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Adaptive Learning in Regime-Switching Models
By William A. Branch,
Troy Davig, and Bruce McGough |
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Abstract 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.
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