Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder

TL;DR

This paper demonstrates that causal effects can be identified using proxy variables for unmeasured confounders under certain conditions, even when the measurement error mechanism is not fully known, and provides testing strategies when these conditions are not met.

Contribution

It generalizes existing identification methods by allowing for multiple proxies and relaxes the need to identify the measurement error mechanism, also offering hypothesis testing procedures.

Findings

Causal effects are identifiable with at least two independent proxies under a rank condition.

The measurement error mechanism need not be fully identified for causal effect identification.

Strategies are developed to test for no causal effect when proxies are limited or conditions are unmet.

Abstract

We consider a causal effect that is confounded by an unobserved variable, but with observed proxy variables of the confounder. We show that, with at least two independent proxy variables satisfying a certain rank condition, the causal effect is nonparametrically identified, even if the measurement error mechanism, i.e., the conditional distribution of the proxies given the con- founder, may not be identified. Our result generalizes the identification strategy of Kuroki & Pearl (2014) that rests on identification of the measurement error mechanism. When only one proxy for the confounder is available, or the required rank condition is not met, we develop a strategy to test the null hypothesis of no causal effect.