Optimal Bandwidth Choice for the Regression Discontinuity Estimator

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ID: 290961
2011
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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which was shown to have attractive properties (Porter, J. 2003, "Estimation in the Regression Discontinuity Model" (unpublished, Department of Economics, University of Wisconsin, Madison)).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 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.
Reference Key
openalex_W2145411167 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Guido W. Imbens, Kaushik Kalyanaraman
Journal The Review of Economic Studies
Year 2011
DOI
10.1093/restud/rdr043
URL
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