The Correlation of Durations in Multivariate Hazard Rate Models

Abstract

This empirical analysis of multiple durations using multivariate mixed proportional hazard rate models is widespread. In such models, the duration variable are dependent if their unobserved determinants are dependent on each other. In this paper it is shown that these models restrict the magnitude of the correlation of the duration variable. For example, if the baseline hazards are constant, then this correlation necessarily lies between -1/3 and 1/2. Similar results hold for more general models. The usefulness for empirical analysis is twofold. First, the results can be used to assess the ability of the model to describe certain phenomena, relative to the models that impose less restrictions on the values the correlation can attain. Secondly, they suggest that, in parametric analyses, it is important to take a family of heterogeneity distributions that is flexible in the sense that it does not restrict the values the correlation can attain either further. We show that some frequently used parametric families are much more restrictive than others.Multivariate hazard rate models, competing risks, proportional hazards, correlation of nonnegative random variables.