Lu Zhang, Xiaomeng Zhang, Xinyu Zhang
arXiv 2 May 2024 · Econometrics
arXiv:2405.00953 · PDF · DOI · OpenAlex · Extracted main text
As an alternative to synthetic control, the distributional Synthetic Control (DSC) proposed by Gunsilius (2023) provides estimates for quantile treatment effect and thus enabling researchers to comprehensively understand the impact of interventions in causal inference. But the asymptotic properties of DSC have not been built. In this paper, we first establish the DSC estimator's asymptotic optimality in the essence that the treatment effect estimator given by DSC achieves the lowest possible squared prediction error among all potential estimators from averaging quantiles of control units. We then establish the convergence rate of the DSC weights. A significant aspect of our research is that we find the DSC synthesis forms an optimal weighted average, particularly in situations where it is impractical to perfectly fit the treated unit's quantiles through the weighted average of the control units' quantiles. Simulation results verify our theoretical insights.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Gunsilius, Florian F (2023) Distributional synthetic controls | 1.000 | 14 | 3 | 100% |
| 2 | Abadie, Alberto and Diamond, Alexis and Hainmueller, Jens (2010) Synthetic control methods for comparative case studies: Estimating the effect of California's tobacco control program | 1.000 | 5 | 3 | 100% |
| 3 | Abadie, Alberto and Gardeazabal, Javier (2003) The economic costs of conflict: A case study of the Basque Country | 0.737 | 3 | 2 | 100% |
| 4 | Zhang, Xiaomeng and Wang, Wendun and Zhang, Xinyu (2022) Asymptotic Properties of the Synthetic Control Method self | 0.737 | 3 | 2 | 100% |
| 5 | Abadie, Alberto (2021) Using synthetic controls: Feasibility, data requirements, and methodological aspects | 0.511 | 2 | 1 | 100% |
| 6 | Card, David and Krueger, Alan B (1994) Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania | 0.511 | 2 | 1 | 100% |
| 7 | Dube, Arindrajit (2019) Minimum Wages and the Distribution of Family Incomes | 0.511 | 2 | 1 | 100% |
| 8 | Ferman, Bruno (2021) On the properties of the synthetic control estimator with many periods and many controls | 0.511 | 2 | 1 | 100% |
| 9 | Neumark, David and Wascher, William (2000) Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania: Comment | 0.511 | 2 | 1 | 100% |
| 10 | Arkhangelsky, Dmitry and Athey, Susan and Hirshberg, David A and Imb… (2021) Synthetic difference-in-differences | 0.405 | 1 | 1 | 100% |
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| 1 | Recovering Counterfactual Distributions via Wasserstein GANs | 0.405 | 1 | 1 |