Human Capital and Pensions with Endogenous Fertility and Retirement

We study an OLG model with child policies and a PAYG pension with endogenous retirement and fertility. The result of the planned economy is compared to the decentralized competitive equilibrium deriving optimal policies. We show that in the presence of a PAYG pension system, the optimal policy mix includes an education subsidy and a subsidy for the supply of labor in old age. Fertility should be taxed or incentivized depending on whether there is full or partial retirement, and on the parameters. We focus on the parameter reflecting the deterioration of human capital and show that a child tax may be required