Third moment-based causal inference

Abstract

In observational data, covariance-based measures of dependence are of limited use for detecting reverse-causation (using y → x instead of x → y when quantifying the causal effect) and confounding biases (ignoring common causes). However, within the last decades, methodological progress has been made and, under certain conditions, scholars are now able to make evidence-based statements about causal mechanisms of variables from observational data alone. One such condition is to consider higher than second variable moments. This article introduces principles of causal structure learning and direction dependence modeling in linear models focusing on third moments and presents measures for causal structure learning and causal effect identification under hidden confounding. Results of a simulation study suggest that third moment-based causal effect estimators tend to show smaller biases than ordinary least squares estimators. Thus, third moment-based causal inference methods constitute a valuable add-on to existing approaches to causal inference.