Nonparametric Measures of Returns to Scale: An Application to German Water Supply

Abstract

The evaluation of market structures and the quantification of returns to scale in network industries usually are of high interest for researchers and policy makers. Regarding the debate on optimal market structures in German potable water supply, we use a cross-sectional sample of 364 German water utilities observed in 2006 to derive a nonparametric measure of scale elasticity for the water industry. The data sample is validated by applying a super-efficiency approach and a statistical testing procedure for outlier detection. Besides using a standard data envelopment analysis approach, a conditional efficiency approach is applied to account for the water utilities' operating environments. The results indicate non-decreasing returns to scale for the majority of water utilities and constant or non-increasing returns for larger utilities. Optimal firm size is found to be generally larger than the current sample median firm size. Efficiency improvements could be realized by increases in firm sizes and through a consolidation of the industry.