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On the Misspecification of Linear Assumptions in Synthetic Control

Achille Nazaret, Claudia Shi, David M. Blei

arXiv 24 Feb 2023 · Statistics — Methodology

arXiv:2302.12777 · PDF · DOI · OpenAlex · Extracted main text

Abstract

The synthetic control (SC) method is a popular approach for estimating treatment effects from observational panel data. It rests on a crucial assumption that we can write the treated unit as a linear combination of the untreated units. This linearity assumption, however, can be unlikely to hold in practice and, when violated, the resulting SC estimates are incorrect. In this paper we examine two questions: (1) How large can the misspecification error be? (2) How can we limit it? First, we provide theoretical bounds to quantify the misspecification error. The bounds are comforting: small misspecifications induce small errors. With these bounds in hand, we then develop new SC estimators that are specially designed to minimize misspecification error. The estimators are based on additional data about each unit, which is used to produce the SC weights. (For example, if the units are countries then the additional data might be demographic information about each.) We study our estimators on synthetic data; we find they produce more accurate causal estimates than standard synthetic controls. We then re-analyze the California tobacco-program data of the original SC paper, now including additional data from the US census about per-state demographics. Our estimators show that the observations in the pre-treatment period lie within the bounds of misspecification error, and that the observations post-treatment lie outside of those bounds. This is evidence that our SC methods have uncovered a true effect.

Citation extraction

34
references
55
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distinct cited
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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, Alberto, Diamond, Alexis, Hainmueller, Jens (2010) Synthetic control methods for comparative case studies: Estimating the effect of California’s tobacco control program1.00083100%
2Shi, Claudia, Sridhar, Dhanya, Misra, Vishal, Blei, David (2022) On the Assumptions of Synthetic Control Methods self0.87492100%
3Ben-Michael, Eli, Feller, Avi, Rothstein, Jesse (2021) The augmented synthetic control method0.64422100%
4Ferman, Bruno, Pinto, Cristine (2021) Synthetic controls with imperfect pretreatment fit0.64422100%
5(2009) Optimal Transport: Old and New0.5112250%
6Abadie, Alberto, Gardeazabal, Javier (2003) The economic costs of conflict: A case study of the Basque Country0.51121100%
7Abadie, Alberto, Diamond, Alexis, Hainmueller, Jens (2015) Comparative politics and the synthetic control method0.51121100%
8Amjad, Muhammad, Shah, Devavrat, Shen, Dennis (2018) Robust synthetic control0.51121100%
9Abadie, Alberto, Imbens, Guido W (2011) Bias-corrected matching estimators for average treatment effects0.40511100%
10Abadie, Alberto (2021) A penalized synthetic control estimator for disaggregated data0.40511100%

Showing the top 10 of 34 scored citations.