On the specification and estimation of the production function for cognitive achievement

This paper considers methods for modelling the production function for cognitive achievement in a way that captures theoretical notions that child development is a cumulative process depending on the history of family and school inputs and on innate ability. It develops a general modelling framework that accommodates many of the estimating equations used in the literatures. It considers different ways of addressing data limitations, and it makes precise the identifying assumptions needed to justify alternative approaches. Commonly used specifications are shown to place restrictive assumptions on the production technology. Ways of testing modelling assumptions and of relaxing them are discussed.