We analyze optimal social security in an overlapping generations model with demographic change and endogenous retirement. Households choose to spend the second period of their lives in full retirement if the tax rate on labor income exceeds a threshold. 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: both an increase in life expectancy and a drop in fertility imply that retirement is delayed. We also show that when the government decides about retirement, the command optimum can be replicated through social security policies if the laissez-faire equilibrium features capital overaccumulation. When households decide about their retirement themselves, however, replication of the command optimum is not possible. In both cases, it is optimal to expand social security when longevity increases and to reduce it when fertility drops.

我们分析了人口变化和内生退休的重叠世代模型中的最优社会保障。如果劳动收入税率超过阈值，家庭就会选择完全退休来度过人生的第二阶段。这个阈值是预期寿命的增加和生育率的下降，这意味着两种类型的人口变化都增加了部分退休案例的相关性：预期寿命的增加和生育率的下降都意味着退休被推迟。我们还表明，当政府决定退休时，如果自由放任的话，命令最优可以通过社会保障政策复制均衡的特征是资本过度积累。然而，当家庭自己决定退休时，复制最优命令是不可能的。在这两种情况下，最佳做法是在寿命延长时扩大社会保障，在生育率下降时减少社会保障。