This paper discusses the specification and estimation of seemingly unrelate
d multivariate count data models. A new model with negative binomial margin
als is proposed. In contrast to a previous model based on the multivariate
Poisson distribution, the new model allows for over-dispersion, a phenomeno
n that is frequently encountered in economic count data. Semi-parametric es
timation is possible if some of the assumption of the fully specified model
are violated.