Measuring Potential Sub-unit Efficiency to Counter the Aggregation Bias in Benchmarking

The paper deals with benchmarking cases where highly aggregated decision making units are part of the data set. It is shown that these units – consisting of sub-units which are not further known by the evaluator – are likely to receive an unjustifiable harsh evaluation, here referred to as aggregation bias. To counter this bias, we present an approach which allows to calculate the potential sub-unit efficiency of a decision making unit by taking into account the possible impact of its sub-units' aggregation without having disaggregated sub-unit data. Based on data envelopment analysis, the approach is operationalized in several ways. Finally, we apply our method to the benchmarking model actually used by the Brazilian Electricity Regulator to measure the cost efficiency of the Brazilian distribution system operators. For this case, our results reveal that the potential effect of the aggregation bias on the operators' efficiency scores is enormous.