Large sample properties of matching estimators for average treatment effects
Large sample properties of matching estimators for average treatment effects
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DOI：
10.1111/j.1468-0262.2006.00655.x
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发表时间：
2006-01-01
期刊：
影响因子：
6.1
通讯作者：
Imbens, GW
中科院分区：
文献类型：
--
作者：
Abadie, A;Imbens, GW
平均处理效应的匹配估计量在评价研究中得到了广泛的应用，尽管在许多情况下它们的大样本性质还没有得到证实。在这方面没有正式的结果可能部分是由于这样一个事实，即标准的渐近展开不适用于匹配估计与固定数量的匹配，因为这样的估计是高度非光滑的数据泛函。本文发展了分析匹配估计量大样本性质的新方法，建立了一些新的结果。我们专注于匹配替换与固定数量的匹配。首先，我们证明了匹配估计一般不是N-1/2-一致的，并描述了匹配估计达到N-1/2-一致性的条件。其次，我们表明，即使在匹配估计是N-1/2一致的设置，简单的匹配估计与固定数量的匹配不达到半参数效率界。第三，我们提供了一个一致的估计大样本方差，不需要一致的未知函数的非参数估计。用于实现这些方法的软件在Matlab、Stata和R中可用。
Matching estimators for average treatment effects are widely used in evaluation research despite the fact that their large sample properties have not been established in many cases. The absence of formal results in this area may be partly due to the fact that standard asymptotic expansions do not apply to matching estimators with a fixed number of matches because such estimators are highly nonsmooth functionals of the data. In this article we develop new methods for analyzing the large sample properties of matching estimators and establish a number of new results. We focus on matching with replacement with a fixed number of matches. First, we show that matching estimators are not N-1/2-consistent in general and describe conditions under which matching estimators do attain N-1/2-consistency. Second, we show that even in settings where matching estimators are N-1/2-consistent, simple matching estimators with a fixed number of matches do not attain the semiparametric efficiency bound. Third, we provide a consistent estimator for the large sample variance that does not require consistent nonparametric estimation of unknown functions. Software for implementing these methods is available in Matlab, Stata, and R.