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Regression discontinuity design with covariates

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Markus Frölich

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Abstract

In this paper, the regression discontinuity design (RDD) is generalized to account for differences in observed covariates X in a fully nonparametric way. It is shown that the treatment effect can be estimated at the rate for one-dimensional nonparametric regression irrespective of the dimension of X. It thus extends the analysis of Hahn, Todd and van der Klaauw (2001) and Porter (2003), who examined identification and estimation without covariates, requiring assumptions that may often be too strong in applications. In many applications, individuals to the left and right of the threshold differ in observed characteristics. Houses may be Cconstructed in different ways across school attendance district boundaries. Firms may differ around a threshold that implies certain legal changes, etc. Accounting for these differences in covariates is important to reduce bias. In addition, accounting for covariates may also reduces variance. Finally, estimation of quantile treatment effects (QTE) is also considered.

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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP27/07.

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Date of creation: Nov 2007
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Handle: RePEc:ifs:cemmap:27/07

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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References listed on IDEAS
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  1. Erich Battistin & Enrico Rettore, 2002. "Testing for programme effects in a regression discontinuity design with imperfect compliance," Journal Of The Royal Statistical Society Series A, Royal Statistical Society, vol. 165(1), pages 39-57. [Downloadable!] (restricted)
  2. Wilbert van der Klaauw, 2002. "Estimating the Effect of Financial Aid Offers on College Enrollment: A Regression-Discontinuity Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(4), pages 1249-1287, November. [Downloadable!] (restricted)
  3. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-75, March. [Downloadable!] (restricted)
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  4. Rafael Lalive, 2006. "How do Extended Benefits Affect Unemployment Duration? A Regression Discontinuity Approach," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
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  5. Patrick Puhani & Andrea Weber, 2007. "Does the early bird catch the worm?," Empirical Economics, Springer, vol. 32(2), pages 359-386, May. [Downloadable!] (restricted)
  6. Sandra E. Black, 1999. "Do Better Schools Matter? Parental Valuation Of Elementary Education," The Quarterly Journal of Economics, MIT Press, vol. 114(2), pages 577-599, May. [Downloadable!] (restricted)
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  7. Hahn, Jinyong & Todd, Petra & Van der Klaauw, Wilbert, 2001. "Identification and Estimation of Treatment Effects with a Regression-Discontinuity Design," Econometrica, Econometric Society, vol. 69(1), pages 201-09, January.
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