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Tables of Contents for Macroeconomics of Self-Fulfilling Prophecies
Chapter/Section Title
Page #
Page Count
Preface to Second Edition
xv
1 Introduction
1
10
1.1 Equilibrium Theory as an Approach to Macroeconomics
1
2
1.2 Preview of the Argument
3
1
1.3 Example
4
5
1.3.1 Regular Case
6
1
1.3.2 Irregular Case
7
2
1.4 Concluding Remarks
9
1
1.5 Problems
9
2
2 Linear Difference Equations: Part 1
11
30
2.1 Introduction
11
1
2.2 Linearizing Nonlinear Models
11
6
2.2.1 Nonlinear Models to Represent Economies
11
1
2.2.2 Linearizing Autonomous Equations
12
1
2.2.3 Linearizing Nonautonomous Equations
13
1
2.2.4 Example of Linearization: The Solow Model
14
3
2.3 Solving First-Order Linear Models
17
8
2.3.1 First-Order Deterministic Equations
18
1
2.3.2 First-Order Stochastic Equations
18
3
2.3.3 Sequences of Probability Distributions
21
1
2.3.4 The Solow Model Revisited
22
3
2.4 Solving Higher-Order Linear Models
25
13
2.4.1 Eigenvalues and Eigenvectors
27
2
2.4.2 Higher-Order Deterministic Equations
29
3
2.4.3 Diagonalizing Systems of Nonstochastic Equations
32
1
2.4.4 Stochastic Vector Difference Equations
33
1
2.4.5 Example of a Vector System-The Behavior of the Solow Residual
34
4
2.5 Concluding Remarks
38
1
2.6 Problems
39
2
3 Linear Difference Equations: Part 2
41
22
3.1 Introduction
41
1
3.2 Linear Rational Expectations Models
42
5
3.2.1 Optimal Growth as an Illustration of a Rational Expectations Model
44
3
3.3 Solving Linear Rational Expectations Models
47
6
3.3.1 Different Types of Rational Expectations Models
47
2
3.3.2 Case of a Regular Equilibrium
49
1
3.3.3 Solving a Rational Expectations Model by Iterating into the Future
50
1
3.3.4 Completing the Solution by Solving Equations that Depend on the Past
51
1
3.3.5 Optimal Growth Model and the Solow Model Compared
52
1
3.4 Cross-equation Restrictions and the Lucas Critique
53
5
3.4.1 Dynamics of a Monetary Model-A Second Example
53
2
3.4.2 Solving the Example Explicitly
55
2
3.4.3 Lucas Critique and the Cross-equation Restrictions
57
1
3.4.4 Irregular Solutions
57
1
3.5 Concluding Remarks
58
1
3.6 Problems
59
4
4 General Equilibrium Theory under Certainty
63
22
4.1 Introduction
63
4
4.2 Idea of Equilibrium
67
1
4.3 Theory of Consumer Choice
68
3
4.3.1 Assumptions about Preferences
68
2
4.3.2 Consumer's Problem
70
1
4.4 Excess Demand Functions
71
3
4.4.1 Individual Excess Demand Functions
71
1
4.4.2 Aggregate Excess Demand Functions
72
2
4.5 Equilibria and Their Properties
74
5
4.5.1 Some Definitions and Development of Notation
75
1
4.5.2 Geometry of Equilibrium
76
2
4.5.3 Debreu-Sonnenschein-Mantel Theorem
78
1
4.6 General Equilibrium Theory and Efficient Allocations of Resources
79
3
4.6.1 First Welfare Theorem
79
1
4.6.2 Second Welfare Theorem
80
2
4.7 Concluding Remarks
82
1
4.8 Problems
83
2
5 Infinite Horizon Economies and Representative Agents
85
30
5.1 Introduction
85
3
5.2 Representative Agent Economy
88
7
5.2.1 Assumptions about Structure
88
2
5.2.2 Assumptions about Preferences
90
2
5.2.3 Budget Sets and Market Structure
92
2
5.2.4 Consumer's Problem
94
1
5.3 Competitive Equilibrium and the Planner's Problem
95
4
5.3.1 Competitive Equilibrium
95
1
5.3.2 Planner's Problem
96
3
5.4 Using the Representative Agent Model to Explain Time Series Data
99
10
5.4.1 Removing the Trend from Data
99
3
5.4.2 Simple RBC Model and Its Implications
102
1
5.4.3 Regression on a Common Trend: What the Model Tells Us to Do
103
3
5.4.4 Hodrick-Prescott Filter: What RBC Economists Actually Do
106
2
5.4.5 Calibration and Summary Statistics: How RBC Theorists Measure Success
108
1
5.5 Concluding Remarks
109
1
5.6 Appendix: Transversality Condition
110
2
5.7 Problems
112
3
6 Infinite Horizon Economies and Overlapping Generations
115
26
6.1 Introduction
115
1
6.2 Structure of the Overlapping Generations Economy
116
1
6.3 Consumer's Problem
117
2
6.3.1 Problem of a Young Agent
117
1
6.3.2 Problem of an Old Agent
118
1
6.4 Example of a Pareto Inferior Equilibrium
119
1
6.4.1 Case of Early Endowments
119
1
6.4.2 Case of Late Endowments
120
1
6.5 Institutions that May Improve Allocations
120
2
6.6 Set of Equilibria in the Overlapping Generations Model
122
6
6.6.1 Equilibria as Solutions to Difference Equations
122
2
6.6.2 Stationary Equilibria
124
1
6.6.3 Classifying Economies by Types of Stationary Equilibria
125
2
6.6.4 Dynamic Equilibria
127
1
6.7 Some Questions about the Model
128
4
6.7.1 Why Does the First Welfare Theorem Break Down?
129
1
6.7.2 When Does Indeterminacy Occur?
129
1
6.7.3 When Are Equilibria Efficient?
130
2
6.8 More General Examples of Overlapping Generations Economies
132
3
6.8.1 Kehoe-Levine Approach
134
1
6.8.2 Indeterminacy in the OG Model
135
1
6.9 Concluding Remarks
135
1
6.10 Problems
136
5
7 Infinite Horizon Economies with Nonconvexities
141
30
7.1 Introduction
141
1
7.2 Growth Model with Increasing Returns
142
7
7.2.1 Equations That Characterize an Equilibrium
142
1
7.2.2 Behavior of the Representative Family
143
1
7.2.3 Interpretation 1: Externalities in Production
144
1
7.2.4 Interpretation 2: Monopolistic Competition
145
4
7.3 Empirical Evidence for Increasing Returns
149
3
7.4 Equilibria in the Increasing Returns Economy
152
3
7.4.1 Finding a Balanced Growth Path
152
2
7.4.2 Approximate Linear Model
154
1
7.5 Comparing the Theoretical Properties of RA and IR Models
155
5
7.5.1 Why Does the IR Model Display Different Dynamics?
155
2
7.5.2 RA Model: An Example of a Regular Equilibrium
157
1
7.5.3 IR Model: An Example of an Irregular Equilibrium
158
2
7.6 Comparing Some Empirical Predictions of RA and IR Models
160
4
7.6.1 Contemporaneous Statistics
160
3
7.6.2 Dynamic Responses--The Impulse Response Function
163
1
7.7 Concluding Remarks
164
2
7.8 Problems
166
5
8 Some Recent Developments
171
20
8.1 Introduction
171
1
8.2 New Evidence against Big Increasing Returns
171
2
8.3 Nonseparable Preferences
173
7
8.3.1 Households
173
1
8.3.2 Technology
174
1
8.3.3 Solving the Consumer's Problem
175
1
8.3.4 Equations That Characterize Equilibrium
176
2
8.3.5 Example
178
2
8.4 Two-Sector Models
180
7
8.4.1 Technology
180
1
8.4.2 Production Possibilities Frontier
181
2
8.4.3 Behavior of the Representative Family
183
2
8.4.4 Indeterminacy and the Two-Sector Model
185
1
8.4.5 Procyclical Consumption
185
2
8.4.6 Calibrated Two-Sector Model
187
1
8.5 Concluding Remarks
187
1
8.6 Problems
188
3
9 General Equilibrium Theory and Uncertainty
191
20
9.1 Introduction
191
1
9.2 Debreu's Formulation of the Problem
191
6
9.2.1 Preferences under Uncertainty
191
5
9.2.2 Budget Constraints
196
1
9.3 Arrow's Formulation of the Problem
197
5
9.3.1 Trade in Financial Securities
197
2
9.3.2 Complete and Incomplete Markets
199
2
9.3.3 Multiple Budget Constraints and Incomplete Markets
201
1
9.4 Infinite Horizon Economies with Uncertainty
202
6
9.4.1 Asset Pricing in Lucas Tree Economies
202
2
9.4.2 Digression on Market Structure
204
2
9.4.3 Asset Pricing in the Representative Agent Case
206
2
9.5 Concluding Remarks
208
1
9.6 Problems
209
2
10 Sunspots
211
20
10.1 Introduction
211
1
10.2 Do Sunspots Matter?
212
5
10.2.1 Complete and Incomplete Participation
212
1
10.2.2 Setting up the Environment
213
2
10.2.3 Sunspot Theorems
215
2
10.3 Example of a Macroeconomic Model Where Sunspots Matter
217
11
10.3.1 Description of the Environment
217
3
10.3.2 Set of Equilibria
220
3
10.3.3 Supporting Sunspot Equilibria with Beliefs
223
3
10.3.4 Sunspots, Bubbles, and Regular Equilibria
226
2
10.4 Concluding Remarks
228
1
10.5 Problems
229
2
11 Macroeconomic Models of Money
231
28
11.1 Introduction
231
2
11.1.1 Rate of Return Dominance and Legal Restrictions Theory
231
1
11.1.2 Some Quick Fixes to Rate of Return Dominance
232
1
11.2 Models of Money
233
6
11.2.1 Budget Sets: the Opportunity Cost of Holding Money
234
3
11.2.2 Objective Functions: Cash in Advance and Its Relationship to Money in the Utility Function
237
2
11.3 Dynamics of a Cash-in-Advance Model
239
4
11.3.1 Different Types of Monetary Policy
239
1
11.3.2 Government's Budget Constraints
240
2
11.3.3 Typology of Policy Regimes
242
1
11.4 Equilibrium under Interest Rate Control
243
7
11.4.1 Policy Mix A: Fixed Interest Rates and Zero Debt
243
3
11.4.2 Equilibrium of the Real Economy under Interest Rate Control
246
1
11.4.3 Equilibrium Rates of Change of Nominal Variables under Interest Rate Control
247
1
11.4.4 Indeterminacy of the Nominal Scale of the Economy under Interest Rate Control
248
1
11.4.5 Economics of Indeterminacy under Interest Rate Control
249
1
11.5 Equilibrium under a Fixed Money Growth Rate Rule
250
4
11.5.1 Policy Mix B: Fixed Money Growth Rate and Zero Debt
251
1
11.5.2 Equilibrium of the Real Economy with a Fixed Money Growth Rate
251
1
11.5.3 Example of Indeterminate Equilibria in a Simple Economy
252
2
11.6 Concluding Remarks
254
1
11.7 Problems
255
4
12 Applied Monetary Theory
259
22
12.1 Introduction
259
1
12.2 Monetary Facts: What There Is to Explain
260
3
12.3 Simple Monetary Model: Using Equilibrium Theory to Explain the Facts
263
7
12.3.1 Modeling the Exchange Process
265
1
12.3.2 Formalizing the Exchange Technology
266
1
12.3.3 How to Describe an Equilibrium
267
3
12.4 How Do Equilibria Behave?
270
7
12.4.1 Choosing Functional Forms
270
1
12.4.2 What Do Equilibria Look Like?
271
4
12.4.3 Alternative Views of the Money-Income Correlation?
275
1
12.4.4 What Does All of This Have to Do with Sticky Prices?
276
1
12.5 Concluding Remarks
277
1
12.6 Problems
278
3
Notes
281
8
Bibliography
289
6
Index
295