Inference for functions of partially identified parameters in moment inequality models

This paper introduces a new hypothesis test for the null hypothesis H₀ : f(θ) = y0, where f(
.) is a known function, y0 is a known constant, and θ is a parameter that is partially identied by a moment (in)equality model. The main application of our test is sub-vector inference in moment inequality models, that is, for a multidimensional θ, the function f(θ) = θ_k selects the kth coordinate of θ. Our test controls asymptotic size uniformly over a large class of distributions of the data and has better asymptotic power properties than currently available methods. In particular, we show that the new test has asymptotic power that dominates the one corresponding to two existing competitors in the literature: subsampling and projection-based tests.