Proxy variables are often used in linear regression models with the aim of removing potential confounding bias. In this paper we formalise proxy variables within the potential outcome framework, giving conditions under which it can be shown that causal effects are nonparametrically identified....

Proxy variables are often used in linear regression models with the aim of removing potential confounding bias. In this paper we formalise proxy variables within the potential outcome framework, giving conditions under which it can be shown that causal effects are nonparametrically identified....

The identification of average causal effects of a treatment in observational studies is typically based either on the unconfoundedness assumption or on the availability of an instrument. When available, instruments may also be used to test for the unconfoundedness assumption (exogeneity of the...