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Recovering Counterfactual Distributions via Wasserstein GANs

Xinran Liu

arXiv 24 Jan 2026 · Econometrics

arXiv:2601.17296 · PDF · DOI · OpenAlex · Extracted main text

Abstract

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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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Gunsilius, F. F (2023) Distributional synthetic controls1.00053100%
2Abadie, A., Diamond, A., and Hainmueller, J (2010) Synthetic control methods for comparative case studies: Estimating the effect of california’s tobacco control program0.92843100%
3Athey, S., Bayati, M., Doudchenko, N., Imbens, G., and Khosravi, K (2021) Matrix completion methods for causal panel data models0.81142100%
4Ben-Michael, E., Feller, A., and Rothstein, J (2021) The augmented synthetic control method0.64422100%
5Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C… (2018) Double/debiased machine learning for treatment and structural parameters0.64422100%
6Firpo, S., Fortin, N. M., and Lemieux, T (2009) Unconditional quantile regressions0.64422100%
7Galichon, A (2016) Optimal transport methods in economics0.64422100%
8Gulrajani, I., Ahmed, F., Arjovsky, M., Dumoulin, V., and Courville,… (2017) Improved training of wasserstein gans0.51121100%
9Abadie, A. and Gardeazabal, J (2003) The economic costs of conflict: A case study of the basque country0.40511100%
10Abadie, A. and L’hour, J (2021) A penalized synthetic control estimator for disaggregated data0.40511100%

Showing the top 10 of 25 scored citations.