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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 in ﬁnite, or uncountably in ﬁnite. 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 random-coeﬀicients binary-outcome example support the theoretical results.
Andrews, Donald W.K. and Shi, Xiaoxia, "Inference Based on Many Conditional Moment Inequalities" (2015). Cowles Foundation Discussion Papers. 2447.