Open AccessConvergence in models of misspecified learning
Author(s) -
Heidhues Paul,
Kőszegi Botond,
Strack Philipp
Publication year - 2021
Publication title -
theoretical economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.404
H-Index - 32
eISSN - 1555-7561
pISSN - 1933-6837
DOI - 10.3982/te3558
Subject(s) - computer science , generalization , convergence (economics) , statistic , action (physics) , class (philosophy) , parametric statistics , artificial intelligence , econometrics , mathematical economics , economics , mathematics , statistics , mathematical analysis , physics , quantum mechanics , economic growth
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.