Bayesian and Frequentist Inference in Partially Identified Models

A large sample approximation of the posterior distribution of partially identified structural parameters is derived for models that can be indexed by a finite-dimensional reduced form parameter vector. It is used to analyze the differences between frequentist confidence sets and Bayesian credible sets in partially identified models. A key difference is that frequentist set estimates extend beyond the boundaries of the identified set (conditional on the estimated reduced form parameter), whereas Bayesian credible sets can asymptotically be located in the interior of the identified set. Our asymptotic approximations are illustrated in the context of simple moment inequality models and a numerical illustration for a two-player entry game is provided.