Estimation in the Regression Discontinuity Model
Estimation in the Regression Discontinuity Model
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发表时间：
2003
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通讯作者：
J. Porter
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作者：
J. Porter
断点回归模型最近已成为经济学实证研究中常用的框架。 Hahn、Todd 和 Van der Klaauw（2001）在此框架中提供了治疗效果识别的正式发展，并指出了其估计中潜在的偏差问题。这种偏差困难是回归不连续性处理效果估计问题的特定特征的结果，该特征将其与缺乏平滑性的典型半参数估计问题区分开来。在这里，不连续性不仅仅是估计中需要克服的障碍；相反，不连续性的大小本身就是估计感兴趣的对象。在本文中，我推导了用于估计回归不连续性处理效果的最佳收敛速度。最优率表明，通过适当选择估计量，偏差困难并不比通常的非参数条件均值估计问题（在协变量支持的内部点）中发现的困难更差。提出了两种在不同条件下获得最优速率的估计器。一种新的估计量基于 Robinson (1988) 的部分线性估计量。另一个估计器使用局部多项式估计，并且在更广泛的条件下是最优的。
The regression discontinuity model has recently become a commonly applied framework for empirical work in economics. Hahn, Todd, and Van der Klaauw (2001) provide a formal development of the identification of a treatment effect in this framework and also note the potential bias problems in its estimation. This bias difficulty is the result of a particular feature of the regression discontinuity treatment effect estimation problem that distinguishes it from typical semiparametric estimation problems where smoothness is lacking. Here, the discontinuity is not simply an obstacle to overcome in estimation; instead, the size of discontinuity is itself the object of estimation interest. In this paper, I derive the optimal rate of convergence for estimation of the regression discontinuity treatment effect. The optimal rate suggests that with appropriate choice of estimator the bias difficulties are no worse than would be found in the usual nonparametric conditional mean estimation problem (at an interior point of the covariate support). Two estimators are proposed that attain the optimal rate under varying conditions. One new estimator is based on Robinson’s (1988) partially linear estimator. The other estimator uses local polynomial estimation and is optimal under a broader set of conditions.