Wealth Composition, Endogenous Fertility and the Dynamics of Income Inequality

This paper analyzes how differences in the composition of wealth between human and physical capital among families affect fertility choices. These in turn influence the dynamics of wealth and income inequality across generations through a tradeoff between quantity and quality of children. Wealth composition affects fertility because physical capital has only a wealth effect on number of children, whereas human capital increases the time cost of child-rearing in addition to the wealth effect. I construct a model combining endogenous fertility with borrowing constraints in human capital investments, in which wealth composition is determined endogenously. The model is calibrated to the PNAD, a Brazilian household survey, and the main findings of the paper can be summarized as follows. First, the model implies that the cross-section relationship between fertility and wealth typically displays a U-shaped pattern, reflecting differences in wealth composition between poor and rich families. Also, the quantity-quality tradeoff implies a concave cross-section relationship between investments per child and wealth. Second, as the economy develops and families overcome their borrowing constraints, the negative effect of wealth on fertility becomes smaller, and persistence of inequality declines accordingly. The empirical evidence presented in this paper is consistent with both implications.