  Inference in models where the parameter is defined by moment inequalities is
of interest in many areas of economics. This paper develops a new method for
improving the performance of generalized moment selection (GMS) testing
procedures in finite-samples. The method modifies GMS tests by tilting the
empirical distribution in its moment selection step by an amount that maximizes
the empirical likelihood subject to the restrictions of the null hypothesis. We
characterize sets of population distributions on which a modified GMS test is
(i) asymptotically equivalent to its non-modified version to first-order, and
(ii) superior to its non-modified version according to local power when the
sample size is large enough. An important feature of the proposed modification
is that it remains computationally feasible even when the number of moment
inequalities is large. We report simulation results that show the modified
tests control size well, and have markedly improved local power over their
non-modified counterparts.
