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Combining Matching and Synthetic Control to Tradeoff Biases From Extrapolation and Interpolation

Author

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  • Maxwell Kellogg
  • Magne Mogstad
  • Guillaume A. Pouliot
  • Alexander Torgovitsky

Abstract

The synthetic control (SC) method is widely used in comparative case studies to adjust for differences in pretreatment characteristics. SC limits extrapolation bias at the potential expense of interpolation bias, whereas traditional matching estimators have the opposite properties. This complementarity motives us to propose a matching and synthetic control (or MASC) estimator as a model averaging estimator that combines the standard SC and matching estimators. We show how to use a rolling-origin cross-validation procedure to train the MASC to resolve tradeoffs between interpolation and extrapolation bias. We use a series of empirically based placebo and Monte Carlo simulations to shed light on when the SC, matching, MASC and penalized SC estimators do (and do not) perform well. Then, we apply these estimators to examine the economic costs of conflicts in the context of Spain.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:jnlasa:v:116:y:2021:i:536:p:1804-1816
    DOI: 10.1080/01621459.2021.1979562
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    Cited by:

    1. Callaway, Brantly & Karami, Sonia, 2023. "Treatment effects in interactive fixed effects models with a small number of time periods," Journal of Econometrics, Elsevier, vol. 233(1), pages 184-208.
    2. Robert Kraemer & Jonne Lehtimäki, 2024. "Government debt, European Institutions and fiscal rules: a synthetic control approach," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 31(4), pages 1112-1157, August.
    3. Omid M. Ardakani & N. Kundan Kishor & Suyong Song, 2024. "Does membership of the EMU matter for economic and financial outcomes?," Contemporary Economic Policy, Western Economic Association International, vol. 42(3), pages 416-447, July.
    4. Roberta Di Stefano & Giovanni Mellace, 2020. "The inclusive synthetic control method," Working Papers 21/20, Sapienza University of Rome, DISS.
    5. Li, Xingyu & Shen, Yan & Zhou, Qiankun, 2024. "Confidence intervals of treatment effects in panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 240(1).
    6. Marco Francesconi & Jonathan James, 2022. "Alcohol Price Floors and Externalities: The Case of Fatal Road Crashes," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 41(4), pages 1118-1156, September.
    7. Bogatyrev, Konstantin & Stoetzer, Lukas, 2024. "Synthetic Control Methods for Proportions," OSF Preprints brhd3, Center for Open Science.
    8. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," Papers 2311.15458, arXiv.org, revised Jun 2024.
    9. Guillaume Allaire Pouliot & Zhen Xie, 2022. "Degrees of Freedom and Information Criteria for the Synthetic Control Method," Papers 2207.02943, arXiv.org.
    10. Maria Petrillo & Daniel Valdenegro & Charles Rahal & Yanan Zhang & Gwilym Pryce & Matthew R. Bennett, 2024. "Estimating the Cost of Informal Care with a Novel Two-Stage Approach to Individual Synthetic Control," Papers 2411.10314, arXiv.org, revised Nov 2024.
    11. 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.
    12. Guido W. Imbens & Davide Viviano, 2023. "Identification and Inference for Synthetic Controls with Confounding," Papers 2312.00955, arXiv.org.
    13. Rong J. B. Zhu, 2023. "Synthetic Regressing Control Method," Papers 2306.02584, arXiv.org, revised Oct 2023.
    14. Sandro Heiniger, 2024. "Data-driven model selection within the matrix completion method for causal panel data models," Papers 2402.01069, arXiv.org.

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