Accounting for Time-Varying Unobserved Ability Heterogeneity within Education Production Functions

Traditional strategies to estimate education production functionsdo not explicitly allow either the productivity or development of unobservedskills to vary as a child ages, which appears inconsistent with a growing body of scientific evidence. Empirically if one wishes to obtain unbiased parameter estimates of observed educational inputs researchers must properly account for these unobservedskills. In this paper, we introduce a strategy to estimate education production functionsthat allows for time-varying unobservedability within individuals and a more general decaying pattern of observed inputs. Using experimental data from Project STAR we present evidence that accounting for both features is important in practice. We find that the effects of unobservedability on cognitive achievement vary significantly not only between grades in the same subject area but also there is substantial heterogeneity in the impacts within grades.