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On the Role of Covariates in the Synthetic Control Method

Author

Listed:
  • 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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    File URL: https://mpra.ub.uni-muenchen.de/81940/1/MPRA_paper_81940.pdf
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    References listed on IDEAS

    as
    1. Ferman, Bruno & Pinto, Cristine Campos de Xavier & Possebom, Vitor Augusto, 2016. "Cherry picking with synthetic controls," Textos para discussão 420, FGV/EESP - Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
    2. Ferman, Bruno & Pinto, Cristine Campos de Xavier, 2016. "Revisiting the synthetic control estimator," Textos para discussão 421, FGV/EESP - Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
    3. Kaul, Ashok & Klößner, Stefan & Pfeifer, Gregor & Schieler, Manuel, 2015. "Synthetic Control Methods: Never Use All Pre-Intervention Outcomes Together With Covariates," MPRA Paper 83790, University Library of Munich, Germany.
    Full references (including those not matched with items on IDEAS)

    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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