Using Descendants as Instrumental Variables for the Identification of Direct Causal Effects in Linear SEMs

In this paper, we present an extended set of graphical criteria for the identification of direct causal effects in linear Structural Equation Models (SEMs). Previous methods of graphical identification of direct causal effects in linear SEMs include methods such as the single-door criterion, the instrumental variable and the IV-pair, and the accessory set. However, there remain graphical models where a direct causal effect can be identified and these graphical criteria all fail. As a result, we introduce a new set of graphical criteria which uses descendants of either the cause variable or the effect variable as “path-specific instrumental variables” for the identification of the direct causal effect as long as certain conditions are satisfied. These conditions are based on edge removal and the existing graphical criteria of instrumental variables, and the identifiability of certain other total effects, and thus can be easily checked.