Specification tests for partially identified models defined by moment inequalities

This paper studies the problem of specification testing in partially identified models defined by moment (in)equalities. This problem has not been directly addressed in the literature, although several papers have suggested a test based on checking whether confidence sets for the parameters of interest are empty or not, referred to as Test BP. We propose two new specification tests, denoted Test RS and Test RC, that achieve uniform asymptotic size control and dominate Test BP in terms of power in any finite sample and in the asymptotic limit.