The Proximal Surrogate Index: Long-Term Treatment Effects under Unobserved Confounding

2026-01-25

AI Summary

This study addresses the challenging problem of identifying and estimating long-term treatment effects in the presence of unobserved confounding. By integrating experimental data with only short-term outcomes and observational data containing long-term outcomes but unknown treatment assignment, the authors leverage proxy variables to account for unmeasured confounders and construct a proximal proxy index that enables nonparametric identification of long-term causal effects. The proposed approach synthesizes proximal causal inference, multiply robust estimation, and semiparametric inference techniques, establishing—for the first time—the nonparametric identifiability of long-term treatment effects under unobserved confounding. In an empirical application to the Job Corps data, the method successfully replicates benchmark experimental findings and substantially outperforms conventional proxy index approaches that are susceptible to confounding bias.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI
• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We study the identification and estimation of long-term treatment effects under unobserved confounding by combining an experimental sample, where the long-term outcome is missing, with an observational sample, where the treatment assignment is unobserved. While standard surrogate index methods fail when unobserved confounders exist, we establish novel identification results by leveraging proxy variables for the unobserved confounders. We further develop multiply robust estimation and inference procedures based on these results. Applying our method to the Job Corps program, we demonstrate its ability to recover experimental benchmarks even when unobserved confounders bias standard surrogate index estimates.

Problem

• long-term treatment effects
• unobserved confounding
• surrogate index
• proxy variables
• causal inference

Innovation

• proximal surrogate index
• unobserved confounding
• proxy variables
• long-term treatment effects
• multiply robust estimation