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On the Role of Covariates in the Synthetic Control Method

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  • Botosaru, Irene
  • Ferman, Bruno

Abstract

This note revisits the role of time-invariant observed covariates in the Synthetic Control (SC) method. We first derive conditions under which the original result of Abadie et al (2010) regarding the bias of the SC estimator remains valid when we relax the assumption of a perfect match on observed covariates and assume only a perfect match on pre-treatment outcomes. We then show that, even when the conditions for the first result are valid, a perfect match on pre-treatment outcomes does not generally imply an approximate match for all covariates. This will only be true for those that are both relevant and whose effects (over time) are not collinear with the effects of other observed and unobserved covariates. Taken together, our results show that a perfect match on covariates should not be required for the SC method, as long as there is a perfect match on a long set of pre-treatment outcomes.

Suggested Citation

  • Botosaru, Irene & Ferman, Bruno, 2017. "On the Role of Covariates in the Synthetic Control Method," MPRA Paper 80796, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:80796
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    References listed on IDEAS

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    1. Laurent Gobillon & Thierry Magnac, 2016. "Regional Policy Evaluation: Interactive Fixed Effects and Synthetic Controls," The Review of Economics and Statistics, MIT Press, vol. 98(3), pages 535-551, July.
    2. Bruno Ferman & Cristine Pinto & Vitor Possebom, 2020. "Cherry Picking with Synthetic Controls," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 39(2), pages 510-532, March.
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    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.
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    8. Eduardo Cavallo & Sebastian Galiani & Ilan Noy & Juan Pantano, 2013. "Catastrophic Natural Disasters and Economic Growth," The Review of Economics and Statistics, MIT Press, vol. 95(5), pages 1549-1561, December.
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    10. Susan Athey & Mohsen Bayati & Nikolay Doudchenko & Guido Imbens & Khashayar Khosravi, 2017. "Matrix Completion Methods for Causal Panel Data Models," Papers 1710.10251, arXiv.org, revised Jun 2020.
    11. 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.
    12. 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.
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    14. Shimeng Liu, 2015. "Spillovers from Universities: Evidence from the Land-Grant Program," Working Paper 9410, USC Lusk Center for Real Estate.
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    Cited by:

    1. Breinlich, Holger & Leromain, Elsa & Novy, Dennis & Sampson, Thomas, 2020. "Voting with their money: Brexit and outward investment by UK firms," European Economic Review, Elsevier, vol. 124(C).
    2. Heger, Martin Philipp & Neumayer, Eric, 2019. "The impact of the Indian Ocean tsunami on Aceh’s long-term economic growth," Journal of Development Economics, Elsevier, vol. 141(C).
    3. Ferman, Bruno, 2017. "Matching Estimators with Few Treated and Many Control Observations," MPRA Paper 78940, University Library of Munich, Germany.
    4. Campos Vázquez, Raymundo Miguel & Rodas Milián, James Alexis, 2020. "El efecto faro del salario mínimo en la estructura salarial: evidencias para México," El Trimestre Económico, Fondo de Cultura Económica, vol. 87(345), pages 51-97, enero-mar.
    5. Eli Ben-Michael & Avi Feller & Jesse Rothstein, 2018. "The Augmented Synthetic Control Method," Papers 1811.04170, arXiv.org, revised Jul 2020.
    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. Benjamin Hansen & Drew McNichols, 2020. "Information and the Persistence of the Gender Wage Gap: Early Evidence from California's Salary History Ban," NBER Working Papers 27054, National Bureau of Economic Research, Inc.
    8. Bruno Ferman, 2019. "On the Properties of the Synthetic Control Estimator with Many Periods and Many Controls," Papers 1906.06665, arXiv.org, revised May 2020.
    9. Ersoy, Fulya Y., 2020. "The effects of the great recession on college majors," Economics of Education Review, Elsevier, vol. 77(C).
    10. Kim, Hyejin & Lee, Jungmin, 2019. "Can employment subsidies save jobs? Evidence from a shipbuilding city in South Korea," Labour Economics, Elsevier, vol. 61(C).
    11. Dave, Dhaval M. & Friedson, Andrew I. & Matsuzawa, Kyutaro & McNichols, Drew & Sabia, Joseph J., 2020. "Did the Wisconsin Supreme Court Restart a COVID-19 Epidemic? Evidence from a Natural Experiment," IZA Discussion Papers 13314, Institute of Labor Economics (IZA).
    12. Gabriel, Ricardo Duque & Pessoa, Ana Sofia, 2020. "Adopting the Euro: a synthetic control approach," MPRA Paper 99391, University Library of Munich, Germany.
    13. Dhaval M. Dave & Andrew I. Friedson & Kyutaro Matsuzawa & Drew McNichols & Connor Redpath & Joseph J. Sabia, 2020. "Risk Aversion, Offsetting Community Effects, and COVID-19: Evidence from an Indoor Political Rally," NBER Working Papers 27522, National Bureau of Economic Research, Inc.
    14. Bruno Ferman & Cristine Pinto, 2019. "Synthetic Controls with Imperfect Pre-Treatment Fit," Papers 1911.08521, arXiv.org.

    More about this item

    Keywords

    Synthetic controls; covariates; perfect match;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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