Intergenerational Risk Sharing: Myth or Possibility

In this paper we develop an algorithm to numerically solve dynamic stochastic overlapping generations economies. In our model agents live for six periods and face idiosyncratic as well as aggregate uncertainty with respect to their labor and capital income. Insurance markets are absent and individuals can only self-insure by risk-free borrowing and lending. Our algorithm is based on Chebychev collocation methods and allows us to compute recursive competitive equilibria in an economy where the state space includes the distribution of assets across ages, in addition to the exogenous discrete Markov chain describing aggregate and idiosyncratic uncertainty. We employ our numerical techniques to study the intergenerational risk sharing properties of a pay-as-you go social security system and the welfare effects of a hypothetical reform towards a fully funded system. Although an unfunded social security system provides partial intergenerational insurance against aggregate and intragenerational insurance against idiosyncratic uncertainty, the detrimental effects for aggregate capital accumulation more than outweigh the insurance aspect of an unfounded system. The ergodic distribution of ex ante utilities with an unfounded system is stochastically dominated by the corresponding distribution with a fully funded system for a large range of the structural parameters of the model. More surprisingly, sequentially completing the markets, i.e. providing perfect risk sharing against idiosyncratic uncertainty can lead to substantial welfare losses for future generations. This is due to the fact that precautionary saving in the absence of complete markets leads to higher capital accumulation and hence higher equilibrium wages for future generations.