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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.01793 |
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| _version_ | 1866914573110476800 |
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| author | Liao, Chengwang Shi, Zhentao Zheng, Yapeng |
| author_facet | Liao, Chengwang Shi, Zhentao Zheng, Yapeng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01793 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Relaxation Approach to Synthetic Control Liao, Chengwang Shi, Zhentao Zheng, Yapeng Econometrics 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. |
| title | A Relaxation Approach to Synthetic Control |
| topic | Econometrics |
| url | https://arxiv.org/abs/2508.01793 |