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Unformatted text preview: Estimation in the Regression Discontinuity Model * Jack Porter Harvard University Department of Economics Littauer Center 121 Cambridge, MA 02138 firstname.lastname@example.org May 7, 2003 Abstract The regression discontinuity model has recently become a commonly applied framework for empirical work in economics. Hahn, Todd, and Van der Klaauw (2001) provide a formal devel- opment of the identification of a treatment effect in this framework and also note the potential bias problems in its estimation. This bias difficulty is the result of a particular feature of the regression discontinuity treatment effect estimation problem that distinguishes it from typical semiparametric estimation problems where smoothness is lacking. Here, the discontinuity is not simply an obstacle to overcome in estimation; instead, the size of discontinuity is itself the object of estimation interest. In this paper, I derive the optimal rate of convergence for estimation of the regression discontinuity treatment effect. The optimal rate suggests that with appropriate choice of estimator the bias difficulties are no worse than would be found in the usual non- parametric conditional mean estimation problem (at an interior point of the covariate support). Two estimators are proposed that attain the optimal rate under varying conditions. One new estimator is based on Robinsons (1988) partially linear estimator. The other estimator uses local polynomial estimation and is optimal under a broader set of conditions. Keywords: Regression Discontinuity Design, Optimal Convergence Rate, Asymptotic Bias JEL Classification: C13, C14 * I am grateful to Gary Chamberlain, Michael Murray, Whitney Newey, numerous seminar participants, and especially Guido Imbens for comments and suggestions. I thank the National Science Foundation for research support under grant SES-0112095. This paper has also circulated under the title Asymptotic Bias and Optimal Convergence Rates for Semiparametric Kernel Estimators in the Regression Discontinuity Model. 1 1 Introduction The regression discontinuity [RD] design has recently become a commonly applied framework for identification of treatment effects in economics. The RD design can be useful when there is a cut-off point in treatment assignment or in the probability of treatment assignment. Under weak smoothness conditions, the assignment near the cut-off behaves almost as if random. Regression discontinuity models typically use only the information very close to the shift to identify the treat- ment effect of interest without reliance on functional form assumptions. For example, Van der Klaauw (1996) examined the effect of a universitys scholarship offer on the probability of an appli- cant choosing to attend that university. The scholarship amount offered was based on an underlying index of various individual characteristics observable to the econometrician. Cut-off points in the index were used by the college to group applicants into categories, and scholarship offers were given...
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