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Optimal bandwidth choice for the regression discontinuity estimator

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  • Guido Imbens

    ()
    (Institute for Fiscal Studies and Harvard University)

  • Karthik Kalyanaraman

    ()
    (Institute for Fiscal Studies and UCL)

Abstract

We investigate the problem of optimal choice of the smoothing parameter (bandwidth) for the regression discontinuity estimator. We focus on estimation by local linear regression, which was shown to be rate optimal (Porter, 2003). We derive the optimal bandwidth. This optimal bandwidth depends on unknown functionals of the distribution of the data and we propose specific, consistent, estimators for these functionals to obtain a fully data-driven bandwidth choice that has the "asymptotic no-regret" property. We illustrate our proposed bandwidth, and the sensitivity to the choices made in this bandwidth proposal, using a data set previously analyzed by Lee (2008), as well as a small simulation study based on the Lee data set. The simulations suggest that the proposed rule performs well.

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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 CWP05/10.

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Date of creation: Mar 2010
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Handle: RePEc:ifs:cemmap:05/10

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  1. Jens Ludwig & Douglas L Miller, 2007. "Does Head Start Improve Children's Life Chances? Evidence from a Regression Discontinuity Design," The Quarterly Journal of Economics, MIT Press, vol. 122(1), pages 159-208, 02.
  2. Imbens, Guido W. & Lemieux, Thomas, 2008. "Regression discontinuity designs: A guide to practice," Journal of Econometrics, Elsevier, vol. 142(2), pages 615-635, February.
  3. Wilbert van der Klaauw, 2008. "Regression-Discontinuity Analysis: A Survey of Recent Developments in Economics," LABOUR, CEIS, vol. 22(2), pages 219-245, 06.
  4. 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.
  5. 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.
  6. Frölich, Markus & Melly, Blaise, 2008. "Quantile Treatment Effects in the Regression Discontinuity Design," IZA Discussion Papers 3638, Institute for the Study of Labor (IZA).
  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. 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.
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