The Danish water regulator uses, among other things, Data Envelopment Analysis to create a pseudo-competitive environment for the water companies. The benchmarking results are used to set an individual revenue cap for each company. The benchmarking model is currently criticized for not including the companies' supply quality and thereby has an omitted variable bias problem. The regulator has, therefore, initiated an extensive effort to try to incorporate supply quality in the regulation. One problem the regulator has encountered is that incorporating supply quality in the benchmarking model tends to increase the revenue caps more than desired. The regulator does, however, not have any prior information about the quality variables and their trade-offs to the remaining variables which make it challenging to reduce the supply quality's impact on the revenue caps. In this paper, we analyze the facet structure when incorporating three quality variables into the existing model. The facet structure gives important insights into the trade-offs between the companies costs and their level of quality. We argue that it is generally sensible to investigate the facet structure and ensure that it is trustworthy before calculating efficiency scores, in order to increase the credibility of the results. By using an outlier detection model on the estimated trade-offs we use the insights for the facet structure to create weight restrictions between costs and quality, which gives the companies incentives to reveal private information about their true trade-offs. This can help the regulator incorporate quality in the model without allowing the efficiency scores to increase excessively due to the increase in dimensionality. In addition, we propose to set weight restrictions based on the consumer's willingness to pay for quality to avoid the companies choosing a level of quality that is higher than what the consumers are willing to pay.
Data Envelopment Analysis Regulation Facet structure Weight restrictions Trade-off