Learning and Expectations in Macroeconomics (Frontiers of Economic Research)

Contents......Page 10
Preface......Page 16
Part I. View of the Landscape......Page 22
1.1 Expectations in Macroeconomics......Page 24
1.2 Two Examples......Page 27
1.3 Classical Models of Expectation Formation......Page 28
1.4 Learning: The New View of Expectations......Page 31
1.5 Statistical Approach to Learning......Page 34
1.6 A General Framework......Page 35
1.7 Overview of the Book......Page 38
2.1 Introduction......Page 44
2.2 The Cobweb Model......Page 45
2.3 Econometric Learning......Page 46
2.4 Expectational Stability......Page 49
2.6 Recursive Least Squares......Page 51
2.7 Convergence of Stochastic Recursive Algorithms......Page 53
2.8 Application to the Cobweb Model......Page 56
2.9 The E-Stability Principle......Page 58
2.10 Discussion of the Literature......Page 62
3.2 Heterogeneous Expectations......Page 64
3.3 Learning with Constant Gain......Page 67
3.4 Learning in Nonstochastic Models......Page 69
3.5 Stochastic Gradient Learning......Page 74
3.6 Learning with Misspecification......Page 75
4.1 Introduction......Page 78
4.2 The Overlapping Generations Model......Page 79
4.3 A Linear Stochastic Macroeconomic Model......Page 82
4.4 The Ramsey Model......Page 87
4.5 The Diamond Growth Model......Page 90
4.6 A Model with Increasing Social Returns......Page 91
4.7 Other Models......Page 100
4.8 Appendix......Page 101
Part II. Mathematical Background and Tools......Page 104
5.1 Introduction......Page 106
5.2 Difference Equations......Page 107
5.3 Differential Equations......Page 112
5.4 Linear Stochastic Processes......Page 118
5.5 Markov Processes......Page 127
5.6 Ito Processes......Page 129
5.7 Appendix on Matrix Algebra......Page 134
5.8 References for Mathematical Background......Page 137
6.1 Introduction......Page 140
6.2 Stochastic Recursive Algorithms......Page 142
6.3 Convergence: The Basic Results......Page 147
6.4 Convergence: Further Discussion......Page 153
6.5 Instability Results......Page 157
6.6 Expectational Stability......Page 159
6.7 Global Convergence......Page 163
7.1 Introduction......Page 166
7.2 Algorithms for Nonstochastic Frameworks......Page 167
7.3 The Case of Markovian State Dynamics......Page 173
7.4 Convergence Results for Constant-Gain Algorithms......Page 181
7.5 Gaussian Approximation for Cases of Decreasing Gain......Page 185
7.6 Global Convergence on Compact Domains......Page 186
7.7 Guide to the Technical Literature......Page 188
Part III. Learning in Linear Models......Page 190
8.1 Introduction......Page 192
8.2 A Special Case......Page 193
8.3 E-Stability and Least Squares Learning: MSV Solutions......Page 198
8.4 E-Stability and Learning: The Full Class of Solutions......Page 202
8.5 Extension 1: Lagged Endogenous Variables......Page 212
8.6 Extension 2: Models with Time-t Dating......Page 217
8.7 Conclusions......Page 223
9.2 Muth’s Inventory Model......Page 224
9.3 Overparameterization in the Special Case......Page 225
9.4 Extended Special Case......Page 230
9.5 Linear Model with Two Forward Leads......Page 234
9.6 Learning Explosive Solutions......Page 238
9.7 Bubbles in Asset Prices......Page 239
9.8 Heterogeneous Learning Rules......Page 242
10.1 Introduction......Page 246
10.2 MSV Solutions and Learning......Page 248
10.3 Models with Contemporaneous Expectations......Page 255
10.4 Real Business Cycle Model......Page 258
10.5 Irregular REE......Page 262
10.7 Appendix 1: Linearizations......Page 268
10.8 Appendix 2: Solution Techniques......Page 271
Part IV. Learning in Nonlinear Models......Page 284
11.1 Introduction......Page 286
11.3 Noisy Steady States......Page 288
11.5 E-Stability and Learning......Page 292
11.6 Applications......Page 295
12.1 Introduction......Page 306
12.2 Overview of Results......Page 307
12.3 Deterministic Cycles......Page 310
12.4 Noisy Cycles......Page 312
12.5 Existence of Sunspot Equilibria......Page 319
12.6 Learning SSEs......Page 323
12.7 Global Analysis of Learning Dynamics......Page 329
12.8 Conclusions......Page 332
Part V. Further Topics......Page 334
13.1 Learning in Misspecified Models......Page 336
13.2 Misspecified Policy Learning......Page 344
13.3 Conclusions......Page 348
14.1 Introduction......Page 350
14.2 Constant-Gain Learning in the Cobweb Model......Page 352
14.3 Increasing Social Returns and Endogenous Fluctuations......Page 356
14.4 Sargent’s Inflation Model......Page 367
14.5 Other Models with Persistent Dynamics......Page 375
14.6 Conclusions......Page 378
15.1 Models from Computational Intelligence......Page 380
15.2 Alternative Gain Sequences......Page 389
15.4 Eductive Learning......Page 391
15.5 Calculation Equilibria......Page 395
15.6 Adaptively Rational Expectations Equilibria......Page 397
15.7 ExperimentalWork......Page 399
15.8 Some Empirical Applications......Page 401
16 Conclusions......Page 404
Bibliography......Page 408
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