The Dispersion of Completed Birth Parity: Empirical Patterns and Modelling Options

Existing studies of fertility concentration have focused on nonparametric measures such as `have half', `half have', and the well-known Gini index. Here, we review the literature and discuss the nature of fertility variation, as well as the behavioural patterns leading to over- and underdispersion respectively and their theoretical implications. We demonstrate that commonly used concentration measures are less informative than is generally believed, and cannot be used to study changes in fertility variation in the presence of changes in the level of fertility, or to draw inferences about behavioural heterogeneity or change. Instead, we focus on the statistical measure of dispersion (i.e. the variance-to-mean ratio), and present a collection of empirical results on patterns of over- and underdispersion in relation to the overall level of fertility, and discuss their significance. The finding that, especially when fertility is low, instances of under-dispersion are common, which are difficult to model with the statistical toolkit customary in demographic analysis, motivates an introduction to alternative count models recently revived in the statistical literature and an examination of their ability to fit both over- and under-dispersed distributions of complete parity.