This paper explores the optimal risk sharing arrangement between generations in an overlapping generations model with endogenous growth. We allow for nonseparable preferences, paying particular attention to the risk aversion of the old as well as overall life-cycle risk aversion. We provide a fairly tractable model, which can serve as a starting point to explore these issues in models with a larger number of periods of life, and show how it can be solved. We provide a general risk sharing condition, and discuss its implications. We explore the properties of the model quantitatively. Among the key findings arethe following. First and for reasonable parameters, the old typically bear a larger burden of the risk in productivity surprises, if old-age risk-aversion is smaller than life risk aversion, and vice versa. Thus, it is not necessarily the case that the young ensure smooth consumption of the old. Second, consumption of the young and the old always move in the same direction, even for population growth shocks. This result is in contrast to the result of a fully-funded decentralized system without risk-sharing between generations. Third, persistent increases in longevity will lead to lower total consumption of the old (and thus certainly lower per-period consumption of the old) as well as the young as well as higher work effort of the young. The additional resources are instead used to increase growth and future output, resulting in higher consumption of future generations.
social optimum pension systems risk sharing overlapping generations.