Quantile Treatment Effects in Regression Discontinuity Designs with Covariates

Estimating treatment effect heterogeneity conditional on a covariate has become an important research direction for regression discontinuity (RD) designs. In this paper, we go beyond conditional average treatment effect and propose a new method to estimate the conditional quantile treatment effect (CQTE) in RD designs. The proposed CQTE estimator is based on local quantile regression and hence remains local to the cutoff. Moreover, it captures the relations between treatment effects and the covariate directly for each quantile of the outcome variable. The estimated CQTE thus allows us to assess treatment effect heterogeneity with respect to covariates and the outcome variable simultaneously. As such, the proposed procedure renders a more comprehensive picture of treatment effect in RD designs than conventional methods.