Learning in Economic Systems with Expectations Feedback (eBook)

Preface 6
Contents 7
1 Introduction 9
2 Economic SystemsWith Expectations Feedback 15
2.1 An Introductory Example 16
2.2 The General Setup 18
2.3 Forecasting Rules With Finite Memory 20
2.4 Consistent Forecasting Rules 22
2.5 Unbiased Forecasting Rules 25
Concluding Remarks 30
3 Adaptive Learning in Linear Models 31
3.1 Linear Models 32
3.2 Unbiased Forecasting Rules 36
3.3 Approximating Unbiased Forecasting Rules 45
3.4 Convergence of an AML-Based Learning Scheme 47
Summary and Conclusions 52
3.5 Mathematical Appendix 53
4 Economic Models Subject to Stationary Noise 65
4.1 Forecasting Rules for Stationary Noise 67
4.2 Existence of Unbiased Forecasting Rules 76
4.3 MSV Predictors 81
4.4 Random Fixed Points 83
Concluding Remarks 87
4.5 Mathematical Appendix 87
5 Nonparametric Adaptive Learning 93
5.1 The Method of Stochastic Approximation 94
5.2 A Basic Convergence Result 98
5.3 Some Probabilistic Prerequisites 107
5.4 Sufficient Conditions for Contractions 110
Concluding Remarks 115
5.5 Mathematical Appendix 116
6 Stochastic Exchange Economies 135
6.1 A Model of Pure Exchange 135
6.2 The Existence of Perfect Forecasting Rules 137
6.3 Perfect Foresight Dynamics 139
6.4 Adaptive Learning of Perfect Forecasting Rules 142
Concluding Remarks 144
6.5 Mathematical Appendix 144
7 Heterogeneous Beliefs in a Financial Market 147
7.1 The Model 149
7.2 Heterogeneous Beliefs 153
7.3 Risk Premia and Reference Portfolios 155
7.4 Mean-Variance Preferences 157
7.5 Perfect Forecasting Rules 160
7.6 Dynamics Under Rational Expectations 164
7.7 Adaptive Learning With Heterogeneous Beliefs 169
Concluding Remarks 175
7.8 Mathematical Appendix 176
References 179