SEEMINGLY UNRELATED NEGATIVE BINOMIAL REGRESSIONy

The seemingly unrelated Poisson (SUP) model (King (1989a), see also Aptech (1994)) is a model for bior multi-variate counted outcomes. Correlation between equations is introduced through a convolution structure with a common additive factor. Previous economic applications include the joint analysis of voluntary and involuntary labour mobility (Jung and Winkelmann, 1993) and the number of recreational trips to each of two sites (Ozuna and Gomez, 1994). From a methodological point of view, these studies have been subject to a serious limitation of the seemingly unrelated Poisson model, namely its inability to account for over-dispersion, or extra-Poisson variation in the data. But this phenomenon is widespread in economic applications, as is well documented for univariate models (Winkelmann, 2000), and the usefulness of the SUP model is thus limited. Indeed, much of the recent literature on multivariate count data has turned away from a convolution structure and rather introduced correlation by mixing over a multiplicative error (see, for instance, Cincera, 1998, Gurmu and Elder, 1998, Chib and Winkelmann, 1999). Over-dispersion arises naturally in this context. In this paper, I propose an alternative simple new model for seemingly unrelated counts with over-dispersion. The distinctive feature of this model is that it does not abandon the basic convolution structure of the seemingly unrelated Poisson model but rather generalizes some of its assumptions in order to allow for over-dispersion. The new model has negative binomial marginals and is referred to as a `seemingly unrelated negative binomial' (SUNB) model. The SUNB generalizes the SUP model by introducing one additional dispersion parameter, the statistical signi®cance of which can be tested by standard tests.