Accounting for Missing Covariates in Heterogeneous Treatment Estimation

Abstract

Many applications of causal inference require using treatment effects estimated on a study population to then make decisions for a separate target population that lacks treatment and outcome data. We consider the challenging setting where there are important covariates that are observed in the target population but are missing from the original study. Our goal is to estimate the tightest possible bounds on heterogeneous treatment effects conditioned on such newly observed covariates. We introduce a novel partial identification strategy based on ideas from ecological inference; the main idea is that estimates of conditional treatment effects for the full covariate set must marginalize correctly when restricted to only the covariates observed in both populations. Furthermore, we introduce a bias-corrected estimator for these bounds and prove that it enjoys fast convergence rates and statistical guarantees (e.g., asymptotic normality). Experimental results on both real and synthetic data demonstrate that our framework can produce bounds that are much tighter than would otherwise be possible.