The relationship between school inputs and educational outcomes is critical for educational policy. The authors recognize that households will respond optimally to changes in school inputs and study how such responses affect the link between school inputs and cognitive achievement. To incorporate the forward-looking behavior of households, the authors present a household optimization model relating household resources and cognitive achievement to school inputs. In this framework, if household and school inputs are technical substitutes in the production function for cognitive achievement, the impact of unanticipated inputs is larger than that of anticipated inputs. The authors test the predictions of the model for nonsalary cash grants to schools using a unique data set from Zambia. They find that household educational expenditures and school cash grants are substitutes with a coefficient of elasticity between -0.35 and -0.52. Consistent with the optimization model, anticipated funds have no impact on cognitive achievement, but unanticipated funds lead to significant improvements in learning. This methodology has important implications for educational research and policy.
