Identifying causal effects with proxy variables of an unmeasured confounder

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