We develop a nonparametric instrumental variable approach for the estimation of average treatment effects on hazard rates and conditional survival probabilities, without model structure. We derive constructive identification proofs for average treatment effects under noncompliance and dynamic selection, exploiting instrumental variation taking place during ongoing spells. We derive asymptotic distributions of the corresponding estimators. This includes a detailed examination of noncompliance in a dynamic context. In an empirical application, we evaluate the French labor market policy reform PARE which abolished the dependence of unemployment insurance benefits on the elapsed unemployment duration and simultaneously introduced additional active labor market policy measures. The estimated effect of the reform on the survival function of the duration of unemployment duration is positive and significant. Neglecting selectivity leads to an underestimation of the effects in absolute terms.