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Synthetic Controls for Experimental Design

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  • Alberto Abadie
  • Jinglong Zhao

Abstract

This article studies experimental design in settings where the experimental units are large aggregate entities (e.g., markets), and only one or a small number of units can be exposed to the treatment. In such settings, randomization of the treatment may result in treated and control groups with very different characteristics at baseline, inducing biases. We propose a variety of synthetic control designs (Abadie, Diamond and Hainmueller, 2010, Abadie and Gardeazabal, 2003) as experimental designs to select treated units in non-randomized experiments with large aggregate units, as well as the untreated units to be used as a control group. Average potential outcomes are estimated as weighted averages of treated units, for potential outcomes with treatment -- and control units, for potential outcomes without treatment. We analyze the properties of estimators based on synthetic control designs and propose new inferential techniques. We show that in experimental settings with aggregate units, synthetic control designs can substantially reduce estimation biases in comparison to randomization of the treatment.

Suggested Citation

  • Alberto Abadie & Jinglong Zhao, 2021. "Synthetic Controls for Experimental Design," Papers 2108.02196, arXiv.org, revised Dec 2023.
    • Handle: RePEc:arx:papers:2108.02196
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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.
    2. Firpo Sergio & Possebom Vitor, 2018. "Synthetic Control Method: Inference, Sensitivity Analysis and Confidence Sets," Journal of Causal Inference, De Gruyter, vol. 6(2), pages 1-26, September.
    3. Duflo, Esther & Glennerster, Rachel & Kremer, Michael, 2008. "Using Randomization in Development Economics Research: A Toolkit," Handbook of Development Economics, in: T. Paul Schultz & John A. Strauss (ed.), Handbook of Development Economics, edition 1, volume 4, chapter 61, pages 3895-3962, Elsevier.
    4. Dmitry Arkhangelsky & Susan Athey & David A. Hirshberg & Guido W. Imbens & Stefan Wager, 2021. "Synthetic Difference-in-Differences," American Economic Review, American Economic Association, vol. 111(12), pages 4088-4118, December.
    5. Lea Bottmer & Guido Imbens & Jann Spiess & Merrill Warnick, 2021. "A Design-Based Perspective on Synthetic Control Methods," Papers 2101.09398, arXiv.org, revised Jul 2023.
    6. Bruno Ferman, 2021. "On the Properties of the Synthetic Control Estimator with Many Periods and Many Controls," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1764-1772, October.
    7. 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.
    8. Alberto Abadie & Javier Gardeazabal, 2003. "The Economic Costs of Conflict: A Case Study of the Basque Country," American Economic Review, American Economic Association, vol. 93(1), pages 113-132, March.
    9. 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.
    10. Nikolay Doudchenko & Guido W. Imbens, 2016. "Balancing, Regression, Difference-In-Differences and Synthetic Control Methods: A Synthesis," NBER Working Papers 22791, National Bureau of Economic Research, Inc.
    11. 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.
    12. Alberto Abadie & Jérémy L’Hour, 2021. "A Penalized Synthetic Control Estimator for Disaggregated Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1817-1834, October.
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