Social Security, Optimality, and Equilibria in a Stochastic Overlapping Generations Economy

Social security institutions implement intergenerational transfers and distribute risks over time. To compare various social security designs, we study an overlapping generations model with demographic shocks. Production takes place through a neoclassical production function subject to productivity shocks. We give a near characterization of optimal allocations. We study rational expectations equilibria when contributions are mandatory, based on labor and capital income. We also describe the equilibria of an economy with a voluntary pay-as-you-go social security fund, and show that they have a long-run optimality property. An example with Cobb–Douglas production and utility functions illustrates the results.