RD Local Quantile Effects

RD Local Quantile Effects - A Nonparametric Estimator for...

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Electronic copy available at: http://ssrn.com/abstract=1216062 A Nonparametric Estimator for Local Quantile Treatment E/ects in the Regression Discontinuity Design Brigham R. Frandsen ° ; y Massachusetts Institute of Technology First draft: July 2008 Last updated: October 29, 2008 Abstract I introduce a procedure to nonparametrically estimate local quantile treatment e/ects in a regression discontinuity (RD) design with a binary treatment. Analogously to Hahn, Todd, and van der Klaauw°s (2001) estimator for average treatment e/ects 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 e/ects for the subgroup of ±RD compliers². 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 e/ects of universal pre-K programs, and ³nd that while evidence for an e/ect on the upper end of the distribution is weaker, participation in a pre-K program signi³cantly raises the lower end and middle of the distribution of test scores, with the greatest gains in the middle of the distribution. 1 Introduction The regression discontinuity (RD) design has received increased attention in recent years as a means of quasi-experimentally estimating treatment e/ects. To cite only a few examples of many recent studies using this design, Jacob and Lefgren (2004) and Matsudaira (2008) estimate the e/ect of remedial education programs, exploiting assessment test cuto/s in assignment to summer school programs; Black, Smith, Berger, ° I bene³ted immeasurably from conversations with and suggestions from Josh Angrist, Whitney Newey, and Raymond Guiteras. Any errors, however, are entirely my own. y MIT E52-391, 77 Massachusetts Ave., Cambridge, MA, 02139; e-mail: [email protected] 1
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Electronic copy available at: http://ssrn.com/abstract=1216062 and Noel (2003) use a feature of the UI ±pro³ling score² to evaluate the e/ect of the Worker Pro³ling and Reemployment Services program; Angrist and Lavy (1999) exploit maximum class size rules in Israeli public schools to estimate the e/ect of class size on educational outcomes; and DiNardo and Lee (2004) use certi³cation elections to estimate the impact of new unions on employers. Studies comparing RD estimates to results based on randomized trials suggest the popularity of the RD design is justi³able 1 . The studies mentioned above and others using the RD design focus on estimating average treatment e/ects. In many contexts, however, the e/ect of a treatment on the distribution of outcomes is of interest. For example, economists often evaluate the social welfare implications of a policy based on the di/erences in the distribution of outcomes under various alternatives (Atkinson, 1970). Furthermore, a zero average e/ect may mask sign³cant o/setting e/ects at di/erent points in the distribution. Examples where distributional
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