This paper develops a three-period overlapping generations model to study the impacts of life expectancy, retirement and a social security system (a fully-funded system and a pay-as-you-go system) on long-run economic performance. We assume that agents can only live safely for the first two periods and face uncertainty as to whether they will survive to the third period. We find that an increase in life expectancy will be beneficial to the long-run output per head. However, delaying retirement or increasing the tax burden of young agents under the pay-as-you-go system will be harmful to the long-run output per head. Under a fully-funded system, the Ricardian equivalence will hold if the capital market is perfect. If the capital market is imperfect, increasing the tax rate will increase the long-run output per head.