Moments of Causal Effects

TL;DR

This paper extends causal inference by defining and estimating moments and product moments of causal effects, providing new tools to analyze their distribution and relationships in practical scenarios.

Contribution

It introduces definitions, identification theorems, and bounds for moments of causal effects, advancing the analysis beyond average effects.

Findings

Established bounds for moments of causal effects

Demonstrated estimation methods from finite samples

Applied techniques to a real-world medical dataset

Abstract

The moments of random variables are fundamental statistical measures for characterizing the shape of a probability distribution, encompassing metrics such as mean, variance, skewness, and kurtosis. Additionally, the product moments, including covariance and correlation, reveal the relationships between multiple random variables. On the other hand, the primary focus of causal inference is the evaluation of causal effects, which are defined as the difference between two potential outcomes. While traditional causal effect assessment focuses on the average causal effect, this work provides definitions, identification theorems, and bounds for moments and product moments of causal effects to analyze their distribution and relationships. We conduct experiments to illustrate the estimation of the moments of causal effects from finite samples and demonstrate their practical application using a real-world medical dataset.