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Generalized Synthetic Control Method: Causal Inference with Interactive Fixed Effects Models


  • Xu, Yiqing


Difference-in-differences (DID) is commonly used for causal inference in time-series cross-sectional data. It requires the assumption that the average outcomes of treated and control units would have followed parallel paths in the absence of treatment. In this paper, we propose a method that not only relaxes this often-violated assumption, but also unifies the synthetic control method (Abadie, Diamond, and Hainmueller 2010) with linear fixed effects models under a simple framework, of which DID is a special case. It imputes counterfactuals for each treated unit using control group information based on a linear interactive fixed effects model that incorporates unit-specific intercepts interacted with time-varying coefficients. This method has several advantages. First, it allows the treatment to be correlated with unobserved unit and time heterogeneities under reasonable modeling assumptions. Second, it generalizes the synthetic control method to the case of multiple treated units and variable treatment periods, and improves efficiency and interpretability. Third, with a built-in cross-validation procedure, it avoids specification searches and thus is easy to implement. An empirical example of Election Day Registration and voter turnout in the United States is provided.

Suggested Citation

  • 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.
  • Handle: RePEc:cup:polals:v:25:y:2017:i:01:p:57-76_00

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    Cited by:

    1. Dmitry Arkhangelsky & Guido Imbens, 2018. "The Role of the Propensity Score in Fixed Effect Models," NBER Working Papers 24814, National Bureau of Economic Research, Inc.
    2. Victor Chernozhukov & Kaspar Wuthrich & Yinchu Zhu, 2019. "Distributional conformal prediction," Papers 1909.07889,
    3. Davide Viviano & Jelena Bradic, 2019. "Synthetic learner: model-free inference on treatments over time," Papers 1904.01490,
    4. Victor Chernozhukov & Kaspar Wüthrich & Yu Zhu, 2017. "An exact and robust conformal inference method for counterfactual and synthetic controls," CeMMAP working papers CWP62/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Susan Athey & Mohsen Bayati & Nikolay Doudchenko & Guido Imbens & Khashayar Khosravi, 2017. "Matrix Completion Methods for Causal Panel Data Models," Papers 1710.10251,, revised Sep 2018.
    6. Klößner, Stefan & Pfeifer, Gregor, 2015. "Synthesizing Cash for Clunkers: Stabilizing the Car Market, Hurting the Environment," Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113207, Verein für Socialpolitik / German Economic Association.
    7. Cheng Hsiao & Qiankun Zhou, 2018. "Panel Parametric, Semi-parametric and Nonparametric Construction of Counterfactuals - California Tobacco Control Revisited," Departmental Working Papers 2018-02, Department of Economics, Louisiana State University.
    8. repec:eee:eecrev:v:98:y:2017:i:c:p:240-263 is not listed on IDEAS
    9. repec:kap:qmktec:v:17:y:2019:i:3:d:10.1007_s11129-019-09211-9 is not listed on IDEAS
    10. Eberhardt, Markus, 2019. "Democracy Does Cause Growth: Comment," CEPR Discussion Papers 13659, C.E.P.R. Discussion Papers.
    11. Jan Bruha & Jaromir Tonner, 2018. "An Exchange Rate Floor as an Instrument of Monetary Policy: An Ex-Post Assessment of the Czech Experience," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 68(6), pages 537-549, December.
    12. repec:eee:jeeman:v:95:y:2019:i:c:p:227-256 is not listed on IDEAS
    13. Jushan Bai & Serena Ng, 2019. "Matrix Completion, Counterfactuals, and Factor Analysis of Missing Data," Papers 1910.06677,, revised Nov 2019.
    14. Bernini, Cristina & Cerqua, Augusto, 2019. "Do sustainability policies finance local economies?," MPRA Paper 91882, University Library of Munich, Germany.
    15. Eli Ben-Michael & Avi Feller & Jesse Rothstein, 2018. "The Augmented Synthetic Control Method," Papers 1811.04170,, revised Nov 2019.
    16. Muhammad Jehangir Amjad & Devavrat Shah & Dennis Shen, 2017. "Robust Synthetic Control," Papers 1711.06940,
    17. Dmitry Arkhangelsky & Guido W. Imbens, 2019. "Double-Robust Identification for Causal Panel Data Models," Papers 1909.09412,
    18. Daniel Kinn, 2018. "Synthetic Control Methods and Big Data," Papers 1803.00096,

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