A Course in Monetary Economics Sequential Trade, Money, and Uncertainty To My Parents Zahava and Shevach Eden A COURSE IN MONETARY ECONOMICS SEQUENTIAL TRADE, MONEY, AND UNCERTAINTY Benjamin Eden © 2005 by Benjamin Eden 350 Main Street, Malden, MA 02148-5020, USA 108 Cowley Road, Oxford OX4 1JF, UK 550 Swanston Street, Carlton, Victoria 3053, Australia The right of Benjamin Eden to be identified as the Author of this Work has been asserted in accordance with the UK Copyright, Designs, and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs, and Patents Act 1988, without the prior permission of the publisher. First published 2005 by Blackwell Publishing Ltd Library of Congress Cataloging-in-Publication Data Eden, Benjamin.
A course in monetary economics : sequential trade, money, and uncertainty / Benjamin Eden. ISBN 0-631-21565-4 (cloth : alk. paper) ISBN 0-631-21566-2 (pbk. Money–Mathematical models.
Uncertainty–Mathematical models.4 01 51–dc22 2003020730 A catalogue record for this title is available from the British Library. Set in 10/12 12 Dante by Newgen Imaging Systems (P) Ltd, Chennai, India Printed and bound in the United Kingdom by MPG Books, Bodmin, Cornwall For further information on Blackwell Publishing, visit our website: http://www.com Brief Contents Preface xiii Part I: Introduction to Monetary Economics 1 1 Overview 5 2 Money in the Utility Function 26 3 The Welfare Cost of Inflation in a Growing Economy 57 4 Government 72 5 More Explicit Models of Money 86 6 Optimal Fiscal and Monetary Policy 100 7 Money and the Business Cycle: Does Money Matter? 123 8 Sticky Prices in a Demand-satisfying Model 147 9 Sticky Prices with Optimal Quantity Choices 155 10 Flexible Prices 170 Part II: An Introduction to the Economics of Uncertainty 179 11 Preliminaries 182 12 Does Insurance Require Risk Aversion? 197 13 Asset Prices and the Lucas “Tree Model” 202 Part III: An Introduction to Uncertain and Sequential Trade (UST) 207 14 Real Models 210 15 A Monetary Model 250 vi BRIEF CONTENTS 16 Limited Participation, Sticky Prices, and UST: A Comparison 261 17 Inventories and the Business Cycle 280 18 Money and Credit in the Business Cycle 302 19 Evidence from Micro Data 313 20 The Friedman Rule in a UST Model 327 21 Sequential International Trade 333 22 Endogenous Information and Externalities 356 23 Search and Contracts 369 References 385 Index 395 Contents Preface xiii Part I: Introduction to Monetary Economics 1 1 Overview 5 1.1 Money, Inflation, and Output: Some Empirical Evidence 5 1.2 The Policy Debate 8 1.1 The Fisherian diagram 15 1.2 Efficiency and distortive taxes 18 1.3 Asset pricing 21 2 Money in the Utility Function 26 2.1 Motivating the Money in the Utility Function Approach: The Single-period, Single-agent Problem 26 2.2 The Multi-period, Single-agent Problem 28 2.3 Equilibrium with Constant Money Supply 33 2.4 The Social and Private Cost for Accumulating Real Balances 34 2.5 Administrative Ways of Getting to the Optimum 36 2.6 Once and for All Changes in M 36 2.7 Change in the Rate of Money Supply Change: Technical Aspects 37 2.8 Change in the Rate of Money Supply Change: Economics 38 2.9 Steady-state Equilibrium (SSE) 41 2.10 Transition from One Steady State to Another 41 2.12 Introducing Physical Capital and Bonds 45 viii CONTENTS 2.13 The Golden Rule and the Modified Golden Rule 47 Appendix 2A A dynamic programming example 53 3 The Welfare Cost of Inflation in a Growing Economy 57 3.1 Steady-state Equilibrium in a Growing Economy 57 3.2 Generalizing the Model in Chapter 2 to the Case of Growth 58 3.3 Money Substitutes 64 Appendix 3A A dynamic programming formulation 69 4 Government 72 4.1 The Revenues from Printing Money 72 4.1 Steady-state revenues 72 4.2 Out of the steady-state revenues 73 4.3 The present value of revenues 75 Appendix 4A Non-steady-state equilibria 76 4.2 The Government’s “Budget Constraint” 78 4.1 Monetary and fiscal policy: Who moves first? 81 4.2 The fiscal approach to the price level 81 4.3 Policy in the Absence of Perfect Commitment: A Positive Theory of Inflation 82 5 More Explicit Models of Money 86 5.1 A Cash-in-advance Model 86 5.1 A two-goods model 87 5.2 An analogous real economy 89 5.3 Money super-neutrality in a one-good model 92 5.2 An Overlapping Generations Model 94 5.3 A Baumol–Tobin Type Model 96 Appendix 5A 98 6 Optimal Fiscal and Monetary Policy 100 6.1 The Second-best Allocation 100 6.2 The Second Best and the Friedman Rule 103 6.3 Smoothing Tax Distortions 109 6.4 A Shopping Time Model 112 7 Money and the Business Cycle: Does Money Matter? 123 7.1 VAR and Impulse Response Functions: An Example 125 7.2 Using VAR Impulse Response Analysis to Assess the Money–Output Relationship 127 CONTENTS ix 7.3 Specification Search 135 7.4 Variance Decomposition 142 8 Sticky Prices in a Demand-satisfying Model 147 9 Sticky Prices with Optimal Quantity Choices 155 9.1 The Production to Order Case 156 9.2 The Production to Market Case 161 10 Flexible Prices 170 10.1 Lucas’ Confusion Hypothesis 170 10.2 Limited Participation 174 Part II: An Introduction to the Economics of Uncertainty 179 11 Preliminaries 182 11.1 Trade in Contingent Commodities 185 11.2 Efficient Risk Allocation 190 12 Does Insurance Require Risk Aversion? 197 12.1 The Insurance-buying Gambler 200 12.2 Socially Harmful Information 201 13 Asset Prices and the Lucas “Tree Model” 202 Part III: An Introduction to Uncertain and Sequential Trade (UST) 207 14 Real Models 210 14.1 Downward sloping demand 215 14.3 Demand and supply analysis 221 14.2 Estimating the markup 227 14.3 Relationship to the Arrow–Debreu Model 228 14.4 Heterogeneity and Supply Uncertainty 231 14.1 The model 233 x CONTENTS 14.2 Solving for a temporary equilibrium 240 14.4 Efficiency 243 Appendix 14A The firm’s problem 247 Appendix 14B The planner’s problem 248 15 A Monetary Model 250 15.2 Working with the Money Supply as the Unit of Account 253 15.3 Anticipated and Unanticipated Money 255 15.4 Labor Choice, Average Capacity Utilization and Welfare 256 15.5 A Generalization to Many Potential Markets 256 15.6 Asymmetric Equilibria: A Perfectly Flexible Price Distribution is Consistent with Individual Prices That Appear to Be “Rigid” 258 15.7 Summary of the Implications of the Model 259 16 Limited Participation, Sticky Prices, and UST: A Comparison 261 16.4 A Real Business Cycle Model with Wedges: Some Equivalence Results 274 16.5 Additional Tests Based on Unit Labor Cost and Labor Share 276 17 Inventories and the Business Cycle 280 17.1 Introducing Costless Storage 282 17.2 Adding Supply Shocks 288 17.3 Testing the Model with Detrended Variables 292 17.4 Using an Impulse Response Analysis with Non-detrended Variables to Test for Persistence 297 Appendix 17A The Hodrick–Prescott (H–P) filter 300 18 Money and Credit in the Business Cycle 302 18.1 A UST Model with Credit 302 18.2 Inventories Are a Sufficient Statistic for Past Demand Shocks 305 18.3 Estimating the Responses to a Money Shock 306 CONTENTS xi 18.4 Estimating the Responses to an Inventories Shock 310 18.5 Concluding Remarks 312 19 Evidence from Micro Data 313 19.1 A Menu Cost Model 313 19.2 The Serial Correlation in the Nominal Price Change 315 19.3 A Two-Sided Policy 316 19.4 Relative Price Variability and Inflation 317 19.5 A Staggered Price Setting Model 319 20 The Friedman Rule in a UST Model 327 20.1 A Single-Asset Economy 327 20.2 Adding a Costless Bonds Market 330 20.3 Costly Transactions in Bonds 331 21 Sequential International Trade 333 21.3 Exchange Rates 348 Appendix 21A Proofs of the Claims in the Monetary Model 350 Appendix 21B Example 7 in detail 353 22 Endogenous Information and Externalities 356 22.3 Relationship to the New Keynesian Economics 367 23 Search and Contracts 369 23.1 Search over Time 369 23.2 Random Choice of Markets 371 23.3 Capacity Utilization Contracts and Carlton’s Observations 375 References 385 Index 395 Preface The aim of this book is to integrate the relatively new uncertain and sequential trade (UST) models with standard monetary economics. I therefore combine exposition of well-known material with that of new and sometimes yet unpublished. The exposition is at the gradu- ate level but since mathematics is de-emphasized, it can and was used at the advanced undergraduate level.
I wrote this book while teaching monetary economics during the period 1987–2002 at the joint Master program of the Technion and the University of Haifa. I also taught earlier versions at Florida State University (First year Ph. level, 2001) at the University of Chicago (Second year Ph. level, 2002) and at Vanderbilt University (First and second year Ph.
I have benefited from policy discussion at the Bank of Israel during the period 1992–7 where I was a consultant to the research department. This served as a reminder that monetary economics is a slow moving field not because all the problems are solved but because there are many unsolved problems that are difficult. My interest in UST type models has started in 1979–80 while visiting Carnegie Mellon university. Initially I was motivated by the observation that the standard Walrasian model is incomplete because it uses the Walrasian tatonnement process to find the market clearing price.
As a result my earlier models focused on the question of who will gather information about the market-clearing price. In these models sellers could buy information about demand but there were informational externalities arising from the fact that advertised prices can be observed by all sellers. These type of models were published in the years 1981–3 and are discussed in chapter 22. I then moved to simpler models that abstract from information acquisition.
This simpler set-up proved to be rich enough and occupied most of my research efforts. The motivation has also changed. Instead of complaining about the tatonnement process I now focus on the performance of the model in explaining the monetary economy. Since this book represents more than 20 years of effort it is difficult to remember and thank all the numerous useful comments and discussions.
I have benefited mostly from comments made by students over the years. Ben Bental and Don Schlagenhauf read parts of an earlier version of the manuscript and made useful comments. I have also benefited from comments xiv PREFACE and discussions with Rick Bond, Boyan Jovanovic, Bob Lucas and Michael Woodford. Michael Bar provided excellent research assistance.
My wife Sveta contributed more than moral support and understanding. She has written a Master thesis on the subject and simulated the UST model with inventories. I hope that this book will also be of some interest to my daughter Maya and to my sons Michael and Ittai at some point in the future. Finally, I want to thank my parents Shevach and Zahava Eden for moral support and gentle push.
A Course in Monetary Economics: Sequential Trade, Money, and Uncertainty Benjamin Eden Copyright © 2005 by Benjamin Eden PART I Introduction to Monetary Economics 1 Overview 2 Money in the Utility Function 3 The Welfare Cost of Inflation in a Growing Economy 4 Government 5 More Explicit Models of Money 6 Optimal Fiscal and Monetary Policy 7 Money and the Business Cycle: Does Money Matter? 8 Sticky Prices in a Demand-satisfying Model 9 Sticky Prices with Optimal Quantity Choices 10 Flexible Prices 3 In the first part of this book we use standard monetary models to talk about the joint behavior of nominal and real variables. We start with the long-run relationship focusing on the relationship between money and inflation. The focus then shifts to the short-run relationship between money and output. Special attention is devoted to the choice of fiscal and monetary policy.
This introductory part sets the stage for a less standard approach in the third part of the book. A Course in Monetary Economics: Sequential Trade, Money, and Uncertainty Benjamin Eden Copyright © 2005 by Benjamin Eden CHAPTER 1 Overview Monetary economics is about the relationship between real and nominal variables.