Fertility and Female Labour Supply

The estimated relationship between the number of children and female labour supply is often negative; however, it is not clear whether this arises because of a causal effect of children on labour supply, or whether it is the result of heterogeneous preferences (women who have a preference for home-based activities have more children and a lower preference for market work). The fact that parents in industrialized countries prefer their families to consist of roughly equal numbers of girls and boys, and are therefore more likely to have a third child if their first two children are of the same sex, is used as an exogenous instrument for the birth of a third child in the female labour supply equation. This paper shows that heterogeneity is likely to be important in the female labour supply function, and that failure to account for heterogeneity leads to exaggerated estimates of the negative effect of children on female labour supply. A similar effect in the female hours of work equation is also demonstrated. NON-TECHNICAL SUMMARY Economists and other social scientists are interested in the relationship between the number of children a woman has, and her labour supply: how likely she is to go out to work, and if she does go out to work, for how many hours. There is no reason to believe a priori that the effect should go in either direction: one may argue that a woman with more children will be less inclined to go out to work, since the time she spends at work will be time foregone with her children, and the expense of childcare will reduce her effective wage. On the other hand, children are extremely expensive, and a mother may have to work more with every additional child to maintain the family income. Nevertheless, most estimates of this relationship have found a negative relationship between the number of children and a woman’s labour supply: that is, that women with more children on average go out to work less than women with fewer children. The problem with these estimates is that most are not able to say anything about causality, since the observed relationship may be due (A) to more children may ‘causing’ women to work less; or (B) to some third factor driving both the desire to have children and the desire to go out to work, so that the two appear to be related but in fact they are not causally related at all. In the language of econometrics, if women did indeed constitute a heterogeneous population, with some having a preference for family-based activity while others had a preference for market-based work, then fertility variables would be ‘endogenous’ in the labour supply function, and estimates of the relationship between the number of children and labour supply would yield no information about the effect of children on labour supply. This paper uses a technique called instrumental variables to get round this problem. This technique relies on finding a variable which is correlated with the number of children a woman has, but not with her likelihood of going out to work. Demographers have known for a long time that women whose first two children are of the same sex (two girls or two boys) are more likely to go on to have a third child than women whose first two children are of different sexes (one boy and one girl). These variables can be used to predict the probability that a woman with two children will go on to have a third child, and this predicted probability can be used in regressions instead of the observed ‘third child’ variable, to obtain estimates of the relationship between children and female labour supply, which more truly reflect the effect of children on whether a woman goes out to work, and for how many hours. This paper finds that under ‘standard’ techniques which do not take account of the endogeneity of fertility variables, having a third child is associated with a reduction in the probability that a woman will go out to work of between 12% and 15%. On the other hand, if endogeneity is accounted for, having a third child is associated with an increase in the probability of going out to work, of between 7% and 13%. This second set of estimates is rather imprecise and statistical tests do not rule out that the estimated effects are in fact equal to zero. However, the second set of estimates is significantly different from the first set, which shows that if the researcher fails to correct for the endogeneity of fertility variables, the estimated effect of fertility on female labour supply will be exaggerated in a negative direction.