Chapter 7 Learning dynamics

Abstract

Abstract This chapter provides a survey of the recent work on learning in the context of macroeconomics. Learning has several roles. First, it provides a boundedly rational model of how rational expectations can be achieved. Secondly, learning acts as a selection device in models with multiple REE (rational expectations equilibria). Third, the learning dynamics themselves may be of interest. While there are various approaches to learning in macroeconomics, the emphasis here is on adaptive learning schemes in which agents use statistical or econometric techniques in self-referential stochastic systems. Careful attention is given to learning in models with multiple equilibria. The methodological tool is to set up the economic system under learning as a SRA (stochastic recursive algorithm) and to analyze convergence by the method of stochastic approximation based on an associated differential equation. Global stability, local stability and instability results for SRAs are presented. For a wide range of solutions to economic models the stability conditions for REE under statistical learning rules are given by the expectational stability principle, which is treated as a unifying principle for the results presented. Both linear and nonlinear economic models are considered and in the univariate linear case the full set of solutions is discussed. Applications include the Muth cobweb model, the Cagan model of inflation, asset pricing with risk neutrality, the overlapping generations model, the seignorage model of inflation, models with increasing social returns, IS-LM-Phillips curve models, the overlapping contract model, and the Real Business Cycle model. Particular attention is given to the local stability conditions for convergence when there are indeterminacies, bubbles, multiple steady states, cycles or sunspot solutions. The survey also discusses alternative approaches and recent developments, including Bayesian learning, eductive approaches, genetic algorithms, heterogeneity, misspecified models and experimental evidence.