A Nonparametric Estimator for Local Quantile Treatment Effects in the Regression Discontinuity Design
35 Pages Posted: 12 Aug 2008 Last revised: 30 Oct 2008
Date Written: October 29, 2008
I introduce a procedure to nonparametrically estimate local quantile treatment effects in a regression discontinuity (RD) design with a binary treatment. Analogously to Hahn, Todd, and van der Klaauw's (2001) estimator for average treatment effects using local linear regression, the estimator developed here uses local linear quantile regression to estimate the marginal distributions of potential outcomes to infer the quantile treatment effects for the subgroup of "RD compliers". I describe the estimation procedure, derive the asymptotic distribution, and provide Monte Carlo results. I apply the procedure to Gormley, et al's (2005) study of the effects of universal pre-K programs, and find that while evidence for an effect on the upper end of the distribution is weaker, participation in a pre-K program significantly raises the lower end and middle of the distribution of test scores, with the greatest gains in the middle of the distribution.
Keywords: regression discontinuity, nonparametric regression, quantile treatment effects, LATE, local linear
JEL Classification: C13, C14, C21
Suggested Citation: Suggested Citation