Learning and Expectations in Macroeconomics

Online-Ressource (440 p)

Description based upon print version of record

Cover; Title; Copyright; Contents; Preface; Part I: View of the Landscape; 1 Expectations and the Learning Approach; 1.1 Expectations in Macroeconomics; 1.2 Two Examples; 1.3 Classical Models of Expectation Formation; 1.4 Learning: The New View of Expectations; 1.5 Statistical Approach to Learning; 1.6 A General Framework; 1.7 Overview of the Book; 2 Introduction to the Techniques; 2.1 Introduction; 2.2 The Cobweb Model; 2.3 Econometric Learning; 2.4 Expectational Stability; 2.5 Rational vs. Reasonable Learning; 2.6 Recursive Least Squares; 2.7 Convergence of Stochastic Recursive Algorithms

2.8 Application to the Cobweb Model2.9 The E-Stability Principle; 2.10 Discussion of the Literature; 3 Variations on a Theme; 3.1 Introduction; 3.2 Heterogeneous Expectations; 3.3 Learning with Constant Gain; 3.4 Learning in Nonstochastic Models; 3.5 Stochastic Gradient Learning; 3.6 Learning with Misspecification; 4 Applications; 4.1 Introduction; 4.2 The Overlapping Generations Model; 4.3 A Linear Stochastic Macroeconomic Model; 4.4 The Ramsey Model; 4.5 The Diamond Growth Model; 4.6 A Model with Increasing Social Returns; 4.7 Other Models; 4.8 Appendix

Part II: Mathematical Background and Tools5 The Mathematical Background; 5.1 Introduction; 5.2 Difference Equations; 5.3 Differential Equations; 5.4 Linear Stochastic Processes; 5.5 Markov Processes; 5.6 Ito Processes; 5.7 Appendix on Matrix Algebra; 5.8 References for Mathematical Background; 6 Tools: Stochastic Approximation; 6.1 Introduction; 6.2 Stochastic Recursive Algorithms; 6.3 Convergence: The Basic Results; 6.4 Convergence: Further Discussion; 6.5 Instability Results; 6.6 Expectational Stability; 6.7 Global Convergence; 7 Further Topics in Stochastic Approximation; 7.1 Introduction

7.2 Algorithms for Nonstochastic Frameworks7.3 The Case of Markovian State Dynamics; 7.4 Convergence Results for Constant-Gain Algorithms; 7.5 Gaussian Approximation for Cases of Decreasing Gain; 7.6 Global Convergence on Compact Domains; 7.7 Guide to the Technical Literature; Part III: Learning in Linear Models; 8 Univariate Linear Models; 8.1 Introduction; 8.2 A Special Case; 8.3 E-Stability and Least Squares Learning: MSV Solutions; 8.4 E-Stability and Learning: The Full Class of Solutions; 8.5 Extension 1: Lagged Endogenous Variables; 8.6 Extension 2: Models with Time-t Dating

8.7 Conclusions9 Further Topics in Linear Models; 9.1 Introduction; 9.2 Muth's Inventory Model; 9.3 Overparameterization in the Special Case; 9.4 Extended Special Case; 9.5 Linear Model with Two Forward Leads; 9.6 Learning Explosive Solutions; 9.7 Bubbles in Asset Prices; 9.8 Heterogeneous Learning Rules; 10 Multivariate Linear Models; 10.1 Introduction; 10.2 MSV Solutions and Learning; 10.3 Models with Contemporaneous Expectations; 10.4 Real Business Cycle Model; 10.5 Irregular REE; 10.6 Conclusions; 10.7 Appendix 1: Linearizations; 10.8 Appendix 2: Solution Techniques

Part IV: Learning in Nonlinear Models

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