Copula-Based Endogeneity Correction for Doubly Robust Estimation of Treatment Effect

Abstract

Doubly Robust (DR) estimation of treatment effect relies on an untestable assumption that is the absence of unobserved confounding. This assumption is par- ticularly problematic in the context of healthcare research, where variables like pre- scription refill rates serve as proxies for unobserved behaviors such as medication adherence. These proxy variables are often endogenous, exhibiting correlation with the regression error term due to unmeasured confounding or measurement error. We propose a copula-corrected doubly robust estimator that addresses endogeneity in both the treatment and outcome models without requiring instrumental variables. Gaussian copulas model the joint distribution of endogenous covariates and the error term, enabling consistent estimation while preserving the doubly robust property that requires correct specification of either the treatment or outcome model, not both. Monte Carlo simulations demonstrate that naive DR estimation exhibits substantial bias under endogeneity, whereas our corrected estimator recovers unbiased treatment effects across different data-generating processes. We apply our method to examine the effect of nutritional counseling on blood pressure using the National Health and Nutrition Examination Survey (NHANES) data. Naive DR estimation suggests counseling is associated with increased blood pressure. After copula correction, this effect becomes statistically insignificant, consistent with literature showing modest effects of nutri- Counseling in reducing blood pressure. Our methodology provides researchers with a practical tool for obtaining treatment effects in the presence of endogeneity.