Adaptive learning in regime-switching models

This paper studies adaptive learning in economic environments subject to recurring structural change. Stochastically evolving institutional and policy-making features can be described by regime-switching rational expectations models whose parameters evolve according to a finite state Markov process. We demonstrate that in non-linear models of this form, two natural schemes emerge for learning the conditional means of endogenous variables: under mean value learning, the equilibrium's lag structure is assumed exogenous and therefore known to agents; whereas, under vector autoregession learning (VAR learning), the equilibrium lag structure depends endogenously on agents' beliefs and must be learned. We show that an intuitive condition, analogous to the 'Long-run Taylor Principle' of Davig and Leeper (2007), ensures convergence to a regime-switching rational expectations equilibrium. However, the stability of sunspot equilibria, when they exist, depends on whether agents adopt mean value or VAR learning. Coordinating on sunspot equilibria via a VAR learning rule is not possible. These results show that, when assessing the plausibility of rational expectations equilibria in non-linear models, out of equilibrium behavior is important.