Escape Dynamics in Learning Models

This article illustrates and characterizes how adaptive learning can lead to recurrent large fluctuations. Learning models have typically focused on the convergence of beliefs towards an equilibrium. However in stochastic environments, there may be rare but recurrent episodes where shocks cause beliefs to escape from the equilibrium, generating large movements in observed outcomes. I characterize the escape dynamics by drawing on the theory of large deviations, developing new results which make this theory directly applicable in a class of learning models. The likelihood, frequency, and most likely direction of escapes are all characterized by a deterministic control problem. I illustrate my results with two simple examples.