Rational Expectations and Econometric Practice This page intentionally left blank Rational Expectations and Econometric Practice Edited by Robert E. Lucas, Jr. University of Chicago and Thomas J. Sargent University of Minnesota and Federal Reserve Bank of Minneapolis The University of Minnesota Press Minneapolis Copyright ©1981 by the University of Minnesota All rights reserved. Published by the University of Minnesota Press, 2037 University Avenue Southeast, Minneapolis, MN 55414 Printed in the United States of America. Fifth printing, 1988. Library of Congress Cataloging in Publication Data Main entry under title: Rational expectations and econometric practice. Bibliography: p. 1. Econometrics-Addresses, essays, lectures. 2. Time-series analysis-Addresses, essays, lectures. 3. Monetary policy-Mathematical models-Addresses, essays, lectures. 4. Economic policy-Mathematical models-Addresses, essays, lectures. I. Lucas, Robert E. II. Sargent, Thomas J. HB139.R37 33'.028 80-24602 ISBN 0-8166-0916-0 ISBN 0-8166-0917-9 v. I (pbk.) ISBN 0-8166-1071-1 v. II (pbk.) ISBN 0-8166-1098-3 Set (pbk.) The University of Minnesota is an equal-opportunity educator and employer. To our parents This page intentionally left blank Contents xi Introduction 1. Implications of Rational Expectations and Econometric Practice 3 John F. Muth, "Rational Expectations and the Theory of Price Movements." 23 John F. Muth, "Optimal Properties of Exponentially Weighted Forecasts." 33 Thomas J. Sargent, "A Note on the 'Accelerationist' Controversy." 39 Robert E. Lucas, Jr., "Distributed Lags and Optimal Investment Policy." 55 Robert E. Lucas, Jr., "Optimal Investment with Rational Expectations." 67 Robert E. Lucas, Jr., and Edward C. Prescott, "Investment under Uncertainty." 91 Lars Peter Hansen and Thomas J. Sargent, "Formulating and Estimating Dynamic Linear Rational Expectations Models." 127 Lars Peter Hansen and Thomas J. Sargent, "Linear Rational Expectations Models for Dynamically Interrelated Variables." 2. Macroeconomic Policy 159 Thomas J. Sargent, "Rational Expectations, the Real Rate of Interest, and the Natural Rate of Unemployment." 199 Thomas J. Sargent and Neil Wallace, "Rational Expectations and the Theory of Economic Policy." 215 Thomas J. Sargent and Neil Wallace, "'Rational' Expectations, the Optimal Monetary Instrument, and the Optimal Money Supply Rule." 229 Robert J. Barro, "Rational Expectations and the Role of Monetary Policy." 261 Stanley Fischer, "Long-Term Contracts, Rational Expectations, and the Optimal Money Supply Rule." vii viii CONTENTS 277 Bennett T. McCallum, "Price-Level Stickiness and the Feasibility of Monetary Stabilization Policy with Rational Expectations." 285 Bennett T. McCallum, "The Current State of the Policy- Ineffectiveness Debate." 3. Econometric Methods: General 295 Robert E. Lucas, Jr., and Thomas J. Sargent, "After Keynesian Macroeconomics." 321 John F. Muth, "Estimation of Economic Relationships Containing Latent Expectations Variables." 329 Kenneth F. Wallis, "Econometric Implications of the Rational Expectations Hypothesis." 355 Gregory C. Chow, "Estimation of Rational Expectations Models." 4. General Applications 371 C. W.J. Granger, "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods." 387 Christopher A. Sims, "Money, Income, and Causality." 405 Thomas J. Sargent and Neil Wallace, "Rational Expectations and the Dynamics of Hyperinflation." 429 Thomas J. Sargent, "The Demand for Money during Hyperinflations under Rational Expectations." 453 Thomas J. Sargent, "A Note on Maximum Likelihood Estimation of the Rational Expectations Model of the Term Structure." 463 Thomas J. Sargent, "Estimation of Dynamic Labor Demand Schedules under Rational Expectations." 501 Robert E. Hall, "Stochastic Implications of the Life Cycle— Permanent Income Hypothesis: Theory and Evidence." 5. Testing for Neutrality 521 Thomas J. Sargent, "A Classical Macroeconometric Model for the United States." 553 Thomas J. Sargent, "The Observational Equivalence of Natural and Unnatural Rate Theories of Macroeconomics." 563 Robert J. Barro, "Unanticipated Money Growth and Unemployment in the United States." 585 Robert J. Barro, "Unanticipated Money, Output, and the Price Level in the United States." CONTENTS ix 6. Macroeconomic Control Problems 619 Finn E. Kydland and Edward C. Prescott, "Rules Rather than Discretion: The Inconsistency of Optimal Plans." 639 Guillermo A. Calvo, "On the Time Consistency of Optimal Policy in a Monetary Economy." 659 John B. Taylor, "Estimation and Control of a Macroeconomic Model with Rational Expectations." 681 Gregory C. Chow, "Estimation and Optimal Control of Dynamic Game Models under Rational Expectations." This page intentionally left blank Introduction I After a remarkably quiet first decade John Muth's idea of "rational expec- tations" has taken hold, or taken off, in an equally remarkable way. The term now enjoys popularity as a slogan or incantation with a variety of uses. It may also suffer some notoriety due to presumed links with conserv- ative political views or with excessive concern over the consequences of money supply changes. The term "rational expectations" carries, it seems, a charge of some magnitude. In our view, this charge is not incidental or uninteresting: Muth's hy- pothesis is a contribution of the most fundamental kind, an idea that compels rethinking on many dimensions, with consequent enthusiasm and resistance. One of the purposes of this volume is to collect in a convenient place some of the papers which conveyed this fact most forcefully to econ- omists concerned with the connections between observed behavior and the evaluation of economic policies. Yet how, exactly, does the economist who is persuaded of the usefulness of this idea, or is at least interested enough to give it an honest test, alter the way he practices his trade? A full answer to this question is, we believe, a central issue on the current research agenda of time-series econometrics and dynamic economic theory. We do not presume to answer it in this volume. At the same time, progress on this question has been rapid in recent years, scattered in articles in many journals and conference vol- umes. In the main, these articles are motivated by a variety of specific substantive concerns, but they also contain many operational ideas and methods of much wider applicability. The function, we hope, of the pres- ent collection will be to increase the accessibility to these ideas and to display their methodological contributions as clearly as possible. The papers in this collection deal with various aspects of the general problem of drawing inferences about behavior from observed economic time series: we observe an agent, or collection of agents, behaving through time; we wish to use these observations to infer how this behavior would have differed had the agent's environment been altered in some specified We would like to thank John Taylor, Gregory Chow, Finn Kydland, Edward Prescott, and Christopher Sims for thoughtful comments on earlier versions of this introduction. xi xii INTRODUCTION way. Stated so generally, it is clear that some inferences of this type will be impossible to draw. (How would one's life have been different had one married someone else?) The belief in the possibility of a nonexperimental empirical economics is, however, equivalent to the belief that inferences of this kind can be made, under some circumstances. The dimensions of this generally stated problem can be clarified by reference to an example, which we will use as a device for clarifying the relationships among the various papers. Consider a single decision maker, whose situation or state at time t is completely described by two variables xt and zt. Here ztS1 is thought of as selected by "nature," and evolves through time according to where the "innovations" eteS are independent drawings from a fixed cu- mulative probability distribution function <I>('):8 —» [0, 1]. (At the formal level at which this discussion will be conducted, the set S1 can be conceived very generally; for example, one may think of zt as the entire history of a process from — oo through t.) We will refer to the function f:S1.xS —> S1 as the decision maker's environment. Think of xttS2 as a state variable under partial control of the decision maker. Each period, he selects an action uttU. There is a fixed technology g:S1xS2xU —» S2 describing the motion of xt given actions ut by the agent and actions zt by "nature": The agent is viewed as purposively selecting his action ut as some fixed function h:S1xS2 —> U of his situation: As econometricians, we observe some or all of the process {zt, xt, ut }, the motion of which is given by (1), (2), and (3). With the model suitably specialized, the estimation of the functions/ g, and h from such observa- tions is a well-posed statistical problem, and given long enough time series we can speak of observing/, g, and h. Under what circumstances, then, do these observations amount to an answer to our original question: how would the agent's behavior have differed had his environment been differ- ent in some particular way? To answer this, we need to be somewhat more specific about what we mean by a "change in the environment." One form of change, or interven- tion, one can imagine is the alteration of one, or a "few," realizations of the shocks ct which enter into (1). If carried out in such a way as not to lead the agent to perceive that either/or <I> has changed, it is reasonable to suppose that such an intervention would not induce any change in the decision rule h and hence that knowledge of f, g, and h amounts to having the ability accurately to evaluate the consequences of the intervention. INTRODUCTION xiii In typical economic applications, however, and certainly in macroeco- nomic applications, the policy interventions we are interested in are not one-time interventions but rather systematic changes in the way policy variables react to the situation: changes in the function f. Thus a change from balanced-budget peacetime fiscal policy to Keynesian countercycli- cal policy affects not just one year's deficit, but how fiscal policy is formu- lated, year in and year out.