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 production function for achievement and test their assumptions. We do not find support for commonly used restrictive models that assume test scores depend only on contemporaneous inputs or that assume conditioning in a lagged score captures the effects of all past inputs. Instead, the results show that both contemporaneous and lagged inputs matter in the production of current achievement and that it is important to allow for unobserved child-specific endowment effects and endogeneity of inputs. Using a specification that incorporates these features, we analyze sources of test score gaps between black, white and Hispanic children. The estimated model captures key patterns in the data, such as the widening of minority-white test score gaps with age, which is most pronounced for black children.