Suppose we tried to check the assumption that the entire effect of a proposed instrument on the outcome is mediated by the exposure of interest by regressing the outcome on exposure, the instrument,...

Suppose we tried to check the assumption that the entire effect of a proposed instrument on the outcome is mediated by the exposure of interest by regressing the outcome on exposure, the instrument, and measured confounders, on the hypothesis that if there is no direct effect of the instrument on the outcome, it should appear unimportant in this regression. Using a directed acyclic graph, as described in Sect. 10.2.5, show that in the presence of unmeasured confounding of the exposure–outcome relationship (the motivation for use of an instrumental variable), exposure is a collider on a backdoor path between the instrument and the outcome and thus controlling for it will induce an association between them.