This paper analyzes to what extent a pay-as-you-go, pension scheme can be justified under uncertainty. It is widely known that a funded scheme is preferable to a pay-as-you go scheme if the interest rate is higher than the rate of wage income growth. Under uncertainty about the interest rate, however, there is a chance that a pay-as-you-go scheme can be justified. Our simulation suggests that a substantial reduction of the size of the current pay-as-you-go pension scheme would be optimal, given the expected interest rate and wage income growth as well as their volatility observed in the past twenty years in Japan.