Learning with Heterogeneous Misspecfied Models: Characterization and Robustness

This paper develops a general framework to study how misinterpreting information impacts learning. Our main result is a simple criterion to characterize long-run beliefs based on the underlying form of misspeci?cation. We present this characterization in the context of social learning, then highlight how it applies to other learning environ-ments, including individual learning. A key contribution is that our characterization applies to settings with model heterogeneity and provides conditions for entrenched disagreement. Our characterization can be used to determine whether a representative agent approach is valid in the face of heterogeneity, study how di?ering levels of bias or unawareness of others’ biases impact learning, and explore whether the impact of a bias is sensitive to parametric speci?cation or the source of information. This uni?ed framework synthesizes insights gleaned from previously studied forms of misspeci?ca-tion and provides novel insights in speci?c applications, as we demonstrate in settings with partisan bias, overreaction, naive learning, and level-k reasoning.