Description
A crucial challenge for economists is figuring out how people interpret the world and form expectations that will likely influence their economic activity. Inflation, asset prices, exchange rates, investment, and consumption are just some of the economic variables that are largely explained by expectations. Here George Evans and Seppo Honkapohja bring new explanatory power to a variety of expectation formation models by focusing on the learning factor. Whereas the rational expectations paradigm offers the prevailing method to determining expectations, it assumes very theoretical knowledge on the part of economic actors. Evans and Honkapohja contribute to a growing body of research positing that households and firms learn by making forecasts using observed data, updating their forecast rules over time in response to errors. This book is the first systematic development of the new statistical learning approach.
Depending on the particular economic structure, the economy may converge to a standard rational-expectations or a "rational bubble" solution, or exhibit persistent learning dynamics. The learning approach also provides tools to assess the importance of new models with expectational indeterminacy, in which expectations are an independent cause of macroeconomic fluctuations. Moreover, learning dynamics provide a theory for the evolution of expectations and selection between alternative equilibria, with implications for business cycles, asset price vola
Chapter
3.3 Learning with Constant Gain
3.4 Learning in Nonstochastic Models
3.5 Stochastic Gradient Learning
3.6 Learning with Misspecification
4.2 The Overlapping Generations Model
4.3 A Linear Stochastic Macroeconomic Model
4.5 The Diamond Growth Model
4.6 A Model with Increasing Social Returns
Part II: Mathematical Background and Tools
5 The Mathematical Background
5.3 Differential Equations
5.4 Linear Stochastic Processes
5.7 Appendix on Matrix Algebra
5.8 References for Mathematical Background
6 Tools: Stochastic Approximation
6.2 Stochastic Recursive Algorithms
6.3 Convergence: The Basic Results
6.4 Convergence: Further Discussion
6.6 Expectational Stability
7 Further Topics in Stochastic Approximation
7.2 Algorithms for Nonstochastic Frameworks
7.3 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
8.3 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
9 Further Topics in Linear Models
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
10.2 MSV Solutions and Learning
10.3 Models with Contemporaneous Expectations
10.4 Real Business Cycle Model
10.7 Appendix 1: Linearizations
10.8 Appendix 2: Solution Techniques
Part IV: Learning in Nonlinear Models
11 Nonlinear Models: Steady States
11.2 Equilibria under Perfect Foresight
11.4 Adaptive Learning for Steady States
11.5 E-Stability and Learning
12 Cycles and Sunspot Equilibria
12.3 Deterministic Cycles
12.5 Existence of Sunspot Equilibria
12.7 Global Analysis of Learning Dynamics
13 Misspecification and Learning
13.1 Learning in Misspecified Models
13.2 Misspecified Policy Learning
14 Persistent Learning Dynamics
14.2 Constant-Gain Learning in the Cobweb Model
14.3 Increasing Social Returns and Endogenous Fluctuations
14.4 Sargent’s Inflation Model
14.5 Other Models with Persistent Dynamics
15 Extensions and Other Approaches
15.1 Models from Computational Intelligence
15.2 Alternative Gain Sequences
15.3 Nonparametric Learning
15.5 Calculation Equilibria
15.6 Adaptively Rational Expectations Equilibria
15.8 Some Empirical Applications