Choices about childbearing and childrearing involve not only the number of children but also the `quality' of each child, which depends on the amount of their own time and of purchased goods and services that parents devote to childrearing. Models explaining family size have not tended to include the quantity of purchased childcare (i.e. childminders) as a separate explanatory variable; this has been included only in a composite variable representing all purchased goods and services. In Discussion Paper No. 238, Research Fellow John Ermisch develops a model in which couples choose explicitly a combination of mother's time and purchased childcare for the rearing of their children. For simplicity, it is assumed that the father's time does not enter into the model.)
In Ermisch's model, a couple seek to maximize their lifetime utility, which depends on both child quality multiplied by the number of children and other parental consumption. They choose values for the amount of mother's time that is devoted to children, to work and to consumption (or leisure); the amount of purchased childcare time; and the amount of goods and services devoted to childrearing and to other consumption. The theoretical model implies that the mother's wage has an ambiguous impact on her completed fertility. The net impact depends on whether the income effect of higher wages (i.e. ability to afford more purchased childcare as well as other goods) dominates the substitution effect (i.e. the increased opportunity cost of childbearing). The main new implication of the model is that, while it is likely that an increase in the mother's wage will have a negative effect on family size at low to moderate levels of wages, the effect will become less negative as the level of wages increases (or the price of purchased childcare falls). At low wages it is more likely that no childcare is purchased: all the time employed in rearing the children is provided by the mother and so it is more likely that the opportunity cost of higher mothers' wages reduces family size. At very high wages, when the wage rate exceeds the `efficiency-adjusted' cost of purchased childcare, there is no substitution effect at all and a higher wage may even lead to a larger family size.
Ermisch tests the predictions of this theoretical model by analysing the factors influencing family size at the fifteenth anniversary of marriage in a sample of 5,320 women from the 1980 Women and Employment Survey (WES). The WES provides data on the timing of all demographic events and changes of employment, as well as relevant background information. The econometric analysis provides empirical evidence that women with a higher wage at the start of marriage have smaller families; this effect on fertility becomes `less negative' as the mother's wage increases. This supports one of the primary predictions of the theoretical model. Ermisch also uses the WES data to analyse the effects of a woman's wage and her husband's earnings on her paid employment after marriage. As the theoretical model predicts, higher husband's earnings reduce the amount of time the wife spends in paid employment after marriage, and increase the family size. The theoretical model indicates that subsidizing childcare could either increase or decrease married women's labour supply, but unfortunately the absence of appropriate British data makes it impossible to answer this conclusively: the predictions of the model about the effects of the cost of childcare on fertility and labour supply are currently being tested with Swedish data

Purchased Child Care, Optimal Family Size and Mothers' Employment: Theory and Econometric Analysis John Ermisch

Discussion Paper No. 238, April 1988 (HR)