We construct and estimate a model of child development in which both the parents and children make investments in the child's skill development. In each period of the development process, partially altruistic parents act as the Stackelberg leader and the child the follower when setting her own study time. We then extend this non-cooperative form of interaction by allowing parents to offer incentives to the child to increase her study time, at some monitoring cost. We show that this incentive scheme, a kind of internal conditional cash transfer, produces efficient outcomes and, in general, increases the child's cognitive ability. In addition to heterogeneity in resources (wage offers and non-labor income), the model allows for heterogeneity in preferences both for parents and children, and in monitoring costs. Like their parents, children are forward looking, but we allow children and parents to have different preferences and for children to have age-varying discount rates, becoming more "patient" as they age. Using detailed time diary information on the allocation of parent and child time linked to measures of child cognitive ability, we estimate several versions of the model. Using model estimates, we explore the impact of various government income transfer policies on child development. As in Del Boca et al. (2016), we find that the most effective set of policies are (external) conditional cash transfers, in which the household receives an income transfer given that the child's cognitive ability exceeds a prespecified threshold. We find that the possibility of households using internal cash transfers greatly increases the cost effectiveness of external cash transfer policies.