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Using Multiple Outcomes to Improve the Synthetic Control Method

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  • Liyang Sun
  • Eli Ben-Michael
  • Avi Feller

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

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  • Liyang Sun & Eli Ben-Michael & Avi Feller, 2023. "Using Multiple Outcomes to Improve the Synthetic Control Method," Papers 2311.16260, arXiv.org.
    • Handle: RePEc:arx:papers:2311.16260
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    1. Esther Duflo & Pascaline Dupas & Michael Kremer, 2011. "Peer Effects, Teacher Incentives, and the Impact of Tracking: Evidence from a Randomized Evaluation in Kenya," American Economic Review, American Economic Association, vol. 101(5), pages 1739-1774, August.
    2. Joseph Fry, 2023. "A Method of Moments Approach to Asymptotically Unbiased Synthetic Controls," Papers 2312.01209, arXiv.org, revised Mar 2024.
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