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

TL;DR

This paper introduces a sensitivity analysis framework for the surrogate index approach to estimate long-term treatment effects, accounting for unknown dependencies and providing valid inference methods.

Contribution

It develops Weighted Surrogate Indices (WSIs), establishes identification under known and unknown copulas, and offers debiased estimators with asymptotic inference for long-term effect estimation.

Findings

Sensitivity analysis highlights importance of copula assumptions.

Debiased estimators perform well in simulations.

Application to Pakistani program data demonstrates practical utility.

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.