Wenzelburger Learning in Economic Systems with Expectations Feedback

2006
ISBN: 978-3-540-38050-4
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 555, 176 Seiten

Reihe: Lecture Notes in Economics and Mathematical Systems

Recently economists have more and more focussed on scenarios in which agents' views of the world may be erroneous. These notes introduce the concept of perfect forecasting rules which provide best least-squares predictions along the evolution of an economic system. The framework for nonparametric adaptive learning schemes is developed and it is argued that plausible learning schemes should aim at estimating a perfect forecasting rule taking into account the correct feedback structure of an economy. A link is provided between the traditional rational-expectations view and recent behavioristic approaches.

Autoren/Hrsg.

Wenzelburger, Jan

Inhaltsverzeichnis

1;Preface;6
2;Contents;7
3;1 Introduction;9
4;2 Economic SystemsWith Expectations Feedback;15
4.1;2.1 An Introductory Example;16
4.2;2.2 The General Setup;18
4.3;2.3 Forecasting Rules With Finite Memory;20
4.4;2.4 Consistent Forecasting Rules;22
4.5;2.5 Unbiased Forecasting Rules;25
4.6;Concluding Remarks;30
5;3 Adaptive Learning in Linear Models;31
5.1;3.1 Linear Models;32
5.2;3.2 Unbiased Forecasting Rules;36
5.3;3.3 Approximating Unbiased Forecasting Rules;45
5.4;3.4 Convergence of an AML-Based Learning Scheme;47
5.5;Summary and Conclusions;52
5.6;3.5 Mathematical Appendix;53
6;4 Economic Models Subject to Stationary Noise;65
6.1;4.1 Forecasting Rules for Stationary Noise;67
6.2;4.2 Existence of Unbiased Forecasting Rules;76
6.3;4.3 MSV Predictors;81
6.4;4.4 Random Fixed Points;83
6.5;Concluding Remarks;87
6.6;4.5 Mathematical Appendix;87
7;5 Nonparametric Adaptive Learning;93
7.1;5.1 The Method of Stochastic Approximation;94
7.2;5.2 A Basic Convergence Result;98
7.3;5.3 Some Probabilistic Prerequisites;107
7.4;5.4 Sufficient Conditions for Contractions;110
7.5;Concluding Remarks;115
7.6;5.5 Mathematical Appendix;116
8;6 Stochastic Exchange Economies;135
8.1;6.1 A Model of Pure Exchange;135
8.2;6.2 The Existence of Perfect Forecasting Rules;137
8.3;6.3 Perfect Foresight Dynamics;139
8.4;6.4 Adaptive Learning of Perfect Forecasting Rules;142
8.5;Concluding Remarks;144
8.6;6.5 Mathematical Appendix;144
9;7 Heterogeneous Beliefs in a Financial Market;147
9.1;7.1 The Model;149
9.2;7.2 Heterogeneous Beliefs;153
9.3;7.3 Risk Premia and Reference Portfolios;155
9.4;7.4 Mean-Variance Preferences;157
9.5;7.5 Perfect Forecasting Rules;160
9.6;7.6 Dynamics Under Rational Expectations;164
9.7;7.7 Adaptive Learning With Heterogeneous Beliefs;169
9.8;Concluding Remarks;175
9.9;7.8 Mathematical Appendix;176
10;References;179