To explore the role of child care policies in the development of early cognitive skills, I embed a value-added cognitive achievement production function into a dynamic, discrete choice model of maternal labor supply and child care decisions. I use the model to explore how two types of child care policies, Head Start and child care price subsidies, affect child care use and quality decisions and how those decisions in turn affect cognitive achievement. To estimate the model, I use rich panel data from the Early Childhood Longitudinal Survey - Birth cohort (ECLS-B). There are three key findings: (1) Expanding Head Start to children who are currently not eligible has beneficial effects on cognitive achievement, because even children from relatively high quality home environments spend significant amounts of time in low quality child care. An universal expansion of Head Start increases average cognitive achievement scores by 0.21 standard deviations at kindergarten entry. (2) For the typical subsidy-eligible population, child care subsidies have small positive effects on cognitive skills by inducing children from low quality home environments to enter relatively higher quality child care environments. Six months of exposure to a subsidy program increases cognitive achievement scores by .036 standard deviations on average. (3) Without Head Start the black-white achievement gap at kindergarten entry increases by 9 percent and child care subsidies decrease the black-white achievement gap at kindergarten entry by 3 percent.