Aggregation and the Estimated Effects of School Resources
Eric A. Hanushek, Steven G. Rivkin, Lori L. Taylor
NBER Working Paper No. 5548
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.
Published: Review of Economics and Statistics, 78(4), November 1996, pp.611-627.