Specification analysis in mixed hazard models and a test of crossing survival functions

The paper investigates diagnostic procedures for the specification of common hazard models in duration analysis. It is shown that under mixed hazard specifications the survival functions of different subgroups cannot cross. A nonparametric test for the crossing of two survival functions is provided and its applications in duration analysis are discussed. In particular, the proportional hazard model with unobserved heterogeneity (PHU) is investigated, and procedures are developed to test whether given data are consistent with the PHU model and whether they contain unobserved heterogeneity within the PHU specification. Examples in which crossing survivals are of substantive concern are discussed, including the dynamics of infectious diseases and the demand for vaccination.