On Differential Fertility and the Intergenerational Dynamics of Inequality

We study the implications of differential fertility on cross-sectional inequality in a canonical model of the intergenerational transmission of capital. Our main theoretical result shows that, with differential fertility, there exist stable atomless steady state distributions of capital where there would be only degenerate steady states without differential fertility. We establish convergence results and derive a mathematical expression for these novel atomless steady states in terms of the primitives of the model, thus providing the tools to analytically study the implications on inequality that result from differential fertility within the standard family economics framework. We use our framework to extend existing comparative static results on the relationship between differential fertility and inequality, and to shed new light on the question of public versus private education by developing an intergenerational model with endogenous differential fertility in which there is a long run equity-efficiency trade-off in the choice of educational provision.