Inference Based on Many Conditional Moment Inequalities

In this paper, we construct confidence sets for models defined by many conditional moment inequalities/equalities. The conditional moment restrictions in the models can be finite, countably infinite, or uncountably infinite. To deal with the complication brought about by the vast number of moment restrictions, we exploit the manageability (Pollard (1990)) of the class of moment functions. We verify the manageability condition in five examples from the recent partial identification literature. The proposed confidence sets are shown to have correct asymptotic size in a uniform sense and to exclude parameter values outside the identified set with probability approaching one. Monte Carlo experiments for a conditional stochastic dominance example and a randomcoefficients binary-outcome example support the theoretical results. ∗Andrews gratefully acknowledges the research support of the National Science Foundation via grant numbers SES-1058376 and SES-1355504. Shi gratefully acknowledges the research support of the University of Wisconsin-Madison Graduate School with funding from the Wisconsin Alumni Research Foundation. The first version of the results of this paper were given in Section 9 of Andrews and Shi (2009).