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? How does social security change the cross-sectional relationship between fertility and income? Does social security further affect the dynamics of the earnings distribution by changing differential fertility? We answer these questions in a three-period OLG model with heterogeneous agents and endogenous fertility. We argue that given its redistributional property, social security affects people's fertility behavior differentially by income. In the model, earning ability is transmitted from parents to children. Hence, social security can have a significant impact on the dynamics of the earnings distribution through its effects on differential fertility. 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) child-rearing cost and expect their children will have higher (lower) earnings than themselves and give back relatively more (less) in transfers. Social security reduces fertility by substituting children out of parents' old-age portfolio. It reduces fertility of the poor proportionally more than it reduces fertility of the rich because social security payments are a larger portion of old-age savings for poor people. These results are consistent with features of the U.S. fertility data. We calibrate the model to the U.S. data and find that social security can explain 32% of the decline in poor-rich fertility differential between the cohort of women born during 1891-1895 and the cohort of women born during 1946-1950.