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

TL;DR

This paper introduces the Proximal Surrogate Index, a method for estimating long-term treatment effects in the presence of unobserved confounding by using proxy variables, combining experimental and observational data.

Contribution

It provides novel identification results and robust estimation procedures leveraging proxies for unobserved confounders, enabling accurate long-term effect estimation.

Findings

Successfully applied to Job Corps data, recovering experimental benchmarks.

Outperforms standard surrogate methods under unobserved confounding.

Provides a practical approach for long-term causal inference with proxies.

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.