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A Sensitivity Analysis of the Surrogate Index Approach for Estimating Long-Term Treatment Effects

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  • Yanqin Fan
  • Carlos A. Manzanares
  • Hyeonseok Park
  • Yuan Qi

Abstract

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.

Suggested Citation

  • Yanqin Fan & Carlos A. Manzanares & Hyeonseok Park & Yuan Qi, 2026. "A Sensitivity Analysis of the Surrogate Index Approach for Estimating Long-Term Treatment Effects," Papers 2603.00580, arXiv.org.
    • Handle: RePEc:arx:papers:2603.00580
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    References listed on IDEAS

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    2. Chen, Jiafeng & Ritzwoller, David M., 2023. "Semiparametric estimation of long-term treatment effects," Journal of Econometrics, Elsevier, vol. 237(2).
    3. James J. Heckman & Jora Stixrud & Sergio Urzua, 2006. "The Effects of Cognitive and Noncognitive Abilities on Labor Market Outcomes and Social Behavior," Journal of Labor Economics, University of Chicago Press, vol. 24(3), pages 411-482, July.
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    6. Yechan Park & Yuya Sasaki, 2024. "The Informativeness of Combined Experimental and Observational Data under Dynamic Selection," Papers 2403.16177, arXiv.org.
    7. Susan Athey & Raj Chetty & Guido Imbens, 2025. "The Experimental Selection Correction Estimator: Using Experiments to Remove Biases in Observational Estimates," NBER Working Papers 33817, National Bureau of Economic Research, Inc.
    8. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
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