The effect of social security on the steady state distribution of consumption

Abel has shown that the introduction of a fully funded social security (SS) would decrease the variances of the steady state distribution of young-period and old-period consumptions. Eckstein et al. have shown that a perfect SS would increase the steady state expected utility of consumptions. We intend to give a caveat on their positive results by showing that the assumptions from which the above propositions are derived have some unrealistic implications, and that by replacing these assumptions with more reasonable ones, we may obtain very different results. The only positive conclusion we are certain of is that a marginal SS insurance in the no insurance situation can always reduce the steady state coefficient of variation of both young- and old-period consumption distributions.