arXiv 2 Dec 2023 · Econometrics · publishedJournal of Econometrics (2024) · 2 citations (OpenAlex)
arXiv:2312.01209 · PDF · DOI · OpenAlex · Extracted main text
A common approach to constructing a Synthetic Control unit is to fit on the outcome variable and covariates in pre-treatment time periods, but it has been shown by Ferman and Pinto (2019) that this approach does not provide asymptotic unbiasedness when the fit is imperfect and the number of controls is fixed. Many related panel methods have a similar limitation when the number of units is fixed. I introduce and evaluate a new method in which the Synthetic Control is constructed using a General Method of Moments approach where units not being included in the Synthetic Control are used as instruments. I show that a Synthetic Control Estimator of this form will be asymptotically unbiased as the number of pre-treatment time periods goes to infinity, even when pre-treatment fit is imperfect and the number of units is fixed. Furthermore, if both the number of pre-treatment and post-treatment time periods go to infinity, then averages of treatment effects can be consistently estimated. I conduct simulations and an empirical application to compare the performance of this method with existing approaches in the literature.
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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 | Abadie, Diamond, and Hainmueller (2010) Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California's Tobacco Control Program | 1.000 | 11 | 5 | 100% |
| Powell2021 | unmatched citation key Powell2021 | 1.000 | 11 | 3 | 100% |
| 3 | Ferman and Pinto (2021) Synthetic controls with imperfect pretreatment fit | 1.000 | 6 | 4 | 100% |
| 4 | Abadie, Diamond, and Hainmueller (2015) Comparative Politics and the Synthetic Control Method | 1.000 | 6 | 3 | 100% |
| 5 | Ferman (2021) On the Properties of the Synthetic Control Estimator with Many Periods and Many Controls | 0.961 | 9 | 4 | 89% |
| 6 | Andrews and Lu (2001) Consistent model and moment selection procedures for GMM estimation with application to dynamic panel data models | 0.894 | 14 | 3 | 71% |
| 7 | Arkhangelsky, Athey, Hirshberg, Imbens, and Wager (2021) Synthetic Difference-in-Differences | 0.874 | 6 | 4 | 67% |
| 8 | Chernozhukov, Wüthrich, and Zhu (2021) An Exact and Robust Conformal Inference Method for Counterfactual and Synthetic Controls | 0.874 | 6 | 2 | 100% |
| 9 | Li (2020) Statistical Inference for Average Treatment Effects Estimated by Synthetic Control Methods | 0.855 | 8 | 4 | 62% |
| 10 | Andrews (2003) End-of-Sample Instability Tests | 0.811 | 4 | 2 | 100% |
Showing the top 10 of 59 scored citations. 1 of these could not be matched to a bibliography entry, so only the citation key is shown.
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