Hazard rate models are used to study the instantaneous probability (hazard) of a transition from one state to another, given that the transition has not already occurred.  An implicit assumption in standard models is that of certain exit implying that all observations will eventually experience the event of interest if the observation period is sufficiently prolonged.  In an application of unemployment durations, it implies that all unemployed individuals will eventually find employment.  In studying criminal recidivism, Schmidt and Witte (1989) argue that some criminals are “cured” in that they will never commit another crime that sends them back to prison.  They introduce a split hazard model that takes into account the possibility that the transition from one state to another may never occur.[1]

In this paper I argue I show that although split models have an obvious intuitive appeal in social sciences, they are prone to certain identification problems.  In particular, a split parameter can spuriously be influenced by the misspecification of the functional form of the underlying hazard function.  Similarly an incorrect functional form of the hazard may be inferred when the hazard model is split.  For illustration, I show that when the underlying model is Weibull-gamma, the estimated split Weibull model spuriously indicates that a fraction of observations will never experience an exit.  Similarly, researchers may confuse split data with the presence of neglected heterogeneity in the model.  The allowance for both split and neglected heterogeneity may just be compensating for a restrictive Weibull specification that only allows monotonic hazards.  It is difficult to discriminate between the split Weibull and the Weibull-gamma models since the reduced form of both models permit an ‘inverted U’ shape of the hazard.  This result is highlighted with Monte Carlo experiments.  I argue that although the reduced forms are somewhat similar, the interpretation of the results for the two models can be quite different.