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
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.
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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Doudchenko, N. and Imbens, G. W (2016) Balancing, regression, difference-in-differences and synthetic control methods: A synthesis self | 1.000 | 5 | 3 | 100% |
| 2 | Imbens, G. W. and Rubin, D. B (2015) Causal Inference in Statistics, Social, and Biomedical Sciences self | 1.000 | 5 | 3 | 100% |
| 3 | Abadie, A., Diamond, A., and Hainmueller, J (2010) Synthetic control methods for comparative case studies: Estimating the effect of california's tobacco control program | 0.979 | 16 | 5 | 94% |
| 4 | Abadie, A. and Gardeazabal, J (2003) The economic costs of conflict: A case study of the basque country | 0.928 | 4 | 3 | 100% |
| 5 | Firpo, S. and Possebom, V (2018) Synthetic control method: Inference, sensitivity analysis and confidence sets | 0.874 | 5 | 2 | 100% |
| 6 | Arkhangelsky, D., Athey, S., Hirshberg, D. A., Imbens, G. W., and Wa… (2019) Synthetic difference in differences self | 0.843 | 3 | 3 | 100% |
| 7 | Chen, J (2022) Synthetic control as online linear regression | 0.843 | 3 | 3 | 100% |
| 8 | Rambachan, A. and Roth, J (2020) Design-Based Uncertainty for Quasi-Experiments | 0.644 | 2 | 2 | 100% |
| 9 | Abadie, A., Athey, S., Imbens, G. W., and Wooldridge, J. M (2020) Sampling-based versus design-based uncertainty in regression analysis self | 0.644 | 2 | 2 | 100% |
| 10 | Athey, S., Bayati, M., Doudchenko, N., Imbens, G., and Khosravi, K (2021) Matrix completion methods for causal panel data models self | 0.644 | 2 | 2 | 100% |
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