Quantile Treatment Effects in Regression Kink Designs

Abstract: The literature on regression kink designs develops identification results for average effects of continuous treatments (Card, Lee, Pei, and Weber, 2015), average effects of binary treatments (Dong, 2018), and quantile-wise effects of continuous treatments (Chiang and Sasaki, 2019), but there has been no identification result for quantile-wise effects of binary treatments to date. In this paper, we fill this void in the literature by providing an identification of quantile treatment effects in regression kink designs with binary treatment variables. For completeness, we also develop large sample theories for statistical inference and a practical guideline on estimation and inference.