Robust Comparative Statics with Misspecified Bayesian Learning

We present novel monotone comparative statics results for steady-state behavior in a dynamic optimization environment with misspecified Bayesian learning. Building on \cite{ep21a}, we analyze a Bayesian learner whose prior is over parameterized transition models but is misspecified in the sense that the true process does not belong to this set. We characterize conditions that ensure monotonicity in the steady-state distribution over states, actions, and inferred models. Additionally, we provide a new monotonicity-based proof of steady-state existence, derive an upper bound on the cost of misspecification, and illustrate the applicability of our results to several environments of general interest.