Causal Effect Estimation with Learned Instrument Representations

ICLR 2026 Conference Submission21848 Authors

Keywords: instrumental variable regression, learning instruments, unobserved confounding, structural causal models

Abstract: In many applications, we aim to assess the impact of a policy or intervention on outcomes of interest using retrospective data. This setting is challenging due to unobserved confounding, which can bias causal estimates. One approach to address this issue—in statistics, econometrics, and epidemiology—is to use instrumental variables (IVs) within two-stage regression frameworks. An IV is a variable that influences the treatment but has no direct effect on the outcome or influence from unobserved confounders. However, across many applications, suitable and valid IVs are difficult to find or may not be available at all. We propose a method for decomposing the observed variables to find a representation which satisfies the standard IV assumptions of relevance, exclusion restriction, and unconfoundedness. To implement this decomposition, we introduce a deep learning model, ZNet, with an architecture that mirrors the structural causal model of IVs and is compatible with a wide range of two-stage IV estimators. Our experiments demonstrate that ZNet can (i) recover ground-truth instruments when they exist and (ii) construct proxy latent instruments that reduce bias due to unobserved confounding when no explicit instruments are available. These results suggest that ZNet can be used as a plug-in module for causal effect estimation in general observational settings, regardless of whether the (untestable) assumption of unconfoundedness is satisfied.

Primary Area: causal reasoning

Submission Number: 21848