The past years have seen an increasing interest in approaches which model demographic counts in populations as realizations of random variables. A basic assumption is the distribution of counts, in particular its conditional variance. Established models have often applied the Poisson regression model or semiparametric extensions like Poisson quasi likelihood. We review the underlying assumptions of the Poisson process and their apparent violations in migration flows. For cross-sectional migration counts we propose a two-parameter variance function which represents, respectively, clustering by household migration and unobserved heterogeneity. The variance function has an interpretation as quasi negative binomial distribution with specified nuisance parameter. Provided the mean function is correctly specified, consistent and asymptotically efficient estimation can be achieved by quasi-generalized pseudo maximum likelihood, using a root-n-consistent estimator of the nuisance parameter. A possible misspecification of the mean function arises from simultaneity between migration count and person-years lived, which can be handled by two-stage residual inclusion. Our model is applied to migration inflows and outflows of the 171 municipalities of Burgenland in 2011. Several predictors such as geographic location or population shares of non-nationals and young adults are identified as significant. Estimation of the variance function parameters should be based on robust procedures.
