Identifiability of causal effects with non-Gaussianity and auxiliary covariates

TL;DR

This paper proposes a method to identify and estimate causal effects using non-Gaussianity and auxiliary covariates, addressing unmeasured confounding without relying on instrumental variables.

Contribution

It introduces a novel identification approach leveraging non-Gaussian noise and observed covariates, extending to multi-treatment scenarios, with a consistent estimation procedure.

Findings

The proposed estimator achieves $\

The method successfully identifies causal effects in simulations.

Application to trade and income demonstrates practical utility.

Abstract

Assessing causal effects in the presence of unmeasured confounding is challenging. Although auxiliary variables, such as instrumental variables, are commonly used to identify causal effects, they are often unavailable in practice due to stringent and untestable conditions. To address this issue, previous researches have utilized linear structural equation models to show that the causal effect is identifiable when noise variables of the treatment and outcome are both non-Gaussian. In this paper, we investigate the problem of identifying the causal effect using the auxiliary covariate and non-Gaussianity from the treatment. Our key idea is to characterize the impact of unmeasured confounders using an observed covariate, assuming they are all Gaussian. We demonstrate that the causal effect can be identified using a measured covariate, and then extend the identification results to the multi-treatment setting. We further develop a simple estimation procedure for estimating causal effects and derive a $\sqrt{n}$-consistent estimator. Finally, we evaluate the performance of our estimator through simulation studies and apply our method to investigate the effect of the trade on income.