Title: Instrumental Variable Estimation of the Proportional Hazards Model by Presmoothing

 

Abstract: In this study, we delve into the instrumental variable estimation of the proportional hazards model. This model accommodates discrete instruments and endogenous variables, along with the possibility of having continuous exogenous covariates. By applying a rank invariance assumption, the model is transformed into a semiparametric version of the instrumental variable quantile regression model. The direct estimation approach, which relies on conditional moment conditions from the model, results in a complex and challenging objective function that is both nonconvex and nonsmooth. To tackle this issue, we introduce a novel presmoothing methodology. The process starts with a nonparametric estimation of the model, which, in leading cases like randomized experiments with one-sided noncompliance, offers a closed-form solution. Following this, we generate "proxy" observations based on the nonparametric estimator where exogeneity is assumed. These proxy observations are then subjected to the usual partial likelihood estimator. While the focus is on the proportional hazards model, the presmoothing technique could also be applicable in estimating other semiparametric instrumental variable quantile regression models. Our methodology also allows for the consideration of random right-censoring. The estimator's asymptotic normality is established, and its practical application is demonstrated through simulation studies and an empirical analysis of the Illinois Unemployment Incentive Experiment.