Optimal Bandwidth Choice for the Regression Discontinuity Estimator
Optimal Bandwidth Choice for the Regression Discontinuity Estimator
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DOI：
10.1093/restud/rdr043
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发表时间：
2012-07-01
影响因子：
5.8
通讯作者：
Kalyanaraman, Karthik
中科院分区：
文献类型：
--
作者：
Imbens, Guido;Kalyanaraman, Karthik
我们研究了回归间断估计带宽的选择问题。我们关注的是局部线性回归估计，它被证明具有吸引人的性质(Porter，J.2003，《回归不连续性模型中的估计》(未出版，威斯康星大学经济系，麦迪逊))。我们得到了误差平方损失下的渐近最优带宽。这一最优带宽取决于数据分布的未知泛函，我们对这些泛函提出了简单且一致的估计器，以获得完全数据驱动的带宽算法。根据Li(1987，“C-p的渐近最优性，C-L，交叉验证和广义交叉验证：离散指数集”，统计年鉴，15,958-975)的准则，我们证明了这种带宽估计器是最优的，尽管它不是唯一的，因为未知泛函的替代一致估计器将导致带宽估计器具有相同的最优性性质。我们通过将这些方法应用于Lee先前分析的数据集(2008年，《来自美国众议院选举中的非随机选择的随机实验》，Journal of Econometrics，142,675-697)，以及通过进行小型模拟研究，来说明建议的带宽以及对我们算法中所做选择的敏感性。
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which was shown to have attractive properties (Porter, J. 2003, "Estimation in the Regression Discontinuity Model" (unpublished, Department of Economics, University of Wisconsin, Madison)).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 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.