Uniform Inference on Quantile Effects under Sharp Regression Discontinuity Designs

This paper builds upon conditional quantile processes to develop methods for conducting uni- form inference on quantile treatment effects under sharp regression discontinuity (RD) designs. It begins by developing Score and Wald type tests for a range of hypotheses that are related to treatment significance, homogeneity and unambiguity. It gives conditions under which the asymptotic distributions of these tests are unaffected by the biases from the nonparametric es- timation without requiring under-smoothing. Further, for situations where the conditions can be stringent, the paper develops a procedure that explicitly accounts for the effects of the bi- ases while paying special attention to their estimation uncertainty. The paper also provides a procedure for constructing uniform confidence bands for the quantile treatment effects. As an empirical application, we apply the methods to study the e§ects of cash-on-hand on unemploy- ment durations. The results reveal pronounced treatment heterogeneity and also point to the importance of considering the long-term unemployed.