Testing conditional symmetry without smoothing

Abstract

We test the assumption of conditional symmetry used to identify and estimate parameters in regression models with endogenous regressors, without making any distributional assumptions. The Kolmogorov–Smirnov-type statistic we propose is consistent, computationally tractable because it does not require optimisation over an uncountable set, free of any kind of nonparametric smoothing, and can detect n ^1/2-deviations from the null. Results from a simulation experiment suggest that our test can work very well in moderately sized samples.

Keywords:

• testing conditional symmetry
• endogenous regressors

Acknowledgements

We thank an anonymous referee for helpful comments.