A child-allowance system is to raise fertility beyond the individual optimum. The more heterogeneous the population …

heterogeneity of rearing costs and of enjoying children is introduced. Two major results: (i) excluding negative savings, fertility … decreases with pension contributions and increases with taxes; (ii) the introduction of fertility-dependent pensions may … strengthen heterogeneity in fertility. …

Since the seminal work of Becker, the dynamics of endogenous fertility has been based on the trade-off faced by parents … upstream, so as to keep fertility endogenous. We do that by adding a negative "sibship size effect" on human capital formation …, the possibility of a jump from a state with high fertility and low income to a state with low fertility and high income …