Chengwang Liao, Zhentao Shi, Yapeng Zheng
arXiv 3 Aug 2025 · Econometrics
arXiv:2508.01793 · PDF · DOI · OpenAlex · Extracted main text
The synthetic control method (SCM) is widely used for constructing the counterfactual of a treated unit based on data from control units in a donor pool. Allowing the donor pool contains more control units than time periods, we propose a novel machine learning algorithm, named SCM-relaxation, for counterfactual prediction. Our relaxation approach minimizes an information-theoretic measure of the weights subject to a set of relaxed linear inequality constraints in addition to the simplex constraint. When the donor pool exhibits a group structure, SCM-relaxation approximates the equal weights within each group to diversify the prediction risk. Asymptotically, the proposed estimator achieves oracle performance in terms of out-of-sample prediction accuracy. We demonstrate our method by Monte Carlo simulations and by an empirical application that assesses the economic impact of Brexit on the United Kingdom's real GDP.
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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 | Shi, Z., L. Su, and T. Xie (2025) $_2$-Relaxation: With Applications to Forecast Combination and Portfolio Analysis self | 1.000 | 5 | 3 | 100% |
| 2 | Abadie, A (2021) Using Synthetic Controls: Feasibility, Data Requirements, and Methodological Aspects | 0.928 | 4 | 3 | 100% |
| 3 | Ferman, B (2021) On the Properties of the Synthetic Control Estimator with Many Periods and Many Controls | 0.928 | 4 | 3 | 100% |
| 4 | Ferman, B. and C. Pinto (2021) Synthetic Controls with Imperfect Pretreatment Fit | 0.843 | 3 | 3 | 100% |
| 5 | Abadie, A., A. Diamond, and J. Hainmueller (2010) Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California's Tobacco Control Program | 0.811 | 4 | 2 | 100% |
| 6 | Hainmueller, J (2012) Entropy Balancing for Causal Effects: A Multivariate Reweighting Method to Produce Balanced Samples in Observational Studies | 0.811 | 4 | 2 | 100% |
| 7 | Bühlmann, P. and S. van de Geer (2011) Statistics for High-Dimensional Data: Methods, Theory and Applications | 0.737 | 3 | 2 | 100% |
| 8 | Wainwright, M. J (2019) High-Dimensional Statistics: A Non-Asymptotic Viewpoint | 0.737 | 3 | 2 | 100% |
| 9 | Zheng, X. and S. X. Chen (2024) Dynamic Synthetic Control Method for Evaluating Treatment Effects in Auto-Regressive Processes | 0.737 | 3 | 2 | 100% |
| 10 | Abadie, A. and J. Gardeazabal (2003) The Economic Costs of Conflict: A Case Study of the Basque Country | 0.644 | 2 | 2 | 100% |
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