Using Multiple Outcomes to Improve the Synthetic Control Method
针对多个结果变量，提出估计共同权重而非单独权重的方法，通过平衡所有结果或它们的均值来降低偏差，并用弗林特水危机对教育影响的再分析加以验证。
Abstract When there are multiple outcome series of interest, Synthetic Control analyses typically proceed by estimating separate weights for each outcome. In this paper, we instead propose estimating a common set of weights across outcomes, by balancing either a vector of all outcomes or an index or average of them. Under a low-rank factor model, we show that these approaches lead to lower bias bounds than separate weights, and that averaging leads to further gains when the number of outcomes grows. We illustrate this via a re-analysis of the impact of the Flint water crisis on educational outcomes.