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

2026-02-28

AI Summary

Existing surrogate index methods for estimating long-term treatment effects are highly sensitive to surrogate assumptions yet lack systematic sensitivity analyses. This work proposes a Weighted Surrogate Index (WSI) framework that achieves point identification of the long-term average treatment effect when the copula is known, and constructs a partial identification set when the copula is unknown, accompanied by debiased estimation and asymptotically efficient inference procedures. The study establishes, for the first time, a unified sensitivity analysis framework for surrogate index methods, combining theoretical rigor with practical robustness. Empirical analysis using data from a poverty alleviation program in Pakistan demonstrates the necessity of sensitivity analysis and validates the effectiveness and reliability of the proposed approach.

Technology Category

• Reasoning under Uncertainty: Causality
• Multiagent Systems: Mechanism Design
• Search and Optimization: Evaluation and Analysis

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• Economics, Online Markets and Human Computation: Sustainability of Web economics

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.

Problem

• surrogate index
• sensitivity analysis
• long-term treatment effects
• copula
• average treatment effect

Innovation

• Weighted Surrogate Indices
• Sensitivity Analysis
• Copula
• Average Treatment Effect
• Partial Identification