IV estimation without distributional assumptions

It is widely known that Instrumental Variable (IV) estimation allows the researcher to estimate causal effects between an exposure and an outcome even in face of serious uncontrolled confounding. The key requirement for IV estimation is the existence of a variable, the instrument, which only affects the outcome through its effects on the exposure and that the instrument-outcome relationship is unconfounded. Countless papers have employed such techniques and carefully addressed the validity of the IV assumption just mentioned. However, less appreciated is that fact that the IV estimation also depends on a number of distributional assumptions in particular linearities. In this paper, we propose a novel bounding procedure which can bound the true causal effect relying only on the key IV assumption and not on any distributional assumptions. For a purely binary case (instrument, exposure, and outcome all binary), such boundaries have been proposed by Balke and Pearl in 1997. We extend such boundaries to non-binary settings. In addition, our procedure offers a tuning parameter such that one can go from the traditional IV analysis, which provides a point estimate, to a completely unrestricted bound and anything in between. Subject matter knowledge can be used when setting the tuning parameter. To the best of our knowledge, no such methods exist elsewhere. The method is illustrated using a pivotal study which introduced IV estimation to epidemiologists. Here, we demonstrate that the conclusion of this paper indeed hinges on these additional distributional assumptions. R-code is provided in the Supporting Information.