Distortions of Asymptotic Condence Size in Locally Misspecied Moment Inequality Models

Abstract

This paper studies the behavior under local misspecification of several confidence sets (CSs) commonly used in the literature on inference in moment inequality models. We suggest the degree of asymptotic confidence size distortion as an alternative criterium to power to choose among competing inference methods, and apply this criterium to compare across critical values and test statistics employed in the construction of CSs. We find two important results under weak assumptions. First, we show that CSs based on subsampling and generalized moment selection (GMS, Andrews and Soares (2010)) suffer from the same degree of asymptotic confidence size distortion, despite the fact that the latter can lead to CSs with strictly smaller expected volume under correct model specification. Second, we show that CSs based on the quasi-likelihood ratio test statistic have asymptotic confidence size that can be an arbitrary fraction of the asymptotic confidence size of CSs obtained by using the modified method of moments. Our results are supported by Monte Carlo simulations.

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