Can Social Security be welfare improving when there is demographic uncertainty?

This paper studies the welfare implications of a PAYG pension system in a neoclassical growth model with overlapping generations, demographic uncertainty and sequentially incomplete markets. In absence of public pensions, small cohorts tend to be favored by the changes in relative prices implied by demographic shocks. As described in Bohn (1999), PAYG Define Benefit systems can help to share the financial risks created by demographic uncertainty across the generations. The overall welfare impact depends on the balance between this insurance effect and the well known crowding-out effect stemming from the unfunded character of the system. Therefore, the question about the total welfare impact of PAYG pensions is intrinsically quantitative. In this paper we use a four-periods OLG model calibrated to the US economy to provide a first quantitative assessment of the relative size of the different effects involved.The findings are unfavorable for PAYG pension systems: the size of the crowding-out effect is large enough to offset the benefits from risk sharing, making the introduction of public pensions a welfare decreasing process (even in ex-ante terms). In particular, with a marginal PAYG pension scheme (providing a 2\% replacement rate of the average wage) small cohorts lose the equivalent to a 1.9% of their consumption in the age interval 20/40, while larger cohorts loss is 1.5%.