Uniform Inference on Quantile Effects under Sharp Regression Discontinuity Designs

Abstract

This study develops methods for conducting uniform inference on quantile treatment e¤ects for sharp regression discontinuity designs. We develop a score test for the treatment signi…cance hypothesis and Wald-type tests for the hypotheses related to treatment signi…cance, 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 una¤ected 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 con…dence bands for quantile treatment e¤ects. As an empirical application, we use the proposed methods to study the e¤ect of cash-on-hand on unemployment duration. The results reveal pronounced treatment heterogeneity, and also emphasize the importance of considering the long-term unemployed.

Robust uniform inference for quantile treatment effects in regression discontinuity designs

“…As their method is limited to mean-regression-based designs, one may need to seek alternative methods for quantile-regression-based designs. The pivotal methods of Qu and Yoon (2015b) and Chiang and Sasaki (2017) are probably superior to our method if a practitioner is interested in sharp quantile RDD and sharp quantile RKD, respectively. The bootstrap method proposed in this paper, to the best of our knowledge, is the only option if a practitioner is interested in the fuzzy quantile RDD and the fuzzy CDF discontinuity design.…”

“…For technical matters, we mainly refer to Porter (2003) in deriving the general Bahadur representation for higher-order local polynomial mean regression. While it mostly evolved around the RDD, recent additions to this local design literature include the RKD (e.g., Nielsen, Sørensen, and Taber, 2010;Chen and Fan, 2011;Landais, 2015;Simonsen, Skipper, and Skipper, 2015;Card, Lee, Pei, and Weber, 2016;Dong, 2016), quantile extensions (e.g., Frandsen, Frölich, and Melly, 2012;Qu and Yoon, 2015b), and their combination (Chiang and Sasaki, 2017). While we focus on the fuzzy quantile RDD for most parts of this paper, we note that all these different frameworks are uniformly encompassed by the general framework developed in this paper.…”

“…3 Bartalotti, Calhoun, and He (2017) adapt this idea of bias correction to a wild bootstrap method of inference for the sharp mean RDD. Qu and Yoon (2015b) adapt this idea of bias correction to a simulation method of uniform inference for the sharp quantile RDD.…”

“…This estimand τ will be denoted by τ SQRD for Sharp Quantile RD design. For this estimand, Qu and Yoon (2015b) propose a method of uniform inference based on uniform random sampling, and hence we are not the first to propose a bootstrap method for τ SQRD . Our method adds the property of robustness to this existing method, besides the main result that it applies to other estimands too.…”

“…The pivotal method proposed by Qu and Yoon (2015b) covers robust uniform inference for the sharp quantile RDD, and is also extensible to the sharp quantile RKD (Chiang and Sasaki, 2017).…”