  Instrumental variables are widely used to deal with unmeasured confounding in
observational studies and imperfect randomized controlled trials. In these
studies, researchers often target the so-called local average treatment effect
as it is identifiable under mild conditions. In this paper, we consider
estimation of the local average treatment effect under the binary instrumental
variable model. We discuss the challenges for causal estimation with a binary
outcome, and show that surprisingly, it can be more difficult than the case
with a continuous outcome. We propose novel modeling and estimating procedures
that improve upon existing proposals in terms of model congeniality,
interpretability, robustness or efficiency. Our approach is illustrated via
simulation studies and a real data analysis.
