The Proximal ID Algorithm

TL;DR

The paper introduces the proximal ID algorithm, a comprehensive method that combines external aids and graphical models to achieve nonparametric causal identification in complex multivariate systems with unobserved confounders.

Contribution

It develops the most general identification algorithm in multivariate causal systems, integrating proxies and graphical models for broader applicability.

Findings

Successfully identifies causal effects in complex systems.

Demonstrates effectiveness through simulations and real data.

Provides estimation strategies for identified causal parameters.

Abstract

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.