Nonparametric Identification of a Time-Varying Frailty Model

In duration analysis, the Mixed Proportional Hazard model is the most common choice among practitioners for the specification of the underlying hazard rate. One major drawback of this model is that the value of the frailty term (i.e. unobserved factors) is time-invariant. This paper introduces a new model, the Mixed Random Hazard (MRH) model, which allows the frailty term to be time-varying. We provide sufficient conditions under which the new model is nonparametrically identified. Moreover, a theoretical framework is proposed for testing whether the true model is MRH. We conclude this paper with a discussion of how the arguments for the univariate MRH model can be extended to various multivariate problems.