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Using Multiple Outcomes to Improve the Synthetic Control Method

Author

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

Suggested Citation

  • Liyang Sun & Eli Ben-Michael & Avi Feller, 2023. "Using Multiple Outcomes to Improve the Synthetic Control Method," Papers 2311.16260, arXiv.org, revised Feb 2025.
    • Handle: RePEc:arx:papers:2311.16260
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    1. Acemoglu, Daron & Johnson, Simon & Kermani, Amir & Kwak, James & Mitton, Todd, 2016. "The value of connections in turbulent times: Evidence from the United States," Journal of Financial Economics, Elsevier, vol. 121(2), pages 368-391.
    2. Joseph Fry, 2023. "A Method of Moments Approach to Asymptotically Unbiased Synthetic Controls," Papers 2312.01209, arXiv.org, revised Mar 2024.
    3. 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.
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    1. repec:ces:ceswps:_119333 is not listed on IDEAS
    2. Chen, Qian & Koch, Christoffer & Richardson, Gary & Sharma, Padma, 2025. "Suspensions of payments and their consequences," Journal of Financial Stability, Elsevier, vol. 78(C).
    3. Brox, Enzo & Krieger, Tommy, 2025. "Far-right mass protests and their effects on internal migration," ZEW Discussion Papers 25-045, ZEW - Leibniz Centre for European Economic Research.
    4. Fry, Joseph, 2024. "A method of moments approach to asymptotically unbiased Synthetic Controls," Journal of Econometrics, Elsevier, vol. 244(1).
    5. Maximilian Langer & Joshua Hassib & Lars P. Feld & Daniel Nientiedt, 2025. "Evaluating the Effects of the German Debt Brake: A Synthetic Control Approach," CESifo Working Paper Series 11933, CESifo.
    6. Stefano DellaVigna & Guido Imbens & Woojin Kim & David M. Ritzwoller, 2025. "Using Multiple Outcomes to Adjust Standard Errors for Spatial Correlation," NBER Working Papers 33716, National Bureau of Economic Research, Inc.

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