Hazard models naturally arise in applications in which agents make discrete decisions at random and discrete (Poisson) times (Heckman and Singer, 1985, 1986). A prime example of such an application is the empirical analysis of labor market transitions using sequential job search models. Labor economists have both empirically implemented job search models as structural models (Eckstein and Van den Berg, 2007) and used such models to motivate the application of mixed proportional hazards (MPH) models (Van den Berg, 2001). The MPH model is an extension of Cox’s (1972) proportional hazards model with a multiplicative unobserved heterogeneity factor. It was introduced by Lancaster (1979) for the analysis of state dependence and heterogeneity in unemployment duration data.
Specification and identification
In a MPH model with gamma distributed unobserved heterogeneity, the hazard rates among survivors up to any given point in time are gamma distributed as well, but with smaller scale parameter. In a paper with Gerard van den Berg, I show that, much more generally, the distribution of the unobserved heterogeneity, appropriately rescaled, converges to a gamma distribution.