PAY-AS-YOU-GO PUBLIC PENSIONS WITH ENDOGENOUS FERTILITY

Veall's (1986) model of public pensions is generalized to allow for endogenous fertility. We show that gifts to the old, which can be viewed as social security contributions, are always positive in the steady state. An optimal stationary allocation is sustainable if savings are zero and fertility is exogenous. However, the optimal allocation is in general not sustainable. In particular, if a government enforces a social security plan setting the pension level at the optimal gifts and individuals optimize under the pension constraint. the resulting sustainable outcome is in general different from either the optimal or Nash outcome.