Convergence in Misspecified Learning Models with Endogenous Actions
23 Pages Posted: 14 Jan 2019
Date Written: December 6, 2018
We establish convergence of beliefs and actions in a class of one-dimensional learning settings in which the agent’s model is misspecified, she chooses actions endogenously, and the actions affect how she misinterprets information. The crucial assumptions of our model are that the state and action spaces are continuous, the state has a unidirectional effect on output, and the prior and noise are normal. These assumptions imply that the agent’s posterior admits a one-dimensional summary statistic, allowing us to apply tools from stochastic approximation theory to establish convergence. Applications of our framework include learning by a person who has an incorrect model of a technology she uses, is subject to confirmatory bias, conservatism, or base-rate neglect, or is overconfident about herself, learning by a representative agent who misunderstands macroeconomic outcomes, as well as learning by a firm that has an incorrect parametric model of demand.
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