Dynamic Efficiency and Pareto Optimality in a Stochastic OLG Model with Production and Social Security

We analyze the interaction between risk sharing and capital accumulation in a stochastic OLG model with production. We give a complete characterization of interim Pareto optimality. Our characterization also subsumes equilibria with a PAYG social security system. In a competitive equilibrium interim Pareto optimality is equivalent to intergenerational exchange efficiency, which in turn implies dynamic efficiency. Furthermore, contrary to the case of certainty, dynamic efficiency does not rule out a Pareto-improving role for a social security system. Social security can provide insurance against macroeconomic risk, namely aggregate productivity risk in the second period of life (old age) through dynamic risk sharing. The mechanism through which social security can Pareto-improve market allocations resembles a Ponzi scheme. But instead of rolling over debt, we can interpret our scheme as one that raises contributions and then rolls over an insurance contract.