Journal Article

Optimal Bandwidth Choice for the Regression Discontinuity Estimator

Guido Imbens and Karthik Kalyanaraman

in The Review of Economic Studies

Published on behalf of Review of Economic Studies Ltd

Volume 79, issue 3, pages 933-959
Published in print July 2012 | ISSN: 0034-6527
Published online November 2011 | e-ISSN: 1467-937X | DOI: http://dx.doi.org/10.1093/restud/rdr043
Optimal Bandwidth Choice for the Regression Discontinuity Estimator

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  • Econometric and Statistical Methods and Methodology: General
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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which was shown to have attractive properties (Porter, J. 2003, “Estimation in the Regression Discontinuity Model” (unpublished, Department of Economics, University of Wisconsin, Madison)).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 Cp, CL, 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.

Keywords: Optimal bandwidth selection; Local linear regression; Regression discontinuity designs; Cross-validation; C13; C14; C21

Journal Article.  9586 words.  Illustrated.

Subjects: Econometric and Statistical Methods and Methodology: General ; Single Equation Models; Single Variables

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