Key demographic variables, such as the number of children and the number of marriages or divorces, can only take integer values. This papers deals with the estimation of single equation models in which the counts are regressed on a set of observed individual characteristics such as age, gender, or nationality. Most empirical work in population economics has neglected the fact that the dependent variable is a nonnegative integer. In the few cases where this feature was recognized, the authors advocated the use of the Poisson regression model. The Poisson model imposes, however, the equality of conditional mean and variance, a restriction which is often rejected by the data. We propose a generalized event count model to simultaneously allow for a wide class of count data models and account for over- and underdispersion. This model is successfully applied to German data on fertility, divorces and mobility.