Open Access
2023 Estimating causal effects with hidden confounding using instrumental variables and environments
James P. Long, Hongxu Zhu, Kim-Anh Do, Min Jin Ha
Author Affiliations +
Electron. J. Statist. 17(2): 2849-2879 (2023). DOI: 10.1214/23-EJS2160


Recent works have proposed regression models which are invariant across data collection environments [24, 20, 11, 16, 8]. 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.

Funding Statement

James P. Long was partially supported by National Institutes of Health SPORE [P50CA127001, P50CA140388] and CCTS [UL1TR003167]. Kim-Anh Do was partially supported by the National Institutes of Health [P30CA016672], SPORE [P50CA140388], CCTS [TR000371] and CPRIT [RP160693].


Download Citation

James P. Long. Hongxu Zhu. Kim-Anh Do. Min Jin Ha. "Estimating causal effects with hidden confounding using instrumental variables and environments." Electron. J. Statist. 17 (2) 2849 - 2879, 2023.


Received: 1 April 2023; Published: 2023
First available in Project Euclid: 10 November 2023

arXiv: 2207.14753
Digital Object Identifier: 10.1214/23-EJS2160

Primary: 62D20 , 62D20

Keywords: Causal Dantzig , Causal inference , hidden confounding , instrumental variables

Vol.17 • No. 2 • 2023
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