Controlling for Latent Confounding with Triple Proxies

TL;DR

This paper introduces a novel triple proxy method for nonparametric causal effect identification with noisy proxies for unobserved confounders, extending previous double proxy approaches and capturing more complex variations.

Contribution

It develops a new triple proxy identification strategy that generalizes and improves upon existing double proxy methods for causal inference with measurement error.

Findings

Triple proxy approach identifies additional causal objects.

It captures variation in treatment effects across unobserved strata.

The assumptions for double and triple proxies are non-nested.

Abstract

We present new results for nonparametric identification of causal effects using noisy proxies for unobserved confounders. Our approach builds on the results of \citet{Hu2008} who tackle the problem of general measurement error. We call this the `triple proxy' approach because it requires three proxies that are jointly independent conditional on unobservables. We consider three different choices for the third proxy: it may be an outcome, a vector of treatments, or a collection of auxiliary variables. We compare to an alternative identification strategy introduced by \citet{Miao2018a} in which causal effects are identified using two conditionally independent proxies. We refer to this as the `double proxy' approach. The triple proxy approach identifies objects that are not identified by the double proxy approach, including some that capture the variation in average treatment effects between strata of the unobservables. Moreover, the conditional independence assumptions in the double and triple proxy approaches are non-nested.