Cover image for Macroeconomics of self-fulfilling prophecies
Title:
Macroeconomics of self-fulfilling prophecies
Author:
Farmer, Roger E. A.
Personal Author:
Edition:
Second edition.
Publication Information:
Cambridge, Mass. : MIT Press, 1999.
Physical Description:
xvi, 300 pages : illustrations ; 24 cm
Language:
English
ISBN:
9780262062039
Format :
Book

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HB172.5 .F37 1999 Adult Non-Fiction Central Closed Stacks
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Summary

Summary

For many years it was fashionable to treat macroeconomics and microeconomics as separate subjects without looking too deeply at the relationship between the two. But in the 1970s there occurred an episode of high inflation and high unemployment, which was inconsistent with orthodox theory. As a result, macroeconomists began to pay much greater attention to the microfoundations of their subject.

In this book Roger E. A. Farmer takes a somewhat controversial point of view, arguing for the future of macroeconomics as a branch of applied general equilibrium theory. His main theme is that macroeconomics is best viewed as the study of equilibrium environments in which the welfare theorems break down. This approach makes it possible to discuss the role of government policies in a context in which policy may serve some purpose.

Since the publication of the first edition in 1993, self-fulfilling prophecies has become a major competitor to the real business-cycle view of economic fluctuations. The second edition has been updated in three ways: (1) problems are included at the end of every chapter, and a study guide containing sample answers to all of the problems is available; (2) a new chapter discusses research from the past five years on business fluctuations in multisector models; and (3) the chapter on representative agent growth models now includes an appendix that explains the transversality condition.


Author Notes

Roger E. A. Farmer is Professor of Economics at the University of California, Los Angeles. He also teaches at the European University Institute in Florence, Italy.


Table of Contents

Preface to Second Editionp. XV
1 Introductionp. 1
1.1 Equilibrium Theory as an Approach to Macroeconomicsp. 1
1.2 Preview of the Argumentp. 3
1.3 Examplep. 4
1.3.1 Regular Casep. 6
1.3.2 Irregular Casep. 7
1.4 Concluding Remarksp. 9
1.5 Problemsp. 9
2 Linear Difference Equations: Part 1p. 11
2.1 Introductionp. 11
2.2 Linearizing Nonlinear Modelsp. 11
2.2.1 Nonlinear Models to Represent Economiesp. 11
2.2.2 Linearizing Autonomous Equationsp. 12
2.2.3 Linearizing Nonautonomous Equationsp. 13
2.2.4 Example of Linearization: The Solow Modelp. 14
2.3 Solving First-Order Linear Modelsp. 17
2.3.1 First-Order Deterministic Equationsp. 18
2.3.2 First-Order Stochastic Equationsp. 18
2.3.3 Sequences of Probability Distributionsp. 21
2.3.4 The Solow Model Revisitedp. 22
2.4 Solving Higher-Order Linear Modelsp. 25
2.4.1 Eigenvalues and Eigenvectorsp. 27
2.4.2 Higher-Order Deterministic Equationsp. 29
2.4.3 Diagonalizing Systems of Nonstochastic Equationsp. 32
2.4.4 Stochastic Vector Difference Equationsp. 33
2.4.5 Example of a Vector System--The Behavior of the Solow Residualp. 34
2.5 Concluding Remarksp. 38
2.6 Problemsp. 39
3 Linear Difference Equations: Part 2p. 41
3.1 Introductionp. 41
3.2 Linear Rational Expectations Modelsp. 42
3.2.1 Optimal Growth as an Illustration of a Rational Expectations Modelp. 44
3.3 Solving Linear Rational Expectations Modelsp. 47
3.3.1 Different Types of Rational Expectations Modelsp. 47
3.3.2 Case of a Regular Equilibriump. 49
3.3.3 Solving a Rational Expectations Model by Iterating into the Futurep. 50
3.3.4 Completing the Solution by Solving Equations that Depend on the Pastp. 51
3.3.5 Optimal Growth Model and the Solow Model Comparedp. 52
3.4 Cross-equation Restrictions and the Lucas Critiquep. 53
3.4.1 Dynamics of a Monetary Model--A Second Examplep. 53
3.4.2 Solving the Example Explicitlyp. 55
3.4.3 Lucas Critique and the Cross-equation Restrictionsp. 57
3.4.4 Irregular Solutionsp. 57
3.5 Concluding Remarksp. 58
3.6 Problemsp. 59
4 General Equilibrium Theory under Certaintyp. 63
4.1 Introductionp. 63
4.2 Idea of Equilibriump. 67
4.3 Theory of Consumer Choicep. 68
4.3.1 Assumptions about Preferencesp. 68
4.3.2 Consumer's Problemp. 70
4.4 Excess Demand Functionsp. 71
4.4.1 Individual Excess Demand Functionsp. 71
4.4.2 Aggregate Excess Demand Functionsp. 72
4.5 Equilibria and Their Propertiesp. 74
4.5.1 Some Definitions and Development of Notationp. 75
4.5.2 Geometry of Equilibriump. 76
4.5.3 Debreu-Sonnenschein-Mantel Theoremp. 78
4.6 General Equilibrium Theory and Efficient Allocations of Resourcesp. 79
4.6.1 First Welfare Theoremp. 79
4.6.2 Second Welfare Theoremp. 80
4.7 Concluding Remarksp. 82
4.8 Problemsp. 83
5 Infinite Horizon Economies and Representative Agentsp. 85
5.1 Introductionp. 85
5.2 Representative Agent Economyp. 88
5.2.1 Assumptions about Structurep. 88
5.2.2 Assumptions about Preferencesp. 90
5.2.3 Budget Sets and Market Structurep. 92
5.2.4 Consumer's Problemp. 94
5.3 Competitive Equilibrium and the Planner's Problemp. 95
5.3.1 Competitive Equilibriump. 95
5.3.2 Planner's Problemp. 96
5.4 Using the Representative Agent Model to Explain Time Series Datap. 99
5.4.1 Removing the Trend from Datap. 99
5.4.2 Simple RBC Model and Its Implicationsp. 102
5.4.3 Regression on a Common Trend: What the Model Tells Us to Dop. 103
5.4.4 Hodrick-Prescott Filter: What RBC Economists Actually Dop. 106
5.4.5 Calibration and Summary Statistics: How RBC Theorists Measure Successp. 108
5.5 Concluding Remarksp. 109
5.6 Appendix Transversality Conditionp. 110
5.7 Problemsp. 112
6 Infinite Horizon Economies and Overlapping Generationsp. 115
6.1 Introductionp. 115
6.2 Structure of the Overlapping Generations Economyp. 116
6.3 Consumer's Problemp. 117
6.3.1 Problem of a Young Agentp. 117
6.3.2 Problem of an Old Agentp. 118
6.4 Example of a Pareto Inferior Equilibriump. 119
6.4.1 Case of Early Endowmentsp. 119
6.4.2 Case of Late Endowmentsp. 120
6.5 Institutions that May Improve Allocationsp. 120
6.6 Set of Equilibria in the Overlapping Generations Modelp. 122
6.6.1 Equilibria as Solutions to Difference Equationsp. 122
6.6.2 Stationary Equilibriap. 124
6.6.3 Classifying Economies by Types of Stationary Equilibriap. 125
6.6.4 Dynamic Equilibriap. 127
6.7 Some Questions about the Modelp. 128
6.7.1 Why Does the First Welfare Theorem Break Down?p. 129
6.7.2 When Does Indeterminacy Occur?p. 129
6.7.3 When Are Equilibria Efficient?p. 130
6.8 More General Examples of Overlapping Generations Economiesp. 132
6.8.1 Kehoe-Levine Approachp. 134
6.8.2 Indeterminacy in the OG Modelp. 135
6.9 Concluding Remarksp. 135
6.10 Problemsp. 136
7 Infinite Horizon Economies with Nonconvexitiesp. 141
7.1 Introductionp. 141
7.2 Growth Model with Increasing Returnsp. 142
7.2.1 Equations That Characterize an Equilibriump. 142
7.2.2 Behavior of the Representative Familyp. 143
7.2.3 Interpretation 1: Externalities in Productionp. 144
7.2.4 Interpretation 2: Monopolistic Competitionp. 145
7.3 Empirical Evidence for Increasing Returnsp. 149
7.4 Equilibria in the Increasing Returns Economyp. 152
7.4.1 Finding a Balanced Growth Pathp. 152
7.4.2 Approximate Linear Modelp. 154
7.5 Comparing the Theoretical Properties of RA and IR Modelsp. 155
7.5.1 Why Does the IR Model Display Different Dynamics?p. 155
7.5.2 RA Model: An Example of a Regular Equilibriump. 157
7.5.3 IR Model: An Example of an Irregular Equilibriump. 158
7.6 Comparing Some Empirical Predictions of RA and IR Modelsp. 160
7.6.1 Contemporaneous Statisticsp. 160
7.6.2 Dynamic Responses--The Impulse Response Functionp. 163
7.7 Concluding Remarksp. 164
7.8 Problemsp. 166
8 Some Recent Developmentsp. 171
8.1 Introductionp. 171
8.2 New Evidence against Big Increasing Returnsp. 171
8.3 Nonseparable Preferencesp. 173
8.3.1 Householdsp. 173
8.3.2 Technologyp. 174
8.3.3 Solving the Consumer's Problemp. 175
8.3.4 Equations That Characterize Equilibriump. 176
8.3.5 Examplep. 178
8.4 Two-Sector Modelsp. 180
8.4.1 Technologyp. 180
8.4.2 Production Possibilities Frontierp. 181
8.4.3 Behavior of the Representative Familyp. 183
8.4.4 Indeterminacy and the Two-Sector Modelp. 185
8.4.5 Procyclical Consumptionp. 185
8.4.6 Calibrated Two-Sector Modelp. 187
8.5 Concluding Remarksp. 187
8.6 Problemsp. 188
9 General Equilibrium Theory and Uncertaintyp. 191
9.1 Introductionp. 191
9.2 Debreu's Formulation of the Problemp. 191
9.2.1 Preferences under Uncertaintyp. 191
9.2.2 Budget Constraintsp. 196
9.3 Arrow's Formulation of the Problemp. 197
9.3.1 Trade in Financial Securitiesp. 197
9.3.2 Complete and Incomplete Marketsp. 199
9.3.3 Multiple Budget Constraints and Incomplete Marketsp. 201
9.4 Infinite Horizon Economies with Uncertaintyp. 202
9.4.1 Asset Pricing in Lucas Tree Economiesp. 202
9.4.2 Digression on Market Structurep. 204
9.4.3 Asset Pricing in the Representative Agent Casep. 206
9.5 Concluding Remarksp. 208
9.6 Problemsp. 209
10 Sunspotsp. 211
10.1 Introductionp. 211
10.2 Do Sunspots Matter?p. 212
10.2.1 Complete and Incomplete Participationp. 212
10.2.2 Setting up the Environmentp. 213
10.2.3 Sunspot Theoremsp. 215
10.3 Example of a Macroeconomic Model Where Sunspots Matterp. 217
10.3.1 Description of the Environmentp. 217
10.3.2 Set of Equilibriap. 220
10.3.3 Supporting Sunspot Equilibria with Beliefsp. 223
10.3.4 Sunspots, Bubbles, and Regular Equilibriap. 226
10.4 Concluding Remarksp. 228
10.5 Problemsp. 229
11 Macroeconomic Models of Moneyp. 231
11.1 Introductionp. 231
11.1.1 Rate of Return Dominance and Legal Restrictions Theoryp. 231
11.1.2 Some Quick Fixes to Rate of Return Dominancep. 232
11.2 Models of Moneyp. 233
11.2.1 Budget Sets: the Opportunity Cost of Holding Moneyp. 234
11.2.2 Objective Functions: Cash in Advance and Its Relationship to Money in the Utility Functionp. 237
11.3 Dynamics of a Cash-in-Advance Modelp. 239
11.3.1 Different Types of Monetary Policyp. 239
11.3.2 Government's Budget Constraintsp. 240
11.3.3 Typology of Policy Regimesp. 242
11.4 Equilibrium under Interest Rate Controlp. 243
11.4.1 Policy Mix A: Fixed Interest Rates and Zero Debtp. 243
11.4.2 Equilibrium of the Real Economy under Interest Rate Controlp. 246
11.4.3 Equilibrium Rates of Change of Nominal Variables under Interest Rate Controlp. 247
11.4.4 Indeterminacy of the Nominal Scale of the Economy under Interest Rate Controlp. 248
11.4.5 Economics of Indeterminacy under Interest Rate Controlp. 249
11.5 Equilibrium under a Fixed Money Growth Rate Rulep. 250
11.5.1 Policy Mix B: Fixed Money Growth Rate and Zero Debtp. 251
11.5.2 Equilibrium of the Real Economy with a Fixed Money Growth Ratep. 251
11.5.3 Example of Indeterminate Equilibria in a Simple Economyp. 252
11.6 Concluding Remarksp. 254
11.7 Problemsp. 255
12 Applied Monetary Theoryp. 259
12.1 Introductionp. 259
12.2 Monetary Facts: What There Is to Explainp. 260
12.3 Simple Monetary Model: Using Equilibrium Theory to Explain the Factsp. 263
12.3.1 Modeling the Exchange Processp. 265
12.3.2 Formalizing the Exchange Technologyp. 266
12.3.3 How to Describe an Equilibriump. 267
12.4 How Do Equilibria Behave?p. 270
12.4.1 Choosing Functional Formsp. 270
12.4.2 What Do Equilibria Look Like?p. 271
12.4.3 Alternative Views of the Money-Income Correlation?p. 275
12.4.4 What Does All of This Have to Do with Sticky Prices?p. 276
12.5 Concluding Remarksp. 277
12.6 Problemsp. 278
Notesp. 281
Bibliographyp. 289
Indexp. 295