Répartition des familles selon le nombre des enfants : un modèle et son application à la fécondité différentielle

Degiovanni Patrick, Deville Jean-Claude, Gubian Alain. ? A Model of the Distribution of Family Size and its Application to the Study of Differential Fertility. The lognormal distribution is fitted to the distribution of family sizes by using three parameters : the proportion of childless families, for those with one child or more the maximum likelihood estimate of the mean and variance of the corresponding normal distribution is used. The method is applied to a number of distributions of family size obtained from various surveys carried out by INSEE. Variations in the mean which depend on the social environment, the age at marriage, the number of children of the spouses' parents, the difference between the age of the spouses and the educational level achieved by the mother are well known, but relatively less is known about fluctuations in the variance. These show up differences in the behaviour of certain social groups and also show the process of convergence of behaviour which is currently in progress in France. A reduction of the variance when the mean remains constant will result in a decline of fertility.