The Production of Cognitive Achievement in Children: Home, School, and Racial Test Score Gaps

This paper studies the determinants of children's scores on tests of cognitive achievement in math and reading. Using rich longitudinal data on test scores, home environments, and schools, we implement alternative specifications for the cognitive achievement production function that allow achievement to depend on the entire history of lagged home and school inputs as well as on parents' ability and unobserved endowments. We use cross-validation methods to select among competing specifications and find support for a variant of a value-added model of the production function augmented to include information on lagged inputs. Using this specification, we study the sources of test score gaps between black, white,…