Causal Inference on Distributional Outcomes under Continuous Treatments

YIJUN LI, Cheuk Hang LEUNG, Qi WU

Keywords: causal inference, distributional outcome, continuous treatments, doubly machine learning

Abstract: Causal inference is widely practiced in various domains. Existing literature predominantly focuses on causal estimators for scalar or vector outcomes. However, real-world scenarios often involve response variables that are better represented as distributions. This paper addresses the need for causal inference methods capable of accommodating the distributional nature of responses when the treatments are continuous variables. We adopt a novel framework for causal inference within a vector space that incorporates the Wasserstein metric. Drawing upon Rubin's causal framework, we introduce three estimators, namely the Distributional Direct Regression (Dist-DR), Distributional Inverse Propensity Weighting (Dist-IPW), and Distributional Doubly Machine Learning (Dist-DML) estimators, tailored for estimating target quantities, i.e., causal effect maps. We thoroughly examine the statistical properties of these estimators. Through two experiments, we validate the efficacy of the proposed methodology, establishing its practical utility.

Primary Area: causal reasoning

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Submission Number: 5297