On the Choice of Test Statistic for Conditional Moment Inequalities

TL;DR

This paper compares the power of CvM and KS tests for inference on set-identified parameters defined by conditional moment inequalities, recommending KS tests with truncated variance weighting for optimal performance.

Contribution

It provides asymptotic power approximations for CvM and KS tests, guiding the choice of test statistic, weighting function, and bandwidth in set-identified inference.

Findings

KS tests outperform CvM tests in the considered setting

Truncated variance weighting is preferred over bounded weightings

Guidelines for selecting test parameters based on asymptotic power

Abstract

This paper derives asymptotic approximations to the power of Cramer-von Mises (CvM) style tests for inference on a finite dimensional parameter defined by conditional moment inequalities in the case where the parameter is set identified. Combined with power results for Kolmogorov-Smirnov (KS) tests, these results can be used to choose the optimal test statistic, weighting function and, for tests based on kernel estimates, kernel bandwidth. The results show that, in the setting considered here, KS tests are preferred to CvM tests, and that a truncated variance weighting is preferred to bounded weightings.