Bootstrap Inference in Partially Identified Models

This paper introduces a novel bootstrap procedure to perform inference in a wide class of partially identified econometric models. We consider econometric models defined by finitely many moment inequalities and equalities, which are shown to encompass many applications of economic

interest. We provide two different versions of our inferential method: one to cover each element of the

identified set with a prespecified probability and the other to cover the identified set itself with a prespecified probability. We compare our bootstrap procedure, a competing asymptotic approximation and the subsampling procedure proposed by Chernozhukov, Hong and Tamer (2007) in terms of the rate at which they achieve the desired coverage, also known as the error in the coverage probability. Under certain conditions, we show that our bootstrap procedure and the asymptotic approximation have the same order of error in the coverage probability, which is eventually 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 confirms this finding in a small sample simulation.

For more information, contact Frank Schorfheide.