Ulric B. and Evelyn L. Bray Social Sciences Seminar

Abstract: We link two approaches to biased belief formation: non-Bayesian updating and misspecified models. The former parameterizes a bias with an updating rule mapping signals to posterior beliefs or a belief forecast describing anticipated beliefs; the latter is an incorrect model of the signal generating process. Our main result derives necessary and sufficient conditions for an updating rule and belief forecast to have a misspecified model representation, shows that these two components uniquely pin down a representation, and constructs it. This clarifies the belief restrictions implicit in the misspecified model approach. It also allows leveraging of the distinct advantages of each approach by decomposing a model into empirically identifiable components, showing these components isolate the two forms of bias that the model encodes---the retrospective bias after information arrives and the prospective bias beforehand, and rendering off-the-shelf tools to characterize asymptotic learning and equilibrium predictions in misspecified models applicable to non-Bayesian updating.

Written with Daniel N. Hauser