Most studies fail to find an impact of school inputs on outcomes such as test scores. We argue that this might be a consequence of ignoring the possibility that households respond optimally to changes in school inputs and thus obscure the real effect of such provision on cognitive achievement. To incorporate the forward-looking behaviour of households, we 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. We test the predictions of the model for non-salary cash grants to schools using a unique data set from Zambia. We find that household educational expenditures and school cash grants are substitutes with a coeffcient 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. We are thus able both to order the effects of different kinds of spending and capture their impact on cognitive achievement.
