Aggregation and the Estimated Effects of School Resources

TLDR

Data aggregation can alter the magnitude of omitted‑variables bias, and its overall theoretical impact is ambiguous. The study seeks to reconcile conflicting findings on school resources and effectiveness by emphasizing how aggregation interacts with omitted‑variables bias. When omitted variables stem from state‑level policy differences, aggregation produces a clear upward bias in estimated school‑resource effects. Analysis of High School and Beyond data shows that aggregation inflates school‑resource coefficients, the pattern rules out errors‑in‑variables, and that studies using aggregate data are more likely to report positive effects, supporting the conclusion that extra spending alone does not improve student outcomes.

Abstract

This paper attempts to reconcile the contradictory findings in the debate over school resources and school effectiveness by highlighting the role of aggregation in the presence of omitted variables bias. While data aggregation for well-specified linear models yields unbiased parameter estimates, aggregation alters the magnitude of any omitted variables bias. In general, the theoretical impact of aggregation is ambiguous. In a very relevant special case where omitted variables relate to state differences in school policy, however, aggregation implies clear upward bias of estimated school resource effects. Analysis of High School and Beyond data provides strong evidence that aggregation inflates the coefficients on school resources. Moreover, the pattern of results is not consistent with an errors-in-variables explanation, the alternative explanation for the larger estimated impact with aggregate estimates. Since studies using aggregate data are much more likely to find positive school resource effects on achievement, these results provide further support to the view that additional expenditures alone are unlikely to improve student outcomes.