Endogenous fertility cycles and childcare services

We construct a two-sector overlapping generation model with endogenous fertility, where one sector produces goods and the other produces childcare services. The elasticity of fertility-related expenditures on services is crucial for determining labor participation and whether fertility converges to a steady state with monotone or oscillation. If capital intensity in the goods sector is greater than the products of elasticity and capital intensity in the service sector, then capital per capita and fertility converge to a steady state monotonically. Conversely, they converge to a steady state with oscillations, otherwise. We find an inverse J-shaped relationship between fertility and elasticity.