  Time-to-event analyses are often plagued by both -- possibly unmeasured --
confounding and competing risks. To deal with the former, the use of
instrumental variables for effect estimation is rapidly gaining ground. We show
how to make use of such variables in competing risk analyses. In particular, we
show how to infer the effect of an arbitrary exposure on cause-specific hazard
functions under a semi-parametric model that imposes relatively weak
restrictions on the observed data distribution. The proposed approach is
flexible accommodating exposures and instrumental variables of arbitrary type,
and enables covariate adjustment. It makes use of closed-form estimators that
can be recursively calculated, and is shown to perform well in simulation
studies. We also demonstrates its use in an application on the effect of
mammography screening on the risk of dying from breast cancer
