Implications of Aggregation Uncertainty in DEA

Researchers and practitioners who use Data Envelopment Analysis often want to incorporate several inputs and outputs in their model to consider as much relevant information as possible. However, too many inputs and outputs can result in the well-known dimensionality problem referred to as the “curse of dimensionality”. Several studies suggest how to solve, or at least reduce, this problem. One solution is to aggregate the inputs and outputs before using them in the model. This paper examines the implications when the methods used to aggregate the inputs and outputs contain uncertainty. The uncertainty can, for example, be price uncertainty if we use input and/or output prices for the aggregation. We show that the implications for a unit under analysis depend entirely on its input and output mixes relative to those of its peers, and that the implications are higher the more heterogeneous the sector is. As an example, we use the Danish benchmarking regulation of the waste water companies. We find that uncertainty in the regulator's aggregation scheme does not, on average, influence the companies' efficiency scores a lot. Still, individual companies can be greatly affected by this uncertainty.