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Imperfect Synthetic Controls

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  • David Powell

Abstract

The synthetic control method assumes the existence of a perfect synthetic control, which cannot exist if the outcomes are functions of transitory shocks with nonzero asymptotic variance and may not exist even in expectation for the treated unit. This paper first shows the benefits of estimating synthetic controls for all units. If the treated unit composes part of the synthetic control for any untreated unit, the treatment effect is independently identified by the synthetic outcome minus the outcome of the untreated unit in the post‐treatment period (divided by the synthetic control weight on the treated unit outcome). This paper introduces an estimator which generates synthetic controls for all units and develops moment conditions which are valid given transitory shocks. I also introduce a weighting metric which asymptotically excludes units without appropriate synthetic controls. The paper exploits the estimator's construction of multiple estimates of the treatment effect to produce valid inference even when the number of control units is small. The estimator is used to evaluate the repeal of Wisconsin's handgun purchase waiting period on suicide rates.

Suggested Citation

  • David Powell, 2026. "Imperfect Synthetic Controls," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 41(3), pages 253-264, April.
    • Handle: RePEc:wly:japmet:v:41:y:2026:i:3:p:253-264
    DOI: 10.1002/jae.70035
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    References listed on IDEAS

    as
    1. David Powell, 2022. "Synthetic Control Estimation Beyond Comparative Case Studies: Does the Minimum Wage Reduce Employment?," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1302-1314, June.
    2. 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.
    3. 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.
    4. Alberto Abadie & Alexis Diamond & Jens Hainmueller, 2015. "Comparative Politics and the Synthetic Control Method," American Journal of Political Science, John Wiley & Sons, vol. 59(2), pages 495-510, February.
    5. 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.
    6. 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.
    7. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-161, January.
    8. Fry, Joseph, 2024. "A method of moments approach to asymptotically unbiased Synthetic Controls," Journal of Econometrics, Elsevier, vol. 244(1).
    9. Joseph Fry, 2023. "A Method of Moments Approach to Asymptotically Unbiased Synthetic Controls," Papers 2312.01209, arXiv.org, revised Mar 2024.
    10. Susan Athey & Guido W. Imbens, 2017. "The State of Applied Econometrics: Causality and Policy Evaluation," Journal of Economic Perspectives, American Economic Association, vol. 31(2), pages 3-32, Spring.
    11. Ashok Kaul & Stefan Klößner & Gregor Pfeifer & Manuel Schieler, 2022. "Standard Synthetic Control Methods: The Case of Using All Preintervention Outcomes Together With Covariates," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1362-1376, June.
    12. Susan Athey & Mohsen Bayati & Nikolay Doudchenko & Guido Imbens & Khashayar Khosravi, 2021. "Matrix Completion Methods for Causal Panel Data Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1716-1730, October.
    13. 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.
    14. 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.
    15. 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.
    16. Hollingsworth, Alex & Wing, Coady, 2020. "Tactics for design and inference in synthetic control studies: An applied example using high-dimensional data," SocArXiv fc9xt, Center for Open Science.
    17. repec:osf:socarx:fc9xt_v1 is not listed on IDEAS
    18. Maxwell Kellogg & Magne Mogstad & Guillaume A. Pouliot & Alexander Torgovitsky, 2021. "Combining Matching and Synthetic Control to Tradeoff Biases From Extrapolation and Interpolation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1804-1816, October.
    Full references (including those not matched with items on IDEAS)

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