2022 Volume 51 Issue 3 Pages 91-108
This paper assumes that cause-effect relationships in the process can be described by a linear structural equation model and the corresponding directed acyclic graph. When unmeasured confounders exist, we consider a situation where the total effect can be estimated by both the instrumental variable estimator and the front-door estimator. In this situation, there is no qualitative superiority/inferiority relationship between these two estimators in terms of the estimation accuracy of the total effects. Taking this into account, in order to estimate the total effect with better estimation accuracy, we propose a novel integrated estimator based on these two estimators. In addition, through numerical experiments, from the viewpoint of the estimation accuracy of the total effects, we show that (i) the integrated estimator is better than the individual estimators, and (ii) in some situations, the integrated estimator is better than the back-door estimator even when the back-door estimator is better than the individual estimators.
