Proximal Causal Inference for Hidden Outcomes

2026-05-10

AI Summary

This study addresses the challenge of identifying and estimating causal effects when the outcome variable is unobserved. The authors propose a novel nonparametric approach leveraging proxy variables, which reconstructs the latent outcome distribution through an eigenvalue–eigenvector decomposition. This method achieves full nonparametric identification of the complete data distribution under hidden outcomes without requiring strong assumptions such as unbiased proxies or partial observability—conditions commonly imposed in existing literature. Building on influence function theory, the authors further develop an estimator that simultaneously attains multiple robustness and high statistical efficiency. Simulation studies demonstrate that the proposed method exhibits excellent estimation accuracy and robustness across a variety of data-generating settings.

Abstract

Methods that rely on proxies, without imposing strong parametric structure, are increasingly used to deal with unobserved variables in causal inference. One influential line of this work reconstructs latent distributions used to identify the target functional by exploiting eigenvalue eigenvector structure. Within this framework, we first establish identification of the full data law in the presence of hidden outcomes, and then develop influence function based estimators for causal effects. To the best of our knowledge, this is the first work to develop influence function based estimators in this setting without relying on unbiased proxy measurements or partial observation, while achieving multiple robustness and desirable efficiency properties. We demonstrate the performance of our approach through simulation studies.

Problem

• proximal causal inference
• hidden outcomes
• unobserved variables
• causal effect estimation
• proxy variables

Innovation

• proximal causal inference
• hidden outcomes
• influence function
• multiple robustness
• nonparametric identification