摘要翻译:
当预处理周期和控制单元数都较大时,我们考虑了合成控制(SC)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单元的因子负荷在概率上收敛于被处理单元的因子负荷的条件。当在越来越多的控制单元中有权重被稀释,使得控制单元的因子负荷的加权平均值渐近地重建被处理单元的因子负荷时,就会发生这种情况。在这种情况下,即使当处理分配与时变不可观测项相关时,SC估计也是渐近无偏的。该结果即使在控制单元的数目大于预处理周期的数目时也可以有效。
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英文标题:
《On the Properties of the Synthetic Control Estimator with Many Periods
and Many Controls》
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作者:
Bruno Ferman
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最新提交年份:
2020
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分类信息:
一级分类:Economics 经济学
二级分类:Econometrics 计量经济学
分类描述:Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论,微观计量经济学,宏观计量经济学,通过新方法发现的经济关系的实证内容,统计推论应用于经济数据的方法论方面。
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英文摘要:
We consider the asymptotic properties of the Synthetic Control (SC) estimator when both the number of pre-treatment periods and control units are large. If potential outcomes follow a linear factor model, we provide conditions under which the factor loadings of the SC unit converge in probability to the factor loadings of the treated unit. This happens when there are weights diluted among an increasing number of control units such that a weighted average of the factor loadings of the control units asymptotically reconstructs the factor loadings of the treated unit. In this case, the SC estimator is asymptotically unbiased even when treatment assignment is correlated with time-varying unobservables. This result can be valid even when the number of control units is larger than the number of pre-treatment periods.
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PDF链接:
https://arxiv.org/pdf/1906.06665