A Semiparametric Approach to Causal Inference

TL;DR

This paper introduces a semiparametric density ratio model framework for causal inference that estimates entire counterfactual distributions, providing deeper insights than mean effects alone.

Contribution

It develops a flexible, nonparametric approach using empirical likelihood to infer counterfactual distributions, advancing causal analysis from a distributional perspective.

Findings

Effective in synthetic data simulations

Validated on real-world datasets

Enables distributional causal inference

Abstract

In causal inference, an important problem is to quantify the effects of interventions or treatments. Many studies focus on estimating the mean causal effects; however, these estimands may offer limited insight since two distributions can share the same mean yet exhibit significant differences. Examining the causal effects from a distributional perspective provides a more thorough understanding. In this paper, we employ a semiparametric density ratio model (DRM) to characterize the counterfactual distributions, introducing a framework that assumes a latent structure shared by these distributions. Our model offers flexibility by avoiding strict parametric assumptions on the counterfactual distributions. Specifically, the DRM incorporates a nonparametric component that can be estimated through the method of empirical likelihood (EL), using the data from all the groups stemming from multiple interventions. Consequently, the EL-DRM framework enables inference of the counterfactual distribution functions and their functionals, facilitating direct and transparent causal inference from a distributional perspective. Numerical studies on both synthetic and real-world data validate the effectiveness of our approach.