Estimating Treatment Effects with Observed Confounders and Mediators

2020/03/26 by Shantanu Gupta, Zachary C. Lipton, Gupta, Shantanu +3 · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Causal Inference Techniques #Applied mathematics #Causal inference #Computer science #Confounding #Econometrics #Econometrics (econ.EM) #Estimator #FOS: Computer and information sciences #FOS: Economics and business #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Mathematics #Methodology (stat.ME) #Observational study #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics #Variance (accounting) #cs.LG #econ.EM #stat.ME #stat.ML

paper · pdf · doi:10.48550/arxiv.2003.11991

openalex publication_date 2020/03/26 · arxiv created 2021/06/14 · arxiv updated 2021/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a causal graph, the do-calculus can express treatment effects as functionals of the observational joint distribution that can be estimated empirically. Sometimes the do-calculus identifies multiple valid formulae, prompting us to compare the statistical properties of the corresponding estimators. For example, the backdoor formula applies when all confounders are observed and the frontdoor formula applies when an observed mediator transmits the causal effect. In this paper, we investigate the over-identified scenario where both confounders and mediators are observed, rendering both estimators valid. Addressing the linear Gaussian causal model, we demonstrate that either estimator can dominate the other by an unbounded constant factor. Next, we derive an optimal estimator, which leverages all observed variables, and bound its finite-sample variance. We show that it strictly outperforms the backdoor and frontdoor estimators and that this improvement can be unbounded. We also present a procedure for combining two datasets, one with observed confounders and another with observed mediators. Finally, we evaluate our methods on both simulated data and the IHDP and JTPA datasets.

Citations

• Large Sample Properties of Generalized Method of Moments Estimators
• Causal diagrams for empirical research
• Gaussian Graphical Models: An Algebraic and Geometric Perspective
• Estimating individual treatment effect: generalization bounds and algorithms
• Potential Outcome and Directed Acyclic Graph Approaches to Causality: Relevance for Empirical Practice in Economics
• Efficient adjustment sets for population average treatment effect estimation in non-parametric causal graphical models
• Causal Inference and Data Fusion in Econometrics

Cited by

• Conditional Front-door Adjustment for Heterogeneous Treatment Assignment Effect Estimation Under Non-adherence

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