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This paper is concerned with tests and conﬁdence intervals for parameters that are not necessarily identiﬁed and are deﬁned by moment inequalities. In the literature, diﬀerent test statistics, critical value methods, and implementation methods (i.e., the asymptotic distribution versus the bootstrap) have been proposed. In this paper, we compare these methods. We provide a recommended test statistic, moment selection critical value method, and implementation method. We provide data-dependent procedures for choosing the key moment selection tuning parameter kappa and a size-correction factor eta.
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. 1990.