This paper is concerned with tests and conﬁdence intervals for partially-identiﬁed parameters that are deﬁned by moment inequalities and equalities. In the literature, diﬀerent test statistics, critical value methods, and implementation methods (i.e., asymptotic distribution versus the bootstrap) have been proposed. In this paper, we compare a wide variety of these methods. We provide a recommended test statistic, moment selection critical value method, and implementation method. In addition, we provide a data-dependent procedure for choosing the key moment selection tuning parameter and a data-dependent size-correction factor.
Andrews, Donald W.K. and Barwick, Panle Jai, "Inference for Parameters Defined by Moment Inequalities: A Recommended Moment Selection Procedure" (2008). Cowles Foundation Discussion Papers. 1989.