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Optimal bandwidth choice for the regression discontinuity estimator

Author

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  • Guido Imbens

    () (Institute for Fiscal Studies and Stanford Graduate School of Business)

  • Karthik Kalyanaraman

    (Institute for Fiscal Studies and American Enterprise Institute)

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.

Suggested Citation

  • Guido Imbens & Karthik Kalyanaraman, 2010. "Optimal bandwidth choice for the regression discontinuity estimator," CeMMAP working papers CWP05/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:05/10
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    References listed on IDEAS

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    1. 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.
    2. 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, Oxford University Press, vol. 122(1), pages 159-208.
    3. 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.
    4. Imbens, Guido W. & Lemieux, Thomas, 2008. "Regression discontinuity designs: A guide to practice," Journal of Econometrics, Elsevier, vol. 142(2), pages 615-635, 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. Wilbert van der Klaauw, 2008. "Regression-Discontinuity Analysis: A Survey of Recent Developments in Economics," LABOUR, CEIS, vol. 22(2), pages 219-245, June.
    7. 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.
    8. 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.
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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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