On the Properties of the Synthetic Control Estimator with Many Periods and Many Controls
On the Properties of the Synthetic Control Estimator with Many Periods and Many Controls
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DOI：
10.1080/01621459.2021.1965613
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发表时间：
2021-09-17
影响因子：
3.7
通讯作者：
Ferman, Bruno
中科院分区：
文献类型：
--
作者：
Ferman, Bruno
研究了预处理周期和控制单元都较大时，综合控制估计量的渐近性质。如果潜在结果遵循线性因子模型，我们提供了SC单元渐近恢复处理单元的因子结构的条件，即使预处理拟合是不完美的。当权重在越来越多的控制单元中被稀释，使得控制单元的因子结构的加权平均值渐近地重建被处理单元的因子结构时，就会发生这种情况。在这种情况下，SC估计量是渐近无偏的，即使当处理分配与时变不可观测值相关。本文的补充材料，包括可用于复制作品的材料的标准化描述，可作为在线补充。
We consider the asymptotic properties of the synthetic control (SC) estimator when both the number of pretreatment periods and control units are large. If potential outcomes follow a linear factor model, we provide conditions under which the SC unit asymptotically recovers the factor structure of the treated unit, even when the pretreatment fit is imperfect. This happens when there are weights diluted among an increasing number of control units such that a weighted average of the factor structure of the control units asymptotically reconstructs the factor structure of the treated unit. In this case, the SC estimator is asymptotically unbiased even when treatment assignment is correlated with time-varying unobservables. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.