Exchange Rate Volatility, Trade, and Capital Flows under Alternative Exchange Rate Regimes (Japan-US Center UFJ Bank Monographs on International Financial Markets)

Exchange Rate Volatility, Trade, and Capital Flows under Alternative Exchange Rate Regimes Recent years have seen a substantial increase in the volatility of exchange rates. This trend has prompted economists and financial analysts to question if the observed behavior of exchange rates is consistent with a rational model. Does that volatility, further, hinder trade? What are financial markets' effects on countries' investment decisions, and how would changes in fixed exchange rates affect growth and welfare? What are the requirements to make such changes feasible? Professors Sercu and Uppal examine these issues in the context of dynamic generalequilibrium models, explicitly considering the role of financial markets while allowing for commodity markets to be segmented across countries. They show that the theoretical models for exchange rates in this context are quite different from those put forth by monetary theorists and proponents of purchasing power parity arguments. The authors also find that an increase in exchange rate volatility may be associated with either an increase or decrease in trade, and they conclude by identifying the particular conditions under which a regime of fixed exchange rates maximizes welfare. Piet Sercu is Professor of International Finance at the Catholic University of Leuven. He has also taught at the Flemish Business School in Brussels and held visiting professorships at Cornell and New York Universities, the University of British Columbia, and the London Business School. Professor Sercu served in 1995 as President of the European Finance Association and was awarded the 1996 Francqui Chair of Economics at FUNDP, Namur, Belgium. He has published in journals such as the Journal of Finance, Journal of Banking and Finance, and Journal of International Money and Finance and is the coauthor with Raman Uppal of International Financial Markets and the Firm (1995). His current research focuses on general equilibrium models of exchange rate pricing, international trade and consumption, and forward and future markets. Raman Uppal is Associate Professor in the Faculty of Commerce and Business Administration, University of British Columbia, and has served as Visiting Professor of Finance at the Catholic University of Leuven and at the Sloan School of Management, Massachusetts Institute of Technology. His recent research focuses on understanding how market imperfections affect the welfare of investors, their optimal portfolios and hedging strategies, aggregate trade and capital flows, and exchange rate and other asset prices. He is coauthor with Piet Sercu of the above-named text, and Professor Uppal's articles have appeared in journals such as the Journal of Finance, Journal of Financial and Quantitative Analysis, Journal of International Money and Finance, and Review of Financial Studies.

Japan-U.S. Center Sanwa Monographs on International Financial Markets Selection Committee Ryzuo Sato, New York University (Ex Officio Chairman and Editor) Akiyoshi Horiuchi, University of Tokyo Paul Krugman, Massachusetts Institute of Technology Marti Subrahmanyam, New York University James Tobin, Yale University Richard Zeckhauser, Harvard University The Sanwa Bank has established "The Sanwa Bank Research Endowment Fund on International Financial Markets" at The Center for Japan-U.S. Business and Economic Studies of The Stern School of Business, New York University, to support research on international financial markets. One part of this endowment is used to offer an award for writing a monograph in this field. The Sanwa award is made annually on a competitive basis by the Selection Committee, and the winning published titles and proposals are listed below. 1992, Richard C. Marston, University of Pennsylvania: International Financial Integration: A Study of Interest Differentials between the Major Industrial Countries (published 1995; paperback ISBN 0 521 59937 7) 1993, Willem H. Buiter, University of Cambridge, Giancarlo Corsetti, Yale University, and Paolo A. Pesenti, Federal Reserve Bank of New York: Financial Markets and European Monetary Cooperation: The Lessons of the 1992-1993 Exchange Rate Mechanism Crisis (published 1998; ISBN 0 521 49547 4, paperback ISBN 0 521 79440 4) 1994, Lance E. Davis, California Institute of Technology, and the late Robert E. Gallman, University of North Carolina, Chapel Hill: Evolving Financial Markets and International Capital Flows: Britain, the Americas, and Australia, 1865-1914 (ISBN 0 521 55352 0) 1995, Piet Sercu, Catholic University ofLeuven, and Raman Uppal, University of British Columbia: Exchange Rate Volatility, Trade, and Capital Flows under Alternative Exchange Rate Regimes (published 2000; ISBN 0 521 56294 5) 1996, Robert P. Flood, International Monetary Fund, and Peter M. Garber, Brown University: Speculative Attacks on Fixed Exchange Rates 1997, Maurice Obstfeld, University of California, Berkeley, and Alan M. Taylor, University of California, Davis: Global Capital Markets: Growth and Integration 1998, Pravin Krishna, Brown University: Regional Trading Blocs and Preferential Trading Systems 1999, Kose John, New York University: Corporate Governance and Agency Problems: Theory and Empirical Evidence

Exchange Rate Volatility, Trade, and Capital Flows under Alternative Exchange Rate Regimes Piet Sercu Catholic University ofLeuven

Raman Uppal University of British Columbia

CAMBRIDGE UNIVERSITY PRESS

CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 2RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521562942 © Piet Sercu and Raman Uppal 2000 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2000 This digitally printed first paperback version 2006 A catalogue record for this publication is available from the British Library Library of Congress Cataloguing in Publication data Sercu, Piet. Exchange rate volatility, trade, and capital flows under alternative exchange rate regimes / Piet Sercu, Raman Uppal. p. cm. — (Japan-U.S. Center Sanwa monographs on international finance markets) Includes bibliographical references. ISBN 0-521-56294-5 (hb) 1. Foreign exchange rates — Mathematical models. I. Title. II. Series. III. Uppal, Raman. HG3823 .S465 2000 332.4'5 21 - dc21 ISBN-13 978-0-521-56294-2 hardback ISBN-10 0-521-56294-5 hardback ISBN-13 978-0-521-03423-4 paperback ISBN-10 0-521-03423-X paperback

99-040246

To my parents, Jan Sercu and Therese Reynaert, and to my wife, Rita Mosselmans Piet Sercu

To my grandparents, Jaswant Singh and Gobind Kaur Raman Uppal

Contents

Acknowledgments Guide to Notation 1

2

3

page xiii xv

Introduction and Overview 1.1 Our Objective and the Contribution of Our Work 1.2 Outline of the Monograph and Summary of Major Results

1 1

Modeling Exchange Rates: A Survey of the Literature 2.1 Exchange Rates and National Price Levels 2.2 Spot Exchange Rates, Forward Exchange Rates, and Interest Rates 2.3 Exchange Rates and the Balance of Payments 2.4 Asset Models of the Exchange Rate 2.5 Exchange Rate Models with Microeconomic Foundations

5 6

A Simple General-Equilibrium Model of an International Economy 3.1 Motivation for the Modeling Assumptions 3.1.1 Advantages of the General-Equilibrium Modeling Approach 3.1.2 Modeling the Distinction between Nations 3.1.3 Monetary Policy and Exchange Rate Regimes 3.1.4 Advantages of the General-Equilibrium Approach for Empirical Tests 3.2 Details of the Basic Model of an Endowment Economy 3.3 Extension of the Basic Model to a Production Economy 3.3.1 The Dynamics of the Spot Exchange Rate 3.3.2 The Nominal Exchange Rate in the Production Economy 3.4 Other Extensions

2

9 11 12 15 17 17 17 18 22 22 23 29 32 33 34 ix

Contents

4

5

6

7

The Spot Exchange Rate in a Large Class of General-Equilibrium Models 4.1 The Economy and the Equilibrium Exchange Rate 4.2 Characterizing the Level of the Exchange Rate 4.2.1 The Exchange Rate under Homothetic, CRRA Utility 4.2.2 Purchasing Power Parity 4.2.3 Implications of the General Model for PPP Tests on First-Differenced Data 4.3 Empirical Tests of PPP 4.3.1 Review of the Empirical Methodology Used to Test PPP 4.3.2 Data 4.3.3 ADF and Cointegration Tests of PPP 4.4 Empirical Tests of the Model with Homothetic CRRA Utility 4.5 Conclusion Forward Exchange Rates in a Model with Segmented Goods Markets 5.1 Related Literature 5.2 Implications of General-Equilibrium Model for UIP in Real Terms 5.3 The UIP Relation in Nominal Terms 5.4 Conclusion International Trade Flows, Exchange Rate Volatility, and Welfare 6.1 Background and Related Literature 6.2 The Economy 6.3 The Relation between Trade and Exchange Rate Risk 6.3.1 The Effect of Output Volatility on Exchange Risk and Expected Trade 6.3.2 The Effect of Segmentation on Exchange Rate Volatility and Trade 6.4 Discussion of the Model and Its Implications for Empirical Work 6.5 Conclusion International Capital Flows and Welfare 7.1 The Risk-Sharing Gains from Financial-Market Integration 7.2 Other Sources of Gains from Financial-Market Integration

35 36 39 39 42 43 45 45 48 48 52 54 57 58 60 63 64 66 67 70 73 73 75 76 78 82 83 85

Contents

7.3 7.4

The Welfare Costs of Segmented Commodity Markets International Financial Flows 7.4.1 Determining the International Financial Flows 7.4.2 Analysis of International Financial Flows Conclusion

87 90 91 94 97

Tariff Policy with International Financial Markets 8.1 Optimal Tariff Rates and Financial-Market Integration 8.1.1 The Model with Endogenous Tariff Policy 8.1.2 Results on Optimal Tariffs 8.2 Tariff Policy, Financial Markets, and Welfare 8.3 Implications of Financial Markets for Policy Coordination 8.4 Conclusion

99 100 100 101 102

7.5 8

9

10

Endogenous Monetary Policy and the Choice of Exchange Rate Regime 9.1 Money and Exchange Rate Regimes: A Review 9.1.1 Money Demand 9.1.2 Money Supply and the Government's Economic Role 9.1.3 The Exchange Rate Regime 9.2 The Model 9.3 The Derived Utility of Absorption and Effects of Monetary Policy 9.3.1 The Derived Utility of Absorption 9.3.2 The Effect of Monetary Policy on Hiring and Production Decisions 9.3.3 The International Sharing Rule 9.3.4 The Nominal Exchange Rate 9.4 The Exchange Rate under Alternative Monetary Rules 9.4.1 An Idealized EMS: Fully Coordinated Monetary Policy 9.4.2 The Nash Game 9.4.3 Monetary Union 9.5 Conclusion

103 103 104 104 105 107 108 110 113 113 115 116 117 118 119 121 122 123

Concluding Thoughts

125

References Author Index Subject Index

129 147 151

Acknowledgments

Over the past ten years, our research effort has been devoted to understanding the behavior of exchange rates, the relation of exchange rates to interest rates, international trade and cross-country capital flows, and the effect on these variables of tariff and monetary policy. Given our focus on large developed economies, such as Japan, the United States, and countries in Western Europe, our view has been that the economic models used to analyze the relation between exchange rates and trade in goods and financial capital should be general equilibrium in nature rather than those of small open economies. In 1995, our proposal was chosen for the fourth Sanwa Monograph Award. In this monograph we present the results of our research based on general-equilibrium models, along with a description of related work on the analyses of exchange rates, trade flows, financial flows, and monetary policy in international economies. We gratefully acknowledge the support of the Sanwa Bank through its promotion of the Sanwa Monograph Program. We are particularly indebted to Professor Ryuzo Sato and Professor Rama Ramachandran of the Center for Japan-U.S. Business and Economic Studies at New York University for their encouragement. We would also like to acknowledge the help of two anonymous referees who made several suggestions for improving the substance and exposition of this monograph. While working on this research we received helpful comments from several individuals, whom we would like to thank: David Backus, Richard Baillie, Anton Barten, Suleyman Basak, Geert Bekaert, Martin Boileau, Jim Brander, Menzie Chinn, Marnik Dekimpe, Harris Delias, Mick Devereux, Glen Donaldson, Silverio Foresi, Ken Froot, Mike Gallmeyer, Geert Gielen, Robert Hodrick, Michelle Lee, Kai Li, Ronald MacDonald, Geert Rouwenhorst, Gonzalo Rubio, Gregor Smith, Frans Spinnewyn, Jim Storey, Rene Stulz, Linda Van de Gucht, Simon van Norden, Tom Vinaimont, Simon Wheatley, and seminar participants at Boston University, Carnegie Mellon University, Erasmus University, HEC School of Management, Catholic University of Leuven, Massachusetts Institute of Technology, Northwestern University, Universidad del Pais Vasco, University of Alberta, University of British Columbia,

Acknowledgments

University of Vienna, the 1995 meetings of the Center for European Policy Research, the 1995 and 1997 meetings of the European Finance Association and the European Financial Management Association, the 1996 conference on Exchange Rates at the National Bureau for Economic Research (NBER), and the 1995, 1996, 1997, and 1998 meetings of the Western Finance Association. We are especially beholden to Prakash Apte, Paul De Grauwe, Bernard Dumas, Burton Hollifield, Khang Min Lee, Maurice Levi, Vasant Naik, Cynthia Van Hulle, and Tan Wang with whom we have worked on issues related to those discussed in this monograph and from whom, in the course of this research, we have learned much. Raman Uppal was visiting Catholic University of Leuven and MIT during the course of this project and would like to thank these institutions for the hospitality extended to him. Finally, we would like to thank our home institutions, Catholic University of Leuven and the University of British Columbia, for providing us with a rich intellectual environment over the past ten years.

Guide to Notation

English Alphabet ck(t) ck](t) dki(t) F(t) F(t, t + 1) FP(t, t + 1) gk i j k K(t) Lk mk Mk nB(t) n Pk (t) Pk Pki(t) pkj{t) rk qk(t) RP(t, t + 1) S{t)

vector of consumption quantities ckj(t) of good j (=1, . . . , N) in country k consumption of good j in country k at time t the dividend paid by security /, in units of currency k net foreign investment account forward exchange rate at time t for a transaction at F{tJ

V(t)~S{t)'the f ° r w a r d exchange rate premium consumption of the government (public) good in country k subscript used to refer to a particular security subscript used to refer to a particular good subscript used to refer to a particular country (k = 1 is home country) stock of physical goods located in the home country at time t supply of labor (time spent working) in country k money supply in country k YlNj=\ ckj(t)Pkj(O, nominal spending in country k number of bonds owned by the domestic resident number of shares of the firm k owned by the domestic resident log Uk(t) the price of security / in units of currency k the local currency price of good j in country k the interest rate in country k the endowment in country k at time t E,[S{t+\)\-F{tj+\)^ t h e foreign-exchange risk premium nominal exchange rate (value of one unit of foreign currency)

Guide to Notation

Tk

uk V(Mkit), pk(t)) viMkit), pkit)) , Kiit)] wk Wit)

Z(t) Zkit) V[Ktit),

,t]

log of the nominal exchange rate for country k tax in country k time-additive utility function (with a constant discount rate) utility function of the representative investor in country k indirect utility of nominal spending in country k indirect utility of nominal spending in the linear homogenous case maximum undiscounted value of central planner's objective function wage rate in country k wealth of the home investor at time t amount of goods exported from country k cumulative amount of goods exported from country k quantity of private good that is used by government to produce gk the real exchange rate random white noise affecting the production process in country k maximum value of central planner's objective function

Greek Alphabet impatience parameter for country fc's future consumption function indicating a positive monotone transformation, reflects risk aversion relative risk aversion r](t)

fl

n*

~ dv./dc. k' d e £ r e e of relative risk aversion (in real terms) slope of the upper ray of the region of no trade aV( ?Q(0 A ' (0) ' m a r g i n a l indirect utility of nominal spending in country k instantaneous mean return of the home production process price level, computed on the basis of marginal consumption price level, computed on the basis of average consumption

Guide to Notation Ok a r Vk(ck(t)) co(t)

xvii

a constant reflecting the relative wealth of two countries instantaneous volatility of the aggregate production process proportional cost for transferring goods from one country to another function that is linear homogenous in consumption quantities ln[ATi (t)/K2(t)], log of the ratio of physical capital at home and abroad

1

Introduction and Overview

1.1

Our Objective and the Contribution of Our Work

As summarized by Krugman (1989), there are two prominent puzzling facts since the collapse of the Bretton Woods system. First, why has the floating-rate regime led to an increase in the volatility of real exchange rates? The consensus expectation in the late 1960s and the early 1970s was that real rates would be more stable, but the experience has been quite to the contrary (see Frankel, 1993, chap. 10). Second, why has the impact of these enormous swings in the real exchange rate on national outputs and inflation rates been so limited? Baxter and Stockman (1989) and also Frankel and Rose (1995) provide empirical evidence that, except for an increase in real exchange rate volatility, other macroeconomic aggregates have not been affected by the change in the exchange rate system in the 1970s. Perhaps more controversially, Krugman also holds that the large fluctuations in the value of, in particular, the U.S. dollar relative to the deutsche mark and the Japanese yen, are irrational bubbles. Furthermore, international capital flows have not smoothed out fluctuations in outputs and investments as expected. Many academics and politicians also think that the volatility of the exchange rate hinders international trade and international investments and conclude that a return to a system of fixed exchange rates, if feasible, would be desirable. One illustration of such a system is the European Union's singlecurrency plan. In light of these considerations, and given the widespread perception that an increase in exchange rate volatility leads to a reduction in the level of international trade, various questions arise. Is the observed behavior of the exchange rate consistent with a rational model? Does exchange rate volatility hinder trade? What type of capital flows are consistent with a rational model? What are the channels and dynamics of the international transmission of shocks and what is the role of financial markets in dealing with these shocks? What is the effect of financial markets on a country's investment decisions and, through such decisions, on its growth and welfare? What is the effect of capital markets on a nation's optimal tariff policy? How would a return to fixed foreign-exchange rates affect macroeconomic aggregates and welfare, and 1

2

Exchange Rate Volatility

what are the requirements to make this feasible? Finally, how are the answers to these questions affected by the segmentation of the real sectors of international economies? While addressing these issues, our focus is on a world consisting of large developed economies. Thus, the model that we consider is a general-equilibrium one, rather than that of a small open economy. Moreover, consistent with the current state of the financial system, our analysis considers explicitly the role of financial markets in the determination of spot and forward exchange rates, trade flows, capital flows, and the setting of tariff and monetary policy.1 At the same time, our model allows for commodity markets to be segmented across countries so that nations are distinct.

1.2

Outline of the Monograph and Summary of Major Results

The remaining chapters in this monograph can be divided into three parts. The first part, consisting of Chapters 2 and 3, provides background information. In Chapter 2, we survey existing models of international economies, and in Chapter 3 we describe a simplified version our general model - one that is limited to a single consumption good and only two countries that are symmetric in their initial endowments and preferences - and also elucidate on the motivation for the assumptions that we make. The model is described in two versions: in the first, output is given exogenously and in the second the production decision is modeled explicitly. Our main objective in Chapter 3 is to contrast the general-equilibrium modeling approach with previous models of international economies, and to build some intuition in the context of these simple models that will be useful when analyzing variants of these models in later chapters. The principal contribution of this chapter is to show how one can develop a fairly simple framework to analyze macroeconomic quantities and policies. In the second part of the monograph, comprising Chapters 4, 5, and 6, our focus is on macroeconomic variables. The variables that we study are the spot exchange rate, the forward exchange rate, short-term interest rates, and trade flows. In Chapter 4 we extend our basic model to a multicountry, multigood setting that allows for international differences in preferences and endowments. We then derive the exchange rate in this setting. The contribution of this chapter is both on the modeling front, and in the empirical testing of the model. On the theoretical side, we show that the implications of the general-equilibrium model 1

Andersen and Moene (1995) present work on the effect of the opening of financial markets on macroeconomic variables.

Introduction and Overview of the exchange rate are quite different than those implied by the monetary theory of exchange rates and purchasing-power parity (PPP). On the empirical front, we show that our model nests several specifications tested in the literature and that the general model provides a better explanation of exchange rate behavior than the standard models. In Chapter 5 our attention shifts from the spot exchange rate to the forward exchange rate and interest rates. Using a model with endogenous production, we study the implications of segmented commodity markets for the behavior of the forward exchange risk premium. We describe how a model with proportional shipping costs, and therefore deviations from PPP, can generate exchange rate behavior that is closer to the data than predicted by earlier models. In Chapter 6 we examine trade flows and the relation between exchange rate volatility, trade, and welfare. Existing models analyze exchange rate volatility in a partial-equilibrium setting (see, e.g., De Grauwe, 1988; Franke, 1991; and Viaene and de Vries, 1992), whereas the model that we construct is a general-equilibrium one, which implies that it is internally consistent and permits welfare analysis. We find that while an increase in exchange rate volatility always lowers welfare, the increase in exchange rate volatility could be associated with either an increase or a decrease in trade. That is, the model offers one explanation for the empirical observation that there is little evidence of a negative relation between exchange rate volatility and the volume of international trade. Finally, in the third part of the monograph, we look at policy issues. In Chapter 7 we investigate the policy of opening financial markets. We start by discussing the effect of opening financial markets on welfare. One implication of our model is that integration of financial markets can have a substantial effect on welfare. The welfare gains can be direct ones, arising from improved risk sharing, or indirect ones, arising from the ability to invest in high-return, high-risk production technologies because of the improved opportunities to share risk across countries. A second finding is that the gains from opening financial markets are significant even when commodity markets are not perfectly integrated. The policy implication is that it is important to encourage theflowof financial capital even in the absence of perfect commodity market integration. In the models that we develop, we also find that the volume of capital flows exceeds the volume of trade flows; this is consistent with the data, which show that less than 20% of transactions in capital markets are related to trade flows. In Chapter 8 we examine the interaction between financial markets and the choice of tariff rates. We describe how the structure of financial markets influences directly the choice of optimal tariff rates: whereas in the absence of capital markets the optimal tariff is strictly positive, with perfectly integrated

4

Exchange Rate Volatility

financial markets the welfare-maximizing tariff rate is zero. Thus, there is an additional source of welfare gains from the integration of financial markets: besides the gains from risk sharing and improved production decisions, welfare improves also because the optimal tariff rate is driven down to zero. It turns out that the welfare gain from the reduction in tariffs is substantially larger than the gain from risk sharing. The analysis described in this chapter also suggests that financial markets can play an important role in coordinating international trade policy. Although money has been introduced in the basic models described in Chapter 3, and the models with money have been used in our analysis of spot and forward exchange rates in Chapters 4 and 5, the process driving money supply has been taken to be exogenous in these chapters. In Chapter 9 we examine monetary policies and the choice of an exchange rate regime in an economy where money supply is determined endogenously. In the context of a specific model, we identify the particular conditions under which a regime of fixed exchange rates is welfare maximizing. Chapter 10 contains our conclusions and some thoughts for future research. In this chapter, we also discuss the issues that we have not touched upon in our analysis.

Modeling Exchange Rates: A Survey of the Literature

With the collapse of the fixed exchange rate system established at Bretton Woods, the behavior of exchange rates changed dramatically. The demise of the fixed exchange rate system came at about the same time as the oil crisis, which meant that the substantial increase in exchange rate volatility was accompanied by high inflation. These changes in the economic environment led to a renewed interest in understanding movements in exchange rates and their effects on prices, wages, and employment. In this chapter, we survey different approaches to modeling exchange rates. In this survey, we limit our attention to the literature on exchange rate determination; the literature related to the other issues addressed in later chapters of the monograph is discussed in those chapters. Our discussion starts with the early models of exchange rates, lists the weaknesses of each model from both a theoretical and an empirical perspective, and then progresses to the next, more sophisticated, model.1 In this presentation, rather than attempting to provide the minute details of each model in the literature,2 we focus on highlighting the essential features of each modeling approach and relating it to our work in the chapters to follow. In the next chapter, we describe the features of the model that we use for the analysis in this book and contrast this model with other models described in this chapter. Limitations of our model, and the extensions to it that might lead to interesting insights, are listed in Chapter 10. Traditionally, economists have tried to explain the behavior of exchange rates based on three variables: price levels, interest rates, and the balance of payments. Hence, in Section 2.1 we consider models that relate the exchange rate to national price levels; in Section 2.2 we discuss the relation between spot 1

2

For a general overview of exchange rate models, see Isard (1995). De Grauwe (1990) presents a historical account of the development of exchange rate theories placed in the context of macroeconomic events. For the interested reader we provide references to articles where the details of each model are available.

6

Exchange Rate Volatility

exchange rates, forward rates, and interest rates in money markets. We examine exchange rate models based on the balance of payments in Section 2.3. In Section 2.4 we evaluate monetary models with and without flexible prices and also models based on the portfolio balance approach. Finally, in Section 2.5 we discuss general-equilibrium models of exchange rates.

2.1

Exchange Rates and National Price Levels

Although Cassel (1918) was the first to use the phrase "purchasing-power parity" (PPP), the idea that exchange rates should be related to the national price levels can be traced back to the School of Salamanca in Spain in the sixteenth century.3 In a single-good setting, the quantity of goods one can buy with one unit of currency defines the purchasing power of the currency. In an economy with many goods, purchasing power is defined in terms of a representative bundle of goods. One PPP condition, called absolute PPP, relates the absolute price levels in two countries to the level of the exchange rate between them. If, at a particular time t, the cost of the representative consumption bundle translated into domestic terms equals the cost of the representative bundle at home, we say that absolute PPP holds.4 If we denote the prices of the representative bundles at home and abroad by P\(t) and /M0> respectively, then absolute PPP holds when:

where S(t) is the number of units of the currency of country 1 required to buy one unit of the currency of country 2. As a theory of exchange rate determination, absolute PPP states that the exchange rate must adjust so that the foreign price level translated at the spot rate is the same as the domestic price level. Relative PPP, on the other hand, states that the percentage change in the exchange rate must equal the difference between the inflation at home and abroad. Although PPP is an intuitively appealing concept, there is little theoretical justification for it. In Chapter 4 we show that in a general-equilibrium model with optimizing agents, PPP holds only under very restrictive conditions. Most economists would also agree that empirically PPP is not a very good model for describing exchange rates in the short run. Thus, most of the recent debate 3 4

See Grice-Hutchinson (1952). In testing the PPP relation, one should compare the cost of the same consumption bundle across the two countries. In practice, the representative consumption bundles are different across countries, and so in testing for PPP one may need to construct a basket of goods that is identical across countries; see Kravis et al. (1975).

Modeling Exchange Rates: A Survey of the Literature

7

has centered around whether PPP is a good description of exchange rates in the long run.5 Balassa (1964) and Samuelson (1964) developed exchange rate models that link deviations from PPP to differences in productivity in an attempt to explain the empirical regularity that currencies of more developed economies tend to be overvalued by PPP standards. These models assume that there is a nontradable good in each country, and one perfectly tradable good. Balassa and Samuelson argue that the relative prices are determined by relative production costs and, hence, by relative productivities in the sectors producing traded and nontraded goods. Nontradables are associated with services and tradables with industrial goods; and in a more developed economy the weight for services in the consumption bundle, and therefore also in the price index, is larger than it is in a less developed economy. Deviations from absolute PPP are then explained as follows. The productivity of labor in the industrial sector relative to that in the service sector is higher the more developed the economy. Thus, if country 2 is the more developed country, then the relative price of nontradables versus tradables is higher in country 2 than in country 1. If equal weights are assigned across countries, this produces a real exchange rate in excess of unity; and this conclusion holds a fortiori if the weight for services is higher in the richer country. Similarly, it is argued that, over time, relative prices of services tend to rise everywhere; however, as the weight for services is higher in the richer country, this effect leads to an appreciation of the real value of the currency of the more developed country, country 2. The equilibrium model that we develop in Chapter 4 is consistent with this argument. Empirical evidence for PPP in the short run is weak; long and persistent deviations from PPP have been documented extensively in the empirical literature. To test the relative PPP hypothesis, one common regression equation that is used in the literature is:

where the left-hand-side variable is the percentage change in the exchange rate between times t and t + 1, and the term within the square brackets on the righthand side is the difference between the domestic and foreign inflation rates over this period. The null hypothesis that relative PPP holds implies that the slope coefficient, b, should be equal to unity and the intercept, a, should equal zero. A frequently cited study of relative PPP is the one by Cumby and Obstfeld (1984) where they test an equation that is similar to the one given here. They reject the relative PPP hypothesis for all five countries (against the United 5

Froot, Kim, and Rogoff (1995) use 700 years of data to evaluate the relation between exchange rates and commodity prices.

8

Exchange Rate Volatility

States) in their sample. This test was extended to the case of eleven countries by Roger Huang (1987), and PPP was rejected for most of these countries as well. Other empirical tests of PPP, which focus on the time series properties of the real exchange rate, have also found that the PPP relation is quite weak. Some authors tested (and often could not reject) the hypothesis that deviations from relative PPP accumulated randomly over time (Roll, 1979; Adler and Lehman, 1983). That is, it seemed that even in the long run relative PPP would fail. But these discouraging results appear partly due to the fact that the tests being conducted by these authors are not very powerful. Abuaf and Jorion (1990), using a different methodology, show that cumulative deviations from relative PPP tend to halve after three years - that is, cumulative deviations from relative PPP have some tendency to correct themselves in the long run. In other words, the variance of PPP deviations does not increase proportionately with time. These results are consistent with those of other tests: for example, Huizinga (1987) and Huang (1990), using a wide range of techniques, have found some support for the hypothesis that exchange rates have a tendency to revert back to their PPP values over the long run. Chapter 4 describes in greater detail these and other tests that are based on cointegration analysis.6 We conclude that the relative PPP relation may have some power in the medium to long run (several years rather than several months). Relative PPP may also hold rather well in the short run if the source of shocks is nominal.7 It may also do well when inflation is high, as was the case in Germany around 1930 and after the Second World War, and in Brazil in the 1970s. McNown and Wallace (1989) conduct an empirical study of relative PPP in high-inflation countries such as Argentina (where prices increased by a factor of 250,000 between 1976 and 1986), Brazil, Chile, and Israel and find support for PPP. But even in these cases there are substantial period-by-period deviations from relative PPP - deviations as large as 800% per month. Thus, the exchange rate and the difference in inflation levels across countries usually do not fully and perfectly offset each other, consistent with the Keynesian view of the world. The sluggish response of prices to changes in the nominal exchange rate also implies that movements in the real and nominal exchange rates are closely related. As pointed out by Krugman (1990, 1993), the close relation between real and nominal exchange rates suggests that nominal shocks do have real effects. Bayoumi and Eichengreen (1994) and Eichenbaum and Evans (1992) find that 6 7

Froot and Rogoff (1995) provide an extensive survey of this literature. This was already recognized by Cassell (1922).

Modeling Exchange Rates: A Survey of the Literature

nominal shocks can explain a large proportion of the variance of the exchange rate since the end of the Bretton Woods agreement. Clarida and Gali (1994) obtain similar results using a very different identification scheme. These results indicate that a country can use monetary policy to affect the real exchange rate.8 However, given the large variation in the nominal spot rate relative to that in inflation rates, it is unlikely that exchange rates can be explained by international inflation differentials in the short run. More likely the short-term variation in exchange rates is caused by interest rate changes, or news about the relative state of the domestic and foreign economies, or even changes in the prices of other assets.

2.2

Spot Exchange Rates, Forward Exchange Rates, and Interest Rates

The PPP approach to determining the exchange rate is based on the view that the demand for currencies is derived from the demand for goods. But, as early as the nineteenth century, policy makers knew that they could influence the demand for money, and hence the exchange rate, by changing interest rates. There are, in fact, two relations between interest rates and exchange rates. The first one, covered interest rate parity, is an arbitrage-based relation. It states that, in the absence of impediments to international capital flows, the return from investing in a domestic riskless asset should be the same as that from investing in a foreign riskless asset and covering the exchange risk with a forward contract: [1 + r,(f, t + 1)] = [1 + r2(f, t + 1)] x

F

where r^t, t + 1) is the riskless rate between t and t + 1 in country k and F(t, t + 1) is the forward exchange rate between time t and t + 1. This relation between spot exchange rates, forward rates, and interest rates was known to Italian bankers as far back as the Renaissance. As far as we know, the first published version of this relation is in Cournot's Recherches sur les principes mathematiques de la theorie des richesses (1838). This relation was later rediscovered by Paul Einzig (1937), a reporter for the Financial Times, who picked it up from London bankers. Marston (1995) examines this relation for the G-5 countries and finds that the returns from investing in any of these currencies is the same in both national and Eurocurrency markets. 8

We will analyze such a setting in Chapter 9.

10

Exchange Rate Volatility

The second relation, uncovered interest rate parity (UIP), relates the current forward rate to the future spot rate. This relation hypothesizes that the return from investing in a riskless domestic asset should be the same as the expected return from investing in a riskless asset denominated in terms of the foreign currency - even when the foreign investment is not hedged with a forward contract: [ l + r , ( M + l)] = [ l + r 2 ( M + l ) ] x

S(t)

where Et is the expectation conditional on all information available at time t. To obtain an equation for the determination of the current spot rate, the UIP equation is rewritten with the current exchange rate as the dependent variable:

The problem in using regression analysis to test the UIP relation as it is expressed here is that the right-hand side is in terms of expectations, which are unobservable; all one can observe is the realized value of the spot rate at time t + 1, S(t + 1). This problem is solved by noting that in an informationally efficient market, the deviation between the market's forecast and the actual outcome must be totally unpredictable. Thus, tests of UIP are joint tests of the relation and of market efficiency. With the assumption of efficient markets, one can rewrite the preceding equation in terms of the observed spot rate, S(t + 1), and its forecast error, e(t, t + 1). In terms of percentage changes, this gives us:

[

L

S(t)

J

[\+r2(t,t+\)]

which, using the covered interest parity relation, can be expressed as

For notational ease, one can define the percentage change in the spot rate as s(t, t + 1), and the percentage difference between the forward and spot rates as the forward premium FP(t, t + 1): »

and

This allows us to rewrite equation (2.1) as: (2.2)

s(t, t + 1) = a + 0 FP(t, t + 1) + e(t, t + 1).

Under UIP, s(t, t + 1) = FP(t, t + 1) + e(t, t + 1) so the null hypothesis is that a = 0andj8 = 1.

Modeling Exchange Rates: A Survey of the Literature

11

Although UIP would lead us to expect a value of /3 that is statistically close to 1, Froot and Thaler (1990) report that the average slope coefficient obtained from seventy-five empirical studies is, in fact, —0.88. While some studies find a slope coefficient that is positive, not a single study finds a slope that is equal to or greater than unity; details of this literature are provided in Baillie and McMahon (1989b), Engel (1994), Hodrick (1987), Lewis (1995), and Marston (1995). Note that since )3 is typically not equal to zero in the regression tests of UIP, the forward premium does have some power to predict the future spot rate although the sign of the relation is often opposite to what we would expect under UIP. In practice, however, the unpredictable component e(t, t + 1) is very large in comparison with the predictable component, FP(t, t +1), and thus the exchange rate remains difficult to forecast. Because of the overwhelming evidence from many regression tests, we can safely conclude that /3 is significantly below unity. That is, the forward rate is a biased predictor of the future spot rate. One interpretation is that investors are not risk-neutral and that the bias in the forward rate's prediction of the spot rate reflects a risk premium.9 Fama (1984) provides a nice characterization of the risk premium: his analysis shows that to explain the bias in the forward rate, the risk premium needs to be large in magnitude and strongly negatively correlated with the forward premium. In Chapter 5, we provide the details of Fama's analysis and then evaluate this risk premium in a general-equilibrium model where commodity markets are segmented, giving rise to deviations from PPP.

2.3

Exchange Rates and the Balance of Payments

The balance-of-payments (BOP) theory is a Keynesian flow approach to the determination of the exchange rate. According to the BOP theory of exchange rates, the supply and demand for a currency arise from the items of the current and capital accounts of the BOP. The objective of the BOP theory of exchange rates is to explain (a) why exchange rates and prices are not as predicted by PPP and (b) why we see continuous capital flows between countries. The explanation offered for these two observations is based on a Keynesian view of the world that prices of goods are sticky in the short run. Moreover, given that prices adjust slowly to a change in economic conditions, economies are in a state of persistent disequilibrium leading to the flow of capital between countries. According to the early proponents of the BOP approach to exchange rates,10 the current account is determined by prices of goods at home (P\) and prices 9 10

Other explanations for a slope coefficient of less than unity are discussed in Chapter 5. See, for example, Marshall (1923), Lerner (1944), Robinson (1947), and Metzler (1949).

12

Exchange Rate Volatility

of goods abroad, translated into domestic terms using the spot rate (SP2), with the added assumption that the functional relation between the current-account balance and the relative prices abroad and at home, SP2/ P\, is greater than unity. The main point made by these models is that the exchange rate can affect the current account only if it changes domestic absorption relative to domestic production. The limitations of this early elasticities approach are that it assumes the demand for exports and imports depends only on prices and ignores the role of other variables (such as income), and it also ignores items of the capital accounts. Moreover, this analysis is static rather than intertemporal and is not based on microeconomic principles. The Mundell (1960, 1961, 1963) and Fleming (1962) approach added to the goods and money markets a consideration of the international flow of capital. The transactions in the capital account are assumed to depend on the relative interest rates at home and abroad. The functional relation between the domestic interest rate and foreign investment is assumed to be positive; that is, an increase in the interest rate at home attracts foreign investment and leads to an inflow of international funds. Analogously, the relation between the capital-account balance and the foreign interest rate is negative. Finally, the capital account depends also on the exchange rate S, because the value of S will determine the value of the foreign return in terms of domestic units. Thus, in contrast to the PPP theory of exchange rates, the BOP theory acknowledges that the demand for a currency may arise also from investors' direct and portfolio investment decisions. Within this framework, the foreign interest rate and price level are assumed to be constant, and then one can analyze the effects of domestic monetary and fiscal policies. One of the major results of the Mundell-Fleming framework is that the relative effectiveness of monetary and fiscal policies depends on the exchange rate regime and the mobility of financial flows. A major weakness of this approach, however, is that it ignores the fact that investors can hold assets with different risk-return trade-offs, and that agents would make this choice in an optimal fashion.1' In contrast, when we evaluate tariff policy in Chapter 8 and monetary policy in Chapter 9, we consider an intertemporal framework, where investors choose portfolios of financial assets in an optimal fashion.

2.4

Asset Models of the Exchange Rate

The asset approach to exchange rate determination shifted attention from the trade balance to capital flows as a determinant of exchange rates. We can divide 1

' See Frenkel and Razin (1987) and Krugman and Obstfeld (1991) for extensions of the MundellFleming model.

Modeling Exchange Rates: A Survey of the Literature

13

the asset models of the exchange rate into two groups: those that consider only moneys (Johnson, 1972), and those that consider portfolios of risky assets (Branson, 1968; Girton and Henderson, 1973).12 The monetary approach was developed by Mussa (1976), Frenkel (1976), and Bilson (1978, 1979). Its building blocks are the quantity theory of money, UIP, and PPP. It shows that the exchange rate today is the discounted value of future expected money stocks and output levels at home and abroad. Thus, the monetary approach views the exchange rate like any other asset price and, hence, the value of the spot rate changes whenever relevant information is released. In that respect, the asset approach overcomes a major limitation of the PPP approach: because the arrival of new information is much more frequent than changes in relative commodity prices, the asset approach can potentially explain the frequent changes observed in the exchange rate. The monetary approach is also different from the BOP (Keynesian) approach because it does not assume that prices are sticky or that the economy is in a state of constant disequilibrium. The monetary model relies on the assumption that PPP holds. Given the poor performance of PPP in the data, Dornbusch (1976) developed a rationalexpectations model in which prices are sticky in the short run, but the exchange rate, treated as an asset price, can respond to new information instantly.13 He then shows that in such a model, the exchange rate could overshoot: for example, in response to an unanticipated monetary shock, the exchange rate responds more than proportionately to the shock in order to compensate for the stickiness in prices of goods. In the long run, as prices adjust, the exchange rate then returns to its equilibrium value. In contrast to the monetary approach, the portfolio-balance approach does not assume that investors ignore risk and, therefore, regard domestic and foreign bonds as perfect substitutes. In this model, risk-averse investors choose how to allocate their wealth across different risky assets. The demand for these assets depends on expectations of changes in the exchange rate. Meese and Rogoff (1983) find that the empirical performance of the flexibleprice model, the model with sticky prices, and the portfolio-balance approach to be very poor; these structural models typically fail to outperform a randomwalk model in predicting exchange rates out of sample, even when one assumes that the driving variables could be forecasted perfectly. Various extensions of these structural models, such as a model with time-varying parameters 12 13

See Branson and Henderson (1985) for a survey of these models. A review of this paper, and related models, can be found in Obstfeld and Stockman (1985) and also in Obstfeld and Rogoff (1996).

14

Exchange Rate Volatility

(Wolff, 1987; Schinasi and Swamy, 1989)14 and models with nonlinearities (Diebold and Nason, 1990; Meese and Rose, 1991) outperform the randomwalk model, but not by much.15 The poor performance of models based on fundamentals, especially at short horizons, suggests that changes in nominal exchange rates must either be due to unobservable fundamentals or to nonfundamental factors such as speculative bubbles. However, the observed difference in exchange rate volatility under different exchange rate regimes suggests that the first explanation is unlikely, and Frankel and Rose (1995) show that the evidence in favor of speculative bubbles is also not strong. From a theoretical viewpoint, a shortcoming of these models is that they are static and partial-equilibrium models in that they take the return process on risky assets to be exogenous. In the general model that we describe in Chapter 4, returns on risky assets are determined by market-clearing conditions, and the demand for these assets is the outcome of an intertemporal optimization exercise. Moreover, the exchange rate in our model is nonlinear and characterized by changing coefficients. The models described here were developed to understand the behavior of a freely floating exchange rate. However, as attention of policy makers shifted toward a regime where there were limits on the flexibility of exchange rates, models were developed to analyze the dynamics of the exchange rate within a target zone.16 Krugman (1991), assuming that the target zone was perfectly credible, showed that the distribution of the exchange rate would be U-shaped, implying that the exchange rate would spend most of its time near the edges of the zone.17 Dumas (1992) showed that one could obtain a similar result in a general-equilibrium model where the commodity markets of the two countries were segmented by shipping costs. The details of the model by Dumas are given in Chapter 3, and the implications of this model for UIP and capital flows are explored in Chapters 5 and 7, respectively. 14

15

16 17

Another approach, especially for characterizing the behavior of exchange rates at high frequencies, is to use time-series models. For a description of the high-frequency properties of nominal exchange rates, see de Vries (1994). For time-series models of the exchange rate, see Baillie and McMahon (1989a, 1989b) and Baillie and Bollerslev (1989, 1990). See Dornbusch (1988), Meese (1990), and Frankel and Rose (1995) for a review of such models and tests of their empirical performance; Baillie and McMahon (1989b) also provide extensive details on the econometric evidence. See also De Grauwe (1994), Evans and Lothian (1993), and Mark (1995). Engel and Hakkio (1993) conclude that a target zone system for the U.S. dollar, yen, and mark is unlikely to lead to a decline in exchange rate volatility. Other models in the target zone literature allow for the possibility of a change in the zone itself (through a shift in the central parity). This literature is surveyed in Svensson (1992) and Bertola(1994).

Modeling Exchange Rates: A Survey of the Literature

2.5

15

Exchange Rate Models with Microeconomic Foundations

To address the shortcomings of the static models described here, intertemporal models of the real exchange rate with strong microeconomic foundations have emerged. The early contributors to this approach were Lucas (1982), based on the work in Lucas (1978), Helpman and Razin (1979, 1982), and Stockman (1980, 1983, 1987). Under this approach, the equilibrium exchange rate is a consequence of the optimizing behavior of individuals who can invest in financial claims and face an intertemporal budget constraint.18 Some of these models are partial-equilibrium models because they assume that one country is small and, therefore, takes world prices as given; other models are general equilibrium in nature and allow each country's decisions to affect world prices. The early models assumed that all goods were perfectly tradable (Stockman, 1980; Lucas, 1982; Hodrick, 1987). This, however, implied that the real exchange rate was always equal to unity. Later models assumed that in each country at least one good was nontradable: see, for instance, Stulz (1987), Devereux (1989), Stockman and Delias (1989), and Stockman and Tesar (1995). Based on this work, Backus, Kehoe, and Kydland (1992) developed international real business-cycle models to evaluate the ability of dynamic generalequilibrium models to match features of the international business cycle data. Dumas (1992), instead of assuming that some goods are nontraded, introduces a cost for transferring goods from one country to another; thus, in this setting whether a particular good is traded or nontraded on a given date is determined endogenously. To extend the models of real exchange rates to include a role for money, several approaches have been adopted. In the first, money is introduced via a cash-in-advance constraint (Lucas, 1982, 1990; Svensson, 1985a, 1985b; Fuerst, 1992; Bekaert, 1994). Grillio and Roubini (1992) extend the Lucas (1990) modeling device of a participation constraint to a two-country setting; they use this model to show that the exchange rate can exhibit excess volatility.19 Alternatively, money is introduced through the utility function: see Sidrauski (1967) and Brock (1974) for early contributions (in the context of a closed economy) followed by Karekan and Wallace (1980), McCallum (1983), LeRoy (1984), Feenstra (1986), Danthine and Donaldson (1986), Stulz (1986a, 1986b), Bakshi and Chen (1996), and Basak and Gallmeyer (1998). Finally, one can introduce a stochastic demand for money via a transaction-cost technology, as in Bansal et al. (1993), Bekaert (1996), and Bekaert, Hodrick, and Marshall (1996). 18 19

See Dumas and Solnik (1995) for empirical tests of a particular equilibrium model of exchange rates. For a discussion of these models, and an extension to a continuous-time setting, see Wang (1998).

16

Exchange Rate Volatility

Another stream of the literature developed models of price stickiness: Svensson and van Wijnbergen (1989) extended the Lucas (1982) model to require that prices must be set one period in advance (by monopolistically competitive firms). More recently, Obstfeld and Rogoff (1995a) have modeled imperfections in the commodity market via the assumption of monopolistic competition and nominal price rigidity (and the results are quite different from those in the Mundell-Fleming model). Because all goods are freely traded in these models, however, there are no deviations from PPP. These models were followed by the model of Chari, McGratten, and Kehoe (1996), which employs staggered price setting, and that of Kollmann (1997, 1998), where prices have to be set two to four periods in advance.20 Devereux (1997b) provides a survey of recent models of the real exchange rate. He divides the class of models with money nonneutralities into two sets: first, the "liquidity approach," where the focus is on the effect of monetary policy via the financial markets; and second, the "sticky-price" approach, where money has an effect because prices are sticky in the short run. Devereux argues that the empirical evidence supports many aspects of the general-equilibrium approach to exchange rates based on sticky prices. Allen and Stein (1995) also provide strong empirical evidence in support of equilibrium models of the exchange rate in the medium and long term. The framework that we use in this monograph belongs to this class of intertemporal, general-equilibrium models. Our model can be considered an extension of the Lucas (1982) model, and in its most general version (see Chapter 4) allows for multiple goods, some tradable, others nontradable, and still others that are tradable at a cost. We allow for international differences in commodity prices by introducing a cost for shipping goods across countries. We introduce money using the cash-in-advance constraint, where it will have an effect on real variables because of the assumption that prices (wages) may be sticky in the short run (see Chapter 9). The next chapter provides the details of a simple version of this model. 20

Extensions of Obstfeld and Rogoff's (1995a) model are also in Hau (1997a, 1997b). See also Atkeson and Kehoe (1997).

3

A Simple General-Equilibrium Model of an International Economy

In this chapter, we describe the basic framework that we use to undertake most of our analysis. In Section 3.1 we motivate our modeling assumptions and provide empirical support for these assumptions. In Section 3.2 we provide the details of the analytical model of a two-country endowment economy that we use throughout our analysis. In Section 3.3 we extend this model to allow for endogenous production decisions. Other extensions to the simple model that will be undertaken in the chapters to follow are described in Section 3.4.

3.1

Motivation for the Modeling Assumptions

Our objective is to understand the exchange rates between developed economies. We also wish to analyze the influence of financial markets on the flow of goods and financial capital between such economies, and through these flows, the effect on welfare and growth. Given these objectives, the framework we consider has the following characteristics: 1. The model is of a dynamic, stochastic, general-equilibrium world economy in which decision rules for individual agents are derived from optimizing behavior. 2. The model is one in which the economies of individual countries are distinct in that their commodity and financial markets need not be perfectly integrated. 3. Monetary policy and the exchange regime matters, in the sense that they affect the allocation of real resources. We indicate below why these three features are important for a model used to address the issues considered in this monograph. 3.1.1

Advantages of the General-Equilibrium Modeling Approach

Given that the focus of our analysis is on large developed economies such as the countries of Western Europe, Japan, and the United States, it is important that we consider a general-equilibrium model where prices are determined 17

18

Exchange Rate Volatility

endogenously rather than one where the country of interest is assumed to be "small" so that its actions have no impact on prices. Moreover, because the real and financial decisions of investors are interlinked, a general-equilibrium approach is needed to analyze simultaneously the effect of these decisions on prices in commodity and capital markets. Our general-equilibrium model is also firmly based on dynamic optimization rather than on ad hoc linear behavioral rules.1 As Stockman (1988a, p. 534) states, "Dynamic stochastic general equilibrium models based on individual optimization generally give different results from the kind of models that were previously in general use. The results obtained in the older models often failed to be robust to these ad hoc assumptions about portfolio allocations." Helpman and Razin (1979a) likewise list a dynamic optimization-based, general-equilibrium approach as one of the requirements for a framework used to compare alternative exchange rate regimes. Their other requirements, all of which are satisfied by the model that we consider, are that: the economy's real resource constraint should be independent of the exchange rate regime; all demand functions should be derived from intertemporal utility-maximizing behavior, and these utility functions should also be used for making welfare comparisons; exchange rates should be determined endogenously; and the financial transactions that agents can engage in should not depend on the exchange rate regime. The general-equilibrium analysis also enables us to make welfare comparisons, and, thus, we can study issues related to changes in policies. In contrast, older models studying policy changes are subject to the Lucas critique because they postulated the decision rules of individual agents rather than deriving them from optimizing behavior.2 Finally, our model provides stronger testable restrictions for empirical work, as will be described in greater detail.

3.1.2

Modeling the Distinction between Nations

In the model we develop, countries are distinct from one another in an economically material way, which is necessary if one is to explain the stylized facts of international data. Dumas (1994) lists four stylized facts about international data that cannot be explained in perfectly integrated markets: deviations from purchasing-power parity tend to persist for long periods of time; investors' portfolios are biased toward domestic assets; cross-country consumption correlations are low; and there are violations of uncovered interest rate parity. Our model is consistent with all four facts. 1 2

See also the model in Gavin (1989). A survey of such models is provided in the previous chapter.

A Simple General-Equilibrium Model of an International Economy

19

Factors that could make "countries" distinct include: segmentation of commodity (and labor) markets, segmentation of capital markets, differences in output functions (supply factors), and differences in commodity preferences or attitudes toward risk (demand factors). The effects of different output and commodity-preference functions have been extensively studied in the (neo)classical theory of trade and are therefore well understood. Moreover, these differences are much less important for the issues that we wish to study. Thus, in our analysis, we typically assume that preferences and output processes are the same across countries and our focus is on the segmentation of commodity and capital markets. We explain how we model the segmentation of commodity and capital markets, why it is important to model this segmentation, and what it implies for our results. 3.1.2.1 Segmentation of Commodity Markets. In the literature on international macroeconomics, segmentation of commodity markets has typically been modeled either by introducing nontraded goods (e.g., Stulz, 1987, and Stockman and Delias, 1989) or costs for transferring goods across countries (e.g., Black, 1973, and Dumas, 1992).3 Ideally, one should allow for both types of commodity market segmentation. This is because nontraded goods constitute a large proportion of total expenditure; for example, OECD countries spend 60% to 80% of their incomes on services, which are essentially nontradable. Moreover, as noted in Stockman and Tesar (1995), it is important that a model include nontraded and partially tradable goods because a model with just one (tradable) good is likely to overstate the linkages between economies. Stockman (1990, p. 136) likewise states that, "Both theory and evidence on open economies suggest the inclusion of nontraded goods and multiple traded goods. Nontraded goods are quantitatively important and can play a role in breaking the link between foreign and domestic consumption."4 Krugman (1989) also stresses the importance of "home bias in consumption" for the analysis of the trade balance. Along with nontraded goods, tariffs and especially nontariff barriers5 are also a significant source of segmentation. Deardorff and Stern (1990) report that the average tariff in industrialized countries is about 6.6% (their table A7). Deardorff (1989) reports, on the basis of several studies, the low (high) estimates of ad valorem equivalents of nontariff barriers for the various traded goods in the major industrialized countries (in his tables 4 and B5). For example, in the United States the low (high) estimates range from 0% (0%) for machinery to 14.5% (20.5%) for food products. For Japan, the low (high) estimates are 3 4 5

Chapter 2 contains additional references to articles using these modeling approaches. See Devereux, Gregory, and Smith (1992) and Kollmann (1995, 1996) for evidence on low consumption correlations across countries. The nature of these barriers is described in van Nunen (1990).

20

Exchange Rate Volatility

0% (0%) for machinery and 27.1% (58.1%) for food. Melo and Tarr (1992, p. 200), based on their study of the textile, automobile, and steel industries in the United States, estimate that the average tariff that would generate the same welfare costs as those resulting from quotas in the three sectors is 49%. Cooper (1986) also provides empirical evidence on the openness of the U.S. economy. Finally, besides tariffs and nontariff barriers, factors such as pricingto-market (Marston, 1990) and transportation costs play a role in segmenting international commodity markets. Given the importance of nontraded goods and of tariffs and other trading costs, in its most general version our model (presented in Chapter 4) allows for three classes of goods: nontraded goods, traded goods (in the strict sense - that is, goods that are traded all the time), and tradable goods that are traded only if the cost of trading is smaller than the benefit. The three classes of goods, as well as the proportional costs we introduce for shipping goods internationally, are important to obtain a reasonable model for the real exchange rate and for the pattern of trade. A model in which all goods can be traded without friction is unrealistic; in such a model commodity prices would be equated across countries, thus flatly denying the possibility of a major phenomenon that we study: widely fluctuating real exchange rates. The introduction of shipping costs in a one-good setting is obviously a step in the right direction. This modeling choice is supported by the recent work of Engel and Rogers (1995), who study price differences for the same good across the United States and Canada. They find that distance matters: price differences increase with distance, even within a country. Second, national borders are important: price differences across U.S. and Canadian cities that are just across the border from each other are of the same magnitude as the price differences across two U.S. cities that are 2,500 miles away from each other. Wei and Parsley (1995) study the variability of commodity prices in OECD countries. They also find that distance is a significant determinant of price variability. The shipping cost specification is also supported by the recent tests by Obstfeld and Taylor (1997) and O'Connell and Wei (1997) that use Threshold AutoRegressive statistical models (TAR) and the Smooth Transition AutoRegressive models (STAR) in Michael, Nobay, and Peel (1997).6 3.1.2.2 Segmentation of Capital Markets. Highlighting the importance of financial markets, Keynes stated that, "The exchange rate is determined in the stock market." Along the same lines, according to Stockman (1988a, p. 546), "a serious model of exchange rates must be based on a general equilibrium model of financial markets." In our view, it is important that a model of developed 6

See also O'Connell (1996, 1998).

A Simple General-Equilibrium Model of an International Economy

21

economies include an explicit analysis of capital markets and capital flows for three reasons. First, from an empirical point of view, the volume of international financial transactions is very large (at least U.S. $1.5 billion daily in just the exchange markets), of which only a small proportion is estimated to be related to trade in goods and services. Second, results from general-equilibrium models in the presence of financial markets are very different from those obtained under incomplete markets. Likewise, as Stockman (1988a) remarks, the development of the financial sector influences the equilibrium in the real sector in significant ways, and government restrictions on capital flows (quantitative or tax-based) alter the real equilibrium in a way that is not a priori obvious.7 Thus, it is important to specify the structure of asset markets and the role of international financial flows. Third, there is some controversy as to whether the capital flows, enormous as they are, actually play the role that economists expect them to play.8 If true, this may have policy implications. Segmentation of capital markets can be modeled in at least three ways. One way is to introduce a tax on capital transactions, as in Black (1974) and Stulz (1981a). Alternatively, one could impose capital controls so that trade is possible in only a limited number (or quantity) of financial claims, usually implying that financial markets are incomplete. This approach is adopted in Subrahmanyam (1975), Errunza and Losq (1985), Sellin and Werner (1993), Basak (1995), and Lee (1998). Finally, one could explicitly model informational asymmetries as a source of home bias (as in Brennan and Cao, 1996). Although the third approach is beyond the scope of our current research agenda, our model can incorporate the first two types of capital market segmentation. Thus, our analysis extends the work of Cole and Obstfeld (1991), Sellin and Werner (1993), and Basak (1995), by allowing us to consider the effect on welfare of the interaction between imperfectly integrated commodity markets and capital markets (see Chapter 7).9

See Bayoumi (1997) for empirical evidence on the effect of capital flows on real activity. The absence of formal capital controls is not a sufficient condition for perfect integration. On the individual level, although theory predicts a high degree of international diversification (Solnik, 1974; Sercu, 1980; Adler and Dumas, 1983), in practice portfolios are characterized by substantial home bias (French and Porterba, 1991; Uppal, 1993; Cooper and Kaplanis, 1994). On the macroeconomic level, it is a puzzle why fluctuations in investment are mostly financed by fluctuations in savings rather than by international capital flows (Feldstein and Horioka, 1980; Krugman, 1989). However, Obstfeld (1986) shows that even in a model with high capital mobility, it is possible to generate the correlations between saving and investment observed in the data. A review of this literature can be found in Tesar (1991); Baxter and Crucini (1993) show that productivity shocks in a real business cycle model can also generate high correlations between national savings and investments. Our work also extends the analysis in Feeney (1994), where she evaluates whether trade in goods and financial securities are complements or substitutes; her analysis is in a setting where the country of interest is assumed to be small.

22

Exchange Rate Volatility

3.1.3

Monetary Policy and Exchange Rate Regimes

Having described segmentation of commodity and capital markets as the crucial factors that distinguish countries in our model, we now turn to the monetary sector and the choice of monetary policy and the exchange rate regime. Stockman (1983) lists the conditions under which a model of an international economy may be neutral to the exchange rate regime: Ricardian equivalence holds; there are no informational asymmetries about the policy maker; the exchange rate peg should not be maintained through assets that are not included in the efficient portfolios of households; unanticipated changes in future nominal prices should not affect the wealth of individuals; and, finally, money should not play any real role. The remarkable break in the volatility of the real exchange rate around 1973 strongly suggests that monetary arrangements can have significant effects. To obtain a model that does not preclude the possibility of any such effect, we permit monetary policy to influence real wages and, through that, the allocation of real resources. Thus, depending on the focus of our analysis, we consider both models where the monetary rule is given exogenously (Chapters 4 and 5) and where the choices of exchange rate regime and of monetary policy are endogenous (Chapter 9). 3.1.4

Advantages of the General-Equilibrium Approach for Empirical Tests

We now describe the advantages of the general-equilibrium modeling approach for understanding the data. In the empirical literature on exchange rates, researchers have typically tested reduced forms of theoretical models.10 In this case, although it is possible to determine whether a reduced-form model is rejected or not, one cannot identify the reason for the rejection. The main strength of our work is that the tests we consider are of a structural, general-equilibrium model. Because we are testing a particular structural model, it is possible to identify the source of any model rejection. That is, the empirical tests of the theoretical model (and those based on calibrations) indicate which features of a model must change if one wishes to explain the date. Moreover, as shown in Chapter 4, tests for several competing models can be implemented in nested form. Another potential advantage of testing a well-specified model is that the model yields the precise nonlinear relations between the relevant variables or parameters and imposes restrictions not only on expected values but also on higher moments. For instance, in the model described in Section 3.3, the 10

See Chapter 2 for references to the body of work testing structural models in reduced form. Edison and Melvin (1989) provide a survey of empirical work on the determinants of exchange rate regimes.

A Simple General-Equilibrium Model of an International Economy

23

exchange rate is nonlinear; and in Chapter 6 our model predicts a particular nonlinear functional form for the relation between exchange rate volatility and the volume of trade. Thus, tests can be formulated to take advantage of the knowledge of higher moments and of the particular functional form and thus will have much more power to reject a particular null hypothesis. Working with a general-equilibrium model is useful also because empirical tests that are in terms of consumption variables can often be restated in terms of financial variables (such as interest rates) by using the first-order conditions implied by the theoretical economy. Thus, this can eliminate the need for consumption data that are difficult to collect and are generally not of as good quality as financial data. This will prove to be useful when we evaluate the model using numerical calibration techniques, as in Chapters 5 and 7. A related advantage of the general-equilibrium approach is that it has immediately testable implications in terms of the aggregate data that are available. In contrast, partial-equilibrium models based on the behavior of a single firm, such as the ones used to analyze the relation between exchange rate volatility and trade, are inconsistent with the aggregate data that are used for empirical tests of this relation.

3.2

Details of the Basic Model of an Endowment Economy

In this section we present a general-equilibrium model of an international endowment economy and describe how to solve for the exchange rate, consumption policies, and trade volume. To simplify the exposition, we will start with the most basic version of our model. In the next section we extend the model to allow for endogenous production. Finally, in Section 3.4 we describe the various extensions to this model that we consider in later chapters.1' In the basic model, we assume that there are only two countries. The home and foreign country (k = 1 and 2, respectively) are similar in three respects. First, they are assumed to be populated by a large and equal number of infinitely lived consumers. Second, their financial markets are perfectly integrated, complete, and frictionless. Third, the countries are assumed to have started out with identical endowments, the firms generating the endowments are assumed to be perfectly competitive, and the parameters of the stochastic processes that determine future endowments are identical.12 The factors that distinguish one economy from another are the following. First, after the initial date the outputs of the good generally differ across countries, and costs for shipping goods across countries make 11 12

A glossary containing a guide to the notation used in this monograph is included in the frontmatter. These assumptions about symmetry across countries are relaxed in Chapter 4.

24

Exchange Rate Volatility

the commodity markets less than perfectly integrated. Second, each country has its own money, and the nominal stocks of money may differ across countries. In every period, each country is endowed with a quantity of a single good that is homogenous across countries, imperfectly tradable, and nonstorable. In each country, the available quantity of the good, qk(t), is assumed to be characterized by discrete-time, exogenous stochastic processes, as in Lucas (1982). There is a proportional cost,r, for shipping the good internationally. This cost is modeled as a waste of resources: if one unit is shipped, only 1/(1 H-r) units actually arrive. The simplest way to introduce money in the model is by using the cash-inadvance constraint and the timing convention used in Lucas (1982).13 Denote the money supply in country k by m/dt) and let the evolution of m^t) be given by a deterministic or stochastic process. We assume that domestic money is used to purchase goods consumed in the home country and foreign money for goods consumed abroad. The domestic and foreign goods prices referred to in this book are expressed in units of the corresponding country's currency. These prices may change over time because the local money supply changes, or because quantities available for consumption change. Let Ck(t) be the consumption quantity of the good in country k, and Xk(t) the exports from country k (before transactions costs). Given our assumption of complete and frictionless financial markets and perfectly competitive commodity markets, the decentralized solution is identical to that of the central planner because individuals can implement the optimal solution of the central planner through trading in financial claims. If we assume that the utility function in each country, u^, is time-additive with constant relative risk aversion (CRRA), (3.1)

VS

the central planner's objective is to choose the amounts of trade so as to maximize the aggregate utility: 14 (3.2a)

13

14

Max Et

That is, we assume that investors can purchase goods only with currency. The timing convention is such that investors learn about the current state of the world, including monetary shocks, before trading in the markets for securities and consumption goods. Given that investors can hold riskless securities with a positive nominal return, money will be held only within a period (to buy the known amount of current period consumption), and not across periods. The absence of weights preceding the utilities reflects the assumption that the two countries have started out with identical amounts of the good and that the endowment processes have identical parameters across countries. In the decentralized solution, the initial endowments determine the initial relative wealth of the two countries; and this, in complete markets, then determines how the claims on future consumption are distributed among the countries.

A Simple General-Equilibrium Model of an International Economy

25

subject to: (3.2b)

ci(r) =

(3.2c)

c2(t) = q2(t) - x2(t) •

1+T JC|(O 1+T

(3.2d) where 5 is the impatience parameter and r\ > 0 is the degree of relative risk aversion (RRA). To solve the problem in (3.2a), note that the utility function in (3.1) is time-separable, trade affects consumption only within the same period, and the constraints apply period by period. It follows that we can rewrite the intertemporal problem in (3.2a) as a static problem, Max C l ( r ) I -r]

+

C2(r)

1 -r]

subject to (3.2b, c, d).

We now explain the implications of the shipping cost. Given that it is costly to transfer the good from one country to another, it will be optimal to trade only when the price of the tradable good at home is sufficiently different from the price abroad. Note that in constraints (3.2b) and (3.2c), a shipment of x\(t) from the home country leads to an increase in foreign consumption of only xi (0/(1 + r), and likewise for shipments in the other direction. In the absence of shipping costs, it would be optimal to set the relative amount of consumption in the two countries equal to unity and correct any deviation of q2(t)/q\ (0 from unity by shipping goods. But in the presence of shipping costs, there will be a no-trade zone within which deviations of c2{t)/c\{t) from unity will be left uncorrected (see Figure 3.1). Only if q2(t)/q\(t) is outside the no-trade region will goods be exported from one country to another, and the shipped amounts will be such that C2(0/^i(0 remains on the nearest boundary of the no-trade region. We identify this region later. From the first-order conditions of this static problem, we immediately obtain the condition that indicates when to ship goods across countries. This condition implies that the ratio of the marginal utilities of the home and foreign investor are bounded above and below by the transactions cost:

0.3)

J_(t) = \n[K\(t)/K2(t)]:

where dz = (dz\ — dz2)/V2 is a standardized Brownian motion. 3.3.1

The Dynamics of the Spot Exchange Rate

Dumas (1992) finds that in the preceding model, the real exchange rate given in equation (3.10) has several properties that are consistent with the data: the exchange rate is heteroskedastic, with a tendency to revert back to PPP. Moreover, the deviations from PPP generated by the proportional shipping cost are persistent. This implies that even though there is some mean-reversion tendency, these deviations can last a very long time.26 The stationary (unconditional) probability distribution is U-shaped, indicating that the probability mass of the exchange rate is concentrated in the area close to the edges of the no-trade region. To see the intuition underlying the last result, note that the drift of the process for co(t) is positive. That is, imbalances in K\/K2 tend to increase 24

25 26

The value-matching boundary conditions state that one exports or imports goods only when the change in lifetime expected utility is exactly offset by the cost incurred by trading the good; these conditions are: when K\/K2 = I/A. then (1 — x)V\ = V2, and when K\/K2 = A. then Vi = (1 — T ) V2. The smooth pasting conditions ensure that the decision to ship is made optimally: when K\/K2 = I/A. : (1 — T)V\\ = V\2 and (1 — r)V2i = Vn\ and analogously for the case when K\/K2 = A.. It can be shown that if 8 > (1 — r])[/jL — 0.5 r\ a2], then a solution to this problem exists and is unique. Abuaf and Jorion (1990) find the half-life of exchange rate deviations from PPP is about three years.

A Simple General-Equilibrium Model of an International Economy

33

rather than decrease, implying that the deviations from the law of one price are persistent. To understand the reason for this, consider the situation where the home capital stock increases relative to that abroad. In the decentralized setting, the foreign investor owns a fraction of the domestic capital stock in order to diversify output risk; thus, the increase in the domestic capital stock should lead to a higher dividend being paid out to the foreign investor. Because of the shipping cost, however, it is not optimal to ship the foreign investor's share of the dividend. Instead, the foreign investor invests this dividend in the domestic production process, leading to an increase in the already larger domestic capital stock. This additional investment has the effect of increasing the foreign investor's wealth; consequently, in order to consume more (because of the wealth effect), she decreases investment locally, thereby decreasing the already smaller foreign capital stock. Consequently, the capital stock in the home country, relative to that in the foreign country, tends to increase rather than decrease. A major implication of the results in Dumas is that the linear mean equations typically used in empirical characterizations of the exchange rate are unlikely to identify a process that, as this model shows, is nonlinear with heteroskedasticity. Moreover, the long-run behavior of the derived exchange rate is very different from its behavior in the short run, implying that an appropriate empirical model must distinguish between these two. 3.3.2

The Nominal Exchange Rate in the Production Economy

The model just described is of a real economy. As in the model of the endowment economy described in Section 3.2, we introduce money via the cash-in-advance constraint in equation (3.5). In this simple setup, we assume that the exogenously given process for money in the domestic economy is,

dm\(t) = iim]m\(t)dt + crmim\(t)dzmi(t), where /xm, is the drift of the money supply process, ani] is its volatility, and dzm] is the Wiener shock. We denote the covariances between the shock to money supply and the shocks to domestic and foreign output as crK]in] and oKimx. The conditional covariance of domestic money and the capital imbalance is denoted by awm,; the covariance of foreign money and the capital balance from the foreign perspective is cr_wm,. The process for the foreign-money supply is given analogously. Again, if we assume that the nominal interest rates at home and abroad are positive, the cash-in-advance constraints bind in equilibrium, implying that the process for domestic prices is: dIn p\(t) = dInm\(t) -

dInc{(t).

34

Exchange Rate Volatility

Denote the nominal spot exchange rate by S(t), and define s(t) = In S(t) = e(t) + Inp(t) — In/?. Then, the stochastic process for the log of the nominal exchange rate is as follows: ds(t) = ([/Zm, - fJLnt2] - 0.5[a^ - O^J) dt + CTmidzmi(t) - om2dzm2{t)

dZ(t),

where we remind the reader that Z(t) denotes the real exchange rate while Zkif) is the Wiener shock. In Chapter 5 we use this model to study the relation between forward and spot exchange rates; and in Chapter 7 we use it to examine how the presence of financial markets influences social welfare.

3.4

Other Extensions

We now list other extensions to the model described here that we consider in later chapters. In Chapter 4, on exchange rates, we extend the model to multiple countries that can differ in terms of their preferences and endowments. Also, we allow for multiple goods with different degrees of tradability: these goods can be tradable without cost, tradable at a cost (fixed or proportional), or nontradable. We will also see that one does not need to assume explicitly the cash-in-advance constraint; money can enter as an argument of the utility function. In fact, for the task of exchange rate determination, it turns out that it is not necessary to specify the exact role that money plays in the economy. Also, one can relax the assumption on preferences: while the utility function still needs to be time-additive, it is not restricted to be homothetic, nor of the hyperbolic absolute risk aversion (HARA) class. In Chapter 7, on capital flows, we consider explicitly the role of financial markets by computing the equilibria for both the case of integrated financial markets and also when they are segmented. In this chapter, we also see that one is not limited to CRRA time-additive utility: one can extend the analysis to recursive utility functions, proposed by Kreps and Porteus (1978), Epstein and Zin (1989), and Duffie and Epstein (1992), that allow one to distinguish between risk aversion and the elasticity of intertemporal substitution. In Chapter 8, on tariffs, we no longer assume that the shipping cost is exogenous; instead, we will interpret the shipping cost as an endogenously determined tariff that the government chooses to realize its objectives. Then, in Chapter 9, we endogenize monetary policy and also the choice of the exchange rate regime.

The Spot Exchange Rate in a Large Class of General-Equilibrium Models

In this chapter we characterize the exchange rate in a general-equilibrium setting using an extended version of the model described in Chapter 3. Relative to the monetary models of the exchange rate, equilibrium models offer the advantage of being based on strong microeconomic foundations. However, existing equilibrium models of the exchange rate, like the basic model described in the previous chapter, often depend on very specific assumptions about the number of goods and countries, the utility functions and production processes, and the type of frictions in the international-goods markets. See, for example, Stockman (1980), Lucas (1982), Domowitz and Hakkio (1985), S vensson (1985a, 1985b), Hodrick and Srivastava (1986), Stulz (1987), Stockman and Delias (1989), Dumas (1992), Engel (1992a, 1992b), Backus and Smith (1993), Bekaert (1994), and Sercu, Uppal, and Van Hulle (1995). In contrast, the framework we develop in this chapter is one where utility functions are quite general and can differ across countries, and where commodity markets may be imperfect. We find that with financial markets that are complete and integrated, the nominal exchange rate mirrors differences in initial wealths and marginal indirect utilities of nominal spending. Differences in marginal indirect utilities may arise from commodity market imperfections and/or differences in consumption preferences, time preferences, or risk aversions. To relate these marginal indirect utilities to observable variables so that one can evaluate the model empirically, we then restrict utility functions to be homothetic with constant relative risk aversion (CRRA). In this CRRA model, we show that the nominal exchange rate is loglinear in time and in the nominal spendings and price levels of the two countries. Thus, according to the CRRA model there are, generally, three missing variables in the standard purchasingpower parity (PPP) equation: time, and the nominal spendings in the two countries. Moreover, the elasticities of the exchange rate with respect to the price indices need not be identical across countries, and their signs are likely to differ from what PPP predicts. We find that PPP holds only under very restrictive assumptions: if either relative risk aversion (RRA) equals zero and time 35

36

Exchange Rate Volatility

preferences are identical across countries, or if there is a fully pooled equilibrium with one (composite) good that can be traded costlessly. On the empirical front, the questions we ask are, first, whether we can reject PPP and, second, whether the addition of the variables implied by the CRRA model improves our ability to explain the behavior of exchange rates. By nesting PPP as a special case of the CRRA equilibrium model of exchange rates, we can test a much richer set of hypotheses than the ones addressed in the standard cointegration analysis of PPP. Analyzing exchange rates, prices, and differentialtrend-corrected aggregate consumption data in a Johansen and Juselius (1992) cointegration framework and in error-correction regressions, we reject the standard PPP hypothesis and find evidence in support of the CRRA model. In Section 4.1 we present an equilibrium model of exchange rates that is a generalized version of the model described in Chapter 3. In Section 4.2 we derive the level of exchange rate for the case where preferences are homothetic and exhibit constant relative risk aversion; we also determine the conditions that yield PPP. Then we examine empirical tests of PPP in Section 4.3 and compare the results to those from tests of the CRRA model of exchange rates in Section 4.4.

4.1

The Economy and the Equilibrium Exchange Rate

In this section we first describe a model of a multicountry, multigood economy with imperfect commodity markets. We impose only a few (very standard) restrictions on preferences, and none on the endowment processes. In the second part of this section, we characterize the exchange rate in this general setting. The economy that we consider consists of M > 2 countries. We focus on two arbitrarily selected countries that are referred to as the home country (subscript k = 1) and the foreign country (k = 2). Each country has a representative consumer with a standard, strictly quasi-concave utility function defined over N > 1 goods. Across countries these representative individuals may differ in terms of risk aversion, consumption preferences, and initial wealths. The outputs of each of the TV goods can be stochastic over time. The economies could be exchange economies where output is given by exogenous endowment processes (as in Stockman, 1980, and Lucas, 1982) or production economies with endogenous investment decisions (as in Dumas, 1992, and Stulz, 1987). The specification of the production or endowment processes is quite general: some goods may be produced everywhere, while other goods may be produced only in some countries. International shipment of these goods may be costly for some or even all of these goods; these shipping costs are assumed to be purely variable costs (as in the models described in Chapter 3). Given these costs for transferring goods across countries, some goods may be traded all

The Spot Exchange Rate in a Large Class of General-Equilibrium Models

37

the time, some may be ixdidable in the strict sense (i.e., traded only if the price difference is sufficiently large to justify incurring the shipment costs), and some goods may be de facto nontradable.1 For simplicity, money is introduced into the model via the Lucas (1982) cash-in-advance constraint.2 We assume that financial markets are complete and perfect. Thus, the outcome of decentralized consumption and investment decisions is identical to the solution of a central planner's problem of the form M

(4.1)

9kEt\ J^ Uk(ck(t))\

Max£ r k=2

which is the multicountry analog to equation (3.2a) in the case of the basic twocountry model described in Chapter 3. This optimization is constrained by an opportunity set that depends on the currently available outputs, the production functions, and the technology for transferring goods across countries.3 We do not need to specify the opportunity set explicitly. In (4.1), ck(t) is the vector of consumption quantities ckj(t) of good j ( = 1 , . . . , N) consumed by the representative individual in country k ( = 1 , . . . , M) and Uk is the utility function of the representative investor in country k. The relative weight assigned by the central planner to each of the other countries, 0k, generally is a function of the initial distribution of wealth in the equivalent decentralized problem.4 In turn, these initial wealths depend on the initial endowments, the characteristics of the (stochastic) investment functions or endowment processes, the frictions in the international markets for consumption and capital goods, and the utility functions. For example, one sufficient (but not necessary) set of assumptions to obtain 0k — 1 is when the utility functions, the initial endowments, and the parameters of the output processes of all countries are identical. Given these assumptions, we now derive the exchange rate. Define the net endowment of each good in each country as the amount available for consumption. In an exchange economy the net endowments are, of course, identical to the 1

2

3 4

Other frictions could be introduced, like shipment lags (goods sent from one country at time t arrive only at time t + 1) and transaction lags (a trade arranged at time t is implemented at time t + 1 only). It can be shown that neither transaction lags nor shipment lags affect any of our conclusions. Essentially the same results would be obtained if real money balances were introduced as an argument in the utility function, except that the price index will contain the interest cost of money balances - see, for instance, Stulz (1987). See equations (3.2b, c, d) for a particular example of these constraints. In a decentralized economy with a complete capital market, there exists a portfolio strategy that allows investors to implement the central planner's solution. For example, consider the case where 6k = 1, utility functions are equal, and shipment costs are zero. The central planner's solution then is to give each of the M countries an equal amount of consumption. The portfolio strategy that implements this plan is that each country holds 1/M-th of the shares of each productive asset, so that each country can obtain 1/M-th of world output.

38

Exchange Rate Volatility

gross endowments, whereas in a production economy we need to set aside the resources needed for the optimal investments identified from the solution of the problem defined in equation (4.1). If the objective function in (4.1) is maximized, it must be impossible to further increase the utility from current consumption in one country without reducing either consumption in another country or investments. Denote the aggregate utility of the central planner from immediate consumption by (boldface) U(.): M

(4.2)

U(c(O) = tfi(c,(O) + ][>t/*(c*(O). k=2

Thus, in the optimum identified from (4.1), U(c(f)) must be at its maximum subject to the feasibility conditions. From this Pareto optimality of consumption, it follows that the relative price for any pair of goods can be read off as the marginal rate of substitution (MRS), along U(c(t)), in the optimum. Let us choose, as the pair of goods, one unit of good j located in country 1 and one unit of the same good j located in country 2. The local-currency prices of these goods are denoted by p\j(t) and P2j(t). Because the relative price has to be computed from nominal prices expressed in a common numeraire, we need a reference currency and an exchange rate. Without loss of generality, we select currency 1 as the numeraire, and use S(t) to denote the nominal exchange rate (units of country 1 currency per unit of currency 2). Here, we write the condition that equates the relative price to the MRS:5

S(t)p2j(t)

=

dV(t)/dc2j(t)

We can now link the nominal exchange rate to the marginal indirect utility function. The indirect utility function, V(Mk(t), pAt)), is defined as (4.4)

V(Mk(t), pk(t)) = Max |t/*(c*(f)) - A*(f) (t)

ckj(t)pkj(t)-Mk(t) where Mk (t) is the amount of nominal spending, expressed in units of currency k. The marginal indirect utility of nominal spending in country k is the multiplier, A(0, in the preceding optimization problem:

dV(Mk(t\pk(t)) This corresponds to equation (3.6a) in the basic model.

The Spot Exchange Rate in a Large Class of General-Equilibrium Models

39

Then, we have our first result: the nominal exchange rate, S(t), is proportional to the ratio of the marginal indirect utility of total nominal spending in the two countries:6 (4.5, We wish to study the implications of this result for the real exchange rate and deviations from PPP. The focus is on the level of the exchange rate and most of this discussion is confined to the special case of time-additive homothetic utility functions.

4.2

Characterizing the Level of the Exchange Rate

In this section we first discuss the general implications for the exchange rate equation (4.5) when preferences are restricted to be homothetic and the discount factors for the utility of future consumption are constant over time. This assumption of constant time preference is abbreviated as CTP. Following this, we derive the exchange rate under the additional assumption of constant relative risk averse (CRRA) utility functions, and show that PPP holds only as a very special case. The motivation for restricting the analysis to homothetic utility functions is that these induce a price index, without which popular concepts like the real exchange rate or PPP deviations are not well defined. The assumption of constant relative risk aversion is motivated by the desire to express the level of the exchange rate in terms of observable variables. 4.2.1

The Exchange Rate under Homothetic, CRRA Utility

With time-additive utility functions and a constant discount rate, lifetime utility Yju(ck(O, t) is of the form ^JSjwfotW). When, in addition, utility is homothetic, the period-by-period utility function uk(ck(t)) can be written as O[u^(cjt(0)], where vk(ck(t)) is linear homogenous in the consumption quantities and [vk(ck(t))] is at its maximum value given a consumption budget constraint, then vk(ck(t)) must also be at its maximum value subject to the same constraint. It is well known (see, e.g., Samuelson and Swamy, 1974) that the solution of the linear-homogenous problem,

vk(Mk(t), pk{t)) = Max \vk(ck(t)) - Xk{t)\Yckj(t)

pkj{t) - Mk(t)]\,

is of the form vk(t) = Mk(t)/Ylk(pk(t)). The function Uk(pk(t)) is independent of nominal spending, Mk(t), and is linear homogenous in the prices. Accordingly, Uk(pk(t)) is interpreted as the price level in country k, and vk(t) = Mk(t)/Uk(pk(t)) the total real spending. These properties of homothetic functions allow us to specialize the result in equation (4.5): with homothetic utility functions, the nominal exchange rate, S(t), and the real exchange rate, Z(t) 9 are given by:7

and ,4.7, Given that the marginal utilities of aggregate real spending are not observable, equations (4.6) and (4.7) cannot be used to study the empirical behavior of the level of the nominal and real exchange rates; we will make the additional assumptions that investors have CRRA utility functions, with risk aversion Equations (4.6) and (4.7) follow upon using the relations 8rk Vk[Mk(t), Pk(t)] = vk(t) = Mk(t)/Ylk(t), which means that we can specify the marginal indirect utility of nominal spending as: dVk(Mk(t),

Pk{t))

8Mk(t)

dk{vk{t)) dvk(t)

dvk{t)

8Mk(t)

dvk(t)

Uk(pk(t))

To understand the role of (82/81Y, note that different impatience factors mean that the two countries are depleting their wealths at different rates. Thus, (82/81Y continuously updates the initial 62 so as to capture this divergence of the two countries' wealths. Stated differently, (i(ui(0) + ^2^2(^2(0)- As the composite good can be transferred internationally costlessly, this marginal rate of substitution of v\(t) for V2(t) always equals unity. Case (2) follows immediately from setting <J>(I>A(O) = and 82 =S\ in (4.6).

The Spot Exchange Rate in a Large Class of General-Equilibrium Models

43

From the foregoing result we see that it is possible to obtain PPP as a special case of the CRRA model: equation (4.10) can be obtained by setting the RRA coefficients, rjk, in (4.8) equal to zero and eliminating the time trend on the righthand side. In case (1) this is valid by direct assumption. In case (2) the terms in r] and 8 cancel out because under the assumptions of perfect markets and identical homothetic consumption preferences - that is, one common composite good - the marginal utilities of real spending are equalized; specifically, if, in (4.6), 8t2d®2(t)/dv2(t) equals 8\d\{t)/dvx{t), then PPP obtains. 4.2.3

Implications of the General Model for PPP Tests on First-Differenced Data

In the traditional test of relative PPP, one regresses changes in the log exchange rate on inflation differentials across countries: (4.11)

A l n S = a + £ [ A l n n i - A l n n 2 ] + e,

with the null hypothesis that /3 = 1.12 Our theoretical analysis has the following implications for these tests. First, consider the special case of our model where consumption preferences are homothetic, time preference is constant, and relative risk aversion is equal across countries and constant over time. In this case, equation (4.8) simplifies to: (4.12)

AlnS =

(6.4)

x2(t) =

, ( 1 + T ) + 1 M a x ( g 2 ( O - K2qi (0, 0).

To obtain equations (6.3) and (6.4), note that in the absence of trade, we have c2(t)/c\(t) = q2(t)/q\(t), implying that x\(t) = x2(t) = 0. In the region / = 1, with exports from country 1, (6.2) implies that country 1 must be exporting an amount xi (0 such that c2(t)/c\ (f)) = (1 + r)~ 1/?? . The amount of good being exported from country 1 can then be identified from the sharing rule c2(t) = K\C\(t) (with K\ defined in (6.2)) and the market-clearing condition c\(t) = q\(t) — x\(t) and c2(t) = q2(t) + x\{t)/{\ + r). The solution is

„.

X\{t)

=

q\(f)-qi{f)/KX

which is positive because we are considering states where q\(t)K\ > q2(t). This condition also implies that, in these states, x2(t) = 0. We can obtain x2(t) in similar fashion. Lastly we derive the real exchange rate, which in a one-good economy is given by the ratio of the marginal utility of consumption abroad to that at home, Z(t) = [c2(t)/c\(t)]~ri.l0 Substituting into this expression the consumption ratios derived in (6.2) gives: -« = 1 + r (6.5)

Z(t) =

\qw)/

1

if i = 1

if / = 2.

From equations (6.2) to (6.5), we see that it is possible to express explicitly the real exchange rate and the volume of international trade as functions of r, rj, and the state variables (the outputs of the two goods). Now, we can examine how a change in either r or the volatility of the relative endowment process affects the expected volume of trade and the volatility of the exchange rate. 10

This is the same as the expression in equation (3.4).

International Trade Flows, Exchange Rate Volatility, and Welfare

6.3

73

The Relation between Trade and Exchange Rate Risk

In this section, we examine the change in exchange rate volatility and expected trade for two experiments: first, where there is a change in the volatility of the relative endowment processes; second, where there is a change in the degree of commodity market segmentation, measured by r. 6.3.1

The Effect of Output Volatility on Exchange Risk and Expected Trade

To consider the effect of an increase in volatility in the endowment processes on the expected level of trade, we obtain analytical expressions for the expected volume of domestic and foreign exports by noting that the expression for the realized volume of domestic [foreign] exports in (6.3) [(6.4)] is similar to the payoff of an option to exchange two risky assets at the rate K2 [1/K\]. The properties of such options have been studied in the finance literature by Margrabe (1978). Thus, we can use the insights from the theory of option pricing to determine the expected volume of trade. Given the assumption that the distribution of the two endowment processes is jointly lognormal, we obtain an expression for the expected foreign exports that is similar to the value of an option to exchange two risky assets whose prices are lognormally distributed. From option-pricing theory, we also know that the value of an option is increasing in the volatility of the underlying stochastic process. In our context, the expected volume of foreign exports is a positive function of the volatility of the relative output process, q2(T)/q\(T). This follows from the result that the conditional expectation at time t, of foreign exports at a later date 7\ is given by the expression in (6.6), which is a nonlinear positive function of the variance of q2(T)/q\(T): ,,,, (6.6)

,™ Et[qi(T)-\N{d\) - K2Et[qx(T)}N{d2) vf Et(x2(T)) = , K2/(\ + T)+ 1

where Et(qk{T)) = qk(t)exp{/jk(T

- t)},

k = {1, 2}

0 2 = o\ — 2po\o2 + through Kk(t) as defined in (9.15a) and (9.16a). Thus, a fixed-rate regime is incompatible with optimal (noncooperative) monetary policies. 9.4.3

Monetary Union

In both cases discussed thus far, each of the countries had its own monetary policy. A monetary union differs from a fixed-rate system not only in the sense that its fixed-rate commitment is much more final but also in the sense that there is just one monetary policy.28 The mathematics of a monetary union is considerably more complicated than the model developed thus far. For this reason, we just describe the main differences in the setup and verbally describe the conclusions. In a monetary union, seigniorage is split among the participating countries. Thus, in a model where the member states are initially equal, the obvious rule regarding seigniorage would be a 50-50 split. The government's budget equation then is

(9.27) 28

pk(t)qk(t)yk(t) = Tk(t) + ^AAf(f),

See Bayoumi (1997) for a review of the literature on optimum currency areas. Miller and Williamson (1988) and De Grauwe (1997) contain an extensive discussion of the costs and benefits of monetary integration; Dominguez (1996) and Eichengreen (1997) provide empirical evidence on the success of central bank intervention in foreign exchange markets.

Endogenous Monetary Policy and the Choice of Exchange Rate Regime

123

where the total money supply is denoted by (unsubscripted) M(t). An immediate implication of (9.27) is that, as each government no longer has two countryspecific policy tools, one can no longer separate the issue of the government's share in total absorption from the issue of optimal inflation. The second major change in the setup is the cash-in-advance constraint. As money freely circulates across countries, the constraint now is 29

(9.28)

M(t) = px(t)Qx{t) + S(t)P2(t)Q2(t).

Because real market imperfections are not affected by monetary union, the real exchange rate can still fluctuate between 1/(1 + r) and (1 + r). The cooperative formulation of the problem is then to (9.29)

Max

V,(r) + V2(t)

\LpAt) + L?(f) .

Already from the modified setup it is clear that the outcome cannot be as good as the one from a cooperative game with independent monetary policies. Not surprisingly, then, even when f$ equals unity, the exchange rate that results from (9.29) no longer simplifies to (9.22), implying that in the presence of a fixed-rate regime and asymmetric shocks the monetary policies are always suboptimal.

9.5

Conclusion

The formal analysis in the preceding section has examined the proposition that, in the presence of asymmetric shocks, afixedexchange rate regime is incompatible with welfare maximization. We confirmed this proposition provided that f$ < 1; however, when the welfare cost of reduced leisure is invariant to the amount of time spent at work, a fixed-relative wage policy combined with a fixed exchange rate has no welfare costs. A monetary union, in contrast, always implies some welfare cost. Some of the benefits of monetary union are clear: there will be a decrease in transactions costs. A second benefit is that a monetary union will remove one source of uncertainty about relative prices; however, the effects of this on welfare and growth seem to be small (see, e.g., De Grauwe, 1997, table 3.2). There exist large differences across the real sectors of countries. These differences can be accommodated via changes in the exchange rate, monetary 29

Of course, in a true monetary union, S(t) equal unity; however, as in the previous section our approach is to let S(t) be free and to see under what circumstances the resulting exchange rate is constant.

124

Exchange Rate Volatility

policy, and fiscal policy; typically, the easiest way is to allow the exchange rate to change (compared with, say, contractionary fiscal policy). The cost of monetary union is that a country gives up the exchange rate as a policy instrument. In view of the analysis presented in this chapter, one could question the EMS and especially the European Monetary Union (EMU) plans. What, then, might explain the (admittedly, often lukewarm) preference for fixed rates? One could, first, question whether asymmetric shocks can be all that important in economies that are becoming more and more alike and where technological improvements spread quickly. One view is that integration of trade will make the effect of demand shocks more symmetric across regions. On the other hand, Krugman (1991) argues that trade integration may lead to regional concentration - for the automobile industry in the United States, a highly integrated economic area, is highly concentrated - and therefore the effects of shocks might be asymmetric. Recent empirical work by Fatas (1997) and Frankel and Rose (1997) seems to indicate that, with the integration of trade in Europe, the correlations of real activity have increased, making currency union more attractive. However, institutional differences across countries (such as the power of trade unions in the economy) are unlikely to disappear in the near future.30 Another legitimate concern with the asymmetric-shock argument is whether the authorities are as efficient, benevolent, and surgically precise as they are assumed to be in this literature. If monetary policy is blunt and sluggish in its effects, or based on outdated and partial information, or used for political purposes, the arguments for monetary independence lose much of their appeal. For instance, one often cannot help noticing that many European politicians, especially those from fiscally profligate countries, were not overly unhappy to abdicate their role as economic policy makers. 30

See Atkeson and Bayoumi (1993) for a discussion of how financial capital can substitute for physical capital mobility; that is, how agents can diversify against region-specific shocks by holding financial assets whose returns are not correlated with these shocks.

10 Concluding Thoughts

We have developed a general-equilibrium, intertemporal framework of a stochastic world economy. In this framework, decision rules of individual agents with rational expectations are derived based on optimizing behavior, and the prices of goods and financial securities, the interest rate, and the exchange rate are determined endogenously. We have explicitly modeled the segmentation of commodity markets by introducing a cost for shipping goods across countries; thus, our model allows for deviations from the law of one price. We have also considered the effect of the opening international financial markets on welfare. We have used this framework to understand the behavior of the spot and forward exchange rates and international trade in goods and financial claims. We have also evaluated tariff policy, monetary policy, and the choice of the exchange rate regime in this setting. We characterize the spot exchange rate in a fairly general setting: without restricting the number of goods and countries, the utility functions, production processes, or the nature of frictions in international goods markets, but assuming that financial markets are complete and integrated, we show that the nominal exchange rate reflects cross-country differences in initial wealths, and marginal indirect utilities of nominal spending.1 More important, the expression that we get for the exchange rate is a nonlinear one, with changing coefficients. De Grauwe, Dewachter, and Embrechts (1993) report that the behavior of exchange rate returns is complex and nonlinear. To explain this, instead of using a model with fully rational agents,2 they assume that the interaction between traders using fundamentals and those using technical rules (chartists) generates chaotic motion in exchange markets. Consequently, even very simple versions of their models of the exchange rate can generate very complex behavior with some predictability. However, they find that the evidence in favor of 1 2

Differences in marginal indirect utilities may arise from commodity market imperfections and/or differences in consumption preferences, time preference, and risk aversion. In their model, one type of agent does not take into account that there is another type of agent in the economy. 125

126

Exchange Rate Volatility

nonlinearities in exchange rates is stronger than that for chaos. In contrast to this work, our model shows that one can get nonlinear exchange rate returns even in a model where agents are fully rational. For the version of our model with production, we describe the exact nature of this nonlinearity, and the persistence that it generates in exchange rates. In trying to understand forward currency rates, and their relation to spot exchange rates, two main hypotheses that have been advanced are (1) market participants make systematic expectational errors (Lewis, 1989; Alapat, 1994), and (2) there are time-varying risk premia in the forward exchange market. In spite of the large number of articles trying to generate the observed risk premia, this line of research has met with limited success. Rather than abandon the rational expectations view, we examine forward rates in a model where agents behave rationally but where, in contrast to the existing literature, commodity markets are segmented. By allowing for deviations in the law of one price in commodity markets, the ability of the model to generate observed risk premia improves. Similarly, Backus et al. (1993) find that the performance of the general-equilibrium model improves when preferences are generalized to allow for habit persistence. In our analysis of trade flows, we examine the relation between the volatility of real exchange rates and the volume of international trade. The consensus view is that, if there is one change in going from fixed exchange rates under the Bretton Woods system to a regime of floating exchange rates, it is an increase in exchange rate volatility. However, numerous studies examining the effect of this volatility on trade flows find little evidence of a negative impact. We provide a theoretical model consistent with this result. The main point of this analysis is to highlight that both exchange rates and trade flows are endogenous variables. Thus, the association between them depends on the changes in the underlying factors in the economy. Moreover, it is incorrect to identify welfare with the volume of trade; depending on the changes in the underlying factors, it is quite possible that the volume of trade declines but welfare improves. In the last part of the book, we focused our attention on policy regarding the opening of capital markets and also on tariff and monetary policy. In our study of capital flows, calibrations based on data for the United States, Europe, and Japan indicate that the gains from sharing risk in international financial markets can have a significant effect on welfare. Even more important is the insight from Feeney (1994) and Obstfeld (1994) that financial markets can influence welfare also indirectly - for example, by changing the investment decisions of a country. We also measure the gain from the opening of financial markets when commodity markets are not fully integrated: our calibration analysis indicates

Concluding Thoughts

127

that these gains are still large. Thus, the policy implication is that it is worthwhile to pursue the integration of financial markets even if goods (and labor) markets are not yet fully integrated. For the case of tariff policy, we saw that the presence of financial markets could have a strong influence on the optimal tariff. In the models we described, the opening of financial markets serves to reduce the optimal tariff. Moreover, upon integrating financial markets, the welfare gains from tariff reduction are about sixteen times as large as the direct gains from risk sharing. In the chapter on monetary policy, we showed how one could evaluate the choice over fixed and flexible exchange rates in a framework with segmented-goods markets and optimizing agents. Wefindthat in the presence of shocks that are not symmetric across countries, a flexible exchange rate dominates a regime with fixed rates. A fixed exchange rate regime has no welfare costs only when the marginal cost of reducing leisure is constant; a monetary union, on the other hand, always implies some welfare cost in our model. Throughout the work presented in this book, we have adopted the perspective that agents are rational and markets are efficient. While many may consider this view to be an extreme one, we believe that before we abandon the rationalexpectations paradigm, we should explore it fully by allowing for features of the real world that we observe but do not always model: imperfect commodity markets, incomplete financial markets,3 participation constraints and trading costs, more general preference structures that, for example, allow for habit persistence, and separation between risk aversion and the elasticity of intertemporal substitution. In our models, we have assumed that within a country all agents are identical and have homogenous expectations, and that agents are fully informed about the parameters of the economy and that there are no information asymmetries across countries; also, in our analysis of policy issues, we have ignored the issue of credibility. The work described in this book indicates that rational-expectations models that reflect the more realistic features of the economy can have considerably more success in explaining the empirical regularities observed in the data compared with standard models that ignore these factors. The results in Devereux (1997b) and the empirical work in Allen and Stein (1995) suggest that fundamentals can explain a major proportion of the trends in real exchange rates over the medium and long run. We hope that this book, by showing that the ability of rational-expectations models to explain the data improves once we model the real world more accurately, will serve to encourage research in this area. 3

For evidence that international economies are less than perfectly correlated, see Bayoumi (1997), Devereux et al. (1992), Kollmann (1990, 1995, 1996), and Lewis (1996).

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Author Index

Abuaf, N., 8, 32n26, 45, 47, 48 Adler,M., 8, 21n8 Alapat, P., 58, 126 Allen, P. R., 16,79,82, 127 Alogoskoufis, G., 104 Andersen, T., 2nl Apte,P,43nl2,44nl4 Arndt, S., 82 Asseery, A., 68, 69 Atkeson, A., 16n20,97, 107, 124n30 Backus, D., 15, 35, 41, 44-5, 58, 65, 77, 126 Baillie,R., 11, 14nnl4,15, 57, 58 Bakshi,G., 15,42 Balassa, B., 7 Baldwin, R., 68n4 Bansal,R., 15,58,60 Barari, M., 100 Baron, D. P., 67 Basak,S., 15,21,42 Baxter, M , I,21n8,61n3 Bayoumi, T., 8, 21n7, 97, 109nl 1, 122n28, 124n30, 127n3 Bekaert,G., 15,35,57,58,60 Benes, V., 30n20 Benninga, S., 28nl7 Bertola, G., 14nl7 Betton, S.,43nl2 Bilson, J., 13 Bini-Smaghi, L., 68 Black, E, 19,21,29nl8,74 Bollerslev, T., 14nl4,58 Brada, J. C , 69 Branson, W., 13nl2 Brock, W., 15 Broil, U., 67 Brooks, R., 68, 69 Buiter,W., 109nl3 Caballero, R. J., 69n6 Cagan, P., 107 Campbell, J., 61 n3

Canova, E, 57, 58 Canzoneri, M., 104 Cao,H.,21 Cassel, G., 6, 8n7 Chang, R., 103n2 Chari,V., 16, 107 Chen,Z., 15,42 Cheung, Y. W., 49, 56 Cho,D., 83nl Claessens, S., 80nl7 Clarida, R., 9, 61n3 Clark, P. B., 67 Clower, R., 105 Cole,H.,21,68n3, 82, 85,95 Cooper, L, 21 n8 Cooper, R., 20 Corsetti, G., 109nl3 Costello, D., 85n2 Cote, A., 67 Cournot, A.-A., 9 Cox, J., 61, 91 Crucini, M., 21n8 Cumby, R., 7, 58 Cushman, D. O., 67n2 Dan thine, J., 15 Davis, M., 30 Deardorff, A., 19,62,90 DeGrauwe,P, 3,5nl, 14nl5, 67, 68, 80, 108, 109nll, 110nl4, 122n28, 123, 125 Delias, H., 15, 19, 35, 68, 77, 99, 100 Devereux,M., 15, 16, 19n4,99, 100, 102, 107nl0, 127 de Vries, C , 3, 14nl4,67 Dewachter, H., 125 Dickey, D. A., 46 Diebold, E, 14 Dixit, A., 30n20, 99 Dominguez, K., 79nl5, 122n28 Domowitz, I., 35, 58 Donaldson, J., 15 Dooley,M., 80nl7,97nl4

147

148

Author Index

Dornbusch, R., 13 Duffie,D., 34,91 n8 Dumas, B., 14, 15, 18, 19, 21n8, 28nl7, 29, 30, 32, 33, 35, 36, 83, 90 Edison, H., 22nlO, 46, 47n20, 61n3, 67 Eichenbaum, B., 8 Eichengreen, B., 8, 80, 104nl, 122n28 Einzig, P., 9 Embrechts, M., 125 Engel,C, 11, 14nl6,20, 35,47n21, 57, 58, 69n7 Engle, R. R, 46 Epstein, L., 34 Errunza, V., 21,83nl Ethier, W., 67 Eun,C, 83nl Evans, C , 8 Evans, M., 14nl5 Fama, E., 58, 59-60, 107 Farber, A., 107 Fatas, A., 124 Feeney, J., 21n9, 82, 87n4, 95nl2, 126 Feenstra, R., 15, 106 Feldstein, M , 21n8 Fleming, J. M., 12 Flores, R., 46 Franke, G., 3, 68 Frankel, J., 1,14, 44nl5, 47n21, 69, 80nl8, 97nl4, 124 French, K., 21 n8 Frenkel,J., 12nl 1, 13, 99nl Froot, K., 7n5, 8n6, 11, 46, 47n21, 52,57 Fuerst, T., 15 Gagnon, J., 46, 68, 69 Gali, J., 9 Gallmeyer, M., 15,42 Gavin, M., 18nl Girton, L., 13 Godbout, M.-J., 49 Gokey, T., 57 Goldstein, N., 68 Gotur, P., 68, 69 Granger, C. W. J., 46 Greenwood, J., 104nl Gregory, A., 19n4, 58 Grice-Hutchinson, M., 6n3 Grillio,V., 15 Grunberg, I., 80nl8 Guidotti, P., 106 Gultekin, B., 83nl Gultekin, M., 83nl

Hakkio,C, 14nl6, 35,58 Halliday,L., 83nl Hansen, H., 49n23, 58, 112 Haq,M., 80nl8, 109nl2 Harberger, A. C.,97nl4 Harrison, J., 30n20 Hau,H., 16n20, 107 Haug, A., 49n23 Helpman, E., 15, 18, 82, 99, 100, 104nl Henderson, D., 13 Hendrickson, M., 47n21 Heston, A., 62 Hietala,R, 83nl Hodrick, R. J., 11, 15,35,57,58 Hollifield, B., 29, 57, 63-4 Hooper, P., 67 Horioka, C , 21n8 Horvath,M.,47,51n24,52 Huang, C , 91 n8 Huang, J., 91 Huang, R., 8 Huizinga, J., 8 Ingersoll, J., 31n22, 61 International Monetary Fund (IMF), 67 Isard,P,5nl,80, 108 Jenkins, M., 69n7 Johansen, S., 36, 46, 49n23, 52 Johnson, H. G., 13,99 Jorion, P., 8, 32n26, 45, 47, 48 Juselius, K., 36, 46, 49n23, 52 Kane,M.,43nl2 Kaplanis, E., 21n8 Karekan,J., 15,79nl4, 105n3 Kaul,I.,80nl8 Kehoe,P, 15, 16, 107 Kennan, J., 99 Khan, M., 68 Kim, A., 7n5 Kimbrough, K., 107nl0 King,R.,79nl4 Koedijk, C , 47 Kohlhagen, S. W., 67 Kollmann, R., 16, 19n4,45nl6, 107, Illnl6,112, 127n3 Korajczyk, R., 58 Koray, F, 68-9 Kravis,I.,6n4,43nl2 Kreps, D., 34 Kroner, K. F, 69 Krugman,P, 1,8, 12n 11, 14, 19,21n8, 68n4, 124

Author Index Kydland,R, 15 Kyotaki,N., 105n4

Mundell,R., 12,95, 109nll Mussa, M., 13

Lai, Kon S., 49, 56 Lapan, H., 100 Lastrapes, W. D., 68-9 Laursen, S., 97nl4 Lee, K.M.,21,99, 100, 102 Lehman, B., 8 Lerner, A., llnlO LeRoy, S., 15 Levi,M.,43nl2 Levine, R., 57 Lewis, K., 11,57,58,85, 126, 127n3 Losq,E.,21 Lothian, J., 14nl5,47n21 Lucas, R. E., 15, 16, 24, 27, 35, 36, 37,60,70,91

Nason, J., 14 Nessen, M., 46, 47, 52 Nissen, R, 47 Nobay, A., 20 Norman, A., 30

McCallum,B., 15 McCurdy, T., 58 MacDonald, R., 47n20 McGratten, E., 16 McKenzie, M., 68, 69 MacKinnon, J., 49n23 McKinnon, R., 109n 11 Macklem, R., 58 McMahon, H., 11, 14nnl4,15, 57 McMillan, J., 99 McNown, R., 9 Manuelli,R.,79nl4 March, J. W., 47n20 Margrabe, W., 73 Mark,N., 14nl5,58 Marrinan, J., 58 Marshall, A., llnlO Marshall, D., 15 Marston, R., 9, 11,20,57 Martin, P., 107nl0, 110nl5 Mathieson, D., 97nl4 Meese,R., 13, 14,61 n3 Melick, W., 46 Melo, J. de, 20, 90 Melvin,M.,22nlO,67 Mendez, J., 69 Mendoza, E., 85 Merton, R., 74, 84 Metzler, L., llnlO, 97nl4 Michael, R., 20 Michelis, L., 49n23 Miller, M., 122n28 Mishkin, E, 57 Moen, K.,2nl Morgan, I., 58

149

Obstfeld, M., 7, 12n 11, 13nl3, 16,20,21, 62, 70n8, 82, 83, 85, 90, 95, 97nl4, 107, 108, 109nl3, 118, 126 O'Connell,RG.J.,20,47n21 Padmanabhan, P., 83nl Parsley, D., 20, 47n21 Pauls, B. D., 61 n3 Peck,J., 79nl4 Peel, D., 20, 68, 69 Penati, A., 83nl Peree, E., 66, 67, 68 Persson, T., 97nl4, 104nl Pesenti, P., 109nl3 Phillips, P. C. B., 46 Pindyck, R., 30n20 Poole, W., 80 Porteus, E., 34 Poterba, J., 21n8, 137 Pozo, S., 68 Protopapdakis, A., 28nl7 Razin, A., 12nl 1, 15, 18, 82, 97nl4, 99, 100, 104nl Reinhart, V., 80nl8 Richards, A., 49, 51, 56 Richardson, J., 82 Riezman, R., 99 Robinson, J., llnlO Rogers, C. A., 104 Rogers, J., 20, 47n21,69n7 Rogoff,K.,7n5,8n6,13,16,46,52,61n3,70n8, 106n8, 107, 108, 109nl3, 118, 121n27 Roll, R., 8 Rose, A., 1, 14,44nl5, 47n21, 124 Ross, S., 61 Rossana, R. J., 46 Roubini, N., 15 Sachs, J.,97n 14 Samuelson, P. A., 7, 40 Schinasi, G., 14 Scholes, M., 74 Sellin,P,21 Senbet, L., 83nl Sercu,R,21n8,35,41,43nl2,44,68,74nll,77

150

Author Index

Shepp, L., 3On2O Shrikhande, M., 28n 17 Sidrauski, M , 15 Smith, G., 19n4, 35, 41, 44-5, 77 Solnik, B., 15nl8, 21n8 Srivastava, S., 35, 58 Stein, J. L., 16, 79, 82, 127 Steinherr, A., 66, 67, 68 Stern, R., 19, 62, 90 Stock, J. H., 46 Stockman, A., 1, 13n 13, 15, 18, 19, 20, 21, 22, 29nl9, 35, 36, 77, 97, 99, 100, 104nl Stulz, R., 15, 19, 21, 35, 36, 37n2, 41, 43nl2, 60, 77, 97nl4 Subrahmanyam, M., 21 Summers, L., 80 Summers, R., 62 Summers, V, 80 Sutherland, A., 70n8 Svensson, L. E. O., 14nl7, 15, 16, 35, 60, 97, 97nl4, 104nl, 106n8, 107, 109nl3 Swamy, S., 40 Sway, P., 14 Taksar, M., 30n20 Tarr, D., 20, 90 Taylor, A., 20, 47n21 Telmer, C , 58 Tesar, L., 15, 19, 21n8, 77, 85, 97nl4 Thaler, R., 11,57 Tobin,J., 80, 109nl2

Uppal, R., 21 n8, 29, 35, 43n 12, 44, 57, 63-4, 83, 90, 91 n8 Van Hulle, C , 35, 44, 68 van Norden, S., 49 van Nunen, A., 19n5 van Wijnbergen, S., 16, 107 Van Wincoop, E., 85 Viaene, J.-M., 3, 67 Viallet, C , 58 Vittorio, C , 69n6 Wallace, M. S., 8 Wallace, N., 15, 79nl4, 105n3 Wang, T., 15nl9, 90n6 Warner, A., 80nl7 Watson, M. W., 46, 47, 51 n24, 52 Weber, W., 79n 14 Wei, S.-J., 69 Wei, S. J., 20, 47n21 Werner, I., 21 Wheatley, S., 83nl Williamson, J., 122n28 Williamson,S., 104nl Witsenhausen, H., 30n20 Wolff, C , 13-14 Wright, R., 105n4 Wyplosz, C , 80 Zilberfarb, B.-Z., 68 Zin, S., 34

Subject Index

absorption: derived utility in model of monetary policy effects, 113-15 arbitrage: covered interest rate parity and exchange rates, 9 ARCH (autoregressive conditional heteroskedasticity) process, 69 Augmented-Dickey-Fuller (ADF) tests: differences from cointegration analysis, 46-7; quarterly data, 48-9; of real exchange rate data, 45; unit-root hypothesis for exchange rates, 48-9 balance of payments: approach to exchange rate determination, 11-12; current-account balance, 93—4; relation between current account and relative prices, 11-12 barriers to trade: nontariff barriers as source of segmentation, 19-20; recommended removal, 97 Bretton Woods: exchange rate behavior with collapse of, 5; stabilization of value of moneys, 108 capital flows: analysis in models, 20-21; analysis of international, 94-7; definition of flows between two countries, 9 2 ^ ; determinants of, 90-2; as determinants of exchange rates, 12-14; with integrated financial markets, 90-7; Mundeil-Fleming framework, 12; policy to encourage, 3; relation to trade flows, 3; sharing risk in financial markets, 126 capital markets: analysis in models, 20-1; effect on tariffs in international, 99; risk sharing in integrated, 86-7; segmentation of, 20-1; welfare cost of segmented, 85-6. See also capital flows; financial markets cointegration analysis: applied to multilateral exchange rate data, 47; differences from ADF tests, 46-7; to test PPP empirically, 46; tests for relationships in data, 49-50

commodity markets: in basic model of endowment economy, 23-9; effect of integration or segmentation on capital flows, 94-8; interactions between decisions in financial markets and, 101-2; in model of multicountry, multigood economy, 36-9; segmentation by tariff rate, 100 commodity markets, segmented: effect on trade and exchange rate volatility, 75-6; general-equilibrium model for UIP, 60-3; of international, 19-20, 57; with rational expectations, 126 constant relative risk aversion (CRRA), 35; in basic model of endowment economy, 24-5; in intertemporal production economy, 29 constant time preference (CTP), 39 consumer price index (CPI): relative price data of,42nlO countries: in basic model of endowment economy, 23-9; distinctions among, 18-21; in endowment economy model of trade-exchange rate volatility relation, 70-2; in intertemporal production economy, 29-34; in model of monetary policy effects, 110-18; in model of multicountry, multigood economy, 36-9; with open financial markets, 102; price differences in, 20 covered interest rate parity: relation to exchange rates, 9 CRRA. See constant relative risk aversion (CRRA) CTP. See constant time preference (CTP) data: cointegration and likelihood tests of PPP, 48-52; first-differenced, 43-5; PPP deviations in exchange rate data, 57; stylized facts about international, 18-19 data sources: CPI, 42nlO; in review of empirical testing of PPP, 48

151

152

Subject Index

demand for money: cash-in-advance constraints, 105-6; money-in-the-utility-function, 106 Dickey-Fuller tests, augmented, 48-9 economic shocks, symmetric and asymmetric, 118,124 endogeneity: of exchange rates in general-equilibrium model, 18; of financial markets' mechanism related to trade policy, 103; of production in model of forward exchange risk, 3; in tariff policy model, 100-1; of tariff rates in Nash game, 100, 121-2; of trade and exchange rate volatility, 78; of trade policy, 103; of trade volume and exchange rate volatility in general-equilibrium model, 76-8 endowment economy: in analysis of trade-exchange rate volatility relation, 70-2; basic model of, 23-9; extension of model to production economy, 29-34 endowments: in model of multicountry, multigood economy, 37-9 European Monetary System (EMS): crisis (1992), 109; exchange rate mechanism, 108; idealized, 119-21; need for policy coordination, 119; preference for fixed exchange rates, 124 European Union (EU): single-currency plan, 1 exchange rate models: assets approach, 12-14; balance-of-payments (BOP) approach, 11-12; constant relative risk aversion (CRRA), 35; deviation from PPP of tradable and nontradable goods, 7; general-equilibrium model, 17-18; interest rates in relation spot and forward exchange rates, 9-11; with microeconomic foundations, 15-16; monetary approach, 13; relation of exchange rate to national price levels, 5-6; test of CTP/CRRA model, 44-5 exchange rate regime: effect of changes from fixed to floating, 1,5; monetary policy with fixed rate, 108-9 exchange rate volatility: effects on trade and welfare, 3; effects on trade volume of, 1, 66-9; measurement of risk, 68; nonlinear relation between trade volume and, 66; related to segmented capital markets, 85-6; risk with change in degree of commodity market segmentation, 73, 75-6; risk with change in endowment processes of the economy, 73-5 exchange rates: advantages of generalequilibrium model, 17-18, 22-3; balance-of-payments theory of, 11-13;

capital flows as determinants of, 12-14; conditions for increased volatility, 126; with CRRA, 41; under CRRA utility functions, 39-42; determinants of, 54; nonlinearities in, 126; related to PPP, 6-9; under relative and absolute PPP, 42-3 exchange rates, equilibrium: in model of multicountry, multigood economy, 36-9 exchange rates, fixed: constraints on monetary policy, 108; economic cost of, 109; monetary policies leading to, 118; return to regime of, 1 exchange rates, forward: effect of commodity market segmentation on, 57; as predictor of future spot rate, 10-11; relation to spot exchange rate, 10, 58-60, 126; risk premia, 58; in segmented commodity markets, 126. See also forward bias puzzle; forward premium exchange rates, nominal: in model of monetary policy effects, 117-18; in model of production economy, 33-4 exchange rates, real: effect of commodity market segmentation on, 61; in general-equilibrium model for UIP, 60-3; intertemporal models of, 15; in monetary union, 123—4; relation between trade volume and volatility of, 126; relation to wealth differences and time preferences, 54-6 exchange rates, spot: in model of production economy, 32-3; relation to forward currency rates, 126; relation to forward rate, 10, 58; UIP in determination of current, 10 exogeneity: in model of endowment economy, 24; of trade policy, 103 factors of production: in model of monetary policy effects, 110-18 financial markets: in basic model of endowment economy, 23-9; gains from trade with integrated, 102-3; influence on setting trade policy, 102-3; interactions between decisions in commodity markets and, 101-2; in model of multicountry, multigood economy, 36-9; opening, 102-3, 127; optimal tariff in integrated, 3-4, 101; tariffs in segmented, 101; trade dividend of, 102. See also capital markets forward bias puzzle, 57 forward premium: forward and spot rates in determining, 10-11; UIP hypothesis related to, 58. See also forward bias puzzle free-trade policy: conditions for choice of, 102

Subject Index

GARCH (Generalized Autoregressive Conditional Heteroskedastic) model, 68, 69 government: choice of tariff in Nash game, 102; in model of monetary policy effects, 110-18 hedging: against changes in terms of trade, 101; for exchange rate risk, 67 incentives: in Nash tariff game, 101 interest rates: in basic model of endowment economy, 27; effect of changes on exchange rates, 9; influence on demand for money, 9; relation to exchange rates in nominal terms, 6 3 ^ . See also covered interest rate parity; uncovered interest rate parity (UIP) Johansen-Juselius tests: cointegration, 52-4; likelihood, 51-2; likelihood tests of PPP, 51-2;PPPin,48 Keynesian theory: balance-of-payments approach to exchange rate determination, 11-12; government spending under, 107 law of one price: in model of production economy, 33 monetary policy: choice of exchange rate regime and, 22; constraints of fixed nominal exchange rate, 108; in idealized EMS, 119-21; leading to fixed exchange rates, 118; model of economic effects, 110-18; Nash game, 121-2 monetary union: seigniorage in, 122-3; welfare benefits and costs in, 123-4 money: assumptions of model of supply and demand for, 110-13; cash-in-advance constraints, 105-6, 123; effect of interest rate changes on demand for, 9; implications of model of demand and supply of, 113-18; in models of real exchange rates, 15; money-in-the- utility-function, 106; as store of value in overlapping generations, 105 Nash game: conditions for noncooperative, 118; countries' choice of monetary policy in coordinated, 119; endogenous tariff rates in, 100-1, 121-2; monetary policy choices in, 121-2 prices, relative: determinants of, 54 production economy: additional extensions to model of, 34; extension of endowment

153

economy to, 29-34; gains from financial-market integration, 83-7 purchasing power parity (PPP): absolute and relative, 6-8, 42; ADF and cointegration tests of, 48-52; alternative sufficient sets of conditions for, 42; approach to determining exchange rate, 9; in CRRA exchange rate model, 35-6; deviations in data from, 18, 57; deviations in segmented commodity markets, 57; empirical tests of, 7-8, 43-6; implications for traditional test of relative, 43-4; panel analysis of bilateral, 47-8; relation to exchange rate, 6-9; as special case of CRRA model, 43; test in multilateral analysis, 47 rational expectations, 127 rational-expectations models: explanation of empirical regularities, 127; of monetary policy with PPP holding, 13 relative risk aversion (RRA): in basic model of endowment economy, 25 risk aversion: effect on capital flow volume, 94; related to segmented capital markets, 85-6; relative risk aversion (RRA), 25 risk premia: capital-asset pricing model (CAPM), 60; in forward exchange market, 58-60; forward exchange rates, 58, 126; in general-equilibrium model, 11; for holding forward contracts, 58-60; in prediction of future spot rate, 11; in prediction of spot rate, 11 risk sharing: in financial markets, 85; gains from financial-market integration, 83-5; in integrated financial markets, 86-7 seigniorage: government income from, 106; in monetary union, 122-3 sharing rule: in model of monetary policy effects, 116-17 tariff, optimal, 101-2; in absence of financial markets, 102; choice of optimal policy, 99, 127; in presence of financial markets, 103 tariffs: in complete and integrated financial market, 102; government choice in Nash game, 102; Nash tariff game, 101; segmented commodity markets by rates, 100; as source of segmentation, 19-20; wealth effect and price effect, 101; welfare gain from reduced, 4. See also barriers to trade terms of trade: government influence on, 101; hedging against changes in, 101 Trace test statistic, 49n23

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Subject Index

trade: effect of exchange rate volatility on, 1, 3, 68-9; in financial securities, 95; integration in Europe, 124; no-trade region in endowment economy, 26-7, 71, 75; regions of trade and no-trade in model of endowment economy, 25-9; relation to exchange rate risk, 73-6; three state space regions, 26-7, 71, 75; trade and no-trade regions in model of production economy, 30-1; trade and no-trade regions in model of trade-exchange rate volatility relation, 70-2 trade flows: relation between exchange rate volatility and trade volume, 126 trade policy: role of financial markets in setting, 102; welfare gains from endogenous, 103 uncovered interest rate parity (UIP): in determination of current spot exchange rate, 10; function of, 10; in general-equilibrium model in real terms, 60-3; in international

data, 18; relation between forward and spot rates under, 58; tests of, 10-11; violations of, 57 VAR (vector autoregressive) models, 69 welfare: comparisons in general-equilibrium model, 18; effect of exchange rate volatility on, 3; effect of financial market integration on, 3; related to exchange rate risk, 79 welfare gains: from financial-market integration, 4, 83-7; from opening of financial markets, 3, 102-3, 127; from segmented capital markets, 85-7; from sharing financial market risk, 126; from trade in financial markets, 102; without fully integrated commodity markets, 126-7 welfare loss: costs of segmented commodity markets, 87-90; from segmented commodity markets, 83, 87-90; from segmented financial markets, 89-90