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When there are multiple outcome series of interest, Synthetic Controlanalyses typically proceed by estimating separate weights for each outcome. Inthis paper, we instead propose estimating a common set of weights acrossoutcomes, by balancing either a vector of all outcomes or an index or averageof them. Under a low-rank factor model, we show that these approaches lead tolower bias bounds than separate weights, and that averaging leads to furthergains when the number of outcomes grows. We illustrate this via simulation andin a re-analysis of the impact of the Flint water crisis on educationaloutcomes.

Using Multiple Outcomes to Improve the Synthetic Control Method