Welfare Effect of Social Security: With Uninsured Income Risk (with Gaetano Bloise) 

Abstract:

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 a standard two-period lived overlapping generations economy with productive uncertainty and old age idiosyncratic labor income risks. 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, and a "general equilibrium" effect, that takes into account the reallocation of capital and labor. 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. The former is negative (positive) under dynamic efficiency (inefficiency) and latter is positive under crowding out, because a lower capital accumulation reduces the risk associated with the interaction between aggregate and individual uncertainty. In a calibration exercise, we show that the net effect is positive for empirically plausible values of the long run average safe rate, GDP growth and for a large enough risk aversion.