Transferring Causal Effects using Proxies

TL;DR

This paper develops methods to estimate causal effects across multiple domains using proxy variables for unobserved confounders, providing theoretical guarantees and practical estimation techniques.

Contribution

It introduces a novel approach for causal effect estimation with proxies in multi-domain settings, including identifiability proofs and consistent estimators.

Findings

Proved identifiability of causal effects with proxy variables.

Developed two consistent estimation techniques.

Validated methods through simulations and real-world data.

Abstract

We consider the problem of estimating a causal effect in a multi-domain setting. The causal effect of interest is confounded by an unobserved confounder and can change between the different domains. We assume that we have access to a proxy of the hidden confounder and that all variables are discrete or categorical. We propose methodology to estimate the causal effect in the target domain, where we assume to observe only the proxy variable. Under these conditions, we prove identifiability (even when treatment and response variables are continuous). We introduce two estimation techniques, prove consistency, and derive confidence intervals. The theoretical results are supported by simulation studies and a real-world example studying the causal effect of website rankings on consumer choices.