On the Optimality of PAYG Pension Systems in an Endogenous Fertility Setting

In order to help in designing an accurate pension reform, we determine the optimal resource allocation in an endogenous fertility model generating a demographic transition. Extending Samuelson's (1975) work in such a setting, we analyze the problem of the interiority of the optimal solution and discuss the serendipity theorem. We then characterize the decentralization of the first best, showing that a pension policy linking pension benefits to the number of children constitutes an optimal social security program able to restore both the optimal capital stock and the optimal rate of population growth as a unique instrument. We also show that neither a Beveridgean pension scheme nor a Bismarckian one can decentralize the first best.