Old-age social security tends to be unsustainable in nature in that it reduces individuals' demand for children as a measure to support their old age, which in turn undermines the financial base of social security. Using a simple overlapping-generations model with endogenous fertility and income transfer from children to parents, we discuss the maximum size of a pay-as-you-go social security program that can prevent a cumulative reduction of fertility and make the program sustainable. We also show that childcare allowance raises the maximum size of the program and raises an individuals' lifetime utility, and derive the optimal combination of social security and childcare allowance.
