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 simulation and in a re-analysis of the impact of the Flint water crisis on educational outcomes.

翻译：当存在多个感兴趣的结果序列时，合成控制分析通常通过为每个结果估计独立的权重来进行。本文中，我们提出通过平衡所有结果的向量或它们的指数/平均值，来估计跨结果的共同权重集。在低秩因子模型下，我们证明这些方法相比独立权重可降低偏差上限，并且当结果数量增加时，取平均值能带来进一步的增益。我们通过模拟实验以及重新分析弗林特水危机对教育结果的影响来验证这一结论。