This project is on the field of family macroeconomics and requires me to solve a medium-scaled dynamic programming problems, which would not be made available without high-level computing facility. This study concerns how family planning policies explain the demographic transition and human capital accumulation in China (1970-2016). Literature such as Becker and Barro (1988) and Barro and Becker (1989) claimed the quantity-quality trade-off in that the restriction in child number would bring higher quality of the children. I then claim that these policies deliver effects more than just birth control and quantity-quality trade-off. First, birth restriction reduces the number of child per family, but the reduction differs across different socioeconomic groups. This heterogenous response changes the share of different family type in the next generation, and therefore change the mean level of human capital. Second, out-of-quota birth mostly happened to low socioeconomic groups. Penalties applied to these groups imply that low socioeconomic groups end up worse-off and result in human capital dispersion. I decompose the human capital transition into these channels and study the intergenerational consequences on inequality, urbanization and economic development. In addition, the extended model reveals important interactions between rural-urban migration restriction and family planning policy. For example, when agents face stringent migration restrictions, fertility differential directly results in the rural-urban divide.
To this end, I built a model based on quantity-quality trade-off literature with endogenous fertility, consumption-saving and educational investment decision. This study has important policy implications, because birth control policy is widely believed to alleviate poverty and help the accumulation of human capital by restricting fertility and encourage human capital investment. We reveal that multiple different mechanisms would work against each other, and the overall effect would be mixed. Social problems such as high old age dependency ratio, low labor participation rate arising from the drastic demographic transition undermined the initial goals and has unintended long-run consequences. In addition, differential fertility induced inequality (De La Croix and Doepke, 2003) cannot be undone by imposing a fine-based birth restriction.