In this paper, we propose an instrumental variable approach to constructing conﬁdence sets (CS’s) for the true parameter in models deﬁned by conditional moment inequalities/equalities. We show that by properly choosing instrument functions, one can transform conditional moment inequalities/equalities into unconditional ones without losing identiﬁcation power. Based on the unconditional moment inequalities/equalities, we construct CS’s by inverting Cramér–von Mises-type or Kolmogorov–Smirnov-type tests. Critical values are obtained using generalized moment selection (GMS) procedures. We show that the proposed CS’s have correct uniform asymptotic coverage probabilities. New methods are required to establish these results because an inﬁnite-dimensional nuisance parameter aﬀects the asymptotic distributions. We show that the tests considered are consistent against all ﬁxed alternatives and have power against some n –1/2 -local alternatives, though not all such alternatives. Monte Carlo simulations for three diﬀerent models show that the methods perform well in ﬁnite samples.
Andrews, Donald W.K. and Shi, Xiaoxia, "Inference Based on Conditional Moment Inequalities" (2010). Cowles Foundation Discussion Papers. 2092.