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Synthetic Control as Online Linear Regression

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  • Jiafeng Chen

Abstract

This paper notes a simple connection between synthetic control and online learning. Specifically, we recognize synthetic control as an instance of Follow‐The‐Leader (FTL). Standard results in online convex optimization then imply that, even when outcomes are chosen by an adversary, synthetic control predictions of counterfactual outcomes for the treated unit perform almost as well as an oracle weighted average of control units' outcomes. Synthetic control on differenced data performs almost as well as oracle weighted difference‐in‐differences, potentially making it an attractive choice in practice. We argue that this observation further supports the use of synthetic control estimators in comparative case studies.

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  • Jiafeng Chen, 2023. "Synthetic Control as Online Linear Regression," Econometrica, Econometric Society, vol. 91(2), pages 465-491, March.
    • Handle: RePEc:wly:emetrp:v:91:y:2023:i:2:p:465-491
    DOI: 10.3982/ECTA20720
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    References listed on IDEAS

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    1. Eli Ben-Michael & Avi Feller & Jesse Rothstein, 2021. "The Augmented Synthetic Control Method," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1789-1803, October.
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    4. Victor Chernozhukov & Kaspar Wüthrich & Yinchu Zhu, 2021. "An Exact and Robust Conformal Inference Method for Counterfactual and Synthetic Controls," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1849-1864, October.
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    8. Xu, Yiqing, 2017. "Generalized Synthetic Control Method: Causal Inference with Interactive Fixed Effects Models," Political Analysis, Cambridge University Press, vol. 25(1), pages 57-76, January.
    9. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    10. Janet Currie & Henrik Kleven & Esmée Zwiers, 2020. "Technology and Big Data Are Changing Economics: Mining Text to Track Methods," AEA Papers and Proceedings, American Economic Association, vol. 110, pages 42-48, May.
    11. Alberto Abadie, 2021. "Using Synthetic Controls: Feasibility, Data Requirements, and Methodological Aspects," Journal of Economic Literature, American Economic Association, vol. 59(2), pages 391-425, June.
    12. Alberto Abadie & Matias D. Cattaneo, 2021. "Introduction to the Special Section on Synthetic Control Methods," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1713-1715, October.
    13. Abadie, Alberto & Diamond, Alexis & Hainmueller, Jens, 2010. "Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California’s Tobacco Control Program," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 493-505.
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    Cited by:

    1. Anish Agarwal & Keegan Harris & Justin Whitehouse & Zhiwei Steven Wu, 2023. "Adaptive Principal Component Regression with Applications to Panel Data," Papers 2307.01357, arXiv.org, revised Oct 2023.
    2. Daniel Ngo & Keegan Harris & Anish Agarwal & Vasilis Syrgkanis & Zhiwei Steven Wu, 2023. "Incentive-Aware Synthetic Control: Accurate Counterfactual Estimation via Incentivized Exploration," Papers 2312.16307, arXiv.org, revised Feb 2024.

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