Child Human Capital – The Importance of Parenting Style

Investments in the human capital of children during their upbringing determine the opportunities available in adulthood. Recognizing that the parent-child interaction plays a significant role in the accumulation of child human capital, we develop a differential game in which the parent may invest directly in child human capital and the child consumes goods that influence the accumulation of their human capital. We compare the accumulation of child human capital between three different parenting styles, formalized as three different solution concepts to the differential game: (i) the parent and the child maximizes a joint utility function (cooperative solution), (ii) the parent announces a strategy dependent on time only (open-loop Stackelberg), (iii) the parent’s strategy depends on the accrued amount of human capital (feedback Stackelberg). We show that under rather general assumptions the open-loop Stackelberg equilibrium is time consistent, and coincides with a feedback Stackelberg equilibrium. Using cooperative parenting as a benchmark, we find that less or more child human capital may be accumulated over the family’s planning horizon under “open-loop Stackelberg” parenting, depending on parental and child preferences for human capital and wealth at the terminal time of the family’s planning horizon, and on the extent to which child consumption influences the accumulation of their human capital. In particular, if the child’s preference for terminal time wealth is strong enough, more human capital will be accumulated under “open-loop Stackelberg” parenting.