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

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 productivity analysis.7

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

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.

<sup>7</sup> For a detailed description, see Coelli et al. (2005).

<sup>8</sup> 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.

Here, in contrast to the linear regression model, the deviation from the optimum need not be resulting purely from inefficiencies, but also from so called "White Noise". Hence, interpreting these deviations purely as efficiency potentials may be misleading and should be avoided.

The aim of the Data Envelopment Analysis (DEA) is also to measure the efficiencies of respective firms relative to a threshold firm. The productivity of single entities is compared to an efficiency frontier, which is derived from a linear connection between efficient firms (so called "peers"). The DEA is a non-parametric method so that the efficiency frontier is not estimated empirically but calculated by a linear optimization program.

In other grid-reliant sectors (like electricity, gas, telecommunications and even water supply in other countries) the DEA and SFA methods are well established, while the linear regression model does not provide robust and consistent results.
