Xiaomeng Zhang, Wendun Wang, Xinyu Zhang
arXiv 22 Nov 2022 · Econometrics · 1 citations (OpenAlex)
arXiv:2211.12095 · PDF · DOI · OpenAlex · Extracted main text
This paper provides new insights into the asymptotic properties of the synthetic control method (SCM). We show that the synthetic control (SC) weight converges to a limiting weight that minimizes the mean squared prediction risk of the treatment-effect estimator when the number of pretreatment periods goes to infinity, and we also quantify the rate of convergence. Observing the link between the SCM and model averaging, we further establish the asymptotic optimality of the SC estimator under imperfect pretreatment fit, in the sense that it achieves the lowest possible squared prediction error among all possible treatment effect estimators that are based on an average of control units, such as matching, inverse probability weighting and difference-in-differences. The asymptotic optimality holds regardless of whether the number of control units is fixed or divergent. Thus, our results provide justifications for the SCM in a wide range of applications. The theoretical results are verified via simulations.
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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 | B. Ferman and C. Pinto (2021) Synthetic controls with imperfect pretreatment fit | 1.000 | 27 | 3 | 100% |
| 2 | I. Botosaru and B. Ferman (2019) On the role of covariates in the synthetic control method | 1.000 | 8 | 3 | 100% |
| 3 | A. Abadie, A. Diamond, and J. Hainmueller (2010) Synthetic control methods for comparative case studies: Estimating the effect of California's tobacco control program | 1.000 | 7 | 3 | 100% |
| 4 | N. Doudchenko and G. W. Imbens (2016) Balancing, regression, difference-in-differences and synthetic control methods: A synthesis | 1.000 | 6 | 4 | 100% |
| 5 | B. Ferman (2021) On the properties of the synthetic control estimator with many periods and many controls | 0.961 | 27 | 5 | 89% |
| 6 | J. Chen (2022) Synthetic control as online linear regression | 0.874 | 7 | 2 | 100% |
| 7 | C. Hsiao and Q. Zhou (2019) Panel parametric, semiparametric, and nonparametric construction of counterfactuals | 0.843 | 3 | 3 | 100% |
| 8 | L. Bottmer, G. W. Imbens, J. Spiess, and M. J. Warnick (2021) A design-based perspective on synthetic control methods | 0.737 | 3 | 2 | 100% |
| 9 | X. Zhang (2021) A new study on asymptotic optimality of least squares model averaging | 0.737 | 3 | 2 | 100% |
| 10 | Y. Xu (2017) Generalized synthetic control method: Causal inference with interactive fixed effects models | 0.693 | 5 | 1 | 100% |
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