Model selection tests for moment inequality models

We propose Vuong-type tests to select between two moment inequality models based on their Kullback–Leibler distances to the true data distribution. The candidate models can be either non-overlapping or overlapping. For each case, we develop a testing procedure that has correct asymptotic size in a uniform sense despite the potential lack of point identification. We show both procedures are consistent against fixed alternatives and local alternatives converging to the null at rates arbitrarily close to n−1/2. We demonstrate the finite-sample performance of the tests with Monte Carlo simulation of a missing data example. The tests are relatively easy to implement.