Convergence in models of misspecified learning
研究了一类一维学习环境中，当代理人的模型设定错误、行动影响信息误解时，信念和行动的收敛性，适用于技术误用、过度自信、宏观误解等场景。
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.