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

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