The future of the social security system is a big issue in industrial world. Population aging raises the question of the adjustment, or even the replacement of unfunded public pension schemes. The ratio between over-60-year-olds and the working age is expected to double between now and 2040, and should reach a 70% level. Chile was the first to establish a private funded system in 1981. Since then, these schemes spread over Latin America. In these countries, the aim was obviously the eradication of the pay-as-you-go mechanism, though the demographic argument did not fit. In fact, financial markets development is the main cause of the privatization. In the US, liberals argue that the implementation of compulsory subscription private funded system (in order to warrant minimum savings) would eradicate beneficently public unfunded schemes. Feldstein states that the difference between the 2.6 percent Social Security return and the 9.3 percent real pretax return on nonfinancial corporate capital average corresponds to a privatization gain of $18 trillion. However, in Europe, replacement of public systems is not a current topic. Still, to support savings, it is considered introducing private funded schemes, but only as a complement of pay-as-you-go system. Therefore the question is: Are private funded systems designed to replace public schemes as in Latin America, or on the contrary, are private funded systems designed to consolidate public schemes? In order to provide some perspective to that question, we develop in this paper a two living periods OLG model where endogenous growth comes from the time individuals spend to increase their educational level and the average human capital they inherit from the previous generation. In such a framework, we show that the public unfunded pension scheme, which calculates the pension benefits according to the historic of individual wages, generates an incentive to increase the schooling time. Therefore, this retirement system raises economic growth. But since it reduces the need for further private savings, it has a depressive effect on the physical capital stock and leads to an increase in the real interest rate. Faced with a non-debt constraint, the introduction of compulsory subscription private funded system may offset the lack of private savings, without damaging the incentive to increase educational time generated by the public system. Hence, we compute the optimal pension scheme which is consistent with a generational utilitarist criterion. This optimal system is a mixed-system, which reconciles the public unfunded pension scheme with the private funded one, although the yield of the second system dominates the former. Classification JEL: H55, 041, D60
