Recent European fertility patterns: Fitting curves to ‘distorted’ distributions

Abstract

Recent patterns of fertility in Europe show marked differences between countries. Recent United Kingdom and Irish fertility curves show 'distortions' in terms of a 'bulge' in early age fertility, distinct from the smoother curves of other European countries. These patterns may not be adequately described by mathematical functions used by previous studies to model fertility curves. A mixture model with two component distributions may be more appropriate. The suitability of the simple and mixture Hadwiger functions is examined in relation to the fertility curves of a number of European countries. While the simple Hadwiger model fits recent period age-specific fertility distributions for some countries, others which display a 'bulge' in early age fertility distributions for some countries, others which display a 'bulg' in early age fertility require a mixture Hadwiger model. Some of the parameters of the Hadwiger models appear to be related to familiar demographic indices. The simple and mixture Hadwiger models appear useful in describing and comparing fertility patterns across European countries.

Modeling fertility curves in Africa

“…The Coale-Trussell function can be considered unsuitable because of its orientation to fertility control. It focuses on marital fertility; the parameters determining the shape of the curve are age of marriage, proportion marrying, and the degree of fertility control (Chandola, Coleman, and Hiorns 1999). The contribution of non-marital fertility to the current fertility patterns in Africa cannot be overlooked in any fertility study in the region.…”

“…However, the modified versions of these distributions by Hoem et al (1981) were found to be useful for fitting Danish fertility curves. Also, studies have revealed that the Hadwiger function is more suited for smooth fertility curves (see Chandola, Coleman, and Hiorns 1999), and that it has a common problem of overestimating fertility data towards the end of the reproductive age (Hoem et al 1981). Hence, it may not be appropriate for fitting African fertility curves.…”

“…Chandola, Coleman, and Hiorns (1999) first considered the possibility of incorporating a separate term into the Hadwiger functions to handle excess early-age fertility. Similar work was done by Peristera and Kostaki (2007) in Model 2 when modeling the excess early age fertility of the UK, Ireland and the US.…”

Multistate modelling extended by behavioural rules: An application to migration

“…Because of the limited number of cases, the single-year-of-age transition rates for the migrants are assumed to be time constant. In the second step, these rates are used to fit two types of parametric models to derive smooth age profiles: the Hadwiger model is used to fit fertility rates and the Coale-McNeil model to fit marriage rates (Hadwiger 1940;Gilje 1969;Coale and McNeil 1972;Chandola et al 1999). Age-specific rates are estimated for all years from 1982 to 2014.…”

The use of a new indirect method to estimate ethnic-group fertility rates for subnational projections for England

“…The literature reports various ways in which the estimates of five-year rates can be converted to rates by single year of age, by modelling age-specific fertility curves as mathematical functions (McNeil et al 1977;Hoem et al 1981;Chandola et al 1999;Schmertmann 2003;Peristera and Kostaki 2007). These methods often include the fitting of splines and the application of the Hadwiger function (Hadwiger 1940), which was used for smoothing ASFRs in London boroughs (Hay and Hollis 2005).…”