  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.
