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Unformatted text preview: 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 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 e/ects of universal pre-K programs, and £nd that while evidence for an e/ect on the upper end of the distribution is weaker, participation in a pre-K program signi£cantly 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 bene£ted 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 Electronic copy available at: http://ssrn.com/abstract=1216062 and Noel (2003) use a feature of the UI &pro¡ling score¢ to evaluate the e/ect of the Worker Pro¡ling 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 certi¡cation 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 justi¡able 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....
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This note was uploaded on 12/26/2011 for the course ECON 245a taught by Professor Staff during the Fall '08 term at UCSB.
- Fall '08