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Aggregation and the Estimated Effects of School Resources
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.
Budget-Constrained Frontier Measures of Fiscal Equality and Efficiency in Schooling
Equality and efficiency are key issues in educational reform. Here the authors analyze the efficiency and equality consequences of various school finance reforms using a cost-indirect output distance function. This function readily models multiple-output production under conditions of budgetary constraint, and provides a natural measure of performance that is closely related to Farrell-type measures of efficiency. The analysis suggests that despite school district inefficiency, finance reforms can affect student achievement. However, any potential gains in output from redistribution are dwarfed by the potential gains from increased efficiency. More strikingly, the analysis demonstrates that budgetary reforms designed to equalize expenditures could actually increase the inequality of student achievement.