**4. Data set**

276 Current Issues of Water Management

institutions are investigating those companies which have high prices per m³. This is particularly ridiculous because, due to very different conditions, a company with high water prices might be much more efficient than a company with low ones. An incentive for companies to participate in metric benchmarking projects could, therefore, be to either start investigations in companies which are not participating in metric benchmarking projects at all or which seem to be relatively inefficient at first sight. For other European countries it might be worth considering attaching the granting for subsidies to a successful participation

Scientific efficiency and productivity analysis can be differentiated into parametric and nonparametric methods (Coelli et al., 2005). Parametric approaches, like Ordinary Least Squares (OLS) or Stochastic Frontier Analysis (SFA), estimate cost or production functions and an (in-) efficiency value per observation. Therefore, one has to specify a functional form (like log-linear, Cobb Douglas or Translog). This, indeed, leads to implicit assumptions about the underlying production technology (Jamasb and Pollitt, 2003), for instance, about factor substitution etc. A major advantage of parametric methods is that they allow for statistical inference and their robustness against outliers and statistical noise (Coelli et al, 2003). Nonparametric techniques like the Data Envelopment Analysis (DEA) rather calculate than estimate multi-input/multi-output productivities. The major advantage of Data Envelopment Analysis is its flexibility, i.e. that the analyst does not have to specify a functional form (Coelli et al, 2003). This section briefly discusses the different methods of

The statistical method of Ordinary Least Squares (OLS) is a parametric method estimating the explanatory power of so called exogenous variables (regressors) on an endogenous variable (regressand). The parameters are estimated by minimizing the squared deviances of modeled to actual values (sum of squared residuals). A widespread application of this relatively easy method is the linear regression analysis. The central problem of the linear regression model is, however, that the deviation of one firm's value to the regression line is declared to result from relative efficiencies, which does not always have to be the case.

But, even if the linear regression analysis provides substantially better information to a firm than the average cost approach used up until now, further improvement in efficiency evaluation is in order. For "operational distribution costs", as well as for "total costs" and the other most important costs along the value chain "operational costs production and treatment", "administrative costs" and "capital costs", two additional analyses should be

Stochastic Frontier Analysis (SFA) is another parametric method to determine the efficiency frontier and an advancement of the OLS method in some ways. It requires assumptions about the functional form of the relationship between costs and output values.8 Essentially, the actual costs of one firm are compared to the minimum (efficient) costs of another firm.

8 Different models are used nationally and internationally in benchmarking grid connected infrastructure services. Next to Cobb Douglas and translog specifications, mostly log-linear and

standardized functions, using only one input variable obtained by division, are used.

employed to make the linear regression results more robust when analyzed in detail.

**3. Brief introduction into efficiency analysis techniques** 

in benchmarking projects.

productivity analysis.7

7 For a detailed description, see Coelli et al. (2005).

We use the dataset of Rödl & Partner, the biggest consultancy which conducts metric benchmarking for German water supply utilities. The original data set comprised 612 observations from the years 2000 to 2007. Each of these observations contained 179 firm specific units of information. First, all observations from different years of the same company were eliminated, keeping the most current one.9 Second, all observations from before 2006 were deleted in order to minimize the problems of inflating cost data from older years to the base year of 2007. Third, all companies without any distribution network, or with mainly bulk water supply, were removed from the dataset. Fourth, all observations where crosschecks revealed inconsistencies were deleted.10 196 observations remained.

2007 served as the base year. Using the producer-price index "Water and Water Services" from the German Federal Statistical Office, the data were made comparable by restating 2006 data in terms of 2007 prices. To reach a maximum of comparability we then deducted the concession levy from the operational distribution costs.11

The sample is as close in line with the overall structure of the German water supply sector as possible. However, Figure 4 shows that the distribution, according to the size of the companies between our sample and the overall situation, differs. 30.2 % of approximately 6,400 water supply utilities (ATT et al., 2008, p. 12) in the German water sector supply more than 500,000 m³ annually. In our sample this percentage of companies, which supply more than 500,000 m³ annually, is nearly 80 %. In the whole German water supply sector 92.6 % of water output is supplied by companies with an annual water delivery of more than 500,000 m³. The figure for our sample is nearly 99 %. This implies that our sample contains relatively bigger companies than the overall German average.

<sup>9</sup> Panel data might be interesting in the future to follow the efficiency development of a single company over time.

<sup>10</sup> Rödl & Partner have been very cautious to crosscheck, in particular, all cost data. No inconsistencies were found. Over time however, the set of data slightly changed. Particular older observations with lacking structural variables were, therefore, removed from the data set.

<sup>11</sup> For our calculations in the production/treatment segment we deduct the water abstraction charges. DEA and SFA for total costs imply that concession levy, water abstraction charges and compensatory payments for agriculture have to be subtracted.

Analysis of the Current German Benchmarking

**5.2 Variables and cost driver analysis** 

or associated operational costs, respectively.

and specifically Ordinary Least Squares conditions.

data quality they were also not able to analyze other than total costs. 14 For more detailed data on German water losses see IGES (2010, p.30).

insignificant.

Approach and Its Extension with Efficiency Analysis Techniques 279

We assume that the objective of a water service provider is not solely to produce drinking water. The objective rather is to provide the option for clients to use as much drinking water as they wish at any time. This implies that the set-up of the network with transportation and distribution pipes, tanks, pumps, valves and service areas should also be considered as

Correlation analysis provides an initial determination of the statistical relationship between costs on the one hand and potential explanatory variables reflecting the specific frameworks faced by each water supplier on the other hand. Such correlation analyses are the basis for estimating costs as a function of multiple drivers, i.e., regressors, as they help specifying the efficiency-analyzing models later on. In this step it is made sure that the exogenous variables,

Analyses revealed, particularly for the bigger companies, that the five variables of group one in Table 1 are highly correlated, both with operational distribution costs as well as with one another. Both the technical common understanding and the analysis of the empirical literature stress the explanatory power of these variables.13 It thus makes sense to always have at least one of these variables in the DEA- or SFA-functions in a cost or production function model. Variables of group two to four were tested for additional explanatory value. Walter et al. (2010, p. 228) refer to a number of studies which display the significance of "water losses" as an explanatory variable. For countries like Brazil, Spain or Peru this might certainly be of importance due to high variations in the quality of the network. For a country like Germany however, where the level of water losses is only about 6.5 % (ATT et al., 2011, p. 56) on average,14 water losses cannot serve as a good proxy for the quality of the network

The two variables "downturn of demand since 1992" and "downturn of demand since 1998" are surely interesting for explaining the development of prices. Many companies, which face a significant decrease of demand due to various reasons, need to increase prices if they lack the appropriate tariff models. Too often only a minor share of the total fixed costs is actually covered by earnings, which are independent from actual demand. However, for a cost benchmarking – particularly the operational distributional costs - these variables are

Whereas all variables of the fourth group were not taken into account any longer, the variables of the third group were tested in DEA- and SFA-functions, where a certain combination of variables made sense from a technical water perspective. Particularly, the client structure ("Household supply relative to accounted water") is quite often used to explain differences in both operational distribution costs as well as total costs. We, however,

<sup>12</sup> Tests for heteroskedasticity (Breusch-Pagan/Cook-Weisberg test) and multicollinearity (Variable Inflation Factor, VIF) have been applied to fulfill general conditions of multivariate regression analysis

<sup>13</sup> Besides the literature discussed in Walter et al. (2010) also see Lin (2005), Picazo-Tadeo et al. (2009) and Coelli & Walding (2006). All of them, however, only apply either DEA or SFA. Due to rather bad

outputs, which at least in the short-run cannot be influenced by the company.

like outputs and cost drivers, explain the endogenous variable, costs, sufficiently.12

Fig. 4. Size structure of water supply utilities in Germany (ATT et al., 2009, p. 14)
