Estimating Causal Effects with Hidden Confounding using Instrumental Variables and Environments

TL;DR

This paper introduces new estimators for causal effects under hidden confounding, leveraging invariance across environments and GMM theory, demonstrating improved performance over existing methods in simulations and real data.

Contribution

It derives the Causal Dantzig as a GMM estimator and proposes the GCD and Hybrid estimators, extending applicability and improving causal inference under hidden confounding.

Findings

GCD outperforms CD and TSLS in simulations

Hybrid estimator combines strengths of GCD and TSLS

New estimators show superior results in real data application

Abstract

Recent works have proposed regression models which are invariant across data collection environments. These estimators often have a causal interpretation under conditions on the environments and type of invariance imposed. One recent example, the Causal Dantzig (CD), is consistent under hidden confounding and represents an alternative to classical instrumental variable estimators such as Two Stage Least Squares (TSLS). In this work we derive the CD as a generalized method of moments (GMM) estimator. The GMM representation leads to several practical results, including 1) creation of the Generalized Causal Dantzig (GCD) estimator which can be applied to problems with continuous environments where the CD cannot be fit 2) a Hybrid (GCD-TSLS combination) estimator which has properties superior to GCD or TSLS alone 3) straightforward asymptotic results for all methods using GMM theory. We compare the CD, GCD, TSLS, and Hybrid estimators in simulations and an application to a Flow Cytometry data set. The newly proposed GCD and Hybrid estimators have superior performance to existing methods in many settings.