MEASURING PRODUCTION EFFICIENCY USING AGGREGATE DATA

This paper develops a measure of efficiency when data have been aggregated. Unlike the most commonly used efficiency measures, our estimator handles the heteroskedasticity created by aggregation appropriately. Our estimator is compared to estimators currently used to measure school efficiency. Theoretical results are supported by a Monte Carlo experiment. Results show that for samples containing small schools (sample average may be about 100 students per school but sample includes several schools with about 30 students), the proposed aggregate data estimator performs better than the commonly used OLS and only slightly worse than the multilevel estimator. Thus, when school officials are unable to gather multilevel or disaggregate data, the aggregate data estimator proposed here should be used. When disaggregate data is available, standardizing the value-added estimator should be considered.