© 2016 The Department of Economics, University of Oxford and John Wiley & Sons Ltd Accumulation of cognitive achievement is investigated using an indirect production function, a dynamic econometric model and a rich data set. Gaps between scores of black and white children remain constant, narrow, or disappear entirely as children grow older, depending upon the measure and the family structure. Income elasticities are higher for children of black families, and there are differences in elasticities with respect to parents' educational levels. The effects of fathers' and mothers' educational levels differ. Between children of two-parent families and mother-only families, there is a gap that is at least as important as the racial gap.