Instrumental Variable Estimators for Binary Outcomes

Instrumental variables (IVs) can be used to construct estimators of exposure effects on the outcomes of studies affected by nonignorable selection of the exposure. Estimators that fail to adjust for the effects of nonignorable selection will be biased and inconsistent. Such situations commonly arise in observational studies, but are also a problem for randomized experiments affected by nonignorable noncompliance. In this article, we review IV estimators for studies in which the outcome is binary, and consider the links between different approaches developed in the statistics and econometrics literatures. The implicit assumptions made by each method are highlighted and compared within our framework. We illustrate our findings through the reanalysis of a randomized placebo-controlled trial, and highlight important directions for future work in this area.