Assessing causal effects in the presence of unmeasured confounding is a challenging problem. 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 can be 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 auxiliary covariates 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. The auxiliary covariate can be an invalid instrument or an invalid proxy variable. We demonstrate that the causal effect can be identified using this measured covariate, even when the only source of non-Gaussianity comes from the treatment. We then extend the identification results to the multi-treatment setting and provide sufficient conditions for identification. Based on our identification results, we propose a simple and efficient procedure for calculating causal effects and show the $\sqrt{n}$-consistency of the proposed estimator. Finally, we evaluate the performance of our estimator through simulation studies and an application.

翻译：在存在未观测混杂因素的情况下评估因果效应是一个具有挑战性的问题。尽管工具变量等辅助变量通常被用于识别因果效应，但由于其严格且不可检验的条件，这些变量在实践中往往难以获得。为解决此问题，已有研究利用线性结构方程模型证明，当处理变量和结果变量的噪声项均服从非高斯分布时，因果效应是可识别的。本文研究利用辅助协变量和处理变量的非高斯性来识别因果效应的问题。我们的核心思想是：假设所有未观测混杂因素均为高斯分布，通过观测协变量刻画其影响。该辅助协变量可以是无效工具变量或无效代理变量。我们证明，即使非高斯性仅来源于处理变量，仍可借助该测量协变量识别因果效应。随后，我们将识别结果扩展至多处理设置，并给出识别充分条件。基于识别结果，我们提出一种简洁高效的计算因果效应的流程，并证明所提估计量具有$\sqrt{n}$-相合性。最后，通过模拟研究与应用实例评估估计量的性能。