• Asymptotic size;
  • asymptotic power;
  • bootstrap;
  • confidence set;
  • generalized moment selection;
  • moment inequalities;
  • partial identification;
  • refined moment selection;
  • test;
  • unidentified parameter

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.