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Optimal Bandwidth Choice for the Regression Discontinuity Estimator

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  • Guido Imbens
  • Karthik Kalyanaraman

Abstract

We investigate the choice of the bandwidth for the regression discontinuity estimator. We focus on estimation by local linear regression, which was shown to have attractive properties (Porter, J. 2003, "Estimation in the Regression Discontinuity Model" (unpublished, Department of Economics, University of Wisconsin, Madison)). We derive the asymptotically optimal bandwidth under squared error loss. This optimal bandwidth depends on unknown functionals of the distribution of the data and we propose simple and consistent estimators for these functionals to obtain a fully data-driven bandwidth algorithm. We show that this bandwidth estimator is optimal according to the criterion of Li (1987, "Asymptotic Optimality for C p, C L, Cross-validation and Generalized Cross-validation: Discrete Index Set", Annals of Statistics, 15, 958--975), although it is not unique in the sense that alternative consistent estimators for the unknown functionals would lead to bandwidth estimators with the same optimality properties. We illustrate the proposed bandwidth, and the sensitivity to the choices made in our algorithm, by applying the methods to a data set previously analysed by Lee (2008, "Randomized Experiments from Non-random Selection in U.S. House Elections", Journal of Econometrics, 142, 675--697) as well as by conducting a small simulation study. Copyright , Oxford University Press.

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File URL: http://hdl.handle.net/10.1093/restud/rdr043
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Bibliographic Info

Article provided by Oxford University Press in its journal The Review of Economic Studies.

Volume (Year): 79 (2012)
Issue (Month): 3 ()
Pages: 933-959

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Handle: RePEc:oup:restud:v:79:y:2012:i:3:p:933-959

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  1. Lee, David S., 2008. "Randomized experiments from non-random selection in U.S. House elections," Journal of Econometrics, Elsevier, vol. 142(2), pages 675-697, February.
  2. Powell, James L. & Stoker, Thomas M., 1996. "Optimal bandwidth choice for density-weighted averages," Journal of Econometrics, Elsevier, vol. 75(2), pages 291-316, December.
  3. Imbens, Guido W. & Lemieux, Thomas, 2008. "Regression discontinuity designs: A guide to practice," Journal of Econometrics, Elsevier, vol. 142(2), pages 615-635, February.
  4. Wilbert van der Klaauw, 2008. "Regression-Discontinuity Analysis: A Survey of Recent Developments in Economics," LABOUR, CEIS, vol. 22(2), pages 219-245, 06.
  5. Ludwig, Jens & Miller, Douglas L., 2006. "Does Head Start Improve Children's Life Chances? Evidence from a Regression Discontinuity Design," IZA Discussion Papers 2111, Institute for the Study of Labor (IZA).
  6. Frandsen, Brigham R. & Frölich, Markus & Melly, Blaise, 2012. "Quantile treatment effects in the regression discontinuity design," Journal of Econometrics, Elsevier, vol. 168(2), pages 382-395.
  7. McCrary, Justin, 2008. "Manipulation of the running variable in the regression discontinuity design: A density test," Journal of Econometrics, Elsevier, vol. 142(2), pages 698-714, February.
  8. Cook, Thomas D., 2008. ""Waiting for Life to Arrive": A history of the regression-discontinuity design in Psychology, Statistics and Economics," Journal of Econometrics, Elsevier, vol. 142(2), pages 636-654, February.
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