Abstract
Suppose that causal relationships among variables can be described by a causal diagram and the corresponding linear structural equation model. In order to identify total effects, Brito and Pearl (2002) have suggested the conditional instrumental variable method, which is provided as a generalization of the instrumental variable method. However, the selection of conditional instrumental variable given a set of covariates is not unique. In this paper, when a total effect can be estimated through the conditional instrumental variable method, we formulate the asymptotic variance of the total effect. In addition, when there are some conditional instrumental variables given a set of covariates, the difference between them is investigated based on the formulation.
