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This paper introduces Graph-Regularized Synthetic Control (Graph-SC), a method that uses graph Laplacian penalties to stabilize counterfactual estimation when donor pools are large, correlated, or redundant. By encoding similarity among donor trajectories, the approach ensures coherent weights over structurally related units while maintaining interpretability and offering theoretical convergence guarantees. The results demonstrate that this regularization is particularly effective for selecting stable counterfactuals in scenarios where classical methods yield unstable solutions due to near-equivalent donor options.
Graph-Regularized Synthetic Control for Stable Counterfactual Estimation under Donor Redundancy
arXiv:2610.24113v1 Announce Type: new Abstract: Synthetic control methods estimate counterfactual outcomes by weighting untreated donor units to match a treated unit before treatment. In recent applications, however, the donor pool can be large, highly correlated, and short in pre-treatment history, yielding many near-equivalent solutions with unstable and difficult-to-interpret donor weights. We propose Graph-Regularized Synthetic Control (Graph-SC), a convex estimator that augments the classical pre-treatment matching objective with a graph Laplacian penalty. The graph encodes similarity among donor trajectories, encouraging coherent weights over structurally related donors while preserving the transparency of synthetic controls. We provide theoretical results characterizing the bias-variance tradeoff induced by graph regularization and establish efficient convergence guarantees with an accelerated proximal gradient method. Across a controlled simulation under donor redundancy, the California Proposition 99 benchmark, and observational counterfactual analyses on the Waymo Open Motion Dataset, Graph-SC improves weight stability, reduces sensitivity to redundant donor pools, and maintains competitive pre- and post-treatment accuracy relative to classical and regularized synthetic control baselines. Our results suggest that graph regularization is most valuable not as a universal accuracy booster, but as a principled mechanism for selecting stable and interpretable counterfactuals from near-equivalent synthetic controls with comparable pre-treatment fit.
Abstract:Synthetic control methods estimate counterfactual outcomes by weighting untreated donor units to match a treated unit before treatment. In recent applications, however, the donor pool can be large, highly correlated, and short in pre-treatment history, yielding many near-equivalent solutions with unstable and difficult-to-interpret donor weights. We propose Graph-Regularized Synthetic Control (Graph-SC), a convex estimator that augments the classical pre-treatment matching objective with a graph Laplacian penalty. The graph encodes similarity among donor trajectories, encouraging coherent weights over structurally related donors while preserving the transparency of synthetic controls. We provide theoretical results characterizing the bias-variance tradeoff induced by graph regularization and establish efficient convergence guarantees with an accelerated proximal gradient method. Across a controlled simulation under donor redundancy, the California Proposition 99 benchmark, and observational counterfactual analyses on the Waymo Open Motion Dataset, Graph-SC improves weight stability, reduces sensitivity to redundant donor pools, and maintains competitive pre- and post-treatment accuracy relative to classical and regularized synthetic control baselines. Our results suggest that graph regularization is most valuable not as a universal accuracy booster, but as a principled mechanism for selecting stable and interpretable counterfactuals from near-equivalent synthetic controls with comparable pre-treatment fit.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Econometrics (econ.EM); Methodology (stat.ME); Machine Learning (stat.ML)
arXiv:2610.24113 [cs.LG]
(or arXiv:2610.24113v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.24113 Focus to learn more arXiv-issued DOI via DataCite
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