prices vary widely. Based on a data set with price information on 765 German water utilities, Ruester and Zschille (2010) show that consumer bills for

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1 Cost Efficiency and Economies of Scale and Density in German Water Distribution Michael Zschille and Matthias Walter June 14, 2010 Abstract This paper studies the cost structure of water distribution utilities in Germany. Stochastic cost frontier models are applied to an unbalanced panel of 371 observations of 72 companies in the period from 1998 to The results suggest that some utilities could reduce their costs by more than 20%. Water losses and elevation differences in a service area turn out to be significant cost driver. Moreover, there is evidence for unexploited economies of scale and substantial economies of density. With the German water distribution sector being a natural monopoly, the analysis supports the introduction of an incentive based ex-ante yardstick regulation and merger initiatives. JEL-Codes: L25, L43, L95, C1 Keywords: Cost Efficiency, Economies of Scale, Economies of Density, Water Distribution, Stochastic Frontier Analysis 1 Introduction A controversial discussion about adequate water supply in Germany is going on for several years now. The customers face the highest prices for drinking water in comparison to other European countries and within Germany, the German Institute for Economic Research (DIW), Mohrenstrasse 58, Berlin, Germany. mzschille@diw.de Corresponding author. Address: Dresden University of Technology, Faculty of Business and Economics, Chair of Energy Economics and Public Sector Management, Dresden, Germany. Phone: +49-(0) , Fax: +49-(0) , matthias.walter@tu-dresden.de 1

2 prices vary widely. Based on a data set with price information on 765 German water utilities, Ruester and Zschille (2010) show that consumer bills for a representative household consuming 150 m 3 of water per year vary between Euro per year and Euro per year, so that the highest bill is by a factor of 5.86 higher than the lowest one. For France, this factor amounts to 7.48, using data from Chong et al. (2006). For England and Wales, where water supply is regulated for several years now, this factor is by far lower with a level of 2.37 based on price information from the Office of Water Services (2009). While some of those differences in prices might be explained by structural differences between the service areas of different water suppliers, there still remain unexplained reasons for this variation. Traditionally, water utilities can be characterized as natural monopolies so that customers do not have the possibility to choose between different suppliers. This lack of competitive pressure raises the presumption of possible inefficiencies within water supply. Beside the lack of competitive pressure, regulatory activities with incentives to reduce costs and corresponding prices are still missing in Germany so that there is no need for water utilities to supply water in an efficient way. Nevertheless, the obvious need for public intervention has raised the public debate about the need of an adequate, incentive-based regulation of German water utilities. For this purpose, an incentive-based price cap regulation similar to the German electricity and natural gas supply industry is discussed, see Hirschhausen et al. (2009). Beside this issue of cost inefficiency, also scale inefficiencies are an important research topic. The German water supply industry is characterized by a high fragmentation with around 6,500 water utilities so that in most cases each municipality has an own water utility. Based on data from Statistisches Bundesamt (2010), in the year 2007 the 389 largest water utilities out of the 6,500 water utilities in total had revenues of 6.7 billion Euros. In contrast to the high fragmentation of the water supply industry in Germany, only 21 water utilities are operating in England and Wales and around 1,200 water utilities in Japan. Hence, a possible public intervention in German water supply should take the issue of economies of scale into account as well. When looking at other countries, methods of scientific efficiency analysis have already been used broadly and were involved into the price regulation of water utilities. A good overview of scientific efficiency analysis for the regulation of water utilities in England and Wales is given in Saal and Parker (2000, 2001) and Saal et al. (2007). Information about the use of scientific efficiency analysis for the regulation of water utilities in Italy are given in Antonioli and Filippini (2001). Similar methods have also been used for 2

3 the incentive regulation in the German natural gas and electricity sector, so that they seem to be accepted in Germany. Nevertheless, there is a lack of studies with an application to the German water sector. There have only been few studies from Hanusch and Cantner (1991), Sauer (2003, 2004, 2005) and Sauer and Frohberg (2007), but all only using very small data samples. Based on a bigger sample of 373 German water utilities, Zschille et al. (2010) determine efficiency scores applying a Data Envelopment Analysis (DEA) approach and find out a low mean efficiency level of 65%. A brief overview of studies concerning economies of scale and density in the international literature with a focus on Europe is given in Table 1. Garcia and Thomas (2001) analyze the French water supply industry, which is similar to the German one. For a sample of 55 water utilities over a period from 1995 to 1997, they find slight economies of scale for a mean output level of 0.41 m m 3 of delivered water. Saal and Parker (2005) use a sample of 30 water utilities in England and Wales for the period from 1993 to 2003 and can show that economies of scale decreased over the sample period due to mergers between water utilities. For the year 2003, they already find out diseconomies of scale so that the consolidation of the water supply industry in England and Wales has probably created too large water utilities. In contrast to the results of Saal and Parker (2005), Bottasso and Conti (2009) find out slight economies of scale for a sample of 20 English and Welsh water only companies between 1995/96 and 2004/05. For the case of Italy, Antonioli and Filippini (2001) use a data sample of 31 water utilities over the time horizon from 1991 to They estimate a Cobb-Douglas variable cost function and calculate slight diseconomies of scale with a level of 0.95 for the sample median. In another study on Italian water utilities, Fabbri and Fraquelli (2000) estimate economies of scale with a value of 0.99 for the mean output level, using a data sample on 173 Italian water utilities in For a sample of 52 Slovenian water utilities, Filippini et al. (2008) point out positive but low economies of scale estimating a translog total distribution cost function. The paper from Sauer (2005) is so far the only one on German water supply with respect to the issue of economies of scale. For a sample of 47 rural German water utilities, he estimates significant economies of scale with values around 2.09 for the short run as well as for the long run. Following Walter et al. (2009), the point of constant returns to scale seems to be around an output level of 20 m m 3. However, as can bee seen in Table 1, the optimal scale always depends on the operating environment and the specific circumstances facing the water utilities, so that no universal conclusions can be drawn with respect to optimal firm size. The structure of this work is as follows: Section 2 gives an overview of the 3

4 Table 1: Studies estimating economies of scale and density Author(s) Data sample Functional form and cost specification Garcia and Thomas (2001) 55 French water utilities from 1995 to 1997 Sauer (2005) 47 German water utilities in 2000 Filippini 52 Slovenian water et al. (2008) utilities from 1997 to 2003 Antonioli and Filippini (2001) Fabbri and Fraquelli (2000) Saal and Parker (2005) Bottasso and Conti (2009) 32 Italian water distribution firms from 1991 to Italian water utilities in English and Welsh water utilities from 1993 to English and Welsh WoCs from 1995/96 to 2004/05 Translog variable cost function SGM operating cost function Translog total distribution cost function Cobb-Douglas variable cost function Translog hedonic total cost function Translog input distance function, Malmquist and generalized Malmquist productivity index Translog variable cost function Model and method of estimation GMM (IV method), SUR method Estimated economies of density EPD (SR/LR): / a ECD (SR/LR): / a Estimated economies of scale SUR method (SR) a (LR) Pooled, RE, True Fixed Effects (ML, EoD: b, ECD: b, GLS) RE model EoD: 1.46 a Pooled model (OLS) Time-varying inefficiency Baltagi and Wu (1999) random effects model Corresponding mean output level a 0.41 m m m m b, 2.30 m m 3 ECD: 1.16 a 0.95 a 6.77 m m a 0.99 a m m 3 - From in 1993 decreasing to a EoD: b, ECD: b, ESD: b, in 2003 Small negative scale effects for WoCs m m b, Ml/day ECD = economies of customer density, END = economies of network density, EPD = economies of production density, LR = long run, SR = short run, WoC = water only companies a : estimated at the sample mean, b : estimated at the sample median, : depending on the econometric model Source: updated from Walter et al. (2009) 4

5 methodology used for this study while the data set is described in Section 3 and the results are shown in Section 4. Section 5 concludes. 2 Methodology 2.1 Cost Functions and Econometric Models The assumption of cost-minimizing behavior given input prices and output quantities is necessary in order to estimate a cost function, see Coelli et al. (2005). In the case of water supply, this assumption is hard since water supply is a natural monopoly where no incentives for efficient operations do exist. The output quantities on the other hand can be regarded as more or less exogenously given since a water utility can not directly influence the demand of the customers. Following Chambers (1988), the cost function framework has the form c(w, y) =min x 0 [w x x V (y)] (1) where w denotes the vector of input prices and x the vector of inputs used to produce a given output level y given the production technology V (.). Expression 1 states that total costs are a function of the exogenously given input prices and the fixed output vector. Due to this, variation is only possible in input quantities in order to obtain allocative efficiency. The cost frontier represents the minimum costs for all inputs which are required to obtain a given output level, see Kumbhakar and Lovell (2000). For the estimation of a cost function, different econometric models can be applied. In the pooled model (ALS) as proposed by Aigner et al. (1977), the error term is divided into the two components v i and u i. The error term v i is normally distributed and aimed to capture statistical noise due to omitted variables or measurement errors. The random term u i is half-normally distributed and non-negative in order to capture inefficiency. The pooled model has the form ln T C it = α 0 + x itβ + v it + u it (2) with v it iid N(0,σv) 2 and u it iid N + (0,σu). 2 In this model, the deterministic part of the cost frontier is represented by α 0 + x it β with α 0 being the intercept of the frontier, x it the vector of explanatory variables and β the vector of the estimated coefficients. The inefficiency term u it only takes non-negative values of the normal distribution, while the error term v it can take positive as well as negative values of the normal distribution. The 5

6 inefficiency term u i is estimated using an estimator proposed by Jondrow et al. (1982). Using the Jondrow et al. estimator, the inefficiency of each observation is estimated as the conditional mean of the inefficiency term u i as given by E[u it u it + v it ]. As a main drawback, the pooled model is a cross-section model and can not take the panel structure of a data set into account, so that even multiple observations of one firm are considered as independent observations. Panel data models can overcome this drawback of the pooled model. They allow the consideration of multiple observations for one individual firm and accordingly enable to take firm-specific heterogeneity among several firms into account. However, the random and the fixed effects model interpret unobserved firm-specific heterogeneity as inefficiency so that inefficiency tends to be overestimated. The true fixed effects model (TFE) is an extension of the traditional fixed effects model and can be formulated as ln T C it = α i + x itβ + v it + u it (3) with v it iid N(0,σv) 2 and u it iid N + (0,σu). 2 According to this formulation, a set of firm-specific dummy variables α i is included into the model as shown in Greene (2004). They are used to take firm-specific unobserved heterogeneity into account and lead to a shift in the cost frontier. The TFE model is estimated using Maximum Likelihood estimation. The inefficiency term is again estimated using the Jondrow et al. (1982) estimator E[u it α i + u it + v it ]. Due to the additional inclusion of firm-specific dummy variables, the number of parameters to be estimated increases significantly, what can lead to consistency problems in short data panels. For the purpose of estimating a cost function, it is necessary to assume a functional form. The Cobb-Douglas function and the translog function are the most common functional forms used in the literature. Following Christensen et al. (1973), the translog function is derived from the Cobb-Douglas function by adding the square and cross-product terms of the explanatory variables to the already contained linear terms. Mathematically, the translog function is a Taylor approximation of the true function around some point x 0 of the data sample using a polynomial of degree 2. For the analysis of economies of density and scale, the use of the translog function is preferable since the Cobb-Douglas function does not allow elasticities to vary across different data points, see Coelli et al. (2005). 1 1 The coefficient estimates in Table 3 also underline the appropriate use of the translog function since all cross and square-terms are highly significant. This result is also 6

7 For the true fixed effects model, our final translog total cost function is specified as ln T C it = α i + α 1 ln wdel it + α 2 ln net it α 3 ln wdel it ln wdel it α 4 ln net it ln net it + α 5 ln wdel it ln net it (4) + α 6 ln wage it + α 7 t + α 8 ln wlos it + α 9 ln high it + v it + u it with subscript i denoting firm i with i = 1,..., N and N = 72 and the subscript t denoting the year with t = 1 (1998),..., 10 (2007). The amount of water delivered is used as output measure and in line with Caves et al. (1984) and Filippini et al. (2008) the length of the whole distribution network is included as further characteristic variable representing a quasi-fixed input. Both are included in linear, square and cross terms. Further explanatory variables characterizing the production process are included in a linear way. Traditionally, cost functions include factor prices for the input factors labor, capital and materials to account for regional differences e.g. in the wage levels the firms face. Due to a lack of data, we cannot include prices so that our model is in contrast to traditional cost function approaches used in the literature. However, a similar approach has been used in Martins et al. (2006). For the case of the Portuguese water industry, they estimate a cubic cost function without input prices and argue that differences in the input prices are quite small since Portugal is only a small country. For Germany, it would be preferable to include input prices in order to take the regional differences in the prices of labor and energy input into account. However, it is arguable that such regional differences will be covered by the fixed effects of the true fixed effects model. With respect to the costs of materials and capital, we assume that those input prices are quite similar across Germany. In order to include a measure of labor costs into the cost function, we use a labor cost index measuring the change in labor costs of water supply in Germany. This labor cost index is confirmed by a Likelihood-Ratio test testing the use of the translog functional form against the use of a Cobb-Douglas function in the case of the true fixed effects model (TFE). With a value of 66.80, the test statistic is higher than the corresponding χ 2 value of at a significance level of 0.95% with 3 degrees of freedom, so that the null hypothesis of the restricted model being appropriate is rejected and the translog functional form is recommendable. 7

8 aimed to represent the differentiated development of labor costs over time in comparison to inflation and the producer price index. Similarly, Smith et al. (2010) estimate a cost function for rail infrastructure only using a measure for maintenance costs as input price without including further input price measures. 2.2 Economies of Density and Scale Based on the coefficient estimates of a cost function, the calculation of economies of density and scale is possible. Economies of output density (EoD) measure the change in total costs due to a change in output quantities, holding all other variables, i.e. the network characteristics, constant. According to Panzar and Willig (1977) and Hanoch (1975), economies of output density are calculated as the reciprocal value of the output elasticity according to EoD = 1 ε y (5) with ε y being the output elasticity. The output elasticity is calculated as ln T C ε y = (6) ln wdel what is the derivative of the total cost function with respect to the output quantity. For the translog cost function shown above, this results in ε y = α 1 + α 3 ln wdel it + α 5 ln net it. (7) A value of EoD greater than one indicates the existence of economies of output density in the sense of decreasing average costs when output increases, so that an increase in output quantities results in a less than proportional increase in total costs. EoD equal to one indicate constant economies of output density; a value less than one diseconomies of output density. In contrast to the economies of output density, economies of scale (EoS) measure the change in total costs when the output quantities as well as the network characteristics are changed proportionally. Similar to the EoD, the derivative of the total cost function with respect to output and with respect to the output characteristic is used. According to this, the derivative of the total cost function is ε s = ln T C ln T C + ln wdel ln net (8) 8

9 with ε s denoting the scale elasticity of the total cost function. Thus, for the specific cost function we have ε s = α 1 + α 2 + α 3 ln wdel it + α 4 ln net it + α 5 (ln net it + ln wdel it ) (9) for the scale elasticity. As for the economies of output density, the scale elasticity is used for the calculation of the economies of scale EoS = 1 ε s (10) as reciprocal of the scale elasticity, see Panzar and Willig (1977), Hanoch (1975) and Caves et al. (1981). A value of EoS greater than one indicates the existence of economies of scale, that is to say that average costs decrease when the output and the length of the distribution network are increased. According to this, a water utility could increase efficiency by increasing overall firm size. A value of EoS equal to one indicates constant economies of scale while a value less than one indicates diseconomies of scale. In this case, the water utility is already operating under increasing average costs and is therefore already beyond optimal firm size indicated by the minimum of the average cost function. 3 Data The analysis is based on a unique data set provided by the Cartel Office for Energy and Water of the German federal state of Hesse. Questionnaires were used for the creation of the data set and were directly answered by several German water utilities. The original data set is an unbalanced panel including 422 observations of 80 German water utilities with data from the years 1998 to Most water utilities in the data set are located in the federal states of Hesse, North Rhine-Westphalia, Bavaria and Baden-Wuerttemberg. Only four water utilities are located in East Germany, so that the representativeness of the sample for Germany as a whole is restricted. Due to data inconsistencies regarding the network length, where significant changes over time were caused by the application of so-called geographical information systems (GIS) for the correct measurement of the network length in a service area, the data set 9

10 had to be reduced. 2 The final data set includes 371 observations of 72 water utilities. Table 2: Descriptive statistics Min. Median Mean Max. Std. dev. Total cost (tc) [1000 Euro] Water delivered (wdel) [1000 m 3 ] Network length (net) [km] Elevation differences (high) [m] Wage index (wage) [index number] Share water losses (wlos) Share households (wdel hh ) Private ownership (D private ) [dummy] Sewage services (D sew ) [dummy] Table 2 provides the descriptive statistics for the data set. Total costs are used as dependent variable and are calculated as sum of costs for third party supply of treated water, own water extraction, own water treatment and water distribution. Thus, all costs of water supply including labor costs, capital costs and material costs are taken into account. Total costs are adjusted for inflation using the producer price index for water supply and related services offered by Statistisches Bundesamt (2006, 2008) in order to make the observations from different years comparable. According to this adjustment, total costs are measured in year 2007 Euros. As no data on the prices of labor, capital and materials was available in the data set, it is not possible to include input prices in the estimation. But in order to take the differentiated development of labor costs compared to the producer price index into account, a labor cost index based on Statistisches Bundesamt (2009) is considered. The total amount of water delivered to households and non-households 2 Beforehand, the water utilities only estimated the length of their total network. With the implementation of the geographical information systems, reliable data on the network length has been available for the first time. 10

11 is used as output measure. Water deliveries to non-residential customers consist of deliveries to municipalities, industry and other water utilities. The bandwidth of total water deliveries, varying between m 3 and m 3, underlines the high differences in firm sizes within the data set. This fact also becomes obvious when looking at the length of mains. The network length varies between 29 km and 1268 km and is included as additional variable. It measures the length of the entire distribution network including the length of the connections to customers. In order to characterize the production process of the different water utilities, we include the share of water losses and the elevation differences in a service area as additional variables. The variable wlos measures the amount of water losses in relation to the total amount of water injected into the water distribution system and is assumed to have a cost increasing impact. Water losses are not fully influenceable by the management since they also depend e.g. on the soil type and other factors within a service area. For example, acidic or porous soils increase the probability of pipe bursts. However, the management could reduce water losses by better maintenance efforts and higher investments into the network infrastructure. The variable high measures the elevation difference between the highest and the lowest point with water supply facilities within a service area. The elevation differences are assumed to have a cost increasing influence since they make higher pumping efforts for water distribution necessary. Both variables, the water losses as well as the elevation differences within a service area are taken out of the basic data sample and were measured by the water utilities themselves. A linear time trend is included in order to consider possible cost-influencing technological progress. Except for total costs, all variables within the data set are standardized through division by their mean values. According to Farsi et al. (2007), total costs are not mean corrected. We take the logarithm of all variables since the application of the translog functional form requires the use of logarithmized variables. By taking the logarithm of all variables, it is also possible to directly interpret the estimated coefficients as cost elasticities. For a broader analysis, we try to determine the impact of further variables on efficiency. We conduct Kruskal-Wallis tests to find out possible differences in the mean efficiency levels of different groups of water utilities. For the Kruskal-Wallis tests we take variables into account, which are not included into the cost function as we assume that they do not influence the production process of water utilities. All utilities within the data set are characterized by a private governance form, while most of them are still fully owned by the responsible municipality. However, in some cases private 11

12 partners are involved into the ownership of the utilities. Most often, those private partners are subsidiaries of E.On or RWE, the large German energy companies. In order to take those different types of ownership into account, we define the dummy variable D private, which takes a value of one, if a private partner holds shares in the utility, and zero otherwise. The degree of private involvement is neglected here. But in all cases of the involvement of a private partner, the share held by the private partners is at least 20%. There are no cases of full privatization. In addition to water supply, some of the utilities also offer other services, as for example sewage services, electricity, natural gas, heat deliveries, public bathes or local public transport. The dummy variable D sew takes a value of one if the firm jointly provides water and sewage services, and zero otherwise. The variable wdel hh is used in order to determine the impact of different customer structures on efficiency. It measures the share of water deliveries to residential customers in relation to the total amount of water delivered. An inclusion of the amount of water delivered to residential and non-residential customers into the cost function as separate variables is not possible since some water utilities do not deliver water to non-residential customers. Such an approach is not possible since the translog functional form does not allow the inclusion of such zero values for estimation purposes. 4 Results 4.1 Regression Results The regression results of the pooled model (ALS) and the true fixed effects model (TFE) are given in Table 3. 3 The coefficients of both the amount of delivered water and the network length show the expected signs in each model. Nevertheless, the coefficient of the network length is not found to be significant for the pooled model. Furthermore, the coefficient of the network length is very low in comparison to the coefficient of the amount of water delivered. Using the coefficient estimates of the TFE model, a 1% increase in the amount of water delivered would result in a 0.87% increase in total costs while a 1% increase of the length of mains would only result in a 0.06% increase in total costs. The second order terms of the amount of delivered water and the network length are negative and significant in both models. The labor cost index is positive 3 Estimation procedures have been conducted using the LIMDEP 9.0 econometric software by W. H. Greene. 12

13 Table 3: Coefficient estimates Variable Par. ALS TFE constant α ** - (0.0971) wdel α ** ** (0.0306) (0.0181) net α ** (0.0412) (0.0141) wdel wdel α ** ** (0.0969) (0.0336) net net α ** ** (0.1348) (0.0409) wdel net α ** ** (0.1131) (0.0365) wage α ** (0.9449) (0.1979) t α ** (0.0148) (0.0016) wlos α ** ** (0.0111) (0.0044) high α ** ** (0.0086) (0.0036) ** significant at 1%, * significant at 5%, Standard errors in parentheses. in both models but is only found to be significant for the TFE model. This underlines the high importance of the wage level for total costs and that the development of labor costs is different in comparison to the development of the producer price index used to adjust total costs for inflation. In the TFE model, the coefficient of the wage index has a value larger than one. This could indicate that over the sample period, the rate of increase of the wage level in the water supply industry is higher than for the overall wage level in Germany. This result is confirmed when looking at a nationwide wage index measuring the development of overall wages in the German industry, manufacturing and service sectors based on data from Statistisches Bundesamt (2009). As compared to this overall development of wages in 13

14 Germany, the wages in the German water supply industry rose more sharply during the last years. The linear time trend is slightly negative, but again only found to be significant for the TFE model. The coefficients of the share of water losses and the elevation differences are both positive and highly significant. Based on the TFE model, the results indicate that a 1% increase in water losses leads to an increase in total costs by 0.04%. Similarly, higher elevation differences within a service area lead to an increase in total costs, what confirms the presumption that higher elevation differences in a service area increase the need for pumping in order to distribute drinking water in hilly regions. The insignificance of the coefficient estimates of the network length, the wage index and the linear trend in the ALS framework might be explained by the fact that the pooled model can not take the panel structure of the data set into account. Hence, the results of the TFE model are preferable and we will focus on those results within the following sections. 4.2 Efficiency Estimates The descriptive statistics for the efficiency estimates of the TFE model are given in Table 4. The efficiency estimates cover a broad range with a minimum value of and a maximum value of while the standard deviation is low with The mean efficiency level is Inefficiencies can be interpreted as relative excess costs in comparison to a best practice frontier. At the mean, around 22% of total costs could be saved. Using the efficiency estimates, it is possible to determine annual cost saving potentials. For the year 2007, data of 30 water utilities is available and included into the analysis. For these 30 water utilities, total costs summed up to more than 209 million Euros. Based on the individual efficiency scores, the individual cost saving potentials sum up to 57.3 million Euros. This underlines the very high potentials for cost savings in German water supply as well as the need for an active price control with incentives for the water utilities to save costs. The results of the Kruskal-Wallis tests are given in Table 5. The mean efficiency level of the utilities under full public ownership is , while the mean efficiency level is for the utilities with private shareholders. A Kruskal-Wallis test does not suggest a rejection of the null hypothesis of both sub-samples having an equal mean efficiency level. A similar result is obtained with respect to the joint provision of water and sewage services, where no significant differences in the mean efficiency levels can be indicated. Based on this result, there do not exist efficiency advantages 14

15 Table 4: Efficiency estimates TFE Minimum Median Mean Maximum Standard deviation of utilities offering both services in comparison to utilities only supplying water. Further research is necessary to find out the possible existence of economies of scope between water and sewerage services. Only with respect to the share of water deliveries to residential customers, the Kruskal-Wallis test indicates the existence of significant differences in the mean efficiency levels of water utilities with high and low shares of water deliveries to residential costumers with a p-value of For the Kruskal-Wallis test, the entire sample is divided into two sub-samples at the median value of the share of water deliveries to residential costumers. For the water utilities with a low share of deliveries to residential costumers, i.e. with a share below the median value, the mean efficiency level is , while it is for the utilities with a high share of residential costumers. This result may appear counterintuitive since large-scale costumers usually only require one connection for the delivery of a high amount of water while more connections are needed for residential customers. Laying more connections in order to supply residential costumers with low water demand usually results in higher costs for water distribution. But on the other hand, an explanation for this result could be that especially water utilities in densely settled downtowns are characterized by a high share of residential costumers. Supplying water to costumers in such densely settled downtowns may lead to efficiency advantages due to economies of density. 4.3 Economies of Scale and Density Using the estimated coefficients of the cost function, economies of scale and output density are calculated. The summary statistics of the results for the economies of scale of observed firms are listed in Table 6. The estimated economies of scale vary significantly depending on firm size. Diseconomies of scale are already existent for the largest firms, what is indicated by the minimum of the observed economies of scale. Thus, those firms are already operating under increasing average costs and are therefore already larger 15

16 Model Table 5: Kruskal-Wallis tests TFE Private ownership (D private ) Mean efficiency for D private = Mean efficiency for D private = χ 2 1-value p-value Sewage services (D sew ) Mean efficiency for D sew = Mean efficiency for D sew = χ 2 1-value p-value Deliveries to households (wdel hh ) Mean efficiency for low wdel hh Mean efficiency for high wdel hh χ 2 1-value p-value than the optimum scale. Table 6: Economies of density and scale for observed firms EoD for TFE EoS for TFE Minimum % - quartile Median Mean % - quartile Maximum Standard deviation An illustration of the economies of scale is given in Figure 1. On the x-axis, the observations are sorted in ascending order of their total amount of water delivered as measure for firm size. The y-axis represents the corresponding economies of scale for each output level. The dotted line indicates economies of scale equal to one. The graph underlines the result, that the economies of scale decrease when output increases. The estimates indicate that the optimal firm size lies around a level of 10 million m 3 of annual water delivered because economies of scale with a value around 1 are estimated for the water utilities with this output level. Diseconomies of scale are shown for the largest firms within our data set, i.e. those firms are already beyond optimal 16

17 firm size. As mentioned by Fraquelli and Moiso (2005), such diseconomies may be caused by a higher bureaucracy and complexity in the management of large firms. Figure 1 also shows clearly that most of the considered water utilities are actually smaller than the derived optimal firm size. Similar results can be found when looking at the number of connections of each water utility. In this case, economies of scale are existent up to a level of between 25,000 and 30,000 connections. The majority of water utilities with a number of connections lower than 25,000 exhibits significant economies of scale. Those water utilities should try to expand their service area or increase the connection rate in order to benefit from cost savings. Figure 1: Estimates of economies of density and scale depending on water output Economies of density [EoD] and scale [EoS] EoD EoS Firm size [water delivered in 1000 m³] In addition to the economies of scale for real firms, economies of scale are also calculated for hypothetic output levels. For this purpose, several representative sample points for water output and the length of mains (sample minimum, 25%-quartile, mean, median, 75%-quartile and maximum) are used. The corresponding results are shown in Table 7. Obviously, the economies of scale decrease with increasing output levels. Economies of scale are existent up to the 75%-quartile of the output level of water delivered and the length of the distribution network. For the maximum output level, the hypothetic utility already exhibits diseconomies 17

18 of scale. Therefore, the optimal firm size lies between the 75%-quartile and the maximum of the amount of water delivered and the network length. Table 7: Estimated economies of density and scale for hypothetic output levels wdel net EoD for TFE EoS for TFE [1000m 3 ] [km] Minimum % - quartile 1, Median 2, Mean 3, % - quartile 3, Maximum 46, , The high values of the economies of scale underline the presumption, that the German water supply industry is highly fragmented and that this fragmentation leads to scale inefficiencies and corresponding cost disadvantages. Therefore, efficiency gains could be obtained by increasing the service area of the water utilities through mergers with other water utilities. In this case, the costs of the management overhead could probably be reduced compared to the independent water utilities. However, the impact of mergers on efficiency needs to be analyzed in more detail since mergers might also have a negative influence on efficiency. Possible efficiency gains could probably also already result from cooperations of water utilities, for example due to a higher utilization rate of water treatment plants. In relation to the joint operation of a modern water treatment plant, older and smaller treatment plants with possibly higher operating costs could be abandoned, what could lead to cost savings as well. Beside the economies of scale, economies of output density are considered. For the mean amount of water delivered, the economies of output density (EoD) take a value of The results for the hypothetic output values are given in Table 7. For all levels of the amount of water delivered, the economies of output density result in values higher than one. This indicates that the water utilities are operating under decreasing average costs, so that cost saving potentials could be realized when the amount of water delivered would increase. This result seems to be intuitive, since a higher amount of water delivered usually results in a fixed costs degression. The existence of the high economies of output density underlines the problems of water utilities arising from the decrease in per capita water consumption during the last decades, since the reduced demand leads to the problem of covering the fixed costs block so that average costs per cubic meter of water delivered tend 18

19 to increase. This result also gives scope for future urban planning. Instead of developing new, spreadly settled residential areas, city planner should focus on developing already existing residential areas and downtowns in order to increase the population density in those areas. The results for the economies of output density for real firms are given in Table 6. An illustration of the results is given in Figure 1. Firms with low water output levels are characterized by economies as well as diseconomies of density, what might be explained by different capacity utilization rates of the distribution networks. Interestingly, the larger companies are all characterized by high economies of density. This indicates that the distribution networks of those companies could be over-dimensioned such that the utilization rate of the distribution network is quite low. However, from a technical point of view one should keep in mind that water distribution networks are constructed such that the highest possible peak demand can be met. This guideline is common practice when planning water distribution networks. Especially for larger cities, this implies that the distribution networks are planned such that peak demand during the days, for example caused by a high number of commuters and tourists, has to be taken into account. However, during the nights, the demand for water is quite low and the huge distribution networks are only utilized at a low degree. These circumstances might lead to a low overall utilization of the water distribution networks and corresponding high levels of economies of density. The result of the economies of output density in most cases being higher than the economies of scale is in line with Farsi et al. (2006). 5 Conclusions The German water supply industry is subject to an intensive discussion about appropriate prices and supply structures due to its characteristic as a natural monopoly and a high variety in prices for the end customers. The differences in prices do not only seem to be explainable by structural differences across the service areas of the water suppliers, but also by inefficiencies. In this paper, we estimate a total cost function for a sample of German water utilities using stochastic frontier methods. For this purpose, the translog functional form is chosen. The results for the derived cost efficiency predictions indicate high cost saving potentials and hence also high potentials for price reductions. Based on the efficiency predictions, a price regulation with incentives for the water utilities to reduce costs seems to be 19

20 necessary. Furthermore, a change in the current water supply structures of the German water supply industry also seems to be recommendable. Looking at the currently high fragmentation into approximately 6,500 utilities supplying water to around 80 million inhabitants, the results of the analysis indicate that a consolidation of water supply could result in cost benefits due to the existence of high economies of scale. While the largest water utilities in the data sample already exhibit diseconomies of scale, most other water utilities are still operating below optimal firm size and should therefore expand their service area. We also show the existence of economies of output density, what can be explained by the possibility of fixed cost degression under increasing output levels. Nevertheless, this result also underlines the problem of the decreasing per capita consumption of water in Germany since several decades. Further research is necessary in order to consolidate the results of this analysis. The use of the traditional inputs capital and labor for the estimation of a total cost function would be desirable. The consideration of quality measures would be beneficial for an analysis of the water supply industry as well. Therefore, increased transparency and data availability in the German water industry must be given. Acknowledgements This paper is a product of the research program on Efficiency Analysis in Network Industries and Water Economics and Management, run jointly between the Chair of Energy Economics and Public Sector Management (EE 2 ) at Dresden University of Technology, the German Institute for Economic Research in Berlin and partner institutions. Earlier versions were presented at the Waterday 2010 in Berlin and the XV. Spring Meeting of Young Economists 2010 in Luxembourg. In particular, we thank David Saal and Christian von Hirschhausen for discussions and suggestions. Special thanks go to the Hessian Cartel Office for Energy Water within the Hessian Ministry for Economics, Traffic, Urban and Regional Development; the usual disclaimer applies. References Aigner, D., Lovell, C. A. K., Schmidt, P., Formulation and estimation of stochastic frontier production function models. Journal of Econometrics 6 (1),

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