Identification and Estimation of Treatment Effects with a Regression-Discontinuity Design

Abstract

Ž. THE REGRESSION DISCONTINUITY RD data design is a quasi-experimental design with the defining characteristic that the probability of receiving treatment changes discontinuously as a function of one or more underlying variables. This data design arises frequently in economic and other applications but is only infrequently exploited as a source of identifying information in evaluating effects of a treatment. In the first application and discussion of the RD method, Thistlethwaite and Campbell Ž. 1960 study the effect of student scholarships on career aspirations, using the fact that awards are only made if a test score exceeds a threshold. More recently, Van der Klaauw Ž. 1997 estimates the effect of financial aid offers on students’ decisions to attend a particular college, taking into account administrative rules that set the aid amount partly on the basis of a discontinuous function of the students’ grade point average and SAT Ž. score. Angrist and Lavy 1999 estimate the effect of class size on student test scores, taking advantage of a rule stipulating that another classroom be added when the average Ž. class size exceeds a threshold level. Finally, Black 1999 uses an RD approach to estimate parents’ willingness to pay for higher quality schools by comparing housing prices near geographic school attendance boundaries. Regression discontinuity methods have potentially broad applicability in economic research, because geographic boundaries or rules governing programs often create discontinuities in the treatment assignment mechanism that can be exploited under the method. Although there have been several discussions and applications of RD methods in the literature, important questions still remain concerning sources of identification and ways of estimating treatment effects under minimal parametric restrictions. Here, we show that identifying conditions invoked in previous applications of RD methods are often overly strong and that treatment effects can be nonparametrically identified under an RD design by a weak functional form restriction. The restriction is unusual in that it requires imposing continuity assumptions in order to take advantage of the known discontinuity in the treatment assignment mechanism. We also propose a way of nonparametrically estimating treatment effects and offer an interpretation of the Wald estimator as an RD estimator.