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Inference on finite-population treatment effects under limited overlap

机译：关于有限群体治疗效应的推断在有限的重叠下

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This paper studies inference on finite-population average and local average treatment effects under limited overlap, meaning that some strata have a small proportion of treated or untreated units. We model limited overlap in an asymptotic framework, sending the propensity score to zero (or one) with the sample size. We derive the asymptotic distribution of analogue estimators of the treatment effects under two common randomization schemes: conditionally independent and stratified block randomization. Under either scheme, the limit distribution is the same and conventional standard error formulas remain asymptotically valid, but the rate of convergence is slower the faster the propensity score degenerates. The practical import of these results is two-fold. When overlap is limited, standard methods can perform poorly in smaller samples, as asymptotic approximations are inadequate owing to the slower rate of convergence. However, in larger samples, standard methods can work quite well even when the propensity score is small.
机译：本文研究了有限的重叠有限群体平均水平和局部平均治疗效果的推断，这意味着一些地层具有少量的处理或未治疗的单位。我们在渐近框架中模拟了有限的重叠，将倾向分数与样本大小发送到零（或一个）。我们在两种常见随机化方案下导出了种族估算器的渐近分布：条件独立和分层块随机化。在任一方案中，限制分布是相同的，传统的标准误差公式保持渐近有效，但收敛速度速度较慢，倾向得分退化速度越快。这些结果的实际导入是两倍。当重叠有限时，标准方法可以在较小的样本中表现不佳，因为由于收敛速度较慢，渐近近似是不充分的。然而，在较大的样品中，即使倾向得分小，标准方法也可以很好地工作。

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