Unmeasured confounding of the exposure-outcome relationship is a major concern in any observational study. Very few methods have been developed to address the problem of unmeasured confounding in the competing risks setting. Further, existing methods focus on estimating causal effects on a single, primary cause of interest. In doing so, these methods tend to overlook important features of the exposure-outcome relationship and ignore the interplay between causes. We develop an instrumental variable (IV) analysis method that enables simultaneous inference of exposure effects on the absolute risk of all competing cause-specific events, in the presence of unmeasured confounding. By using a semiparametric mixture component model, we ensure that the additivity constraint for the cause-specific cumulative incidence functions is satisfied. Our method makes no restriction about the type of exposure or IV and can accommodate exposure-dependent censoring. We examine finite sample properties through simulation studies. We apply the proposed methods to data from the United States Renal Data System (USRDS).