Sustainability of social security in a model of endogenous fertility

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 individual's lifetime utility.