We re-examine the theoretical concept of a production function for cognitive achievement, and argue that an indirect production function that depends upon the variables that constrain parents' choices is both moretractable from an econometric point of view, and more interesting from an economic point of view than is a direct production function that depends upon a detailed list of direct inputs such as number of books in the household. We estimate flexible econometric models of indirect production functions for two achievement measures from the Woodcock-Johnson Revised battery, using data from two waves of the Child Development Supplement to the PSID. Elasticities of achievement measures with respect to family income and parents' educational levels are positive and significant. Gaps between scores of black and white children narrow or remain constant as children grow older, a result that differs from previous findings in the literature. The elasticities of achievement scores with respect to family income are substantially higher for children of black families, and there are some notable difference in elasticities with respect to parents' educational levels across blacks and whites
