Evans / Honkapohja Learning and Expectations in Macroeconomics

Core Textbook
ISBN: 978-1-4008-2426-7
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 424 Seiten

Reihe: Frontiers of Economic Research

No detailed description available for "Learning and Expectations in Macroeconomics".

Autoren/Hrsg.

Evans, George W.

Honkapohja, Seppo

Fachgebiete

• Wirtschaftswissenschaften Wirtschaftswissenschaften Wirtschaftsgeschichte

Inhaltsverzeichnis

Preface xv

Part I. View of the Landscape

1 Expectations and the Learning Approach 5

1.1 Expectations in Macroeconomics 5

1.2 Two Examples 8

1.3 Classical Models of Expectation Formation 9

1.4 Learning: The New View of Expectations 12

1.5 Statistical Approach to Learning 15

1.6 A General Framework 16

1.7 Overview of the Book 19

2 Introduction to the Techniques 25

2.1 Introduction 25

2.2 The Cobweb Model 26

2.3 Econometric Learning 27

2.4 Expectational Stability 30

2.5 Rational vs. Reasonable Learning 32

2.6 Recursive Least Squares 32

2.7 Convergence of Stochastic Recursive Algorithms 34

2.8 Application to the Cobweb Model 37

2.9 The E-Stability Principle 39

2.10 Discussion of the Literature 43

3 Variations on a Theme 45

3.1 Introduction 45

3.2 Heterogeneous Expectations 45

3.3 Learning with Constant Gain 48

3.4 Learning in Nonstochastic Models 50

3.5 Stochastic Gradient Learning 55

3.6 Learning with Misspecification 56

4 Applications 59

4.1 Introduction 59

4.2 The Overlapping Generations Model 60

4.3 A Linear Stochastic Macroeconomic Model 63

4.4 The Ramsey Model 68

4.5 The Diamond Growth Model 71

4.6 A Model with Increasing Social Returns 72

4.7 Other Models 81

4.8 Appendix 82

Part II. Mathematical Background and Tools

5 The Mathematical Background 87

5.1 Introduction 87

5.2 Difference Equations 88

5.3 Differential Equations 93

5.4 Linear Stochastic Processes 99

5.5 Markov Processes 108

5.6 Ito Processes 110

5.7 Appendix on Matrix Algebra 115

5.8 References for Mathematical Background 118

6 Tools: Stochastic Approximation 121

6.1 Introduction 121

6.2 Stochastic Recursive Algorithms 123

6.3 Convergence: The Basic Results 128

6.4 Convergence: Further Discussion 134

6.5 Instability Results 138

6.6 Expectational Stability 140

6.7 Global Convergence 144

7 Further Topics in Stochastic Approximation 147

7.1 Introduction 147

7.2 Algorithms for Nonstochastic Frameworks 148

7.3 The Case of Markovian State Dynamics 154

7.4 Convergence Results for Constant-Gain Algorithms 162

7.5 Gaussian Approximation for Cases of Decreasing Gain 166

7.6 Global Convergence on Compact Domains 167

7.7 Guide to the Technical Literature 169

Part III. Learning in Linear Models

8 Univariate Linear Models 173

8.1 Introduction 173

8.2 A Special Case 174

8.3 E-Stability and Least Squares Learning: MSV Solutions 179

8.4 E-Stability and Learning: The Full Class of Solutions 183

8.5 Extension 1: Lagged Endogenous Variables 193

8.6 Extension 2: Models with Time-t Dating 198

8.7 Conclusions 204

9 Further Topics in Linear Models 205

9.1 Introduction 205

9.2 Muth's Inventory Model 205

9.3 Overparameterization in the Special Case 206

9.4 Extended Special Case 211

9.5 Linear Model with Two Forward Leads 215

9.6 Learning Explosive Solutions 219

9.7 Bubbles in Asset Prices 220

9.8 Heterogeneous Learning Rules 223

10 Multivariate Linear Models 227

10.1 Introduction 227

10.2 MSV Solutions and Learning 229

10.3 Models with Contemporaneous Expectations 236

10.4 Real Business Cycle Model 239

10.5 Irregular REE 243

10.6 Conclusions 249

10.7 Appendix 1: Linearizations 249

10.8 Appendix 2: Solution Techniques 252

Part IV Learning in Nonlinear Models Nonlinear Models: Steady States 267

11.1 Introduction 267

11.2 Equilibria under Perfect Foresight 269

11.3 Noisy Steady States 269

11.4 Adaptive Learning for Steady States 273

11.5 E-Stability and Learning 273

11.6 Applications 276

12 Cycles and Sunspot Equilibria 287

12.1 Introduction 287

12.2 Overview of Results 288

12.3 Deterministic Cycles 291

12.4 Noisy Cycles 293

12.5 Existence of Sunspot Equilibria 300

12.6 Learning SSEs 304

12.7 Global Analysis of Learning Dynamics 310

12.8 Conclusions 313

Part V. Further Topics

13 Misspecification and Learning 317

13.1 Learning in Misspecified Models 317

13.2 Misspecified Policy Learning 325

13.3 Conclusions 329

14 Persistent Learning Dynamics 331

14.1 Introduction 331

14.2 Constant-Gain Learning in the Cobweb Model 333

14.3 Increasing Social Returns and Endogenous Fluctuations 337

14.4 Sargent's Inflation Model 348

14.5 Other Models with Persistent Dynamics 356

14.6 Conclusions 359

15 Extensions and Other Approaches 361

15.1 Models from Computational Intelligence 361

15.2 Alternative Gain Sequences 370

15.3 Nonparametric Learning 372

15.4 Eductive Learning 372

15.5 Calculation Equilibria 376

15.6 Adaptively Rational Expectations Equilibria 378

15.7 Experimental Work 380

15.8 Some Empirical Applications 382

16 Conclusions 385

Bibliography 389

Author Index 407

Subject Index 411

Über Autor(innen)

George W. Evans is John B. Hamacher Professor of Economics at the University of Oregon and has held positions at the London School of Economics, Stanford University, and the University of Edinburgh. Seppo Honkapohja is Professor of Economics at the University of Helsinki, where he has currently been appointed Academy Professor. Professors Evans and Honkapohja have published extensively in economic journals, and each is best known for his respective research on expectations and learning in dynamic models. This book is the outgrowth of over fifteen years of collaboration between them.