Birth Rates, Factor Shares, and Growth

Increases in capital shares affect the marginal productivity of capital, stimulating capital accumulation. Can a decrease in labor shares reduce the supply of labor? We explore this question using a model of fertility inspired by Caldwell (1982) and Boldrin and Jones (2002). Individuals may transfer wealth to the future in two ways: by saving and by having children. Raising children has a cost in terms of current consumption but generates future income through intergenerational transfers. In this setting, a redistribution of income from labor to capital affects the return of savings and children in opposite ways and generates incentives for more savings and fewer children. Two pieces of evidence motivate our model. First, recent historical evidence shows that the increases in capital shares that preceded the Industrial Revolution coincided with falling birth rates. Second, for current developed economies, changes in labor shares correlate positively with changes in fertility rates, and negatively with changes in saving rates