Competing Risks Modelsusing Mortgage Duration Data under the Proportional Hazards Assumption

This paper demonstrates two important results related to the estimation of a competing risks model under the proportional hazards assumption with grouped duration data, a model which has become the canonical model for the termination of mortgages with prepayment and default as two competing risks. First we show that the model with non-parametric baseline hazards is unidentifiable with only grouped mortgage duration data. Therefore assumption on the functional form of the baseline hazard is necessary for any meaningful inference. Secondly we demonstrate that under some parametric assumption such as piece-wise constant baseline hazards, the sample likelihood function has an explicit analytical form. Therefore there is no need for the approximation formula widely adopted in the previous literature. Both Monte Carlo simulations and actual mortgage data are used to demonstrate the adverse impact of the approximation.