For pay-as-you-go financed pension systems, claims may be calculated according to individual contributions (income) or the number of children of a family. We analyse the optimal structure of these parameters in a model with endogenous fertility. It is shown that for both structural determinants there exists no interior solution of the problem of intragenerational utility maximisation. Thus, pure systems are always welfare maximizing. Furthermore, children-related pension claims induce a fiscal externality that tends to be positive. The determination of the optimal contribution rate shows that the widely accepted Aaroncondition is in general a misleading indicator for the comparison of fully funded and pay-as-you-go financed pension systems.