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On the Properties of the Synthetic Control Estimator with Many Periods and Many Controls

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  • Bruno Ferman

Abstract

We consider the asymptotic properties of the synthetic control (SC) estimator when both the number of pretreatment periods and control units are large. If potential outcomes follow a linear factor model, we provide conditions under which the SC unit asymptotically recovers the factor structure of the treated unit, even when the pretreatment fit is imperfect. This happens when there are weights diluted among an increasing number of control units such that a weighted average of the factor structure of the control units asymptotically reconstructs the factor structure of the treated unit. In this case, the SC estimator is asymptotically unbiased even when treatment assignment is correlated with time-varying unobservables. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

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  • 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.
    • Handle: RePEc:taf:jnlasa:v:116:y:2021:i:536:p:1764-1772
    DOI: 10.1080/01621459.2021.1965613
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    Cited by:

    1. Lu Zhang & Xiaomeng Zhang & Xinyu Zhang, 2024. "Asymptotic Properties of the Distributional Synthetic Controls," Papers 2405.00953, arXiv.org, revised Aug 2024.
    2. Timo Schenk, 2023. "Time-Weighted Difference-in-Differences: Accounting for Common Factors in Short T Panels," Tinbergen Institute Discussion Papers 23-004/III, Tinbergen Institute.
    3. Absher, Samuel & Grier, Robin & Grier, Kevin, 2023. "The consequences of CIA-sponsored regime change in Latin America," European Journal of Political Economy, Elsevier, vol. 80(C).
    4. Zongwu Cai & Ying Fang & Ming Lin & Zixuan Wu, 2023. "A Quasi Synthetic Control Method for Nonlinear Models With High-Dimensional Covariates," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202305, University of Kansas, Department of Economics, revised Aug 2023.
    5. David Gilchrist & Thomas Emery & Nuno Garoupa & Rok Spruk, 2023. "Synthetic Control Method: A tool for comparative case studies in economic history," Journal of Economic Surveys, Wiley Blackwell, vol. 37(2), pages 409-445, April.
    6. González-Rozada, Martín & Ruffo, Hernán, 2024. "Do trade agreements contribute to the decline in labor share? Evidence from Latin American countries," World Development, Elsevier, vol. 177(C).
    7. Ignacio Martinez & Jaume Vives-i-Bastida, 2022. "Bayesian and Frequentist Inference for Synthetic Controls," Papers 2206.01779, arXiv.org, revised Jul 2024.
    8. Alberto Abadie & Jaume Vives-i-Bastida, 2022. "Synthetic Controls in Action," Papers 2203.06279, arXiv.org.
    9. Luis A. F. Alvarez & Bruno Ferman, 2024. "On “Imputation of Counterfactual Outcomes when the Errors are Predictable'': Discussions on Misspecification and Suggestions of Sensitivity Analyses," Working Papers, Department of Economics 2024_16, University of São Paulo (FEA-USP).
    10. Ferman, Bruno, 2021. "Matching estimators with few treated and many control observations," Journal of Econometrics, Elsevier, vol. 225(2), pages 295-307.
    11. Joseph Fry, 2023. "A Method of Moments Approach to Asymptotically Unbiased Synthetic Controls," Papers 2312.01209, arXiv.org, revised Mar 2024.
    12. Guido W. Imbens & Davide Viviano, 2023. "Identification and Inference for Synthetic Controls with Confounding," Papers 2312.00955, arXiv.org.
    13. Alberto Abadie & Jinglong Zhao, 2021. "Synthetic Controls for Experimental Design," Papers 2108.02196, arXiv.org, revised Dec 2023.
    14. Guido Imbens & Nathan Kallus & Xiaojie Mao, 2021. "Controlling for Unmeasured Confounding in Panel Data Using Minimal Bridge Functions: From Two-Way Fixed Effects to Factor Models," Papers 2108.03849, arXiv.org.
    15. Bruno Ferman & Cristine Pinto, 2021. "Synthetic controls with imperfect pretreatment fit," Quantitative Economics, Econometric Society, vol. 12(4), pages 1197-1221, November.
    16. Wei Tian & Seojeong Lee & Valentyn Panchenko, 2023. "Synthetic Controls with Multiple Outcomes," Papers 2304.02272, arXiv.org, revised Jul 2024.
    17. Luis Alvarez & Bruno Ferman, 2023. "Extensions for Inference in Difference-in-Differences with Few Treated Clusters," Papers 2302.03131, arXiv.org.
    18. Xiaomeng Zhang & Wendun Wang & Xinyu Zhang, 2022. "Asymptotic Properties of the Synthetic Control Method," Papers 2211.12095, arXiv.org.
    19. Yiping Lu & Jiajin Li & Lexing Ying & Jose Blanchet, 2022. "Synthetic Principal Component Design: Fast Covariate Balancing with Synthetic Controls," Papers 2211.15241, arXiv.org.

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