Instrumental variable estimation of the proportional hazards model by presmoothing

We consider instrumental variable estimation of the proportional hazards model. The instrument and the endogenous variable are discrete but there can be (possibly continuous) exogenous covariables. We can reformulate the proportional hazards model into a semiparametric instrumental variable quantile regression model by assuming rank invariance. A naive estimation approach based on conditional moment conditions generated by the model would lead to a highly nonconvex and nonsmooth objective function. To overcome this problem, we propose a new presmoothing methodology. First, we estimate the model nonparametrically-and show that this nonparametric estimator has a closed-form solution in the leading case of interest of randomized experiments with one-sided noncompliance. Second, we use the nonparametric estimator to generate “proxy” observations for which exogeneity holds. Third, we apply the usual partial likelihood estimator to the “proxy” data. While the paper focuses on the proportional hazards model, our presmoothing approach could be applied to estimate other semiparametric formulations of the instrumental variable quantile regression model. Our estimation procedure allows for random right-censoring. We show asymptotic normality of the resulting estimator. The approach is illustrated via simulation studies and an empirical application to the Illinois Unemployment Incentive Experiment.