Bootstrap Inference in Partially Identified Models Defined by Moment Inequalities: Coverage of the Identified Set

Abstract

This paper introduces a novel bootstrap procedure to perform inference in a wide class of partially identi…ed econometric models. We consider econometric models de…ned by …nitely many weak moment inequalities y , which encompass many applications of economic interest. The objective of our inferential procedure is to cover the identi…ed set with a prespeci…ed probability z . We compare our bootstrap procedure, a competing asymptotic approximation and subsampling proce- dures in terms of the rate at which they achieve the desired coverage level, also known as the error in the coverage probability. Under certain conditions, we show that our bootstrap procedure and the asymp- totic approximation have the same order of error in the coverage probability, which is smaller than the one obtained by using subsampling. This implies that inference based on our bootstrap and asymptotic approximation should eventually be more precise than inference based on subsampling. A Monte Carlo study con…rms this …nding in a small sample simulation.