Asymptotically exact inference in conditional moment inequality models

Abstract

This paper derives the rate of convergence and asymptotic distribution for a class of Kolmogorov–Smirnov style test statistics for conditional moment inequality models for parameters on the boundary of the identified set under general conditions. Using these results, I propose tests that are more powerful than existing approaches for choosing critical values for this test statistic. I quantify the power improvement by showing that the new tests can detect alternatives that converge to points on the identified set at a faster rate than those detected by existing approaches. A Monte Carlo study confirms that the tests and the asymptotic approximations they use perform well in finite samples. In an application to a regression of prescription drug expenditures on income with interval data from the Health and Retirement Study, confidence regions based on the new tests are substantially tighter than those based on existing methods.