Optimal policies in an aging society

We analyze optimal social security in a two-period overlapping generations model with endogenous retirement and demographic change. In this model, households choose to spend the second period of their lives in full retirement if the tax rate on labor income exceeds a certain threshold. We find that this threshold is increasing in life expectancy and decreasing in the fertility rate, which implies that both types of demographic change increase the relevance of the partial retirement case in which households participate on the labor market. Related, both an increase in life expectancy and a drop in fertility imply that retirement is delayed in the partial retirement case. We also show that when the government decides about the retirement age, the command optimum can be replicated through social security policies as long as the laissez-faire equilibrium features an overaccumulation of capital. When households decide about their retirement age themselves, however, replication of the command optimum is not possible, even if overaccumulation of capital applies. In both cases, it is optimal to expand social security when longevity increases and to reduce it when fertility drops.