Working Paper

Using multiple outcomes to improve the synthetic control method


Liyang Sun, Eli Ben-Michael, Avi Feller

Published Date

11 December 2023


Working Paper (CWP24/23)

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.