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

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.