Abstract

Instrumental variable approaches have gained popularity for estimating

causal effects in the presence of unmeasured confounders. However, the availability of instrumental variables in the primary dataset is often challenged due

to stringent and untestable assumptions. This paper presents a novel method to

identify and estimate causal effects by utilizing instrumental variables from the

auxiliary dataset, incorporating a structural equation model, even in scenarios

with nonlinear treatment effects. Our approach involves using two datasets: one

called the primary dataset with joint observations of treatment and outcome, and

another auxiliary dataset providing information about the instrument and treatment. Our strategy differs from most existing methods by not depending on the

simultaneous measurements of instrument and outcome.

The central idea for

identifying causal effects is to establish a valid substitute through the auxiliary

dataset, addressing unmeasured confounders. This is achieved by developing a

control function and projecting it onto the function space spanned by the treatment variable.

We then propose a three-step estimator for estimating causal

effects and derive its asymptotic results.

We illustrate the proposed estimator

through simulation studies, and the results demonstrate favorable performance.

We also conduct a real data analysis to evaluate the causal effect between vitamin

D status and body mass index.

Key words and phrases: Control function, Data fusion, Instrumental variable, Unmeasured confounder

Information

Preprint No.SS-2024-0006
Manuscript IDSS-2024-0006
Complete AuthorsKang Shuai, Shanshan Luo, Wei Li, Yangbo He
Corresponding AuthorsShanshan Luo
Emailsshanshanluo@btbu.edu.cn

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Acknowledgments

We sincerely thank the editor, associate editor, and reviewers for their insightful and helpful comments, which have significantly improved our pa-

per. Kang Shuai and Yangbo He are supported by the National Key R&D

Program of China (2022ZD0160300). Wei Li is supported by the Beijing

Natural Science Foundation (1232008), the National Natural Science Foundation of China (12101607, 12071015), the National Key R&D Program of

China (2022YFA1008100), and the MOE Project of Key Research Institute

of Humanities and Social Sciences (22JJD910001). Shanshan Luo is supported by the National Natural Science Foundation of China (12401378),

the Beijing Key Laboratory of Applied Statistics and Digital Regulation,

and the BTBU Digital Business Platform Project by BMEC.

Supplementary Materials

The supplementary material available online includes additional technical

proofs and simulation results.

Supplementary materials are available for download.