Nonparametric Tests for the Effect of a Treatment on the Conditional Variance

Abstract

This paper proposes nonparametric tests for the null hypothesis that a treatment has a zero effect on the conditional variance for all subpopulations characterized by the values of the covariates. Rather than the mean of an outcome, which measures the extent to which a treatment changes the level of the outcome, researchers are sometimes interested in how the treatment affects the dispersion of the outcome. We use the variance to measure dispersion and estimate the conditional variances using the series method. We provide a test rule that compares a Wald-type test statistic with the critical value of a chi-squared distribution. We also construct a normalized test statistic that is asymptotically standard normal under the null hypothesis. We illustrate the usefulness of the proposed test by Monte Carlo simulations and an empirical example that investigates the effect of unionism on wage dispersion.