Welfare Effects of Social Security With Uninsured Income Risk

We provide an analytical decomposition of the welfare effect of raising the contribution rate of a pay-as-you-go social security at equilibrium in an overlapping generations economy with productive uncertainty and idiosyncratic labor income risks. Based on the observed long-run pattern of GDP growth and safe rate for most advanced economies, we argue that social security is likely to be a Pareto improving policy due to the over accumulation of capital that arise from individual risk at competitive equilibria. Assuming Epstein-Zin preference representation and Cobb-Douglas technology, the welfare effect can be decomposed into a "direct" effect, which takes into account the inter-generations reallocation of consumption and risk at status quo, a "general equilibrium" effect, that takes into account the reallocation of capital and labor and an "idiosyncratic risk" component. The relevant statistics that affect these two components are the growth-adjusted dominant root of the stochastic discount factor at the competitive equilibrium and the covariance between wages and individual labor productivity. Since the estimated direct and general equilibrium effects are very small, the net effect of social security is almost entirely determined by the idiosyncratic risk component, which is shown to affect positively individuals’ welfare under crowding out.