Semiparametric proportional hazards estimation of competing risks models with time-varying covariates

Abstract Recent research has focused on the class of proportional hazards models which are nonparametric with respect to the form of the baseline hazard [Han and Hausman (1990), Meyer (1986), Kiefer (1987)]. This paper extends the previous literature on these semiparametric duration estimators in two distinct ways. First, I extend the regression form of the competing risks, proportional hazards model to allow covariates to vary over time. I demonstrate identification and asymptotic normality of the general estimator for the competing risks models with time-varying covariates. Second, I develop Monte Carlo simulations to assess the performance of the bivariate risk estimator for various sample sizes, in the presence and absence of unobserved heterogeneity of various forms and given temporal aggregation. The results indicate that the estimator performs well in finite samples, but that the estimates are sensitive to misspecification of the error distribution. The qualitative results are, however, relatively insensitive to an incorrect error assumption. In contrast, the effects of aggregation are potentially quite serious with parameters for the time-varying variables, in particular, showing considerable sensitivity to the degree of aggregation.