Synthetic controls

Joaquim Estopinan | June 23, 2025

Table of Contents

1. Description & principle
2. Reference articles
3. Packages
4. Assessment table

Description & principle

The synthetic control (SC) method originates from the early 2000s, with its first introduction in the influential Abadie & Gardeazabal (2003) article. It consists in combining a selection of control sites to best mimick the treatment site’s counterfactual, based on the pre-intervention similarity of their respective outcome and covariates. It is an effect estimation method shifting the causal sufficiency assumption (no unobserved confounders) to the good pre-intervention fit condition, still assuming no time-varying unobserved confoundinfing after the intervention.

Major variants

The success of this method has also led to numerous variants. We can cite among others:

• Robust SC from Amjad, Shah, & Shen (2018): Adds de-noising, uncertainty estimation and handles missing data
• Augmented SC from Ben-Michael, Feller, & Rothstein (2020) (2022): Relaxes constraints on the synthetic control combination to improve pre-treatment fit and allows staggered adoption of treatment between various units
• Sparse SC from Quistorff, Goldman, & Thorpe (2021): Helps pre-treatment variables selection and add regularization to meet big data context needs
• Penalized SC from Abadie (2021): An adaptation of the SC method to deal with disaggregated data gathering varied treated units
• Finally, a number of recent developement merge the SC method with other approaches:
  • Generalized SC relaxes the parallel trend assumption and unifies the SC method with linear fixed effects models (Xu, 2016)
  • Synthetic Diff-in-diffs combines SCs with the difference-in-differences estimator (Arkhangelsky et al., 2021)
  • Chernozhukov, Wüthrich, & Zhu (2021) exploit conformal prediction and structural breaks in conjunction with SCs
  • Imai, Kim, & Wang (2023) developped a flexible estimation procedure combining matching and SCs ideas with diff-and-diffs.

Further online resources

• A pedagocial blog decomposing the method: 15 - Synthetic Control
• On the covariate selection: Botosaru & Ferman (2019)
• Discussion on the violation of the parallel trends assumption and its consequences: Cross Validated

Reference articles

Method

An updated review paper positioning the method by its original author: Abadie & L’Hour (2021)

Research applications

With RS data in Ecology / Biodiversity

• Fick et al. (2021)
• Sharma et al. (2023)
• Rana & Miller (2019)
• West et al. (2020)

Without RS data (Ecology domain)

• Lépissier & Mildenberger (2021)
• Nakanishi et al. (2022)
• Kaiser, Dee, & Resasco (2025)

Packages

Python

• pysyncon

R

• Synth
• augsynth
• tidysynth
• microsynth
• gsynth
• SparseSC

Assessment table

Category	Criteria	Assessment
Outcome	Objective	automatically filled
	Estimand
	Validity
Data compatibility	Type
	Required TS length
	Handles few samples
	Handles huge datasets (n)
	Handles missing data
	RS-data proven
Assumptions	Functional form
	No unobserved confounders
	No interference
	Well-defined treatments
	Common support (positivity)
	Causal Markov Condition
	Faithfulness
	IDD
	Model specific assumption
Model properties	Requires explicit processes
	Exposure type
	Number of variables
	Handles lag effects
	Propagates uncertainty
	Parametric nature
Packages	Language
	Usage

References

1. Abadie, A., & Gardeazabal, J. (2003). The Economic Costs of Conflict: A Case Study of the Basque Country. American Economic Review, 93, 113–132. https://doi.org/10.1257/000282803321455188
2. Amjad, M., Shah, D., & Shen, D. (2018). Robust Synthetic Control. Journal of Machine Learning Research, 19, 1–51. http://jmlr.org/papers/v19/17-777.html
3. Ben-Michael, E., Feller, A., & Rothstein, J. (2020). The Augmented Synthetic Control Method. arXiv. http://arxiv.org/abs/1811.04170
4. Ben-Michael, E., Feller, A., & Rothstein, J. (2022). Synthetic Controls with Staggered Adoption. Journal of the Royal Statistical Society Series B: Statistical Methodology, 84, 351–381. https://doi.org/10.1111/rssb.12448
5. Quistorff, B., Goldman, M., & Thorpe, J. (2021). Sparse Synthetic Controls: Unit-Level Counterfactuals from High-Dimensional Data.
6. Abadie, A. (2021). Using Synthetic Controls: Feasibility, Data Requirements, and Methodological Aspects. Journal of Economic Literature, 59, 391–425. https://doi.org/10.1257/jel.20191450
7. Xu, Y. (2016). Generalized Synthetic Control Method: Causal Inference with Interactive Fixed Effects Models [SSRN Scholarly Paper]. https://doi.org/10.2139/ssrn.2584200
8. Arkhangelsky, D., Athey, S., Hirshberg, D. A., Imbens, G. W., & Wager, S. (2021). Synthetic Difference-in-Differences. The American Economic Review, 111, 4088–4118. https://www.jstor.org/stable/27086719
9. Chernozhukov, V., Wüthrich, K., & Zhu, Y. (2021). An Exact and Robust Conformal Inference Method for Counterfactual and Synthetic Controls. Journal of the American Statistical Association, 116, 1849–1864. https://doi.org/10.1080/01621459.2021.1920957
10. Imai, K., Kim, I. S., & Wang, E. H. (2023). Matching Methods for Causal Inference with Time-Series Cross-Sectional Data. American Journal of Political Science, 67, 587–605. https://doi.org/10.1111/ajps.12685
11. Botosaru, I., & Ferman, B. (2019). On the Role of Covariates in the Synthetic Control Method. The Econometrics Journal, 22, 117–130. https://doi.org/10.1093/ectj/utz001
12. Abadie, A., & L’Hour, J. (2021). A Penalized Synthetic Control Estimator for Disaggregated Data. Journal of the American Statistical Association, 116, 1817–1834. https://doi.org/10.1080/01621459.2021.1971535
13. Fick, S. E., Nauman, T. W., Brungard, C. C., & Duniway, M. C. (2021). Evaluating Natural Experiments in Ecology: Using Synthetic Controls in Assessments of Remotely Sensed Land Treatments. Ecological Applications, 31, e02264. https://doi.org/10.1002/eap.2264
14. Sharma, R., Jones, S., Robinson, D., & Gordon, A. (2023). Evaluating the Impact of Private Land Conservation with Synthetic Control Design. Conservation Biology, 37, e14150. https://doi.org/10.1111/cobi.14150
15. Rana, P., & Miller, D. C. (2019). Explaining Long-Term Outcome Trajectories in Social–Ecological Systems. PLOS ONE, 14, e0215230. https://doi.org/10.1371/journal.pone.0215230
16. West, T. A. P., Börner, J., Sills, E. O., & Kontoleon, A. (2020). Overstated Carbon Emission Reductions from Voluntary REDD+ Projects in the Brazilian Amazon. Proceedings of the National Academy of Sciences, 117, 24188–24194. https://doi.org/10.1073/pnas.2004334117
17. Lépissier, A., & Mildenberger, M. (2021). Unilateral Climate Policies Can Substantially Reduce National Carbon Pollution. Climatic Change, 166, 31. https://doi.org/10.1007/s10584-021-03111-2
18. Nakanishi, K., Yokomizo, H., Fukaya, K., Kadoya, T., Matsuzaki, S.-ichiro S., Nishihiro, J., Kohzu, A., & Hayashi, T. I. (2022). Inferring Causal Impacts of Extreme Water-Level Drawdowns on Lake Water Clarity Using Long-Term Monitoring Data. Science of The Total Environment, 838, 156088. https://doi.org/10.1016/j.scitotenv.2022.156088
19. Kaiser, A., Dee, L., & Resasco, J. (2025). Synthetic Control Methods Enable Stronger Causal Inference Using Participatory Science Data in Cities. In Review. https://doi.org/10.21203/rs.3.rs-6213868/v1