Modelling Multiple Unemployment Spells from Longitudinal Survey Data

1. INTRODUCTION The modelling problem addressed in this paper has been called correlated failure-time modelling, multivariate survival modelling, multiple spells modelling, or a recurrent events problem, and is studied in biomedical Generally this type of modelling is required for data that arise in time-to-event studies when two or more events happen to the same subject. In such a case, the failure times are correlated within subject, and thus the assumption of independence of failure times conditional on given measured covariates, required by standard survival models, is violated. The research interest is usually to assess the effect of various covariates considered as potential risk factors. In studies of duration of spells (poverty, jobless-ness, etc.), the 'failure' is equivalent to 'exit' out of the state of interest. The dependence among the observed spells from the same individual comes from the fact that these spells share certain unobserved characteristics of the individual. The effect of these unobserved characteristics can be explicitly modelled as a random effect (e.g., Clayton and Cuzick, 1985). When this is done, it is assumed that the random effect follows a known statistical distribution. The gamma distribution with mean 1 and unknown variance seems to be the distribution of choice in many applications. Then, estimates of random and fixed effects can be obtained by some suitable method (e.g., two-stage likelihood (Lancaster, 1979), using an EM algorithm (Klein, 1992), etc.). The paper does not explore this method any further. Another approach is to treat the dependence among multiple spells as a nuisance, and to model the marginal distributions of the individual spells without explicit modelling of the dependencies among the spells, with a possible utilization of the order of the spells in the model specification. Following Lin and Wei (1989) it is possible to modify only the 'naive' covariance matrix of the estimated model parameters obtained under the assumption of independence since the correlated durations need to be accounted for in the variance estimates but not in the estimates of parameters per se. An additional property of many multiple spells, often ignored, is that they are ordered 'events': the second spell cannot occur before the first. This approach of working independence and corrected variance can easily be made to account for the order of the spells.