Optimal social security in a dynastic model with investment externalities and endogenous fertility

This paper studies optimal pay-as-you-go social security with positive bequests and endogenous fertility. With an investment externality, a competitive solution without social security su?ers from under-investment in capital and over-reproduction of population. We show that social security can improve welfare by reducing fertility and increasing capital intensity. We also illustrate numerically that a small degree of this externality is enough to justify the observed high ratios of social security spending to GDP.