  This paper discusses endogenous treatment models with duration outcomes,
competing risks and random right censoring. The endogeneity issue is solved
using a discrete instrumental variable. We show that the competing risks model
generates a non-parametric quantile instrumental regression problem. The
cause-specific cumulative incidence, the cause-specific hazard and the
subdistribution hazard can be recovered from the regression function. A
distinguishing feature of the model is that censoring and competing risks
prevent identification at some quantiles. We characterize the set of quantiles
for which exact identification is possible and give partial identification
results for other quantiles. We outline an estimation procedure and discuss its
properties. The finite sample performance of the estimator is evaluated through
simulations. We apply the proposed method to the Health Insurance Plan of
Greater New York experiment.
