Aggregation and the Estimated Effects of School Resources
通过分析遗漏变量偏误下数据加总的影响，解释学校资源与学校效能研究中看似矛盾的发现，并利用高中及以后数据证明加总会高估学校资源效应，支持仅增加支出难以提高学生成绩的观点。
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.