**5.3 Methods**

280 Current Issues of Water Management

encountered that this criterion did not have any significant explanatory power. The reason for it might be that the companies within our three groups are actually quite homogenous, which again stresses our hypothesis that companies need to be analyzed according to groups. Our findings might have been different if we would have followed the same path as other researchers which have not had such a detailed database, both quality and quantity

Number of household connections No. Accounted water € Transportation and distribution pipes Km Distribution pipes Km Inhabitants No.

Tanks No. Tank capacity m³ Valves No. Service areas No. Height difference m

distribution) m/m³ Distribution pipes to accounted water (excl. re-distribution) m/m³ Distribution and transportation pipes per household connection m Distribution pipes per household connection m

Supply to re-distributors m³ Household supply relative to accounted water (excluding re-distribution) % Pipe damages No. Peak supply relative to supply of the day % Energy consumption per transported and distributed m³ of water kWh/m³

Area km² Inhabitants per m³ (area) No. Water losses m³ Downturn in demand since 1992 % Downturn in demand since 1998 % Area km² Supply (adjusted for re-distribution) per tank m³ Household connections per tank No.

Distribution and transportation pipes to accounted water (excl. re-

Table 1. Variables for explaining operational distribution costs

**Variable Unit** 

wise, and therefore were not able to cluster their observations.

**Group one:** 

**Group two:** 

**Group three:** 

**Group four:** 

Based on the definition of relevant cost drivers we apply a parametric and a non-parametric benchmarking approach, namely SFA and DEA (compare Section 3). Because DEA is sensitive towards extreme values, an outlier analysis is applied in addition. Therein, firms that are most efficient in many of the observations are iteratively taken out of the sample and, hence, the efficiency analysis. The process stops when the average value of efficiency of all transmission system operators, including the potential outliers, is statistically indifferent (at 95% confidence) to the average value of efficiency excluding the potential outliers. A t-test (according to Satterthwaite) is used to compare the expected values. Identified outliers are removed from the sample.

Multiple specifications of SFA models are estimated to compare specifications given by similar correlation coefficients in earlier phases of the analysis. To conclude on an improved goodness of fit of one specification against the other, Akaike's and Schwarz's information criteria are used as well as a comparison of the log-likehood values. Given insignificant parameters, a likelihood ratio test is performed. Also, we test different functional forms: Cobb-Douglas, Translog, and log-linear models.

## **5.4 Results**

The best model for the largest companies is displayed in the following table.


Table 2. SFA-Model Large Companies (2.5-50 Mill. m³ per year) for operational distribution costs

The results of the DEA- and SFA-analysis have shown that a combination of the variables Distribution pipes, Distribution pipes per household connection and Distribution pipes to accounted water (excl. re-distribution) suits particularly well for an efficiency evaluation of operational distribution costs in the group of the largest water suppliers (2.5 mio. m³ up to 50 mill. m³ annual supply): All three indicators are significant with a minimum confidence level of 99%. Besides, the combination of those three variables explains about 70% of operational distribution costs in this group of firms (R² = 0,706). The English water regulation authority OFWAT, in comparison, uses models sometimes with less than 30% explanatory power. Last, but not least, the sign on the coefficients for Distribution pipes and Distribution pipes per household connection is positive, as expected. Increasing absolute, as well as relative grid length, independently increases costs. Only the regressor Distribution pipes to accounted water (excl. re-distribution) is expected to have a negative influence on costs as it increases with population per km². Because of simultaneous modeling of Distribution pipes per household and Distribution pipes to accounted water (excl. redistribution) the result can additionally be interpreted in the way that costs of a one unit increase in grid length overcompensate the grid density advantages.

Analysis of the Current German Benchmarking

willingness-to-pay-studies.

**7. Summary and outlook** 

Approach and Its Extension with Efficiency Analysis Techniques 283

Fig. 5. Rank comparison DEA and SFA, Cluster "Large companies" (Bottom [Upper] arrow:

**# Company Actual Costs Expected Costs Efficiency Potential in %**  2.884.076 2.721.218 5,98% 4.929.511 3.608.453 36,61% 1.833.783 1.670.595 9,77% 6.551.907 4.243.461 54,40% 2.261.552 1.574.094 43,67% 2.169.827 1.953.611 11,07% Table 5. Efficiency analysis techniques and implications for individual efficiency potential

We would certainly always suggest to not only analyze the results of the "operational distribution costs". It is worth doing the same calculations for "total costs" and the remaining sub-categories "operational production costs", "capital costs" and "administration costs". In such a way potential trade-offs between, for example, operational and capital costs can be observed and interpreted. In addition, an analysis would also need to take into account different quality provision between companies which would need to be backed by

Benchmarking is an already well established concept in the German water supply sector. It is performed in all of the German *Bundesländer*. However, if we compare the number of companies which take part in such a metric benchmarking with the total number of water suppliers the percentage will be less than 2 %. One reason for the companies to not

Relatively efficient [inefficient] companies according to both DEA and SFA]


The best models for the two other groups of companies are as follows:

Table 3. SFA-Model Medium Companies (0.5-2.5 mill. m³ per year) for operational distribution costs


Table 4. SFA-Model Small Companies (< 0.5 mill. m³ per year) for operational distribution costs

The DEA and SFA results for the largest group of companies are plotted in the figure below to verify consistency of the efficiency analyses. Because the efficiency measures are not always comparable due to the different methods used, the rank correlation of the results are determined (according to Spearman) and plotted. A value of, for example, 0,78, means that the ranks of a firm resulting from DEA and SFA analyses correlate with 78%.15
