Transferring Causal Effects using Proxies
This work addresses causal inference challenges in multi-domain settings for researchers and practitioners, though it is incremental as it builds on existing proxy-based methods.
The paper tackles the problem of estimating causal effects across domains when confounders are unobserved but proxies are available, proving identifiability and introducing consistent estimation methods with confidence intervals, validated through simulations and a real-world example on website rankings and consumer choices.
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.