It is been well established by numerous studies that cognitive achievement, measured by various tests, is related to future labor market outcomes. In light of these results, a large body of empirical research has focused on the determinants of cognitive achievement. This study contributes to this literature by identifying and estimating a technology of skill formation as a function of family and school investments. In the model, cognitive skills, family investments and school investments are latent variables measured by a series of proxies. As families may adjust their investment in home inputs in reaction to some exogenous change in school investments this study jointly estimates the production function for cognitive achievement and the parental reaction function to school investment. Using this framework, the total effect of a change in school investment on cognitive achievement is indentified. As policy-makers want to implement school reforms intended to enhance the cognitive achievement of children, knowing whether school investment will crowd out home investments or will be complemented by them may facilitate more informed policy decisions