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Single proxy synthetic control

Author

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  • Park Chan

    (Department of Statistics, University of Illinois Urbana-Champaign, Champaign, Illinois, United States)

  • Tchetgen Tchetgen Eric J.

    (Department of Statistics and Data Science, University of Pennsylvania, Philadelphia, Pennsylvania, United States)

Abstract

Synthetic control methods are widely used to estimate the treatment effect on a single treated unit in time-series settings. A common approach to estimate synthetic control weights is to regress the treated unit’s pretreatment outcome and covariates’ time series measurements on those of untreated units via ordinary least squares. However, this approach can perform poorly if the pretreatment fit is not near perfect, whether the weights are normalized. In this article, we introduce a single proxy synthetic control approach, which views the outcomes of untreated units as proxies of the treatment-free potential outcome of the treated unit, a perspective we leverage to construct a valid synthetic control. Under this framework, we establish an alternative identification strategy and corresponding estimation methods for synthetic controls and the treatment effect on the treated unit. Notably, unlike existing proximal synthetic control methods, which require two types of proxies for identification, ours relies on a single type of proxy, thus facilitating its practical relevance. ∣In addition, we adapt a conformal inference approach to perform inference about the treatment effect, obviating the need for a large number of posttreatment observations. Finally, our framework can accommodate time-varying covariates and nonlinear models. We demonstrate the proposed approach in a simulation study and a real-world application.

Suggested Citation

  • Park Chan & Tchetgen Tchetgen Eric J., 2025. "Single proxy synthetic control," Journal of Causal Inference, De Gruyter, vol. 13(1), pages 1-22.
  • Handle: RePEc:bpj:causin:v:13:y:2025:i:1:p:22:n:1001
    DOI: 10.1515/jci-2023-0079
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    References listed on IDEAS

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    1. 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.
    2. Caroline Fohlin & Zhikun Lu, 2021. "How Contagious Was the Panic of 1907? New Evidence from Trust Company Stocks," AEA Papers and Proceedings, American Economic Association, vol. 111, pages 514-519, May.
    3. Manuel Arellano & Stephen Bond, 1991. "Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(2), pages 277-297.
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