This paper studies the dynamic relationship between parental labor supply, children’s cognitive development and intra-household bargaining power. To do so, I construct a model that incorporates preference heterogeneity across and within households, cooperative bargaining with explicit outside options, a dynamic technology of the child’s cognitive development, and endogenous parental human capital and wages. Using detailed U.S. panel data on married households, I identify and estimate the model with the Method of Simulated Moments, and show that it replicates observable trends and heterogeneity in parental time use, the use of formal childcare arrangements and child test scores. With estimates of the model primitives in hand, I simulate the effects of cash transfers and formal childcare subsidies. First, I find that the cost-effectiveness of the Child Tax Credit could be improved by giving cash to mothers directly and by making the credit increase with the child’s age, which would foster child cognition and reduce intra-household inequality. Second, I consider expansions of the Child and Dependent Care Tax Credit which offer larger formal childcare subsidies and relax the employment requirements. I estimate that a 25 percent subsidy could boost young children’s skills by over 0.1 standard deviations, increase maternal labor supply even when there is no work requirement, and be financed at no additional cost through a 50 percent reduction in the Child Tax Credit for households with young children. (author abstract)