  Unobserved confounding is a fundamental obstacle to establishing valid causal
conclusions from observational data. Two complementary types of approaches have
been developed to address this obstacle: obtaining identification using
fortuitous external aids, such as instrumental variables or proxies, or by
means of the ID algorithm, using Markov restrictions on the full data
distribution encoded in graphical causal models. In this paper we aim to
develop a synthesis of the former and latter approaches to identification in
causal inference to yield the most general identification algorithm in
multivariate systems currently known -- the proximal ID algorithm. In addition
to being able to obtain nonparametric identification in all cases where the ID
algorithm succeeds, our approach allows us to systematically exploit proxies to
adjust for the presence of unobserved confounders that would have otherwise
prevented identification. In addition, we outline a class of estimation
strategies for causal parameters identified by our method in an important
special case. We illustrate our approach by simulation studies and a data
application.
