Instrumental variable estimation for duration data

In this article we focus on time-to-event studies with arandomised treatment assignment that may be compromised byselective compliance. Contrary to most of the extensive literatureon evaluation studies we do not consider the effect of thetreatment on some average outcome but on the hazard rate. Intime-to-event studies the treatment may vary over time. Anothercomplication of duration data is that they are usually heavycensored. Censoring limits the observation period, but is not afeature of the treatment program. Therefore, a natural choice isto relate the treatment to the hazard rate. We show that even ifthe compliance is selective, we can still use the randomisation toestimate the impact of the program corrected for selectivecompliance on the hazard. The only requirement is thatparticipation in the program is affected by a variable that is notcorrelated with the baseline duration.We develop an Instrumental Variable estimation procedure for theGeneralized Accelerated Failure Time (GAFT) model. The GAFT modelis a duration data model that encompasses two competing approachesto such data; the (Mixed) Proportional Hazard (MPH) model and theAccelerated Failure Time (AFT) model. We discuss the large sampleproperties of this Instrumental Linear Rank Estimation and showhow we can improve its efficiency. The estimator is used tore-analyze the data from the Illinois unemployment bonusexperiment.Duration model;Endogenous treatment;Instrumental variable;Semi-parametric