Social Security, Differential Fertility and the Dynamics of the Earnings Distribution

Economists and demographers have long argued that fertility differs by income (differential fertility), and that social security creates incentives for people to rear fewer children. Does the effect of social security on fertility differ by income? Does social security further affect the dynamics of the earnings distribution through its differential effects on fertility? We answer these questions in a three-period OLG model with heterogeneous agents and endogenous fertility. We find that given its redistributional property, social security reduces fertility of the poor proportionally more than it reduces fertility of the rich. Assuming that earning ability is transmitted from parents to children, the differential effects of social security on fertility can have a significant impact on the dynamics of the earnings distribution: a relatively lower fertility rate among the poor can lead to a new earnings distribution with a smaller portion of poor people and a higher average earnings level. With reasonable parameter values, our numerical exercise shows that the effects of social security on differential fertility and the dynamics of the earnings distribution are quantitatively important. It is worth mentioning that the mechanism used in the model to generate differential fertility is novel. We follow the line of the “old-age security” hypothesis and assume that children are an investment good in parents’ old-age consumption. Thus, the optimal fertility choice depends on how much transfer is expected from children in relation to the cost of rearing these children to adult life. Since the intergenerational earnings process is mean-reverting, poor (rich) parents tend to have more (fewer) children because they have lower (higher) childrearing cost and expect their children will have higher (lower) earnings than themselves and give back relatively more (less) in transfers.