Convergence in models of misspecified learning

• 成果类型: Article
• 署名作者: Heidhues, Paul; Koszegi, Botond; Strack, Philipp
• 署名单位: Heinrich Heine University Dusseldorf; Yale University
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1933-6837
• DOI: 10.3982/TE3558
• 发表日期: 2021-01-01
• 页码: 73-99
• 关键词: Misspecified model; Bayesian learning; CONVERGENCE; Berk-Nash equilibrium

摘要

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. Our stochastic-approximation-based methods rely on two crucial features: that the state and action spaces are continuous, and that the agent's posterior admits a one-dimensional summary statistic. Through a basic model with a normal-normal updating structure and a generalization in which the agent's misinterpretation of information can depend on her current beliefs in a flexible way, we show that these features are compatible with a number of specifications of how exactly the agent updates. Applications of our framework include learning by a person who has an incorrect model of a technology she uses or is overconfident about herself, learning by a representative agent who may misunderstand macroeconomic outcomes, and learning by a firm that has an incorrect parametric model of demand.