Uniform Inference on Quantile Effects under Sharp Regression Discontinuity Designs

ABSTRACT

This study develops methods for conducting uniform inference on quantile treatment effects for sharp regression discontinuity designs. We develop a score test for the treatment significance hypothesis and Wald-type tests for the hypotheses related to treatment significance, homogeneity, and unambiguity. The bias from the nonparametric estimation is studied in detail. In particular, we show that under some conditions, the asymptotic distribution of the score test is unaffected by the bias, without under-smoothing. For situations where the conditions can be restrictive, we incorporate a bias correction into the Wald tests and account for the estimation uncertainty. We also provide a procedure for constructing uniform confidence bands for quantile treatment effects. As an empirical application, we use the proposed methods to study the effect of cash-on-hand on unemployment duration. The results reveal pronounced treatment heterogeneity and also emphasize the importance of considering the long-term unemployed.

KEY WORDS:

• Heterogeneity
• Quantile regression
• Regression discontinuity
• Treatment effect
• Unemployment duration.

SUPPLEMENTARY MATERIALS

Supplementary Materials are available on the journal's website, including an R package that reproduces empirical findings and simulation results of the article, a readme file that explains how to use functions in the R package, the dataset for the empirical application, and an online appendix that provides proofs, methods of bandwidth selections, and further extensions.

ACKNOWLEDGMENTS

We thank the seminar participants at Iowa, UC-Irvine, USC, UC-Davis, and the 2013 North American Summer Meeting of the Econometric Society for their useful comments and suggestions, and Youming Liu and Andres Sagner for their research assistance. We thank the co-editor, the associate editor, and two referees for their constructive comments that have substantially improved the article.