School inputs and skills: Complementarity and self-productivity

Using administrative data on schools in England, we estimate an education production model of cognitive skills at the end of secondary school. We provide empirical evidence of self-productivity of skills and of complementarity between secondary school inputs and skills at the end of primary school. Our inference relies on idiosyncratic variation in school expenditure and child fixed effect estimation that controls for the endogeneity of past skills. The persistence in cognitive ability is 0.22 and the return to school expenditure is three times higher for students at the top of the past attainment distribution than for those at the bottom.