Optimal social security in a dynastic model with human capital externalities, fertility and endogenous growth

In this paper we investigate the optimal scale of pay-as-you-go social security in a dynastic family model with human capital externalities, fertility and endogenous growth. Human capital externalities reduce the return to human capital investment and hence lead to under-investment in human capital and over-reproduction of the population. If the taste for the number of children is sufficiently weak relative to the taste for the welfare of children, social security can be welfare enhancing by reducing fertility and raising human capital investment per child.