Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder

Understand

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.