In this article we propose and implement an instrumental variable estimation procedure to obtain treatment effects on duration outcomes. The method can handle the typical complications that arise with duration data of time-varying treatment and censoring. The treatment effect we define is in terms of shifting the quantiles of the outcome distribution based on the Generalized Accelerated Failure Time (GAFT) model. The GAFT model encompasses two competing approaches to duration data; the (Mixed) Proportional Hazard (MPH) model and the Accelerated Failure Time (AFT) model. We discuss the large sample properties of the proposed Instrumental Variable Linear Rank (IVLR), and show how we can, with one additional step, improve upon its efficiency. We discuss the empirical implementation of the estimator and apply it to the Illinois re-employment bonus experiment.