Inference for Parameters Defined by Moment Inequalities: A Recommended Moment Selection Procedure


  • Donald W. K. Andrews,

    1. Cowles Foundation for Research in Economics, Yale University, 30 Hillhouse Avenue, New Haven, CT 06520-8281, U.S.A.;
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  • Panle Jia Barwick

    1. Dept. of Economics, Massachusetts Institute of Technology, Cambridge, MA 02142, U.S.A.;
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    • Andrews gratefully acknowledges the research support of the National Science Foundation via Grants SES-0751517 and SES-1058376. The authors thank Steve Berry for numerous discussions and comments. The authors also thank a co-editor, three referees, Michael Wolf, and Giovanni Compiani for very helpful comments.


This paper is concerned with tests and confidence intervals for parameters that are not necessarily point 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, and implementation method. We provide data-dependent procedures for choosing the key moment selection tuning parameter κ and a size-correction factor η.