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Bayesian and Frequentist Inference for Synthetic Controls

Ignacio Martinez, Jaume Vives-i-Bastida

arXiv 3 Jun 2022 · Statistics — Methodology

arXiv:2206.01779 · PDF · DOI · OpenAlex · Extracted main text

Abstract

The synthetic control method has become a widely popular tool to estimate causal effects with observational data. Despite this, inference for synthetic control methods remains challenging. Often, inferential results rely on linear factor model data generating processes. In this paper, we characterize the conditions on the factor model primitives (the factor loadings) for which the statistical risk minimizers are synthetic controls (in the simplex). Then, we propose a Bayesian alternative to the synthetic control method that preserves the main features of the standard method and provides a new way of doing valid inference. We explore a Bernstein-von Mises style result to link our Bayesian inference to the frequentist inference. For linear factor model frameworks we show that a maximum likelihood estimator (MLE) of the synthetic control weights can consistently estimate the predictive function of the potential outcomes for the treated unit and that our Bayes estimator is asymptotically close to the MLE in the total variation sense. Through simulations, we show that there is convergence between the Bayes and frequentist approach even in sparse settings. Finally, we apply the method to re-visit the study of the economic costs of the German re-unification and the Catalan secession movement. The Bayesian synthetic control method is available in the bsynth R-package.

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31
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Abadie, A., Diamond, A., and Hainmueller, J (2010) Synthetic control methods for comparative case studies: Estimating the effect of California’s tobacco control program0.69361100%
2He, X. and Shao, Q.-M (2000) On parameters of increasing dimensions0.69361100%
3Abadie, A., Diamond, A., and Hainmueller, J (2015) Comparative politics and the synthetic control method0.69351100%
4Esteller-Moré, A. and Rizzo, L (2022) The economic costs of a secessionist conflict: The case of catalonia0.64441100%
5Ferman, B (2021) On the properties of the synthetic control estimator with many periods and many controls0.64441100%
6Firpo, S. and Possebom, V (2018) Synthetic Control Method: Inference, Sensitivity Analysis and Confidence Sets0.51121100%
7Abadie, A. and Vives-i Bastida, J (2022) Synthetic controls in action0.51121100%
8Chernozhukov, V., Wüthrich, K., and Zhu, Y (2021) An exact and robust conformal inference method for counterfactual and synthetic controls0.51121100%
9Hsiao, C., Steve Ching, H., and Ki Wan, S (2012) A panel data approach for program evaluation: Measuring the benefits of political and economic integration of Hong Kong with mai…0.51121100%
10Imbens, G. W. and Viviano, D (2023) Identification and inference for synthetic controls with confounding0.51121100%

Showing the top 10 of 31 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Bayesian Synthetic Control with a Soft Simplex Constraint0.73732
2Inference with few treated units0.40511