Identifying Causal Effects Using Instrumental Variables from the Auxiliary Dataset

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.