Pay-as-you-go social security and endogenous fertility in a neoclassical growth model

This paper theoretically studies how unfunded pay-as-you-go social security affects economic growth, the fertility rate, and welfare in a neoclassical growth model. In addition, this paper considers a more general form of child-rearing cost, which is a mixture of time and money. The first observation is that whether the fertility rate increases or not by the expansion of the pay-as-you-go social security depends on (1) the size of the monetary child-rearing cost relative to the time spent on child-rearing and (2) the current fertility and interest rate in laissez faire. The second observation is that income per worker can increase by an expansion in pay-as-you-go social security when the output elasticity of capital is sufficiently small and the payroll tax rate is high. The last finding is that welfare can be improved even though capital is underaccumulated in an economy.