Asymptotically Exact Inference in Conditional Moment Inequality Models

TL;DR

This paper develops new asymptotic theory for Kolmogorov-Smirnov style tests in conditional moment inequality models, leading to more powerful tests with better finite-sample performance and tighter confidence regions.

Contribution

It introduces a novel asymptotic distribution for these tests, improving power and accuracy over existing methods, especially for parameters on the boundary of the identified set.

Findings

Faster than root-n convergence rate.

New tests outperform existing methods in power.

Finite sample performance is validated through simulations.

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. In contrast to other moment inequality settings, the rate of convergence is faster than root-$n$, and the asymptotic distribution depends entirely on nonbinding moments. The results require the development of new techniques that draw a connection between moment selection, irregular identification, bandwidth selection and nonstandard M-estimation. 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.