Optimal parental leave subsidization with endogenous fertility and growth

In a life-cycle dynastic family model with endogenous fertility, labor-leisure, and accumulations of human and physical capital, this study examines the growth and welfare effects of parental leave subsidization when there is human capital externality. Compared with the social optimum, such externality causes higher fertility and less parental time and expenditure inputs in child human capital development, and thus lower growth and welfare in the laissez-faire equilibrium. Parental leave subsidization financed by a lump-sum tax (PLS_LS) promotes economic growth and welfare by improving the quantity-quality trade-off of children. There exists an optimal rate of parental leave subsidy but it cannot achieve the social optimum. Parental leave subsidization financed by a labor income tax (PLS_LI) increases the parental time input in child human capital and economic growth. It may improve welfare despite the distortionary effects of labor income taxes in exacerbating the problems of excessive fertility and under-investment of parental expenditure in child human capital. By calibrating the laissez-faire model economy to the U.S. data, our quantitative results show that for an empirically plausible degree of human capital externalities, the optimal parental leave subsidy under PLS_LI implies a fully-covered leave duration of 8.7 weeks per parent, which increases the annual growth rate of output per worker by 0.3 percentage points and welfare by 0.02 percent from the laissez-faire equilibrium.