Testing for covariate balance using quantile regression and resampling methods

Consistency of propensity score matching estimators hinges on the propensity score's ability to balance the distributions of covariates in the pools of treated and nontreated units. Conventional balance tests merely check for differences in covariates' means, but cannot account for differences in higher moments. Specification tests constitute an alternative, but might reject misspecified, but yet balancing propensity score models. This paper proposes balance tests based on (i) quantile regression to check for differences in the distributions of continuous covariates and (ii) resampling methods to estimate the distributions of the proposed Kolmogorov-Smirnov and Cramer-von-Mises-Smirnov test statistics. Simulations suggest that the tests capture imbalances related to higher moments when conventional balance tests fail to do so and correctly keep misspecified, but balancing propensity scores when specification tests reject the null.