Generalized Synthetic Control Method: Causal Inference with Interactive Fixed Effects Models
Open accessAbstract
Difference-in-differences (DID) is commonly used for causal inference in time-series cross-sectional data. It requires the assumption that the average outcomes of treated and control units would have followed parallel paths in the absence of treatment. In this paper, we propose a method that not only relaxes this often-violated assumption, but also unifies the synthetic control method (Abadie, Diamond, and Hainmueller 2010) with linear fixed effects models under a simple framework, of which DID is a special case. It imputes counterfactuals for each treated unit using control group information based on a linear interactive fixed effects model that incorporates unit-specific intercepts interacted with time-varying coefficients. This method has several advantages. First, it allows the treatment to be correlated with unobserved unit and time heterogeneities under reasonable modeling assumptions. Second, it generalizes the synthetic control method to the case of multiple treated units and variable treatment periods, and improves efficiency and interpretability. Third, with a built-in cross-validation procedure, it avoids specification searches and thus is easy to implement. An empirical example of Election Day Registration and voter turnout in the United States is provided.
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The IFE estimator relaxes the assumption of parallel trends required by alternative models such as difference-in-differences.
“By conditioning on the factors and factor loadings, the IFE estimator relaxes the assumption of parallel trends required by alternative models such as difference-in-differences (19).”
From Procedural justice training reduces police use of force and complaints against officers (2020) · cites this paper as [19]
The estimated effects of the STAR program are similar when based on generalized synthetic control and comparative interrupted time series designs that accommodate preexisting trends.
“Second, the estimated effects of the STAR program are also similar when based on generalized synthetic control design (45) and comparative interrupted time series design (46) that explicitly accommodate the presence of preexisting trends across treatment and comparison precincts (see table S7 for results and Supplementary Text for details on these procedures).”
From A community response approach to mental health and substance abuse crises reduced crime (2022) · cites this paper as [45]
The results remain consistent when utilizing the generalized synthetic control method and in the presence of substantial measurement error.
“Our results remain consistent even when utilizing GSCM and in the presence of substantial measurement error.”
From Generative artificial intelligence, human creativity, and art (2024) · cites this paper as [12]
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- Authors
- Xu, Y.
- Affiliations
- University of California San Diego (US)
- Corresponding author
- Xu, Yiqing
- ORCID
- Xu, Yiqing
- Venue
- Political Analysis
- Publisher
- Cambridge University Press (CUP)
- Published
- 2017-01
- Volume
- 25
- Issue
- 1
- Pages
- 57-76
- ISSN
- 1047-1987 (ISSN-L)
- 1476-4989
- OpenAlex
- W3121705696
- Cited by
- 938
- References
- 61
- Citations by year
- 2026: 119 · 2025: 140 · 2024: 127 · 2023: 119 · 2022: 108 · 2021: 155 · 2020: 88 · 2019: 47 · 2018: 15 · 2017: 12 · 2016: 4 · 2015: 3 · 2013: 1
- FWCI
- 30.81
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Political Analysis (publishedVersion)
- SSRN Electronic Journal (acceptedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Funders
- Yale University
- University of Cambridge
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Spatial and Panel Data Analysis
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Keywords
- synthetic control method, difference-in-differences, causal inference, parallel trends assumption, time-varying parameters, cross-validation, election day registration, voter turnout
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