  We show that moment inequalities in a wide variety of economic applications
have a particular linear conditional structure. We use this structure to
construct uniformly valid confidence sets that remain computationally tractable
even in settings with nuisance parameters. We first introduce least favorable
critical values which deliver non-conservative tests if all moments are
binding. Next, we introduce a novel conditional inference approach which
ensures a strong form of insensitivity to slack moments. Our recommended
approach is a hybrid technique which combines desirable aspects of the least
favorable and conditional methods. The hybrid approach performs well in
simulations calibrated to Wollmann (2018), with favorable power and
computational time comparisons relative to existing alternatives.
