Limit Points of Endogenous Misspecified Learning
59 Pages Posted: 3 Apr 2020 Last revised: 26 May 2020
Date Written: March 12, 2020
We study how a misspecified agent learns from endogenous data when their prior belief does not impose restrictions on the distribution of outcomes, but can assign probability 0 to a neighborhood of the true model. We characterize the stable actions, which have a very high probability of being the long-run outcome for some initial beliefs, and the positively attracting actions, which have a positive probability of being the long-run outcome for any initial full support belief. A Berk-Nash equilibrium is uniformly strict if the equilibrium action is a strict best response to all the outcome distributions that minimize the Kullback-Leibler divergence from the truth, and uniform if the action is a best response to all those distributions. Uniform Berk-Nash equilibria are the unique possible limit actions under a myopic policy. All uniformly strict Berk-Nash equilibria are stable. They are positively attractive under causation neglect, where the agent believes that their action does not influence the outcome, and under correlation neglect, where the agent believes that the outcome distribution associated with one action does not convey information about the outcomes associated with others. We generalize these results to settings where the agent observes a signal before acting.
Keywords: Misspecified Learning, Berk-Nash Equilibrium
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