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 √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.

Information

Preprint No.SS-2023-0315
Manuscript IDSS-2023-0315
Complete AuthorsKang Shuai, Shanshan Luo, Yue Zhang, Feng Xie, Yangbo He
Corresponding AuthorsYangbo He
Emailsheyb@math.pku.edu.cn

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Acknowledgments

The research work is supported by National Key R&D Program of China

(2022ZD0160300). The authors thank the referees and an editor for helpful

comments.

Supplementary Materials

available online includes additional technical

proofs and simulation results including two treatments case and sensitivity

analysis of the Gaussianity of unmeasured confounders.

Supplementary materials are available for download.