Inference in nonparametric/semiparametric moment equality models with shape restrictions

This paper studies the inference problem of an infinite-dimensional parameter with a shape restriction. This parameter is identified by arbitrarily many unconditional moment equalities. The shape restriction leads to a convex restriction set. I propose a test of the shape restriction, which controls size uniformly and applies to both point-identified and partially identified models. The test can be inverted to construct confidence sets after imposing the shape restriction. Monte Carlo experiments show the finite-sample properties of this method. In an empirical illustration, I apply the method to ascending auctions held by the US Forest Service and show that imposing shape restrictions can significantly improve inference.