Robust Comparative Statics with Misspecified Bayesian Learning

TL;DR

This paper develops new monotone comparative statics results for steady-state behavior in dynamic models where Bayesian learners are misspecified, providing insights into the effects of model misspecification.

Contribution

It introduces novel monotonicity conditions and proofs for steady-states in misspecified Bayesian learning environments, extending prior work.

Findings

Monotonicity in steady-state distributions under misspecification

Bound on the cost of model misspecification

Applicability to various dynamic environments

Abstract

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.