A Comparison of Inferential Methods in Partially Identified Models in Terms of Error in the Coverage Probability
50 Pages Posted: 6 Jul 2011
Date Written: June 9, 2011
Abstract
This paper considers the problem of coverage of the elements of the identified set in a class of partially identified econometric models with a prespecified probability. In order to conduct inference in partially identified econometric models defined by moment (in)equalities, the literature has proposed three methods: the bootstrap, subsampling, and an asymptotic approximation. The objective of this paper is to compare these methods in terms of the rate at which they achieve the desired coverage level, i.e., in terms of the rate at which the error in the coverage probability (ECP) converges to zero.
Under certain conditions, we show that the ECP of the bootstrap and the ECP of the asymptotic approximation converge to zero at the same rate, which is a faster rate than the rate of the ECP of subsampling methods. As a consequence, under these conditions, the bootstrap and the asymptotic approximation produce inference that is more precise than subsampling. A Monte Carlo simulation study confirms that these results are relevant in nite samples.
Keywords: partial identification, moment inequalities, inference, hypothesis test, bootstrap, subsampling, asymptotic approximation, rates of convergence, error in the coverage probability
JEL Classification: C01, C12, C15
Suggested Citation: Suggested Citation