arXiv 24 Jan 2026 · Econometrics
arXiv:2601.17296 · PDF · DOI · OpenAlex · Extracted main text
Standard Distributional Synthetic Controls (DSC) estimate counterfactual distributions by minimizing the Euclidean $L_2$ distance between quantile functions. We demonstrate that this geometric reliance renders estimators fragile: they lack informative gradients under support mismatch and produce structural artifacts when outcomes are multimodal. This paper proposes a robust estimator grounded in Optimal Transport (OT). We construct the synthetic control by minimizing the Wasserstein-1 distance between probability measures, implemented via a Wasserstein Generative Adversarial Network (WGAN). We establish the formal point identification of synthetic weights under an affine independence condition on the donor pool. Monte Carlo simulations confirm that while standard estimators exhibit catastrophic variance explosions under heavy-tailed contamination and support mismatch, our WGAN-based approach remains consistent and stable. Furthermore, we show that our measure-based method correctly recovers complex bimodal mixtures where traditional quantile averaging fails structurally.
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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 | Gunsilius, F. F (2023) Distributional synthetic controls | 1.000 | 5 | 3 | 100% |
| 2 | Abadie, A., Diamond, A., and Hainmueller, J (2010) Synthetic control methods for comparative case studies: Estimating the effect of california’s tobacco control program | 0.928 | 4 | 3 | 100% |
| 3 | Athey, S., Bayati, M., Doudchenko, N., Imbens, G., and Khosravi, K (2021) Matrix completion methods for causal panel data models | 0.811 | 4 | 2 | 100% |
| 4 | Ben-Michael, E., Feller, A., and Rothstein, J (2021) The augmented synthetic control method | 0.644 | 2 | 2 | 100% |
| 5 | Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C… (2018) Double/debiased machine learning for treatment and structural parameters | 0.644 | 2 | 2 | 100% |
| 6 | Firpo, S., Fortin, N. M., and Lemieux, T (2009) Unconditional quantile regressions | 0.644 | 2 | 2 | 100% |
| 7 | Galichon, A (2016) Optimal transport methods in economics | 0.644 | 2 | 2 | 100% |
| 8 | Gulrajani, I., Ahmed, F., Arjovsky, M., Dumoulin, V., and Courville,… (2017) Improved training of wasserstein gans | 0.511 | 2 | 1 | 100% |
| 9 | Abadie, A. and Gardeazabal, J (2003) The economic costs of conflict: A case study of the basque country | 0.405 | 1 | 1 | 100% |
| 10 | Abadie, A. and L’hour, J (2021) A penalized synthetic control estimator for disaggregated data | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 25 scored citations.