Volatility, Heterogeneous Agents and Chaos

Agent heterogeneity, alongside several types of learning rules, has been used in recent economic literature to justify nonlinear dynamics for the time paths of aggregate economic variables. In this paper, the mechanism through which heterogeneous agents leads to chaotic motion is explained.Adding to a system with initial behavior heterogeneity an adaptive learning rule based on discrete choice theory, one is able to encounter a reasonable explanation for nonlinear motion. The adaptive learning / bounded rationality rule is not the only ingredient necessary for the absence of a long run steady state; heterogeneity must also imply that the several behavior possibilities alternate as the best behavioral choice. Only in such circumstances heterogeneity persists and an unpredictable outcome is likely to arise.After a review of the literature, the paper develops two models. The first is a generic approach that exemplifies how heterogeneity concerning the volatility of two stochastic processes may lead to chaotic motion; the second is a utility maximization setup, where the source of heterogeneity is investment decisions. For the utility problem, we find that the time path concerning consumption growth tends to stabilize around a constant value (a constant expected value is observable), but the steady state will be characterized by periods of low volatility that alternate with periods of high volatility.