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Asymptotically Unbiased Synthetic Control Methods by Density Matching

Masahiro Kato, Akari Ohda

arXiv 20 Jul 2023 · Econometrics

arXiv:2307.11127 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Synthetic Control Methods (SCMs) have become a fundamental tool for comparative case studies. The core idea behind SCMs is to estimate treatment effects by predicting counterfactual outcomes for a treated unit using a weighted combination of observed outcomes from untreated units. The accuracy of these predictions is crucial for evaluating the treatment effect of a policy intervention. Subsequent research has therefore focused on estimating SC weights. In this study, we highlight a key endogeneity issue in existing SCMs-namely, the correlation between the outcomes of untreated units and the error term of the synthetic control, which leads to bias in both counterfactual outcome prediction and treatment effect estimation. To address this issue, we propose a novel SCM based on density matching, assuming that the outcome density of the treated unit can be approximated by a weighted mixture of the joint density of untreated units. Under this assumption, we estimate SC weights by matching the moments of the treated outcomes with the weighted sum of the moments of the untreated outcomes. Our method offers three advantages: first, under the mixture model assumption, our estimator is asymptotically unbiased; second, this asymptotic unbiasedness reduces the mean squared error in counterfactual predictions; and third, our method provides full densities of the treatment effect rather than just expected values, thereby broadening the applicability of SCMs. Finally, we present experimental results that demonstrate the effectiveness of our approach.

Citation extraction

38
references
141
in-text mentions
38
distinct cited
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self-citations
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main-text words

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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
1F. F. Gunsilius (2023) Distributional synthetic controls1.000235100%
2Alberto Abadie and Javier Gardeazabal (2003) The economic costs of conflict: A case study of the basque country1.000165100%
3Bruno Ferman and Cristine Pinto (2021) Synthetic controls with imperfect pretreatment fit1.000144100%
4Alberto Abadie, Alexis Diamond, and Jens Hainmueller (2010) Synthetic control methods for comparative case studies: Estimating the effect of california’s tobacco control program1.000104100%
5Claudia Shi, Dhanya Sridhar, Vishal Misra, and David Blei (2022) On the assumptions of synthetic control methods1.000103100%
6Victor Chernozhukov, Kaspar Wüthrich, and Yinchu Zhu (2021) An exact and robust conformal inference method for counterfactual and synthetic controls1.00063100%
7Alberto Abadie (2002) Bootstrap tests for distributional treatment effects in instrumental variable models1.00053100%
8Achille Nazaret, Claudia Shi, and David M. Blei (2023) On the misspecification of linear assumptions in synthetic control, 20231.00053100%
9Shui-Ki Wan, Yimeng Xie, and Cheng Hsiao (2018) Panel data approach vs synthetic control method0.87452100%
10Joseph Fry (2024) A method of moments approach to asymptotically unbiased synthetic controls, 20240.81142100%

Showing the top 10 of 38 scored citations.