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A Design-Based Perspective on Synthetic Control Methods

Lea Bottmer, Guido Imbens, Jann Spiess, Merrill Warnick

arXiv 23 Jan 2021 · Econometrics · publishedJournal of Business and Economic Statistics (2023) · 10 citations (OpenAlex)

arXiv:2101.09398 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Since their introduction in Abadie and Gardeazabal (2003), Synthetic Control (SC) methods have quickly become one of the leading methods for estimating causal effects in observational studies in settings with panel data. Formal discussions often motivate SC methods by the assumption that the potential outcomes were generated by a factor model. Here we study SC methods from a design-based perspective, assuming a model for the selection of the treated unit(s) and period(s). We show that the standard SC estimator is generally biased under random assignment. We propose a Modified Unbiased Synthetic Control (MUSC) estimator that guarantees unbiasedness under random assignment and derive its exact, randomization-based, finite-sample variance. We also propose an unbiased estimator for this variance. We document in settings with real data that under random assignment, SC-type estimators can have root mean-squared errors that are substantially lower than that of other common estimators. We show that such an improvement is weakly guaranteed if the treated period is similar to the other periods, for example, if the treated period was randomly selected. While our results only directly apply in settings where treatment is assigned randomly, we believe that they can complement model-based approaches even for observational studies.

Citation extraction

43
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distinct cited
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appendix boundary found by appendix_titled_section at “SUPPLEMENTARY MATERIAL” · 68% of the source is main text. Read the extracted text to check this.

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
1Doudchenko, N. and Imbens, G. W (2016) Balancing, regression, difference-in-differences and synthetic control methods: A synthesis self1.00053100%
2Imbens, G. W. and Rubin, D. B (2015) Causal Inference in Statistics, Social, and Biomedical Sciences self1.00053100%
3Abadie, A., Diamond, A., and Hainmueller, J (2010) Synthetic control methods for comparative case studies: Estimating the effect of california's tobacco control program0.97916594%
4Abadie, A. and Gardeazabal, J (2003) The economic costs of conflict: A case study of the basque country0.92843100%
5Firpo, S. and Possebom, V (2018) Synthetic control method: Inference, sensitivity analysis and confidence sets0.87452100%
6Arkhangelsky, D., Athey, S., Hirshberg, D. A., Imbens, G. W., and Wa… (2019) Synthetic difference in differences self0.84333100%
7Chen, J (2022) Synthetic control as online linear regression0.84333100%
8Rambachan, A. and Roth, J (2020) Design-Based Uncertainty for Quasi-Experiments0.64422100%
9Abadie, A., Athey, S., Imbens, G. W., and Wooldridge, J. M (2020) Sampling-based versus design-based uncertainty in regression analysis self0.64422100%
10Athey, S., Bayati, M., Doudchenko, N., Imbens, G., and Khosravi, K (2021) Matrix completion methods for causal panel data models self0.64422100%

Showing the top 10 of 43 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
1Synthetic Control As Online Linear Regression1.00054
2Inference for Synthetic Controls via Refined Placebo Tests0.81142
3Same Root Different Leaves: Time Series and Cross-Sectional Methods in Panel Data0.69361
4Synthetic Difference in Differences0.40511
5Debiasing and $t$-tests for synthetic control inference on average causal effects0.40511
6Synthetic learner: Model-Free Inference on Treatments over Time0.40511
7Direct and spillover effects of a new tramway line on the commercial vitality of peripheral streets. A synthetic-control approach0.40511
8Synthetic Interventions0.40511
92108.021960.40511
10On the Assumptions of Synthetic Control Methods0.40511