The Empirical Content of Bayesian Updating under Misspecification

Pooya Molavi

Papers from arXiv.org

Abstract: An agent is a misspecified Bayesian if she updates her belief using Bayes' rule given a subjective, possibly misspecified model of her signals. This paper shows that a belief sequence is consistent with misspecified Bayesian updating if and only if the set of posteriors admits a countable partition such that the prior contains a grain of the conditional average posterior on each cell. The condition imposes essentially no restrictions on posteriors given a full-support prior over a finite state space and reduces to a support inclusion condition on compact state spaces under mild regularity assumptions. However, it rules out posterior beliefs with heavier tails than the prior on unbounded state spaces. In Gaussian environments, it implies that posterior uncertainty cannot exceed prior uncertainty. The results delineate the boundary between updating rules that are observationally equivalent to Bayesian updating under misspecification and genuinely non-Bayesian rules. As an application, the paper shows that diagnostic expectations are consistent with misspecified Bayesianism, whereas some parameterizations of smooth diagnostic expectations are not.

Date: 2025-07, Revised 2026-03
New Economics Papers: this item is included in nep-mic
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