On the behaviour of Bayesian credible intervals in partially identified models

Abstract

Partially identified models typically involve set identification rather than point identification. That is, the distribution of observables is consistent with a set of values for the target parameter, rather than a single value. Interval estimation procedures therefore behave differently than for identified models. For instance, a Bayesian credible set arising from a proper prior distribution will tend to a non-degenerate set as the sample size goes to infinity. A natural question arising is for what parameter values does the limit of the Bayesian credible interval fail to cover its target? Intuition suggests this would arise for parameter values which are not very consistent with the prior distribution. The aim of this paper is to quantify this intuition.