorse model, extended to include 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 docs not obtain if the central bank is behaving in a rule-like fashion. Svensson ( 1 996) recognizes this point but his discussion emphasizes the discretionary case. Y This exposition docs not explicitly refer to the rcputational models pioneered by Barro and Gordon ( l983b) the reason being that the author finds these models implausible. Of course the argument here advanced relies upon reputational effects, but does not utilize the type of equilibria featured in the reputation literature. 10 Empi1ically it is - unlike the usual position - consistent with the "free lunch" finding that increased CB independence provides improved inflation performance without increased output employment variability. On this finding, see Fischer ( 1 995) or Debelle and Fischer ( 1 995, p. 201 ). It should be noted, incidentally, that my hypothesis is quite different from that of Mervyn King ( 1 996), who suggests that CBs do not aim for output in excess of the natural rate value (as they do in the workhorse model). The latter implies, since inflation and output desires are reflected in separate terms in King's loss fi.mction, that actual CBs would not want to keep output above the natural rate value euen if they could do so without generating any inflationary tendency. ,

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fashion 1 1 so that there is no necessary (i.e. , inescapable) tradeoff between "flexibility and connnitment", as has often been suggested 1 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 of 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 of debate can be sustained on the subject of 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 optimal monetary policy rule would be. This would have to be done for a number of different economies, of 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 ( 1 976), but that necessity has been well understood for many years by now 1 3 . In fact, however, such an argument fails entirely to recognize one basic and fundamental difficulty that underlies a large fraction of the issues concerning monetary policy rules. This difficulty stems from the lack of professional agreement concerning the appropriate specification of a model suitable for the analysis of monetary policy issues. There are various aspects of 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 ( 1 997a), by contrast, contends that it is the dynamic connection between monetary policy actions and real aggregative responses that is the main source of difficulty 14• Others, including 1 1 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 n, a0 + a1E1_ 1 n1 + a2 u1, with different coefficient values. Here E1 1 n1 represents prevailing expectations and u1 is a current macroeconomic shock. There is nothing tangible to prevent ai choices that represent conunitment. 1 2 The absence of any inescapable tradeoff is implicit in the central bank contracting approach pioneered by Walsh (1995) and Persson and Tabellini (1993). Taylor ( 1979) conducted an optimal policy exercise in the context of a dynamic macro model with rational expectations ahnost 20 years ago. 1 4 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: real 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 ( 1 993) and Fuhrer ( 1 997) would point to weaknesses in modeling investment or consumption behavior, and of course empirical understanding of 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 ( 1 989, p. 582), McCallum ( 1 988, 1 997a), and to some extent Brunner ( 1 980) - is to search for a policy rule that possesses "robustness" in the sense of yielding reasonably desirable outcomes in policy simulation experiments in a wide variety of models. In effect, the same type of approach is collectively utilized by the various teams of researchers participating in the Brookings projects directed by Ralph Bryant [Bryant et al. 1 988, 1 993)] 1 5 . It i s worth mentioning briefly that the research strategy based on robustness may serve to some extent as a protection against failures of the Lucas-critique type. That critique is best thought of not as a methodological imperative regarding model building strategies, but as a reminder of the need to use policy-invariant relations in simulation studies and especially as a source of striking examples in which policy invariance is implausible. The construction of a policy-invariant model faces a major difficulty, however, in the above-mentioned absence of professional agreement about model specification. Thus it would seem sensible to consider a variety of 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 of them 1 6 . Of 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 assmnptions regarding the nature of different types of unobservable shocks and the time­ series 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. 1 5 For the optimal-design point of view, see Fair and Howrey ( 1 996). 1 6 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 (1 990b, pp. 2 1 -22).

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of the overall proj ect. Thus there is no necessary conflict between a robustness­ oriented strategy and studies by individual researchers that involve construction of single models [e.g., Ireland ( 1 997), Rotemberg and Woodford ( 1 997)] . The lack of professional agreement over model specification also makes it difficult to reach any firm conclusions about the proper goals of monetary policy, as is discussed at the end of this section, before the related but more pragmatic issue of 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 teclmiques 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 of 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 non­ operational 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 of the first three. The choice among target variables will be considered in some detail in Section 4. At the opposite end of 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 1 0:30--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

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20-30 basis points on any given day. Thus writers such as Cook and Hahn ( 1 9 89) or Rudebusch ( 1 995) will distinguish between "actual" and "target" values at the daily level. But the Fed keeps the FF rate within a few basis points of 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 b e thought o f a s a formula that specifies instrument settings that are designed to keep a target variable close to its specified target path. If r 1 and x1 were the instrument and target variables, then, the simplest prototype rule might be of the form (3 . 1 ) which specifies that the instrument setting should be decreased if x1 fell short of its target value x; 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 of 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 ( 1 994, p. 79), for example, recommend that the central bank behave so as to keep each period's externally­ generated forecast of future nominal income equal to a value given by a selected target path, but beyond that "we see no need to tell it how to go about achieving the peg." Also, Svensson ( 1 997a) distinguishes between "instrument rules" and "target rules" and expresses a preference for the latter, which specify target values but not instrument settings 1 7 . 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 of designing instrument settings would be extremely simple or uninteresting, but in general such will not be the case. McCallum's series of rule studies ( 1 988, 1 993a, 1 995a), for example, was undertaken partly in response to a claim by Axilrod ( 1 985) - 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 of a rule expressed in terms of a feasible instrument variable becomes 1 7 As a related matter, Svensson has suggested that behavior conforming to a rule of the form (3. 1 ) should not b e referred t o a s involving a x 1 target; that terminology should b e reserved (he suggests) to cases in which the central bank's instrument is set so as to make E1x1 1i = x�+j · But a rule such as (3 . 1 ) with A(x7 - E1 x10 i) on the right-hand side leads t o equivalent behavior i n the limit as A-->oo, and s o is v : a compatible but more general formulation.

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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 ( 1 997a) 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 ( 1 997a), pp. 1 1 36-1 1 3 7]. 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 obj ectives. 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 . 1 ), 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 ( 1 997) and Rotemberg and Woodford ( 1 997), 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 non­ negligibly upon the specification of the model at hand 1 8 . Consequently, the marked

1g One rather prominent issue is whether there exists some externality that makes the appropriate output reference value greater than the natural-rate value that is relevant for price and wage behavior. Another crucial issue concerns the validity or invalidity of strict natural-rate hypothesis, i.e., the proposition that

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absence of 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 of an economy's individuals. In practice, nevertheless, there seems to be a substantial amount of 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 1 9 . Although it cannot be established that these objectives are optimal, it would seem to this writer that they probably provide a fairly good specification of appropriate CB macroeconomic goals.

4. Choice of target variable After a long dose of preliminaties, let us now finally turn to substantive issues in the design of a monetary rule. In this section we shall be concerned with the choice of a target variable - both its identity and the question of 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 Almeida and Goodhart ( 1 996), Bernanke and Mishkin ( 1 997), Goodhart and Vinals ( 1 994), McCallum ( 1 997a), and others, as well as the individual authors represented in books edited by Leiderman and Svensson ( 1 995) and Haldane ( 1 995). Other leading target-variable choices are aggregate spending magnitudes such as nominal GNP or GDP - often in growth rate form - and a "hybrid" variable that sums inflation and real output measured relative to some sort of trend or reference value 20 . All of 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 of exchange rate policy should be appropriate.

output cannot 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 ( 1 972)]. 19 This variable capacity value may, however, exceed the natural-rate value, as mentioned in footnotes I 0 and 1 8, and as is typically assumed in the CB credibility literature. 20 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 for annual periods to percentage output deviations. It would be equivalent to use inflation over a quarter plus one-fourth 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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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 ( 1 96 1 ) and extended by McKinnon ( 1 963) and Kenen ( 1 969). Basically, these all boil down to the question of whether the microeconomic (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 2 1 . Some analysts [e.g., Bruno ( 1 993), Fischer ( 1 986)] have contended that there are some macroeconomic advantages of a fixed exchange rate 22 but the arguments seem actually to be based on political or public-relations considerations, not economic costs and benefits 23 . Thus in the case of small economies for which large fractions of their market exchanges are intemational 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 co1111o11 n currency) with a specified currency or basket of currencies 24 . And at the other extreme, the macroeconomic advantages of 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

I f a set o f countries i s t o have permanently fixed exchange rates, i t would seem that fi·om 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 obviously be significant changeover costs, as in the EMU example.) As for rates that are fixed, but not permanently, the European experiences of 1 992 and 1 993 support Friedman's ( 1953) classic argument that such an arrangement is tmdesirable because of the self�destructive speculative impulses that are encomaged. 22 From the monetary-policy perspective, a moving peg or narrow band falls into the same category as a fixed exchange 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 lmion, of course. 24 A relatively clear-cut example is provided by Luxembomg, which has had a monetary union with Belgimn since 192 1 (except for an intenuption during World War II), Belgian francs serving as a legal tender in both nations. Luxembourg also 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 could alternatively be thought of as an inflation target with an unusual specification of the price index to be utilized.

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1 497

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 functions, 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 ( 1 983), West ( 1 986), Aizenman and Frenkel ( 1 986), Henderson and McKibbin ( 1 993), Frankel and Chinn ( 1 995), Ratti ( 1 997), and Ireland ( 1 998), while well­ known simulation studies with estimated models have been conducted by Taylor ( 1 979, 1 993a), Feldstein and Stock ( 1 994), Haldane and Salmon ( 1 995), and the individual authors in Bryant et al. ( 1 988, 1 993). 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, Aizenman-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 for 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 agreement 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-business­ cycle 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., whether the target should be specified in a difference­ stationary 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

2(' These

are the two va1iables that arc most closely related to the utility fimctions of individuals in explicit optimizing models such as those of Ireland ( 1 997) or Rotembcrg and Woodford ( 1 997).

1 498

B. T. McCallum

a money-stock variable 27 . Specifically, the weakness of 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 of the disturbance is itself of a permanent nature. Since any such action entails general macroeconomic stimulus or restraint, this type of targeting procedure would tend to induce extra cyclical variability in demand conditions, which may imply extra variability in real output if price-level stickiness prevails. Furthermore, variability in output and other real aggregative variables is probably more costly in terms of human welfare than is an equal amount of 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 of 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 of 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 if the (log of 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 if it is assumed that the random, unpredictable component at the quarterly frequency has a standard deviation of0.0045 (which is approximately the standard deviation of one-step ahead forecast errors for the USA over 1 954-1991) 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 0 . This, it seems to the writer, represents a rather small amount of 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 arguments that reach this conclusion, which is taken for granted by Feldstein and Stock ( 1 994), see Fischer ( 1 995) and Fillion and Tetlow ( 1994). The opposing position is taken by Hall and Mankiw ( 1994) and Svensson ( 1 996) [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. 30 I am taking the control error to be serially 1mcorrelated. Then the 80-period ahead error would have variance (80) (0.00452 ) = 0.001 62 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 mah'11itudes that prevailed over the 1 960s, 1 970s, 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 of the growth-rate and growing-level types 3 1 . 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 of nominal GDP, and (iii) the above-mentioned hybrid variable. As some notation will be useful, henceforth let X t . y1, and p1 denote logs of nominal GDP, real GDP, and the price level (as represented by the deflator so that x1 y1 + p1), with time periods referring to quarter­ years. Then the three contending target variables in their simplest form are 1'1p1, 1'1x1, and h1 = 1'1pr + 0. 25y1, where y1 = y1 - y1 with ji1 denoting the reference value of real GDP. 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 h1 might be the most appropriate of the three, a point of view taken implicitly by Blinder ( 1 996), with 1'1x1 arguably ranking second 3 2 . But among actual central banks that have adopted formal numerical targets, virtually all have (as of early 1 997) 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 1'1p1 over the others as their formal target, but three of 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 of scholars that monetary policy has, from a =

�o 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. 3 1 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-tern1 perspective, provide almost as good inflation control as direct inflation targeting, since average real output growth will be virtually independent of monetary policy and reasonably forecastable, 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 1 4 . 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 ( 1 997) is, it is argued below, fundamentally misguided.

1 500

B.T. McCallum

long-run perspective, no substantial effect on y1 y1 - y1 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 11p1 variable that their policy actions affect strongly on a long­ run basis 34. Second, measurement of y1 and therefore ji1 is difficult and controversial, even in comparison to measurement of 11p1 • We have described y1 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 y1 are likely to be much larger than errors in measuring the long-term average value of 11y1 , which is all that is necessary for correct design of a /1x1 target. Thus the h1 target is more demanding of knowledge concerning the economy than is either of 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 of the concept of inflation, so the argument goes, but not of the national income accounting concepts x1 and y1, much less the reference value y1 • 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 of 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 of "supply shocks" - such as crop failures, terms-of-trade changes, or indirect tax-rate changes - will entail temporary modification of 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 of 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 hypothesis", is subscribed to by a large fraction of macroeconomic researchers. 34 This position is explicitly expressed by McCallum (l 997a) and by Reserve Bank of New Zealand ( 1 993 ). 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" concepts 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 ( 1 972), 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-accelerating­ inflation rate of nnemployment) approach posits a stable relationship between unemployment (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 smi of averaging could be applied to the Ax, and h1 variables. 37 On this subject, see Reserve Bank of New Zealand ( 1 993).

Ch. 23:

Issues in the Design of Monetary Policy Rules

E DLXGAP

1 501

------- DLPGAP

-----

J

ZERO

fig. 1 . Gap measures for inflation and nominal GDP targets, 1 960-1995.

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 f...p1 is 0.005, which amounts to approximately two percent inflation on an annual basis. Also, for simplicity it will be assumed that y1 values are given by deterministic trends obtained by regression ofy1 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 1 960. 1-1 995 .4, with United States GDP data used for x1 and with y1 based on GDP in 1 992 fixed-weight prices (i.e., using the fixed­ weight rather than the chain-weight deflator). Over this period, the y1 trend variable is given by the expression Yt = 7. 520749 + 0.00688 1 t (with t = 1 in 1 947 . 1). Therefore, f...y = 0.00688 1 is assumed and the target value for f...x 1 is 0.0 1 1 88 1 , with 0.005 being the target value for both f...p1 and h1• For each of the three variables we calculate the gap between actually observed values and these retrospective, hypothetical target values. These gaps are denoted /).p(gap )1 /).Pt 0. 005, f...x(gap )1 = f...x1 - 0. 0 1 1 8 8 1 , and h (gap)1 = 1'1p1 + 0. 25y1 - 0. 005. Their values for the first two variables (over 1 960. 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 f...p1 and !'u1 targets both suggest that monetary policy was excessively expansive most of the time between 1 965 and 1 989. The f...x(gap) measure is considerably more variable from quarter to quarter than the f...p(gap) measure, basically because /).y1 is more variable than 11p1• Averaging over the whole period, the two measures give the same signals simply because the f...x 1 target value was calculated =

--

1 502

B. T. McCallum -- ----0.06 ,------

0.04

0.02

0.00

-0.02

•)

...

.�: ' ,'.' ,'

/'/:

�: :

1 - DLXGAP

------- HGAP

----·

j

ZERO

Fig. 2. Gap measures for hybrid and nominal GDP targets, 1 96()-.1 995.

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 fu1• 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 l'u1 variable suggests that policy should be loosened whereas the /l..p1 variable suggests the opposite, and this situation prevails for over a year during 1 990-199 1 . Those analysts who favor A\:1 targeting believe, of course, that keeping fu1 values steady would result in smaller fluctuations in ji1 than would a policy of keeping /l..p, 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 ( 1 988, 1 997a) 38 . Figure 2 compares gap values for h1 and A\:1 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 1 960s and 1 990s, and tighter monetary policy during much of the 1 970s, in comparison with the At, measure. (Of course both measures signal that policy was too inflationary from 1 965-1 989, as before.) These features of the plots in Figure 2 are basically a consequence of the fact that a linear trend line for y1 implies negative residuals in the early 1 960s and 1 990s and many

38

Sec footnote 1 4 above.

Ch. 23:

1 5 03

Issues in the Design of Moneta1y Policy Rules 0.06 ,---------,

0.04

0.02

0.00

-0.02

85

86

87

88

89

1 - DLXGAP85

90

n-----

91

92

HGAP85

93 ----·

94

95

ZERO

I

Fig. 3. Gap measures for hybrid and nominal GDP targets, 1 985-1995.

positive residuals during the 1 970s, which it does because of the sustained period of rapid growth in real GDP from 1 960 to 1 973. To emphasize this last point, Figure 3 gives results for the same type of exercise but with the sample period limited to 1 985. 1-1995.4. Here it will be noted that the h(gap)1 values are quite different from those for 1 98 5-1995 in Figure 2, solely because the y1 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 of 1 990 and 1 992, the Ax, 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)1 figures shown in Figures 2 and 3 illustrates the main weakness of the hybrid target variable, namely, its sensitivity to alternative calculations of y1 reference values. Proponents of the hybrid variable might argue that more sophisticated measures of y1 should be used, and it is certainly true that our linear trends are not conceptually attractive. But neither are, say, Hodrick­ Prescott (HP) filtered series, for reasons emphasized by Cogley and Nason ( 1 995) plus a recognition of what the HP filter would imply about US GNP for the period 1 929- 1 93 9 4 0 . Other measures exist, but have attracted little professional support. In

39

It also has a reduced slope, which changes the definition of fu:(gap) to l'!.x1 - 0.0 1 0336. 40 If the HP filter were applied to US real GNP over a period including 1 929- 1 939, the HP "trend" series would turn down fairly sharply during the early 1 930s. If this series were used as one's measure 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 1 932-1938 largely because capacity was low. But measured unemployment figures suggest strongly that this conclusion would be misleading.

1 504

B. T. McCallum 0.06 -r---------,

0.04

0.02

-0.02

65

70

1 -- DLXFGAP

75

80

85

------- DLPFGAP

90 -----

ZERO

95

I

Fig. 4. Gap measures for inflation and nominal GDP values forecast 4 quarters ahead, 1 960-1 995.

sum, there is no widely accepted and conceptually sound measure for j!1 , but use of the hybrid target variable requires such a measure and its value is rather sensitive to the particular measure adopted. One weakness of 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 ( 1 997a) has argued rather convincingly that "inflation forecast targeting" has several attractive features. Consequently, indicators of 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 Ax1 , !1p1 , l1bt . and R1 (four lagged values of each), where b1 is the log of the monetary base and R 1 is the 3-month Treasury bill interest rate. Also one lagged value of y1 was included; a second lagged value would create perfect collinearity among the regressors. Values of 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 Ax1 and !1pt . relative to the previous graphs, but the overall messages remain the same: that there is apparently little basis for choice between Ax1 and !1p1 while the h1 indicator appears to give signals that are quite different. Recently, Ball ( 1 997) has put forth, in rather strong language, some striking propositions regarding target variables 4 1 • Among these are claims to the effect that efficient monetary policy 42 consists of a special case of a Taylor rule that is equivalent 4 1 Some of these have been noted favorably by Svensson ( 1 997a,b).

42 The paper's concept of "efficient monetary policy" is one that focuses on the variances of inflation and output (relative to capacity) while assmning unrealistically that the central bank has full contemporaneous

Ch. 23:

Issues in the Design of Monetary Policy Rules

1 505

0.06 -r------,

0.04

0.02

-�-�7�--------------------J�i�-------�\�-�.�A� '

0.00

-0.02

' "

'

.'

65

70

75

1 - DLXFGAP

80

------- HFGAP

85 ----·

90

ZERO

95

I

Fig. 5. Gap measures for hybrid and nominal GDP values forecast 4 quarters ahead, 1 960-- 1 995.

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 ( 1 993b) suggested weights; and that nominal income targeting would be "disastrous" as it would give rise to non-trend-stationary behavior of 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 Phil lips curve, in particular, has a superficial similarity in appearance to the Calvo-­ Rotemberg specification as exposited by Roberts ( 1 995), 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 instrument variable

In this section we consider the choice of a variable to serve as the instrument through which a central bank's policy rule will be implemented. It i s well known that, although a substantial number of academic economists have favored use of a monetary base or

knowledge of all variables (on this, see Section 6 below). Thus it simply assumes away the first-order problem of designing an operational rule that will generate the desired mean value for JT1 while avoiding explosions.

1 506

B. T. McCallum

reserve aggregate instrument, almost all actual central banks utilize some short-term interest rate in that capacity. Before turning to a review of their relative desirability, however, it will be appropriate to consider the sheer feasibility of 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 ( 1 975). 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 ( 1 97 5) paper included a result suggesting that if the interest rate R 1 were set each period by means of a policy feedback rule that specifies R1 as a linear function of data from previous periods, then all nominal variables would be formally indeterminate. Sargent ( 1 979, p. 3 62) summarized this conclusion as follows: "There is no interest rate rule that is associated with a determinate price level." 43 Subsequently, however, McCallum ( 1 9 8 1 , 1 986, p. 1 48) showed that the Sargent­ Wallace 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 ( 1 978) and in the classic static discussion of Patinkin ( 1 96 1 ). The problem with the alleged proof of 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 never­ theless very different both analytically and economically. Consequently, McCallum ( 1 986, p. 1 37) 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 of (say) nominal income, as well as the price level, would not be defined by the model's conditions. Paths of 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 1 975 paper, and attJibuted this difference to their use in ( 1 982) 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 ( 1 975). In fact, however, the main relevant difference is that the 1 982 analysis is based on a model in which monetary and nonmonetary assets cannot be distinguished - and indeterminacy does not actually prevail in any case. On this, see McCallum ( 1 986, pp. 144-154). An impmiant recent contJibution is Benassy ( 1 999). 44 Actually, McCallmn ( 1 986) proposed "indeterminacy" for the former, but the addition of the adjective is clearly desirable.

Ch. 23:

Issues in the Design of Monetary Policy Rules

1 507

if the monetary authority failed entirely to provide a nominal anchor45 . This type of phenomenon has been discussed by Gurley and Shaw ( 1 960), Patinkin ( 1 949, 1 96 1 ), Sargent ( 1 979, pp. 3 60-363), Sargent and Wallace ( 1 975), McCallum ( 1 98 1 , 1 986), and Canzoneri, Henderson and Rogoff ( 1 983), 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 self­ justifying expectations is the source of this type of aberration. It has been discussed by a vast number of writers including Taylor ( 1 977), Sargent and Wallace ( 1 973), McCallum ( 1 983), Brock ( 1 975), B lack ( 1 974), Obstfeld and Rogoff ( 1 983), and Flood and Rodrick ( 1 990). 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 ( 1 975, pp. 1 44-147) and Woodford ( 1 990, pp. 1 1 1 9-1 1 22). 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 well­ specified 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 ( 1 960), Patinkin ( 1 949, 1 96 1), Sargent ( 1 979, pp. 3 60-363), or Sargent and Wallace ( 1 975). To some readers, this fact may diminish the force of Woodford's ( 1 990, 1 994) 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 ( 1 994) 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. It is unclear whether there is any compelling evidence in support of the notion that macroeconomic bubbles or sunspots are empirically relevant [Flood and Hodrick ( 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. 46

1 508

B. T. McCallum

operational guide for its open market operations" (p. 1 424). 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 of several of the crucial institutional features of a modern commercial banking system, notably the need for unchallengeable convertibility, at par, between currency and deposits, and secondly that commercial bank reserves at the CB receive a zero, or below-market, rate of interest" [Goodhart ( 1 994), p . 1 424] . Then as the discussion proceeds it becomes clear that Goodhart is himself taking a position that is predominantly, if not entirely, supportive of the opinions of those who have worked in a CB. Thus he asserts, on his own account, that "if the CB tried to run a system of monetary base control, it would fail" (p. 1 425). And he goes on to outline the putative flaws in logic or factual knowledge that invalidate the cited views of academic economists (pp. 1 424-1426). In fact, however, although Goodhart's discussion is apparently intended to be concerned with feasibility, the actual argumentation presented pertains to desirability. Specifically, the main analytical points are those made in the first three complete paragraphs of p. 1 425, which argue that tight base control would lead in practice to overnight interest rates that at the end of most days would equal either the CB 's penal rate or a value "near zero" 47 . Having developed that point, Goodhart concludes as follows: "Some economists might prefer such a staccato pattern of interest rates, but it would not seem sensible to practitioners" (p. 1 425). But clearly this is an argument that pertains to the desirability, not the feasibility, of tight base control 48 . Having concluded, then, that neither interest rate nor monetary base instruments are infeasible 49, we turn to the task of considering their relative desirability 50 . In that

47 lf 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 arc presented by Whittaker and Theunissen ( 1987) and Okina ( 1 993). 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 banks do not literally control the sum 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 subtract 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 ma!,'llitude 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 instnunent under discussion. 50 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 R1 at some preset value indefinitely, not varying R1 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 ( 1 983) and McCallum ( 1 986) 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

1 509

regard, most proponents of a base instrument do not deny that such a regime would involve substantially more variability of short-term interest rates than is experienced under today's typical procedures, which involve interest-rate instruments and short­ term interest rate smoothing 5 1 . Base proponents would contend, however, that with a base instrument it may be possible to design simple policy rules that are more effective from a macroeconomic perspective than are comparable rules with interest­ rate instruments 5 2 • 53 . In order to illustrate the plausibility of that contention, let us consider some counterfactual historical simulations of the general type used by McCallum ( 1 988, 1 993a, 1 995a) with quarterly US data. In order to keep the model specification from biasing the results, the macroeconometric model in these simulations will be an unconstrained VAR with four lags included for each of the four variables �Yr, �pr , �b1, and R1 54. Here R1 is the three-month treasury bill rate, b1 is the log of the St. Louis Fed adj usted monetary base, and GNP data is utilized for y1 and p1• The estimation and simulation period is 1 954. 1 - 1 99 1 .4. We have seen above that there has not been a large discrepancy, historically, between signals provided by fu1 and �p1 targets, when the target values are gauged so as to imply the same average inflation rate. Accordingly, let us concentrate our attention on rules for �b1 and R1 designed to keep x1 close to three target paths, all of which provide expected fu1 values of 0.01 1 25 (i.e., approximately 4.5 nominal GNP growth per year,

Woodford ( 1 990, 1 994) and Sims ( 1994) extend this type of result to a "pure peg" and conduct their analysis in general equilibrium models with explicit optimization on the part of individual agents. 5 1 The concept of interest rate smoothing that I have in mind is keeping R, close to R,_b but there is no major conflict here with concepts such as a tendency to minimize E(R, � E, 1 R, f [Goodfriend ( 1987)]. 52 The reason why design of a simple interest rate rule may be more difficult stems from 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-nm (i.e., maintained) perspective. This means that the interest rate effects of an open market action are in opposite directions from short-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 for 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 country. 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 GDP, and yields improved base-rule simulation results for the period 1 984- 1 995. 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 ( 1 988) 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 ( 1 993), by contras1, the small macro model discussed on pp. 14�21 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. �

�

B. T McCallum

1510

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 (5 . 1 ) where A > 0 is a policy adj ustment parameter and the target variable x; can be defined in various ways 55. To yield a growing-levels target, we would have x;1 x�� � + 0. 0 1 125 whereas a growth-rate version would use instead x;3 = x1_ + 0. 0 1 125. Besides these, 1 we will consider x72 0.2x; 1 + 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 terrn that reacts to past target misses. Note that =

=

x;� l - Xt-1 = (Xt-2

+

0. 0 1 1 25)

��

Xt-1 = 0. 0 1 1 2 5 - fu:t I

and that

X�21 - X1_1 = 0.2(x7 1 1 - Xt-1) + 0. 8(0. 0 1 125 - fu;t- 1) = 0.2(x;� 1 - Xt-1) + 0.8(fu:� 1 - fu:t- I ) so that use of x;2 is equivalent to having a growing-levels target but using derivative as well as proportional feedback, in the terminology of Phillips ( 1 954). So as to obtain some indication of robustrJess to rule specification, a range of A 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 (5.2) Thus, the value of the mterest rate instrument is lowered relative to the previous quarter when target spending x; exceeds the actual level in the previous quarter. The - 1 00 factor is inserted so as to make the same range of A values as in Equation ( 5. l )

55

This is the type of rule studied in McCallum ( 1 988, 1 993a, 1 995a).

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 te1m). More sophisticated methods of forecasting the pem1anent component of both velocity growth and real output growth would be used in practice by actual central banks.

Ch. 23:

15 1 1

Issues in the Design of Monetary Policy Rules

Table 1 RMS errors with base/interest instruments, rules (5. 1 ) and (5.2), VAR Model, US Data 1 954. 1-199 1 .4 RMS error relative to:

Jc = O.OO

Jc = 0.50

Jc = 0.25

Jc = 1 .00

�-----�·------�--------- - ------------

0.0503 1.153 0.0133 0.24 1 5 0.0097 0.0184

0.0503 1 . 1 53 0.0133 0.2415 0.0097 0.01 84

0.0503 1 . 1 53 0.0133 0.24 1 5 0.0097 0.0184

Panel 0.0235

A:

x;1 target 0.0376

expl "

expl

O.o l l 3

0.0 1 84

expl

expl

0.0 1 1 2

0.0 1 88

expl

expl

Panel B: x;2 target 0.0232 0.0381

0.0284 0.0619 0.0109 0.01 55

0.0100 0.0105

0.0 1 06 0.0123 0.0105 0.0107

Panel C: x;3 target 0.0361 0.0418 0 . 1 825 0.3321 0,0 1 1 7 0.0123 0.0378 0.0680 0.0099 0.0 104

0.0 1 02 0.0 1 00

expl expl expl expl expl expl

0.020 1 0.0254 0.0 1 14 0.0 1 47 0.01 1 8 0.0142

0.0292 0.0959 0.01 1 6 0.02 1 7 0.01 1 1 0.0123 -- ------------

" expl, explosive oscillations.

appropriate again 57 . The same trio of x7 definitions is employed as with the base instrument. Table 1 reports results of counterfactual historical simulations each using rule ( 5 . 1 ) o r (5 .2) with VAR equations for �y1, �pr, and either R 1 or �b1• In these, estimated residuals for �y1, �Ph and either R1 or �b1 are fed into the system as estimates ot shocks that occurred historically, with the simulations beginning with initial conditions

The factor 1 00 is needed because R1 is expressed in tem1s of percentage points whereas [l,h, is in logarithmic (i.e., fractional) units. Comparability is not complete, however, because R, is measured as percentage points on a per annum basis. Use of -400 as the scale factor would, however, result in dynamically unstable behavior for most A values over 0.25. 57

1512

B. T. McCallum

as of 1 954. 1 and running for 1 52 periods 5 8 . The table's entries are RMS errors, i.e., deviations of x1 from target values x7 , with the top figure in each pair pertaining to the t...b1 instrument and the bottom figure to the R1 instrument. The three panels A, B, and C refer to simulations with the three target values (x; 1 , x;2, x;3), and for each simulation the RMS error performance is reported relative to each of the three target paths. Thus, we are able to see if performance relative to alternative criteria is sensitive to the target utilized, for each of the targets. Comparing the three panels we see that when the levels target is used (with only proportional feedback) performance is very bad with the R 1 instrument, explosive fluctuations in x1 resulting with A = 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 A = 1 .0. With A = 0 .25, somewhat better performance relative to the x7 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 x;3 is adopted, successful stabilization of x1 is achieved for all A values with both instruments. Performance relative to the growing levels path x7 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 x;2 seems quite attractive, as was noted for Japan in McCallum ( 1 993a). Equivalently, application of a limited amount of 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 of 30 separate comparisons 60 is the RMS error value smaller with the R1 instrument 61 . And, more significantly, the number of cases in which explosive oscillations result is larger with the interest instrument. These cases, should be noted, all involve the growing-levels target, x; 1 . Some proponents of an interest instrument might argue that it is important that R1 be adjusted relative to a reference level, rather than to the previous quarter's value. Following the practice of Taylor ( 1 993b), therefore, let us also consider performance of a rule of the following type: Rt = 1 00[0. 029 + (Pt- 1 -- Pt s )] - 1 00A (x;_ 1 sg

- Xt-1 ) .

(5.3)

Stochastic simulations, with shocks generated randomly, have been conducted by Judd and Motley ( 1 992) in a related study mentioned below in Section 6. 59 Judd and Motley's ( 1 992) 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* 1 1 path when x*2 1 is the target utilized. 60 Note that the first-column cases are the same with the three different targets, since with A = 0 there i s no feedback from target misses. "1 Michael Woodford has emphasized to me that there is no inherent interest in comparing base and interest instruments with equal values of A; that we want to compare entire families. These comments are correct. But Table 1 attempts to do that by scaling the A values - recall that the factor - 100 has bvcn inserted in Equation (5.2) - so that instrument instability occurs for about the same value of (scaled) },.

Ch. 23:

Issues in the Design ofMonetary Policy Rules

1 5 13

Table 2 RM S errors with level-style interest instruments, rule (5.3), VAR Model, US Data 1 954. 1 - 1 99 1 .4 RMS error relative to:

). = 0.00

). = 0.25

). = 0.50

0.3825

0 . 1 54 1

0.09 1 5

0.0809

0.0326

0.0208

0.0169

0.01 1 8

0.0 1 04

0.01 08

0.0143

0.3825

0.2996

0.24 ! 6

0. 1 702

0.0809

0.0630

0.0507

0.0366

0.0 1 1 8

0.01 1 1

0.0 1 1 0

0.01 29

). = 1 .00

Panel A: x;1 target 0.05 5 1

Panel B: x;2 target

Panel C: x;3 target 0.3825

0.3687

0.3559

0.332S

0.0809

0.0780

0.0754

0.07 1 1

0.0 1 1 8

0.0 1 1 8

0.01 20

0.0 1 53

Here the (P1-t - Pr-s) term uses the past year's inflation rate as a forecast of the next quarter's so as to make the rule one that sets a real interest rate in relation to the (annualized) target value of 0.029, which is designed to be consistent with a long-run real interest rate of 2.9 percent. The latter follows Taylor's ( 1 993b, p. 202) suggestion of using the sample average rate of growth of 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 . It will be seen that the performance is better than with interest instrument rule (5 .2) for all 1 2 comparisons when x� 1 is the target, i.e., when a levels target is utilized. Among the 1 8 remaining comparisons, however, rule (5.3) outperforms (5.2) in only a single case. So, it is unclear whether the levels form of interest instrument rule is superior to the form that calls for adjustment of R1 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 A = 1 and the levels target x; 1 is used, and also does better relative to the x�3 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;2 is used, the RMS 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 concl usive - especially since the model used is of the VA R type

1514

B.T. McCallum

Nevertheless, the apparent superiority of the base instrument gives rise to the question of why it is that, in actual practice, almost all central banks utilize operating procedures that are akin to use of an interest rate instrument. It is almost certainly the case that use of 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 of financial institutions with which they have to work in the course of their central-banking duties. The extent of interest-instrument preference by CBs suggests, however, that there are additional reasons. Accordingly, Goodfriend ( 1 99 1 ) and Poole ( 1 99 1 ) have made interesting efforts to understand the Fed's attachment to an interest rate instrument. Despite their contribution of various insights, however, the question remains unanswered 63 . My 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 of last resort. Regarding the former, consider a grossly simplified base money demand function that includes lagged as well as current interest rates: Ot
I a t l , then the system will be explosive. Belief that market demand for the monetary base is such that I a2 1 > I a 1 I represents the actual state of affairs would then lead one to believe that use of a base instrument would be disastrous, as suggested by Goodhart. And, in fact, there is some reason to 62 Between 1 975 and 1 987 the Swiss National Bank used procedures that were akin to use of a base instrument. [See Rich ( 1 987, pp. 1 1-1 3).] Short-term interest rate variability in Switzerland was much greater than in other economies, but macroeconomic performance was excellent. (In 1 987 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 ( 1 994) 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 fatal for many other issues. In Equation (5.4 ) 1]1 is a stochastic disturbance term. 65 Here I do not literally mean exogenous, but rather that b1 is varied for macroeconomic reasons, not so as to smooth R1 values. ,

Ch. 23:

Issues in the Design of Monetary Policy Rules

1515

think that such beliefs might b e held by central bankers. In particular, econometric estimates of base money demand functions (direct or indirect) sometimes indicate that l a2 1 > l at l in fact. Central bank analysts would be aware of these estimates. My own belief is that it is not true that I a2 1 > I a 1 1 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 ( 1 986 ), Goodfriend and King ( 1 988)]. To prevent such crises, the CB needs to supply base money abundantly in times of stress [Bagehot ( 1 873)]. This is usually conceived of as occurring by the route of discount-window lending. But Goodfriend and King pointed out that a policy involving interest rate smoothing - i.e., not allowing R1 to change much relative to R1_ 1 - would automatically provide base money in times of high demand 67. Then i f a C B i s going to practice R 1 smoothing i t is quite natural for it to use a R1 instrument 68 . 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 ( 1 995a) 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 of 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 of issues concerning procedures used in investigations of the properties of monetary policy rules. One set of issues has to do with the operationality of various rule specifications while another set focuses In part my belief stems from the fact that for base demand in period t the value of R 1 _1 is an irrelevant bygone, so R1_ 1 does not belong in a properly specified demand function. There are reasons, involving omission of expectational variables, why econometric studies would neve1iheless tend to find strong R,_1 effects. On this, see McCallum ( 1 985, pp. 583-585). 67 As would a practice of keeping R1 from rising above some preset penal rate. 68 Goodfriend ( 1 9 9 1 , p. 1 5) and Poole ( 1 9 9 1 , pp. 37-39) observe, however, that this is not a strict logical necessity. Also, many actual CBs apparently do not accept the Goodfriend-King argument that the LLR role can be fulfilled by R1 smoothing without discount-window lending. 66

1516

B. T 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 ( 1 988, 1 993a, 1 995a), 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 ( 1 988) and Bryant et al. ( 1 993), 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 ( 1 99 1 , 1 992) for example, improve upon those of McCallum ( 1 98 8) 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 term. Thus the extent of a tendency for x1 (say) to drift away from a levels target path such as x; 1 is understated by the results in those tables 69. Bryant et al. ( 1 993, 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. ( 1 993). In this study, which is a follow-up to Bryant et al. ( 1 988), 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 in 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; time plots of x1 indicate the absence of any path-restoring behavior except toward the end of the ! 52-quarter simulation (and sample) period.

Ch. 23: issues in the Design of Monetary Policy Rules

1517

and fiscal policy rules (even in the face o f potential weaknesses o f the models' specifications). It is argued in McCallum ( 1 993b, 1 994), however, that this potential was signif­ icantly 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 (6. 1 ) where R1 is an interest rate instrument and z1 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[(z1 - z�)2 ], 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 ) 70. The more obvious is that it is unrealistic to pretend that monetary policymakers can respond to the true value of current-period realizations of z1 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 M l 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. ( 1 993) studies, clearly makes it possible for the simulated performance to be significantly better than could be obtained in reality. Furthennore, 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 zf. Here 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 instrument variable under consideration may be one that can be used to smooth out fiuctua · tions in z1 but not to control the long-term growth of z1 • Then by using fluctuations in z1 70

It should be noted favorably that the instrument variable is operational and realistic.

1518

B.T. McCallum

relative to the baseline path z7 in a performance measure like E[(z1 - z7)2 ], the investigator may conclude that R1 is a desirable instrument when in fact it is highly unsuitable 7 1 . 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 M l . 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 ( 1 993a), Bryant et al. ( 1 993), Fuhrer and Moore ( 1 995)] . 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 per 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. 7 1 Some examples are described in McCallum ( 1 994). 72 Among these contributions are papers by A1esina and Tabellini ( 1 987), Debelle and Fischer ( 1 9 9 5),

Leeper ( 1 99 1 ), Sims ( 1994, 1 995), and Woodford ( 1 994, 1 995).

Ch. 23:

Issues in the Design ofMonetary Policy Rules

1519

An early paper on the subject that has received a great deal o f attention i s the Sargent nd a Wallace ( 1 98 1 ) 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 ( 1 9 8 1 , 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 ( 1 990a, 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 Sargent­ Wallace 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 that 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 r�sult pertains to primary deficits, i.e., deficits exclusive of interest payments, but not to dcficito, 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 private agents to buy its bonds (i.e., lend to it), since such would represent tax ation.

B. T McCallum

1 520

( 1 994, 1 995), Sims ( 1 994, 1 995), and Leeper ( 1 99 1 ) . Perhaps the most dramatic theme in this literature is the presentation of a "fiscal theory of the price level" [Woodford ( 1 995, pp. 5-1 3), Sims ( 1 994)]. For an introductory exposition and analysis, let us consider the simplest case, which involves a Sidrauski-Brock model with constant output y and utility function u(ct , m1) + f3u(c1+ I , mt+! ) + · · · with u(c, m) = ( 1 - at1 A 1 c1-a + ( 1 - 11t 1 Azm H , where a, 11 > 0 and f3 = 11( 1 + p) with p > 0. Also we assume 11 < 1 , in order to facilitate presentation of the fiscalist theory, not the counter-argument outlined subsequently. In this setup, the households' first­ order conditions include

75

A=

(

A a ____!_X_ Az

)-111}

(7. 1 ) ('1.2)

for all t = 1 , 2, . . . . Here P1 is the money price of output, M1 is nominal money at the start of period t, m1 = M/P1 , c1 is consumption during t, and R1 is the rate of interest on government bonds, the household's budget constraint being

1

t

Pt ( Y - Vt) = Pt ct + Mt+l - M t + ( 1 + R r B t+ l - B � o

(7.3)

where v1 is lump-sum taxes and B1 is the nominal stock of bonds at the end of t. ln per-household terms, the government budget constraint with zero purchases is (7.4) so v1 is the per-household value of the fiscal surplus. If the government chooses time paths for M1 and v1 (or B1 ), then Equations (7. 1 )-(7.4) give equilibrium values for c1, P{ , Rt , and B1 (or v1) provided that two transversality conditions are satisfied, these 1 1 requiring that {3 MtfP1 and {3 B11P1 approach zero as t ----+ oo. Note that Equations (7.3) and (7.4) imply c1 y, the constancy of which is utilized in formulations (7. 1 ) and (7.2). Following the fiscalist argument 76, now suppose that the value of M1 is kept constant at M and that v1 = v > 0 for all t = 1 , 2, . . . Then the price level is determined as follows. The GBR can be written as P1 I I (7.5) b1+ 1 = ( l + RI ) pt+ -! [bI - vt ] = f3 -b/ - ut o f3 ,_-

.

_

_

-

implying that b1 = B/P1 will explode as t --+ oo, since 11f3 > 1 , unless it is the case that B 1 /P 1 = v/( 1 - {3), which would induce b1 to remain constant at the level b1 v/( l {3) =

-

75 That is, a model in which infinite-lived households with time-separable preferences make 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 feat11re of the setup is not relevant to the issues at hand. 76 I am indebted to Michael Woodford for special efforts to explain the argument to me, bLI1 he i s certainly not responsible for the point of view expressed here.

Ch. 23:

issues in the Design ofMonetwy Policy Rules

1521

thereafter. Therefore, so the theory says, P 1 = B 1 ( 1 - {3)/u i s determined by the fiscal surplus magnitude u and the initial stock of nominal debt B 1 . At the same time, Equations (7. 1 ) and (7.2) imply a difference equation relating Pt+ 1 to P1 in an unambiguously explosive fashion, starting from P 1 , provided that P 1 exceeds a critical value Pc . That explosion i n P 1 makes MIP1 approach zero and so, with b1 constant, both transversality conditions are satisfied although B1 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 b1 , 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. 1 This more fundamental "monetarist" equilibrium features Pt+l = P1 = 11dp 1rlfA, i.e., a constant price level, together with values Bt+ 1 = 0 for all t = 1, 2, . . . . With these paths for P1 and B1 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 u1 = u 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 u1 = u 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 B1 =0 in the latter. If there were an initial stock of bonds outstanding, B 1 * 0, then they would be retired in period 1 with a resulting real primary surplus of BdP 1 • In sum, a formally correct and arguably more plausible solution than the fiscalisl 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 but 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 striking fiscalist outcomes typically result from emphasizing the possibility of bubble

77 This i� also the basis for the argument in a recent paper by Buiter ( 1 998), which reaches conclusions

predominantly compatible with those presented here. n Note that it is not being claimed that this is the only solution, but merely that it i" a solution (and one that might be thought likely to prevail by analysts who are skeptical of the empirical importance of macroeconomic bubbles),

1 522

B.T. McCallu m

solutions while ignoring the existence of a non-bubble or fundamentals solution that would deliver an entirely traditional policy message. 79 • 80 The third strand of the monetary-fiscal interaction literature to be discussed is represented by papers by Alesina and Tabellini ( 1 987) and Debelle and Fischer ( 1 995) . 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 model. In this setting, Alesina and Tabellini derive outcomes pertaining to both discretionary and rule-like behavior by the CB 8 1 • 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 ( 1 995) have modified the Alesina­ Tabellini 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 inflation. It is not optimal, they find, for the CB's preferences to match those of society - i.e., 79 Dotsey ( ! 996) shows that a realistic specification of 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 authority's policy rule tends to prevent debt explosions. 80 One other feature of the recent fiscalis! literature is its contention that pegging the nominal interest rate at a low value will result in a correspondingly low inflation rate and in no indeterminacy problem, implying that such a policy would be preferable to the maintenance of a low growth rate of the (base) money supply. The analytical key 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 constant) 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 macroeconomic variables 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. 8 1 In the absence of debt, the FA has no incentive for dynamic inconsistency, i.e., no commitment problem. 8 2 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 tenns of both authorities' preferences; the private sector is assun1ed to care only about real wages.

Ch. 23:

Issues in the Design of Monetary Policy Rules

1 523

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 at th 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 under 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 of 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 Of course, i t i s m·gued above that the FA will not be able to dominate if the CB has independence (i.e., can choose its own base money creation rates).

g4

1 524

B. T McCallum

actual central bank objectives, but the absence of any reliable and agreed-upon method of measuring capacity or trend output creates a major drawback for this variable. Also, it is argued that the magnitude of 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 of an instrument variable, the chapter presents a small bit of evidence designed to illustrate why it is that a number of academic economists are inclined to prefer quantity instruments, such as the monetary base, rather than short-tenn 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 of 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 of 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 baPl ""' ""'

Table 1 Major exchange-rate-based inflation stabilization plans a Inflation rate b

Did the program end in crisis?

Begin and end date

Exchange-rate arrangement

Brazil 1 964

March 1 964August 1 968

Fixed exchange rate, with periodic devaluations

93 .6

1 8.9

May 1 968

No. In spite of switching to a regime of minidevaluations after the August 1 968 devaluation, inflation remained stable around 20% per year until 1 974.

Argentina 1 967

March 1 967May 1 970

Fixed exchange rate

26.4

5.7

Feb. 1 969

Yes. The initial 1 4% devaluation was followed by further devaluations and an 82% decline in reserves.

Uruguay 1 968 June 1 968December 1 97 1

Fixed exchange rate

1 82.9

9.5

June 1 969

Yes. The initial 48% devaluation was followed by successive devaluations and an 8 1 % decline i n reserves.

Chilean tablita

February 1 978June 1 982

Feb. 1 978-June 1 979: pre-announced crawling peg June 1 979-June 1 982: fixed exchange rate

52. 1

3.7

May 1 982

Yes. About 65% percent of reserves were lost and by February 1 983 the currency had depreciated by 55%.

Uruguayan tablita

October 1 978November 1 982

Pre-announced crawling

4 1 .2

1 1 .0

Nov. 1 982

Yes. By March 1 983 the central bank had lost 90% of its reserves and the peso had devalued by 70%.

Argentine tablita

December 1 978- Pre-announced crawling peg February 1 9 8 1

1 69.9

8 1 .6

Feb. 1 98 1

Yes. By April 1 982, the currency had depreciated by 4 1 0% and reserves fallen by 7 1 %.

Israel 1 985

July 1 985-present Exchange-rate policy had four stages d

445.4

7.8

Nov. 1 995

No. Inflation has continued to decline gradually.

Austral (Argentina)

June 1 985September 1 986

1 128.9

50.1

June 1 986

Yes. By September 1 987, reserves had fallen by 75% and monthly inflation was above 1 0 percent.

Program

Initial

June 1 985-March 1 986: fixed exchange rate March 1 986-Sept. 1 986: crawling peg

c

Lowest Date achieved

continued on next page

Q ;,..

g

c

c tl ;, "--

0 �

;;;:: �

�

"'

:"-

Table 1 , continued Program

Cruzado (Brazil)

Begin and end date

Exchange-rate arrangement

February 1 986November 1 986

Fixed exchange rate

Inflation rate b

Did the program end in crisis?

5;::,·

Initial c Lowest Date achieved 286.0

76.2

Nov. 1 986

Yes. By March 1 987, reserves had fallen by 58% and by December 1 987, monthly inflation had reached 2 1%.

Mexico 1 987 December 1 987- Feb. 1 988-Dec. 1 988: fixed exchange December 1 994 rate Jan. 1 989-Nov. 1 99 1 : preannounced crawling peg Nov. 1 99 1-Dec. 1 994: exchange-rate band

1 59.0

6.7

Sept. 1 994

Yes. Between February 1 994 and January 1 995, reserves fell by 85% and, following the December 1 994 devaluation, the peso depreciated by about 1 00 percent in four months.

Uruguay 1 990 December 1 990- Exchange-rate band with a declining rate present of devaluation

1 33.7

24.4

Dec. 1 996

No. Uruguay was not much affected by the Mexican crisis, and inflation has continued to decline gradually.

Convertibility April 1 991(Argentina) present

267.0

-0.3

May 1 996

No. As the Mexican crisis of December 1 994 spilled over, reserves fell by 52% between mid-1 994 and March 1 995, but the fixed parity was maintained.

e

a

Currency board with a one-to-one parity to the US dollar

>-.

%, .,

Source: Reinhart and Vegh ( 1 995b), based on data from International Financial Statistics (IMF) and case studies cited in the text. Unless otherwise noted, all pegs are against the US dollar. The fall in reserves is measured with respect to peak reserves during program. Data end in December 1 996. b Twelve-month inflation rate (in percent). c Twelve-month inflation rate in the month in which the program was implemented. d In July 1 985, the New Israeli Shekel was pegged to the US dollar; in August 1 986 the dollar peg was replaced by a peg to a basket of currencies. The second phase of the program consisted of a sequence of devaluations during 1 987 and 1 989. In January 1 989 a band with a fixed central parity was introduced. In December 1 9 9 1 a crawling band was introduced. The exchange-rate fixing followed some initial devaluations between December 1 5, 1 987 and February 29, 1 988.

� [5· ;::,

§

"'­ bo

� Q c:;· [;; ;:;· b �"'

.[ �·

g §

�·

c

�

u, .jo,. v,

1 546

G.A. Caluo and CA. Vegh

on these episodes, the literature has identified the following main empirical regularities associated with exchange-rate-based stabilization 1 2 : (i) Slow convergence of the inflation rate (measured by the CPI) to the rate of devaluation. In heterodox programs, inflation has typically fallen faster due to temporary price controls 1 3 . (ii) Initial increase in real activity -particularly, real GDP andprivate consumption ­ followed by a later contraction. It is less clear whether the same pattern applies to investment 1 4. (iii) Real appreciation of the domestic currency. (iv) Deterioration of the trade balance and current account balance. (v) Ambiguous impact response of domestic real interest rates. Ex-post domestic real interest rates have generally decreased in the initial stages of orthodox plans. However, they appear to have increased substantially in the early stages of the heterodox programs of the mid- 1 980s. To take a closer look at the main stylized facts, we constructed a panel of annual observations for four countries (Argentina, Chile, Israel, and Uruguay), which covers 1 6 years ( 1 978-1993), for a total of 64 observations 1 5 • The panel includes seven of the twelve exchange-rate-based stabilizations listed in Table 1 (the "tablitas" implemented in 1 978 in Argentina, Chile, and Uruguay, the Israeli 1 985 plan, the Argentine 1 985 Austral plan, the Uruguayan 1 990 plan, and the Argentine 1 99 1 Convertibility plan) and ten macroeconomic variables (devaluation rate, inflation rate, rates of growth of GDP, private consumption, durable goods consumption, fixed investment, and public consumption, all expressed in per capita terms, real exchange rate, current account deficit as a proportion of GDP, and real lending rate) 1 6 . 12 See Kiguel and Liviatan ( 1 992), Vegh ( 1992), Calvo and Vegh (1 994b), Reinhart and Vegh ( 1 994, 1 995b), and De Gregorio, Guidotti and Vegh ( 1 998). 1 3 Although less well-documented, casual empiricism suggests that wholesale price inflation (which captures the behavior of tradable goods inflation) converges quite rapidly. 14 Both Kiguel and Liviatan ( 1 992) and Reinhart and Vegh ( 1 995b) report mixed results for investment. Real estate boom-bust cycles also appear to be a hallmark of many of these programs; see Rebelo and Vegh (1 995) and Guerra ( 1 997b). Some spotty data also suggest that output in the non-tradable sector typically expands more rapidly than in the tradable sector [Rebelo and Vegh ( 1 995)]. 1 5 The numerous caveats that apply to the empirical exercises which follow are discussed at the end of the section. 16 The sample chosen was dictated by data availability. The sources of data are as follows. Data on GDP, private consumption, and durable goods consumption were provided by the Central Banks of Argentina, Israel, Uruguay, and the Chilean Ministry of Finance. For Argentina and Uruguay, durable goods consumption is proxied by car sales. Real exchange rate data for Israel were provided by the Bank of Israel. All other data are from International Finance Statistics (IMF). Fixed investment corresponds to gross fixed capital formation adjusted by the GDP deflator. (Ideally, we would have liked to have private fixed investment, but data are hard to come by.) The real exchange rate is a real effective exchange rate, as computed by the IMF, defined as a nominal effective exchange rate index adj usted for relative movements in national price or cost indicators of the home country and its main trading partners. Following common practice, the index is presented in such a way that an increase reflects

Ch. 24:

Inflation Stabilization and BOP Crises in Developing Countries

1 547

3.1 . 1. Stabilization time profiles As a first pass at the data and to illustrate the dynamic response of the different variables to the implementation of an exchange-rate-based stabilization program, we constructed profiles in "stabilization" time (as opposed to "calendar" time) 1 7 Stabilization time is denoted by T + j, where T is the year in which the stabilization program was implemented and j is the number of years preceding or following the year of stabilization (j = -2, . . . , 4) 1 8. We then computed the average value of each variable in stabilization time. The resulting stabilization time profiles, presented in Figures 1 and 2, thus portray the dynamic behavior of key macroeconomic variables for a "representative" exchange-rate-based stabilization plan. Vertical bars indicate the year before stabilization (time T - 1 ) and, where applicable, dashed lines denote the mean of the corresponding variable for the entire sample (i.e., for all 64 observations) . Panel A in Figure 1 illustrates the behavior of the rates of devaluation and inflation 1 9. The U-shaped profile for the rate o f devaluation (the nominal anchor) reflects the fact that, more often than not, policymakers either switch to a more flexible exchange-rate arrangement (often after a brief period with a fixed exchange rate) or abandon the program altogether. While inflation is highly responsive to the reduction in the rate of devaluation, it remains above the rate of devaluation and then lags it as the rate of devaluation increases. Panel B shows that the real exchange rate (set to 1 00 in the year before the stabilization) appreciates for three consecutive years (falling below 80 in year T + 2) before beginning to depreciate, following the higher rate of devaluation. The current account deteriorates up to year T + 3 - reaching a deficit of 4.8 percent of GDP - and then reverses course (Panel C). While the rate of growth of public consumption falls in the year of stabilization presumably reflecting an initial fiscal adjustment - it shows no systematic behavior

a real depreciation. Real interest rates were computed by deflating nominal rates by the same year's inflation rate. Population series from lntemational Finance Statistics (IMF) were used to compute per capita figures. 1 7 Fischer, Sahay and V egh ( 1 996) have used this approach to analyzing stabilization policies in transition economies. Sec also Easterly ( 1 996). 18 If the program began in the last quarter of a given year, the following year is taken as T. Thus, T is 1 978 for the Chilean tablita, 1 979 for the Argentine and the Uruguayan tablitas, 1 985 for the Austral and Israeli plans, and 1 99 1 for the Convertibility and the Uruguayan 1 990 plans. We should also note that we did not allow for any overlapping (i.e., any given year in calendar time corresponds to at most one point in stabilization time). Hence, in the case of Argentina, the first observation in stabilization time for the Austral plan is 1 984 (which corresponds to T I ) and the last one is 1 988 (T + 3). Finally, note that the number of observations for each year in stabilization time may differ, since some stabilizations episodes do not have observations for all years in stabilization time (i.e., from T - 2 through T + 4). For instance, there are 7 observations for T - 1 , T, and T + 1 , but only 4 for T + 4 and 3 for T - 2. 1 9 Since the mean is essentially the same ( 1 79.3 percent for the devaluation rate and 1 77.9 percent fm the inflation rate), the panel contains only one horizontal line. -

G.A. Calvo and CA. Vegh

1 548 A.

1000

\ \

500

� \ \ \

____ _ _

en

( e

er e

(index number, T-1 =100)

120

1 10

' ,,

____

inflation

_::, -----\ \

100 -

\

T-2

B. Real exchange rate

Inflation and devaluation

ar;_ ) p_ p_...:y rc __ __t;_ ----2000 -- --', ,r1500

T-1

T

\ \ \

----����J���t� _n_ _ _ _ ;-- -I o

//

/1

/

\...... ...... devaluation

T+1

T+2

90 80

T+3

T+4

70

T-2

GOP)

C. Current account ( percent of

T-1

T

T+1

T+2

T+4

T+3

D. Public consumption growth

..,.---...:.____:_...:.__;. . ..________��( percent per year)

-1 4

mean

-

-3

mean ---- --- --- - - - ------ ---- - - - --------

-2 -4

-4

-5 +---+-----.--.,----.-----r-----=:-l T-2

T-1

T

E.

T+1

T+2

T+3

Real lending rate

T+4

,

ent _ e_ (_ ea r)_______ rc_ � y;_ per� _;... ----...:.p 60 ,_--, 50

-6 +---1----,---,--____;:....__, T-2

T-1

T

T+1

T+2

T+4

T+3

F. Real deposit rate

10

r---�-----�(p�e��=•n;_t�pe=r�ye=a��-

5

40

mean

30 20

------ - - - - -- --- - - ----- - -- - --- - ----- - -

-5

mean

-10

10 0 +----+-��--�--�----.----4 T-2

T-1

T

T+1

T+2

T+3

T+4

-1 5 +----l---..----...--�---,---! T+4 T+3 T+2 T-2 T-1 T+1 T

Fig. 1 . Exchange-rate-based stabilization.

afterwards. Panels E and F show the behavior of domestic real interest rates 20 Real interest rates fall in the year the plan is implemented (with the real lending rate falling _

20

Some observations are missing for these two variables. The available sample consisted of 59 observations for the real lending rate and 57 observations for the real deposit rate. Note also the different scales used in Panels E and E

Ch. 24:

Inflation Stabilization and BOP Crises in Developing Countries A.

B.

Real GDP growth (percent per year)

12

1 549

Private consumption growth

�---,----�(p=e=�=en�t�pe=r�y=ea=r)�

·------�

4 ------

--

------- ----------

mean

-------------

4

mean

-2 -4

-4

-6 -1--+---,----.--..---.--J T-2 T-1 T T+3 T+4 T+2 T+1

-8:�:-:---+----.�--.----.---.----1 T+4 T-2 T-1 T T+1 T+2 T+3

C. Durables consumption growth

D. Fixed investment growth

e_ roo per�y_ ) -ar� m� __ �e_ (p 60�---�---� -

10 5

40 20

mean

en� ?_ e_ e y_ ea_ rc_ (p _ r) .. ... . --.-----" . r_

------

0

-

7

·--------------

_

----

�.., - -

20

-10

40 +. ----�---� ----4---��---r1---r T+4 T+3 T+ T+2 T T- 1 r2

-15-1---+---.--�--..---,--1 T+4 T+3 T+1 T+2 T-2 T-1 T

E.

Private consumption to GDP

---.:: (i n percent ) ________ -,----- _::�===�

75 74

F. Fixed investment to GDP

18.0

73

(in percent)

18.5

72

1 7. 5

71

1 7.0

mean

70 69. 68

mean

+----�----�---��+4 j�--��----r---�r T T 1 T+2 T-2 T+3 T-1 T

16.5 16.0 +---1---r-�--,..--· --r---1 T+4 T-2 T T-1 T+2 T+3 T+1

Fig. 2. GDP, consumption, and investment in exchange-rate-based stabilization.

for two consecutive years) and increase sharply afterwards. As indicated earlier, the accepted wisdom is that real interest rates have increased on impact in heterodox plans. This does not show up in annual data, suggesting that the initial rise in real interest

1 550

G.A. Calvo and C.A. Vegh

rates in heterodox plans has manifested itself basically as "spikes" immediately after the implementation of the plans 21 . Figure 2 presents the evidence related to the boom-recession cycle in the growth of per capita GDP, consumption, and fixed investment. Panel A shows that real GDP growth increases above the sample mean in the year of stabilization and peaks in T + 1 . In T + 2, growth is back to its mean and decreases sharply thereafter. The same pattern is observed for private consumption (Panel B) and durables consumption (Panel C). In orders of magnitude, however, the cycle in durables goods is much more pronounced than the one in private consumption, which is in turn more pronounced than the one in real GDP. At the peak, durable goods consumption is rising at 47.7 percent per year, private consumption at 8.9 percent, and real GDP at 4.7 percent. Fixed investment growth follows a similar pattern (Panel D). Finally, Panels E and F show the behavior of private consumption and fixed investment as a proportion of GDP. It can be seen that the boom in private consumption is also quantitatively important even relative to GDP. At its peak (in T + 1), the ratio of private consumption to GDP reaches 74.3 percent (compared to a mean of 68.8 percent). In contrast, Panel F shows that the ratio of fixed investment to GDP falls in T and surpasses its mean level only in T + 3 before falling precipitously. The stabilization time profiles thus point to the presence of a boom-recession cycle associated with exchange-rate-based stabilization. Although it is empirically difficult to distinguish a late recession in both successful and unsuccessful programs from the output collapse that typically accompanies the end of failed programs, Figures 1 and 2 are consistent with the idea that the late recession may take hold before the programs collapse. Notice that real activity (i.e., GDP and consumption in Figure 2, Panels A and B) slows down already at T + 2 and falls below the sample mean at T + 3 , which could reflect the effects of rising real interest rates (Figure 1 , panels E and F) and cumulative real exchange appreciation (Figure 1 , Panel B). The fact that this contraction is taking place while the current account deficit continues to grow (Figure 1 , Panel C) suggests that the contraction is not related to the real effects of an eventual collapse.

3. 1.2. Panel regressions By and large, the profiles in stabilization time presented in Figures 1 and 2 are consistent with the stylized facts that have been emphasized in the recent literature. However, while the raw data presented in this manner is clearly suggestive, these plots cannot answer the key questions of whether the boom-recession cycle in GDP, consumption, and investment has been significant in a statistical sense or whether it may have been caused by factors other than the exchange-rate-based stabilization 21

This idea is supported by the quarterly data presented in Vegh ( 1 992) and the evidence in Karninsky and Leiderman ( 1 998). These "spikes" are partly related to the sudden drop in inflation when wages and price controls are part of the stabilization package.

Ch. 24: Infla tion Stabilization and BOP Crises in Developing Countries

1 55 1

programs themselves. While a definite answer to these questions i s far from trivial and remains a challenge for future research - some simple econometric exercises may shed light on these important issues. Specifically - and following Reinhart and Vegh ( 1 994, 1 995b) - we ran panel regressions on dummy variables intended to capture the early and late stages of a program, and test whether growth in per capita GDP, consumption, and fixed investment during those periods was significantly different [rom trend growth 22 . We also test for the significance of the time pattern of public consumption 23 . The regressions control for common external shocks, as suggested by Echenique and Forteza ( 1 997) 24. The sample for the panel regressions remains the same as that used for the stabilization time profiles: four countries (Argentina, Chile, Israel, and Uruguay) with 1 6 observations each ( 1 978- 1 993) for a total of 64 observations. We define the "early" dummy as taking a value of one in the first three years of the programs 25 . If the program lasted less than three years (as was the case for the Argentine "tablita" and the Austral plan), then the "early" dummy takes a value of one in the first two years of the program. In all cases, the "late" dummy takes a value of one in the two years immediately following the "early" stage 26. Notice that the "late" dummy has been defined for all programs, regardless of whether they actually failed or not. While this makes the criterion more stringent (compared to defining the "late" dummy only for those programs that fail), it is more in accordance with the idea that the late recession takes place in both successful and unsuccessful programs. As control variables, we chose the Libor rate (adjusted by US inflation), average growth in OECD countries - both of which are intended to capture the world business cycle and terms of trade 27.

22

See also De Gregorio, Guidotti and Vegh ( 1 998), Gould ( 1 996), and Echenique and Forteza ( 1 997). 23 As will become clear in Section 5, this evidence is relevant for some theories that have emphasized the effects of fiscal policy in explaining the real effects of exchange rate-based stabilization. 24 Of course, one would like to control also for the effects of domestic reforms, which have accompanied several (although certainly not all) of these programs. To that effect, one could construct a "liberalization index" - which would take into account trade, financial, and structural reforms - along the lines of work by De Mclo, Denizer and Gelb ( 1 995) for transition economies. This remains an issue for future research. 25 The year in which the program was implemented is included as part of the "early" dummy if the program started in the first three quarters. Otherwise, the following year is taken as the first year of the "early" dummy. 26 Specifically, the years in which the "early" and "late" dummies take a value of one are the following: Argentine tablita, early = 1 for 1 979 and 1980, late = 1 for 1 98 1 and 1 982; Austral plan, early = 1 for 1985 and 1986, late = 1 for 1 987 and 1 988; Convertibility plan, early = I for 1 99 1 , 1 992, and 1 993; Chilean tablita, early = 1 for 1 978, 1 979, and 1 980, late = 1 for 1 98 1 and 1 982; Israel l 985, early = 1 for 1985, 1 986, and 1 987, late = 1 for 1 988 and 1 989; Uruguayan tab!ita, early = 1 for 1 979, 1980 and 1 98 1 , late = ! for 1 982 and 1 983; Uruguay 1 990, early = ] for 1 99 1 , 1 992, and 1 993. All data were obtained from the International Monetary Fund. Both Libor and OECD growth arc expressed in percentage terms. The terms of trade index measures the relative price of exports in terms of imports.

27

1 552

G.A. Calvo and C.A. Vegh

Table 2 Exchange-rate-based stabilization: Panel regressions " -

Dependent variables Growth in real GDP

(I)

Growth in real private consumption (2)

Growth in real durables consumption (3)

Growth in real fixed investment (4)

Growth in real public consumption (5)

1 4.74* (7.89)

0.80 (3.76)

-3 .78 (2.58)

-4.46 (4.62)

-5.42* (3. 19)

Early dummy

1 .84** (0.73)

3.33 * ( 1 .57)

Late dummy

-3.49*'* (0.82)

-4.60** (1 .93)

-29.61 *** ( 10.0 1 )

Libor (real)

-0.3 1 ** (0 . 14)

-0.68'* (0. 3 1 )

·-3.3 1 ( 1 .59)

-2. 8 1 *" (0.77)

-·1 . 1 8*'' (0.52)

OECD growth

0.71 *** (0.20)

-0. 2 1 (0.47)

1 .97 (2.44)

0.78 ( 1 . 1 5)

0.76 (0.78)

Terms of trade

-0.03 (0.02)

0.02 (0.03)

-0. 1 8 (0.20)

-0. 1 0 (0. 1 0)

0.04 (0.06)

64

64

64

64

64

No. of obs.

*

,;·

a All dependent variables are expressed in per capita terms. The sample includes Argentina, Chile, Israel, and Mexico for the period 1 978-1993. Standard errors are given in parentheses. The method of estimation was a 2-step GLS procedure which allows for groupwise and cross-group heteroscedasticity and groupwise autocorrelation. The regressions include fixed effects (not reported). Significance at the 1 0, 5, and 1 percent level is indicated by one, two, and three asterisks, respectively.

The summary results of the panel regressions are reported in Table 2. Let us first focus on the first three columns (GDP, private consumption, and durables consumption). The "early" and "late" dummies have the expected signs (positive for "early" and negative for "late") and are significant (at least at the 1 0 percent level) in all three cases. For example, column (2) indicates that growth in private consumption per capita is 3.33 percent higher (relative to trend growth) during the early stages of the program and 4.60 lower in the late stages. The size of the coefficients also tends to support the idea _:: suggested by Figure 2 that the boom-recession cycle is the most pronounced for durable goods and the least pronounced for GDP, with consumption falling somewhere in between. The initial rise in durable goods consumption is more than four times larger than the rise in private consumption, which is in turn almost twice as high as the rise in GDP per capita. Increases in Libor (in real terms) negatively affects all three variables (and are always si6rnificant). This result is consistent with the notion that fluctuations in international interest rates also play a key role in generating boom-bust cycles in developing countries [see, for example, Calvo, Leiderman and Reinhart ( 1 993)]. OECD growth matters only for GDP growth, while the effects of terms of trade are never significant. -

Ch. 24:

Inflation Stabilization and BOP Crises in Developing Countries

1553

In sharp contrast, the cycle in fixed investment is not statistically significant [Table 2, column (4)]. Changes in real world interest rates (i.e., real Libor) fully explain the cycles in fixed investment. In any event, this should perhaps not come as a big surprise since casual evidence for a majority of programs suggests that the main force behind the expansionary phase is the sharp increase in private consumption. It is also consistent with evidence from Bruno and Easterly ( 1 998) and Easterly ( 1 996), who find that growth following inflation crises is not driven by investment. Finally, column (5) in Table 2 indicates that the initial fall in public consumption is not statistically significant. We may thus conclude that the econometric evidence is consistent with the notion that exchange-rate-based stabilization leads to boom-recession cycles in real GDP, private consumption, and consumption of durable goods, even when account is taken of external factors. The evidence is inconclusive with regard to investment.

3. 1.3. Do exchange-rate-based stabilizations sow the seeds of their own destruction? A notable aspect of exchange-rate-based stabilization programs is that, as noted in Table 1 , a vast majority have ended in balance-of-payments crises. In fact, of all the major programs listed in Table 1 , the Argentine 1 99 1 Convertibility plan is so far the only successful plan which has maintained the exchange rate at the level chosen at the inception of the program 2 8 . Eight of the twelve plans ended in full-blown crises with large losses of international reserves. Naturally, the stabilization time profiles in Figures 1 and 2 appear to capture this pattern. In T + 4, the current account sharply reverses course (Figure 1 , Panel C), suggesting that a "crisis" has occurred 29 This "crisis" time coincides with a resumption of high inflation, a real exchange rate depreciation, and a collapse in GDP, consumption, and investment. As argued by Reinhart and Vegh ( 1 995b), the dynamics unleashed by exchange-rate based stabilization plans are likely to be partly responsible for the demise of several programs. Prolonged periods of real exchange-rate appreciation and growing current account deficits are seldom sustainable, especially when domestic and external shocks compound the problems. Corrective devaluations do not always work, particularly in a world of increasing financial globalization, as the example of Mexico in December 1 994 dramatically showed. These regimes are also prone to financial and speculative attacks which may be unrelated to problems of current account sustainability. The evidence thus suggests that understanding the links between the dynamics of exchange� rate-based stabilizations and the eventual collapse of most of these programs should 2k The israeli 1 995 plan was also a successful plan in terms of obtaining a lasting reduction in inflation. However, there were several devaluations along the way and finally an exchange rate band was adopted. 29 Kaminsky and Reinhart ( 1 995) show that BOP crises are associated with a sharp rise in exports . which should lead to a dramatic improvement in both the trade and current account balances.

G.A. Calvo and C.A. Vegh

1 554

be an integral part of the research agenda (an analysis of these issues is carried out in Section 7).

3.2.

Money-based stabilization: empirical regularities

Money-based programs in chronic inflation countries have been much less common than programs based on the exchange rate 30. Table 3 presents the main features of five major money-based programs undertaken in the last 25 years 3 1 . As the table makes clear, monetary regimes vary across episodes and pure money-based programs (i.e., a clean floating regime) are rare 32 . Hence, for the purposes of this chapter, the term "money-based" stabilization should be broadly understood as including assorted dirty floating regimes and dual exchange rate systems with a fixed commercial rate (or equivalent systems). The rationale for lumping these regimes together is that in all cases the monetary authority has, to a lesser or greater extent, control over the money supply. This is, of course, in contrast to an exchange-rate-based regime (under perfect capital mobility) in which the money supply is fully endogenous. As will be discussed in detail in Section 5, one should expect regimes in which the monetary authority has control over the money supply to deliver similar outcomes to those that would obtain under a pure money-based regime. Hence, to contrast stylized facts with theory, it makes sense to adopt such a classification. The following empirical regularities have been identified in money-based programs [see Calvo and Vegh ( 1 994b)] : (i) Slow convergence of infla tion to the rate of growth of the money supply. (ii) Real appreciation of the domestic currency. (iii) No clear-cut response of the trade balance and the current account. If anything, there seems to be a short-run improvement in the external accounts. (iv) Initial contraction in economic activity. A sharp, though short-lived, contraction in real GDP, consumption, and investment seems to follow the implementation of money-based programs. (v) initial increase in domestic real interest rates. These empirical regularities are less surprising in that they seem to broadly conform with available evidence for industrial countries. To illustrate some of these empirical regularities, we constructed a panel with five countries (Argentina, Brazil, Chile, 30 As discussed below, there are good reasons to expect the exchange rate to be the prefened anchor

in chronic inflation countries. 31 For case studies, see Harberger ( 1 982), Corbo ( 1 985), Edwards and Cox Edwards (1991), Medeiros ( 1994), Kiguel and Liviatan ( 1 996), and Favaro ( 1 996). 32 Note that, by definition, a pure money-based program implies a clean floating. The reverse, however, is not necessarily true: a clean floating might be adopted in conjunction with, say, interest rate or inflation targeting [see, for instance, Masson, Savastano and Sharma ( 1 997) and Vegh ( 1 997)]. These monetary regimes, however, have not been observed in any major stabilization effort in high inflation countries.

Table 3 Major money-based inflation stabilization plans Program

Begin and end date

�

"'

a

Monetary/exchange-rate policy Initial

Chile 1 975

April 1 975-December 1 977

Bonex (Argentina)

December 1 989-February 1991

Collor (Brazil)

Control of monetary aggregates was cornerstone. Exchange rate adjusted by past inflation d

c

Inflation rate b Lowest

Date achieved

394.3

63.4

Drastic cut in liquidity through forced rescheduling of domestic debt. Floating exchange rate

4923.3

287.3

Feb. 1 99 1

March 1 990-January 1 99 1

Sharp liquidity squeeze through freeze o f 70% of financial assets. Tight monetary policy. Exchange rate had a passive role and simply accommodated inflation

5747.3

1 1 19.5

Jan. 1991

Dominican Republic 1 990

August 1 990-present

Aug. 1990-Dec. 1 990: Exchange controls/black markets. Jan. 1 991-July 1 99 1 : dual exchange rates. July 1 99 1 : exchange market unification and floating.

60.0

2.5

Nov. 1 993

Peru 1 990

August 1 990-present

Control of monetary aggregates; dirty floating.

12 377.8

1 0.2

Sept. 1 995

a

Dec. 1 977

Sources: International Financial Statistics (IMF), Edwards and Cox Edwards (1991), Medeiros ( 1 994), Kiguel and Liviatan ( 1 996), and Favaro ( 1 996). Data end in December 1 996. b Twelve-month inflation rate (in percent). Twelve-month inflation rate in the month in which the program was implemented. d Significant measures toward lifting capital controls enacted only in June 1 979 [Edwards and Cox Edwards ( 1 99 1 )] .

c

: :::t. a ;:,

� §..

�

�· ;:, "

;:, :;:,_ i:l::J

S6

�B: ;;;·

� "'

.[ �6l :;:: ;,

S. B:

'-" '-" V>

1 556

G.A. Calvo and C.A. Vegh

A. Inflation a n d money growth a_:_ r) e..:. pe..:. -Ye_ r :_ t ::..: .:..n..:. rce 0) is the rate of time preference, and u(-), u(-) and z ( - ) are strictly increasing and strictly concave functions. The individual has a constant endowment flow of tradable goods, y T, while output of nontradables, y� , is demand-determined (i.e., in equilibrium, y� = c� for all t). The law of one price holds for the tradable good. The (constant) world real interest rate is denoted by r. (It will be assumed that there is no foreign inflation, so that r is also the world nominal interest rate.) Therefore, the individual's lifetime constraint is given by:

bo + mo +

roo (yT + er +

Jo

�N

Tt

)

exp( -rt) dt =

r= (c; + .��

Jo

et

)

+ itmt exp( rt) dt,

(4.2) where b0 denotes the individual's initial stock of net foreign assets, e1 denotes the real exchange rate (i.e., the relative price of tradable goods in terms of non-tradable goods), it is the nominal interest rate, and it are government lump-sum transfers. Given perfect capital mobility, the interest parity condition i1 = r + ft holds, where £1 is the rate of devaluation. 44 As will become clear below, the other assumptions in the present example make our key t esults

invariant with respect to the price deflator in the definition of real money balances.

1 564

G.A. Calvo and C.A. Vegh

To abstract from fiscal issues, we assume that the government returns back to the consumer all of its revenues. Hence, the government's lifetime budget constraint indicates that the present value of transfers must equal the initial stock of government­ held foreign assets (i.e., international reserves), denoted by R 0 , and revenues from money creation:

1= T1

exp(-rt) d t

=

Ro +

1= (m1

+ E1 m1 ) exp(--rt) dt.

(4. 3)

Combining (4.2) and (4.3), taking into account non-tradable goods market equilibrium, the interest parity condition, and the transversality condition lirn1 0 m1 exp(-rt) = 0, yields the economy's resource constraint _,

T

ko + J!__r

=

•

oc

/ c/ exp(-rt) dt,

fo k(= b + R)

(4.4)

where is the economy's net stock of foreign assets. Equation (4.4) thus constrains this small economy's lifetime consumption of tradable goods to be equal to tradable goods wealth. Maximization of lifetime utility (4 . 1 ) with respect to the budget constraint (4.2) yields the following first-order conditions 45 :

v'(c"{) = A, A N uI (c1 ) = - , et z' (m1 ) = Ait ,

(4.5 ) (4.6) (4.7)

where A is the time-invariant Lagrange multiplier. Equations (4.5) and (4.6) are the familiar conditions whereby, at an optimum, the household equates the marginal utility of consumption to the shadow value of wealth, A, times the relative price of the good (t:nity in the case of tradables and lie in the case of non-tradables). Similarly, at an optimum, the marginal utility of real money balances is set equal to the shadow value of wealth times the opportunity cost of holding real money balances, i [Equation (4.7)]. Equation (4.5) indicates that optimal consumption of tradable goods is constant along a perfect foresight path. From Equation (4.4), it then follows that cT = rk0 +y1, a constant, for all t ;? 0. Further, notice that unanticipated changes in the devaluation rate will not affect consumption of tradable goods. Consequently, from Equation (4.5),

the Lagrange multiplier, A, is invariant with respect to (unanticipated) changes in the rate ofdevaluation 46. This feature will greatly simplifY the ensuing analysis. Backward-looking indexation is introduced along the lines of Calvo and Vegh ( 1 994a). The horne goods sector operates under sticky prices (i.e., the nominal price 4 ·' As usual, we assume that {3 = r to eliminate inessential dynamics. 46 Of course, the multiplier is always invariant to anticipated changes.

Ch 24:

Inflation Stabilization and BOP Crises in Developing Countries

1 565

of home goods, pN , is a predetermined variable). Let the rate of inflation (of non­ tradables) be indicated by :rr . We assume that Jft = Wt +

8(ctN -y-N) '

e > o,

(4.8)

where jiN stands for full-employment output of non-tradables, and w is a predetermined variable which satisfies y > 0.

(4.9)

The variable w can be interpreted as the rate of growth of nominal wages. Hence, Equation (4.8) says that inflation of home goods is equal to the rate of growth of nominal wages plus excess aggregate demand 47 . In tum, equation (4.9) indicates that wage inflation increases (decreases) as price inflation (in terms of nontradables) exceeds (falls short of) wage inflation. This assumption is meant to capture backward­ looking wage indexation mechanisms, whereby the rate of growth of nominal wages is adjusted whenever the inflation rate exceeds the current level of wage growth. To illustrate the implications of this set-up, integrate backwards Equation (4. 9) and substitute the resulting expression for w1 into Equation (4.8) to obtain (4. 1 0) Equation (4. 1 0) shows that current inflation depends on a weighted average of past inflation rates - with inflation rates in the recent past receiving the greatest weight and current excess aggregate demand, which is what the notion of "inflation inertia" is usually taken to mean [see, for instance, Dornbusch and Simonsen ( 1 987)]. We will now study the implications of a once-and-for-all reduction in the rate of devaluation, which is the central exercise in Rodriguez ( 1 982). Given the invariance of the Lagrange multiplier with respect to changes in E1, it follows from first-order condition (4.6) that we can safely write c� as an increasing function of the real exchange rate, e1 ; that is, c� = ¢(e1), with ¢'(e1) > 0. Hence, by Equations (4.8) and (4.9), we have (4. 1 1 )

Furthermore, by definition, e1 = E1P 1*IP� , where E1 i s the nominal exchange rate (in units of domestic currency per unit of foreign currency, pT* is the (constant) foreign 47 Note that, in this specification, JI is not consumption of home goods does so).

a

predetermined variable (i.e., it could jump on 1mpact

1t

1 566

G.A. Calvo and C.A. Vegh (J)

··

ffi = O I I 7•A !

r L

'-------------::c-------··----·--------+ ess e

Fig. 4. Inflation inertia: dynamic system.

currency price of the tradable good and Pr is the price of home goods 48 . Using this definition and Equation (4.8), it follows that (4. 1 2) Equations (4. 1 1) and (4 . 1 2) constitute a system of differential equations in w1 and Since both w1 and e1 are predetermined variables, this ensures that under perfect foresight - and for a given set of parameters all equilibrium paths conyerge to the steady-state. Suppose that initially (i.e., for t < 0), the devaluation rate is expected to remain constant at the value eH . Hence, in the initial steady state (point A in Figure 4), :rr:,5 t:11 and ¢>(ess) _yN . At time 0, policymakers announce an unanticipated and permanent reduction in the devaluation rate from eH to eL. The new steady state is denoted by point B, where inflation of home goods is eL , while the real exchange rate remains unchanged. The dynamics of the adjustment to the new steady state are illustrated by the arrowed path in Figure 4. The time path of the main variables is illustrated in Figure 5 . Nominal wage growth falls monotonically over time (Panel B). The real exchange rate declines (appreciates)

e1 , which can be shown to be locally stable 49.

=

=

48 Note that the real exchange rate is a predetermined vanable because E is a policy variable and pN

is a

predetermined variable. 49 The trace of the matrix associated with the linear approximation around the steady stale is -e,,8rj/(e,J < 0 (where a subscript "ss" denotes steady-state values) and the determinant is ye,,8 ¢'(e,,) > 0, which implies that both roots have negative real parts. For expositional simplicity. roots wi 11 be assnmed to be real.

Ch. 24: Inflation Stabilization and BOP Crises in Developing Countries

mt

A. Rate of devaluation

1 567

B . Nominal wage growth

H E --L E 1

time

0

time

0

C. Real exchange rate

D. Consumption of home goods

\ --

0

-

time

t1

i

�

E. I nflation rate

1t

--

l

-

r

-

___

0

-

-

�

time

t1

-

F. Domestic real i nterest rate

d

H E L E

i

r

-

-

-

-

0

t1

time

�

-0

t1

-

-

-

-•

time

Fig. 5. Disinflation under inflation inertia.

in the early stages of the program, and then returns to its initial steady-state value (Panel C). Given that consumption of tradables remains constant, consumption of nontradables (Panel D) falls in the early stages (as its relative price, 1/e, increases) and increases later on. Hence, during the initial stages of the stabilization program, consumption of home goods (and thus output of home goods) falls - i.e., it does not rise in line with the stylized facts. At some point in time (denoted by t1 in Figure 5), inflation of home goods must fall below its long-run equilibrium value (Panel E) in order for the real exchange rate to return to its unchanged steady-state value. It is this protracted period of deflation needed to restore equilibrium relative prices which underlies the call for a step devaluation at some point during the adjustment

1 568

G.A. Calvo and CA. Vegh

program [see, for instance, Dornbusch and Werner ( 1 994)]. Indeed, in this model, a devaluation at time t 1 in Figure 5 (which corresponds to point C in Figure 4) would immediately take the economy to its new steady state, provided that workers also agreed to reduce the rate of nominal wage growth, w, to EL . It should be noticed that consumption of non-tradables falls in the early stages of the program in spite of the fact that the domestic real interest rate, rd(::= i JT), decreases on impact (Figure 5, Panel F). The reason is that, in utility-maximization models, the real interest rate determines the slope of the consumption path but not the level of consumption. Hence, the initial fall in rd implies that, as long as rd < r, consumption of non-tradable goods will follow a declining path. Calvo and Vegh ( 1 994a) extend this analysis to the case in which instantaneous utility is represented by a constant-elasticity-of-substitution utility function. They show that the results obtained in the context of Dornbusch-Rodriguez models hold true only if the intertemporal elasticity of substitution exceeds the elasticity of substitution between tradables and nontradables. In that case, consumption of both tradable and non-tradables goods increases on impact, which implies that the current account goes into deficit. The relative magnitude of these parameters is, of course, an empirical issue. Estimates provided by Ostry and Reinhart ( 1 992), however, cast some doubts on the relevance of backward-looking models since they show that, for a number of developing countries, the intertemporal elasticity of substitution is typically smaller than that between tradables and nontradables 50 . An important feature of Calvo and Vegh's ( 1 994a) formulation is that the stabilization does not bring about a wealth effect, in the sense that wealth in terms of tradable goods remains unchanged. This appears as the natural assumption to make when the purpose of the exercise is to isolate the effects of inflation inertia on the outcome of an exchange-rate-based stabilization. However, in a more general model with capital accumulation and endogenous labor supply, the wealth effect associated with a permanent reduction in the rate of devaluation will cause an increase in consumption of tradable goods and, given that the real exchange rate cannot change on impact, a corresponding increase in consumption of non-tradable goods [see Rebelo and Vegh ( 1 995), Figure 1 1 ] . Hence, wealth effects associated with supply-side effects (analyzed in more detail below) could help explain the initial boom under backward­ looking indexation even under the more plausible parameter configuration in which the intertemporal elasticity of substitution is smaller than the elasticity of substitution between tradables and non-tradables goods. �

50 The more common criticism of Rodriguez ( 1982) is the assumption of adaptive expectations an assumption that has fallen out of favor among the profession. This criticism is, however, misplaced since Rodriguez's ( 1 982) results still hold under rational expectations, as shown in Calvo and Vegh ( 1 994a) . In other words, the key assumption in Rodriguez ( 1 982) is not adaptive expectations but rather thal aggregate demand depends negatively on the real interest rate (provided, of course, that there is some other source of inflation inertia).

Ch. 24: Inflation Stabilization and BOP Crises in Developing Countries

1 569

4.2. Lack of credibility A common characteristic of stabilization plans is imperfect credibility. As pointed out in S ection 2, there are fundamental reasons for stabilization programs to be less than fully credible. Since stabilization is costly from a political point of view, why would anybody expect that, as a general rule, stabilization programs have no chance to fail? Implementing a program that succeeds in all states of nature is unlikely to be optimal from the policymaker's point of view. Suppose, for the sake of concreteness, that authorities announce a stabilization plan in which the exchange rate is set at a lower and constant level forever, but the private sector believes that the program may eventually be abandoned. To keep matters simple, let us further assume that everybody believes that the program will be abandoned at time T > 0 (where time 0 represents "today"), and the rate of devaluation will, once again, become high after time T (see Figure 6, Panel A). Assuming perfect capital mobility, the latter implies that the nominal interest rate will be low from time 0 to time T, and expected to be high afterwards 51 . Will this have real effects? The answer is negative in the money-in-the-utility-function framework used in subsection 4. 1 to illustrate the effects of backward-looking indexation. In that model, the nominal interest rate does not affect any goods-markets equilibrium condition. Thus, the real economy (under flexible prices) would be undisturbed by the monetary experiment. However, separability between money and goods in the utility function is a very special, and probably umealistic, assumption. It implies that the marginal utility of money is independent of expenditure, a condition that is likely not to hold if money is used for transactions 52 . Following Calvo ( 1 986), let us assume that transactions require holding cash in advance 53 . Thus, using the same notation as before, we postulate 54 T

m1 = a(c1

CN et

+ ...!_ ),

a > 0.

(4. 1 3)

The consumer's preferences are now given by:

r= [v(cl) + u(c� )l

.fo

exp(-/)t) dt.

( 4. 1 4)

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. 53 We adopt a cash-in-advance, fiexible-p1ices specification to illustrate the essential mechanisms behind lack-of-credibility in the simplest possible model. The same results would obtain under a money-in-the­ utility-function specification provided that the cross-derivative between conswnption and real money balances is positive [see Calvo (1 986)]. 54 For the derivation of the cash-in-advance constraint in continuous time, see Feenstra ( 1 985)

1 570

G.A. Calvo and C.A. Vegh

After substituting Equation (4. 1 3) into (4.2), we obtain a lifetime constraint that involves only c� and c'J as c�oice variables (and whose corresponding Lagrange multiplier will be denoted by A). Maximization of Equation (4. 1 4) subject to this lifetime budget constraint yields (4.1 5) (4. 1 6) The term involving the nominal interest rate i, J + 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 lie for the non-tradable good), the cost of the good is augmented by the opportunity cost of holding the needed real money balances. The ejj(xtive 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 yT and yN , respectively. Then, by Equations (4. 1 5) and (4. 1 6), and home goods-market equilibrium (i.e., c� = yN ), it follows that (4. 1 7) 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 e1 ) 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. 1 5), consumption of tradables will be high between 0 and T and low afterwards. Given that the present discounted value of cT 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 e1), as follows fi·om Equation (4. 1 7) (Panel D of Figure 6). .

Ch. 24:

Inflation Stabilization and BOP Crises in Developing Countries A. Rate of devaluation

H

£

£

CT

t

1571

B. Consumption of traded goods

r

I L i

_______.,.

____

T

0

time

T

0

C . Current account e

•

time

D. Real exchange rate

0

�---�

- ------·- ·

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 Vegh ( 1 993) 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 55 The real effects at time T will occur regardless of whether the program is actually abandoned or not, provided that if it is not abandoned, the program becomes fully credible at T. Formally, it can be shown that permanent changes in the rate of devaluation arc everywhere superneutral. 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 dynamic patterns for consumption. In particular, they show that in the absence of state-contingent assets, consumption rises on impact and continues to increase as long as the policy is in effect. See also Lahiri ( 1996a,b), Mendoza and Uribe (1 996), and Venegas-Martinez (1997). Further variations of the basic model include Obstfeld (1 985), who studies a gradual, tablita-type stabilization, and Talvi ( 1997), who analyzes the endogenous impact of higher consumption on fiscal revenues.

1572

G.A. Calvo and C.A. Vegh

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 of devaluation until the time at which the program is expected to be discontinued 5 7 . 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 of 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 of tradables constant and equal to rko + i', instead of setting a path displaying the boom-bust pattern shown in Panel B of Figure 6. Hence, even though consumption rises as a non­ credible 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 equilibrium is independent of permanent changes in the inflation rate). In contrast, in transaction­ costs 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) of temporarily lower inflation more than offset the intertemporal distortion caused by a non-constant path of the nominal interest rate [see Reinhart and Vegh ( 1 995a)] . 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 of credibility thus provides a rich framework to explain the main stylized facts observed in exchange-rate-based disinflations. The most common criticism of this type of model is that it relies critically on intertemporal consumption substitution, which is believed to be small or not significantly different from zero. Reinhart and Vcgh ( 1 995a) have examined the empirical relevance of the "temporariness" hypothesis, by estimating the intertemporal elasticity of 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 In this model, the domestic real interest rate falls on impact. As discussed in Section 3, however, 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 1 985 plan had an explicit target for bank credit, which was to be achieved by a combination of higher reserves requirements and a higher discount rate [Barkai ( 1 990)]. 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 Vegh ( 1 993)]. Agenor (1994) incorporates fiscal considerations into a model with imperfect capital mobility to address this issue. SH Within this framework, Ghezzi ( 1 996) 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 conunon occurrence in practice, as argued in Section 3). 57

Ch. 24: Inflation Stabilization and BOP Crises in Developing Countries

1573

(the three Southern Cone tablitas, the Argentine 1 985 Austral plan, the Brazilian 1 986 Cruzado plan, the Israeli 1 98 5 plan, and the Mexican 1 987 plan) and compare them to the actual increases. They conclude that, in spite of low (but statistically significant) elasticities of substitution ranging from 0 . 1 9 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 Southern­ Cone tablitas 59. If anything, however, the estimates provided by Reinhart and Vegh ( 1 995a) 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 ( 1 9 9 1 ) for Canada. Second, in addition to intertemporal consumption substitution, durable goods introduce the possibility of intertemporal price substitution because goods can be stored [Calvo ( 1 988)] .

5. Exchange-rate-based stabilization II: 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 Vegh ( 1 998) (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 lx misleading, as other factors - such as lower international interest rates - may account for part of the boom.

1 574

G.A. Calvo and CA. Vegh

time

Fig. 7. Conslllllption 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 60 . 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 of 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 of 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 of 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 of 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 of credibility 6 1 . 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 60 ln the absence of transaction costs and given that 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 picture, aggregate purchases of durabk goods would eventually return to the pattern prevailing before the plan was implemented.

Ch. 24:

Inflation Stabilization and BOP Crises in Developing Countries

1 575

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 ( 1 99 1 )] . 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 ( 1 998) 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 ( 1 998), 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 durable­ goods 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 I, say, has perfect access to international capital markets (like in the above examples), and type II 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. 62 See, for instance, Rojas-Suarez and Weisbrod ( 1 995) prevalent in developing than in developed countries.

who

show that domestic bank lending is more

1 576

G.A. Calvo and C.A. Vegh 60

50 en

c 40 Q)

_§

ro u; 30 c

ro Q)

a:: 20

10

time

Fig. 8. Real installments for various nominal interest rates (percent per y(!ar, r = 0.03).

Thus, abstracting from credibility and country-risk problems, and assLm1ing 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

-----

PI

(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. 1 7, 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 fiat. When i = 0. 50, real installments in the early periods are the highest. Naturally, changes in the inflation =

inflation Stabilization and BOP Crises in Developing Countries

Ch. 24:

1 577

(devaluation) rate do not affect the present discounted value of real installments as of time 0, which equals S. Formally, note that

1·oo 0

iS

--

exp(Et)

exp(-rt) dt

=

S,

so that changes in E affect real payments, but not the value of the integral. Therefore, a substantially lower rate of 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 of DGV ( 1 998), contributing to an eventual downturn in economic activity. Hence, this type of scenario should be quite successful in explaining several stylized facts. Existence of credit segmentation may also help to rationalize these phenomena even in the case in which there are no loan-contract constraints on type-11 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-I 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 1 970s 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 1 987 and Argentina's 1 99 1 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-Il individuals, because then comparative advantage stems from their better knowledge of the local market. rA Again, if some of the higher consumption falls on durable goods, a boom-bust pattern may emerge along the lines of DGV ( 1 998). Moreover, there is, in principle, no reason in this example for social welfare to be negatively affected by the rise in consumption.

1 578

G.A. Calvo and C.A.

Vegh

Rebelo ( 1 993), Roldos ( 1 995, 1 997), Uribe ( 1 997a), and Lahiri ( 1 996a, l 996b)] Gs . While the evidence presented in Section 3 casts some doubts on the general empirical relevance of the investment channel, supply-side effects may well have contributed to the initial boom in some instances and thus deserve attention 66 . The role of capital accumulation i n generating a steady rise i n the relative price o f non-tradables (i.e., a real exchange rate appreciation) is emphasized by Rebelo ( 1 993) in the Portuguese context. If reforms increase the economy's steady-state capital stock, then as the capital-labor ratio rises, the price of the capital-intensive good (the tradable good) falls. Roldos ( 1 995) and Uribe ( 1 997a) present models in which domestic money is needed to buy (or install) capital goods, in the spirit of Stockman ( 1 98 1 ) . As a result, inflation drives a wedge between the real return of foreign assets and that of 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 of 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 of non-traded goods (i.e., a real appreciation) and a trade account deficit. A somewhat unsatisfactory aspect of some of 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 of cash transactions. From a qualitative point of view, however, this assumption is not necessary for this type of model to generate the effects just described, as made clear by Lahiri ( 1 996a). In his model, the nominal interest rate introduces a distortion between consumption and leisure [as in Roldos ( 1 997)]. When inflation falls, labor supply increases. This, in turn, leads to a rise in the desired capital stock and, hence, in investment. Rebelo and Vegh ( 1 995), however, argue that the assumption that investment be in some way related to cash transactions is critical for the quantitative performance of a broad class of models 67. A more fundamental problem of supply-side based models is that, given that the driving force behind such models are wealth effects, they cannot explain the late (,o

lt should be noted that these programs were also accompanied by important structural reforms. As stressed in Section 3, it would be important - though far trom 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. 06 There is little systematic evidence on labor supply responses in exchange rate-based stabilization. For some evidence on Mexico and Argentina, see Roldos ( 1 995). 67 Similar results would obtain if money were used as a factor of production [sec Uribe ( 1 997b)]. Thi s 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 ( 1 995) and, in the context of stabilization policies, the discussion below on Edwards and Vegh (1 997)]. Bank-intermediated capital has been used to improve the quantitative predictions of some monetary models; see, for instance, Chari, Jones and Manuelli ( 1 995).

Ch . 24: Inflation Stabilization and BOP Crises in Developing Countries

1 579

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-in­ advance specification presented in Section 4. Consider a one-good economy in which the representative household maximizes

j·oo u(c},f!1)exp(-f3t)dt,

(5 . 1 )

()

where £1 denotes leisure, subject to the lifetime constraint (which already i ncorporates the cash-in-advance constraint m1 acf) 69 : =

b0 + mo + J/oo ( 1 - £1 + rt) o

exp(-rt) dt

=

1= ci (l + ait) o

First-order conditions imply that (assuming t3

Ucr(cJ, f!t ) Ucr(c'J, f!t ) ue(cJ, f!t)

--=--�-'----"----'

= =

=

exp(-rt) dt.

(5 .2)

r):

X ( l + ctit),

(5.3)

1 + ctit ,

(5 .4)

where X 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

-

k0 + /oc ( 1 £1 )

f

. o

exp(-rt) dt =

1= c} o

exp(-rt) dt.

(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., Uc1 eO 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 permanent increase in output =

68

Sec Rebelo and Vegh (1 995), Lahiri ( l 996a,b), Mendoza and Uribe ( 1 996), and Edwards and Vegh ( 1 997). 69 The function u( · ) is assmned to be shictly increasing 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 - f.

1 580

G.A. Calvo and C.A. Vegh

(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, ucrcO < 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 Vegh ( 1 997)]. 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 1 978 tab1ita and 1 985 Austral plan, and the Brazilian 1 986 Cruzado plan. In successful plans (like the Israeli 1 985 plan and the Argentine 1 99 1 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-rate­ based stabilizations. In Helpman and Razin ( 1 987), the reduction in the inflation tax generates a wealth effect due to the lack of Ricardian equivalence. In Drazen and Helpman ( 1 988), the wealth effect comes through the expectation of a future reduction in government spending. Rebelo ( 1 997) 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 0 . 'IO Sec also Giavazzi and Pagano ( 1990) and Bertola and Drazen ( 1 993), who analyze the possibly expansionary role of fiscal policy in the stabilizations of Denmark in 1 982 and Ireland in 1 987.

Ch. 24: inflation Stabilization and BOP Crises in Developing Countries

1581

Rebelo and Vegh ( 1 995) examine the effects of reductions i n 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 counterfactual 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. And the winner 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 Vegh ( 1 995) 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 effects 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 Vegh ( 1 995) 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 useful. 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 Vegh ( 1 995) 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. Vegh

1 582 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 7 1 . 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-specification 72 : ,

1o·= [

log(cJ ) + log(c� ) + log(m1 )] exp(-f3t) d t.

(6. 1 )

The household maximizes Equation ( 6. 1) subject t o (4.2). The first-order conditions imply that (again, assuming that f3 r) =

eN t

1

mt

=

et cJ,

(6.2)

=

Xit ,

(6.3)

where X is the Lagrangean multiplier associated with lifetime constraint (4.2). On the supply side, we follow Calvo 's ( 1 983) staggered-prices formulation a continuous-time version of the overlapping-contracts models a la Fischer (1 977) and Taylor ( 1 979, 1 980) - 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 through changes in the price level. 72 This model is a simplified version of Calvo and Vegh ( 1994c). See also Dornbusch (1 980) and Fischer ( 1986a, 1 988).

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1 5 83

variable at each instant in time), output of home goods is demand-determined, and the rate of change in inflation is a negative function of excess aggregate demand: � > 0.

(6.4)

Equation (6.4) can be derived by assuming that firms set prices in a non-synchronous manner taking into account the future path of aggregate demand and the average price level prevailing in the economy [see Calvo ( 1 983)]. 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 of firms that will change their price diminishes over time, which implies that inflation of 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 + E1 • Output of non-tradable goods is demand determined so that c� = y� 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, m1 (= M/E1PT*), is governed by an unstable differential equation. Note that (6.5) where !J-1(= M/Mt) 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 (6.6) Around the steady state, Equation ( 6.6) is an unstable differential equation 74. Hence, following an unanticipated and permanent reduction in IJ.�> m1 adjusts instantaneously to its higher steady-state value. Hence, from Equation (6.3), it and thus E1 also adjust instantaneously to their lower steady-state values. 73 Note that in this formulation, the price level of home goods (PN ) is sticky (i.e., it is a predermined variable) but the inflation rate of non-tradable goods (n:) 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 N otice that, as before, X is invariant to changes in �!1 .

1 584

G.A. Calvo and C.A. high t Jt l

it = O

I

n=o

L , � --

!-!

�----

..

L

n

-------

Fig. 9. Money-based stabilization: dynamic system.

Intuitively, if E1 fell on impact below f.l1 , then m1 would be increasing over time, which necessitates of a lower i (and lower E) to equilibrate the money market, which further increases m1, and so on. Thus, for m1 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 of home goods; that is, n 1 M/Pf. Then, =

(6.7) The second dynamic equation follows from Equation (6.4), taking into account Equation (6.2) and the fact that, from the definition of m1 and n t ? e1 = n/m1 : (6.8) Equations (6. 7) and ( 6.8) constitute a system of differential equations in n and n, for given cJ, m t , and the policy variable f.l1 • Around the steady state, the system is saddle­ path stable, as it should be since n is the only predetermined variable (Figure 9 depicts the corresponding phase diagram) 75 . 1" The determinant associated with the linear approxnnation around the steady state is -l:;n55ci,Im, which indicates that there is one positive and one negative root.


0. --·

1 594

G.A. Calvo and C.A. Vegh

R

.ilR I

I

0

T

•

T*

time

Fig. 1 1 . Krugman crisis.

multiplicity is not a key theme in Krugman ( 1 979), we will assume that the economy settles down on the lowest rate of devaluation consistent with Equation (7. 7), which will be indicated by £* . 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 demand for money collapses. This is a key feature of the model. Figure 1 1 depicts the central characteristics of an equilibrium path for international reserves assuming that the government runs a fiscal deficit (i.e., r rR0 > 0) and that the nominal exchange rate is a continuous function of 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, rR0 + yT) - L(r + E, rR0 + yT) = 11R. Since the exchange rate is assumed not to jump at time T , it follows that the government suffers a loss of reserves equal to iJR 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 right­ hand 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. If M1- > 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 M1- 0. Thus, if t > T , there will be an excess supply of money at t, which is inconsistent with equilibrium. Suppose now that t = T , and, -

=

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Inflation Stabilization and BOP Crises in Developing Countries

1 595

hence, the jump takes place exactly at switch point. Since M1- = 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: (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, NDA1 = 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 because, 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 monetary 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 8 9 . Of course, if bank credit is easily substitutable x9 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)].

G.A. Calvo and C.A. Vegh

1 596

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 ( 1 996) 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 and 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 sterilizatwn although inconsistent with fixed rates under the above assumptions could, however, be sustained under other set of plausible assumptions. F:ood, Garber and Kramer ( 1 996) and Kumhof ( 1 997) show that fixed-rates-cum­ sterilization is consistent with a situation in which government bonds are imperfect substitute with international bonds. Calvo ( 1 996b) 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 ( 1 979) model i s the possibility of the central bank actively defending the currency by raising short­ term interest rates. Sweden, for instance, raised short-term interest rates to around 500 percent per year in September 1 992 to stave off a speculative attack [see, for instance, Krugman ( 1 996)]. More recently, both Hong Kong and Brazil sharply raised interest rates to defend their currencies in the aftermath of the South East Asian currency crisi s. While not always successful, higher interest rates often buy time for

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Inflation Stabilization and BOP Crises in Developing Countries

1 597

the government to try to uphold the system's credibility by adopting more fundamental measures. Lahiri and Vegh ( 1 997) model interest rate policy by assuming that the government controls the interest rate on highly liquid government debt - along the lines of Calvo and Vegh ( 1 995) - and show that by announcing a policy of higher interest rates in the event of a crisis, the crisis may be postponed until international reserves actually reach zero (i.e., at a point like T* in Figure 1 1). 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 central 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 1 994 BOP cns1s 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 country as a whole 90. To illustrate, let us denote by f and CAD net international debt and current account deficit (both as a share of GDP), respectively. Then,

j; CAD, - rJJ;,

(7.9)

=

where rJ is the rate of growth of output. Sustainability analysis focuses on steady states. Thus, setting j; 0, the steady-state - sustainable - current account deficit satisfies =

(7 . l 0) 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 0), then the sustainable current account deficit the absence of growth (i.e., rJ is necessarily equal to zero. In contrast, with positive growth a sustainable current account deficit is possible. This analysis is unable to give us a definite answer on CADss until we pin down Iss . Recent experience shows that the capital market is reluctant to keep lending to LDCs exhibiting levels of indebtedness that exceed 80 percent of GDP [Williamson =

9° For an elaboration, see Milesi-Ferretti and Razin ( 1 996)"

1 598

G.A. Calvo and C.A. Vegh

( 1 993)] . Hence, this additional piece of information allows us to write the sustainability condition (7 . 1 0) as follows: CADss :(

0. 8rr

(7 . 1 1)

Thus, a country that can be expected to grow at 4 percent per year cannot sustainably run a current account deficit exceeding 3 .2 percent. Since 4 percent growth was, if anything, an upper bound for Mexico, this analysis would conclude that its 8 to 9 percent current account deficits were grossly unsustainable. Notice that CAD1 = r.ft - TS1 , where TS denotes the trade surplus (including non­ financial transfers) as a share of GDP, and rft denotes debt service (r is the international rate of interest). Therefore, by Equation (7 . 1 0), TSss =

(r

�-

TJ) .fss ·

(7. 1 2)

Thus, if we again set the growth rate to 4 percent (i.e., TJ = 0. 04) and, in addition, we assume the international interest rate to be 1 0 percent per annum (i.e., r = 0. 1 0), then, by Equation (7. 12), at the steady state the economy must run a trade balance surplus of 0.06.f.s as a share of GDP. The trade balance surplus increases with the steady-state debt/GDP ratio, .fs5 • In particular, at the upper bound forf�s (80 percent of GDP) the trade balance surplus would be 4.8 percent of GDP. Presumably, the reason for capital markets to be unwilling to extend credit to LDCs beyond 80 percent of GDP is that it may become tempting for those countries to renege on their debt obligations. Temptation, in turn, is likely to be related to the sacrifice associated with servicing the debt. Gross sacrifice of servicing the debt can be measured by the associated trade balance surplus. The previous computation suggests that the capital market becomes nervous about a country's willingness to repay when debt service represents only about 5 percent of GDP. Notice that the net sacrifice from servicing the debt could be much less once one takes into account international penalties from debt delinquency. Thus, one criticism of current account sustainability computations is that they are highly sensitive to the definition of sustainable debt/GDP ratios. Besides, the above example shows that the implied critical sacrifice levels are low when compared to other capital market transactions. For example, mortgages in the USA are easy for a household to get if total mortgage payments are less than 25 percent of the household's income. Thus, if this ratio were also relevant for countries' debt then, using the above parameters, the critical steady-state debt/GDP ratio would be 4.16 ( = 0.25/(r - TJ), where r - TJ = 0.06). Therefore, recalling Equation (7. 1 0), a country growing ai 4 percent per year could run a sustainable current account deficit of more than 1 6 percent of GDP! Of course, countries are not mere households because they are protected by sovereignty clauses. However, prior to the crisis Mexico had given very clear signals that it wanted to belong to the First World and signed treaties that would have made it very costly to engage in strategic repudiation of international debt (or any debt, for that matter).

Ch. 24: Inflation Stabilization and BOP Crises in Developing Countries

1 599

A more fundamental criticism is that steady-state computations could be very misleading for countries that are undergoing deep economic reforms. The current account deficit could in those instances be a temporary phenomenon associated with reform. Once we move away from the steady-state straightjacket, this approach has precious little to say. Finally, the current account approach does not address the BOP-crises issue as such. If the utility function is separable in money and consumption as in expression (7 . 1 ), the demand for money would be impervious to solvency issues. Thus, if we further assume that the government runs no fiscal deficit and there is no expansion in domestic credit, then the currency will never be under attack and a BOP crisis will never take place.

7.5. Financial considerations Financial factors are likely to play a key role in precipitating balance-of-payment crises. We now review several such factors, which we deem particularly relevant.

7. 5. 1. Volatility of monetary aggregates The Krugman model focuses on fiscal deficits as the key determinant of reserves losses. However, even in the absence of domestic credit expansion, international reserves in a fixed-exchange-rate regime may rise or fall as a consequence of fluctuations in the demand for money. This is not a minor consideration for LDCs since some of them exhibit substantially higher fluctuations in their demand for money than advanced industrial countries. To illustrate the significance of these considerations, let us examine the case in which the (log) demand for money follows a random walk and, to abstract from the effects highlighted in Krugman's model, let us assume that the demand for money is totally inelastic with respect to the nominal interest rate, and that there is fiscal balance. To simplify the exposition, we will continue making the assumption that domestic prices equal the nominal exchange rate, which is kept constant unless there is a BOP crisis. Letting m denote the demand for real monetary balances, then we postulate (in discrete time) that (7. 1 3) where m stands for real monetary balances and t 1 is an i.i.d. random variable. Under these circumstances, the demand for money can fall and create a BOP crisis even though there is no fiscal deficit. If L 1 exhibits a mean-zero normal distribution, then the larger its variance, the larger will be the probability of a BOP crisis given an initial level of international reserves. Estimates of Equation (7. 1 3) show Mexico, for instance, with a relatively high standard deviation (about 4 percent per month), while a country like Austria that has successfully pegged to the Deutsche Mark for about 1 5 years shows a standard deviation which is only about 1 percent per month [see Calvo ( 1 996a)] .

1 600

G.A. Calvo and C.A. Vegh

In addition, balance-of-payments problems could be exacerbated by external factors. For example, Calvo and Mendoza ( 1 996) show that there is a significant effect from US short-term interest rates on Mexico's demand for money (specifically, M2). This was reflected in a sizable fall in the demand for money during 1 994 and, we suspect, lay at the heart of the Mexican difficulties at the end of the year. Mexico and other Latin American countries experienced sizable capital inflows in the first half of the 1 990s. As argued by Calvo, Leiderman and Reinhart ( 1 993), about 5 0 percent of these flows stem from external factors, among which US interest rates hold a prominent role. Capital inflows gave rise to an expansion in consumption and investment which, in tum, increased monetary aggregates. Thus, the above-mentioned link between domestic monetary aggregates and external rates of interest may stem from direct opportunity-cost or indirect absorption-type considerations. Experience in several countries, and most notably in Mexico, suggests that the fluctuations in monetary aggregates provoked by external factors - and more specifically, by capital flows - could be substantial [see Calvo, Leiderman and Reinhart ( 1 996) and Calvo and Mendoza ( 1 996)] . An equation like (7. 1 3), enhanced by taking explicit account of external factors, would be needed to assess the implication of different reserve levels. To illustrate, consider the simple case in which external factors are fully captured by the random term in Equation (7. 1 3). We proceed as follows. Let v1 = m tfR1, where R stands for international reserves, and m is interpreted as the monetary base. Hence, a BOP crisis in period t + 1 will take place if m1 - m t+ 1 > R1• Or, equivalently, if

mt+l Vt - 1 log -- = t 1 1 1 < log -- . mr

Vr

(7. 14)

Clearly, the probability of a BOP crisis is an increasing function of v . Notice that this "vulnerability" index is totally independent of the popular index given by the ratio of reserves to one-month worth of imports. The latter hails back to periods in which reserves were held to ensure smooth trade, while the index developed here is associated with the probability of a BOP crisis as a result of financial fluctuations. In the above example there exists a direct connection between m and R because we assume m stands for base money (i.e., monetary liabilities of the central bank). If instead m stood for M2, the connection is more indirect and depends on how the central bank reacts to shocks in the larger monetary aggregates. If the central bank is not responsible for banking problems but defends the exchange rate parity by intervening and swapping base money for international reserves, then the same analysis developed above is applicable, except that one would need to derive the demand for base money from Equation (7. 1 3 ) - which would now apply to M2 - minimum reserve requirements, and an equation describing the demand for banks' excess liquidity. In turn, if the central bank is responsible for ensuring adequate banks' liquidity, then the central bank may be led to expand domestic credit whenever M2 falls. In the extreme case in which banks are fully insulated from any liquidity loss as a

Ch. 24:

Inflation Stabilization and BOP Crises in Developing Countries

1 60 1

consequence of a fall in M2, then M2 is equivalent to base money and the above example is fully applicable. It is worth noting, however, that in practice M2 is much larger than money base and, hence, the probability of a BOP crisis, given international reserves, is likely to be even higher (unless the volatility of M2 is substantially lower than that of base money). However, by providing liquidity to offset the fall in M2 the central bank does not prevent M2 from falling. Thus, if a central bank is keen on not letting monetary aggregates fall, then it will increase domestic credit even more and provoke a large loss of reserves after just a small contraction in monetary aggregates. This seems to have been the case in Mexico during 1 994. As noted above, Calvo and Mendoza ( 1 996) show that the demand for M2 fell in 1 994. Since banks held sizable domestic public debt in their portfolios, rolling back private debt could have been prevented simply by an open market operation that lowered domestic public debt in banks' portfolios by an amount equal to the fall in M2. However, the central bank went beyond that and prior to the crisis succeeded in stabilizing the level of M2. This meant a sizable expansion of banks' credit to the private sector (more than 40 percent from January to December 1 994). This is quite remarkable given that these measures were undertaken concurrently with a sizable loss of international reserves. This illustrates how much a central bank may be willing to risk in order to safeguard the financial system. Similar behavior was observed in Thailand and Malaysia during the more recent currency crises in South East Asia. 7. 5.2.

Short-maturity debt

As pointed out above, the BOP crisis literature has on the whole ignored the role of domestic debt, and followed Krugman ( 1 979) in assuming that fiscal deficits are fully monetized. However, the assumption that fiscal deficits are fully monetized is becoming increasingly unrealistic as governments have started to have access to international capital markets. It has thus become increasingly possible to finance fiscal deficits by floating domestic or international public debt. The maturity structure of this debt varies across countries but it is perhaps fair to say that emerging-markets' governments are likely to exhibit a debt maturity structure slanted towards the short end of the spectrum. Mexico again shows an extreme case in this respect: in December 1 994 about US$ 1 0 billion of domestic debt was due to mature in January, and about US$30 billion during 1 995 (these are large numbers compared to the US$6 billion stock of international reserves held by Mexico prior to the crisis). As argued in Calvo ( 1 998) the demand for emerging markets ' assets (including public debt) could be highly volatile for two basic reasons. In the first place, the effective rate of return on these assets depends on policy - like everywhere else but with the added complication that policy in emerging markets is itself highly volatile, reflecting imperfect knowledge of structural parameters and, most importantly, relatively unstable political equilibria. The instability of the latter has likely increased after the breakdown of communism. Therefore, assessing the "state of nature" in an

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emerging market could be quite costly. It is not enough to know the particulars of the investment project since, in general, its profitability will depend on government regulations. Thus, a project could be very lucrative and yet be unattractive to foreign investors if, for instance, profits are expected to be subject to high taxes (either directly or through the imposition of, for example, foreign exchange controls). Consequently, assessing the state of nature in a given emerging market is likely to entail large "fixed" costs. The second basic ingredient for high volatility of demand for emerging markets' assets is the so-called "globalization" phenomenon, which is characterized by the fact that investors diversify their portfolios across a large number of emerging markets. Portfolio diversification, in the absence of Tequila or contagion effects, helps to lower portfolio risk. Interestingly, however, the benefit from portfolio diversification does not depend on specific knowledge about the actual state of nature in these economies. For risk hedging, it is enough that the return on the different assets across countries not be perfectly correlated. Thus, for instance, by the law of large numbers, risk could become very low if the different investment projects were stochastically mutually independent. It is intuitive, and can be rigorously shown in a canonical example [Calvo ( 1 998)], that under the above circumstances (i.e., high information costs and globalization), (i) investors will be very sensitive to "news" about expected returns, and (ii) their incentives to learn about the state of nature in each emerging market will eventually decrease as the number of emerging markets rises. Consequently, in a globalized capital market, investment in emerging markets' assets is likely to be highly sensitive to rumors and relatively unresponsive to "fundamentals." The above-mentioned phenomenon poses no direct threat of a BOP crisis to the extent that it only involves fluctuations in stock market prices. However, if a large share of domestic debt is coming due in the short run, adverse changes in investors' sentiments about a given emerging market may cause a BOP crisis, particularly if the exchange rate is held fixed. The only available policy under those circumstances (short of devaluing) is to raise interest rates on newly-issued domestic debt. Unfortunately, since investors are ill-informed about fundamentals, the interest-rate hike could possibly be taken as a sign of weakness and not of strength, since they may feel that higher interest rates are due to the "market" being aware of serious difficulties. Furthermore, even if investors were better informed, the bonds-attack could lead to socially costly crises. As an illustration, consider a simple two-period example in which all public debt has one-period maturity and the international riskless interest rate is zero. We assume that debt can be repaid in full, independently of the repayment schedule. However, output is a function of the debt-repayment schedule. Suppose that the economy is controlled by a social planner and is subject to the standard intertemporal budget constraint. Under these circumstances, a social planner will choose the optimal debt-repayment schedule by maximizing the social utility function subject to the budget constraint. A social optimum is attained if the country can freely choose the share of total debt that will be repaid each period. However, if bond-holders insist on getting fully repaid

Ch. 24:

Inflation Stabilization and BOP Crises in Developing Countries

1 603

in the first period, we assume that the effort to comply with the financial obligation is so counterproductive that output next period would fall to zero. Thus, even though the country is able to fully repay its outstanding debt in period 1 , no rescheduling would now be possible because potential investors (rationally) expect output to be zero in period 2 . Thus, the existence of large short-term maturity debt may give rise to multiple equilibria, and make the country vulnerable to socially costly bond-attacks [see Calvo ( 1 998) and Cole and Kehoe ( 1 996)]. 7. 5. 3.

Domestic debt and credibility

In addition, the existence of domestic-currency denominated public debt can generate BOP difficulties if the exchange rate policy is not fully credible. Suppose the government announces a fixed exchange rate but the public believes that the currency will be devalued next period by E times 1 00 with probability p. Then, if investors are risk neutral (in terms of foreign currency) the nominal interest rate satisfies

1 + it

. l - p) = p + ( l + z,)(

--

1+£

1 + r,

(7. 1 5)

where i and r and are the domestic and international one-period interest rates, respectively. Clearly, if E and p are positive numbers, then the domestic interest rate will exceed the international one. This phenomenon is called the "peso problem" and is a common feature of exchange-rate-based stabilization programs. Suppose the government has a fixed debt level d and that, under full credibility (i.e., E = 0), the fiscal deficit is zero (i.e., T - rR, + rd = 0). Assuming, for simplicity, that fiscal deficits are fully monetized, it follows that, if there is an expectation of a devaluation (but the currency is not devalued), the discrete version of Equation (7.4) would be given by Rt+l

-

R,

=

-( T - rR1 + i, d),

with the fiscal deficit now being positive since i, > r due to the peso problem. Hence, the peso problem may put into motion Krugman's B OP-crisis machinery 9 1 . Thus, lack of credibility may result in an unsustainable balance of payments even though "fundamentals" could be fully in line with a sustainable situation. 7. 5. 4.

Credibility, the demand for money and fiscal deficits

Credibility problems may be reflected through other more subtle, but equally important, phenomena. As argued in Section 3, there is typically a consumption boom in the early stages of an exchange-rate-based stabilization. Therefore, the demand for money �1 A related scenario is discussed by Guidotti and Vegh ( 1 999). In their model, the Krugman machinery is put into motion by the probability of a devaluation associated with a fiscal consolidation.

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will contain a cyclical component associated with the stabilization program. Higher monetization at the start of the program may give the impression to policymakers that the program enjoys a high degree of credibility. An argument one commonly hears from policymakers is that higher monetization reflects the return of flight capital due to the higher confidence inspired by the stabilization plan. While this is partially true, policymakers may wrongly conclude that the higher stock of real monetary balances is a permanent positive shock. However, if monetization is provoked by the expectation that the program will be abandoned in the non-too-distant future, then the real stock of money will eventually collapse, possibly generating a BOP crisis. In a recent study, Talvi ( 1 997) shows that if tax revenue is an increasing function of consumption, then prior to crisis the fiscal deficit could shrink, giving the false impression that the fiscal house is in order. In an example, Talvi ( 1 997) shows that the fiscal deficit is nil before the crisis, only to explode afterwards. This pattern of the fiscal deficit is understandably quite confusing to the average policymaker. It is not unusual for the initial slackening of the fiscal constraint to be read as an indication that tax evasion has fallen and, hence, that the higher fiscal revenue has a significant permanent component. As a result, considerable political pressure is built up for more government spending. Unfortunately, if imperfect credibility is the key reason for the initial consumption boom and policymakers give in to pressures to increase government expenditure, then after-crisis fiscal deficits could reach dangerously high levels - which will become apparent only after a crisis erupts and policymakers have little room to manoeuver. 8. C oncluding remarks

We have concluded our long journey through the fascinating world of inflation stabilization and balance-of-payment crises in developing countries. After examining the possible rationale behind the existence of chronic inflation in many developing countries, we carried out some simple econometric exercises which support the existence of two main puzzles in the area of inflation stabilization. First, exchange­ rate-based stabilization leads to an initial boom in real GDP, private consumption, and durable goods consumption. The recession typically associated with disinflation ' programs appears only later in the programs. Second, money-based stabilization leads to an early recession, suggesting that the timing of the contraction depends on the nominal anchor which is used (the "recession-now-versus-recession-later" hypothesis). We did not, however, find support for the existence of an investment cycle in exchange­ rate-based stabilizations. Nor did we find evidence of a significant fall in public consumption around the time of stabilization. We then reviewed the main theories aimed at explaining these puzzles. We first focused on theories that emphasize expansions in demand: inflation inertia, lack of credibility (temporary policy), and durable goods. The first, inflation inertia, relies on a fall in real interest rates to generate the initial boom. However, within an optimizing

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1 605

framework and in the absence of any wealth effect, this theory would require some implausible parameter configurations to rationalize the initial boom. Also, it would have a hard time explaining the boom in programs in which real interest rates rise on impact. The second, lack of credibility, conforms quite well with the stylized facts. Quantitatively, however, it faces the problems of low intertemporal elasticities of substitution. The third, which relies on the timing of purchases of durable goods, may also reproduce the consumption cycle. Its quantitative relevance has not been evaluated yet. We then turned to explanations that rely on wealth effects. The first emphasizes supply-side responses - both in labor supply and investment - to the removal of the inflation distortion. While these theories can explain the boom, they cannot explain the late recession. In addition, the fact that the investment cycle was not found significant casts some doubts on the relevance of this mechanism. A second source of wealth effects - cuts in government spending - faces a similar problem. Quantitatively, however, supply-side effects appear to be a critical component of any story aimed at explaining the empirical regularities associated with exchange-rate­ based stabilization. To explain the stylized facts of money-based stabilization, we resorted to an optimizing version of traditional sticky-prices model a la Taylor-Fischer. A reduction in the rate of money growth decreases expected inflation and thus the nominal interest rate. This induces an incipient excess demand for real money balances. To restore money-market equilibrium, consumption (and thus output) of home goods needs to fall. This is effected through a real appreciation of the domestic currency. It is worth stressing that sticky prices are essential to this type of model. Without this feature, money-based stabilization would yield the same results as exchange-rate-based stabilization. Hence, a model designed to explain both the stylized facts of exchange­ rate-based and money-based stabilization - and, in particular, the recession-now­ versus-recession-later hypothesis - requires sticky prices and an interest-rate elastic money demand [see Calvo and Vegh ( 1 994c)]. Since most exchange-rate-based stabilizations end in full-blown balance-of-payment crises - typically accompanied by banking crises - we took a detailed look at both the mechanics and causes of balance-of-payments crises in the final leg of our journey (Section 7). While the starting point of this section was Krugman's ( 1 979) seminal paper on balance-of-payments crises, most of the issues touched upon have come to light after the December 1 994 Mexican crisis, and represent very much research in progress. It was argued that simple extensions of Krugman's ( 1 979) model may account for some missing links in the original story: (i) bond-financing may mask the fiscal problems by preventing reserve losses; (ii) imperfect substitutability between domestic and foreign assets opens the door for the central bank to sterilize the effects of reserve losses on money supply; and (iii) an active interest rate policy allows the central bank to postpone the abandonment of the peg and avoid a run in the final stages. We then analyzed the current account approach; that is, the view that large current account deficits may be unsustainable and lead to balance-of-payments crises. While

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this channel could provide a concrete link between the dynamics of exchange-rate­ based stabilizations and their demise, it still has precious little to say outside the steady state. In addition, the mechanics through which a BOP crisis would occur are unclear. Finally, we highlighted the role of financial considerations and credibility as contributing factors in unleashing balance-of-payments crises. Under high information costs and globalization, demand for emerging markets' assets is likely to be highly sensitive to rumors and relatively unresponsive to fundamentals. Changes in investors' sentiments could make it difficult for the government to roll-over a large stock of short­ term debt, leading to a bond-led attack. A large stock of short-term debt may also result in self-fulfilling crises. Lack of credibility in the peg - and thus high nominal interest rates - may also put into motion the Krugman-type machinery in the face of a large stock of domestic debt. Where do we go from here? l n the area of inflation stabilization, much work remains to be done on the empirical regularities of disinflation in chronic inflation countries. Numerous problems need to be addressed, including sample selection and small samples for money-based programs. Small samples for successful exchange­ rate-based programs also pose a problem since the econometric finding of a late recession is clearly influenced by events in failed programs. A critical aspect in econometric work is to control for other domestic factors, such as trade and structural reforms. Disentangling the effects of stabilization from other reforms is important not only to make sure that the empirical regularities remain such, but also because we may be asking theoretical models to explain "too much", quantitatively speaking. It would also be important to document in a systematic way the behavior of the home­ goods sector relative to the traded-goods sector. Some available evidence suggests that the initial boom is much more evident in the home-goods sector. The behavior of investment should also be looked at in more detail. The goal of this research agenda would be to establish how much needs to be explained and then build more refined quantitative models to evaluate the alternative hypotheses, along the lines of Rebelo and Vegh ( 1 995). It is clear that we are still far away from a good understanding of the links between the dynamics of exchange-rate-based stabilizations and their ultimate demise. While Krugman's ( 1 979) model and variations thereof provide a good description of the mechanics of BOP crises, they offer in general little insight into the more fundamental causes of such crises - over and above the obvious implication that a deterioration in the fiscal balance during a program will put into motion Krugman-type dynamics. We feel that the notion of current account sustainability needs substantial refinement before it can offer a consistent and complete account of the facts, but is an area definitely worth pursuing. In this respect, a productive area of research would be to focus on the role of the financial and banking sectors in amplifYing the expansionary cycle and possibly contributing to the downturn and eventual crisis. A particularly relevant channel has to do with the real estate market. A sizeable fraction of the lending boom goes to finance real-estate operations [see, for instance, Guerra ( 1 997a)]. These loans are usually made

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1 607

using as collateral temporarily high asset prices. In the context of the temporariness hypothesis, Guerra ( 1 997b) shows an example in which the fall in asset prices (i.e., land prices) before the abandonment of the program may trigger a banking crisis. While this does not explain the end of the program, it does provide a link between the dynamics of these programs and banking crises.

References

Adams, C., and D. Gros ( 1 986), "The consequences of real exchange rate rules for inflation: some illustrative examples", IMF Staff Papers 33 :439-476. Agenor, P.R. ( 1994), "The behavior of real interest rates in exchange rate-based stabilization programs", Working Paper 94/75 (International Monetary Fund). Agenor, P.R., and P. Montiel ( 1 996), Development Macroeconomics (Princeton University Press , Princeton, NJ). Aizenman, J. ( 1 987), "Inflation, tariffs, and tax enforcement costs", Journal of international Economic Integration 2 : 1 2-28. Aizenman, J. ( 1 992), "Competitive externalities and the optimal seigniorage segmentation", Journal of Money, Credit and Banking 24:6 1-7 1 . Alesina, A., and A . Drazen ( 1 99 1 ), "Why are stabilizations delayed?", American Economic Review 8 1 : 1 170-1 1 88. Ball, L. ( 1994), "What determines the sacrifice ratio?", in: N.G. Mankiw, ed., Monetary Policy (University of Chicago Press, Chicago, IL) 1 55-1 82. Barkai, H. ( 1 990), "The role of monetary policy in Israel's 1 985 stabilization effort", Working Paper 90/29 (International Monetary Fund). Bernanke, B.S., and M. Gertler ( 1 995), "Inside the black box: the credit channel of monetary policy transmission", Journal of Economic Perspectives 9:27-48. Bertola, G., and A. Drazen ( 1 993), "Trigger points and budget cuts: explaining the effects of fiscal austerity", American Economic Review 83 : 1 1-26. Bordo, M.D., and A.J. Schwatiz ( 1 996), "Why clashes between internal and external stability goals end in currency crises?", Open Economies Review 7:437-468. Bruno, M. ( 1 993), Crisis, Stabilization, and Economic Reform: Therapy by Consensus (Oxford University Press, Oxford). Bruno, M., and W. Easterly ( 1 998), "Inflation crises and long-run growth", Journal of Monetary Economics 4 1 :3-26. Bruno, M., and S. Fischer (1 986), "The inflationary process: shocks and accommodation", in: Y. Ben­ Porath, ed., The Israeli Economy: Maturing through Crises (Harvard University Press, Cambridge, MA) 347-3 7 1 . Bruno, M., and R . Melnick ( 1 994), "High inflation dynamics: integrating short-run accommodation and long-run steady-states", mimeograph (World Bank/Bank of Israel). Bufinan, G., and L. Leiderman (1 995), "Israel's stabilization: some important policy lessons", in: R. Dornbusch and S. Edwards, cds., Reform, Recovery, and Growth: Latin Ametica and the Middle East (University of Chicago Press, Chicago, IL) 177--2 1 5 . Cagan, P. ( 1 956), "The monetary dynamics of hyperinflation", in: M. Friedman, ed., Studies i n the Quantity Theory of Money (University of Chicago Press, Chicago, IL) 25- 1 1 7 . Calvo, G.A. ( 1 983), "Staggered prices i n a utility-maximizing framework", Journal o f Monetary Economics 12:383-98. Calvo, G.A. ( 1 986), "Temporary stabilization: predetermined exchange rates", Journal of Political Economy 94: 1 3 1 9-1329.

1 608

G.A. Calvo and C.A. Vegh

Calvo, G.A. ( 1987), "Balance of payments crises in a cash-in-advance economy", Journal of Money, Credit and Banking 1 9 : 1 9-32. Calvo, G.A. ( 1988), "Costly trade liberalizations: durable goods and capital mobility", IMP Staff Papers 35:46 1 -473. Calvo, G.A. (1 992), "Are high interest rates effective for stopping high inflation? Some skeptical notes", The World Bank Economic Review 6:55-69. Calvo, G.A. (1 996a), "Capital flows and macroeconomic management: Tequila lessons", International Journal of Finance and Economics 1 :207-223. Calvo, G.A. (1 996b), "On the resilience of money demand under duress: notes from the BOP crisis front", mimeograph (University of Maryland). Calvo, G.A. ( 1 998), "Varieties of capital market crises", in: G.A. Calvo and M. King, eds., The Debt Burden and its Consequences for Monetary Policy (Macmillan Press, London). Calvo, G.A., and A. Drazen ( 1 998), "Uncertain duration of reform: dynamic implications", Macroeconomic Dynamics 2:443-455. Calvo, G.A., and E. Mendoza (1 996), "Mexico's balance of payments crisis: a chronicle of a death foretold", Journal of International Economics 41 :235-264. Calvo, G.A., and C.A. Vegh ( 1 992), "Currency substitution in developing countries: an introduction", Revista de Analisis Economico 7 :3-27. Calvo, G.A., and C.A. Vegh ( 1 993), "Exchange rate-based stabilisation under imperfect credibility", in: H. Frisch and A. Worgotter, eds., Open-Economy Macroeconomics (MacMillan Press, London) 3-28. Calvo, G.A., and C.A. Vegh ( 1 994a), "Stabilization dynamics and backward-looking contracts", Journal of Development Economics 43:59-84. Calvo, G.A., and C.A. Vegh (1 994b), "Inflation stabilization and nominal anchors", Contemporary Economic Policy 1 2:35-45. Calvo, G.A., and C.A. Vegh (1 994c), "Credibility and the dynamics of stabilization policy: a basic framework", in: C.A. Sims, ed., Advances in Econometrics, vol. II (Cambridge University Press, Cambridge) 377-420. Calvo, G.A., and C.A. Vegh ( 1 995), "Fighting inflation with high interest rates: the small-open economy case under flexible prices", Journal of Money, Credit and Banking 27:49--66. Calvo, G.A., L. Leiderman and C.M. Reinhart (1 993), "Capital inflows and real exchange rate appreciation in Latin America: the role of external factors", TMF Staff Papers 40: 1 08-1 5 1 . Calvo, G.A., C.M. Reinhart and C.A. Vegh ( 1 995), "Targeting the real exchange rate: theory and evidence", Journal of Development Economics 47:97-133. Calvo, G.A., L. Leidern1an and C.M. Reinhart ( 1 996), "Inflows of capital to developing countries in the 1 990s", Journal of Economic Perspectives 1 0 : 1 23- 139. Canavese, A.J., and G. Di Tella ( 1 988), "Inflation stabilization or hyperinflation avoidance? The case of the Austral Plan in Argentina, 1 985-1987", in: M. Bruno, G. Di Tella, R. Dornbusch and S. Fischer, eds., Inflation Stabilization: The Experience of Israel, Argentina, Brazil, Bolivia, and Mexico (MIT Press, Cambridge, MA) 1 53-190. Cardoso, E. ( 1 99 1 ), "From inertia to megainflation: Brazil in the 1 980s", in: M. Bruno, S. Fischer, E . Helpman and N. Liviatan, eds., Lessons of Economic Stabilization and its Aftern1ath (MIT Press, Cambridge, MA) 143-186. Chadha, B., P Masson and G. Meredith (1 992), "Models of inflation and the costs of disinflation", IMF Staff Papers 39:395-43 1 . Chari, VV, L.E. Jones and R.E. Manuelli (1 995), "The growth effects of monetary policy", Quarterly Review, Federal Reserve Bank of Minneapolis (Fall): 1 8-32. Cole, I'LL., and T.J. Kehoe (1 996), "A self-fulfilling model of Mexico's 1 994-1995 debt crisis", Journal of International Economics 4 1 :309-330. Corbo, V (1 985), "Reforms and macroeconomic adjustments in Chile during 1 974-84", Wvrld Development 13 :893- 9 1 6.

Ch. 24:

Inflation Stabilization and BOP Crises in Developing Countries

1 609

Corbo, V, J. De Melo and J. Tybout (1 986), "What went wrong with the recent reforms in the Southern Cone?", Economic Development and Cultural Change 34:607-640. Correia, I., and P. Teles ( 1 996), "Is the Friedman rule optimal when money is an intermediate good?", Journal of Monetary Economics 38:223-244. De Gregorio, J., P.E. Guidotti and C.A. Vegh ( 1 998), "Inflation stabilization and the consumption of durable goods", Economic Journal 1 0 8 : 1 05-13 1 . De Melo, M., C . Denizer and A . Gelb ( 1995), "From plan to market: patterns of transition", mimeograph (World Bank). De Pablo, J.C. ( 1 974), "Relative prices, income distribution and stabilization plans: the Argentine experience, 1 967-1 970", Journal of Development Economics 1 : 1 67-189. Diaz-Aiejandro, C.F. ( 1 98 1), "Southern-Cone stabilization plans", in: W.R. Cline and S. Weintraub, eds., Economic Stabilization in Developing Countries (The Brookings Institution, Washington, DC) 1 1 9-141 . Dornbusch, R. (1 980), Open Economy Macroeconomics (Basic Books, New York). Dornbusch, R. ( 1 982), "Stabilization policies in developing countries: what have we learned?", World Development 1 0:701-708. Dornbusch, R. ( 1 995), "Progress report on Argentina", in: R. Dornbusch and S. Edwards, eds., Reform, Recovery, and Growth: Latin America and the Middle East (University of Chicago Press, Chicago, IL) 223-238. Dornbusch, R., and M.H. Simonsen ( 1987), Inflation stabilization with incomes policy supp01i: a review of recent experience in Argentina, Brazil, and Israel (Group of Thirty, New York). Dornbusch, R., and A. Werner ( 1 994), "Mexico: stabilization, refom1, and no growth", Brookings Papers on Economic Activity 1 994(1 ) :253-3 1 5. Dornbusch, R., F. Sturzenegger and H. Wolf ( 1 990), "Extreme inflation: dynamics and stabilization", Brookings Papers on Economic Activity 1 990(2): 1 -84. Dornbusch, R., I. Goldfajn and R. Valdes ( 1 995), "Currency crises and collapses", Brookings Papers on Economic Activity 1 995(2):253-3 1 5. Drazen, A., and V Grilli ( 1 993), "The benefits of crises for economic reforms", American Economic Review 83:598-607. Drazen, A., and E. Helpman ( 1 988), "Stabilization with exchange rate management under uncertainty", in: E. Helpman, A. Razin and E. Sadka, eds., Economic Effects of the Government Budget (MIT Press, Cambridge, MA) 3 1 0-327. Easterly, W. (1 996), "When is stabilization expansionary", Economic Policy 22:67-107. Easterly, W., and K. Schmidt-Hebbel (1 994), "Fiscal adjustment and macroeconomic performance: a synthesis", in: W. Easterly, C.A. Rodriguez and K.K. Schmidt-Hebbel, eds., Public Sectors Deficits and Macroeconomic Performance (Oxford University Press, Oxford) 1 5-78. Easterly, W., P. Mauro and K. Schmidt-Hebbel ( 1 995), "Money demand and seigniorage-maximizing inflation", Journal of Money, Credit and Banking 27:583-603 . Echenique, F., and A. Forteza ( 1997), "Are stabilization programs expansionary?", mimeograph (Berkeiey and Universidad de Ja Republica [Uruguay]). Edwards, S. (1 99 1 ), "Stabilization and liberalization policies in central and eastern Europe: lessons from Latin America", Working Paper No. 3 8 1 6 (NBER). Edwards, S., and A. Cox Edwards ( 1991), Monetarism and Liberalization: The Chilean Experiment (University of Chicago Press, Chicago, IL). Edwards, S., and G. Tabellini ( 1 99 1 ), "Explaining fiscal policies and inflation in developing countries", Journal of international Money and Finance 1 0 : S 1 6-S48. Edwards, S., and C.A. Vegh ( 1 997), "Banks and macroeconomic disturbances under predetermined exchange rates", Journal of Monetary Economics 40:239-278. Eichengreen, B., A.K. Rose and C. Wyplosz ( 1995), "Exchange market mayhem: the antecedents and aftermath of speculative attacks", Economic Policy 2 1 :249-3 1 2.

1610

G.A. Calvo and CA. Vegh

Eichengreen, B., A.K. Rose and C. Wyplosz ( 1 996), "Contagious currency crises", Working Paper No. 568 1 (NBER). Fauvel, Y, and L. Sampson ( 1 99 1 ), "Intertempora1 substitution and durable goods: an empirical analysis", Canadian Journal of Economics 24: 192-205. Favaro, E . ( 1 996), "Peru's stabilization under a floating exchange rate", mimeograph (World Bank). Feenstra, R. ( 1 985), "Anticipated devaluations, currency flight, and direct trade controls in a monetary economy", American Economic Review 75:386-401 . Fernandez, R . ( 1985), "The expectations management approach to stabilization in Argentina, 1 976-82", World Development 1 3:87 1-892. Finch, M.H.J. ( 1 979), "Stabilisation policy in Uruguay since the 1 950s", in: R. Thorp and L. Whitehead, eds., Inflation and Stabilisation in Latin America (Holmes and Meier Publishers, New York) 144-1 80. Fischer, S. ( 1 977), "Long-term contracts, rational expectations, and the optimal money supply rule", Journal of Political Economy 8 5 : 1 9 1-205. Fischer, S. ( l 986a), "Exchange rate versus money targets in disinflation", in: Indexing, Inflation and Economic policy (MIT Press, Cambridge, MA) 247-262. Fischer, S. (1986b), "Contracts, credibility, and disinflation", in: Indexing, Inflation and Economic Policy (MIT Press, Cambridge, MA) 221-245. Fischer, S. ( 1 988), "Real balances, the exchange rate, and indexation: real variables in disinflation", Quarterly Journal of Economics 53:27-49. Fischer, S., R. Sahay and C.A. Vegh (1 996), "Stabilization and growth in transition economies: the early experience", Journal of Economic Perspectives 1 0:45-66. Fischer, S., R. Sahay and C.A. Vegh ( 1 997), "Modern high inflation", mimeograph (International Monetary Flmd). Flood, R.P., and P.M. Garber ( 1 984), "Collapsing exchange rate regimes: some linear examples", Journal of International Economics 1 7: 1- 1 3 . Flood, R.P., P.M. Garber and C . Kramer ( 1 996), "Collapsing exchange rate regimes: another linear example", Journal of lnternational Economics 4 1 :223-234. Foxlcy, A. ( 1980), "Stabilization policies and stagflation: the cases of Brazil and Chile", World Development 8:887-9 1 2. Frankel, J.A., and A.K. Rose ( 1 996), "Currency crises in emerging markets: empirical indicators", Working Paper No. 5437 (NBER). Friedman, M. ( 1 969), "The optimum quantity of money", in: The Optimum Quantity of Money and other Essays (Aldine Publishing Company, Chicago, IL) 1-50. Garber, P.M. ( 1982), "Transition from inflation to p1ice stability", Carnegie-Rochester Conferences Series on Public Policy 1 6: 887-9 1 2. Ghezzi, P. ( 1 996), "Exchange rate-based stabilization: when to switch anchors?", mimeograph (University of California at Berkeley). Giavazzi, F., and M. Pagano ( 1 990), "Can severe fiscal contractions be expansionary? Tales of two small European countries", in: NBER Macroeconomics Annual (MIT Press, Cambridge, MA) 75-1 1 1 . Gordon, R.J. (1 982), "Why stopping inflation may be costly: evidence from fourteen historical episodes", in: R.E. Hall, ed., Inflation: Causes and Effects (University of Chicago Press, Chicago, IL) 1 1-40. Gould, D.M. ( 1 996), "Does the choice of nominal anchor matter?", Working Paper No. 961 1 (Federal Reserve Bank of Dallas). Guerra, A. ( 1 997a), "Residential real estate booms, financial deregulation and capital inflows: an international perspective", mimeograph (Banco de Mexico). Guerra, A. ( 1 997b), "Asset inflation and fmancial crisis: the temporariness hypothesis", mimeograph (Banco de Mexico). Guidotti, P.E., and C.A. Vegh ( 1 992), "Macroeconomic interdependence under capital controls: a two­ country model of dual exchange rates", Journal of International Economics 32:353-367. Guidotti, P.E., and C.A. Vegh ( 1 993), "The optimal inflation tax when money reduces h·ansactions costs: a reconsideration", Journal of Monetary Economics 3 1 : 1 89-205.

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Guidotti, P.E., and C.A. V egh ( 1 999), "Losing credibility: the stabilization blues", International Economic Review 40:23-5 1 . Hanson, J., and J. de Meio ( 1 985), "External shocks, financial reforms, and stabilization attempts in Uruguay during 1 974-1983", World Development 1 3 :9 1 7-939. Harberger, A. C. ( 1 98 1), "In step and out of step with the world inflation: a summary history of countries, 1 952-1976", in: M.J. Flanders and A. Razin, eds., Development in an Inflationary World (Academic Press, New York) 35-46. Harberger, A.C. ( 1982), "The Chilean economy in the 1 970s: crisis, stabilization, liberation, and reform", Carnegie-Rochester Conference Series on Public Policy 1 7 : 1 1 5- 1 52. Helpman, E., and A. Razin ( 1987), "Exchange rate management: intertemporal trade-offs", American Economic Review 77: 1 07-1 2 3 . Heymann, D . ( 199 1 ), "From sharp disinflation t o hyperinflation, twice: the Argentine experience", in: M. Bruno, S. Fischer, E. Helpman and N. Liviatan, eds., Lessons of Economic Stabilization and its Aftermath (MIT Press, Cambridge, MA) 1 03-130. Heymann, D., and A. Leijonhufvud ( 1 995), High Inflation (Clarendon Press, Oxford). Hirschman, A. ( 1 963), Journeys toward Progress: Studies of Economic Policy-making in Latin America (Harvard University Press, Cambridge, MA). Hoffinaister, A., and C.A. Vegh ( 1 996), "Disinflation and the recession-now-versus-recession-later hypothesis: evidence from Uruguay", IMF Staff Papers 43 :355-394. Jones, M., P. Sanguinetti and M. Tommasi (1 997), "Political and institutional determinants of fiscal outcomes in the Argentine provinces", mimeograph (Universidad de San Andres, Argentina). Kafka, A. ( 1 967), "The Brazilian stabilization program, 1 964--66", Journal of Political Economy, 75(Suppl.):596-634. Kaminsky, G.L., and L. Leiderman ( 1 998), "High real interest rates in the aftermath of disinflation: is it a lack of credibility", Journal of Development Economics 5 5 : 1 89-212. Kaminsky, G.L., and C.M. Reinhart ( 1 995), "The twin crises: the causes of banking and balance of payment problems", mimeograph (Board of Governors of the Federal Reserve System and University of Maryland). Keynes, J.M. ( 1 924), Monetary Reform (Harcourt and Brace, New York). Kigucl, M., and N. Liviatan ( 1 9 89), "The old and the new in heterodox stabilization programs", Working Paper WPS 323 (Country Economics Department, The World Bank). Kiguel, M., and N. Liviatan (1 992), "The business cycle associated with exchange rate based stabilization", The World Bank Economic Review 6:279-305. Kiguel, M., and N. Liviatan ( 1 996), "Stopping three big inflations: Argentina, Brazil, and Peru", in: R. Dornbusch and S. Edwards, eds., Reform, Recovery, and Growth: Latin America and the Middle East (University of Chicago Press, Chicago, IL) 369-408. Kimbrough, K.P. ( 1986), "The optimum quantity of money rule in the theory of public finance", Journal of Monetary Economics 1 8:277-284. Krugman, P. ( 1 979), "A model of balance-of-payment crisis", Journal of Money, Credit and Banking 1 1 :3 1 1-325. Krugman, P. ( 1 996), "Arc currency crises self-fulfilling?", in: NBER Macroeconomics Annual (MIT Press, Cambridge, MA) 345-378. Kumhof, M. ( 1 997), "Balance of payments crises: the role of short-term debt", mimeograph (University of Maryland). Kydland, F.E., and C.E. Zarazaga (1 997), "Is the business cycle of Argentina 'different'?", Economic Review, Federal Reserve Bank of Dallas, (Fourth quarter):21-36. Lahiri, A. (1996a), "Exchange rate based stabilization tmder real frictions: the role of endogenous labor supply", mimeograph (UCLA). Lahiri, A. ( 1 996b), "Disinflation programs under policy uncertainty: insights for exchange-rate based stabilization programs", mimeograph (UCLA). Lahiri, A. ( 1997), "Controlling capital flows: targeting stocks versus flows", mimeograph (UCLA)

1612

G.A. Calvo and C.A. Vegh

Lahiri, A., and C.A. Vegh ( 1997), "Krugman balance of payments crises: are they for real?", mimeograph (UCLA). Leiderman, L. ( 1 993), Inflation and Disinflation: The Israeli Experiment (University of Chicago Press, Chicago, IL). Lizondo, J.S. ( 1 99 1), "Real exchange rate targets, nominal exchange rate policies, and inflation", Revista de Amilisis Econ6mico 6:5-22. Lucas Jr, R.E. ( 1 990), "Liquidity and interest rates", Journal of Economic Theory 50:237-264. Masson, P.R., M.A. Savastano and S. Sharma ( 1 997), "The scope for inflation targeting in developing countries" Working Paper 97/130 (International Monetary Fund). Medeiros, C. (1 994), "A case of a monetary stabilization program: the Dominican Republic's economic program, 1 990-1993", mimeograph (International Monetary Fund). Meltzer, A.H. (1 994), "Book review: Heterodox policy and economic stabilization", Journal of Monetary Economics 34:581-600. Mendoza, E., and M. Uribe ( 1 996), "The syndrome of exchange rate-based stabilizations and the uncertain duration of currency pegs", International Finance Discussion Papers No. 548 (Board of Governors of the Federal Reserve System). Milesi-FetTetti, G.-M., and A. Razin ( 1 996), Current-Account Sustainability, Princeton Studies in International Finance No. 81. Modiano, E.M. (1 988), "The Cruzado first attempt: the Brazilian stabilization program of February 1 986", in: M. Bruno, G. Di Tella, R. Dornbusch and S. Fischer, eds., Inflation Stabilization: The Experience of israel, Argentina, Brazil, Bolivia, and Mexico (MIT Press, Cambridge, MA) 2 1 5-258. Mondino, G., F. Sturzenegger and M. Tommasi ( 1 996), "Recurrent high inflation and stabilization: a dynamic game", International Economic Review 37:981-996. Montiel, P., and J. Ostry ( 1 99 1 ), "Macroeconomic implications of real exchange rate targeting in developing countries", IMF Staff Papers 38:872-900. Obstfeld, M. (1 985), "The capital inflows problem revisited: a stylized model of Southern-Cone disinflation", Review of Economic Studies 52:605-625. Obstfeld, M. (1986a), "Capital controls, the dual exchange rate and devaluation", Journal of International Economics 20: 1-20. Obstfeld, M. ( 1 986b), "Speculative attack and the external constraint in a maximizing model of the balance of payments", Canadian Journal of Economics 1 9 : 1-22. Obstfeld, M. ( 1 995), "International currency experience: new lessons and lessons relearned", Brooking Papers on Economic Activity I : 1 1 9-220. Obstfeld, M., and K. Rogoff (1 995), "The mirage of fixed exchange rates", Journal of Economic Perspectives 9:73-96. Okun, A.M. ( 1 978), "Efficient disinflationary policies", American Economic Review, Papers and Proceedings 68:348-352. Ostry, J., and C.M. Reinhart ( 1 992), "Private saving and terms of trade shocks", lMF Staff Papers 39:495-5 17. Pazos, F. ( 1 972), Chronic Inflation in Latin America (Prager Publishers, New York). Phelps, E. S. (1 973 ), "Inflation in the theory of public finance", Swedish Journal ofEconomics 7 5:67-82. Ramos, J. ( 1 986), Neoconservative Economics in the Southern Cone of Latin America, 1 973-1983 (Johns Hopkins University Press, Baltimore, MD). Rebelo, S .T. ( 1 993), "Inflation in fixed exchange rate regimes: the recent Portuguese experience", in: F. Torres and F. Giavazzi, eds., Adjustment and Growth in the European Monetary Union (Cambridge University Press, Cambridge) 1 28-149. Rebelo, S.T. ( 1 997), "What happens when countries peg their exchange rates? (The real side of monetary reforms)", Working Paper No. 6 1 68 (NBER). Rebelo, S.T., and C.A. Vegh ( 1 995), "Real effects of exchange rate-based stabilization: an analysis of competing theories", in: B.S. Bernanke and J.J. Rotembcrg, eds., NBER Macroeconomics Annual (MIT Press, Cambridge, MA) 125-1 74.

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Reinhart, C.M., and C.A. Vegh ( 1994), "Inflation stabilization in chronic inflation countries", mimeograph (International Monetary Fund). Reinhart, C.M., and C.A. Vegh ( 1995a), "Nominal interest rates, consumption booms, and lack of credibility: a quantitative examination", Journal of Development Economics 46:357�378. Reinhart, C.M., and C.A. Vegh ( 1 995b), "Do exchange rate-based stabilizations carry the seeds of their own destruction?", mimeograph (International Monetary Fund). Rodriguez, C.A. (1 982), "The Argentine stabilization plan of December 20th", World Development 1 0:801�8 1 1 . Rojas-Suarez, L., and S.R. Weisbrod ( 1 995), "Financial fragilities in Latin America: the 1 980s and 1 990s", Occasional Paper No. 1 32 (International Monetary Fund). Roldos, J. ( 1995), "Supply-side effects of disinflation programs", IMF Staff Papers 42: 1 5 8 - 1 83. Roldos, J. ( 1997), "On gradual disinflation, the real exchange rate, and the current account", Journal of International Money and Finance 1 6:37�54. Sachs, .T., A. Tornell and A. Velasco ( 1 995), "The collapse of the Mexican peso: what have we learned?", Working Paper No. 5 142 (NBER). Sachs, J., A. Tornell and A. Velasco ( 1996), "Financial crises in emerging markets: the lessons fi·om 1 995", Working Paper No. 5576 (NBER). Sahay, R., and C.A. Vegh ( 1 996), "Inflation and stabilization in transition economies: an analytical interpretation of the evidence", Journal of Policy Reform 1 : 75�108. Sanguinetti, P. ( 1994), "Intergovernmental transfers and public sector expenditure: a game theoretic­ approach", Estudios de Economia (Universidad de Chile) 2 1 : 1 8 1�21 2 . Santaella, J., and A . Vela ( 1996), "The 1987 Mexican disinflation program: an exchange rate-based stabilization?", Working Paper 96/24 (International Monetary Fund). Sargent, T.J. (1 982), "The ends of four big inflations", in: R.E. Hall, ed., Inflation: Causes and Effects (University of Chicago Press, Chicago, IL) 4 1-97. Savastano, M.A. ( 1 996), "Dollarization in Latin America: recent evidence and policy issues", in: P. Mizen and E.J. Pentecost, eds., The Macroeconomics oflnternational Currencies: Theory, Policy and Evidence (Edward Elgar, London) 225-255. Stockman, A. ( 1 9 8 1 ), "Anticipated inflation and the capital stock in a cash-in-advance economy", Journal of Monetary Economics 8:387�393. Talvi, E. (I 995), "Fiscal policy and the business cycle associated with exchange rate-based stabilizations: evidence from Uruguay's 1 978 and 1 99 1 programs", Working Paper Series 3 1 3 (Inter-American Development Bank). Talvi, E. ( 1 997), "Exchange rate-based stabilization with endogenous fiscal response", Journal of Development Economics 54:59�75. Taylor, J.B. ( 1 979), "Staggered wage setting in a macro model", American Economic Review, Papers and Proceedings 69: 1 08� 1 1 3. Taylor, .T.B. ( 1 980), "Aggregate dynamics and staggered contracts", Journal of Political Economy 88: l - 23. Taylor, J.B. ( 1 983), "Union wage settlements during a disintlation", American Economic Review '/3: 9 8 1 �993. Tommasi, M., and A. Velasco ( 1 996), "Where are we in the political economy of reform?", Journal of Policy Reform 1 : 1 87�238. Tornell, A., and A. Velasco ( 1995), "Fixed versus flexible exchange rates: which provides more fiscal discipline?", Working Paper No. 5 1 08 (NBER). Uribe, M. ( 1994), "Comparing the welfare costs and the initial dynamics of alternative temporary stabilization policies", mimeograph (Board of Governors of the Federal Reserve System). Uribe, M. ( 1 995), "Real exchange rate targeting and macroeconomic instability", International Finance Discussion Papers No. 505 (Board of Governors of the Federal Reserve System). Uribe, M. ( 1 997a), "Exchange-rate-based inflation stabilization: the initial real effects of credible plans", Journal of Monetary Economics 39: 1 97--221 .

1614

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Uribe, M. ( 1 997b), "A note on the analytics of credible exchange rate-based disinflation when money facilitates firms' transactions", mimeograph (Board of Governors of the Federal Reserve System). Vegh, C.A. ( 1 989), "Government spending and inflationary finance: a public finance approach", IMF Staff Papers 36:657-677. Vegh, C.A. ( 1 992), "Stopping high inflation: an analytical overview", IMF Staff Papers 39:626-695. Vegh, C.A. ( 1 997), "Monetary policy, interest rate rules, and inflation targets", mimeograph (UCLA). Velasco, A. ( 1 993), "A model of endogenous fiscal deficits and delayed fiscal reforms", C.V. Starr Center Report 93-4 (New York University). Vcncgas-Martinez, F. ( 1 997), "Temporary stabilization: a stochastic analysis", mimeograph (CIDE, Mexico). Viana, L. ( 1990), "Uruguay's stabilization plan of 1 968", mimeograph (CERES, Uruguay). Wicker, E. ( 1 986), "Terminating hyperinflation in the dismembered Hapsburg monarchy", American Economic Review 76:350-364. Williamson, J. ( 1 993), "Issues posed by portfolio investment in developing countries", in: S. Claessens and S. Gooptu, eds., Portfolio Investment in Developing Countries, Discussion paper No. 228 (World Bank). Woodford, M. ( 1990), "The optimum quantity of money", in: B.F. Friedman and F.H. Hahn, eds., Handbook of Monetary Economics (North-Holland, Amsterdam) 1 067- 1 1 52. Zarazaga, C.E. ( 1 996), "Recurrent hyperinflations in a dynamic game with imperfect monitoring in the appropriation of seignorage", mimeograph (Federal Reserve Bank of Dallas).

Chapter 25

GOVERNMENT DEBT DOUGLAS

W

ELMENDORF'

Federal Reserve Board N. GREGORY MANKIW

Harvard University and NBER Contents

Abstract Keywords 1 . Introduction 2. The data 2 . 1 . Debt and deficits in the USA and other countries 2.2. Measurement issues 2.2. 1 . Adjusting for economic conditions 2.2.2. Assets and liabilities beyond the official debt 2.2.3. Capital budgeting 2.2.4. Generational accounting 2.3. Future fiscal policy

3 . The conventional view of debt 3 . 1 . How does debt affect the economy? 3 . 1 . 1 . The short run: increased demand for output 3 . 1 .2 . The long run: reduced national saving and its consequences 3 . 1 .3 . Other effects 3.2. How large is the long-run effect of debt on the economy? 3.2. 1 . The parable of the debt fairy 3.2.2. A closer look at the effect of debt on private savings 3 .2.3. A closer look at international capital flows 3.2.4. A closer look at the marginal product of capital 3.2.5. The deadweight loss of servicing the debt 3.2.6. Summary

4. Ricardian equivalence 4. 1 . The idea and its history 4. 1 . 1 . The essence of the Ricardian argument 4. 1 .2. A brief history of the Ricardian idea 4. 1 .3 . Why Ricardian equivalence is so important Handbook of Macroeconomics, Volume 1, Edited by J.B. Taylor and M. Woodford © 1999 Elsevier Science B. V All rights reserved 1615

1616 1616 1617 1617 1618 1 620 1 620 1 62 1 1 623 1 624 1 625 1 627 1 628 1 628 1 628 1 63 0 1 632 1 632 1 634 1 63 6 1 63 8 1 63 9 1 63 9 1 640 1 640 1 640 1 642 1 644

D. W Elmendorf and N.G. Mankiw

1616 4.2. The debate over Ricardian equivalence: theoretical issues 4.2. 1 . Intergenerational redistribution 4.2.2. Capital market imperfections 4.2.3. Permanent postponement of the tax burden 4.2.4. Distortionary taxes 4.2.5. Income uncertainty 4.2.6. Myopia 4.3. The debate over Ricardian equivalence: empirical issues 4.3 . I . Testing assumptions about household behavior

4.3.2. Testing the implications for consumption 4.3. 3 . Testing the implications for interest rates

4.3.4. Testing the implications for international variables

5 . Optimal debt policy 5. 1 . Fiscal policy over the business cycle 5.2. Fiscal policy and national saving 5.2 . 1 . Life-cycle saving 5.2.2. Intergencrational saving 5.3. Tax smoothing

6. Conclusion References

1 645 1 645 1 648 1 649 1 65 1 1 652 1 653 1 654 1 654 1 655 1 657 1 658 1 659 1 659 1 660 1 660 1 66 1 1 662 1 663 1 663

Abstract

This chapter surveys the literature on the macroeconomic effects of government debt. It begins by discussing the data on debt and deficits, including the historical time series, measurement issues, and projections of future fiscal policy. The chapter then presents the conventional theory of government debt, which emphasizes aggregate demand in the short run and crowding out in the long run. It next examines the theoretical and empirical debate over the theory of debt neutrality called Ricardian equivalence. Finally, the chapter considers various normative perspectives about how the government should use its ability to borrow.

Keywords

JEL classification:

E6, H6

Ch. 25:

Government Debt

1617

1 . Introduction

important economic issue facing policymakers during the last two decades of the twentieth century has been the effects of government debt. The reason is a simple one: the debt of the US federal government rose from 26% of GDP in 1 980 to 50% of GDP in 1 997. Many European countries exhibited a similar pattern during this period. In the past, such large increases in government debt occurred only during wars or depressions. Recently, however, policymakers have had no ready excuse. This episode raises a classic question: how does government debt affect the economy? That is the question that we take up in this paper. It will not surprise the reader to learn that macroeconomists are divided on the answer. Nonetheless, the debates over government debt are fascinating and useful to study. They are fascinating because they raise many fundamental questions about economic behavior. They are useful to study because learning the sources of disagreement can help an impartial observer reach a judgment of his own. Our survey of the effects of government debt is organized as follows. Section l considers some of the data on government debt. These data give some sense of the history of government debt in the USA and elsewhere. This section also discusses some recent projections for the beginning of the twenty-first century. Section 2 then examines the conventional view of the effects of government debt. We call this view "conventional" because it is held by most economists and almost all policymakers. According to this view, the issuance of government debt stimulates aggregate demand and economic growth in the short run but crowds out capital and reduces national income in the long run. Section 3 turns to an alternative view of government debt, called Ricardian equivalence. According to this view, the choice between debt and tax finance of government expenditure is irrelevant. This section discusses the basis of this idea, its history and importance, and the debate over its validity. Section 4 moves from positive to normative analysis. It considers various perspec­ tives on the question of how the government should use its ability to borrow. The discussion highlights the potential significance of cmmtercyclical fiscal policy, optimal national saving, and intertemporal tax smoothing. An

2. The data

In this section we present some basic facts about government debt and deficits in the USA and other countries. We give the official data, and then examine a number of issues regarding the appropriate measurement of fiscal policy. We conclude the section by considering projections of future fiscal policy in a number of countries .

D. W Elmendorfand N G. Mankiw

1618 Panel A

Debt as a Percentage of GNP 1791 - 1996

Percent 120

Panel B

Deficit as a Percentage of GNP 1791 - 1996

Percent 30

25

20

15

1790

1810

1830

1850

1870

1890

1910

1930

1 950

1970

1990

Fig. I .

2. 1 .

Debt and deficits in the USA and other countries

We begin with data from the USA. Panel A of Figure 1 shows US federal debt as a percentage of gross national product over the past 200 years 1 . It is common to exclude the debt of state and local govermnents, as we do, although for many purposes it is more appropriate to consider the consolidated debt of all levels of govermnent. Most 1 We take GNP data from Berry ( 1 978, Table ! B) for 1791 to ! 868, ti-orn Romer (1 989) for 1 869 to 1 928, and from the National Income and Product AccOtmts since 1 929. The end-of-year debt comes from Bureau of the Census ( 1 975, series Y493) for 1791 to 1 939, from Congressional Budget Office (CBO) ( 1 993, Table A-2) for 1 940 to 1 96 1 , and from CBO ( 1 997a, Table F-4) since 1 962. We splice the series multiplicatively at the break points and convert debt from fiscal-year to calendar-year form.

Ch. 25:

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1619

state governments hold positive net assets, because they are prohibited from running deficits in their operating budgets, and because the assets they accumulate to fund employee pensions exceed the debt they issue to finance capital proj ects. The figure shows federal debt "held by the public", which includes debt held by the Federal Reserve System but excludes debt held by other parts of the federal government, such as the Social Security trust fund. The primary cause of increases in the US debt-output ratio has been wars: the War of 1 8 1 2 , the Civil War, World War I, and World War II all produced noticeable upswings in federal indebtedness. The Great Depression and the 1 980s are the only two peacetime intervals when this ratio increased significantly. Between these sharp increases, the debt-output ratio has generally declined fairly steadily. An important factor behind the dramatic drop between 1 945 and 1 97 5 is that the growth rate of GNP exceeded the interest rate on government debt for most of that period. Under such circumstances, the government can collect taxes equal to only its non-interest spending, finance the interest payments on the outstanding debt by issuing more debt, and still watch its debt grow more slowly than the economy. This situation has potentially important implications for the effect of government debt, as we discuss later. Panel B of Figure 1 shows the US federal budget deficit as a share of GNP over the past 200 years 2 . These deficit numbers are for the so-called "unified budget", which includes both "on-budget" items like national defense and "off-budget" items like Social Security, thus capturing essentially all of the fiscal activities of the federal government. Once again, the effect of wars is quite apparent. The small deficits between 1 95 5 and 1 975 were consistent with a declining debt-output ratio for the reason just mentioned: although the debt was growing, output was growing faster. After 1 975, larger deficits and a less favorable relationship between the interest rate and the growth rate caused the debt-output ratio to rise. Government debt and deficits in other industrialized countries span a wide range, as shown in Table 1 . The first column presents general government net financial liabilities as a percentage of GOP. This measure differs in several respects from that shown in panel A of Figure 1 : it includes all levels of government, nets out financial assets where the data are available, and normalizes by GOP rather than GNP. Nevertheless, the US value for 1 996 matches the last point shown in the figure. The second and third columns show the budget surplus and primary budget surplus as percentages of GDP. The primary surplus equals taxes less all non-interest spending. The highest reported debt-income ratios are in Italy and Belgium; their high debt service payments induce substantial budget deficits despite primary budget surpluses. 2

The budget surplus comes from Bureau of the Census ( 1 975, series Y337) for 1791 to 1928, from Bureau of the Census ( 1975, series Y341 ) for 1 929 to 1 96 1 , and rrom Congressional Budget Office ( 1997a, Table F-4) since 1 962. We convert these numbers from a fiscal-year basis to a calendar-year basis. Note that the deficit does not equal the annual change in federal debt. Roughly speaking, the change in debt reflects the government's cash outlays and receipts, while the unified deficit involves a limited amount of capital budgeting. We return to this issue below.

D. W Elmendoif and N.G. Mankiw

1 620

Table 1 Debt and deficits in industrialized countries in 1 996, in percent of GOP

a

Net debt

Budget surplus

USA

49

-2

Japan

14

-4

-4

Germany

48

-4

-1

France

39

-4

-1

1 12

-7

3

Country

Italy

Primary budget surplus

United Kingdom

44

--4

-1

Canada

70

-2

4

Australia

29

-1

0

Austria

51

--4

0

Belgium

1 27

-3

5

Denmark

46

-2

Finland

-8

-3

Greece

n.a.

Iceland

37

-2

Ireland

n.a.

-- 1

3

Korea

-22

4

4

48

-2

2

New Zealand

n.a.

3

4

Norway

-28

6

7

Portugal

n.a.

-4

Spain

53

-5

Sweden

26

-4

-1

TOTAL of these cotmtries

45

-3

0

Netherlands

-

7

-1

4

a

Data are from OECD ( 1 997, pages A33 , A35, and A38) and include all levels of government. "n.a." denotes not available.

2.2. Measurement issues The official US data on federal govermnent debt and deficits obscure a number of interesting and important issues iP assessing fiscal policy. We now discuss some of these measurement issues.

2.2. 1. Adjusting for economic conditions Official data on debt and deficits are often adjusted to reflect three economic variables: the price level, interest rates, and the business cycle. The adjustment for the price level

Ch. 25:

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1621

occurs because the real value of the debt is, for many purposes, more important than the nominal value. For the level of the debt, the price-level adjustment is obvious: if D is the debt and P is the price level, then the real debt is DIP. For the deficit, however, the price-level adjustment is somewhat more subtle. It is natural to define the real deficit to be the change in the real value of the debt. In this case, the real deficit equals the nominal deficit (deflated by the price level) minus the inflation rate times the existing debt. That is, d(DIP)

dD/d t

dP/dt D

� - ---p - ---p -p· The inflation correction, which i s represented by the second term o n the right-hand side of this equation, can be large when inflation is high or the outstanding debt is large. Indeed, it can tum a nominal budget deficit into a real budget surplus. The second adjustment is for the level of interest rates. The adjustment arises because the market value of the debt may be more important than the par value. When interest rates rise, outstanding debt falls in value, and when interest rates fall, the opposite occurs; of course, a given rate change will cause debt with a longer maturity to be revalued more than shorter-term debt. The market value of US debt over time can be calculated using the data and procedures outlined in Seater ( 1 9 8 1 ), Butkiewicz ( 1 983), and Cox and Hirschhorn ( 1 983). The annual change in the market value can differ noticeably from the annual change in the par value, but the series follow the same broad trends. The third common adjustment to the budget deficit is for business cycle conditions. Because the deficit rises automatically when economic activity slows, and vice versa, the budget deficit in a given year may offer a misleading impression of underlying fiscal policy. The "standardized employment deficit" [Congressional Budget Office ( 1 997a)] eliminates the effects of the business cycle on the budget. This deficit is based on estimates of what spending and revenue would be if the economy were operating at normal levels of unemployment and capacity utilization. 2.2.2.

Assets and liabilities beyond the official debt

Debt held by the public is the largest explicit liability of the federal government, but it is not the only liability. Moreover, the federal government also holds significant assets. As emphasized by Eisner and Pieper ( 1 9 84) and Eisner ( 1 986), all of these assets and liabilities should be considered in any overall accounting of the government's financial situation. Unfortunately, it is quite difficult to assess the value of many government assets and liabilities. Some valuation problems are primarily technical. For example, a large share of the government's physical capital is defense-related, and many of these goods are not sold in (legal) markets. As another example, federal insurance of bank deposits may prove to be either very costly to the government or very inexpensive, and it is difficult to assess the probabilities of the alternative outcomes.

D. W Elmend01f and N G. Mankiw

1 622

Table 2 US federal government explicit assets and liabilities Category

a

Estimated value in 1 995 ($ billions)

Liabilities Debt held by the public (excluding the Federal Reserve)

3219

Federal pension liabilities

1513

Insurance liabilities Other

66 498

Assets Financial assets

576

Physical assets

1 737

Net liabilities

2983

a

Data are from Office of Management and Budget ( 1 996).

Other valuation problems are more conceptual. Do the future Social Security benefits specified by current law constitute a govemment liability in the same sense as explicit debt? The answer to this question depends at least partly on how the liability is perceived by households. If households believe that these benefits will be paid with the same probability that the explicit debt will be honored, then it may be sensible to count the present value of the benefits as government debt. In this specific case, the additional debt could be roughly three times the explicit debt, as Feldstein ( 1 996a) estimates the present value of Social Security benefits less taxes for current adults at roughly $ 1 1 trillion in 1 995. Similar questions arise for civil service and military retirement benefits, Medicare, and other entitlement programs. The important general point is that the appropriate measure of government indebtedness largely depends on people's behavior. As a result, deciding what measure of fiscal policy is best requires taking a stand on the correct model of economic behavior. Attempts to measure a range of explicit government assets and liabilities include the presentations of historical federal balance sheets by Eisner ( 1 986), Bohn ( 1 992), and Office of Management and Budget ( 1 996). OMB 's estimates for 1 995 are summarized in Table 2. The largest liabilities are debt held by the public (excluding the Federal Reserve) and expected pension liabilities for federal military and civilian employees. OMB also includes the expected cost of contingent liabilities that arise from loan guarantees and insurance programs. The federal government's financial assets include gold and loans owed to the government; its physical assets include both reproducible plant and equipment (about three-quarters of which relates to national defense) and non-reproducible capital such as land and mineral deposits. OMB does not include in these estimates the cost of future Social Security payments and other "continuing commitments", arguing that the appropriate way "to examine the balance between

Ch. 25:

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1 623

future Government obligations and resources is by projecting . . . total receipts and outlays" (p. 20). As it turns out, OMB estimates the government's assets to be worth roughly as much as its non-debt liabilities in 1 995, so net explicit liabilities are close to the value of debt. Indeed, net liabilities appear to have followed debt fairly closely in recent decades, despite sometimes significant differences in their annual changes. Debt increased by about $2.4 trillion between 1 97 5 and 1 995, while OMB estimates that liabilities rose about $2.6 trillion. Yet, these measures diverged sharply before 1 975. Bohn estimates that the net worth of the federal government was roughly the same share of GNP in 1 975 as in 1 947, as a dramatic decline in the debt share was offset by a drop in military assets and a rise in government employee pension obligations. 2.2.3.

Capital budgeting

One way to incorporate some government assets into the regular budget process is to create separate capital and operating budgets. In this way, current outlays would include not the acquisition of capital goods, but the depreciation of previously purchased capital. One effect of capital budgeting is that it would allow the government to spend money on capital assets without running an explicit deficit. Some observers view this situation as an inducement to profligate spending, particularly because it is difficult to decide exactly what constitutes capital, and many types of spending could acquire that label. For whatever reason, the US federal govermnent (unlike many state govermnents) does not rely on a capital budget as a central element of its budget process. Nevertheless, the principle of capital budgeting does affect budget numbers in two ways. First, the unified budget includes some specific kinds of capital budgeting. Since 1 992, for example, govermnent credit programs have been counted not in terms of their current outlays, but in terms of the present value of their expected future outlays. Thus, the deficit cost of a direct student loan is not the loan amount itself, but the net cost of providing the loan, taking into account the probability of default. Because the govermnent's cash outlays reflect the total amount of the loan, the increase in the debt exceeds the deficit. A similar pattern is repeated for some other fiscal activities where the budget amounts differ from the contemporaneous cash outlays or receipts 3 . Second, the federal budget as recorded in the National Income and Product Accounts does treat govermnent consumption and investment in physical capital differently 4 .

3 Formally, the change in debt equals the deficit less so-called "other means of financing". Much of this category consists of short-term differences between the deficit and borrowing needs, but some other means of financing (such as direct student loans) involve quite long-term divergences. 4 This treatment in the National Income and Product Accounts was introduced in 1 996. There are a number of other discrepancies between unified budget principles and NIPA budget principles. These include geographic differences, timing conventions, and some shifting of items between the revenue and expenditure sides of the budget.

D. W Elmendmj' and N G. Mankiw

1 624

Government consumption includes an estimate of the depreciation of government capital, and government purchases of new capital are tallied separately. The federal government's investment in physical capital is fairly modest, with gross investment less than 1 5% of consumption expenditures in 1 994.

2.2. 4.

Generational accounting

One prominent alternative to standard debt and deficit accounting is "generational accounting", proposed by Auerbach et al. ( 1 99 1 ) and Kotlikoff ( 1 992). These authors argue that the conventional deficit and explicit debt "simply reflect economically arbitrary labeling of government receipts and payments", so that the measured deficit "need bear no relationship to the underlying intergenerational stance of fiscal policy" ( p. 56). Generational accounts measure fiscal policy by its impact on different generations, not by the annual flows of spending and taxes. Generational accounts are constructed by extrapolating current policies through the lifetimes of all people currently alive, and calculating the net taxes they would pay under those policies. The net taxes of future generations are then set at a level which satisfies the government's intertemporal budget constraint. These calculations provide important information about how fiscal policy redistributes resources across generations. For example, most of the transfer from young to old during the postwar period occurred not in the 1 980s when measured deficits were high, but between the 1 95 0s and 1 970s when deficits were low but Social Security benefits were being enhanced. Nevertheless, generational accounts do suffer from some problems, as explored by Cutler ( 1 993) and Congressional Budget Office ( 1 995). One set of problems involves technical issues in constructing the accounts. For example, it is unclear what is the appropriate discount rate for future taxes, and different discount rates produce very different quantitative results. A second issue is whether the labelling of government receipts and payments truly is arbitrary. For instance, the methodology of generational accounting treats Social Security payments and interest payments on government debt as essentially equivalent. Yet it is surely easier for the government to reduce future Social Security benefits than to reduce future coupon payments on existing debt securities. The label "government debt" appears to have some true meaning. A final important problem springs from the fact that generational accounting is inextricably tied to a specific model of individual behavior. In particular, the methodology assumes that people are life-cycle consumers without a bequest motive, so that their behavior and well-being depend on their assessment of government policies over their entire lifetimes and only over their lifetimes. If individuals are liquidity-constrained or myopic, however, then their behavior and well-being may be more sensitive to current taxes than to the present value of the future taxes they expect to pay. Conversely, if individuals have altruistic bequest motives (a possibility we discuss extensively later), then their behavior and well-being will be sensitive to future

Ch. 25:

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1 625

taxes that will be paid by their descendants. In either case, generational accounts fail to provide a good gauge of fiscal policy for either positive or normative purposes. 2.3.

Future fiscal policy

Current patterns of taxes and spending are unsustainable in most indust1ialized countries over the next twenty-five years. The primary causes of this situation are the aging of their populations and the rising relative cost of medical care. Table 3 presents the elderly dependency ratio - defined as the population age 65 and over as a percentage of the population ages 20-64 for a number of countries. Between 1 990 and 2030, longer lifespans and continued low birthrates will sharply increase the ratio of retirees to working adults. The US population is projected to age less dramatically than the population of many other industrialized countries, but the increase in retirees per worker in the USA is still expected to exceed 50%. In most countries, health care has absorbed an increasing share of national income over the past several decades. The cost of producing most specific medical services may not have increased, but the cost of providing medical care that meets the social standard clearly has risen. Predicting future developments in this area is difficult, but most analysts expect the relative cost of medical care to continue to increase for some time. A large share of government outlays involves transfers from working adults to retirees or the financing of health care. (Of course, these categories overlap heavily.) Thus, the aging of the population and the increasing cost of health care will put a significant strain on government finances over the coming decades. Table 4 shows projections for the effect of population aging on various countries' budget surpluses and debts under the assumption that current tax and spending rules remain unchanged. The numbers show only the direct effect of aging, and ignore the problem of paying interest on the accumulating debt. The projections are highly uncertain as well . -

Table 3 Elderly dependency ratios " Country

1 990

2030

Japan

19

49

Gcm1any

24

54 43

France

23

Italy

24

52

United Kingdom

27

43

Canada

19

44

USA

21

36

a Data are from Congressional Budget Office ( l 997b)

.

1 626

D. W Elmendotj'and N. G. Mankiw

Table 4 Projected effect of population aging on fiscal conditions in industrialized countries, in percent of GDP ' Country

Primary budget surplus

Change in debt from 2000 to 2030

1 995

2030

USA

0.4

-3.8

44

Japan

-3.4

-8.7

1 90

Gem1any

-

0. 6

-6.6

45

France

- 1 .6

-4.5

62

3 .4

-5 9

1 09

-2.8

- 1 .4

27

1 .5

-1 .0

39

Italy United Kingdom Canada Australia

.

0.0

- 1 .4

37

Austria

-2.7

-7.7

171

Belgium

4.3

-0.5

42

Demnark Finland Iceland

2.0

-2.3

1 24

-4 .3

-8.8

213

-3.3

41

-

I I .

Ireland

1 .8

Netherlands

14

Norway Portugal

0.0

2

-

6 .0

1 42

3.2

-4. 7

135

0. 6

-

.

56 .

1 10

Spain

-1.1

-4.4

66

Sweden

-5. 1

-2.7

117

a Data are from Roseveare et al. (1 996) and refer only to the direct effect of population aging without incorporating the effect of higher interest payments on the larger outstanding debt. The primary budget surplus equals taxes less non-interest spending.

Nevertheless, they show a marked deterioration in the fiscal situation of almost every country. For the USA, Congressional Budget Office ( 1 997b) (CBO) has performed a careful analysis of the fiscal outlook. The analysis incorporates the need to pay interest on the accumulating debt, as well as the feedback between debt and the economy. Table 5 summarizes CBO 's results. Without economic feedbacks, government debt more than doubles as a share of output by 2030; including feedbacks, this share rises three-fold. A large part of this looming fiscal problem is the expected rise in future payments for Social Security and Medicare. Dealing with this long-term fiscal imbalance will likely be one of the most significant challenges facing policymakers during the next century.

Ch. 25:

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1 627

Table 5 CBO baseline projections for the US budget, in percent of GDP a Variable

1 995

2030

2050

Without economic feedbacks Primary deficit

-1

5

6

Interest payments

3

6

12

Total deficit

2

ll

18

50

1 25

267

·- I

5

n.a.

3

12

n.a.

Debt

With economic feedbacks Primary deficit Interest payments Total deficit Debt

2

17

n.a.

50

159

n.a.

a

Data are from Congressional Budget Office ( 1 997b) and assume that discretionary spending grows with the economy after 2007. "n.a." signifies that the values were too extreme to be reported by CBO.

3. The conventional view of debt

In this section we present what we believe to be the conventional view of the effects of government debt on the economy. We begin with a qualitative description of those effects, focusing on the impact of debt on saving and capital formation, and thereby on output and income, on factor prices and the distribution of income, and on the exchange rate and foreign transactions. We also review some other economic and non-economic consequences of government borrowing. Following our qualitative analysis, we try to quantify some of the long-run effects of debt in a very rough way. Although quantifying these effects precisely is an arduous task, we think it important to have some quantitative sense of what is at stake. Therefore, we present a ballpark estimate of the impact of debt, which is interesting in itself and also illuminates some of the critical assumptions underlying all quantitative analyses of government debt. Our analysis assumes that government spending on goods and services is not affected by debt policy. That is, we examine the effects of issuing a given amount of debt and reducing taxes temporarily by an equal amount. Because the government must satisfy an intertemporal budget constraint, and because debt cannot grow forever as a share of income, this temporary tax reduction will generally be accompanied by a future tax increase. For most of this section, we simply assume that the present value of that tax increase equals the current increase in debt. We defer more careful consideration of the budget constraint to the last part of the section, where we re-examine the effects of debt in a world with uncertainty. The analysis also assumes, except where stated otherwise, that monetary policy is unaffected by debt policy. By

1628

D. W Elmendorf and N G. Mankiw

excluding possible monetization of the debt, we can couch our discussion in real, rather than nominal, terms. 3. 1 .

How does debt affect the economy?

The government's debt policy has important influence over the economy both in the short run and in the long run. We begin by discussing the short-run effects of budget deficits. We then turn to the long-run effects, of which the most important is a reduction in national wealth. In particular, we explain both how deficits affect national saving and how the change in saving affects many aspects of the economy. We also consider several other long-run effects of government debt.

3. 1 . 1. The short run: increased demandfor output Suppose that the government creates a budget deficit by holding spending constant and reducing tax revenue. This policy raises households' current disposable income and, perhaps, their lifetime wealth as well. Conventional analysis presumes that the increases in income and wealth boost household spending on consumption goods and, thus, the aggregate demand for goods and services. How does this shift in aggregate demand affect the economy? According to conventional analysis, the economy is Keynesian in the short nm, so the increase in aggregate demand raises national income. That is, because of sticky wages, sticky prices, or temporary misperceptions, shifts in aggregate demand affect the utilization of the economy's factors of production. This Keynesian analysis provides a common justification for the policy of cutting taxes or increasing government spending (and thereby running budget deficits) when the economy is faced with a possible recession. Conventional analysis also posits, however, that the economy is classical in the long run . The sticky wages, sticky prices, or temporary misperceptions that make aggregate demand matter in the short run are less important in the long run. As a result, fiscal policy affects national income only by changing the supply ofthe factors of production. The mechanism through which this occurs is our next topic. 3. 1.2.

The long run: reduced national saving and its consequences

To understand the effect of government debt and deficits, it is crucial to keep in mind several national accounting identities. Let Y denote national income, C private consumption, S private saving, and T taxes less government transfer payments. The private sector's budget constraint implies that:

Y = C + S + T. National income also equals national output, which can be divided into four types of spending:

Y = C + i + G + NX,

Ch. 25:

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where I is domestic investment, G is government purchases of goods and services, and NX is net exports of goods and services. Combining these identities yields:

S + (T - G) = I + NX. This identity states that the sum of private and public saving must equal the sum of investment and net exports. The next important identity is that a nation's current account balance must equal the negative of its capital account balance. The current account balance is defined as net exports NX plus net investment income by domestic residents and net transfers; for the most part, we ignore these last two, smaller pieces. The negative of the capital account balance is called net foreign investment, or NFI, which is investment by domestic residents in other countries less domestic investment undertaken by foreign residents. Thus, the third identity is simply:

NX = NFI, so that international flows of goods and services must be matched by international flows of funds. Substituting this identity into the other two identities yields:

S + ( T - G) I + NFI. =

The left side of this equation shows national saving as the sum of private and public saving, and the right side shows the uses of these saved funds for investment at home and abroad. This identity can be viewed as describing the two sides in the market for loanable funds. Now suppose that the government holds spending constant and reduces tax revenue, thereby creating a budget deficit and decreasing public saving. This identity may continue to be satisfied in several complementary ways: private saving may rise, domestic investment may decline, and net foreign investment may decline. We consider each of these possibilities in turn. To start, an increase in private saving may ensue for a number of reasons that we discuss below. In fact, some economists have argued that private saving will rise exactly as much as public saving falls, and the next section of the paper examines this case at length. For now, we adopt the conventional view that private saving rises by less than public saving falls, so that national saving declines. In this case, total investment - at home and abroad - must decline as well. Reduced domestic investment over a period of time will result in a smaller domestic capital stock, which in turn implies lower output and income. With less capital available, the marginal product of capital will be higher, raising the interest rate and the return earned by each unit of capital. At the same time, labor productivity would be lower, thereby reducing the average real wage and total labor income. Reduced net foreign investment over a period of time means that domestic residents will own less capital abroad (or that foreign residents will own more domestic capital).

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D. W Elmendoif and N. G. Mankiw

In either case, the capital income of domestic residents will fall. Moreover, the decline in net foreign investment must be matched by a decline in net exports, which constitutes an increase in the trade deficit of goods and services. As this connection between the budget deficit and the trade deficit became better known in the USA during the 1 980s, it led to the popular term "twin deficits". Pushing the trade balance into deficit generally requires an appreciation of the currency, which makes domestically­ produced goods relatively more expensive than foreign-produced goods 5 . 3. 1 . 3.

Other effects

Although increasing aggregate demand in the short run and reducing the capital stock in the long run are probably the most important effects of government budget deficits, debt policy also affects the economy in various other ways. We describe several of these effects here. First, government debt can affect monetary policy. A country with a large debt is likely to face high interest rates, and the monetary authority may be pressured to try to reduce those rates through expansionary policy. This strategy may reduce interest rates in the short run, but in the long run will leave real interest rates roughly unchanged and inflation and nominal interest rates higher. In the USA, at least in recent years, monetary policy has apparently not responded to fiscal policy in this way. For example, the US debt-income ratio rose sharply during the 1 980s, and the US inflation rate declined sharply. Nevertheless, successive Chairmen of the Federal Reserve Board have warned of the possible link between the budget deficit and inflation 6. In extreme cases, a country with a large debt may have difficulty financing an ongoing deficit through additional borrowing and, as a result, will be tempted to raise revenue through seigniorage. If the fiscal authority can force the monetary authority to finance ongoing deficits with seigniorage, then, as Sargent and Wallace ( 1 98 1 ) argue, inflation i s ultimately a fiscal phenomenon rather than a monetary one 7 . This

5

For more complete analyses of the international effects of debt, see Frenkel and Razin ( 1 992, drs. 7, 8, 1 0 and 1 1) and Obstfeld and Rogoff ( l 996, ch. 3). 6 Paul Volcker told .Congress in 1 985 that "the aetna! and prospective size of the budget deficit . heightens skepticism about our ability to control the money supply and contain inflation" (p. I 0). Alan Greenspan said in 1 995 that he expected that "a substantial reduction iu the long-term prospective deficit of the United States will significantly lower very long-term inflation expectations vis-a-vis other countries" (p. 141). Woodford ( 1 995) proposes an alternative "fiscal theory of the price level", based on the effect of prices on the real value of government debt and thus on aggregate demand. Woodford considers an economy of infinitely-lived households, and hypothesizes an increase in goverrunent debt with no offsetting change in future taxes or spending. This policy makes households wealthier and increases aggregate demand. If aggregate supply is unchanged, both goods-market equilibrium and the government's budget constraint require that the price level increases enough to reduce real debt to its initial value. The mechanism is quite similar to the Pigou-Patinkin ( 1 965) real-balance effect, except that it allows for households that appear to be Ricardian, and it involves total government liabilities rather than just outside money. In

7

Ch. 25:

Government Debt

1 63 1

monetization of the debt i s the classic explanation for hyperinflation. For example, staggering budget deficits as a share of national income were the root cause of hyperinflations in 1 920s Germany and 1 980s Bolivia. As Sargent ( 1 983) explains, inflation can fall sharply in such a country when government borrowing is reduced and the central bank commits not to finance future deficits. Yet, this line of reasoning is not very important for most developed countries today, as seigniorage represents a very small share of total government revenue 8 . A second effect o f government debt is the deadweight loss o f the taxes needed to service that debt. The debt-service payments themselves are not a cost to a society as a whole, but, leaving aside any payments to foreigners, merely a transfer among members of the society. Yet effecting that transfer in a world without lump-sum taxes will create some distortion of individual behavior that generates a deadweight loss. Thus, a policy of reducing taxes and running a budget deficit means smaller deadweight losses as the debt is being accumulated but larger deadweight losses when the debt is being serviced with higher taxes. A third effect of government debt is to alter the political process that determines fiscal policy. Some economists have argued that the possibility of government borrowing reduces the discipline of the budget process. When additional government spending does not need to be matched by additional tax revenue, policymakers and the public will generally worry less about whether the additional spending is appropriate. This argument dates back at least to Wicksell ( 1 896), and has been echoed over the years by Musgrave ( 1 959), Buchanan and Wagner ( 1 977), and Feldstein ( 1 995) among others. Wicksell claimed that if the benefit of some type of government spending exceeded its cost, it should be possible to finance that spending in a way that would receive unanimous support from the voters; he concluded that the government should only undertake a course of spending and taxes that did receive nearly unanimous approval. In the case of deficit finance, Wicksell was concerned that "the interests [of future taxpayers] are not represented at all or are represented inadequately in the tax-approving assembly" ( p . 1 06). Musgrave noted that when budget balance is altered for stabilization purposes, "the function of taxes as an index of opportunity cost [of government spending] is impaired" (p. 522). Buchanan and Wagner asserted that a balanced-budget rule "will have the effect of bringing the real costs of public outlays to the awareness of decision makers; it will tend to dispel the illusory ' something for nothing' aspects of fiscal choice" ( p . 1 78). And Feldstein wrote that "only the 'hard budget constraint' of having to balance the budget" can force politicians to judge whether spending's "benefits really j ustify its costs" (p. 405). It is also possible that the existence of government debt reduces the fiscal flexibility of the government. If moderate levels of debt have only small negative effects, but contrast to the Sargent-Wallace analysis, Woodford's point does not depend on any particular response by the monetary authority to changes in fiscal policy. 8 For further analysis of the connections between fiscal policy and monetary policy, see Aiyagari and Gertler ( 1985), Leeper ( 1 991), McCallum ( 1984), and Sims ( 1 994).

D. W. Elmendorf and N.G. Mankiw

1 632

larger debts are perceived to be quite costly, then a country with a moderate debt will be constrained from responding to calls for greater spending or lower taxes. This constraint on future policymakers is, in fact, one of the explanations sometimes given for why governments choose to accumulate large debts. A fourth way in which government debt could affect the economy is by making it more vulnerable to a crisis of international confidence. The Economist (4/1195) noted that international investors have worried about high debt levels "since King Edward III of England defaulted on his debt to Italian bankers in 1 33 5" (p. 59). During the early 1 980s, the large US budget deficit induced a significant inflow of foreign capital and greatly increased the value of the dollar. Marris ( 1 985) argued that foreign investors would soon lose confidence in dollar-denominated assets, and the ensuing capital flight would sharply depreciate the dollar and produce severe macroeconomic problems in the USA. As Krugman ( 1 9 9 1 ) described, the dollar did indeed fall sharply in value in the late 1 980s, but the predicted "hard landing" for the US economy did not result. Krugman emphasized, however, that currency crises of this sort have occurred in countries with higher debt-output ratios, particularly when much of that debt is held by foreigners, as in many Latin American countries in the 1 980s. A fifth effect of government debt is the danger of diminished political independence or international leadership. As with the danger of a hard landing, this problem is more likely to arise when government borrowing is large relative to private saving and when the country experiences a large capital inflow from abroad. Friedman ( 1 988) asserted: "World power and influence have historically accrued to creditor countries. It is not coincidental that America emerged as a world power simultaneously with our transition from a debtor nation . . . to a creditor supplying investment capital to the rest of the world" (p. 1 3). 3.2.

How large is the long-run ejjixt of debt on the economy?

So far we have described the effects of government debt in qualitative terms. We now present rough quantitative estimates of some of these effects. We begin with an extremely simple calculation of the effect on national income of a reduced capital stock, and we then explore the sensitivity of our results to three key assumptions. Our ballpark estimate is, in fact, broadly consistent with the few other quantitative analyses in the literature. We also note the magnitude of the deadweight loss caused by the taxes needed to finance the debt service. We calibrate our calculations for the US economy, but the approach is applicable to other countries as well. 3.2. 1.

The parable of the debt fairy

As we have discussed, a primary effect of government debt is the crowding out of capital and the consequences that result from this crowding out. How large are these effects? To answer this question, consider the parable offered by Ball and Mankiw ( 1 995). Imagine that one night a debt fairy (a cousin of the celebrated tooth fairy)

Ch.

25:

Government Debt

1 633

were to travel around the economy and replace every government bond with a piece of capital of equivalent value. How different would the economy be the next morning when everyone woke up? It is straightforward to calculate the effect of this addition to the capital stock. If factors of production earn their marginal product, then the marginal product of capital equals the capital share of income (MPK x KIY) divided by the capital-output ratio (K/Y). In the USA between 1 960 and 1 994, the gross return to capital was roughly one­ third of income, and the capital-output ratio averaged a little over three 9. The implied marginal product of capital is about 9.5%. More precisely, this figure represents the gross marginal product; it shows how much an extra dollar of capital adds to gross output and income. If the country wants to maintain that dollar of capital, however, then it needs to do replacement investment to offset depreciation. Depreciation amounts to roughly 3 . 5% of capital, so the net marginal product of capital is about 6%. In other words, each dollar of capital raises gross national product by 9.5 cents and net national product by 6 cents. When the debt fairy magically reverses the effects of crowding out, the amount of capital increases by the amount of federal government debt, which in the USA is about one-half of gross output. Our estimates of the marginal product of capital imply that gross output would be increased by about 4.75%, and net output by about 3% 1 0 In 1 997, these increases amount to about $400 billion and $250 billion, respectively. The story of the debt fairy is appealing because it offers a simple way to calculate the effects of government debt on national income. But is this calculation realistic? The debt-fairy calculation implicitly makes three assumptions: ( 1) Deficits do not affect private saving, so debt crowds out other forms of private wealth one for one. (2) The economy is closed, so crowding out takes the form of a reduced capital stock. (3) The profit rate measures the marginal product of capital, so it can be used to gauge the effects of a change in the capital stock.

9 These data are drawn from the National Income and Product Accmmts of the Commerce Department's Bureau of Economic Analysis (BEA). Net capital income is the sum of corporate profits, rental income, net interest, and a share of proprietors' income (all with appropriate adjustments for inventory valuation and capital consumption). Gross capital income equals net income plus depreciation. We use national income plus depreciation as the measure of total output and income. The capital stock is BEA's net stock of fixed reproducible tangible wealth excluding consumer durables. Including the value of inventories and land in the measure of capital would depress the estimated return on capital. On the other hand, Feldstein et a!. ( 1983) note that "pre-tax" corporate profits in the national income accounts actually represent profits afier the payment of state and local property taxes; adding these taxes back into profits would raise the estimated rates of return. Finally, some authors measure the benefit of additional saving by the return to nonfinancial corporate capital. Because corporate capital is more heavily taxed than other capital, it cams a higher pre-tax return. Yet, there is no reason to assume that any addition to the capital stock would flow disproportionately to corporations. 10 The actual effect of adding this much capital would be somewhat smaller, because the marginal product would decline as the capital stock increased.

1 634

D. W Elmendorf and N G. Mankiw

Let us consider how relaxing each of these assumptions might alter the conclusion that current US government debt reduces US national income by about 3%. 3.2.2.

A closer look at the ejj(xt of debt on private savings

The debt fairy replaces each dollar of government debt with one dollar of capital. Is this dollar-for-dollar substitution appropriate? More concretely, if the US government had run sufficient surpluses during the past twenty years to reduce its debt to zero, would national wealth now be larger by the amount of the actual current debt? In actuality, an increased flow of government borrowing will affect the flow of private saving through several channels. First, private saving will rise because some households will save part of the tax reduction to consume later in life. Second, forward­ looking consumers will realize that the increasing debt will force higher future interest payments by the government and, thus, higher future taxes. Third, greater government borrowing will affect interest rates and wages, and these general-equilibrium effects in turn will affect private saving. Fourth, the government's debt policy may affect distortionary capital taxes, which in turn affect private saving. For all of these reasons, the size of the budget deficit affects the amount of private saving. Understanding the long-run effect of debt on capital therefore requires a formal, general equilibrium model, with particular attention paid to household saving behavior. Conventional analysis focuses on models with overlapping generations of life-cycle consumers introduced by Samuelson ( 1 958) and Diamond ( 1 965). Because this model incorporates people at different stages of their life-cycle who differ in both their level of wealth and marginal propensity to consume out of wealth, aggregation is often difficult in realistic models with more than two generations. Blanchard ( 1 985) resolves this problem by making assumptions about the aging process that simplify aggregation analytically. Auerbach and Kotlikoff ( 1 987) and other researchers resolve this problem by simulating a more complicated model numerically. Before turning to the results from these well-known analyses, however, it is instructive to examine a simple, stylized example. Consider an economy in which every person lives for a fixed number of periods. Assume that the interest rate is given (either because this is a small open economy or because the technology is linear in capital and labor). Also assume that the consumers choose the same level of consumption in each period of life (either because their rate of time preference happens to equal the interest rate or because they have Leontief preferences). Now consider how an increase in government debt affects the steady state. Higher debt means higher interest payments and higher taxes. If those taxes are distributed equally across people of different ages, then each person 's after-tax income is reduced by the amount of those interest payments ( per capita) in each period. Because consumers still want to smooth consumption, they respond to this higher tax burden by reducing consumption in each period by the same amount. As a result, after-tax income and consumption fall equally, private saving is unchanged, and private wealth is unchanged. Each dollar of debt crowds out exactly one dollar of capital, as assumed by the debt fairy parable.

Ch. 25:

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1 635

To see what happens when various assumptions are relaxed, we turn to the Blanchard and Auerbach-Kotlikoff analyses. Blanchard develops a continuous-time overlapping­ generations model in which people have log utility and face a fixed probability of dying in each period. He examines the effect of accumulating additional government debt and then holding debt at its new level forever. To establish notation, let D denote debt and W denote national wealth (domestic capital plus net foreign assets), so private wealth equals D + W. For a small open economy, Blanchard confirms the result from our simple example: steady-state dW/dD equals - 1 if the rate of time preference equals the world interest rate. If the world interest rate and the rate of time preference differ, crowding out may be larger or smaller than one for one 1 1 . Matters become more complicated in a closed economy. In this case, as capital is crowded out, the interest rate rises, and households are encouraged to save. As a result, the absolute value of dW/dD is smaller in a closed economy than in an open economy 12 . Calculations using the Blanchard model indicate that the difference between open and closed economies is substantial, but this result appears highly sensitive to the assumption of log utility, according to which households are very willing to substitute consumption between periods in response to a higher interest rate. Most research in the consumption literature suggests a much smaller intertemporal elasticity of substitution than unity 1 3 . Auerbach and Kotlikoff ( 1 987) construct a large-scale general equilibrium model, and simulate the model to examine the effects of alternative debt, tax, and Social Security policies. The numerical simulations reveal not only the steady-state changes in capital and other variables, but also the transition path to the new steady state. The model assumes that people have an economic lifetime of 55 years, have perfect foresight about future economic conditions, and make rational choices regarding their consumption and labor supply. The government raises funds through distortionary taxes and satisfies an intertemporal budget constraint. A production function for net output 1

1

Let p be the probability of dying in each period or, as suggested by Blanchard and Summers ( 1 984), a "myopia coefficient" that reflects mortality or myopia. Let r equal the world interest rate and e the rate of time preference. Then Blanchard reports that dW

dD

12

= -__E__ � p + r p + l:i - r

Blanchard and Fischer (1 989, p. 1 3 1) report that, in the steady state, dK

dD

(p

+

p(p + 1:1) r)(p + 8 - r) - f'ii(; •

where K is the capital stock, C is consumption, and F is the aggregate net production ftmction. 13 For attempts to usc variants of the Blanchard model to estimate the cost of various debt policies, see Romer ( 1 988) and Evans (1991).

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completes the model, which describes a closed economy. Auerbach and Kotlikoff choose values for the key parameters based on the empirical literature. Note, in particular, that they assume that the intertemporal elasticity of substitution is 0.25. Auerbach and Kotlikoff examine the effect of reducing taxes and accumulating debt over a certain number of years, and then boosting taxes to hold the debt at its new per capita level forever. This debt policy reduces saving and capital by transferring resources from younger and future generations, who have a low or zero marginal propensity to consume, to older generations, who have a high marginal propensity to consume. Capital is also diminished by the higher rate of distortionary income taxes in the long run, although the initial reduction in the tax rate can actually crowd-in capital in the short run. Auerbach and Kotlikoff analyze deficits equal to 5% of output that last for one year, 5 years, and 20 years; they do not report the resulting levels of debt, but these can be calculated approximately based on the size of the deficits and the interest rate. For all three experiments, the decline in capital appears to be extremely close to the increase in debt 1 4. We conclude this discussion by emphasizing that the short-run effect o f a budget deficit on consumption and saving is a poor guide to the long-run effect of debt on national wealth. In a model with life-cycle consumers, govemment debt may have only a small short-run effect, as confirmed by Blanchard (who finds that initial saving adjusts by only several percent of a change in debt) and Auerbach and Kotlikoff (who find that at the end of a 20-year tax cut, the capital stock is reduced by only one­ fifth of its eventual decline). Nonetheless, debt has a much larger effect on life-cycle consumers in the long run. Auerbach and Kotlikoff's closed-economy model shows approximately one-for-one crowding out; Blanchard's formulas suggest smaller effects in a closed economy but roughly one-for-one crowding out in an open economy. On balance, the debt fairy's one-for-one substitution of capital for debt may be on the high side of the truth, but it seems a reasonable approximation. 3.2.3.

A closer look at international capital flows

When the debt fairy changes government debt into national wealth, the increment to national wealth is assumed to take the form of domestic capital, with no change in net ownership of foreign assets. This is clearly not a realistic description of an open economy. Yet, altemative assumptions about intemational capital flows would have little effect on the estimated impact of government debt. In actuality, net international capital flows are fairly small. Feldstein and Horioka ( 1 980) examined five-year averages of domestic investment and saving across countries and found these two variables moved almost exactly one for one with each other. More recent estimates suggest that the strength of this relationship declined somewhat in 1 4 The increases in debt fi"om the three alternative policies are roughly 5, 30 and 200% of output. The corresponding declines in the capital stock are 5, 29 and 1 82% of output.

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the 1 980s. Nonetheless, these estimates indicate about 75% of a long-term change in national saving adds to domestic investment and only 25% goes to investment abroad 1 5. Because many countries allow capital to move freely across their borders, i t is surprising that net international capital flows are not larger in the long run. The literature has considered many possible explanations 1 6 . For our purposes, though, the key point is that the existence of international capital flows - or the lack of such :flows has little impact on the ultimate cost of government debt. Suppose that the debt fairy transformed each dollar of reduced debt into an extra dollar of net foreign assets, rather than an extra dollar of domestic capital. In this case, which is the extreme opposite of our original assumption, the debt reduction would not raise domestic output at all. Instead, it would raise foreign output, and some of that output would flow back to this country as the return on our additional overseas assets. As long as the return to wealth is the same at home and abroad, the location of the extra wealth does not affect our income. Another way to understand this point is to note the distinction between domestic income and national income. Domestic income is the value of production occurring within a nation's borders; this is identically equal to domestic output or GDP. Tomorrow's domestic output and income depend on today's domestic investment. But the consumption of domestic residents depends on their income, which is the value of production accruing to a nation's residents. This is called national income, and it is identically equal to national output or GNP. Tomorrow's national output and income depend on today's national saving, wherever this saving is ultimately invested. Naturally, this strong statement requires several caveats. First, the statement ignores the tax implications of the location of capital. Governments receive a higher effective tax rate on capital located in their countries than on capital owned by their residents but located abroad. Thus, the social return to domestic investment is higher than the social return to foreign investment, even if the private (after-tax) returns are the same. Second, additional capital accumulation does not reduce the marginal product of capital as quickly if the capital can flow abroad. As we saw in our earlier discussion of the Blanchard model, the effect of debt on the capital stock is reduced if changes in the capital stock affect the interest rate and thereby private saving. Third, the location of nationally-owned capital does affect the distribution of income. If the domestic capital stock increases, so does the wage, while the return to capital and the interest rate fall; domestic workers benefit and owners of domestic capital are

15

.

See Feldstein and Bacchetta ( 1991) and Dornbusch ( 1 991 ) Frankel ( 1 99 1 ), Mussa and Goldstein ( 1 993), and Gordon and Bovenberg ( 1 996) review the evidence regarding international capital mobility and discuss a number of explanations for the observed immobility. For a recent attempt to explain the Fcldstein�Horioka puzzle within the context of neoclassical growth theory, see Barro et al. ( 1 995). 16

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hurt 1 7 . An increase in the ownership of capital located abroad does not have these effects. Fourth, international capital flows change the composition of domestic production. If a smaller deficit raises net foreign investment, then net exports will rise, while if it increases only domestic investment, then of course investment spending will rise. Moreover, the budget deficit affects the exchange rate if there are significant international capital flows, but not otherwise. On balance, it seems that the issuance of government debt has only a small effect on international capital flows in the long run and that those flows have only a small effect on the return to extra saving. Acknowledging the openness of the economy, therefore, does not substantially alter the estimated impact of govemment debt. 3.2. 4. A

closer look at the marginal product of capital

In describing the impact of the debt fairy, we calculated the marginal product of capital using the capital share of national income and the capital-output ratio. This calculation was based on the standard premise that the factors of production, including capital, are paid their marginal product. Now we reconsider whether that calculation was appropriate. In recent years, there has been a wave of research that proposes a new view of capital. As Mankiw ( 1 995) discusses, a variety of empirical problems with the basic neoclassical growth model would be resolved if the true capital share in the production function is much larger than the one-third measured from the national income accounts. One reason that the true capital share might be larger than the raw data suggest is that capital may have significant externalities, as argued by Romer ( 1 986, 1 987). If the social marginal product of capital is well above the private marginal product that we observe, then reducing government debt and raising the capital stock would have much larger effects than the debt fairy parable suggests. Another possible reason for a large capital share is that the correct measure of capital includes human capital, such as education and training, as well as tangible physical capital, like plant and equipment. Mankiw et al. ( 1 992) propose an extension of the basic Solow ( 1 956) model in which there are fixed saving rates for both physical capital and human capital. They show that cross-country data are consistent with this model and an aggregate production function of the form Y K 1 13 H 113L 113 . If the share of income devoted to human-capital accumulation is unchanged by debt policy, then the reduction in income caused by the crowding out of physical capital will also reduce the stock of human capital; in this case, govemment debt reduces income substantially more than our earlier calculation indicated. By contrast, if the stock of human capital remained fixed, then our earlier calculation would be correct. =

17 Because some owners of domestic capital are foreigners, this shift actually raises national income slightly.

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The deadweight loss of servicing the debt

When discussing the qualitative effects of debt, we reviewed a number of issues beyond the impact of debt on the capital stock. The only one of those effects that is readily quantifiable is the deadweight loss of the additional taxes needed to meet the debt service burden 18. Of course, the deadweight loss of taxation was reduced during the period when taxes were lower and the debt was accumulated, and optimal debt policy requires balancing these effects. Our concern here, however, is just with the cost of an ongoing debt. If the government builds up a certain debt, and then decides to hold that debt constant in real terms, the additional debt service per dollar of accumulated debt is r, the real interest rate on debt. If A is the deadweight loss per dollar of tax revenue, then the loss per dollar of debt is Ar. The total real return on intermediate-maturity government debt averaged about 2% between 1 926 and 1 994 (Stocks, Bonds, Bills and Inflation, 1 995). A standard choice for A is Ballard, Shoven and Whalley's ( 1 985) estimate of one-third, although Feldstein ( 1 996b) argues that incorporating distortions to the form of compensation and the demand for deductions - in addition to the usual distortions to labor and capital supply - makes the true A much larger. If A equals one­ half, then Ar = 0.0 1 , and with the US debt-income ratio at one-half, the deadweight loss from servicing the debt is about half a percent of output. 3.2. 6.

Summary

As concern about current and prospective US budget deficits has grown, quantitative estimates of the effect of debt have begun to appear in official US government documents. For example, in the 1 994 Economic Report of the President ( pp. 8587), the Council of Economic Advisers assumed that the President's deficit-reduction plan would boost national saving by 1 % of output each year for 50 years. Then the Report used a simple Solow growth model to show the effect of that extra saving on the economy. It concluded that the additional saving would eventually raise output by 3.75%. More recently, the Congressional Budget Office ( 1 997b) constructed a complex model of the economy and the federal budget and simulated the model through the year 2050. Because current law would produce an explosive rise in the national debt over that period, CBO 's results do not reflect steady-state effects. In the simulation that includes the economic effects of increasing debt, debt rises by 30% of output by 2020, resulting in output that is 2% smaller than it otherwise would be. Over the following decade, debt increases by another 80% of output, and output is diminished by more than 8% relative to the same baseline. Thus, these calculations are similar in spirit to those found in the academic literature. 1 x Auerbach and Kothkoff's ( 1 987) estimates of the welfare effects of debt policy include th.i.s cost, but isolating its significance from their published results is not possible.

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We have now quantified, in a very rough way, some long-run effects of government debt on the economy. The debt fairy parable implied that each dollar of debt reduces net output by about 6 cents each year. More careful consideration of the strong assumptions embodied in that parable suggested that this estimated cost is at least in the right ballpark. The deadweight loss from the taxes needed to service the debt adds about another one cent per dollar of debt. Thus, the US debt of the late 1 990s, which equals about half of annual output, is reducing net output by about 3 .5%. In 1 997, this amounts to around $300 billion per year. Is this cost large? Labor productivity has increased by about one percent per year in the USA since 1 97 5, so reducing output by three to four percent is like giving up three to four years of productivity growth. That is a significant loss, but it does not qualify as a disaster. One final comparison of the cost of the current debt is with the effect of the upcoming demographic transition in the USA. Congressional Budget Office ( 1 997b) projects that, under current law, population aging and rising health care costs will boost non-interest spending of the federal government by five percent of output between 1 996 and 2025. If the current debt were maintained in real terms, it would represent about one-third of real output in 2025 (because of economic growth). Thus, eliminating that debt would add about two percent to national income, or almost half of the extra income needed to cover the additional government spending. 4. Ricardian equivalence

So far our discussion has focused on the conventional analysis of government debt. By "conventional", we mean that this analysis describes the views held by most economists and almost all policymakers. There is, however, another view of government debt that has been influential in the academic debate, even if endorsed by only a minority of economists. That view is called Ricardian equivalence after the great 1 9th century economist David Ricardo, who first noted the theoretical argument. In recent years, the Ricardian view has been closely associated with Robert Barro, whose work has given the view renewed vigor and prominence. 4. 1.

The idea and its history

Ricardian equivalence is a type of neutrality proposition: it states that a certain type of government policy does not have any important effects. In this section we discuss the general idea, its history, and its importance as a theoretical benchmark. In the following sections we examine the various dimensions of the debate over the validity of Ricardian equivalence as a description of the real world. 4. 1. 1.

The essence of the Ricardian argument

S uppose that the government cuts taxes today without any plans to reduce government purchases today or in the future. As we have seen, conventional analysis concludes

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that this policy will stimulate consumption, reduce national saving and capital accumulation, and thereby depress long-term economic growth. By contrast, the theory of Ricardian equivalence asserts that this policy will not alter consumption, capital accumulation, or growth. The situation with the tax cut and budget deficit is equivalent to the situation without it. The Ricardian argument is based on the insight that lower taxes and a budget deficit today require (in the absence of any change in government purchases) higher taxes in the future. Thus, the issuing of government debt to finance a tax cut represents not a reduction in the tax burden but merely a postponement of it. If consumers are sufficiently forward looking, they will look ahead to the future taxes implied by government debt. Understanding that their total tax burden is unchanged, they will not respond to the tax cut by increasing consumption. Instead, they will save the entire tax cut to meet the upcoming tax liability; as a result, the decrease in public saving (the budget deficit) will coincide with an increase in private saving of precisely the same size. National saving will stay the same, as will all other macroeconomic variables. In essence, the Ricardian argument combines two fundamental ideas: the govern­ ment budget constraint and the permanent income hypothesis. The government budget constraint says that lower taxes today imply higher taxes in the future if government purchases are unchanged; the present value of the tax burden is invariant to the path of the tax burden. The permanent income hypothesis says that households base their consumption decisions on permanent income, which depends on the present value of after-tax earnings. Because a debt-financed tax cut alters the path of the tax burden but not its present value, it does not alter permanent income or consumption. Thus, all of the predictions of the conventional analysis of government debt no longer hold. Another way to view the Ricardian argument is suggested by the title of Robert Barra's classic 1 974 paper "Are Government Bonds Net Wealth?" To the owners of government bonds, the bond represents an asset. But to taxpayers, government bonds represents a liability. A debt-financed tax cut is like a gift of government bonds to those getting the tax cut. This gift makes the holder of the bond wealthier, but it makes taxpayers poorer. On net, no wealth has been created. Because households in total are no richer than they were, they should not alter their consumption in response to the tax cut. It is important to emphasize that the Ricardian argument does not render all fiscal policy irrelevant. If the government cuts taxes today and households expect this tax cut to be met with future cuts in government purchases, then households' permanent income does rise, which stimulates consumption and reduces national saving. But note that it is the expected cut in government purchases, rather than the tax cut, that stimulates consumption. The reduction in expected future government purchases would alter permanent income and consumption because they imply lower taxes at some time, even if current taxes are unchanged. Because the Ricardian view renders some fiscal policies irrelevant but allows other fiscal policies to matter, providing a convincing test of this view has proven difficult. For example, in the early 1 980s, a debt-financed tax cut advocated by President Reagan

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in his first administration was followed by a substantial rise in government debt and a fall in national saving. Some observers, such as Benjamin Friedman ( 1 992), see this episode as a natural experiment that decisively rejects Ricardian equivalence. Yet it is possible that consumers expected this tax cut to mean smaller government in the future; smaller government was, in fact, President Reagan's intention, and to some extent it has been the result. Moreover, other developments, such as a booming stock market, occurred at the same time and surely had some effect on household decisions. In this case, higher consumption and lower national saving could coincide with a tax cut without contradicting Ricardian equivalence. Because neither interpretation of history can be ruled out, both the conventional and Ricardian views of government debt continue to have adherents within the economics profession. 4. 1.2.

A brief history of the Ricardian idea

The modern literature on Ricardian equivalence began with Robert Barra's 1 974 paper. Not only did thi s paper clearly set out the Ricardian argument but it also anticipated much of the subsequent literature by discussing many of the reasons why Ricardian equivalence might not hold. What the paper did not do, however, was credit Ricardo with the idea. It was not until James Buchanan's 1 976 comment on Barra's paper that the term Ricardian equivalence was coined. Ricardo was interested in the question of how a war might be funded. In an 1 820 article, he considered an example of a war that cost 20 million pounds. He noted that if the interest rate were 5%, this expense could be financed with a one-time tax of 20 million pounds, a perpetual tax of 1 million pounds, or a tax of 1 .2 million pounds for 45 years. He wrote, In point of economy, there i� no real difference in either of the mode�; for twenty million� iu one payment, one million per annum for ever, or 1 ,200,0000 pounds for 45 years, are precisely of the same value . . .

Ricardo also was aware that the question raises the issue of intergenerational linkages (which we discuss more fully in a later section): It would be difficult to convince a man possessed of 20,000 pounds, or any other sum, that a perpetual payment of 50 pounds per annum was equally burdensome with a single tax of 1 000 pounds. He would have some vague notion that the 50 pounds per annum would be paid by posterity, and would not be paid by him; but if he leaves his fortune to his son, and leaves it charged with this perpetual tax, where is the difference whether he leaves him 20,000 pounds with the tax, or 1 9,000 pounds without it?

Although Ricardo viewed these different methods of government finance as equivalent, he doubted whether other people in fact had the foresight to act in so rational a manner: The people who pay taxes . do not manage their private affairs accordingly. We are apt to think that the war is burdensome only in proportion to what we are at the moment called to pay for i1 in taxes, without reflecting on the probable duration of such taxes.

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And, indeed, Ricardo did not dismiss government debt as an insignificant policy concern. Before the British parliament, he once declared, This would be the happiest country in the world, and its progress in prosperity would go beyond the powers of imagination to conceive, if we got rid of two great evils - the national debt and the corn laws 1 9

Because Ricardo doubted the practical validity of Ricardian equivalence, O'Driscoll ( 1 977) suggested the term Ricardian non-equivalence, although this phrase has never caught on. Whether or not Ricardo was a Ricardian, he now gets credit for first noting the possible irrelevance of government debt. More recently, several sources have suggested the possibility of debt neutrality, as Barro in fact noted in his 1 974 paper. In 1 952, Tobin posed the Ricardian question: How is it possible that society merely by the device of incurring a debt to itself can deceive itself into believing that it is wealthier? Do not the additional taxes which arc necessary to carry the interest charges reduce the value of other components of private wealth?

Tobin viewed this Ricardian logic as raising an intriguing theoretical question, but he never suggested that it might actually hold in practice. The Ricardian argument also appears in Patinkin's ( 1 965, p. 289) classic treatise, Money, Interest, and Prices, which was based on a 1 947 dissertation at the University of Chicago. In considering whether government bonds should be treated as part of household wealth, Patinkin wrote, The difficulty with this approach is that the interest burden on these bonds must presumably be financed by future taxes. Hence if the private sector discounts its future tax liabilities in the same way that it discounts future interest receipts, the existence of government bonds will not generate any net wealth effect.

Patinkin does not claim originality for this idea. In a footnote, he says, "This point is due to Carl Christ, who cites in turn discussions with Milton Friedman". In 1 962, Martin Bailey's textbook explained clearly ( p. 75) the possibility "that households regard deficit financing as equivalent to taxes". Bailey explains: [Government debt] implies future taxes that would not be necessary if the expenditures were financed with current taxation. If a typical household were to save the entire amount that was made available to it by a switch from current taxation to deficit financing, the interest on the saving would meet the future tax charges to pay interest on the government bonds, while the principal saved would be available to meet possible future taxes imposed to repay the principal on the government bonds. If the household has a definite idea of how it wants to allocate its total present and future resources among consumption at different points of time, and if it recognizes that the shift from current taxation to deficit financing does not change its total resources at all from a long-run point of view, then it will indeed put entirely into saving any 'income' made available to it by a government decision to finance by bond issue rather than current taxation.

IY

Quoted in Buchholz ( 1989, p. 73). Ricardo's opposition to the corn laws (which restricted the import of grain from abroad) suggests that he took his theory of comparative advantage more seriously than he did his theory of debt neutrality.

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D. W Elmend01f and N. G. Mankiw That is, the household will consume exactly the same amount, whichever fmm of financing is used.

Bailey even points out in a footnote that "the same argument applies if no repayment [of the debt's principal] is expected, if the typical household plans to leave an estate". Bailey does not cite Ricardo, but in the text's preface he refers to this section and notes, "a claim to original authorship must be shared with at least two other persons, Gary Becker and Reuben Kessel, who independently developed the same material for their respective courses". The idea of Ricardian equivalence, therefore, has had a long and distinguished history. Yet there is no doubt that Robert Barro's 1 974 paper was a turning point in the literature on government debt. Barro stated the conditions for Ricardian equivalence more clearly than the previous literature had, and he laid out explicitly the intergenerational model needed to establish the result. (We discuss this model below.) Perhaps the greater thoroughness in B arro's treatment of the issue is founded in his apparent belief in debt neutrality. Previous authors, including Ricardo, raised the theoretical possibility of neutrality but often doubted its practical applicability. In a way, Barro can be viewed as the Christopher Columbus of Ricardian equivalence. Columbus was not the first European to discover America, for Leif Ericsson and others had come before. Instead, Columbus' great confidence in the importance of his mission ensured that he was the last European to discover America: after Columbus, America stayed discovered. Similarly, Robert Barro was not the first economist to discover Ricardian equivalence, but he was surely the last. Since Barro's work, Ricardian equivalence has maintained its place at the center of the debate over government debt, and no one will be able to discover it again. 4. 1 . 3.

Why Ricardian equivalence is so important

Although most economists today agree with David Ricardo and doubt that Ricardian equivalence describes actual consumer behavior, the idea of Ricardian equivalence has been extraordinarily important within the academic debate over government debt. There are two reasons for this. The first reason is that a small but prominent minority of economists, including Robert Barro, have argued that Ricardian equivalence does in fact describe the world, at least as a first approximation. This small group has provided a useful reminder to the rest of the profession that the conventional view of government debt is far from a scientific certitude. The inability of macroeconomists to perform true experiments makes macroeconomic knowledge open to debate. Although we believe that policymakers are best advised to rely on the conventional view of government debt, we admit that there is room for reasonable disagreement. The second and more significant reason that Ricardian equivalence is important is that it offers a theoretical benchmark for much further analysis. There are many parallels both inside and outside of economics. Mathematicians study Euclidean geometry (even though we now know that we live in a non-Euclidean world);

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physicists study frictionless planes (even though all real planes exhibit some friction); and economists study Arrow-Debreu general-equilibrium models with complete and perfectly competitive markets (even though markets in actual economies are neither complete nor perfectly competitive). The theoretical benchmark in economics that is most similar to Ricardian equiva­ lence is the Modigliani-Miller theorem. Modigliani and Miller established conditions under which a firm's choice between debt and equity finance is irrelevant. Similarly, Ricardian equivalence is the claim that the govermnent's choice between debt and tax finance is irrelevant. Few finance economists believe that the Modigliani-Miller theorem describes actual firms' financing decisions. Nonetheless, the theorem provides a starting point for many discussions in corporate finance. Similarly, even if Ricardian equivalence does not describe the world, it can be viewed as one natural starting point in the theoretical analysis of government debt. As the next section should make clear, trying to explain why Ricardian equivalence is not true can yield a deeper understanding about the effects of government debt on the economy. 4.2.

The debate over Ricardian equivalence: theoretical issues

Although most economists today are skeptical of the Ricardian propositiOn that government debt is irrelevant, there is less consensus about why government debt matters. The conventional view (which we discussed earlier) begins with the premise that a debt-financed tax cut stimulates consumption. There are various reasons why this might be the case. 4.2.1.

Intergenerational redistribution

One reason govermnent debt might matter is that it represents a redistribution of resources across different generations of taxpayers. When the govermnent cuts taxes and issues govermnent debt today, the govermnent budget constraint requires a tax increase in the future, but that tax increase might fall on taxpayers who are not yet living. This redistribution of resources from future to current taxpayers enriches those who are now living; current taxpayers respond to the increase in their resources by consuming more. This intergenerational redistribution is the mechanism that makes government debt matter in basic overlapping-generations models, such as those of Diamond ( 1 965) and Blanchard ( 1 985). Barra's 1 974 paper built on Becker's ( 1 974) theory of the family to provide a clever rej oinder to this argument. Barra argued that because future generations are the children and grandchildren of the current generation, it is a mistake to view them as independent economic actors. Instead, Barro suggested that current generations might behave altruistically toward future generations. In the presence of this intergenerational altruism, it is no longer natural to presume that current generations will take advantage of the opportunity to consume at the expense of future generations.

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D. W Elmendorf and N G. Mankiw

Barro proposed the following model of the family. Suppose that the total utility of generation t, denoted V�> depends on consumption during its lifetime C1 and on the utility of its children Vt+ 1 , discounted by some factor {3:

Recursive substitution establishes that

That is, the utility of generation t depends on its own consumption and the consumption of all future generations. In essence, the relevant decisionmaking unit is not the individual, who lives only a finite number of years, but the family, which continues forever. As a result, the family member alive today decides how much to consume based not only on his own income but also on the income of future members of his family. Ricardian equivalence is, therefore, preserved: a debt-financed tax cut may raise the income an individual receives in his lifetime, but it does not raise his family's permanent income. Instead of consuming the extra income from the tax cut, the individual saves it and leaves it as a bequest to his descendants, who will bear the future tax liability. The debate over Ricardian equivalence is, therefore, in part a debate over how different generations are linked to one another. This issue has broad significance for macroeconomics. As Kotlikoff and Summers ( 1 98 1) established, a large fraction of wealth in the US economy is eventually bequeathed rather than consumed by its current 2 owner 0 . It is possible that many bequests are accidental rather than intentional; that is, people might leave bequests because they die unexpectedly before consuming their entire wealth. Yet the fact that annuity markets (even if imperfect) are used so rarely suggests that consumers must have some desire to leave bequests. The altruism model proposed by B arro is one possible model of the bequest motive, but there are others. Another popular model is the "joy of giving" or "warm glow" model, according to which a person's utility depends on the size of his bequest rather than on the utility of his children. That is,

where G(B1 ) represents the utility from giving a bequest of size B 1 . Closely related to this model is the "strategic bequest motive" proposed by Bernheim et al. ( 1 985); according to this model, parents use bequests to induce certain types of behavior from their children, such as visiting home more frequently. These alternative models of the bequest motive do not give individuals any reason to look ahead to their children's

2°

For other discussions of the role of intergenerational transfers in wealth accmnulation, see Gale and Scholz ( 1 994), Kessler and Masson ( 1 989), Kotlikoff ( 1 988), and Modigliani ( 1 988).

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tax liabilities and, therefore, do not yield Ricardian equivalence in the presence of policy-induced intergenerational redistributions. It is sometimes mistakenly claimed that the effects of government debt depend on whether people have finite lives (as is the case in the Diamond overlapping-generations model) or infinite lives (as is effectively the case in the Barro intergenerational-altruism model). The key issue, however, is not the finiteness of life but the introduction over time of new taxpayers without links to the past. [This point was established by Philippe Weil ( 1 989).] To see this, imagine an economy in which consumers die (according to some Poisson process) but no new consumers are ever born. In this economy, all future tax liabilities must fall on people who are currently living, so Ricardian equivalence would hold, despite the finiteness of life. By contrast, consider an economy in which new consumers are born over time but, once born, live forever. In this economy, some of the future tax liabilities implied by government debt would fall on future arrivals, and Ricardian equivalence would fail to hold. The Barro model of intergenerational altruism, which links all future arrivals to those currently living, has attracted a variety of theoretical criticisms. One of the more entertaining is that offered by B ernheim and Bagwell ( 1 988), who build on the well established tenet that human reproduction is sexual and that, as a result, people share common descendants. Indeed, if one looks back and forth among everyone's future family trees, one quickly concludes that the entire world population is connected through a web of familial relationships. This observation, together with intergenerational altruism, yields profound predictions. According to the Barro model, a transfer of a dollar (in present value) between Doug Elmendorf and one of his descendants does not affect anyone's consumption. Similarly, a transfer between Greg Mankiw and one of his descendants does not affect anyone's consumption. But if Elmendorf and Mankiw have common descendants, as surely they must, then a transfer between Elmendorf and Mankiw does not affect anyone's consumption. Indeed, because everyone is connected through common descendants, the entire distribution of income is irrelevant - a prediction that is surely false. B ernheim and Bagwell use this argument as a reductio ad absurdum to conclude that the Barro model cannot describe the relationships among generations. A less intriguing, but ultimately more persuasive, critique of the Barro model of intergenerational altruism arises from the work of Evans ( 1 99 1), Daniel ( 1 993), and Smetters ( 1 996). Suppose that we consider a standard model of intergenerational altruism but add the seemingly innocuous wrinkle that the degree of altruism (as measured above by the parameter /3) differs across families. Even if all consumers have some degree of altruism, it is likely in the presence of heterogeneity that many consumers will not have operative bequest motives. In the steady state of such a model, the interest rate is detennined by the time preference of the most patient family (that is, the family with the highest /3). At this interest rate, other families will choose to hit the corner solution of zero bequests and, therefore, will act like a series of overlapping generations: they will save for life-cycle reasons but will leave no bequests. For these zero-bequest families, transfers of resources across generations will have real effects.

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Despite the failure of Ricardian equivalence in this model, the level of government debt does not matter for aggregate variables in the economy's steady state. Because the time preference of the most patient family pins down the steady-state interest rate, it also pins down the capital stock and the level of output. A debt-financed tax cut, for instance, will stimulate consumption, crowd out capital, and raise the real interest rate for a period of time, but the most patient family will respond by increasing saving until, eventually, the capital stock and real interest rate return to their former levels. This result suggests that Ricardian equivalence may work better as a long-run theory than as a short-run theory. Finally, it is worth noting that, for some purposes , the importance of these intergenerational issues may be overstated. Poterba and Summers ( 1 987) claim that, even without intergenerational altruism, people may have long enough time horizons to make Ricardian equivalence approximately true in the short run for some policy interventions. For example, imagine that the government cuts taxes today, issues government debt with an interest rate of 5%, and then services the interest payments with higher taxes over the infinite futme. In this case, about 77% of the future taxes occur within 30 years, indicating that the redistribution of the tax burden toward future generations, though not zero, is relatively small. Moreover, because the marginal propensity to consume out of wealth for life-cycle consumers is relatively small, the redistribution that does occur has only a small effect on consumption. Thus, the immediate result may be an increase in private saving approximately equal to the budget deficit. Poterba and Summers argue that if Ricardian equivalence fails in a substantial way in the short run, the explanation must lie not in the intergenerational redistribution caused by government debt but in some other mechanism 2 1 . 4.2.2.

Capital market imperfections

The simplest, and perhaps most compelling, explanation for the failure of Ricardian equivalence is the existence of capital market imperfections. For households that discount future utility highly or that expect rapidly rising income, the optimal consumption path may require consuming more than their income when young (and less when old) by borrowing in financial markets. The possibility of default and bankruptcy, however, may prevent these households from borrowing for the purposes of current consumption. In this case, the optimal strategy is to consume all of current income and hold exactly zero assets.

2 1 Even if private saving does rise approximately one-for-one with the budget deficit in the short run, there could be substantial crowding out of capital in the long run. The Auerbach-Kotlikoff simulations discussed earlier suggest that the full effects of government debt take a long time to appear in life-cycle models. Thus, the Poterba-Summers argument raises the possibility · in contrast to the model with heterogeneous altruism just discussed - that Ricardian equivalence may work well as a short-run theory but not as a long-run theory. ·

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In the presence of such a binding borrowing constraint, Ricardian equivalence will no longer hold. A debt-financed tax cut effectively gives the constrained household the loan that it wanted but could not obtain from private lenders. The household will respond by increasing consumption, even with the knowledge that the result is higher taxes and lower consumption in the future. The potential importance of capital market imperfections i s highlighted by the small amount of wealth that many people hold compared to the level of government debt in our economy. In recent years, the federal government debt has been about half of national income. If Ricardian equivalence held, the typical household should be holding additional wealth equal to half of annual income. Yet many households have wealth far below that level. To reconcile Ricardian equivalence with these facts, one would need to believe that in the absence of government debt, most households in the economy would have substantially negative net wealth. This seems implausible: few consumers are able to obtain substantial loans without tangible collateral. Thus, it seems that government debt has allowed many households to consume more than they otherwise would. The literature contains some debate over whether capital market imperfections should cause a failure of Ricardian equivalence. Hayashi ( 1 987) and Yotsuzuka ( 1 987) present examples of endogenous capital market imperfections based on asymmet­ ric information that preserve Ricardian equivalence. In these models, asymmetric information about future income, together with the possibility of default, prevents households from borrowing against future income. Yet because taxes are assumed to be lump sum, there is no information problem about the stream of tax payments; as a result, the borrowing constraint does not affect the ability of households to trade off taxes today and taxes in the future. In this case, a debt-financed tax cut causes the borrowing constraint to adjust in such a way as to leave consumption opportunities unchanged. As Bernheim ( 1 987) points out, however, this result is crucially dependent on the assumption that taxes are lump sum. If taxes rise with income, then the asymmetry in information about future income causes a similar asymmetry in information about future tax liabilities. In this more realistic case, these models yield the more conventional result that a debt-financed tax cut relaxes the borrowing constraint, allowing households to consume more. 4.2.3.

Permanent postponement of the tax burden

When a person first hears the case for Ricardian equivalence, a natural response is, "Yes, that theory might apply if a budget deficit today required higher taxation in the future. But, in fact, the government never has to pay off its debts. When the government cuts taxes and runs a budget deficit, it can postpone the tax burden indefinitely". This s imple argument, it turns out, raises a number of complex questions for economic theory. The first point to make is that Ricardian equivalence does not require that the government ever pay off its debts in the sense of reaching zero indebtedness. Imagine

1 650

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that the government cuts taxes for one year by dD, increases the government debt by that amount, and then leaves government debt at the new higher level forever. To service this additional government debt would require additional taxes of r x dD every year, where r is the interest rate on the debt. The present discounted value of these higher taxes is dD, which exactly offsets the value of the tax cut. Hence, if consumers look ahead to all future taxes, Ricardian equivalence holds, even though the government never retires the additional debt it has issued. Matters become more complicated if the government does not raise taxes to finance the interest on this additional debt but, instead, finances these interest payments by issuing even more debt. This policy is sometimes called a "Ponzi scheme" because it resembles investment scams in which old investors are paid off with money from new investors. If the government pursues such a Ponzi scheme, the government debt will grow at rate r, and the initial tax cut and budget deficit do not imply higher taxes in the future. But can the government actually get away with this Ponzi scheme? The literature has explored this question extensively 22 . An important issue is the comparison between the interest rate on government debt r and the growth rate of the economy g. If r is greater than g, then government debt will increase faster than the economy, and the Ponzi scheme will eventually be rendered infeasible: the debt will grow so large that the government will be unable to find buyers for all of it, forcing either default or a tax increase. By contrast, if r is less than g, then government debt will increase more slowly than the economy, and there is nothing to prevent the government from rolling over the debt forever. The comparison between r and g has broader general-equilibrium implications, however, and these implications help explain the effects of government debt. In standard neoclassical growth theory, r reflects the marginal product of capital, and g reflects population growth and technological change. These two variables can be used to gauge whether the economy has reached a dynamically efficient equilibrium. If r is greater than g, then the economy is efficient in the sense of having less capital than at the "Golden Rule" steady state. By contrast, if r is less than g, then the economy is inefficient in the sense of having accumulated too much capital. In this case, a reduction in capital accumulation can potentially increase consumption in all periods of time. A govermnent Ponzi scheme, like the "asset bubbles" studied by Tirole ( 1 985), is both feasible and desirable in such an economy because it helps ameliorate the problem of oversavmg. Dynamic inefficiency and successful, Pareto-improving Ponzi schemes offer an intriguing theoretical possibility, but they are not of great practical relevance for the US economy or other economies around the world. Economists today do not believe that households are saving too much, driving the return to capital below the economy's

22 See, for instance, Ball et al. ( 1 998), Blanchard and Wei! ( 1 992), Bohn { 1 993), and O'Connell and Zeldes ( 1 988).

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growth rate. And, indeed, Abel et al. ( 1 989) present evidence for dynamic efficiency. Hence, Ricardian equivalence cannot be refuted by asserting that the government can roll over the debt forever. Yet one nagging fact remains: in the US economy, the interest rate on government debt has on average been less than the growth rate of the economy. Abel et al. reconcile this fact with their finding of dynamic efficiency by noting that government debt and economic growth have different risk characteristics. They present an example of a dynamically efficient economy in which uncertainty about economic growth drives down the return on risk-free assets, such as government debt, below the average growth rate. Thus, one cannot judge dynamic efficiency (and the feasibility of government Ponzi schemes) simply by comparing the average return on risk-free assets with the average growth rate 23 .

4.2.4. Distortionary taxes The Ricardian equivalence proposition is based on the assumption that taxes are lump sum. If instead taxes are distortionary, then a postponement of the tax burden affects incentives and thereby behavior. These microeconomic distortions could have a large macroeconomic impact, making Ricardian equivalence a poor approximation to reality. To see the potential importance of distortionary taxation, imagine an economy described by the standard Ramsey growth model except that taxes, rather than being lump-sum, are raised with a proportional income tax with rate T. The following equations describe the steady state:

y = f(k),

ry = rD + g,

r =f'(k),

( 1 - T) r = p.

The first equation is the production function. The second equation states that tax revenue ry equals the interest on the debt rD plus government spending g. The third equation states that the interest rate r equals the marginal product of capital. (Both interest income and capital income are assumed to be taxed at the same rate, so the tax does not affect this equation.) The fourth equation states that the after-tax interest rate equals the rate of subjective time preference p; this is the steady-state condition for the Ramsey model. Given these equations, it is straightforward to see how an increase in government debt affects the economy. Higher debt leads to higher debt service; a

23

Ball et al. ( 1 998) build on these ideas and consider policies in dynamically efficient economies called "Ponzi gambles" in which the government cuts taxes and rolls over the resulting debt for as long as is possible. In their model, debt can raise the welfare of all generations in those realizations of history in which taxes do not need to be increased. Yet the policy is a gamble because the government is sometimes forced to raise taxes. Moreover, those tax increases are especially undesirable because they occur in realizations of history in which future generations are already burdened by low economic growth.

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higher debt service requires a higher tax rate; a higher tax rate implies a higher before­ tax interest rate; and a higher interest rate requires a smaller steady-state capital stock. As in the traditional analysis, government debt crowds out capital, even though the mechanism here is quite different. We can easily calibrate the magnitude of this effect for this model. By fully differentiating this system we obtain an expression to show how much debt crowds out capital: dk dD

= {r f

Df"

'

+

1 - T).ff"

( f' )2

}- I

If we specialize the production function to Cobb-Douglas y = k0, then this expression becomes: dk dD

- =

{ r + (l - a)- - (1 - r) a } · I D k

1-

--

a

For the US economy, taxes take about one-third of income ( T = 1 /3), capital earns about one third of income (a = 1 /3 ), and the debt equals about one-seventh of the capital stock (Dik = l /7). For these parameter values, dk/dD = - 1 . 1 1 . That is, an extra dollar of government debt reduces the steady-state capital stock by slightly over one dollar. This example shows that substantial crowding out can occur simply because of distortionary taxation 24. Although this example i s sufficient t o show the potential importance o f distortionary taxation, more realistic analyses of debt policy go beyond this special case. In the steady state of the Ramsey model, national saving is infinitely elastic at the rate of time preference. Other models, such as the life-cycle model of Auerbach and Kotlikoff ( 1 987), would predict a more limited saving response to a change in the after-tax rate of return. In addition, it is important to consider the dynamic effects of tax changes, as in Judd ( 1 987) and Dotsey ( 1 994), and the effects of taxes on labor supply, as in Trostel ( 1 993) and Ludvigson ( 1 996). Perhaps the only certain conclusion is that in a world with distortionary taxation, Ricardian equivalence is unlikely to provide a good first approximation to the true effects of debt policy. 4.2. 5.

Income uncertainty

Another possible reason for the failure of Ricardian equivalence is that government debt may alter consumers' perception of the risks they face. This possibility was 24 The numerical results presented here are, of course, sensitive to a variety of detailed assmnptions. lf we introduce depreciation, so that the production function is .f(k) = ka - Ck, then the degree of crowding as measured by dk/dD falls. If we take a broad view of capital, so that a is larger than 1/3, then the degree of crowding rises.

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explored by Chan ( 1 983), Barsky et al. ( 1 986), Kimball and Mankiw (1989) and Croushore ( 1 996). These authors begin with the axioms that taxes are levied as a function of income and that future income is uncertain. Therefore, when the government cuts taxes today, issues government debt, and raises income taxes in the future to pay off the debt, consumers' expected lifetime income is unchanged, but the uncertainty they face is reduced. If consumers have a precautionary saving motive, this reduction in uncertainty stimulates current consumption. Put differently, consumers discount risky uncertain income and uncertain future taxes at a higher rate than the interest rate on government bonds; a postponement of the tax burden, therefore, encourages current spending. The potential importance of this mechanism is highlighted by the recent interest in buffer-stock theories of saving. [See, for instance, Carroll ( 1 997).] In these models, consumers are impatient (in the sense of having a high subjective discount rate) but are nonetheless prudent (in the sense of having a precautionary saving motive). As a result, consumers maintain a small amount of saving in order to protect themselves against unlikely but very adverse shocks to their income. If consumers do not pay significant taxes when these unlikely, adverse outcomes are realized, then a postponement of the tax burden will stimulate current consumption. 4.2. 6.

Myopia

When non-economists are explained the idea of Ricardian equivalence, they often have trouble taking the idea seriously. The reason for this response goes to the heart of how economists view human behavior. Rational, optimizing, forward-looking homo economicus is a creature of the economist's imagination. Economists are trained in the power of this model, but non-economists are often more skeptical. In particular, non-economists are doubtful about whether people have the foresight to look ahead to the future taxes implied by government debt, as is required for Ricardian equivalence to hold. It is hard to incorporate this sort of myopia into economic theory. Yet there have been some attempts to model short-sightedness. Strotz ( 1 956) and Laibson ( 1 997), for instance, consider preferences according to which consumers give excessive weight to current utility (compared to the benchmark case of exponential discounting). As a result, consumers exhibit time-inconsistent behavior and can be made better off through a binding commitment to increased saving. This model can explain the popular notion that people save too little, but it cannot by itself explain a failure of Ricardian equivalence. In this model, the time-inconsistent consumer faces a standard intertemporal budget constraint, so a postponement of the tax burden does not alter the consumer's opportunities. This consumer saves too little but, without a binding borrowing constraint or other imperfection, is fully Ricardian in response to fiscal policy. Although the Ricardian behavior of Strotz-Laibson consumers shows that myopia by itself need not undermine Ricardian equivalence, this result does not necessarily

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render myopia irrelevant in this debate. The impatience implicit in the Strotz-Laibson preferences can explain the prevalence of liquidity constraints and buffer-stock saving, which in turn highlights the deviations from Ricardian equivalence emphasized earlier. In addition, it is possible that the Strotz-Laibson approach to modelling myopia is not the best one. Developing better models of myopic behavior remains a challenge for future research. 4. 3.

The debate over Ricardian equivalence: empirical issues

The theoretical literature just discussed offers various reasons why government debt may affect consumption and capital accumulation. Yet these deviations from Ricardian equivalence do not prove that the proposition is a bad first approximation of the actual economy. To reach such a judgment, one must assess the quantitative importance of these theoretical deviations from the Ricardian benchmark. Some of the research discussed earlier bears on this issue. As noted above, calculations using the Blanchard model of finite lifetimes imply that debt can crowd out a significant amount of capital, and Auerbach and Kotlikoff's simulations show that the combination of finite lifetimes and distortionary taxes can generate roughly one-for-one crowding out. Moreover, many of the theoretical analyses cited in the previous section include calibrations that illustrate the potential importance of the channels through which debt may affect the economy. Simulations, however, are no substitute for evidence. In this section we review the empirical evidence on the validity of Ricardian equivalence. We begin with tests of the assumptions underlying the proposition and conclude that a substantial fraction of households probably do not behave as the proposition assumes. We next turn to tests of the proposition's implications for various macroeconomic variables. Despite substantial research in this area, we believe that the results are ultimately inconclusive 25 . 4. 3. 1 .

Testing assumptions about household behavior

When testing theories, economists typically focus on the theories' implications rather than their assumptions. Yet, because testing the implications of Ricardian equivalence raises substantial difficulties, examining the underlying assumptions is also worthwhile. The key assumption is consumption smoothing both within lifetimes and across generations. That is, households are assumed to choose consumption and saving based on a rational evaluation of an intertemporal budget constraint that includes both current and future generations. One piece of evidence that many households do not behave in this way is the small amount of wealth that they hold. This situation may arise from a combination of

25

Our review of this literatmc is necessarily brief. For more thorough discussions with additional citations, see Bernheim ( 1 987) and Seater ( 1 993).

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impatience and borrowing constraints, as described earlier, or because some people are not very forward-looking. In either case, a deficit-financed tax cut would spur consumption. Numerous papers also present evidence that people do not smooth consumption fully over time. Campbell and Mankiw ( 1 989) use aggregate data to show that consumption is more sensitive to current income than the basic consumption­ smoothing model predicts. Hall and Mishkin ( 1 982), Zeldes ( 1 989), and Carroll and S ummers ( 1 99 1 ) make the same point using household data. Further confirmation comes from households' responses to changes in taxes and government benefits; for example, see Poterba ( 1 988), Wilcox ( 1 989), and Shapiro and Slemrod ( 1 995). In these studies, deviations from the life-cycle model are economically as well as statistically significant. Some studies, such as Runkle ( 1 99 1), Attanasio and Browning ( 1 995), and Attanasio and Weber ( 1 995), have argued that income and consumption data are in fact consistent with the consumption-smoothing model. But the weight of the evidence from the consumption literature is that consumption smoothing is far from complete. In our view, this conclusion casts serious doubt on the empirical plausibility of Ricardian equivalence.

4.3.2. Testing the implications for consumption A large and contentious literature has focused on the implication of Ricardian equivalence that a reduction in current taxes with no change in current or future government spending should not affect household consumption. The standard approach is to estimate a traditional aggregate consumption function, with consumer spending as the dependent variable and income, wealth, fiscal policy, and various other controls as independent variables. Ricardian equivalence is rejected if the coefficients on taxes and debt are significantly different from zero. Although this approach seems to offer a direct test of the Ricardian view, there are a number of problems with its implementation. The first problem is the treatment of expectations. The behavior of forward-looking households depends on expectations of fiscal policy, not just the measures of current fiscal policy that are included in these regressions. Suppose that the current level of taxation reflects expectations of future government spending. (This is in fact implied by the theory of tax smoothing, which we discuss later.) In this case, a significant negative coefficient on current taxes in the consumption function does not necessarily violate Ricardian equivalence. A second problem is simultaneity. Some of this literature estimates the consumption function with ordinary least squares. This approach is valid only if the shocks to the consumption function do not affect fiscal policy or other right-hand side variables. Other papers attempt to address this problem using instrumental variables, but finding persuasive instruments is close to impossible 26 . 26

For a discussion of the identification problem in the cont Hi , then T; > 1j. Suppose next that the utility function is additively separable. Then

( 1 . 1 8) Let c(p, m), l(p, rn) denote the solution to the problem of maximizing utility subject to L: P; C; = l + m, where m is nonlabor income, so that c;(p, m) is the demand function

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for good i. Letting a denote the Lagrange multiplier on the budget constraint, we can differentiate the first-order condition U;(c(p, m)) = a(p, m)p; with respect to nonlabor income m to obtain

8c; U; 8a U;; am = p; 8a am = a am or

8c; = - -1 8a H1 -1 c; 8m a 8m

(1 . 1 9)

so that H;

Hj

= !}j_ rh

( 1 .20)

where 17; is the income elasticity of demand for good i. Thus necessities should be taxed more than luxuries. The standard partial equilibrium result is that goods with low price elasticities of demand should be taxed more heavily than goods with high price elasticities. In general equilibrium, this result does not necessarily hold. It does hold if preferences are additively separable and there are no income effects. That is, utility is quasi-linear and is given by ( 1 .2 1 ) For such a utility function, Equation ( 1 .20) is not helpful because the income elasticities for all the consumption goods are zero. It is easy to show that for a utility function of the form ( 1 .2 1), H; = li E;, where E; = -(8c/8p;)p;/c; is the price elasticity of demand. To see this, differentiate the first-order condition with respect to p;,

U;(c(p, m), l(p, m)) = ap;,

( 1 .22)

to obtain

8c; = a U'' 8p; '

( 1 .23)

where a is constant because of quasi-linearity. Substituting Equations ( 1 .22) and ( 1 .23) into ( 1 . 1 8) gives H; = 11 E;. Since T; > r1 when H; > H1 , consumption goods which are relatively more price inelastic (have low f;) 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

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1 682

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 ( 1 972).] Consider a utility function of the form

U(c, l) = W(G(c) , l) where

c =

(c l , . . . , c11)

( 1 .24)

and

G

is homothetic.

Proposition 3. !f utility satisfies condition (1.24) - that is, utility is weakly separable across consumption goods and is homothetic in consumption - then U/U; = F;IFJ for i = 1 , . . . , n. That is, optimal commodity taxation is un!form in the sense that the Ramsey taxes satisfy T; = 7j for i = 1 , . . . , n. Proof: Substituting the firm's first-order conditions ( 1 . 1 3) into the consumer's first­ order condition, we have that

Thus T; = 7j if and only if U;IF; U;IFJ. Note that a utility function which satisfies condition ( 1 .24) satisfies =

( 1 .25)

To see this, notice that from homotheticity, it follows that

U;(ac, l) Uk(ac, l) or

_ -

U;(c, l) Uk(c, l)

---

l

U; (c, l) U (ac, l). U; (ac, l) = Uk(c, l) �c

J

Differentiating Equation ( 1 .26) with respect to gives ( 1 .25).

( 1 .26)

a

and evaluating it at

a

=

1

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Consider next the first-order condition for c; from the Ramsey problem, namely,

( I + A) U, 1 A

[�

cpij

1

l

IU,

�

yF, ,

( 1 .27)

where, again, A is the multiplier on the implementability constraint and y is the multiplier on the resource constraint. From Equation ( 1 .25), we have that there is some constant A such that _Li ci Uu = AU; for all i. Using this fact and the form of utility function, we can rewrite Equation ( 1 .27) as ( 1 + A) Wt G; + A [AW1 G; + lW1 2 G;] Since Equation ( 1 .28) holds for all U;

F;

=

Wt G;

F;

=

W1 Gi

Fi

=

=

AF;.

i and ), G;IF;

( 1 .28) =

G/FJ for all

i

and ) and

� Fi

D

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� , . . . , ck , t/J(ck+t , . . . , en ), !)

with tjJ homothetic. Then it is easy to show that the Ramsey taxes Tk + 1 = . . . = Tn . 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 , y1 , which is not taxed. Then the implementability constraint becomes

2:=: U;c; + U1l = U1Y 1 ·

Then even i f U satisfies U (t/J(c 1 , . . . , c11), l) with tjJ homothetic, it i s not true that optimal taxes are uniform (because of the extra terms UlJYt from the derivatives of U1y1 ). If we add the assumption that U is additively separable across c 1 , . . , C11 , 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, r1 = 0. Then the Ramsey problem now must include the constraint .

U; U,

=

F1

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

VV Chari and PJ. Kehoe

1 684

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(c� , c2 , . . . , !1 , !2, . . . ). The assumption that the utility is of the form V(f/J(c 1 , , c1 , ), li , l2 , . . . ) with fjJ homothetic and separable between consumption and all labor goods l� , !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 • . •

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 ( 1 97 1).] 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 / - and an intermediate good z. The utility function is U(x, !). The technology set for producing the final consumption good using labor /1 and the intermediate good is described by f(x, z, l l ) ::( 0,

( 1 .29)

where f is a constant returns to scale production function. There is a technology set for producing the intermediate good and government consumption using labor h described by ( 1 .30) where h also is a constant returns to scale production function. The consumer's problem is to maximize U(x, lt + l2) subject to p( l

+ r) x ::::;

w(/1

+ /2 ) ,

Ch.

26:

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Optimal Fiscal and Monetary Policy

where p and w are the prices of the consumption good and labor and T is the tax on the consumption good. The firm that produces private consumption goods maximizes profits

px - w/ 1 - q( l + 17) z subject to condition ( 1 .29); q is the price of intermediate goods, and 17 is the tax on intermediate goods. The firm that produces intermediate goods and government consumption goods maximizes profits

qz + rg - w/2 , where r is the price of government consumption, subject to condition (1 .30). We can easily show that the Ramsey allocation problem is given by max

U(x, /1 + lz)

subject to conditions

( 1 .29), ( 1 .30),

and

xUx + (!1 + /2 ) Ut = 0.

( 1 .3 1 )

We then have Proposition 4.

The solution to the Ramsey allocation problem satisfies production efficiency; namely, the marginal rates of transformation are equated across technologies. Equivalently, setting the tax on intermediate goods 17 0 is optimal. =

Proof:

For this economy, production efficiency is equivalent to

( 1 .32) Solving the Ramsey allocation problem, we obtain the following first-order conditions for z, h , and /2 , respectively:

ufz

( 1 .33) ( 1 .34) ( 1 .35)

-f.-lhz , U, + A (xUtx + Vt + lUu) + ufi = 0, Ut + J..(xV1x + U, + lUu) + f.-lht = 0, =

where v, f.-l, and A are the multipliers on (1 .29), ( l .30), and ( 1 .3 1). Combining Equations (1 .34) and ( 1 .35) gives vft f.-lh1, which, combined with ( 1 .33), establishes Equation ( 1 .32). The first-order conditions for profit maximization for the firms imply that =

fz_ q(l + 17) .ft

=

w

Thus, if condition

=

_

hz ( l YJ). + h,

( 1 .32)

holds, Equation

( 1 .36) ( 1 .36) implies that

TJ

=

0.

D

V. V. Chari and P.J Kehoe

1 686

The intermediate-goods result holds in general settings in which there are (possibly infinitely) many goods and many production technologies. We have assumed that the production technologies satisfy constant returns to scale. If there are increasing returns to scale, then there are standard problems with the existence of a competitive equilibrium. If there are decreasing returns to scale, then the intermediate-goods result continues to hold, provided that pure profits can be fully taxed away. It turns out that the result for uniform commodity taxation follows from the inter­ mediate-goods result. To see this, consider a utility function of the form

U (c, l) = W(G(c), l),

( 1 .37)

where c = (c 1 , . . . , c17 ) and G is homogeneous of degree 1 . We can reinterpret this economy as an economy with a single consumption good x, which is produced using n intermediate-goods inputs (c 1 , . . . , en ) with the constant returns to scale technology x = G(c). The intermediate-goods result requires that in an optimal tax system, the taxes on the intermediate-goods inputs be zero, so that there are taxes only on final goods x and !. This is clearly equivalent to a uniform tax on (c 1 , . . . , c17 ) . 2. Fiscal policy

In this section, we begin by setting out a general framework for analyzing optimal fiscal policy in a stochastic one-sector growth model. We use a deterministic version of this model to develop results on the taxation of capital income, in both the short and long run. We first show that the optimal capital income taxes are zero in a steady state, even if there are heterogeneous consumers. We then show that for a class of utility functions, there is only one period with nonzero capital income taxes, following which capital income taxes are zero along a transition to the steady state. We then turn to the cyclical properties of optimal fiscal policy. In a stochastic model without capital, we illustrate how debt can act as a shock absorber. We briefly discuss how incomplete markets can alter these results. We then illustrate the main features of optimal fiscal policy over a business cycle using a calibrated version of the model with capital. Finally, we discuss how these results are altered in three other environments: an endogenous growth model, an open economy model, and an overlapping generations model. 2. 1.

General framework

Consider a production economy populated by a large number of identical, infinitely lived consumers. In each period t 0, 1 , . . . , the economy experiences one of finitely many events s1 • We denote by s 1 (so, . . . , st) the history of events up to and including period t. The probability, as of period 0, of any particular history s 1 is fl(s 1 ). The initial realization s0 is given. This suggests a natural commodity space in which goods are differentiated by histories. =

=

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1 687

In each period t, the economy has two goods: a consumption-capital good and labor. A constant returns to scale technology which satisfies the standard Inada conditions is available to transform capital k(s H ) and labor /(s f) into output via F(k(s t-1 ), l(s t) , s )­ t Notice that the production function incorporates a stochastic shock St . The output can be used for private consumption c(s 1 ), government consumption g(s 1 ), and new capital k(s 1 ). Throughout, we will take government consumption to be exogenously specified. Feasibility requires that

c(s t ) + g(s 1 ) + k(s 1 ) = F(k(s 1- 1 ), l(s 1 ), s1 ) + (1 - 6) k(s H ) ,

(2.1)

L f31 /1(S 1 ) U(c(s 1 ), l(s 1 )),

(2.2)

where 0 is the depreciation rate on capital. The preferences of each consumer are given by t, s 1

where 0 < f-3 < 1 and U is strictly increasing in consumption, is strictly decreasing in labor, is strictly concave, and satisfies the lnada conditions. Government consumption is financed by proportional taxes on the income from labor and capital and by debt. Let r(s1) and 8(s 1) denote the tax rates on the income from labor and capital. Government debt has a one-period maturity and a state-contingent return. Let b(s 1 ) denote the number of units of debt issued at state s 1 and Rb(s t+ 1 ) de­ note the return at any state s t+I = (s 1 , s1+ 1 ). The consumer's budget constraint is

c(s 1 ) + k(s 1 ) + b(s 1 ) :::;;;

[1 - r(s 1)] w(s 1 ) l(s 1) + Rk(s 1 ) k(s 1- 1 ) + Rb(s 1 ) b(s H ),

(2.3)

where Rk(s 1 ) 1 + [ 1 - 8(s 1 )] [r(s 1 ) - 0] is the gross return on capital after taxes and depreciation and r(s 1 ) and w(s 1 ) are the before-tax returns on capital and labor. Con­ sumers' debt holdings are bounded by b(s 1 ) ;? -·M for some large constant M . Com­ petitive pricing ensures that these returns equal their marginal products, namely, that =

(2.4) (2.5)

r(s f) Fk(k(s H ), /(sf), s1 ), w(s 1 ) = Ft(k(s 1- 1 ), l(s t ), s1 ). =

Consumers' purchases of capital are constrained to be nonnegative, and the purchases of government debt are bounded above and below by some arbitrarily large constants. We let x(s 1) = (c(s1), /(s 1 ), k(s 1 ), b(s 1 )) denote an allocation for consumers at s 1 and let x = (x(sf)) denote an allocation for all st . We let (w, r, Rh) (w(s 1 ), r(s t ), Rh(s 1 )) denote a price system. The government sets tax rates on labor and capital income and returns for government debt to finance the exogenous sequence of government consumption. The government's budget constraint is =

b(s 1 ) = Rb(s t ) b(s H ) + g(s 1 ) -- r(s 1 ) w(s 1 ) l(s 1 ) 8(: / )[r(s 1 ) - 6] k(s 1 1 ). (2.6) We let n(s 1) (r(sf), 8(s 1 )) denote the government policy at sf and let n; = (n(s1)) denote the infinite sequence of policies. The initial stock of debt, b_ 1 , and the initial stock of capital, k_ 1 , are given. - ·

=

1 688

VV Chari and P.J. Kehoe

Notice that for notational simplicity, we have not explicitly included markets in private claims, so all borrowing and lending is between consumers and the government. Since all consumers are identical, such claims will not be traded in equilibrium; hence their absence will not affect the equilibrium. Thus we can always interpret the current model as having complete contingent private claims markets. A competitive equilibrium for this economy is a policy JC, an allocation x, and a price system (w, r, Rb) such that given the policy and the price system, the resulting allocation maximizes the representative consumer's utility (2.2) subject to the sequence of budget constraints (2. 3), the price system satisfies (2.4) and (2.5), and the government's budget constraint (2.6) is satisfied. Notice that we do not need to impose the feasibility condition (2. 1 ) in our definition of equilibrium. Given our assumptions on the utility function, constraint (2.3) is satisfied with equality in an equilibrium, and this feature, together with (2.6), implies (2. 1 ) . Consider now the policy problem faced by the goverument. We suppose that there is an institution or a commitment technology through which the government, in period 0, can bind itself to a particular sequence of policies once and for all. We model this by having the government choose a policy JC at the beginning of time and then having consumers choose their allocations. Formally, allocation rules are sequences of functions x(JT) (x(s 1 I n)) that map policies JT into allocations x(n). Price rules are sequences of functions w(JT) = (w(s 1 I n)) and r(n) (r(s 1 I n)) that map policies JT into price systems. Since the government needs to predict how consumer allocations and prices will respond to its policies, consumer allocations and prices must be described by rules that associate government policies with allocations. We will impose a restriction on the set of policies that the government can choose. Since the capital stock in period 0 is inelastically supplied, the government has an incentive to set the initial capital tax rate as high as possible. To make the problem interesting, we will require that the initial capital tax rate, 8(s0), be fixed at some rate. A Ramsey equilibrium is a policy JT, an allocation rule x(-), and price rules w ( - ) and r(-) that satisfy the following: (i) the policy JT maximizes =

=

L fJp(s 1 ) U(c(s 1 I n), l(s 1 I n)) t, s '

subject to constraint (2.6), with allocations and prices given by x(lc), w(n), and r(n); and (ii) for every JT1, the allocation x(n'), the price system w(n'), r(n'), and Rb(n'), and the policy JT1 constitute a competitive equilibrium. We now turn to characterizing the equilibrium policies and allocations. In terms of notation, it will be convenient here and throughout the chapter to let Uc(s1) and Ut(s 1) denote the marginal utilities o f consumption and leisure at state s1 and let Fk (s 1) and F1(s1) denote the marginal products of capital and labor at state s 1 • We will show that a competitive equilibrium is characterized by two fairly simple conditions: the resource constraint (2.7)

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1 689

and the implementability constraint

L {31 tJ-(s1) [ Uc(s1) c(s 1 ) + u,(s1) l(s1)] = Uc(so) [Rk (so) L I + Rb(so) b_l ] , (2.8) t,st where Rk(so) = l + [1 - 8(s0 )][Fk(s0 ) - D ] . The implementability constraint should be

thought of as an infinite-horizon version of the budget constraint of either the consumer or the government, where the consumer and firm first-order conditions have been used to substitute out the prices and policies. We have

The consumption, labor, and capital allocations and the capital tax rate and return on debt in period 0 in a competitive equilibrium satisfy conditions (2. 7) and (2.8). Furthermore, given allocations and period 0 policies that sati:;fY (2. 7) and (2.8), we can construct policies, prices, and debt holdings that, together with the given allocations and period-0 policies, constitute a competitive equilibrium. Proposition 5.

We first show that a competitive equilibrium must satisfy (2.7) and (2.8). To see this, note that we can add (2.3) and (2.6) to get (2.7), and thus feasibility is satisfied in equilibrium. Next, consider the allocation rule x(n). The necessary and sufficient conditions for c, l, b, and k to solve the consumer's problem are given as follows. Let p(s 1 ) denote the Lagrange multiplier on constraint (2.3 ) . Then by Weitzman's ( 1 973) and Ekeland and Scheinkman's (1986) theorems, these conditions are constraint (2 . 3), together with first-order conditions for consumption and labor: Proof:

{31 tJ-(s1) Uc(s1) ,::;; p(s 1 ), with equality if c(s 1 ) > 0, {31 tJ-(s1) U1(s1) ,::;; -p(s 1 )( 1 - r(s 1 )) w(s 1 ), with equality if l(s 1 ) > 0;

(2.9) (2. 1 0)

first-order conditions for capital and government debt:

[ [

] ]

p(s1) -- L.:><s t+ 1 ) Rb(s t+ 1 ) b(s 1 ) = 0,

(2. 1 1)

p (s t ) - L P(s t l l ) Rk(s H 1 )

(2. 12)

s t+l

s t+l

k (s t ) = 0 ;

and the two transversality conditions lim

"" p(s 1 ) b(s 1 )

t ---+ oo � s'

=

0,

(2. 13) (2. 14)

We claim that any allocation which satisfies (2.3) and (2.9)-(2. 14) must also satisfy (2.8). To see this, multiply (2.3) by p (s 1), sum over t and s 1 , and use (2. 1 1)-(2.14) to obtain

t,s1

(2. 1 5)

1 690

V.V. Chari and PJ Kehoe

Using (2.9) and (2. 1 0) and noting that interiority follows from the Inada conditions, we can rewrite Equation (2. 1 5) as

(2. 1 6) Thus (2.7) and (2. 8) are necessary conditions that any competitive equilibrium must satisfy. Next, suppose that we are given allocations and period-0 policies that satisfy (2.7) and (2.8). We construct the competitive equilibrium as follows. First, note that for an allocation to be part of a competitive equilibrium, it must satisfy conditions (2.3) and (2.9)-(2 . 1 4). Multiplying (2.3) by p(s 1) and summing over all periods and states following sr and using (2.9)-(2. 1 4), we get (2. 1 7) Thus any competitive equilibrium debt allocation must satisfy (2. 1 7), and hence (2. 1 7) defines the unique debt allocations given consumption, labor, and capital allocations. The wage rate and the rental rate on capital are determined by (2.4) and (2.5) from the capital and labor allocations. The labor tax rate is determined from (2. 5), (2.9), and (2. 1 0) and is given by

UI(st) Uc(s 1 )

- -- =

t

[ 1 - T(s )]h, (s t ) .

(2. 1 8)

We can use Equations (2.3), (2.9), (2. 1 1 ), and (2. 1 2) to construct the capital tax rate and the return on debt. From these conditions, it is clear that given the allocations, the tax rate on capital and the return on debt satisfy (2. 1 9)

8tt l is t

(2.20)

c(sL+ 1 ) + k(s t+ 1 ) + b(s 1+1 ) 1 [ 1 - r(s 1+ )] w(s 1+ 1 ) l(s L+1 ) + Rk (s L+l ) k(s 1 ) + Rh (s tt-1 ) b(s 1 ), =

(2.2 1 )

where Rk(sl+ 1 ) 1 + [ 1 8(s t+ 1 )] [r(s t+ 1 ) - Ci]. l t turns out that these conditions do not uniquely determine the tax rate on capital and the return on debt. To see this, suppose that s1+ t can take on one of N values. Then counting equations and unknowns in Equations (2. 1 9)-(2.2 1 ) gives N + 2 equations and 2N unknowns in each period and state. Actually, however, there is one linear dependency across these equations. To see c�

· ·

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1691

(2.21) by {3f.l(s 1+1) Uc(s1+ 1 ) and sum across states in period t + 1 . Use (2. 17), (2. 1 9), and (2.20) to obtain an equation that does not depend on Rb and 8. Since we can replace any of the N equations from (2.21) with this equation, there are only N + 1 equations left to determine Rb and 8. Thus there are N 1 degrees of

this, multiply

-

indeterminacy in setting the tax rate on capital and determining the return on debt. One particular set of policies supporting a competitive equilibrium has the capital tax rate not contingent on the current state. That is, suppose for each s 1,

(2.22) of (2.21)

We can then use (2. 1 9) to define 8(s 1 ) and use the period-t + 1 version to define R�;(s t+ 1 ). It i s straightforward t o check that the constructed return o n debt satisfies (2.20). Another set of policies supporting the same competitive equilibrium has the return on debt not contingent on the current state. [For details, see Chari et al. (1994), and for a more general discussion of this kind of indeterminacy, see Bohn

(1994). ] 0

If the competitive equilibrium associated with each policy is unique, clearly the Ramsey equilibrium is also unique. If there are multiple competitive equilibria associated with some policies, our definition of a Ramsey equilibrium requires that a selection be made from the set of competitive equilibria. We focus on the Ramsey equilibrium that yields the highest utility for the government. Given our characterization of a competitive equilibrium, the characterization of this Ramsey equilibrium is immediate. We have Proposition 6. The allocations in a Ramsey equilibrium solve the following programming problem:

(2.23)

s'

subject to (2. 7) and (2.8). For convenience, write the Ramsey allocation problem in Lagrangian form:

t, subject to (2.7). The function s1

(2.24)

W simply incorporates the implementability constraint into the maximand and is given by

(2.25) where A is the Lagrange multiplier on the implementability constraint, order conditions for this problem imply that, for t :?: 1 ,

Wt(s1)

·- -- ··

Wc(s 1 )

�

1

Ft(S )

(2.8). The first­ (2.26)

1 692

V.V. Chari and P.J. Kehoe

and

(2.27) A property of the Ramsey allocations which is useful in our analysis of the cyclical properties of optimal fiscal policy is the following. If the stochastic process on s follows a Markov process, then from Equations (2.26) and (2.27) it is clear that the allocations from period 1 onward can be described by time-invariant allocation rules c(k, s; A), l(k, s; A), k'(k, s; A), and b(k, s; A). The period-0 first-order conditions include terms related to the initial stocks of capital and debt and are therefore different from the other first-order conditions. The period-0 allocation rules are thus different from the stationary allocation rules, which govern behavior from period 1 onward. Thus far, we have considered a tax system with capital income taxes and labor income taxes. A wide variety of other tax systems lead to the same Ramsey allocation problem. For example, consider a tax system that includes consumption taxes, denoted rc(s1), as well as labor and capital income taxes. For such a system, the implementability constraint is given by

L f)1 tJ(s 1 ) [ Uc(s 1 ) c(s 1 ) + Ut(s 1 ) l(s 1 )] l,s1

=

� \

(so [Rk(so ) LJ + Rb(so ) b_ I ] , c ( + Teo

(2.28) where Rk(s0) 1 + [ 1 - (;l(s0)][Fk (s0) - b] and Teo is the tax rate on consumption in period 0. The first-order conditions of the competitive equilibrium with such a tax system are given by =

(2.29) and (2.30) where Rk(s t+ 1 ) 1 + [ 1 - {;l(s 1+ 1 )] [Fk(s 1 1 1 ) -- b]. Inspection of these first-order conditions shows that if an allocation satisfies the implementability constraint (2.28) and the resource constraint (2. 1 ) , it can be decentralized as a competitive equilibrium under a variety of tax systems. Examples of such tax systems include those with only consumption taxes and labor income taxes and those with only consumption taxes and capital income taxes. More complicated examples include those in which tax rates on capital and labor income are required to be the same, but are allowed to be different from tax rates on consumption. The message of this analysis is that optimal tax theory implies optimal wedges between marginal rates of substitution and marginal rates of =

Optimal Fiscal and Monetary Policy

Ch. 26:

1 693

transformation and is typically silent on the detailed taxes used to implement these wedges. Recall that with a capital and labor income tax system, we ruled out lump-sum taxes by imposing a constraint on period-0 capital income taxes. In a consumption and labor tax system, an analogous constraint is necessary. Notice that if consumption taxes are constant so that Tc (s 1 ) = Teo for all s and that if labor is subsidized appropriately so that T(s 1 ) = - Teo, then (2.29) and (2.30) become the undistorted first-order conditions. By setting Teo arbitrarily high, it is possible to satisfy (2.28) at the lump-sum tax allocations and thus to achieve the undistorted optimum. One way to rule this out is to impose an upper bound on Tc0- (There seems to be some confusion about this point in the literature.)

1

Capital income taxation 2.2. 1 . In a steady state 2.2.

Here we develop the results on the optimality of zero capital income taxes in a steady state, and we consider various generalizations and qualifications for that result. For simplicity, we consider a nonstochastic version of the model in which the stochastic shock in the production function is constant and government consumption is also constant, so g(s 1 ) = g. Suppose that under the Ramsey plan, the allocations converge to a steady state. In such a steady state, We is constant. Thus, from Equation (2.27), 1 = /3( 1 - D + Fk ) .

(2. 3 1 )

The consumer's intertemporal first-order condition (2. 1 9) in a steady state reduces to 1

=

/3 [ 1 + ( l

- 8)(Fk - l5)].

(2.32)

Comparing (2. 3 1 ) and (2.32), we can see that in a steady state, the optimal tax rate on capital income, e, is zero. This result is due to Charnley ( 1 980, 1 986). A natural conj ecture is that with heterogeneous consumers, a nonzero tax on capital income is optimal to redistribute income from one type of consumer to another. We examine this conjecture in an economy with two types of consumers, indexed i 1 , 2, whose preferences are given by =

OG

L f31Ui (cit , lit), t�O

(2.33)

where cit and /;1 denote the consumption and labor supply of a consumer of type i. Notice that the discount factors are assumed to be the same for both types of consumers. The resource constraint for this economy is given by (2.34) where the production function F has constant returns to scale. Notice that the production function allows for imperfect substitutability between the two types of labor

V. V. Chari and PJ. Kehoe

1 694

and capital. For this economy, the implementability constraints for the two types of consumers i 1 , 2 are given by =

(2.35) where kh and b!1 denote the initial ownership of capital and debt by consumers of type i 1 . If the tax system allows tax rates on capital income and labor income to differ across consumer types, then it is straightforward to establish that the resource constraint and the two implementability constraints completely characterize a competitive equilibrium. For the Ramsey equilibrium, we suppose that the government maximizes a weighted sum of consumers' utilities of the form 00

00

(2.36)

1 . The Ramsey problem where the welfare weights W; E [0, 1 ] satisfy w1 + OJ:2 is to maximize Equation (2.36) subject to the resource constraint (2.34) and the implementability constraints (2.35). Let us define

W(cJt, C2l, llt, l2t, }q , A2 )

=

L [W;Ui (cit, lit) + A;(U�[Cit + uj,lu)]

;�

1,2

(2.37)

for t ? 1 ; and for t = 0, W equals the right-hand side of Equation (2.37) evaluated at t 0 minus 2: A; U�0 (R�cokb + R bO bb ). Here A; is the Lagrange multiplier on the implementability constraint for the consumer of type i. The Ramsey problem is, then, to maximize =

C<J

L {)' W(cu, c21, lu, !2�> }q , A2 ) 1 �0

subject to the resource constraint (2.34). The first-order conditions for this problem imply that for In

a steady state,

Wet

i � l,2

and

t = 0, 1 , 2, . .

(2.38)

is a constant, and thus (2.39)

which as before implies that the steady-state tax on capital income is zero. This result is due to Judd ( 1 985). 1 Notice in (2.35) the initial assets are denoted kb and b0, while in (2.8) they are denoted k 1 and b_ 1 Throughout the chapter in detetministic environments initial assets have a subscript 0, while in stochastic environments initial assets have a subscript 1 . This unfortunate inconsistency stems from the tradition of using kt+ 1 to denote the capital choise in period t. �

Ch. 26:

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1 695

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 (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 of the capital taxes on intertemporal margins makes even the workers prefer the static distortion of 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 (2.4 1) Since the right-hand side of Equation (2.4 1 ) does not vary with

i,

the restriction (2.42)

holds in any competitive equilibrium. Thus Equation (2.42) is an extra restriction that must be added to the Ramsey problem. Let {.1 denote the Lagrange multiplier on (2.42). 1 Defining

where x1 = (c l t , C2 t, li t , l2 �> }"! , A2 ), 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 -

U£

1

·. ---

u�� Fw

=

1

-

T1 .

(2.43)

1 696

V.V. Chari and P.J Kehoe

Since the right-hand side of Equation (2.43) does not vary with i, the restriction

u,) u;; Fn t U}t U17 - F121 _

(2.44)

holds in any competitive equilibrium and thus must be added to the Ramsey problem. We proceed as before and, with no confusion, define (2.45) where v1 is the Lagrange multiplier on (2.44). A first-order condition for the Ramsey problem is

-f3 Vkt+ t + Vc tt = {3Vclt+ 1 [Fkt+ t + ( 1 - b)] . In a steady state, this reduces to

Clearly, unless Vk 0, the steady-state tax on capital income is not zero. Inspection 0 if and only if F1 1 /F121 does not depend of Equation (2.45) shows that Vk on k. Recall that the production function is separable between k and (It , 12) if Fn tfF121 does not depend on k . Such separable production functions can be written in the form F(k, 1� , !2) F(k, H(l1 , 12)) for some function H. [For some related discussion, see Stiglitz ( 1 987).] 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 from period 1 onward, while labor tax rates are unrestricted. Using the consumer's first-order conditions, we see that =

=

=

(2.46) together with the restriction that el+l across allocations:

�

el for all t > 1 , implies the following restriction (2.47)

The appropriate Ramsey problem, then, has constraints of the form (2.47), as well as the implemcntability constraint and the resource constraint. We leave it to the reader

Ch.

26:

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1 697

(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 throughout. 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 1 00 percent. Then in addition to satisfying the analogs of conditions (2.7) and ( 2 . 8), an allocation must satisfy an extra condition to be part of a competitive equilibrium. Rewrite the analog of Equation (2. 1 9) as (2.48) Then if an allocation satisfies (2.49) and 81+ 1 ::S; 1 , Equation (2.48) implies that (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 Charnley ( 1 986), 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 the form

U(c, l)

=

l -o C 1 + - (f

V (l).

(2.5 1 )

One might conjecture that 1 f utility functions o f this form have the property that optimal capital income taxes are exactly zero after period l , then for utility functions that are in

1 698

V.V. Chari and PJ Kehoe

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 (2.52) where q1+I f3 Uet+ I/Uct 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 right­ hand 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 =

P roposition 7 . For utility functions of 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 for t ;? 2. Equivalently,

(2.53)

Proof:

For

1 =

t ;? 1 , the first-order conditions for the Ramsey problem imply that

{3 Wet+ I 1 - u·' --( + Fkl+ I ), Wet

where W is given in Equation (2.25). For for capital imply that

1

=

[3

ucl+l [1 + (1 Uct

--

-

(2.54)

t ;?

1 , the consumer's first-order conditions

et l d (F"t+l - 0. From Equation (2.60), we obtain

b(G) = b(O) =

{3 [nV (G) + ( 1 - n) V(O) ] ' Uc(G) f3[n V(O) + ( 1 -- n) V ( G)] ' Uc(O)

and from Equation

, = R(G) R(O) =

(2.63), we

(2.n)

(2.73)

obtain

Uc(G)

73fnu�(c)-+(l_:_ Ji) uc (o)] '

Uc(O) f3[nUc(O) + ( l -- n) Uc (G)] "

(2.74) (2.75)

Combining these, we obtain expressions for the before-tax obligations of the government:

n V( G) + ( l - n) V (O) n Uc(G) + ( 1 - n) Uc(O) ' n V(O) + ( 1 - n) V (GL_ n U,. (O) + ( 1 - n) Uc (G)

R(G) h(G) =

(2.76)

R(O) b(O) =

(2.

Ch.

Optimal Fiscal and Monetary Policy

26:

1 705

Since H(G) < H(O), Equations (2.70) and (2.7 1 ) imply that V(G) < V(O). Using this result, n > � and Uc(O) < Uc(G), we can see that Equations (2.76) and (2.77) imply ' that

R(G) b(G)


v( G, G) and v(O, 0) > v( G, 0). To establish Equation (2.67), we need only show that v(G, G) > 0 > v(O, 0). But this follows from (2.64) and (2.79), using V(G) < V(O) and Uc(O) < Uc(G). 0 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 the 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 the economy is in wartime than if it is in peacetime, so

b(G)


h1 lu), where k, denotes the physical capital stock in period t, h, denotes the human capital stock in period t, and /11 denotes labor input to goods production in period t. Human capital investment in period t is given by h1G(l21 ) , where !21 denotes labor input into human capital accumulation and G is an increasing concave function. The resource constraints for this economy are (2.90) and (2.9 1 ) where c 1 i s private consumption, g i s exogenously given government consumption, and 15k and Dh are depreciation rates on physical and human capital, respectively. The consumer's preferences are given by 00

� (Jf c} 0V(l l t + lzt )l(l - 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

V. V. Chari and PJ Kehoe

1712

and by debt. Let r, and 81 denote the tax rates on the income from labor and capital. Government debt has a one-period maturity. Let bt+ 1 denote the number of units of debt issued in period t and Rb1 b1 denote the payoff in period t. The consumer's budget constraint is (2.92) where R1a 1 + ( 1 81 )(r1 is the gross return on capital after taxes and depreci­ ation and r1 and w1 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 (2.9 1 ) and (2.92). We assume that consumer debt holdings are bounded above and below by some arbitrarily large constants. Competitive pricin�: ensures that the return:> to factor inputs equal their marginal products, namely, tha' =

-

-b)

r1 = Fk(k1, h,lu), (2.93) (2.94) Wt = Ft (kt, htlu). We let x1 = (c1 , l1 �o !21 , k1 , h 1 , b1 ) denote an allocation for consumers in period t and let x (x1 ) denote an allocation for all t. The government's budget constraint is =

(2.95) We let lft (It, et) denote the government policy at period t and let J[ = (nt) denote the infinite sequence of policies. The initial stock of debt, b . 1 , and the initial stock of capital, /c 1 , are given. A competitive equilibrium is defined in the usual way. We have the following proposition. =

The consumption allocation, the labor aliocation, 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 Proposition 10.

(X)

L iYcr Uct '� Ao,

(2.96)

t�O

where

b1z + G(l2o� .

J

G' (lzo ) Furthermore, given any allocations and period-0 policies that satisfy (2.90), (2.91), (2.96), and

Ult f3 Ult+! f3Utt+l /lt+l --;;,; ' �(2 .97) 1 : G ( l2 H J )J + -ht G'(lztS h1+ 1 c'az�: �5 [ we can construct policies, prices, and debt holdings which, together wtth the given allocations and period-0 policies, constitute a competitive equilibrium. =

�

· u"

,

-

Ch.

26:

Optimal Fiscal and Monetary Policy

1713

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 procedure 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 Proof:

{Jf U,t = At . -(31 U11 = Jc1 ( 1 -- r,) w,h r, 1 -(3 Utt �Lt htG' U2t ) , -�lt + �t+l [ 1 - (jh i G(£21+1 )] + At+ ] ( 1

(2.98) (2.99) (2. 1 00)

=

ft+d Wt+l / lt+ l

=

(2. 1 0 1 )

0.

Multiplying Equation (2. 1 0 1 ) by h n 1 , substituting for {l1 and � 1 1 from (2.99) and 1 (2. 1 00), and using Equation (2. 9 1 ), we obtain

- A1( 1 - T1 ) w1ht+l G' (l2t)

+

Att t ( l - Tt+J ) Wt+J ht+2 + At+l ( l - 'lt-rl ). Wt+l l l t l l hI l l - 0 . G'(l2t+ J ) _

__

(2. 1 02)

From Equation (2. 1 02) and a standard transversality condition, we know that (2. 1 03) Similarly, we can show that oc

(XJ

t�O

t�l

(2 . 1 04)

Next, we multiply the consumer budget constraint (2.92) by A1 and sum from period 0 onward. When we use (2. 1 03) and (2. 1 04), (2.96) follows. To derive (2.97), we substitute (2.99) into (2. 1 02). We leave it to the reader to prove the converse. D The Ramsey problem is to maximize consumer utility subject to conditions (2.90), (2.9 1 ), (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.

V. V. Chari and PJ. Kehoe

1714

Proposition 1 1 . Suppose that the Ramsey allocations converge to a balanced growth path. In such a balanced growth path, all taxes are zero.

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(c1 , l i t + l21 ; A) = U(c1 , l1 1 + /21 ) + Ac1 Uc1 , where A is the Lagrange multiplier on (2.96). For our specified utility function,

Proof:

The Ramsey problem is to maximize

subject to (2.90), (2. 9 1 ), 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 . 0 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(c�, !1 + !2) + 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) = ag1 -0/(1 - a), 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 i n a closed economy because i n the open economy capital is mobile and can flow to the country with the highest rate of return. We consider a small open economy that takes the rates of return on saving in the rest of 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 of 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 of ownership. Residence­ based taxes are taxes that governments levy on the income of their residents regardless of 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 ( 1 995) 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 rt denote the world rental rate on capital absent any domestically levied taxes. The firm's problem is to solve

maxF(kr, Zt ) - ( 1 + 8ft) r1* kt - ( 1 + Tjt) Wr lr, where f)ft and T_tt are the source-based tax rates on capital and labor.

The first-order

conditions are

8ft r; = Fkr - r1* ,

(2. 1 05)

TjtWt F,t - w,.

(2. 106)

=

Consumers solve 00

max 2�)Y U(c1 , l1 )

(2. 1 07)

t�O

subject to

2.:Pt Ct LPrWr ( l - TctH, t�O t�O where Pt = rr: ( l!Rs ), Rs = 1 + ( l

(2. 1 08)

=

f)c_.)(rs -- 6), Po 1 ()s and I's are the residence� I ' based tax rates on capital and labor, and initial assets are set to zero for convenience. The consumer first-order conditions are summarized by �

=

(2. 1 09) (2. 1 1 0)

VV Chari and PJ. Kehoe

1716

The economy-wide budget constraint (which is simply the sum of the consumer and government budget constraints) is given by ()()

00

(2. 1 1 1 )

where q1 = It� 1 ( 1/R;) and R; = r; + 1 D . Notice that the economy as a whole borrows and lends at the before-tax rate R; , while consumers borrow and lend at the after-tax rate R.,. . Intuitively, we know that any taxes on borrowing or lending levied on consumers are receipts of the government and cancel out in their combined budget constraint. N otice also that in the closed economy models studied in earlier sections, the competitive equilibrium has consumer budget constraints, a government budget constraint, and a resource constraint. In this small open economy, there is no resource constraint, and it is convenient to replace the government budget constraint by the economy-wide budget constraint. To derive the constraints for the Ramsey problem, substitute the consumer first-order conditions into Equation (2. 1 08) to get the implementability constraint -

oc

L f:Jf[ Uct Ct + Ult lt] = 0,

(2. 1 12)

t�O

where we have used the fact that Equation (2. 1 1 0) implies that p1 = fY Ucr!Uco . N ext, notice that the first-order conditions of the firm and the consumer can be summarized by Equations (2. 1 05), (2. 1 1 0), and (2. 1 1 3) Thus, for each marginal condition, there is at least one tax rate so that the tax system is complete and there are no additional constraints on the Ramsey problem. Thus, with both source- and residence-based taxes available, the Ramsey problem is to maximize Equation (2. 1 07) subject to (2. 1 1 1 ) and (2. 1 1 2). With purely source-based taxation, ret 8c1 0, so from Equation (2. 1 1 0) it is clear that for such a tax system, the Ramsey problem has the additional constraint =

=

With purely residence-based taxation, Tti 81 1 0, so from Equation (2. 1 05) it is clear that the Ramsey problem has the additional constraint =

=

Ch. 26:

Optimal Fiscal and Monetary Policy

1717

Consider the Ramsey problem when both source- and residence-based taxes are available. For convenience, write the problem as max

CX)

2.:J31 W(c l , ?c) 1,

t�O

1

subject to (2. 1 1 1), where W(c1, l1, A) condition for capital implies that (2. 1 1 4) while the first-order condition for consumption implies that (2. 1 1 5) From Equation (2. 1 14) it is clear that setting 8ft 0 for all that this small economy will have a steady state only if =

t is optimal.

Next, note

(2. 1 1 6) for all t. Under this parameter restriction, Equation (2. 1 1 5) implies that Wet = Wc11 1 , and thus the Ramsey allocations are constant, so in particular, Uct = Uc� 1 1 • Equations (2. 1 1 0) and (2. 1 1 6) imply that Bet = 0 for all t. Under a system with only source-based taxes, the Ramsey problem is to maximize "£�0 fJI W(c1, lt Jc) subject to conditions (2. 1 1 1) and (2. 1 1 5). If we consider a relaxed version of this problem with the constraint (2. 1 1 5) dropped, the above analysis makes clear that the solution to this relaxed problem satisfies this dropped constraint and hence solves the original problem. The first-order condition for capital then implies (2. 1 1 4); hence, eji = 0 for all t. Similarly, under a system with only residence-based taxes, the Ramsey problem is to maximize "£� 0 f31 W(c1 , l1 , A) subject to conditions (2. 1 1 1 ) and (2. 1 1 4). If we consider a relaxed version of this problem with the constraint (2. 1 1 4) dropped, the above analysis makes clear that the solution to this relaxed problem satisfies this dropped constraint and hence solves the original problem . The first-order condition for consumption in the relaxed problem is (2. 1 1 5). Under the parameter restriction (2. 1 1 6), Wet = Wet+ 1 ' so Ucr = Uct+ I . Hence, equations (2. 1 1 0) and (2. 1 1 6) imply that eel = 0 for all t. In sum: .

Under a system with both source- and residence-based taxes, all t. Under a system with only source-based taxes, eft = 0 for all t. Under a system with only residence-based taxes, with the additional restriction (2. 116), Bet 0 for all t.

Proposition 12.

e1r

=

=

Bet

=

0 for

V. V Chari and PJ Kehoe

1718

Notice that the Ramsey allocations from the problem with both source- and residence-based taxes can be achieved with residence-based taxes alone. With the additional restriction (2. 1 1 6), the allocations from the problem with both types of taxes can be achieved with source-based taxes alone. The intuition for why source­ based taxes are zero is that with capital mobility, each country faces a perfectly elastic supply of capital as a factor input and therefore optimally chooses to set capital income taxes on firms to zero. The intuition for why residence-based taxes are zero is that under (2. 1 1 6) the small economy instantly jumps to a steady state, and so the Chamley­ type logic applies for all t. 2.4. 3.

Overlapping generations models

The discussion thus far has focused on models with infinitely lived agents. There is also an extensive literature on optimal policy in overlapping generations models. [See, for example, Atkinson ( 1 97 1 ), Diamond ( 1 973), Pestieau ( 1 974), and Atkinson and Sandmo ( 1 980); the surveys by Auerbach ( 1 985) and Stiglitz ( 1 987); and the applied work of Auerbach and Kotlikoff ( 1 987) and Escolano ( 1 992).] The results in this literature are much weaker than those in standard models with infinitely lived agents. One reason is that in a life cycle model, agents have very heterogeneous preferences over the infinite stream of consumption goods. For example, in a two­ period overlapping generations model, an agent of generation t values consumption goods only in periods t and t + 1 . In this subsection, we show that tax rates on capital income in a steady state are zero if certain homotheticity and separability conditions are satisfied. This result is well known. For an exposition using the dual approach, see, for example, Atkinson and Stiglitz ( 1 980). Here we follow the primal approach used by Atkeson et al. ( 1 999) and Garriga ( 1 999). In this sense, the proposition we prove is more closely connected to the results on uniform commodity taxation than to the results on zero capital taxation in infinitely lived agent economies. We briefly develop a formulation of optimal fiscal policy in an overlapping generations model. Consider a two-period overlapping generations model with a constant population normalized to 1 . The resource constraint is

cu + Czt + k,+ + g = F(k1, lJt, lzt) + ( 1 - D) k�> (2. 1 17) where c11 and c21 denote the consumption of a represemat1ve young agent and a representative old agent in period t, !11 and /21 denote the corresponding labor inputs, k, denotes the capital stock in t, and g denotes government consumption. Each young 1

agent in

t solves the problem

max U (CJt, lJt) + f3U(czt 1 1 , l2t+t ) subject to

CJt + kt+1 + ht.i and

�

(1

TJt ) W]tflt

c21+J = ( 1 - Tzn J ) W2t+ 1 12t+1 + [ 1 + ( I - 8t+ J )(rt+ 1 D)] kt+l + R,+t bt+l ,

Ch. 26:

1719

Optimal Fiscal and Monetary Policy

where T1 1 and Tz1 are the tax rates on the two types of labor inputs and 81 is the tax rate on capital income. The government budget constraint is

To define an optimal policy, we need to assign weights to the utility of agents in each generation. We assume that the government assigns weight )./ to generation t with A < 1 . Then the Ramsey problem can be written as 00

t [U(clr, llr ) + f3 U(c2t l l , l2r+J )]

max U(czo, lzo)IA + L A

t�O

subject to the resource constraint for each

t

and

R(c lr, llt ) + f3R(czt 1 J , l2t l l ) = 0 for each t, where R(c, l) cUc(c, l) + lU1(c, l) and U(c20 , !20)

(2. 1 1 8)

is the utility of the initial = old. There is also an implementability constraint for the initial old, which plays no role in our steady-state analysis. Constraints (2. 1 1 8) are the implementability constraints associated with each generation. It is straightforward to show that if the solution to the Ramsey problem converges to a steady state with constant allocations (cJ t, lJ1, czt+h l2t+l, kt+1 ) (c 1 , / 1 , c2, /2, k), then the Ramsey allocations satisfy =

1

�

A

= F,." + 1 � b.

(2. 1 1 9)

In a steady state, the first-order condition for capital accumulation is (2. 120) Inspecting these equations, we see that unless

Uc(c� , /J ) A f3Uc(Cz, lz) 1

(2. 1 2 1 )

the tax rate on capital income i s not zero. l n general, we would not expect this condition to hold. Notice the contrast with infinitely lived representative consumer models in which, in a steady state, the marginal utility of the representative consumer Uc(ct . It ) is constant. In an overlapping generations model, we would not expect the marginal utility of a consumer to be constant over the consumer's lifetime. If the utility function is of the form

c i--a V (l) U(c, l) = ----+ 1 -- a then we can show the following:

(2. 1 22)

V. V. Chari and PJ. Kehoe

1 720

the utility function is of the form (2. 122), then in a steady state, the optimal tax on capital income is zero.

Proposition 13. If

Proof: To prove this, consider the first-order conditions for the Ramsey problem for consumption evaluated at a steady state:

Uc 1 + atRcl = �tt,

f)[ Uc2 + arRcz]

=

(2. 123)

A�t ,

(2. 1 24)

where },/ �t1 and A 1 a1 are the multipliers on (2. 1 1 7) and (2. 1 1 8), respectively. We can easily see that a1 and �� are constant in a steady state. With a utility function of the form (2. 1 22), Rc is proportional to Uc so that (2. 1 23) and (2. 1 24) imply (2. 12 1 ). D The key properties used in proving this result are homotheticity of the utility function over consumption and the separability of consumption and leisure. In this sense, this proposition is more closely connected to the results on uniform commodity taxation than to the results on zero capital taxation in infinitely lived agent economies. When A f) and F(k, !1 , !2) = F(k, !1 + !2 ) then one can show that for all strictly concave utility functions the optimal tax on capital income is zero in a steady state. [See Atkeson et al. ( 1 999).] =

3. Monetary policy

In this section, we study the properties of monetary policy in three monetary economies. Friedman ( 1 969) argues that to be optimal, monetary policy should follow a rule: set nominal interest rates to zero. For a deterministic version of our economy, this would imply deflating at the rate of time preference. Phelps ( 1 973) argues that Friedman's rule is unlikely to be optimal in an economy with no lump-sum taxes. Phelps' argument is that optimal taxation generally requires using all available taxes, including the inflation tax. Thus Phelps argues that the optimal inflation rate is higher than the Friedman rule implies. In this section, we set up a general framework that allows us to analyze Phelps' arguments. We analyze them in three standard monetary economies with distorting taxes: a cash-credit model, a money-in-the-utility-function model, and a shopping-time model. The conditions for the optimality of the Friedman rule in the first two economies are analyzed by Chari et al. ( 1 996), while those for the shopping-time model are extensively analyzed in the literature. [Sec Kimbrough ( 1 986), Faig ( 1 988), Woodford ( 1 990), Guidotti and Vegh ( 1 993), and Correia and Teles ( 1 996), as well as Chari et al. ( 1 996).) In this section, we show that the Friedman rule is optimal when simple homotheticity and separability conditions are satisfied. These conditions are similar to the ones developed in the uniform taxation results in Section 1 . We explore the cormection between the optimality of the Friedman rule and the intermediate-goods result. For all three monetary economies, when the homotheticity

Ch. 26:

Optimal Fiscal and Monetary Policy

1721

and separability conditions hold, the optimality of the Friedman rule follows from the intermediate-goods result. To prove this, we show that under such conditions, all three monetary economies can be reinterpreted as real intermediate-goods economies, and the optimality of the Friedman rule in the monetary economies follows directly from the intermediate-goods result in the reinterpreted real economies. In contrast, when these conditions do not hold, there is no such connection. To prove this, we show that when these conditions do not hold, there are two possibilities. First, there are monetary economies in which the Friedman rule holds which cannot be reinterpreted as real intermediate-goods economies. Second, there are monetary economies which can be reinterpreted as real intermediate-goods economies but in which the Friedman result does not hold. Finally, we conduct some numerical exercises designed to develop quantitative featnres of optimal monetary policy. We find that if debt has nominal non-state­ contingent retnrns, inflation can be used to make real returns state-contingent so that debt can serve as a shock absorber. 3. 1 .

Three standard monetary models

3. 1 . 1.

Cash-credit

Consider a simple production economy populated by a large number of identical, infinitely lived consumers. In each period t = 0, 1 , . . . , the economy experiences one of finitely many events s • We denote by s1 = (s0, . . . , s ) the history of events up to 1 1 and including period t. The probability, as of period 0, of any particular history s1 is �J(s1). The initial realization so is given. In each period t, the economy has three goods: labor and two consumption goods, a cash good and a credit good. A constant returns to scale technology is available to transform labor /(s 1 ) into output. The output can be used for private consumption of either the cash good c1 (s1) or the credit good c2(s 1 ) or for government consumption g(s1). The resource constraint in this economy is thus

(3 . 1 ) The preferences of each consumer are given by (3.2) s'

where the utility function U is strictly concave and satisfies the Inada conditions. In period t, consumers trade money, assets, and goods in particular ways. At the start of period t, after observing the current state s�> consumers trade money and assets in a centralized securities market. The assets are one-period, non-state-contingent nominal

1 722

V.V. Chari and P.J Kehoe

claims. Let M(s 1 ) and B(s 1 ) denote the money and the nominal bonds held at the end of the securities market trading. Let R(s 1 ) denote the gross nominal return on these bonds payable in period t + 1 in all states s t+1 (s1 , s1 1 J ). Notice that the nominal return on debt is not state-contingent. After this trading, each consumer splits into a shopper and a worker. The shopper must use the money to purchase cash goods. To purchase credit goods, the shopper issues nominal claims, which are settled in the securities market in the next period. The worker is paid in cash at the end of each period. This environment leads to the following constraint for the securities market: =

M(st) + B(s t) R (s t-1 ) B(s t- l ) + M(s t-1 ) - p(st 1 ) c t (st-l ) -p(s t-l ) c2(5t-l ) +p(s t 1 )[1 r(st- 1 )] /(s t-t ) , =

__

(3.3)

where p is the price of the consumption goods and r is the tax rate on labor income. The real wage rate is 1 in this economy given our specification of technology. The left­ hand side of Equation (3.3) is the nominal value of assets held at the end of securities market trading. The first term on the right-hand side is the value of nominal debt bought in the preceding period. The next two terms are the shopper's unspent cash. The fourth term is the payments for credit goods, and the last term is the after-tax receipts from labor services. We will assume that the holdings of real debt B(s 1 )/p(s 1 ) are bounded above and below by some arbitrarily large constants. Purchases of cash goods must satisfy the following cash-in-aduance constraint: (3.4) We assume throughout that the cash-in-advance constraint holds with equality. We let

x(s 1 ) = (c 1 (s1), c2(s 1), l(s 1 ), M(s1), B(s1)) denote an allocation for consumers at s 1, and we let x = (x(s1)) denote an allocation for all s1• We let q (p(s 1 ) , R(s 1)) denote a price system for this economy. The initial stock of money M and the initial stock of 1 nominal debt B_ are given. 1 =

Money is introduced into and withdrawn from the economy through open market operations in the securities market. The constraint facing the government in this market is

M(:/) M(st-1 ) + B(s t) = R(s t 1 ) B(st- l ) +p(s t- 1 ) g(sr-l ) _ p(s t-1) r(s t-1 ) l(s t-1 ). _

(3.5) The terms on the left-hand side of this equation are the assets sold by the government. The first term on the right is the payments on debt incurred in the preceding period, the second term is the payment for government consumption, and the third term is tax receipts from labor income. Notice that government consumption is bought on credit. We let n = (r(s1)) denote a policy for all s 1• Given this description o f an economy, we now define a competitive equilibrium. A competitive equilibrium is a policy n, an allocation x, and a price system q such

Ch. 26:

Optimal Fiscal and Moneta;y Policy

1723

that given the policy and the price system, the resulting allocation maximizes the representative consumer's utility and satisfies the government's budget constraint. In this equilibrium, the consumer maximizes Equation (3.2) subject to (3.3), (3.4), and the bounds on debt. Money earns a gross nominal return of 1 . If bonds earn a gross nominal return of less than 1 , then the consumer can make profits by buying money and selling bonds. Thus, in any equilibrium, R(s 1) � 1 . The consumer's first-order conditions imply that U1 (s 1 )/U2(s 1 ) R(s 1 ); thus in any equilibrium, the following constraint must hold: =

(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 :rr = (r(s 1 )) 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(:rr) = (x(s 1 I :rr)) and q(:rr) = (p(s 1 I :rr) , R(s 1 I :rr) ) that map policies :rr into allocations and prices. A Ramsey equilibrium is a policy :rr, an allocation rule x(-), and a price system q(-) that satisfy the following: (i) the policy :rr maximizes

L f31fJ-(s1) U (c (s 1 I :rr), c2(s 1 I :rr), l(s 1 I :rr)) i

t, s '

subject to (3. 5), with allocations given by x(:rr), and (ii) for every :rr', the allo­ cation x(:rr' ) and the price system q(:rr' ), together with the policy :rr' , 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 _1 B_1 to zero. For convenience, let U;(s ' ) for i = 1 , 2, 3 denote the marginal utilities at state s 1 • Using standard techniques [for example, from Lucas and Stokey ( 1 983), Chari et al. ( 1 99 1 ), 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

(3.7) s'

V.V. Chari and P.J. Kehoe

1 724

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) where

w

is homothetic. We then have

Proposition 15. For utility functions of the form (3.8), the Ramsey equilibrium has R(s 1) = 1 for all s t

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 A denote the Lagrange multiplier on (3 . 7) and /)1 J-l(s 1) y(s 1) denote the Lagrange multiplier on (3 . 1 ) The first-order conditions for ci(s 1) for i = I , 2 in this problem are Proof:

.

(3.9) Recall from Section

I

that a utility function which satisfies (3 . 8) also satisfies (3 . 1 0)

Next, dividing Equation (3.9) by Ui and noting that U3jUi have that

=

V12/V1

for

i

=

I , 2, we

(3. 1 1 ) Using Equation (3 . 1 0), we have that the left-hand side of (3 . 1 1 ) has the same value for i 1 and for i 2. Therefore, U1 (s1)/U2(s ') = 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 U1 (s 1)/U2(s 1) R(s 1) and thus that R(s1) = l . D =

=

=

Now let us relate our results to Phelps' ( 1 973) arguments for taxing liquidity services. Phelps ( 1 973, 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 connection between the interest elasticity of money demand and the desirability of taxing liquidity services is, at best, tenuous.

Optimal Fiscal and Monetary Policy

Ch. 26:

1725

To see this, suppose that the utility function is of the form (3 . 1 2) Then the consumer's first-order condition U/U2 = R becomes

m -a = R' (c - m)a

(3 . 1 3)

---

where m is real money balances and c money demand 17 is given by 17

=

1

R llo -------0 1 + R 1 1a-l ·

=

c1 +

c2 . The implied interest elasticity of

(3 . 1 4)

-

Evaluating this elasticity at R gives 17 = 112a, 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 + a 1

log c +f(R),

wheref(R) is some invertible function of the interest rate. If a 1 = 1 , so the consumption elasticity of money demand is unity, this formulation implies that m/c = e ao+f (Rl , or that there is some function h such that h(m/c) = R. The consumer's first-order condition is U1 /U2 R. Thus U1 /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 production technologies, including those with capital accumulation. To see how, consider modifying the resource constraint (3 . 1 ) to =

(3 . 1 5) where k is the capital stock andf is a constant returns to scale function, and modifying the consumer's and the government's budget constraints appropriately. Let capital

V.V. Chari and P.J. Kehoe

1 726

income net of depreciation be taxed at rate 8(s 1), 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 1) = fi (s 1 ) R(s 1 ) Uz(s1) f2(s 1) . Thus the optimality o f the Friedman rule requires that U1 (s1)/U2 (s 1 ) = f1 (s 1)/f2 (s1). The constraint requiring that R(s 1 ) ? 1 now implies that

U1 (s 1) .fi (s1) ? Uz(s t) h.(s t) '

(3. 1 6)

and the implementability constraint (3.7) now reads

L L /31 ,u(s 1 ) [ U1 (s 1 ) c1 (s 1 ) + Uz(s 1 ) cz(s 1 ) + U3 (s 1 ) l(s 1 )] =

(3. 1 7)

Uc (so ) {[1 - 8(so )] [.fk (so ) - D)] } k_ l ,

where k_ 1 is the initial capital stock. Since the tax on initial capital 8(s0) 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 . 1 5), (3 . 1 6), and (3 . 1 7). For preferences of the form (3 .8), the analog of Equation (3. 1 1) has the right-hand side multiplied by /;(s1) for i = 1 , 2. This analog implies that U1 (s 1)/Uz(s1) fi (s 1 )/fz(s 1), 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 1 , 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 1 ) > 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(s1) 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 =

=

L L q(s 1 ) { [ 1 + r1 (s 1 )] c1 (s 1 ) + [ 1 s'

+

Tz(s 1 )] c2(s 1 )}

=

L q(s 1 ) l(s 1 ),

(3 . 1 8)

and the government's budget constraint is

L L q(s 1 ) g(s 1 ) = L L q(s 1 ) [rl (s 1 ) c 1 (s 1 ) + r2 (s 1 ) c2 (s 1 )] , s'

s'

(3 . 1 9)

where q(s 1) is the price of goods in period t and at state s 1 • 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

U1 (s1) U2(s 1 )

--

_ -

1 + Tt (s1) . 1 + T2(s 1 )

Thus Ramsey taxes satisfy r1 (s1) r2(s1) if and only if in the Ramsey allocation problem of maximizing Equation (3 .2) subject to (3 . 1) and (3.7), the solution has U1 (s1)/U2(s 1 ) = 1 . Recall from Proposition 3 in Section 1 that for utility functions of the form (3 .8), the Ramsey equilibrium has r 1 (s1) r2(s 1) for all s 1. Thus, with homotheticity and separability i n 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, ri(s 1 ) may not equal ij(sr) for t ;e 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 (3.20)

The first-order conditions for the Ramsey problem in the barter economy imply that

UJ (s 1 ) U2(s 1)

=

c 1 (s't� c2(s 1}-02

=

l + A(l - o2) 1 + A( l - 01 ) ·

(3.2 1 )

Clearly, U1 (s1) ; U2(s 1) i f and only i f 01 ; 02 . For cases i n which OJ = o2, these preferences satisfY condition (3 .6), and both uniform commodity taxation and the Friedman rule are optimal. If OJ > 02, 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 r1 (s 1 ) > r2(s 1 ), while in the monetary economy, it is accomplished by setting R(s 1 ) > 1 . More interestingly, when o1 < o2, uniform commodity taxation i s not optimal, but the Friedman rule is. To see this, note that when OJ < o2, the solution in the monetary economy that ignores the constraint UJ (s 1 ) ; U2(s 1) violates this constraint. Thus this constraint must bind at the optimum, and in the monetary economy, U1 (s ') = U2(s1). Thus, in the barter economy, taxing good 1 at a lower rate than good 2 is optimal, and this is accomplished by setting TJ (s 1) < r2(s1). In the monetary economy, taxing

VV. Chari and PJ. Kehoe

1728

good 1 at a lower rate than good 2 is not feasible, since R(s 1 ) ;? 1 , and the best feasible solution is to set R(s 1 ) 1 . =

In this subsection, we have focused on the Lucas and Stokey ( 1 983) 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

� U1� = RtPr f3 Uzt Pt+l where the period utility function is U (c1 l1 ) and R 1 is the nominal interest rate from period t to period t + 1 . Here, only the products R/(1 -- T1 ) and R1p/pt+ 1 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-junction

In this section, we prove that the Friedman rule is optimal for a money-in-the-utility­ function economy under homotheticity and separability conditions similar to those above. Consider the following monetary economy. In this economy, labor is transformed into consumption goods according to (3.22) (We use the same notation here as in the last subsection.) The preferences of the representative consumer are given by (3.23)

s'

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 1 ) c(s 1 ) + M(s 1 ) + B(s 1 )

=

M (s' 1 ) + R(s 1- 1 ) B(s '-1 ) + p(s ' ) [l - r(s 1 )] l(s 1 ). -

(3 .24) The holdings of real debt B(s')lp(s 1 ) are bounded below by some arbitrarily large constant, and the holdings of money are bounded below by zero. Let M_1 and

Ch. 26:

Optimal Fiscal and Monetary Policy

1 729

R_1 B_1 denote the initial asset holdings of the consumer. The budget constraint of the government is given by

B(s 1 ) = R(s 1- 1 ) B(s 1- 1 ) +p(s 1 ) g(s 1 ) - [M(s 1 ) - M(s 1- 1 )] -p(s 1 )[1 -- r(s 1 )]/(s 1 ).

(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 1 ) M(s 1)/p(s 1 ) denote the real balances in the Ramsey equilibrium. Using logic similar to that in Proposition 1 4, we can show that the consumption and labor allocations and the real money balances in the Ramsey equilibrium solve the Ramsey allocation problem =

(3.26) subject to the resource constraint (3 .22) and the implementability constraint (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 (3.28) Thus, for the Friedman rule to hold, namely, for R(s 1 )

=

1, it must be true that (3 .29)

Since the marginal utility of consumption goods is finite, condition (3.29) will hold only if U1 (s 1 ) 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 /, limm�oo Ut (m, c, l) = 0 and limm_,= 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 =

1 730

V. V. Chari and P.J Kehoe

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(s1)

� m,

(3.30)

where m is a finite bound. Consider preferences of the form

U(m, c, V(w(m, c), l), !)

where

w

(3.3 1 )

=

i s homothetic. We then have

Proposition 16.

optimal.

If

the utility function is of the form (3.31), then the Friedman rule is

The Ramsey allocation problem is to maximize Equation (3 .23) subject to (3 .22), (3.27), and (3 .30). Consider a less-constrained version of this problem in which constraint (3.30) is dropped. Let and A, denote the Lagrange multipliers on constraints (3.22) and (3.27). The first-order conditions for real money balances and consumption are

Proof:

{31fl(s1)y(s1)

(3.32) and (3.33)

) m(s1) U11 (s1) c(s1) Un (s1) m(s1) U12 + c(s1) Un(s1) U1(s 1) U2(s 1) +A)+ A [m(s1) U11 (s1)U1 +(s')c(s1) Un (s1) + l(s r) V21V1 (s(s1)1) ] U22(s1) + l(s1) V21(s1)J y(s1) , (l +A)+A [ m(s1) Ul2(s1)U2(s+ c(s1) V1 (s 1) U2(s') 1) y(s r2_ U2(s 1) m(s 1)

Since the utility function satisfies condition (3 . 3 1

,

it follows (as in Section 1) that

+

(3.34)

Using the form of Equation (3 . 3 1 ), we can rewrite conditions (3.32) and (3 .33) as =

(1

and

_

=

0

(3.35)

(3 .36)

From Equation (3.34), we know that =

0

(3 .37)

in the less-constrained problem. Hence the associated is arbitrarily large, and thus for any finite bound m, the constraint (3.30) binds in the original problem. The result then follows from (3.28). D

Ch. 26:

1731

Optimal Fiscal and Monetary Policy

Again, restricting w to be homogeneous does not reduce the generality of the result. Clearly, the Friedman rule is optimal for some preferences which do not satisfy condition (3.3 1 ). Consider (3.38) Note that for cases in which a1 * a2 , Equation (3 .38) does not satisfy condition (3 .3 1). 1 The first-order condition for the Ramsey problem for money balances m (s ) , when the upper bound on money balances is ignored, is (3.39) 1 Unless the endogenous Lagrange multiplier A just happens to equal (a1 - 1 )- , Equation (3 .38) implies that the Friedman rule is optimal. In related work, Woodford ( 1 990) considers the optimality of the Friedman rule within the restricted class of competitive equilibria with constant allocations and policies. Woodford shows that if consumption and real balances are gross substitutes, then the Friedman rule is not optimal. Of course, there are functions that satisfy our homotheticity and separability assumptions which are gross substitutes, for example, l a c i -a m U (m , c , l) = -- + -- + V (l).

1-a

1-a

The reason for the difference in the results arises from the difference implementability constraints. Woodford's problem is max U (m , c, l)

m

the

(3 .40)

subject to

c + g � l, U1 m + U2 c + U3l = ( 1 - (3) U1 ,

(3 .4 1 ) (3 .42)

where (3 .42) is the implementability constraint associated with a competitive equilib­ rium with constant allocations. The first-order conditions for our problem are similar to those for Woodford's problem, except that his include derivatives of the right-hand side of condition (3.42). Notice that in Woodford's problem, if (3 1 and preferences satisfy our homotheticity and separability conditions, then the Friedman rule is optimal. Notice, too, that if the model had state vmiables, such as capital, then constant policies would not typically imply constant allocations. To analyze the optimal constant monetary policy for such an economy, we would analyze a problem similar to that in Equation (3 .26) with extra constraints on allocations that capture these restrictions. [These restrictions would be similar in spirit to those in (2.47).] =

V.V. Chari and PJ. Kehoe

1 732

Shopping-time

3. 1 . 3.

In this subsection, we prove the optimality of the Friedman rule in a shopping-time monetary economy under appropriate homotheticity and separability conditions. Consider a monetary economy along the lines of Kimbrough ( 1 986). Labor is transformed into consumption goods according to

c(s1) + g(s 1) ::;; l(s 1 ).

(3 .43)

The preferences of the representative consumer are given by

L L f31 f.J(s') U (c(s1), l(s1) + ¢(c(s1), M(s1)/p(s1))) ,

(3 .44)

s'

where U is concave, U1 > 0, U2 < 0, 0, and 11{3. For all three parametrizations, the autocorrelation of the inflation rate is small or negative. Thus, in each, the inflation rate is far from a random walk. The correlations of inflation with government consumption and with the technology shock have the expected signs. Notice that these correlations have opposite signs, and in the baseline and high risk aversion models, this leads to inflation having essentially no correlation with output. The most striking feature of the inflation rates is their volatility. In the baseline model, for example, if the inflation rate were normally distributed, it would be higher than 20 percent or lower than -20 percent approximately a third of the time. The inflation rates for the high risk aversion model are even more volatile. The money growth rate has essentially the same properties as the inflation rate. The inflation rates in these economies serve to make the real ret11rn on debt state-contingent. In this sense, =

Ch. 26:

Optimal Fiscal and Monetary Policy

1739 B: Technology Shock

A: Government Consumption Shock

0,75

0

iU

� 8 2 .i'

Labor tax rate

0.5

0.25

Inflation rate -0.25

-0.5 0.2

0.4

0.6

0.8

Autocorrelation of government consumption shock

0.2

0.4

0.6

0.8

Autocorrelation of technology shock

Fig. I . Persistence plots of inflation rates and labor tax rates versus shocks to govemment consumption and technology: (a) government consumption shock; (b) technology shock.

debt, together with appropriately chosen monetary policy, acts as a shock absorber. The inflation rates are volatile in these economies because we have not allowed for any other shock absorbers. The results for the high risk aversion model are basically similar to those for the baseline model, with two exceptions. First, the correlation of the labor tax rate with the shocks has opposite signs from the baseline model. Changing the risk aversion changes the response of the marginal rate of substitution of consumption and leisure to the shocks. This change in the response alters the sign of the correlation. Second, and more significantly, the inflation rate in the high risk aversion model is substantially more variable and has a higher mean than the inflation rate in the baseline model. The reason for the difference is that the higher variability in the inflation rate increases the covariance term in Equation (3.59) and thus increases the average inflation rate. The results for the i.i.d. model are similar to those for the baseline model, with two exceptions. In the i.i.d. model, the autocorrelation of the labor tax rate and the autocorrelation of the inflation rate are quite different from their values in the baseline model. The labor tax rate has basically the same persistence properties as the underlying shocks - and so does the price level. A standard result is that if a random variable is i.i.d., its first difference has an autocorrelation of -0.5. The inflation rate is approximately the first difference of the log of the price level. Thus, in our i . i .d. model, the autocorrelation of the inflation rate is close to -0.5. We investigated the autocorrelation properties of the labor tax rate and the i nflation rate as we varied the autocorrelation (or persistence) of the underlying shocks. We found that the autocorrelation of both the labor tax rate and the inflation rate increased as we increased the persistence of the underlying shocks. Specifically, we set one shock at its mean value and varied the persistence of the other shock. In Figure IA, we plot the autocorrelations of the labor tax rate and the inflation rate as functions of the autocorrelation of govemment consumption. In Figure 1 B, we plot the autocorrelations

V. V. Chari and PJ Kehoe

1 740 A: Shock to Government Consumption

12

�

10

2

iii

" �

*

10

15

20

period

B: Labor Tax Rate

21

� 2 � X

2

20

0 "'

."l 19 0

10

15

20

period C: Inflation Rate

60

c 2 �

40 20

c 0 z ro

E

-20 -40

0

10

period

15

20

Fig. 2. Responses to government consumption shock: (a) the shock to government consumption; (b) labor tax rate; (c) inflation rate.

of these rates as functions of the autocorrelation of the technology shock. In both of these figures, the autocorrelations of the rates increase as the autocorrelations of the shocks increase. The inflation rate and money growth rate are close to i.i.d. These rates are positively correlated with government consumption and negatively correlated with the technology shock. As with the labor tax rate, these shocks have opposing effects on inflation and similar effects on output, implying that the correlation of inflation and money growth with output is roughly zero. To gain some intuition for the labor tax rates and the inflation rates, we simulated a version of the baseline model in which technology shocks were set equal to their mean levels so that the only source of uncertainty is government consumption. In Figure 2, we report a 20-period segment of our realizations. In Figure 2A, we see the shock to government consumption: this variable is constant at a low level from

Ch. 26:

1 74 1

Optimal Fiscal and Monetary Policy

period 0 t o period 5, is then high from period 6 t o period 12, and returns t o its low level from period 1 3 to period 20. In Figure 2B, we plot the optimal labor tax rates. These tax rates follow the same pattern: they are constant between periods 0 and 5, when government consumption is low; are slightly higher between periods 6 and 12, when government consumption is higher; and return to their low level between periods 1 3 and 20, when government consumption returns to its low level. The striking feature is that labor tax rates hardly fluctuate in response to the shocks. In Figure 2C, we plot the optimal inflation rate. There is a large inflation rate from period 5 to period 6, when government consumption rises to its higher level, and a large deflation rate from period 1 2 to period 1 3 , when government consumption falls. In periods without a change in government consumption, the inflation rate is roughly zero. To gain an appreciation of the magnitude of the shock absorber role of inflation, it is useful to trace through the effects of shocks on government debt, revenues, and expenditures. Using the analog of Proposition 7 for this economy, we can show that the allocations c(s 1 ), l(s 1 ), real money balances m(s 1 ), and real debt B(s 1 )/p(s 1 ) depend only on the current state s1 , while the change in the price level p(s 1 )/p(s 1- 1 ) depends on s1 _1 and s1 • We write these functions as c(s1 ), l(st ), m(s1 ), b(s1 ), and n(st- 1 , st ) · Consider now the government's budget constraint under the assumption that the economy in period t - 1 is at the mean level of government consumption and the mean level of the technology shock. Denote this state by s . Consider two scenarios. Suppose first that the economy in period t stays at s . We can rearrange the government's budget constraint to obtain

b(s)

=

[

m(S) 1 R(s) b(s) c- - + ( - [ g(s) - r(s) z(s) /(s)] - m(s) - ( JT s, s ) JT s, s) JT s, s) _ -

_ -

J.

(3 .60)

Suppose next that the economy in period t switches to state s', where g is higher and the technology shock is at its average level. The government budget constraint can then be written as

b(s' ) =

�

R(s b (s) n(s, s')

+

_(

[

J

1 s -_- [ g(s) -- r(s) z(S) l(s)] - m(s') - __1'11 )_ . n(s, s ') n(s, s')

(3 .61)

In both (3 .60) and (3 . 6 1 ), the term on the left is the new debt. The first term on the right is the inherited debt obligations net of the inflation tax. The second term on the right is the inflation-adjusted government deficit from period t - 1 . The inflation adjustment reflects that both government consumption and tax revenues are credit goods that are paid for with a one-period lag. The last term on the right is the seigniorage. Subtracting Equation (3.60) from (3 .61) gives the accounting identity 11 New

debt =

(-23)

11 Value

(-1 9)

of old debt

+ A Tanzi

(+ 1 )

effect -

11

Seigniorage,

(3 .62)

(+5)

where the Tanzi effect is the difference in the inflation-adjusted deficit. [See Tanzi ( 1 977).] (The numbers in parentheses are discussed below.)

1 742

V.V. Chari and PJ Kehoe

We can use our simulation to calculate the terms in Equation (3 .62). We normalize the economy so that mean output is 1 00 units of the consumption good. We consider an innovation in government consumption of 1 unit of this consumption good. This innovation leads to an increase in the present value of government consumption of 28 units of the consumption good. The numbers in parentheses below the terms in Equation (3 .62) are the changes in the relevant terms in units of the consumption good. The value of the old debt falls by 1 9 units because the sharp rise in inflation acts as a tax on inherited nominal debt. In our economy, the government debt is positive when the shocks are at their mean values. The government runs a surplus to pay the interest on the debt. A rise in the inflation rate erodes the value of the nominal surplus, leading to a Tanzi effect of 1 unit. The large inflation rate is, of course, due to a sharp rise in the money growth rate. The government collects 5 units of additional seigniorage by printing this money. Thus the new debt falls by 23 units. Since the present value of government consumption rises by 28 units, the present value of labor tax revenues needs to rise by only 5 units. This result implies that labor tax rates need to change by only a small amount. In this economy, the volatile inflation rate acts as a shock absorber, allowing the labor tax rate to be smooth. In essence, the government pays for 82 percent (23/28) of the increase in the present value of government spending by increasing the price level sharply, which taxes inherited nominal claims, and for only 1 8 percent (5/28) by increasing the present value of labor taxes. Note that our autocorrelation results are quite different from those of Mankiw ( 1 987). Using a partial equilibrium model, he argues that optimal policy implies that both labor taxes and inflation should follow a random walk. It might be worth investigating whether there are any general equilibrium settings that rationalize Mankiw's argument. In the models considered in this subsection, nominal asset markets are incomplete because returns on nominal debt are not state-contingent. The government, however, can insure itself against adverse shocks by varying the ex post inflation rate appropriately. These variations impose no welfare costs because private agents care only about the expected inflation rate and not about the ex post inflation rate. A useful extension might be to consider models in which ex post inflation imposes welfare costs. An open question is whether optimal inflation rates will be roughly a random walk if the welfare costs are high enough.

4. Conclusion

In this chapter we have analyzed how the primal approach can be used to answer a fundamental question in macroeconomics: How should fiscal and monetary policy be set over the long run and over the business cycle? We use this approach to draw a number of substantive lessons for policymaking. Obviously, these lessons depend on the details of the specific models considered. By and large we have considered

Ch. 26:

Optimal Fiscal and Monetary Policy

1 743

environments without imperfections in private markets, such as externalities and missing markets. In models with such imperfections, optimal policy not only must be responsive to the efficiency considerations we have emphasized, but also must attempt to cure the private market imperfections.

References Atkeson, A., VV Chari and P.J. Kehoe (1999), "Taxing capital income: a bad idea", Federal Reserve Bank of Minneapolis Quarterly Review 23(Smruner):3-17. Atkinson, A.B. (1971), "Capital taxes, the redistribution of wealth and individual savings", Review of Economic Studies 38:209-227. Atkinson, A.B., and A. Sandmo (1 980), "Welfare implications of the taxation of savings", Economic Journal 90:529--549. Atkinson, A.B., and J.E. Stiglitz (1 972), "The structure of indirect taxation and economic efficiency", Journal of Public Economics 1 :97-1 1 9. Atkinson, A.B., and J.E. Stiglitz (1 980), Lectures on Public Economics (McGraw-Hill, New York). Auerbach, A.J. (1 985), "The theory of excess burden and optimal taxation", in: A.J. Auerbach and M. Feldstein, eds., Handbook of Public Economics, vol. I (North-Holland, Amsterdam) 61-127. Auerbach, A.J., and L.J. Kotlikoff (1 987), Dynamic Fiscal Policy (Cambridge University Press, Cambridge). Backus, D.K., P.J. Kehoe and EE. Kydland (1 992), "International real business cycles", Journal of Political Economy 1 00:745-775. Barro, R.J. ( 1 979), "On the determination of the public debt", Journal of Political Economy 87:940-971 . Bohn, H . (1 994), "Optimal state-contingent capital taxation: when is there an indeterminacy?", Journal of Monetary Economics 34: 1 25-13 7 . Bull, N . (1 992), "Optimal taxation i n a n endogenous growth model with human capital", Ph.D. Dissertation (University of Minnesota). Cass, D. ( 1965), "Optimum growth in an aggregative model of capital accumulation", Review of Economic Studies 32:233-240. Chamley, C. (1980), "Optimal intertemporal taxation and the public debt", Cowles Foundation Discussion Paper 554 (Yale University). Charnley, C. ( 1 986), "Optimal taxation of capital income in general equilibrium with infinite lives", Econometrica 54:607-622. Chari, V V , and P.J. Kehoe (1 990), "Sustainable plans", Journal of Political Economy 98:783-802. Chari, VV, and P.J. Kehoe ( 1 993), "Sustainable plans and debt", Journal of Economic Theory 6 1 : 230--2 61 . Chari, VV, P.J. Kehoe and E.C. Prescott ( 1989), "Time consistency and policy", in: R.J. Barro, ed., Modern Business Cycle Theory (Harvard University Press, Cambridge, MA) 265-305. Chari, VV, L.J. Christiano and P.J. Kehoe ( 1991), "Optimal fiscal and monetary policy: some recent results", Journal of Money, Credit and Banking 23:5 19-539. Chari, VV, L.J. Christiano and P .J. Kehoe (1994), "Optimal fiscal policy in a business cycle model", Journal of Political Economy 1 02:6 1 7-652. Chari, VV, L.J. Christiano and P..J. Kehoe (1 996), "Optimality of the Friedman rule in economies with distorting taxes", Journal of Monetary Economics 37:203-223. Ch1istiano, L.J., and M. Eichenbaum ( 1 992), "Current real-business-cycle theories and aggregate labor­ market fluctuations", American Economic Review 82:430--450. Cooley, T.F., and G.D. Hansen ( 1989), "The inflation tax in a real business cycle model", American Economic Review 79:733 -748.

1 744

V V Chari and PJ. Kehoe

Cooley, T.F., and G.D. Hansen (1992), "Tax distortions in a neoclassical monetary economy", Journal of Economic Theory 58:290-3 16. Correia, I., and P. Teles ( 1 996), "Is the Friedman rule optimal when money is an inte1mediate good?", Journal of Monetary Economics 38:223-244. Diamond, P.A. ( 1 973), "Taxation and public production in a growth setting", in: J.A. Mirrlees and N.H. Stern, eds., Models of Economic Growth (Wiley, New York) 2 1 5-235. Diamond, P.A., and J.A. Min·lees ( 1 97 1 ), "Optimal taxation and public production I: Production efficiency", American Economic Review 6 1 : 8-27. Ekeland, I., and J. Scheinkman (1 986), "Transversality conditions for some infinite horizon discrete time optimization problems", Mathematics of Operations Research 1 1 :2 1 6-229. Escolano, J. ( 1 992), "Optimal taxation in overlapping generations models", manuscript (University of Minnesota). Faig, M. (1 988), "Characterization of the optimal tax on money when it functions as a medium of exchange", Journal of Monetary Economics 22:1 37-148. Friedman, M. (1 969), "The optimum quantity of money", in: The Optimum Quantity of Money and other Essays (Aidine Publishing Company, Chicago, lL) l-50. Garriga, C. (1 999), "Optimal fiscal policy in overlapping generations models", manuscript (University of Barcelona). Guidotti, P.E., and C. Vegh (1 993), "The optimal inflation tax when money reduces transactions costs: a reconsideration", Journal of Monetary Economics 3 1 : 1 89-205. Jones, L.E., R.E. Manuelli and P.E. Rossi ( 1 997), "On the optimal taxation of capital income", Journal of Economic Theory 73:93-1 17. Judd, K.L. (1 985), "Redistributive taxation in a simple perfect foresight model", Journal of Public Economics 28:59-83. Kimbrough, K.P. (1 986), "The optimum quantity of money rule in the theory of public fin ance", Journal of Monetary Economics 1 8:277-284. Koopmans, T.C. (1 965), "On the concept of optimal growth", in: The Econometric Approach to Development Planning (Rand McNally, Chicago, IL). Kydland, F.E., and E.C. Prescott (1 982), "Time to build and aggregate fluctuations", Econometrica 50: 1 345-1370. Lucas Jr, R.E. (1990), "Supply-side economics: an analytical review", Oxford Economic Papers 42: 293-3 1 6 . Lucas Jr, R.E., and N . L . Stokcy ( 1983), "Optimal fiscal and monetary policy i n an economy without capital", Journal of Monetary Economics 1 2 :55-93. Mankiw, N.G. ( 1 987), "The optimal collection of seigniorage: theory and evidence", Journal of Monetary Economics 20:327-3 4 1 . Marcct, A., T.J. Sargent and J . Seppala ( 1996), "Optimal taxation without state-contingent debt", manuscript (Stanford University). Pestieau, P.M. ( 1 974), "Optimal taxation and discount rate for public investment in a growth setting", Journal of Public Economics 3 : 2 1 7-235. Phelps, E.S. (1 973), "Inflation in the theory ofpublic finance", Swedish Journal of Economics 7 5 : 67-82. Prescott, E.C. (1 986), "Theory ahead of business cycle measurement", Federal Reserve Bank of Minneapolis Quarterly Review 1 O(Fall):9-22. Ramsey, F.P. (1 927), "A contribution to the theory of taxation", Economic Journal 37:47 -61 . Razin, A . , and E . Sadka (1 995), 'The status o f capital income taxation i n the open economy", FinanzArchiv 52:21-32. Stiglitz, J.E. ( 1 987), "Pareto efficient and optimal taxation and the new new welfare economics", in: A.J. Auerbach and M. Feldstein, eds., Handbook of Public Economics, vol. 2 (North-Holland, Amsterdam) 991-1042. Stock, J.H., and M.W. Watson ( 1 993), "A simple estimator of cointegrating vectors in higher order integrated systems", Econometrica 6 1 :783-820.

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Stokcy, N.L. ( 1 99 1 ), "Credible public policy", Journal of Economic Dynamics and Control l 5 : 627-656. Tanzi, V. ( 1 977), "Inflation, lags in collection, and the real value of tax revenue", International Monetary Fund Staff Papers 24: 1 54-1 67. Weitzman, M.L. ( 1 973), "Duality theory for infinite horizon convex models", Management Science 19:783-789. Woodford, M. ( 1 990), "The optimum quantity of money", in: B.M. Friedman and F.H. Halm, eds., Handbook of Monetary Economics, vol. 2 (North-Holland, Amsterdam) 1 067-1 1 52. Zhu, X. ( 1992), "Optimal fiscal policy in a stochastic growth model", Journal of Economic Theory 58:250-289.

AUTHOR INDEX

Abel, A.B. 8 1 8, 83 1 , 834, 835, 994, 1069, 1 237, 125 1 , 1 253, 1 265, 1 266, 1268, 1 27 1 , 1 272, 1 284, 1 285, 1 65 1 Abowd, J. 567, 568, 570, 57 1 , 6 1 6, 759 Abraham, J. I 039 Abraham, K.G. 1 058 Abraham, K.J. 1 1 83, 1 22 1 Abramovitz, M. 208 Abramowitz, M. 865, 887 Acemoglu, D. 852, 1 2 1 5 Adam, M. 500 Adams, C. 1 53 8 Adelman, F.L., see Adelman, 1 . 9 Adelman, L 9 Agenor, P.R. 1 543, 1 572 Aghion, P. 264, 665, 672, 7 1 5, 7 1 9, 1 1 57, 1 208, 1 2 1 0, 1 2 1 3, 1 377, 1 450, 1 454, 1 465 Aiyagari, S.R. 442, 547, 552, 566, 567, 983, 1 140, 1 293, 1 63 1 Aizcnman, J. 1 497, 1538, 1 540 Akaike, H. 2 1 7 Akerlot; G . 1 344 Akerlof, G.A. 1 98, 397, 1 034, 1 035, 1 039, 1 1 57, 1 200 al Nowaihi, A. 1 4 1 5, 1 422, 1 43 7 Alesina, A 1 62, 277-279, 692, 1 404, 1 4 1 6, 1 422-1 426, 1 430, 1 432, 1438, 1 439, 1 446, 1 449, 1 450, 1 454, 1 460, 1 46 1 , 1464-1466, 1469, 1 47 1 , 1 5 1 8, 1 522, 1 540 A1csina, A., see Tabellini, G. 1 456, 1465 Alessie, R. 774, 775 Allais, M. 661 , 1 309 Allen, D.S. 8 7 1 Allen, F. 576 Almeida, A. 1 432, 1 495 Alogoskoufis, G.S. 1 66, 2 1 4, 2 1 5 Altonji, J. 6 1 5 Altonji, J. , see Hayashi, F. 796 Altonji, J.G. 789 Altug, S. 584, 595, 61 1 , 6 12, 785, 786, 792 Alvarez, F. 575, 996 Ambler, S . 944, 1 062, 1 067 American Psychiatric Association 1 325

Amman, H.M . 368, 535 Anderson, E. 564 Anderson, E.W 368, 369 Ando, A., see Modigliani, F 762 Andolfatto, D. 994, 1 1 58, 1 1 73, 1 203, 1 207, 1 22 1 Andres, J., see Blanchard, OJ. 1 2 1 4 Araujo, A . 323 Arellano, M. 787 Arifovic, J. 455, 465, 472, 521-523, 525-527, 53 1 Arrow, K. 664, 1 03 3 , 1 042 Arrow, K.J. 1 2 1 8 Arthur, WB. 454, 476, 534 Ascari, G. 1 04 1 Aschauer, D.A. I 656, 1 657 Asea, P., see Mendoza, E. 1439 Ashenfelter, 0. 6 1 8, 1 03 8 , 1 039 Askildsen, J.E. I 074 Atkcson, A. 575, 6 1 0, 786, 847, 1 298, 1 675, 1 7 1 8, 1 720 Atkinson, A.B. 1 673, 1 676, 1 680, 1 682, 1 7 1 8 Attanasio, O.P. 564, 607, 608, 6 1 0-6 1 3, 752, 753, 756, 759, 769, 777, 779, 781 , 783, 784, 787, 789-794, 796, 797, 802, 1 264, 1 655 Auerbach, A.J. 3 80, 549, 576, 588, 590, 5 9 1 , 5 9 3 , 6 1 6, 82 ! , 1 624, 1 634, 1 63 5, 1 639, 1 652, 1 7 1 8 Auerbach, A.J., see Feldstein, M.S. 904, 906 Auernheimer, L. 1 449 Auster, R. 474 Autor, D. 57'1 Axilrod, S.H. 1 493 Azariadis, C. 262, 264, 271 , 289, 389, 395, 5 1 6, 527, 658, 660, 66 1 , 1 03 5

l-1

Bacchetta, P. 1 344 Bacchetta, P., see Feldstein, M. 1 637 Bachelier, L. 1 3 1 6 Backus, C.K. 549 Backus, D. 1 0 1 7, 1 03 1 , 1 270, 1 405, 1 4 14, 1415 Backus, D.K. 9 , 42, 45, 938, 1 3 1 6, 1708

Author Index

1-2 1432, 1 438 1 55, 1485, 1 5 1 5 Bagwell, K . 1 125 1 647 Bagwell, K., see Bernheim, B.D. Bailey, M.J. 1 643 Bairoch, P 7 1 9, 724 Baker, J. B. 1 1 25 Ba1asko, Y. 427, 506 Balassa, B.A. 705 Balke, N.S. 6, 6 1 , 1 14, 204, 205, 221 Ball, L. 42, 72, 1 99, 1 023, 1 037, 1 039, 1 04 1 , 1 1 27, 1 4 1 5, 1 499, 1 504, 1 542, 1 632, 1 650, 1 65 1 Ball, R . 1 32 1 Ballard, C . 1 639 Baneijee, A., see Aghion, P. 1 377 Bange, M.M., see De Bondt, W.F. 1 32 1 Banks, J. 75 1 , 758, 759, 770, 783, 788, 790-792 756, 759, 793, Banks, J., see Attanasio, O.P. 794 Banneijee, A. V 1 332 Bansal, R. 1 25 5 Barberis, N. 1 294, 1322 Barclays de Zoete Wedel Securities 1 238 Barkai, H. 1 572 Barnett, S. 8 3 1 Barnett, W 538, 540 Barone, E. 702 1 0 1 , 1 57, 1 58, 1 73 , 237, 245, 246, Barro, R.J. 252, 269, 27 1 , 272, 277-28 1 , 284, 643, 65 1 , 657, 659, 67 1 , 675, 68 1 , 683-685, 688, 689, 69 1 -694, 696, 943, 974, 1 023, 1 055, 1 1 55, 1 404, 1 405, 1 4 1 1 , 1412, 1 4 14, 1 4 1 5, 1 425, 1438, 1 439, 1 466, 1 485-1489, 1 637, 1 64 1 , 1 642, 1 645, 1 662, 1 675, 1 702, 1 705, 1 707 Barsky, R. 43, 558, 564, 565 Barsky, R., s e e Solon, G. 579, 1 058, 1 102, 1 1 06 Barsky, R., see Warner, E.J. 1 0 19 Barsky, R.B. 1 82, 2 1 5, 2 1 6, 1 149, 1 237, 1 277, 1 294-1296, 1 653 Barth, J.R. 1 657 Bartle, R.G. 76 Barucci, E. 525 Basar, T. 1 449 Basu, S. 399, 402, 433, 983, 992, 994, 1 069, 1 080-1082, 1 096, 1 097, 1 1 1 7, 1 142 Bates, D.S. 1 3 1 0, 1324 Banrnol, W.J. 252, 269 Bade, R.

Bagehot, W.

9, I I , 1 2, 45, 203, 380, 430, 934, 938, 974, 980, 992, 1 296, 1404 Bayonrni, T. 1 6 1 , 2 1 1 , 2 1 6, 2 1 7, 2 1 9 Bayoumi, T. , see Mussa, M . 208 Bazaraa, M.S. 33 1 1214 Bean, C., see Blanchard, O.J. Bean, C.R. 785, 1 497 Beaudry, P. 99, 395, 4 1 3, 592, 1 264 Beaulieu, .J.J. 801 , 802, 876 Becker, G. 592, 653 Becker, G.S. 3 1 7, 1 645 Becker, G.S., see Ghez, G . 6 15, 752, 759 Becker, R. 369 1 4 1 1 , 1 436, 1438 Beetsma, R. Bekaert, G. 1281 Bell, D.E. 1313 Bellman, R. 336, 340 Belsley, D. 882, 887, 888, 892 Beltratti, A. 524, 525 Ben-David, D. 265, 278 Ben Porath, Y. 577, 582 Benabou, R. 1 0 1 7 , 1 0 1 8, 1 03 1 , 1 128, 1 129, 1 469, 1472, 1 473 Benabou, R. 268 Benartzi, S. 1290, 1 3 1 2 , 1 3 1 3 Benassy, J. 507 Benassy, J.-P. 1 506 Benhabib, J. 283, 395, 399-405, 408, 4 1 2-4 1 4, 4 1 7, 4 1 9, 42 1 , 423-427, 43 1 , 433-435, 437, 442, 505, 550, 847, 1 145, 1 449, 1 465, 1 467, 1 472 1 450 Benigno, P., see Missale, A. Benjamin, D . 161 Bennett, R . 395 Bensaid, B. 1 446, 1 449 Benveniste, A. 476, 5 3 1 Benveniste, L.M. 3 2 1 1 0 1 9, 1 020 Bergen, M . , see Dutta, S. Bergen, M., see Levy, D. 1 0 1 4, 1 0 1 5, 1 0 1 9 Bergen, P.R. 1 04 1 Berger, L.A. 1 330 Bergstrom, V 538 Bcrnanke, B.S. 68, 72, 76, 83, 89, 91-93, 1 14, 1 44, 1 78, 1 82-1 84, 800, 856, 857, 1 036, 1 343, 1 345, 1 346, 1 352, 1 357, 1 3 6 1 , 1 363, 1 365, 1 3 69, 1 3 7 1 , 1 373, 1 376-1 378, 1495, 1 578 Bernard, A.B. 254, 27 1 , 287, 288 Bernard, V.L. 1 32 1 Bernheim, B.D. 1 646, 1 647, 1 649, 1 654, 1 659, 1 660 Baxter, M.

Author Index

Berry, M., see Dreman, D. 1 3 20 Berry, T.S. 1 6 1 8 Bertocchi, G . 474 Bertola, G. 643, 708, 801 , 82 1 , 834, 835, 840,

843, 1 1 87, 1 222, 1 472, 1 580 Bertsekas, D.P. 326 Besley, T. 856 Betts, C.M. 2 1 7 Beveridge, S. 1 062, 1 1 43 Bewley, T. 566, 1 1 55 Bhaskar, V. 1 03 7 Bianchi, M . 290, 292 Bikhchandani, S. 1 332 Bils, M. 694, 9 10, 912, 983, 1 053, 1059, 1 069,

1 070, 1072, 1 075, 1 076, 1 078-1081, 1 085, 1 087, 1 102, 1 1 04, 1 1 1 9, 1 120, 1 130 Bils, M.J. 579 Binder, M. 2 7 1 , 1092 Binmore, K. 462 Binmore, K.G. 1 1 88 Bisin, A. 427 Bismut, C., see Benabou, R . 1 0 1 7, 1 0 1 8, 103 1 Bizer, D. 380 Bjorck, A., see Dahlquist, G. 337 Black, F. 4 1 7, 1 280, 1 3 1 0, 1 3 3 1 , 1 507 Blackwell, D. 320 B1ad, M., see Benassy, l 507 Blanchard, OJ. 40---42 , 2 1 1 , 2 1 6, 2 1 7, 3 9 1 , 4 1 6, 47 1, 504, 643, 660, 8 1 8, 852, 877, 887, 888, 890, 892, 906, 9 1 2, I 0 1 3, 1030, 1 033, 1 034, 1 036, 1 04 1 , 1 1 12, 1 1 30, 1 1 62, 1 173, l l 76, 1 1 83, 1 1 84, 1 1 94, 1 202, 1 2 14, 1 22 1 , 1 266, 149 1 , 1 634, 1 635, 1645, 1 650 Blanchard, OJ., see Missale, A. 1450 Blank, R . 579 Blinder, A. 587, 750, 1 0 1 8--1020, 1038 Blinder, A.S. 41, 876, 8 8 1 , 887, 893, 903, 904, 907, 908, 91 0, 1 0 1 8, 1 085, I l l S, 1344, 1485, 1499, 1 660 Blinder, A.S. , see Bernanke, B.S. 83, 91, 93 Bliss, C. 1461 , 1465 Bliss, R., see Fama, E.E 1 280 Blomstrom, M. 277, 279, 280 Bloomfield, A. 156 Blume, L.E. 321, 322, 474 Blume, L.E., see Bray, M. 474 Blundell, R. 572, 602, 6 1 1 , 6 1 2, 620, 764, 770, 779, 7 8 1 , 783, 788, 790-792, 797 Blundell, R., see Banks, l 758, 759, 770, 783, 788, 790-792

I-3 Boadway, R. 1463 Bodnar, G. 1 3 1 8 Bohm, V 475, 646 Bohn, H . 1 465, 1 622, 1 650, 1691 Boldrin, M. 362, 399, 400, 506, 962, 1 062,

1284, 1 297, 1465 Bolen, D.W 1 325 Bollerslcv, T. 1 236, 1 2 80 Bolton, P., see Aghion, P. 1377, 1450, 1454,

1 465 Bona, J.L 3 1 3 Boothe, PM. 1 658 Bordo, M.D. 1 52, 1 55 - 1 60, 1 62, 1 64-167, 1 82,

1 84, 1 85, 1 94, 202-204, 207-209, 2 1 1 , 2 1 5, 2 1 7-221 , 1404, 1 438, 1 590 Bordo, M.D., see Bayoumi, T. 161 Bordo, M.D., see Betts, C . M . 2 1 7 Borenstein, S . 1 1 24 Boschan, C., see Bry, G. 8 Boschen, J.F. 139 Boskin, M.l 618 Bossaerts, P. 454 Bosworth, B., see Collins, S. 653 Bourguignon, F., see Levy-Leboyer, M. 222 Bovenberg, A.L. , see Gordon, R.H. 1 637 Bovenberg, L., see Beetsma, R. 1 4 1 1 Bowen, W 6 1 9 Bowman, D . 1 3 1 3 Boyd, W H ., see Bolen, D.W 1 325 Boyle, M., see Paulin, G. 751 Boyle, P. 380 Boyle, P.P., see Tan, K.S. 334 Brainard, WC. 8 1 7 Brauch, R., see Paulin, G. 75 1 Braun, R.A. 974 Bratm, S.N., see Krane, S.D. 876, 877 Brav, A. 1 290 Bray, M. 454, 463, 465, 466, 473---4 75, 527 Brayton, F. 1 043, 1 344, 1485 Brayton, F, see Hess, G.D. 1 485, 1 509 Breeden, D. 1 246 Breiman, L. 289 Bresnahan, T.F. 9 1 1 , 9 1 2 Bretton Woods Connnission 208 Broadbent, B. 1 4 1 2 Broadbent, B . , see Barro, R.l 1 4 1 2 Broadie, M., see Boyle, P. 380 Brock, W A . 3 1 9, 407, 455, 528, 532, 547, 552, 556, 942, 9 5 1 , 1 507 Brown, C. 585 Brown, P., see Ball, R. 1 3 2 1

I-4 Brown, S. 1 242 Browning, E. 1463 Browning, M. 598, 606, 607, 6 1 0-6 12, 750, 752, 7 7 1 , 778, 787, 792, 798, 803 Browning, M., see Attanasio, O.P. 607, 608, 6 1 0, 6 1 1 , 6 1 3, 779, 789, 791 , 1 655 Browning, M., see Blundell, R. 6 1 1 , 6 1 2, 779, 7 8 1 , 783, 790, 791 Broze, L . 487, 488 Brugiavini, A. 775 Brugiavini, A., see Banks, J. 770, 788 Brumberg, R., see Modig1iani, F. 761 Brumelle, S.L., see Puterman, M.L. 336, 338 Brunner, A.D. I 04 Brunner, K. 179, 1 83, 1 9 1 , 1 025, 1 491 Bruno, M. 471 , 1 090, 1496, 1 538, 1 539, 1 543, 1 553 Bry, G. 8 Bryant, R.C. 1 043, 149 1 , 1 497, 1 5 1 6 - 1 5 1 8 Bryant, R.R. 1 3 J 3 Buchanan, J.M. 1 63 1 , 1 642 Buchholz, T.G. 1643 Buckle, R.A. 1 0 1 9 Bufman, G. 1 543 Buiter, W. 1 030, 1 52 1 Bulirsch, R., see Stoer, J. 334 Bull, N. 1 675, 1 7 1 1 Bullard, J. 466, 507, 509, 5 1 5, 526 Bullard, J., see Arifovic, J. 527 Bulow, J. 1 448, 1 449 Burdett, K. 1 173, 1 196 Bureau of the Census 1 6 1 8, 1 6 1 9 Burns, A.F. 5, 8 , 93 1 , 934 Burns, A.F., see Mitchell, W.C. 8, 44 Burnside, C. 399, 930, 980-985, 994, 1 078, 1 142, 1 1 62 Burt1ess, G. 6 1 8, 620 Butkiewicz, J.L. 1 621

Caballe, J. 578 Caballero, R.J. 399, 749, 7 7 1 , 794, 801 , 802, 82 1-823, 828, 830, 832, 834-838, 840-842, 844, 846, 847, 852, 855, 856, 994, 1 032, 1 1 57, 1 1 58, 1 1 60, 1 1 87, 1 2 1 0, 1 2 1 1 , 1 2 1 3 , 1 472 Caballero, R.J., see Bertola, G. 801 , 821 , 834, 840, 843, 1 1 87 Cagan, P. 1 57, 1 6 1 , 203, 1 534 Cage, R., see Paulin, G. 75 1 Calmfors, L. 1 2 1 4

Author Index

Calomiris, C.W. 1 69, 1 8 1 , 1 83, 1 87, 1 9 1 , 1 376 Calvo, G .A. 389, 397, 408, 419, 422, 1 030, 1 032, 1 034, 1 1 1 4, 1 346, 1 360, 1 363, 1 389, 1 400, 1415, 1428, 1 445-1447, 1449, 1450, 1 535, 1 538, 1 539, 1 546, 1 552, 1 5 54, 1 557, 1 563, 1 564, 1 568, 1 569, 1 57 1 -1 573, 1 5 82, 1 583, 1 5 87-1589, 1 5 9 1 , 1 592, 1 596, 1 597, 1 599-1603, 1 605 Cameron, S. 589 Campbell, J. 92 Campbell, J.R. 846, 847, 994 Campbell, J.Y. 763, 764, 769, 784, 930, 961, 1 120, 1 140, 1 14 1 , 1 145, 1 1 50, 1235- 1238, 1 25 1 , 1 255, 1 257, 1258, 1 26 1 , 1 264-1266, 1 268, 1 270, 1 272, 1 274, 1 275, 1280, 1 284, 1 286, 1290, 1 320, 1 655 Canavcsc, A.J. 1 543 Canetti, E.D., see Blinder, A.S. I 01 8, 1 1 1 8 Canje1s, E. 55 Canova, F. 283, 376, 377, 379 Cantor, R. 1344 Canzoneri, M.B. 1 59, 1 60, 1405, 1414, 1 4 1 5 , 1 507, 1 508 Capie, F. 1 54, 1 63, 222, 1438 Caplin, A. 849, 850 Caplin, A.S. 801 , 9 1 0, 1 03 1 , 1 032 Card, D. 580, 1 0 1 6, 1 1 48 Card, D., see Abowd, J. 567, 568, 570, 5 7 1 , 6 1 6, 759 Card, D., see Ashenfelter, 0. 1 038, 1 039 Cardia, E. 1 655 Cardia, E., see Ambler, S. 1 062, 1 067 Cardoso, E. 1 543 Carey, K., see Bernankc, B.S. 1 78, 1 82 Carlson, J. 473 Carlson, J.A. 904 Carlson, J.A., see Buckle, R.A. 1 0 1 9 Carlson, J.B. 1 04 Carlstrom, C. 1 348, 1 357, 1 368, 1 378, 1 379 Carlton, D. 1 1 29 Carlton, D.W. 1 0 1 8-1020 Carmichael, H.L. 1 1 55 Carpenter, R.E. 876, 881, 9 1 2, 1 344 Carroll, C.D. 567, 572, 573, 593, 759, 762, 769, 7 7 1 , 785, 788, 793, 1 264, 1 344, 1 653, 1 655 Case, K . E . 1323 Casella, A. 1463, 1 465 Caselli, F. 277-279, 283, 284, 286

Author Index

I-5

244, 246, 247, 295, 389, 5 1 6, 643, 649, 662, 942, 948, 1 673 Cass, D., see Balasko, Y. 427 Castaneda, A. 380 Cazzavilan, G. 426 Cecchetti, S.G. 1 82, 2 1 7, 876, 1 0 1 5, 1 0 1 6, 1 01 8, 1 01 9, 1 25 1 , 1 265, 1 270, 1272, 1 294, 1 296 Cecchetti, S.G., see Ball, L . 1 037 Chadha, B. 1 03 1 , 1 542 Chah, E . Y. 775 Chamberlain, G. 283, 286, 785 Chamberlain, T.W 1334 Charnley, C. 400, 85 1 , 1439, 1 673, 1 675, 1 693, 1 697, 1 699 Champsaur, , P. 53!), 463 Chan, L. 1321 Chan, L.K.C. 1 653 Chandler, L.V 1 76 Chang, C.C.Y., see Chamberlain, T.W. 1 334 Chari, V V 72, 1 24, 397, 422, 672, 697, 698, 700, 7 0 1 , 709, 7 1 5, 720, 722, 723, 974, 1 036, 1 037, 1 040-1 042, 1 37 1 , 1448, 1 449, 1459, 1488, 1489, 1 578, 1 673--1676, 1 69 1 , 1 699, 1 708- 1 7 10, 1 720, 1 723 Chari, VV, see Atkeson, A. 1 675, 1 7 1 8, 1 720 Chatterjee, S. 996, 1 126 Chatterji, S. 475, 507 Chattopadhyay, S.K , see Chatterj i, S. 475, 507 Chen, N. 1281 Chen, X. 476, 532 1 334 Cheung, C . S . , see Chamberlain, T. W. Chevalier, J.A. 1 122, 1 1 23 Chiappori, P.A. 39 1 , 395, 5 1 6 Childs, G.D. 882 Chinn, M., see Frankel, J. 1 497 Chirinko, R.S. 8 1 5 , 8 1 7, 1 058, 1 066, 1 086, 1 344, 1 367 592 Chiswick, B., see Becker, G. Cho, D. 278 Cho, I.-K. 455, 465, 524, 525 Cho, J.O. 974, 976, 1 025, 1 036 Cho, .T.O., see Bils, M. 983, 1 075, 1 079, 1 104 Chou, R.Y. 1 236, 1 280 Chou, R. Y., see Bollerslev, T 1 236, 1280 Choudhri, E.U., see Bordo, M.D. 1 84, 1 94 Chow, C.-S. 326, 334 Chow, G.C. 1 294 Christensen, L.R. 673, 688 Cass, D.

.

L .J. 43, 67-70, 83, 84, 89, 9 1 -94, 99, 1 08, 1 09, 1 14, 1 1 5, 1 24, 1 37, 143, 144, 3 14, 329, 330, 339, 347, 349, 350, 355, 362, 364, 367, 369, 370, 376, 377, 379, 426, 504, 547, 764, 881 , 888, 909, 952, 962, 974, 1 0 1 1 , 1 0 1 7, 1 0 1 8, 1 02 1 , 1 030, 1 038, 1 089, 1 100, 1 296, 1 365, 1 369, 1 708, 1 736 Christiano, L..T., see Aiyagari, S.R. 1 140 Christiano, L.J., see Bo1drin, M. 962, 1 284, 1 297 Christiano, L.J., see Chari, VV 72, 1 449, 1 673, 1 675, 1676, 1 69 1 , 1 699, 1708-17 1 0, 1720, 1 723 Chung, K.L. 299 Clarida, R. 95, 96, 1 36, 422, 1 364, 1 368, 1 486 Clark, D., see Kushner, H. 476 Clark, J.M. 816 Clark, K.B. 602, 1 1 73 Clark, P.B., see Mussa, M. 208 Clark, T.A. 1 73 Clark, T.E . 1 09 1 , 1 485 Cochrane, J. 1 1 20 1 0 1 , 2 1 1 , 796, 1 234, 1 246, Cochrane, J.II. 1 249, 1 296 Cochrane, J.H., see Campbell, J.Y. 1237, 1 25 1 , 1 284, 1 286 Coe, D.T. 265 2 1 1 , 395, 547, 967, 1 142, 1 503 Cogley, T. Cohen, D. 271 Cohen, D . , see Greenspan, A . 798, 844, 847 Cohn, R., see Modigliani, F. 1321 Cole, I-LL. 576, 1 1 63, 1 1 94, 120 1 - 1 203, 1 207, 1446, 1 449, 1 603 Cole, H.L., see Chari, V V 1 459 Coleman, T. 601 Coleman, W.J. 367, 380 Coleman II, W.J. I 14 Coleman II, W. J. , see Bansal, R. 1255 Collins, S. 653 Conference Board 43 Congressional Budget Office 1 6 1 8, 1 6 1 9, 1 62 1 , 1 624-1 627, 1 639, 1 640, 1 660 Conley, J M. , see O'Barr, W.M. 1 332 Conlon, J.R. 1032 Constantinides, G.M. 559, 567, 78 1 , 803, 1 237, 1 284, 1 2 9 1 , 1 293 Constantinides, G.M., see Ferson, W.E. 1 284 Contini, B. 1 177, 1 1 78, 1 1 80, 1 200, 1 222 Cook, T. 1 94, 1 95, 1 493 Christiano,

.

Author Index

I-6 Cooley, T.F. 42, 69, 97, 1 0 1 , 1 1 5, 124, 1 37, 376, 380, 408, 4 1 1 , 549, 847, 954, 962, 974, 1 376, 1463, 1 736 Cooley, T.F., see Cho, J.O. 974, 976, 1 025, 1 036 Cooper, R. 204, 398, 824 Cooper, R., see Azariadis, C. 395 Cooper, R., see Chatterjee, S. 996, 1 1 26 Cootncr, P.H. 1 3 1 6 Corbo, V 1 543, 1 554 Correia, I. 974, 1 537, 1 675, 1 720, 1 733 Cossa, R. 584 Council of Economic Advisers 1 639 Cox, D. 705 Cox, WM. 1 62 1 Cox Edwards, A., see Edwards, S . 1 543, 1 554, 1 555, 1 575 Crawford, VP. 475 Crossley, T., see Browning, M. 6 1 0, 798 Croushore, D. 1485, 1 653 Crucini, M.J. 1 78, 705 Crucini, M.J., see Baxter, M. 1296 Cukiennan, A. 1404, 1 414, 1 4 1 5, 1432, 1 437, 1438, 1450, 1 456, 1 463, 1 465 Cuk:ierman, A., see Alesina, A. 1424, 1 426 Cukierman, A., see Brunner, K. 1 025 Cummings, D., see Christensen, L.R. 673, 688 Cummins, J.G. 822, 856, 1 344 Cunliffe Report 1 6 1 Currie, D . 454, 504 Cuslnnan, D.O. 95, 96 Cutler, D.M. 797, 1 290, 1 320, 1 32 1 , 1 624 Cyrus, T., see Frankel, J.A. 280 Dahlquist, G. 337 Daniel, B.C. 1647 Daniel, K. 1322 Danthine, J.-P. 329, 370, 952, 962, 1 002, 1 157 Darby, M.R. 166 Dasgupta, P. 655, 656 d' Antnmc, A. 487 DaVanzo, J. 6 1 8 Davcri, F. 1 220 Davidson, J. 750 Davies, J.B. 766 Davis, D. 1 033 Davis, P.J. 333 Davis, S.J. 1 1 5 1 , 1 1 52, 1 160, 1 1 6 1 , 1 1 76, 1 1 78, 1 1 80, 1 194, 1 1 99

Davis, S J., see Attanasio, O.P. 796, 797 Davutyan, N. 1 5 6 Dawid, H. 523, 527 De Bond!, WF. 1 307, 1 320, 132 1 , 1 323 de Fontnouvelle, P., see Brock, W.A. 528 De Fraja, G. 1 037 De Gregorio, J. 1 546, 1 55 1 , 1 573, 1 575, 1 577 de Haan, J., see Eijffinger, S. 1404, 1 43 8 d e I a Torre, M . 4 1 De Melo, J., see Corbo, V 1543 de Melo, J., see Hanson, J. 1 543 De Melo, M. 1 535, 1 5 5 1 D e Pablo, J.C. 1 543 de Soto, H. 695 Deaton, A. 752, 756, 764, 771 , 775, 776, 783, 785, 787, 794, 798, 1 344 Deaton, A., see Blinder, A. 750 Deaton, A., see Browning, M. 6 1 1 , 6 1 2, 752, 787, 792 Deaton, AS. 1 264 Deaton, A.S., see Campbell, J.Y. 764 Debelle, G. 1489, 1 5 1 8, 1 522 DeCanio, S. 454, 463 DeCecco, M. 155 Degeorge, F. 1 32 1 DeKock, G . 1 5 8 DeLong, .l.B. 252, 279, 695, 1 042, 1 290, 1 324 DeLong, J.B., see Barsky, R.B. 1 237, 1 277, 1 294-1296 den Haan, W.J. 27 1 , 347, 354, 369, 994, 1 1 66, 1 1 94, 1203, 1 204, 1 206, 1 207 Denardo, E. V 320 Denison, E.F. 237, 653 Denizer, C., see De Melo, M. 1 535, 1 5 5 1 Denson, E.M. 40 Desdoigts, A. 290 DeTray, D.N., see DaVanzo, J. 6 1 8 Devereux, M. 952, 1 466, 1471 Devereux, M., see Alcssie, R. TIS Devereux, M., see Beaudry, P. 395, 4 1 3 Devereux, M.B. 1 126 Devereux, M.B., see Beaudry, P. 99 Devine, T.J. 1 1 66 Dewatripont, M., see Aghion, P. 1 1 57 Dezhbakhsh, H. 1 039 Di Tella, G . , see Canavesc, A.J. 1 543 Diamond, P. 796 Diamond, P., see Shafir, E. 1 3 1 6 Diamond, P .A. 66 1 , 1 157, 1 1 6 1 , 1 1 62, 1 1 73, 1 1 88, 1 634, 1 645, 1 684, 1 7 1 8 .

Author Index

I -7

P.A., see Blanchard, OJ. 4 1 , 42, 1 162, 1 173, 1 183, 1 1 84, 1 194, 1 202, 1221 Diaz-Alejandro, C.F. 1 543 Diaz-Gimenez, J., see Castaneda, A. 380 Dickens, WT., see Akerlof, G.A. 1 98 Dickey, D.A. 53, 54, 2 1 2 Dickinson, J. 6 1 8 1633 Dicks-Mireaux, L . , see Feldstein, M . Diebold, F.X. 6, I I Diehnan, T., see Kallick, M . 1 325 Dixit, A. 824, 829, 844, 1 1 1 5, 1 12 1 , 1 126 835 Dixit, A.K., see Abel, A.B. Dixon, H. 537 Dodd, D.L., see Graham, B. 1 323 Dolado, J. 1437 Dolado, J.J. 1214 Dolde, W 1318 Dolde, W C ., see Tobin, J. 773 Domar, E. 640 Domberger, S. 1019 Dominguez, K. 1 64, 182 Domowitz, I. 1 020, 1 083, 1 093 Doms, M. 823, 838 Diamond,

Donaldson, J.B.,

see

Constantinides, G.M.

1293 J B. , see Danthine, J.-P. 329, 370, 952, 962, 1 002, 1 1 57 Doob, J.L. 299 Dornbusch, R. 1 98, 1 043, 1 543, 1 562, 1 563, 1 565, 1 568, 1 582, 1 590, 1 637 Dotsey, M . 370, 952, 974, 1 032, 1 043, 1 5 22, 1 652 Drazen, A . 1463, 1465, 1 54 1 , 1 580 Drazcn, A., see Alesina, A. 1 62, 1 450, 146 1 , 1 465, 1 540 Drazen, A., see Azariadis, C. 262, 264, 2 7 1 , 289, 527, 658, 660 1 5 80 Drazen, A . , see Bertola, G. 1571 Drazen, A . , see Calvo, G.A. Drcman, D . 1 320, 1 323 Dreze, J. 770 1405, 1 4 1 4 , 1 4 1 5 Driffill, J., see Backus, D. Driskill, R.A. 1 042 Drudi, F. 1 450 Drugeon, J.P. 426 Dueker, M.J. 1485 Duffie, D. 380 Duffie, D., see Constantinides, G.M. 567, 7 8 1 , 1 237, 1 2 9 1 Duffy, J . 257, 439, 473, 500 Duffy, J., see Arifovic, J. 527 Donaldson,

.

J., see Bullard, J. 526 P. 2 1 5 Dumas, B . 561, 564 Dunlop, J.T. 939, 1 059 Dunn, K.B. 800, 1 284 Dwme, T., see Doms, M. 823, 838 Dupor, B . 994 Durkheim, E. 1331 Durlauf, S.N. 254, 262-264, 268, 270, 2 7 1 , 287, 289, 303, 550, 905-907 Dmlauf, S.N., see Bernard, A.B. 254, 27 1 , 287, 288 Dutta, P.K. 3 80 Dutta, S. 1 0 1 9, 1 020 1 0 1 4, 1 01 5, 1 0 1 9 Dutta, S., see Levy, D. Dutton, J . 1 56 Dyl, E.A. 1 334 Dynan, K.E. 770 Duffy,

Duguay,

Easley, D., Easley, D.,

see Blume, L E. 3 2 1 , 322, 474 see Bray, M. 474 .

W. 277-279, 2 8 1 , 675, 703, 1 538, 1 547, 1 553, 1 560, 1 56 1 Easterly, W , see Bruno, M. 1 553 Eaton, .J. 7 1 9 801 , 802, 1 344 Eberly, J.C. Eberly, J.C., see Abel, A.B. 83 1 , 834, 835, 994 Echenique, F. 1551, 1561 Eckstein, 0 . 1 344 Eden, B. 1 0 1 9, 1 023 Edin, D.A. 1457 Edwards, S. 1 538, 1 543, 1 554, 1 555, 1 575, 1 57 8- 1 580 Edwards, S., see Cukierman, A. 1456, 1 465 Edwards, W 1 322 Eichenbaum, M. 83, 94, 96, 99, 1 00, 1 37, 1 84, 549, 550, 785, 799, 800, 803, 885, 888, 905-907, 9 12, 957, 1 084 Eichenbawn, M . , see Aiyagari, S.R. 1 140 Eichenbaum, M . , see Burnside, C. 399, 930, 980-985, 994, 1 078, 1 142, l l 62 Eichenbaum, M., see Chmi, V.V. 72, 1449 Eichenbaum, M., see Christiano, L.J. 43, 6770, 83, 84, 89, 9 1 -94, 99, 108, 1 15, 1 24, 1 37, 1 43, 144, 376, 377, 379, 764, 974, 1 0 1 1 , 1 02 1 , 1 038, 1 089, 1 1 00, 1 365, 1 369, 1 708, 1 736 Eichenbawn, M . S . , see Christiano, L.J. 88 1 , 888 Easterly,

I-8

Author Index

Eichcngreen, B.

1 52, 1 54-- 1 57, 1 60, 1 62-164,

1 68, 1 78, 1 85, 1 87, 1 89, 204, 208, 209,

Evans, M.

1 82

Evans, P.

283, 1 635, 1 647, 1 656-1 659

2 1 1 , 2 1 9, 1 449, 1465, 1 590

see

Eichengreen, B., 2 1 7, 2 1 9

see see

Eichengreen, B., Eichengreen, B.,

Fair, R. 1 62

Bordo, M.D.

1 463, 1465

Casella, A.

Farber,

475, 1 1 24

Elison, R.E.,

see

see

80 1 , 802, 82 1 ,

835-838, 840-842, 994, 1 032, 1 1 5 8

see

Engle, R.F.

1 344

Bollers1ev, T.

1 280

Epstein, L.G.

Chou, R.Y.

1 236, 1280

556, 558, 564, 565, 744, 769,

Erceg, C.

1 04 1

see

Bordo, M.D.

1 208

Ermoliev, Y.M.,

see

see

286 Esteban, J.-M. Estrella, A. Evans, C .

Arthur, W.B.

476

1718

Esquivel, G . ,

Caselli, F.

277-279, 283, 284,

264

1 12 1 69, 2 1 7, 1 4 1 6, 1425, 1437

Fauvel, Y.

1 573

Favaro, E.

1 554, 1 555 1 077, 1 1 03 8 1 8, 1 344

Fazzari, S.M.,

Chirinko, R.S.

Evans,

Christiano, L.J.

Feenstra, R.

1 066, 1 086

15 69

1 76

Feenstra, R.C.,

see

Feiwel, G . R .

535

Feldman, M.

474

Feldstein, M.

44, 1 97, 14!:!5, 1 497, 1 498, 1 622,

Bergen, P.R.

1041

64 1 , 6 57

Fcrcj ohn, J.

1425

see Basu,

Fernald, J.G.,

182 67, 68, 70, 83,

Fernandez, R. Ferris, S . P.

Eichenbaum, M.

83, 94, 96,

Ferson, W. E . Festingcr, L.

425, 426, 453-455, 46 1-465, 468,

S.

399, 402, 433, 994,

1 1 1 7, 1 1 42

1 02 1 , 1038, 1 089, 1 1 00, 1 365, 1 369 1 37

904, 906

1 083, 1 1 22

84, 89, 9 1-94, 99, 1 08, 1 37, 1 43, 1 44, 1 0 1 1 ,

see

8 8 1 , 9 1 2,

1 332

60

Fellner, W. Bordo, M.D.

Evans, G.W.

see

Feenberg, D.

Felli, E.

1 05

Evans, C.L.,

Evans, C.L.,

Carpenter, R.E.

see

Fazzari, S.M.,

Feldstein, M.S.

982

see C . L . , see

395, 399---402,

1 63 1 , 1 633, 1 636, 1 637, 1 639, 1 656, 1 660

43, 1 28 1 , 1485

Evans, C.L.

Faust, J.

Federal Reserve Board

i 82

1 3 14

Escolano, J.

Farrell, J.

Featherstone, M.

Erceg, C.J., Erlich, D.

Benhabib, J.

1 344

1 250, 1 256

Eriksson, C.

see

408 , 4 1 2--4 14, 4 1 7, 425, 427, 4 3 1 , 433--435,

Fazzari, S.M.

9

P.

39 1 , 395, 396, 4 l l -4 1 4, 427--430,

Farmer, R.E.,

Fay, J.A.

50

see

662, 1 002

442, 505

1 14

Balke, N.S.

Caballero, R.J.

Engelhardt, G.

1 200

H.

434, 437, 500, 505

215

see

Emery, K.M.,

855

Farmer, R.E.

see Ball, L. 1 650, 1 6 5 1 see Feldstein, M . 1 65 6

Elmendorf, D.W., Emery, K . M .

1 57

1439

Elmendorf, D.W.,

1 82

1 235, 1 2 80, 1 2 8 1 , 1 307, 1 3 1 6,

Fanner, R.

Bordo, M.D.

Elmendorf, D.W.

Dominguez, K. 326

1 320-1323

835

Ellison, G.

Engllmd,

876, 1 077, 1 49 1

see

Fair, R.C.,

Fama, E .F.

673

Engle, R.F.,

Fair, R . C .

Fallick, B.C.

El Karoui, N.

Engle, R.,

1 675, 1 72 0 1 4 1 6, 1 42 5

8 1 7, 1 3 1 0, 1 62 1 , 1 622 1 689

Elias, VJ.

Faig, M.

Falcone, M.

Ekeland, I.

Engel, E.,

2 1 1 , 2 1 6,

1404, 1 432, 1 43 8

Eijffinger, S. Eisner, R .

Bayomni, T.

Fethke, G.

1 543, 1 562

1314 1 284 1314 1037

see Domberger, see Contini, B .

470, 472--478, 480, 48 1 , 483, 484, 487,

Fiebig, D.G.,

S.

489--492, 495-497, 500, 502, 504--5 07,

Filippi, M . ,

1 1 77, 1 1 78, 1 1 80,

509-5 1 3 , 5 1 6, 5 1 8-52 1 , 526-528, 530-532,

J 025, 1 1 25

1 222 Fillion, J.F.

1 49 8

1019

Author Index

I-9

Finch, M . H .J. Finn, M.

619

W

Frenkel, J. A.

1425

Frenkel, J.A.,

see

Fischer, A.M . , Fischer, S.

Dueker, M.J.

1235, 1 2 8 1 , 1 320,

Fama, E.F.

1 32 3

9 8 1 , 1 091

Fiorina, M .

see

French, K.R.,

1 543

see Bowen,

Finegan, T.A.,

Frcnnberg,

1 485

1 82, 1 97, 202, 2 1 5, 2 1 6, 1025,

2 0 3, 1 63 0

see

Aizenman, J.

1497

1 2 38

P.

Friedman, B.M.

43, 4 4 , 1 632, 1642

1 026, 1 1 5 5 , 1 404, 1405, 1438, 144� 1 489,

Friedman, D.

475

1496, 1498, 1 538, 1 542, 1 547, 1 56 1 , 1 582

Friedman, J.H.,

see Breiman, L.

Friedman, M.

46, 48, 6 1 , 1 37, 1 54, 1 60, 162,

see

Fischer, S.,

Blanchard, OJ.

47 1 , 643, 660,

1 68, 1 72, 1 76, 1 79, 1 80, 1 85, 1 89 , 1 95, 203,

1 0 1 3, 1 03 3 , 1 034, 1036, 1 49 1 , 1 635

see Bruno, M. S., see Debelle, G .

Fischer, S . , Fischer,

Fischhoff, B. Fishe,

222, 275, 376, 572, 7 6 1 , 762, 943, 1 0 1 1 ,

1489, 1 5 1 8, 1 522 S.

1318

173

Froot, K.

1 372, 1 377, 1485 92

464, 474

Fudenberg,

D.

Fuerst, T.

Fisher,

Fuerst,

9 1 0, 1 3 68, 1 375, 1 376, 1 37 8

Fisher, J.D.M.

see

Fisher, J.D.M.,

Campbell, J.R.

see

329-334, 343,

348, 356, 365

see

Flood, R.P. ,

Florovsky, G. Forbes, K.

Garber, P.M.

Gale,

Dickey, D.A.

53, 54, 2 1 2

699

R.

299

155

Fortune, P.

1310

Foufoula-Georgiou, E., 326 Fourgeaud, C.

see

Kitanidis,

1 543 1497

Frankel, J.A.

280, 28 1 , 1 590, 1 637

Franses,

289 1431 577

I016

1280

851

909, 1 086, 1 1 24

395, 405-407, 426, 429, 434, 993, 994,

1 1 1 7 , 1 1 1 9 , l 1 20, 1 1 29 1561

Gali,

67, 69, 2 1 7

J.

P.K.

Gali,

see Benhabib, J. J., see Clarida, R.

424 96, 1 36, 422, 1 3 64,

1 368, 1486 Gallarotti, G.M. Gallego, A.M.

Foxley, A.

R.

Gali, J.

Gali, J.,

454, 465, 473, 475

Frankel, J.

P.H.

Charnley, C. 1 646

Galeotti, M.

326

Fratianni, M .

see

Gale, W.O.

see Roscvearc, D. 1 626 Foresi, S., see Backus, D.K. 1316 Forteza, A., see Echenique, F. 1 5 5 1 ,

1 1 82

389, 475, 849, 8 5 1 , 1 3 76

D.

Gale, D.,

1 326

277, 278

Ford, A.G.

French, K .

769, 785

576, 5 8 8 , 6 1 6

Galbraith, J.K. 1 65

Fore, D . ,

Fregert, K.

see

Fuller, WA., Funkhouser,

Carroll, C.D.

875

1 52, 1 5 8, 202, 408, 1428, 1429,

R.P.

Freeman,

J.C., see

Futia, C.

773

1 438, 1 507, 1 595, 1 596

Fox, B.L.

1348, 1 3 57, 1 368,

454, 905, 908, 1039, 1 040, 1 49 1 ,

Fullerton, D .

572, 749, 763, 784

Flemming, J.S.

Carlstrom, C.

Fukuda, S.-i.

Press, W.H.

475

1518 Fuhrer,

1 54

Flannery, B.P.,

T., see

Fuhrer, J.C.

846

1 55

Flandreau, M.

G.

99, 974, 1 37 8

1 378, 1 3 79

350, 355, 362, 364, 962, 1296

Flood,

455, 475, 1 1 55

see Ellison,

Fudenberg, D.,

see Boldrin, M . 962, 1 284, 1 297 J., see Christiano, L.J. 3 1 4, 347, 349,

Flavin, M .

453, 454, 474, 528, 536, 539

R.

Fuchs, G .

Fisher, J.,

Fishlow, A.

1 266, ! 3 1 6

Frydman,

1 54, 1 57, 203, 1 3 1 6, 1321, 1 343,

Fisher, J.

1 1 7 3, 1 325, 1485, 1 488, 1 496, 1 537, 1 674, 1 720

see Lichtenstein,

R.P.H.

Fisher, I .

1 53 8

1 3 1 9, 1 326

Fischhoff, B. ,

289

Galor, 0.

262, 263, 272, 660

Gandolfi, A.E., Garber, P.M. Garber, P.M.,

Darby, M.R.

see Eichengreen, B. see Flood, R.P. 408,

790

R.

Garibaldi,

see

P.

Garratt, A.

166

1 65 , 1 323, 1 543

Garber, P.M., Garcia,

1 54 3 2 1 , 322

1 1 80, 1 222 504

1 87, 1 89 1 595, 1 596

Author Index

I-10

Garratt, A., see Currie, D. Garriga, C.

454, 504

Gaspar, J.

324, 369

Goff, B.L.

689

Gokhale, J.

Gastil, R.D.

Gatti, R., see Alesina, A. Gavin, W. Gear, C.W.

Goldfajn,

395, 458, 1322

1 535, 1 5 5 1

1 65, 1 428

Geoffard, P. Y. , see Chiappori, P.A. Gerlach, S., see Bacchetta, P.

391

1 344

1376 83, 92-94, 1 040, 1 343, 1348, 1 3 66,

1 373, 1 374, 1376-1378 1 293, 1 63 1

Gertler, M., see Aiyagari, S.R.

92, 144, 1 83,

Gertler, M., see Bernanke, B. S .

856, 8 5 7, 1 03 6 , 1345, 134 6, 1352, 1 357, 1 365, 1 369, 1 3 7 1 , 1 373, 1 376-1378, 1 578 Gertler, M., see Clarida, R.

95, 96, 1 36, 422,

1 364, 1 368, 1486 Geweke, J.

34, 334

Gewcke, J., see Barnett, W. Geweke, J.F.

540 908

167, 203, 1438, 1446, 1449, 1 5 8 0

Gibson, G.R.

1450

1 307

847, 1 344 856, 1 036,

Gilchrist, S., see Bernankc, B.S. 1 345, 1 373, 1 376 Gilchrist, S., see Gertler, M.

83, 92-94, 1 366,

1 373, 1 374, 1 376 Gill, P.E. Gilson, R.J.

1 94-- 1 96, 764, 1 0 1 3 , 1 1 1 7, 1 346, 1 509, 1 5 14, 1 5 1 5 Goodhart, C . , see Capic, Goodhart, C.A.E.

329 1 14

1 1 54

F.

Gizycki, M.C., see Gruen, D.K. Glasserman, P. , see Boyle, P. 1456, 1465

Glomm, G.

7 12, 1472

Glosten, L.

1280

1 432,

1 495 Goodhart, C.E.A.

1 438, 1495, 1 507, 1 508,

1 5 14 Goodman,

797

A.

Goolsbee, A.

839, 843, 848

Gordon, D.B.

128, 1 34 1 5 8, 1 1 5 5 , 1405, 69

1030 1 63 7

Gordon, R.J.

40, 46, 48, 49, 1 8 1 , 1 542

Gordon, RJ., see Balke, N.S.

6, 6 1 , 204, 205,

221 553, 5 5 6 , 782, 803 181

Gottfries, N .

463, 1 12 1 , 1 1 22

Gould, D.M.

1 5 5 1 , 1 559, 1 5 6 1

Gourieroux, C.

487

Gouricroux, C . , see Broze, L

4 8 7 , 488

Gourieroux, C., see Fourgeaud, C.

454, 465,

Goetzmann, W., see Brown, S.

1 67 1316

380

609, 1 344

P.-O.

Graham, B.

1323

Graham, F.C.

156, 1 58, 1 60, 1 66, 1 69, 380

Glazer, A.

1 54

Goodhart, C.A.E., see Almeida, A.

Gourinchas,

Giovannini, A., see Giavazzi,

F.

1 93

473, 475

Gilles, C., see Coleman li, WJ. Giovannini, A.

1 1 57

88, 1 20, 121, 1 56, 173, 1 9 1 ,

Gorton, G., see Calomiris, C.W.

195

Gilchrist, S.

Goodfriend, M.

Gorman, W. M .

1308, 1 3 1 8

Gilbert, R.A.

1 1 73

P., see MacLeod, W.B.

Gordon, R.H.

202, 207, 208

Gigerenzer, G.

962, 1 062

Gomme, P., see Andolfatto, D.

Gordon, R.

Giavazzi, F. , see Missale, A .

208, 1 637

994, 1 1 59

Gomme, P. Gomme,

777

1 590

Gordon, D.B., see Leeper, E.M.

1 572

Giavazzi, F.

R.

1 4 1 1 , 1 4 1 5 , 1438, 1485-1489

6 1 5, 752, 759

Ghosh, A.R.

1 624

O.P.

Gordon, D.B., see Barro, RJ.

89

Ghali, M ., see Surekha, K. Ghezzi, P.

I., see Dornbusch,

Gomes, J.

1 290

Gelb, A., see De Melo, M.

Gersbach, H.

750

Goldstein, M., see Mussa, M.

346

Gertler, M.

159

Goldberg, P.K., see Attanasio,

Geczy, C.C., see Brav, A. Genberg, H .

1 242, 1252, 1 3 14, 1 320,

Gokhale, J., see Auerbach, AJ.

1432

1485

Geanakoplos, J.D.

Ghez, G.

Goetzmam1, W.N. 1 333

1 675, 1 7 1 8

1 656, 1 657

Grandmont, J.-M.

439, 454, 460, 464, 474,

475, 48 1 , 507, 5 14, 526, 661 Granger, C.

34

Granger, C.W.J.

8 8 1 , 903

Granger, C.WJ., see Engle, R.F. Gray, J.A.

Green, D., see MaCurdy, T.E. 1242

Green, E .

50

1025, 1 026, 1 03 8 575

6 1 9, 620

Author Index

I-l l

Green, H . , see Beaudry, P.

592

Haberler, G .

Greenberg, D., see Burtless, G.

618

Greenberg, D.H., see DaVanzo, J .

618

Hahn,

1 85

661

F.

Hahn, T. , see Cook, T.

1 94, 1 493

Greenspan, A.

199, 798, 844, 847, 1630

Greenwald, B.

857, 1 1 22, 1 377

Hairau1t, J.-0.

1 036

Greenwood, J.

380, 550, 576, 664, 692, 962,

Haldane, A.G.

1 432, 1 4 38, 1485, 1495, 1497

980, 995

J.

Greenwood, J., see Gomes,

847 994, 1 1 59

Greenwood, J., see Gomme, P. Gregory, A.W

962, 1 062

376, 377 952

Gregory, A.W, see Devereux, M. 253

Griffiths, M., see Dolado, J. Griliches,

1 430

Grilli, V, see DeKock, G.

158

Grilli, V, see Drazen, A . Grilli, VU.

Gros, D., see Adams, C.

1463, 1465, 1 5 4 1 1 53 8

Gross, D.B., see Goolsbce, A. 1 464

1 58, 1 4 1 5, 1 449

Grossman, S.J.

80 1 , 1 23 7, 1 242, 1 246, 1 268,

1 29 1 , 1 293

Guerra, A .

1 546, 1 606, 1 607 439, 454, 460, 464, 465, 474,

475, 506, 5 1 1 , 5 1 6, 526 Guesnerie, R., see Chiappori, P.A.

391, 395,

516 Guesnerie, R., see Evans, G . W.

464

1 537, 1 5 88, 1 603, 1 675, 1 720

Guidotti, P.E.

Guidotti, P. E. , see Calvo, G.A.

1447, 1450

Guidotti, P.E., see De Gregorio, J.

1 546, 1 5 5 1 ,

1 573 , 1 575, 1 577 Guiso, L. Guiso,

202, 207, 208

1317

Gultekin, N.B., see Gultekin, M . Guo, J.-T., see Farmer,

R.E.

Haltiwanger, J.C., see Davis, S.J. Hamermesh, D. Hamilton, A.

577 1 659

963

Hamilton, J.D.

1 2, 72, 80, 1 82, 1 1 1 8, 1 265

Hammerlin, G.

344

Hammour, M.L., see Caballero, R.J. 1 2 1 0, 1 2 1 1 , 1 2 1 3, 1 472

Hannerz, U.

1 332

Hansen, B.

1 1 94

Hansen, B.E.

3 8 , 39

Hansen, G.D.

547, 5 5 1 , 602, 976, 977, 1 200

Hansen, G.D., see Cooley,

69, 97, 1 0 1 ,

T.F.

1 1 5 , 1 24, 1 37, 3 80, 408, 4 1 1 , 974, 1 736 54 7 , 5 5 5 , 556, 558, 572-574, 768,

1 26 1 , 1 294, 1 295 Hansen, L.P., see Anderson, E.W.

368, 369

Hansen, L.P., see Cochrane, J.H.

1 234, 1 246,

1 249

Hanson,

1 507

1 04 1

Guttman, P., see Erlich, D.

846, 847,

852, 855, 856, 1 1 57, 1 1 58, 1 1 60, 1 1 87,

549, 550,

785, 799, 800, 803

4 1 6, 427

1314

1 05 8

1 1 5 1 , 1 1 52,

Hansen, L.P., see Eichenbaum, M.

Gurley, J.G. Gust, C.

1 3 17

395, 427-430, 434,

505

Guo, J.-T.

824

881

769, 784, 882, 9 1 5, 1 234, 1 246, 1 249, 1 250,

909

Guide, A.M., see Ghosh, A.R. Gultekin, M .

8 2 1 , 837,

Haltiwanger, J.C., see Abraham, K.G.

Hansen, L.P.

772

L., see Galeotti, M.

504

1 460, 1465

Haltiwanger, J., see Caballero, R.J.

Hamilton, J.

1316

Guesnerie, R.

Hallerberg, M.

454, 504

1 1 60, 1 1 6 1 , 1 1 76, 1 1 7 8, 1 1 80, 1 1 94, 1 1 99

Grossman, H.J.

Gruen, D.K.

1 656 Hall, S . , see Currie, D .

Haltiwanger, J.C.

839

852

1 068, 1 070, 1 079, 1 089, 1 092, 1 095, 1 096,

Haltiwanger, J . , see Cooper, R .

264, 639, 672, 7 1 5, 1 2 1 0,

Grout, P.A.

784, 789, 79 1 , 794, 8 1 7, 856, 930, 982,

838, 840-842, 1 1 5 8

8 5 7 , 1 344

Grossman, G.M.

399, 556, 573, 595, 607, 608, 673,

679, 680, 683-686, 702, 765, 767-769,

Hall, S., see Garratt, A .

1 69

Gross, D .

911

Hall, R.E.

1 1 64, 1 200, 1 26 1 , 1 485, 1493, 1 498, 1 655,

95, 1404, 1432, 1 438, 1439, 1465

Grilli, V , see Alesina, A.

Hall, G .

585

1 1 4 1-1 143, 1 1 45, 1 1 5 1-1 1 53, 1 1 57, 1 1 60-

1 437

5 41

Z.

Grilli, V

479

Haley, WJ.

Greenwood, J., see Cooley, T.F.

Grier, K.B.

Hahn, W

J.

1 543

Hansson, B., see Frcnnbcrg, P

Harberger, A . C .

1 554, 1 590

1 23 8

Author Index

1-12

Harden,

I., see

1439, 1460,

von Hagen, J.

Hardouvelis, G.A.

see

Harris, R . ,

Harrison, A.

Estrella, A.

Cox, D .

43, 1 28 1

705

see

Harrison, S.H. Harrod, R.

Christiano, L.J.

426

Hercowitz,

402

Hercowitz,

see Davidson, J. 750 Z. 664 Z., see Sarro, R.J. 1023 Z., see Greenwood, J. 550,

Herrendorf, B.

656

Hess, G.D.

9

Hester, D.A.

Harvey, C.R.

1 236, 1 280

Heston, A.,

1 1 52

Hassler, J.

Fallick, B.C.

822, 856,

see Dezhbakhsh, R.A., see Ferris, S.P

Hause, J.C.

H.

1 039

1 3 14

620

576, 578, 579, 582, 584--5 87,

590, 592, 593, 595, 601-603, 605, 6 1 5-6 1 7, 620-624, 752, 759, 1 1 66 Heckman, J.J.,

Heckman,

1 1 1 9, 1 1 20, 1 1 26

Heinemann, M. Hellwig, M., Helpman, E.

D.

Helpman, Helpman,

Hendershott, P.H.

1333

Henderson, D .W.

1497

51, 412

Hoffmann, K.-H., Holbrook, R.

see

Hammerlin, G .

344

569

Holmstrom, B.

1 376, 1 4 1 7, 1 4 1 8, 1 425

see

Davis, D.

1 033

882, 885, 888, 909, 9 1 0, 9 1 2

see

Bryant, R.C.

1 49 1 , 1 497,

1516 Holtz-Eakin, D.,

see

Hommes, C.H.

529, 532

Honkapohja, S.,

265

see

Blinder, AS. Brock, W.A.

41 455, 528,

464, 481, 507, 535

see

Evans, G.W.

425, 426,

454, 455, 46 1 , 464, 465, 468, 470, 472-478,

1 580 G.M.

1281 1 507

1 5 6 1 , 1 589

Hoffman, D.L.

Honkapohja, S.

203, 1 5 80

672, 7 1 5, 1 2 1 0, 1 464

289

532

1 3 '76

see Coe, D.T. E., see Drazen, A. E., see Grossman,

Helpman, E.,

1 332

1 65 8

Hoffmaister, A.

Hommes, C.H.,

495, 525

see Gale,

Franses, P. H .

see Bekaert, G. see Flood, R.P.

Holtham, G.,

601 , 1 1 48 Heijdra, B.J.

1 62 1

Hodrick, R.J.,

Holt, C.C. 550,

Cox, W.M .

9, 12, 34, 428, 93 1 , 932

Holt, C.A.,

Heckman, J.J.,

Heckman,

see

Hoelscher, G.

1 284, 1 293

1 344

33 1

Hodrick, R. Hodrick, R.J.,

380, 547, 569, 803, 1 242, 1 255,

see Ashenfelter, 0. 6 1 8 see Cameron, S . 589 J.J., see Cossa, R. 584 J.J., see Killingsworth, M.R.

Hobijn, B . ,

1 656, 1 65 7

Gilchrist, S .

see Bikhchandani, S. see Daniel, K. 1 32 2

Hirshleifer, D.,

773, 775, 776, 785, 788, 790, 796,

Heckman, J.J.

see

1 540

Hirshleifer, D.,

see Devereux, M.B. 1 1 26 G., see Dasgupta, P 655, 656 G.M., see Ryder Jr, H.E. 1284

Heaton, J.

Graham, F.C.

see

Hirschman, A .

800, 8 1 8, 1 649 Heal,

535, 537

see

Hirschhorn, E.,

Head, A., Heal,

506, 1 539, 1 540, 1 543

1400, 1 425

Hiriart-Urruti, J.B.

see Burtless, G. 620 C.B., see O'Brien, A.M. 776

Hayashi, F.

Hibbs, D.

Himmelberg, C.P.,

Hausman, J., Hawley,

238, 3 0 1 , 640,

1 80

Heymann, D.

Himarios, D.,

569

Hausman, J.

Summers, R.

Hildenbrand, W.

855

9, 1 23 8

Haug, A.A.,

87 1

see

Hetzel, R.L.

821

1 344

see

1 4 1 5, 1 436, 1 43 8

673-675, 677, 680, 68 1 , 689, 720

8 1 5, 8 1 8, 843, 1 344

see Auerbach, A.J. K.A., see Cummins, J.G.

Hassett, K.A.,

Hassett, K.A.,

664,

9, 1 48 5 , 1 509

Harvey, A.C.

Hassett, K.A.

1 60,

962, 980

852, 1 1 54

Hashimoto, M .

Canzoneri, M.B.

1 507, 1 508 Hercowitz,

640

Hartwick, J.

Haugen,

1 49 1 , 1497,

Hendry, D.,

277, 279, 280

Harrison, S.G.,

Hassett,

Bryant, R.C.

D.W., see

Henderson,

1 28 1

see

Hardouvelis, G.A.,

Hart, 0.

see

Henderson, D.W., 1516

1 465

264, 639,

480, 48 1 , 483, 484, 487, 489-492, 495-497, 502, 504--5 07, 509-5 1 3 , 5 1 6 , 5 1 8-52 1 , 526-528, 530-532, 1025 Hooker, M.A.,

see

Fuhrer, J.C.

454

I 13 -

Author Index

Hooper, P. ,

see

Bryant, R.C.

1 043, 149 1 , 1497,

1 5 1 6-1 5 1 8

Hopenhayn, H . 672, 708, 994 Hopenhayn, H.A. 844 Horioka, C., see Feldstein, M. 1 636 Horn, H. 1 4 1 5 Hornstein, A . 549, 996 Hornstein, A., see Fisher, J.D.M. 9 1 0 Horvath, M. 994 Horvath, M., see Boldrin, M. 962, 1062 Hoshi, T. 1344 Hosios, A.J. 1 1 93, 1224 Hotz, V.J. 792, 803 Houthakkcr, H.S. 803 Howard, R. 336 Howitt, P. 3 89, 399, 455, 506, 507, 5 14, 5 1 5 , 5 1 7 , 5 2 1 , 5 2 7 , 1 1 74, 1 508

Howitt, P., see Aghion, P.

264, 665, 672, 7 1 5 ,

7 1 9, 1 208, 1 2 1 0, 1 2 1 3

Howrey, E.P., see Fair, R.C. 14 91 Hoynes, H.W., see Attanasio, O.P. 753 Hsieh, C.-T. 673, 687 Hubbard, R.G. 567, 569, 572, 573, 593, 77 1 , 776, 794, 797, 856, 1 344, 1 3 76, 1660

Hubbard, R.G., see Cummins, J.G. 822, 1344 Hubbard, R.G., see Domowitz, I. 1 020, 1 083, 1 093

Hubbard, R.G., see Fazzari, S.M. 8 1 8, 1 344 Hubbard, R.G., see Gertler, M. 1 376 Hubbard, R.G., see Hassett, K.A. 8 1 5, 8 1 8, 843, 1 344

Huberman, G., see Kahn, C. 1 1 54 Huffman, G.W. 437 Huffu1an, G.W., see Greenwood, J. 380, 962, 980

Huggett, M. 380, 576, 593 Hulten, C. 664 Hultgren, T. 1 1 00 Humphrey, T.M. 1485 Ihm1phreys, B.R. 909 Hurd, M.D. 780 Hybels, J., see Kallick, M. 1 325 Hyslop, D., see Card, D. 1 0 1 6 Ibbotson, R . 1 3 2 1 Tden, G., see Barth, J.R. 1 657 Ikenberry, G.J. 1 63 Im, K. 28 3 Imrohoroglu, A. 797 Ingberg, M., see 1-lonkapohja, S. Ingram, B. 984

Inman, R., see Bohn, H. 1465 Intriligator, M., see Griliches, Z. 541 Ireland, P.N. 1 29, 1 94, 1 036, 1492, 1 494, 1 497

Irish, M . ,

see

Browning, M.

6 1 1 , 6 1 2, 752,

787, 792

Irons, J., see Faust, J. 1 4 1 6, 1 425 D.A. 1 7 8 Isard, P., see Flood, R . P. 1 58, 1429, 1 4 3 8 Islam, N. 283-285, 287, 653 Ito, T. 1425 Iwata, S., see Hess, G.D. 9 Irwin,

Jackman, R. 1 2 2 1 Jackman, R . , see Layard, R.

1 098, 1 1 76, 1 1 77,

1221

Jackwerth, J.C. 1 3 1 0 Jaeger, A., see Harvey, A.C. 9 Jaffee, D.M. 1 376 Jagannathan, R., see G1osten, L. 1 2 80 Jagannathan, R., see Hansen, L.P. 547, 1 234, 1 246, 1 249

James, H., see Bernanke, B.S. 1 83, 1 84 James, W. 1 330 Janis, I. 1 332 Jappelli, T. 776, 780, 790, 1 344 Jappelli, T. , see Guiso, L. 772 Jeanne, 0. 1 56, 1 04 1 Jeanne, 0., see Bensaid, B. 1446, 1449 Jefferson, P.N . 1 4 85, 1 509 Jegadeesh, N. 1 3 2 1 Jegadeesh, N . , see Chan, L. 1 3 2 1 Jensen, H . 1 4 1 5, 1 427 Jensen, H., see Beetsma, R. 1 436, 1 43 8 Jensen, M. 1 344 Jeon , B.N., see von Furstenberg, G.M. 1 333 Jennann, U.J. 1 296 Jem1ann, U.J., see Alvarez, F. 575 Jermann, U.J., see Baxter, M. 980, 992 Jewitt, I., see Buiter, W. I 030 Jimeno, J.F., see Blanchard, O.J. 1 2 1 4 Jimeno, J.F., see Dolado, J.J. 1 2 1 4 John, A . , see Cooper, R. 398 Johnson, H.G. 702, 704, 705 Johnson, P., see Goodman, A. 797 Johnson, P.A., see Dur1auf, S.N. 254, 263, 264, 270, 2 7 1 , 289, 303

535

Johnson, P.G. , see Banks, J. 75 1 Johnson, S.A. 345, 3 8 1 Jones, C.L 237, 264, 290, 292, 672, 696, 7 1 4--7 1 6, 7 1 8 , 7 1 9

I- 1 4

Author index

673, 679, 680,

Jones, C . ! . , see Hall, R.E. 683-686, 702, 856

245, 257, 26 1 , 380, 672, 709,

Jones, L.E.

7 1 5, 1 57 8

Jonung,

L.

1 59, 1485 1 52, 2 1 5, 2 1 7,

220, 2 2 1 1 0 16

I.,

N.

see E1 Karoui,

Kashyap, A.K., see Cccchetti, S.G.

817

Jorgenson, D. W , see Christensen, L.R.

673,

688

Jorgenson, D.W, see Hall, R.E.

817 1 242, 1 252,

Jorion, P. , see Goetzmann, W N. 1 3 20

Kashyap, A.K., see Hoshi, T.

Kashyap, A.K., see Hubbard, R.G. Katz, L.

Jovanovic, B.

702, 848, 1 200

Jovanovic, B., see Greenwood, J.

1 485, 1487, 1 5 1 2, 1 5 1 6 590, 1 652

Judd, K., see Bizer, D.

Katz, L., see Autor, D.

577

Judd, K.J., see Gaspar, J.

797

324 , 369

354, 1 673, 1 675, 1 694 1 509

549

see Backus, D.K.

9, 42, 45, 938,

1 24, 397, 422, 672,

1 449, 1488, 1489, 1 673-1 676, 1 69 1 , 1 699,

Kaas, L., see Bohm, V.

558, 564, 565

Kehoe, T.J.

646

1446, 1 449, 1 603

Kehrer, K. C., see Moffitt, R.A.

1 1 54

Kahn, C.M., see Blanchard, O.J.

3 9 1 , 504

1 78, 705

Kahn, J., see Crucini; M.J. 897, 9 1 0

9 1 0, 9 1 2, 1 053, 1 078,

Kendtick, D.A., see Amman, H.i\1.

1313

Kahneman, D., see Tversky, A.

1 308, 1 3 1 5,

1 3 1 9, 13 30

Kalaba, R., see Bellman, R.

1 646 1 58, 1 6 1 , 1055, 1 059, 1 53 7

Keynes, J.M.

Kahneman, D., see Thaler, R.H.

Kiefer, J .

476

Kiefer, N.M., see Burdett, K. Kiefer, N.M., see Devine, T.J.

340

237, 238, 240, 640, 941

Kiguel, M.

1 054

Kiley, M.T.

Kallick, M.

1 325

Killian, L.

1 1 73 1 1 66

1 535, 1 543, 1 546, 1 554, 1 55 5

Kihlstrom, R.E.

Kalecki, M.

5 35

1 65 , 1 496

803

Kennan, J. Kessler, D.

1 308, 1 309, 1 3 1 1

1 73

Kemmerer, E. W Kenen, PB.

1 079, 1 085

618

271

Kelly, M.

Kahn, J.A., see Bils, M .

1 449

3 1 4, 380, 389, 3 9 1 , 574, 57 5

Kehoe, T.J., see Cole, H.L.

329, 333

Kahneman, D.

1 70 8- 1 7 1 0, 1 720, 1 723

Kehoe, P.J., see Cole, H.L.

1 543

Kahaner, D.

Kaldor, N.

Kehoe, P.J., see Backus, C.K.

974, 1 036, 1 037 , 1 040-1 042, 1 3 7 1 , 1 448,

777

Juster, T., see Barsky, R .

Kahn, J.A.

847, 1 675, 1 7 1 8,

1 720

697, 698, 700, 70 1 , 709, 720, 722, 723,

474

Kahn, C.

1 466, 1 4 7 1

Kehoe, P.J., see Chari, V.V.

569, 6 1 9

Kafka, A.

608, 609, 786, 790

1 708

Judson, R., see Porter, R.

Juster, F.T.

Keane, M.P.

Kehoe, PJ.,

663

Judson, R.

1 1 76

1 344

Kaufman, H .

Kehoe, PJ., see Atkeson, A.

3 1 4, 324, 340, 343, 347, 348, 350,

Judd, K.L.

1 1 83 , 1 22 1

Katz, L.F., see Abraham, K.J.

Keefer, P., see Knack, S . 380

1 344

577, 578

Katz, L. W, see Blanchard, O..J. 664, 692

876

1 344

Katz, L.F., see Cutler, D.M.

Judd, J.P

217

9 1 2 , 1 0 1 8, 1 344, 1 374, 1 376 664

Jorgenson, D.W

Judd, K.

835

1 37, 877, 8 8 1 , 886, 903, 906,

Kashyap, A.K.

881

Jorgenson, D .

Jun, B .

Karatzas,

476

856, 1 344

Karras, G., see Cecchetti, S.G.

Jonung, L . , see Fregert, K .

Juhn, C.

1 236, 1 280

Kaniovski, Y.M., see Arthur, W.B. Kaplan, S.N.

Jonung, L., see Bordo, M.D.

Jorda, 0.

475

Kane, A., see Chou, R.Y.

1 404, 1 4 1 1 , 1 4 1 5, 1 426, 1 43 8

Jonsson, G.

1 550, 1 553, 1 590

1 235, 1 252, 1 253, 1 265, 1 270,

Kandel, S. Kandori, M.

1 540

Jones, M.

428

1 272

7 1 1 -7 1 3 , 720, 1 675, 1 7 1 1

Jones, L.E., see Chari, V.V.

Kamihigashi, T. Kaminsky, G.L.

563

422, 423, 1 04 1 , 1 1 1 7, 1 1 2 9 87

1- 1 5

Author Index

550, 60 1 , 1 148

Killingsworth, M.R. Kim, J.

129, 1 036

Kim, M.,

see

Kim, K. Kim, S.

Kim, S.-J.

Kocherlakota, N.R.

377, 379

see

see

Kimball, M.S.

558, 564, 565

Barsky, R .

762, 771

Carroll, C.D.

556, 770, 1 036, 1 04 1 , 1 056,

1 1 1 4, 1 1 1 7 , 1 1 27, 1 65 3 see

Kimball, M.S.,

1 73 2

983, 992, 994,

Basu, S .

1 537, 1 675, 1 676, 1 720, 1018

Stigler, G.

Koopmans, T.

278-28 1 , 67 1 , 1 656, 1 657

703

Kornai, J.

see

Kot1ikoff, L.J.,

974

King, R.G.,

see

Dotsey, M.

see

King, R.G.,

974, 1 032, 1 043

Kramer, C.,

Goodfriend, M.

1 0 1 3 , 1 1 1 7,

326

1 378, 1 379

Kiyotaki, N . , Kiyotaki, N.,

see

Blanchard, OJ.

1033, 1 034

399

Boldrin, M.

see

see

Easterly, W

see see

Kreps, D.M.,

Krishnamurthy, A. see

Kroner, K . F.,

1 3 76, 1 378

Bollerslev, T.

94 1

Kmeger, J.T.

702, 705, 707

Klenow, P.J., Klenow, P.J.,

Klock, M., Knack, S .

see

see

see

Kneese, A . Knowles, S.

694

Heckman, J.J.

Silberman, .J.

578 1316

Krusell, P.,

see

Kurz, M.

1281

Meyer, J.R.

576

1 596

474

Kushner, H. Cole, H.L.

Greenwood, J.

476

Kumhof, M .

574, 954, 985, 1 234, 1 25 1 , see

see

Kuan, C.-M. Kuh, E . ,

277, 278

Kocherlakota, N.,

380, 547, 566, 567, 9Y4, 1 2