Optimal Bandwidth Choice for the Regression Discontinuity Estimator
AbstractWe 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which was shown to have attractive properties (Porter, J. 2003, "Estimation in the Regression Discontinuity Model" (unpublished, Department of Economics, University of Wisconsin, Madison)).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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Bibliographic InfoArticle provided by Oxford University Press in its journal The Review of Economic Studies.
Volume (Year): 79 (2012)
Issue (Month): 3 ()
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Other versions of this item:
- Guido Imbens & Karthik Kalyanaraman, 2009. "Optimal Bandwidth Choice for the Regression Discontinuity Estimator," NBER Working Papers 14726, National Bureau of Economic Research, Inc.
- 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.
- Imbens, Guido W. & Kalyanaraman, Karthik, 2009. "Optimal Bandwidth Choice for the Regression Discontinuity Estimator," IZA Discussion Papers 3995, Institute for the Study of Labor (IZA).
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
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- Imbens, Guido W. & Lemieux, Thomas, 2008.
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- Guido Imbens & Thomas Lemieux, 2007. "Regression Discontinuity Designs: A Guide to Practice," NBER Working Papers 13039, National Bureau of Economic Research, Inc.
- Guido Imbens & Thomas Lemieux, 2007. "Regression Discontinuity Designs: A Guide to Practice," NBER Technical Working Papers 0337, National Bureau of Economic Research, Inc.
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- Jens Ludwig & Douglas L. Miller, 2005. "Does Head Start Improve Children's Life Chances? Evidence from a Regression Discontinuity Design," NBER Working Papers 11702, National Bureau of Economic Research, Inc.
- 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.
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- Frölich, Markus & Melly, Blaise, 2008. "Quantile Treatment Effects in the Regression Discontinuity Design," IZA Discussion Papers 3638, Institute for the Study of Labor (IZA).
- 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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