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E-raamat: Learning in Economic Systems with Expectations Feedback

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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.
1 Introduction 1(6)
2 Economic Systems With Expectations Feedback 7(16)
2.1 An Introductory Example
8(2)
2.2 The General Setup
10(2)
2.3 Forecasting Rules With Finite Memory
12(2)
2.4 Consistent Forecasting Rules
14(3)
2.5 Unbiased Forecasting Rules
17(6)
3 Adaptive Learning in Linear Models 23(34)
3.1 Linear Models
24(4)
3.2 Unbiased Forecasting Rules
28(9)
3.2.1 No-Updating Rules
30(4)
3.2.2 Linear MSV Predictors
34(3)
3.3 Approximating Unbiased Forecasting Rules
37(2)
3.4 Convergence of an AML-Based Learning Scheme
39(6)
3.5 Mathematical Appendix
45(12)
3.5.1 On the Stability of Linear Systems
45(2)
3.5.2 Proofs of Theorem 3.2 and Theorem 3.3
47(10)
4 Economic Models Subject to Stationary Noise 57(28)
4.1 Forecasting Rules for Stationary Noise
59(9)
4.1.1 Consistent Forecasting Rules
61(3)
4.1.2 Unbiased Forecasting Rules
64(4)
4.2 Existence of Unbiased Forecasting Rules
68(5)
4.3 MSV Predictors
73(2)
4.4 Random Fixed Points
75(4)
4.5 Mathematical Appendix
79(6)
5 Nonparametric Adaptive Learning 85(42)
5.1 The Method of Stochastic Approximation
86(4)
5.2 A Basic Convergence Result
90(9)
5.3 Some Probabilistic Prerequisites
99(3)
5.4 Sufficient Conditions for Contractions
102(6)
5.5 Mathematical Appendix
108(19)
5.5.1 Sobolev Imbedding Theorem
108(3)
5.5.2 Proofs of Section 5.2
111(7)
5.5.3 Proofs of Section 5.4
118(9)
6 Stochastic Exchange Economies 127(12)
6.1 A Model of Pure Exchange
127(2)
6.2 The Existence of Perfect Forecasting Rules
129(2)
6.3 Perfect Foresight Dynamics
131(3)
6.4 Adaptive Learning of Perfect Forecasting Rules
134(2)
6.5 Mathematical Appendix
136(3)
7 Heterogeneous Beliefs in a Financial Market 139(32)
7.1 The Model
141(4)
7.2 Heterogeneous Beliefs
145(2)
7.3 Risk Premia and Reference Portfolios
147(2)
7.4 Mean-Variance Preferences
149(3)
7.5 Perfect Forecasting Rules
152(4)
7.5.1 Perfect Forecasting Rules for First Moments
152(1)
7.5.2 Perfect Forecasting Rules for Second Moments
153(3)
7.6 Dynamics Under Rational Expectations
156(5)
7.7 Adaptive Learning With Heterogeneous Beliefs
161(7)
7.7.1 The General Idea
161(1)
7.7.2 The Case With Two Mediators
162(6)
7.8 Mathematical Appendix
168(3)
References 171