A Sensitivity Analysis of the Surrogate Index Approach for Estimating Long-Term Treatment Effects
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917301987573760 |
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| author | Fan, Yanqin Manzanares, Carlos A. Park, Hyeonseok Qi, Yuan |
| author_facet | Fan, Yanqin Manzanares, Carlos A. Park, Hyeonseok Qi, Yuan |
| contents | This paper develops a sensitivity analysis of the surrogacy assumption for the surrogate index approach in Athey et al. [2025b]. We introduce "Weighted Surrogate Indices (WSIs)," the analog of the surrogate index under the surrogacy assumption. We show that under comparability, the ATE on WSI identifies the ATE on the long-term outcome when a copula of the treatment and the long-term outcome conditional on baseline covariates and surrogates is known. When the copula is unknown, we establish the identified set of the ATE on the long-term outcome. Furthermore, we construct debiased estimators of the ATE for any given copula and develop asymptotically valid inference in both point-identified and partially identified cases. Using data from a poverty alleviation program in Pakistan, we demonstrate the importance of sensitivity checks as well as the usefulness of our approach. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_00580 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Sensitivity Analysis of the Surrogate Index Approach for Estimating Long-Term Treatment Effects Fan, Yanqin Manzanares, Carlos A. Park, Hyeonseok Qi, Yuan Econometrics This paper develops a sensitivity analysis of the surrogacy assumption for the surrogate index approach in Athey et al. [2025b]. We introduce "Weighted Surrogate Indices (WSIs)," the analog of the surrogate index under the surrogacy assumption. We show that under comparability, the ATE on WSI identifies the ATE on the long-term outcome when a copula of the treatment and the long-term outcome conditional on baseline covariates and surrogates is known. When the copula is unknown, we establish the identified set of the ATE on the long-term outcome. Furthermore, we construct debiased estimators of the ATE for any given copula and develop asymptotically valid inference in both point-identified and partially identified cases. Using data from a poverty alleviation program in Pakistan, we demonstrate the importance of sensitivity checks as well as the usefulness of our approach. |
| title | A Sensitivity Analysis of the Surrogate Index Approach for Estimating Long-Term Treatment Effects |
| topic | Econometrics |
| url | https://arxiv.org/abs/2603.00580 |