This study applies econometric tools to examine the economies of scale of the water and sewage utilities corporation (utilities) in the urban sector in Israel, and to find whether reducing the number of utilities will maximize efficiency in the urban water sector. Using an econometric analysis of an elasticity Translog cost function, which allows the estimation of returns to scale, the authors examined the optimal size for water and sewage utilities in Israel, based on panel data of 51 utilities. According to the study's results, there is a distinct advantage of economies of scale in Israel's water utilities, and the current distribution of the urban water sector in Israel is characterized by inefficiency and high cost. The results indicate that reducing the number of utilities will achieve an increase in water quantities by utility, and the costs of water production will decline due to economies of scale.

Introduction

In Israel, as in most countries, water utilities constitute a regional monopoly on the supply of water in their service areas, due to high infrastructural costs that constitute a barrier to enter the market and cost advantage of the first utility in the market. In optimal conditions, the market structure leads to the exploitation of economies of scale and low supply costs.

Israel's water sector differs from most water sectors around the world. Most of Israel's drinking water is supplied from underground sources or from desalination plants (seawater or brackish water), and after use, approximately 90% of the water is treated and reclaimed for agricultural use (by agricultural water associations). Consequently, the water sector in Israel is divided into two sub-sectors – a national sector and a municipal sector. This study deals only with the municipal water sector.

The national water sector – managed by the national water company, Mekorot – includes all water resources, including water desalination plants, major transmission infrastructures and wastewater treatment plants. The main role of the national water sector is water production (groundwater extraction, desalination, wastewater treatment) and water supply to all parts of Israel (roughly 80% of all the drinking water). The municipal water sector buys water from Mekorot and is responsible for distributing it from the main grid to the end consumer, sewage collection systems and sewage treatment facilities. Some of the municipal utilities also produce water from surface and under surface sources, depending on nearby water sources (approximately 20% of the drinking water). While the national water sector is managed by one central company, the municipal water sector includes 57 local water utilities.

The water price to the end consumers is uniform at a national level and includes all water supply costs (no government subsidy), however the utilities’ water purchase price from Mekorot is set exogenously and differentially by the Water Authority. The method for calculating the water purchasing rate (from Mekorot) for a water utility is based on operational norms (economic efficiency/benchmark regulation). This mechanism is designed to create cross-subsidization between various utilities and is influenced by the utilities’ special characteristics (e.g., regional altitude, socio-economic condition, etc.).

The regulator has set a fixed price for the consumers and the exogenous purchase prices from Mekorot should balance the difference of the various utilities’ costs and tangent the production costs of a cubic meter of water to the consumer price (Figure 1). Figure 2 shows the actual situation, in which the regulator is not aware of the overall utility's costs, and despite the cross-subsidy, some utilities are in a state of excess profit while others are in a state of loss.
Fig 1.

Cross-subsidization in a state of optimal regulation.

Fig 1.

Cross-subsidization in a state of optimal regulation.

Fig 2.

Cross-subsidization at the actual state of the regulation.

Fig 2.

Cross-subsidization at the actual state of the regulation.

As the utility is less efficient, the ‘utility costs’ will be higher and the Mekorot rate will be lower. Proper regulation will bring the weighting of the various components of the water cost to equality with the consumer price. In this study the authors focused only on the total utilities costs, due to the assumption that in the current layout the utilities do not maximize economies of scale. The distributed structure of the utilities raises questions regarding their financial and operational strength and whether the existing structure takes advantage of economies of scale. A market analysis as shown in this study may serve as a basis for future regulation processes of the municipal water system, which will lead to a reduced number of utilities.

The literature does not recognize a universal optimal size for a utility and it remains a challenge to find the optimal size, depending on the unique characteristics of a country and possibly even for a specific area. The objective of this study is to examine the efficiency of the deployment of the water and sewage utilities in the urban sector in Israel. When the range in which economies of scale exist is defined, we may suggest an optimal utility structure layout that would maximize the efficiency in water utilities in the urban sector.

The remainder of this paper continues as follows: Section 2 presents a literature review and Section 3 presents the model and data description. Section 4 presents the empirical estimation results. Section 5 presents and analyzes the spatial utilities’ alternative. Section 6 discusses the results and Section 7 concludes the paper.

Literature review

The volume of research focused on economies of scale of water and sewage utilities has been growing in recent decades. In his study, Ashton (2000) found economies of scale for the water and sewage companies in England. However, a more recent study by Stone and Webster Consultants (2004) concluded that there are diseconomies of scale for the largest water companies in the UK (over 2 million consumers), but on the other hand, economies of scale exist for the smaller companies (350 thousand consumers). In the United States, several studies found economies of scale in companies providing water services (Bhattacharyya et al., 1994; Shih et al., 2006); however, other studies have found that economies of scale are available only for small water utilities whereas for large water utilities, diseconomies of scale were found (Torres & Morrison-Paul, 2006). Other studies have also found similar results in various countries, including Italy (Fabbri & Fraquelli, 2000; Fraquelli & Giandrone, 2003; Fraquelli & Moiso, 2005), France (Garcia & Thomas, 2001), Japan (Mizutani & Urakami, 2001) and South Korea (Kim & Clark, 1988). Nauges & van den Berg (2007) found economies of scale in Colombia, Moldova, and Vietnam for small and medium water companies, but not in Brazil. In other countries, including Portugal (Martins et al., 2006), Germany (Sauer, 2005) and Canada (Renzetti, 1999), most studies have found economies of scale in the water supply services. Studies that have found economies of scale usually examined small water companies and have shown that if they unite to form larger companies, they will benefit from advantages in purchasing inputs and raising capital. On the other hand, it seems that economies of scale are not endless, and they exhaust themselves beyond a certain size in which a company reaches maximum utilization of its infrastructure, and is obligated to provide additional investments.

The literature indicates that there is no consensus regarding the optimal size of a water company. In addition, there is still no full understanding of how the geographical characteristics affect the desired size of a water company. The scales mentioned in the different studies range from 100,000 consumers (Fraquelli & Giandrone, 2003) to approximately 750,000 consumers (Mizutani & Urakami, 2001), and even to one million consumers (Fraquelli & Moiso, 2005). In the field of sewage there is less controversy, but this is mainly due to the small amount of research on the subject. The studies that were conducted in this field generally suggest economies of scale (Renzetti, 1999; Ashton, 2000). Economies of scale can be achieved by an administrative decision, for example, by consolidating two or more utilities into a single utility, thereby increasing the system and the population served. Torres & Morrison-Paul (2006) stated in their study that a consolidation of small utilities in the United States, may help them take advantage of economies of scale and increase profitability. Although there is no consensus regarding an overall optimal size of water utilities, there is a consensus in the literature regarding a number of issues:

  • • The cost function per cubic meter of water is U-shaped. There is a range in which any increase in the quantity will lead to a decrease in the average cost per cubic meter, and a range in which any increase in the quantity will lead to an increase in the average cost per cubic meter.

  • • As the density increases the total cost of the water utility decreases. For example, even if the output of two utilities is the same, the cost structure may be different due to the length of the lines and the deployment of the consumers.

  • • Characteristics of space and topography of the distribution area may affect the utilities’ cost. This effect is reflected in energy, capital and labor costs.

  • • Small water companies will achieve significant benefits from consolidation with other companies. On the other hand, large companies can reach sizes in which they are indifferent to the increase and may even ‘suffer’ from diseconomies of scale, in which the bureaucracy and administrative friction exceed the operational benefits.

There is reference in the literature to several methods for examining the economies of scale and productivity in the infrastructure sector. Among these methods is the Partial and Total Factor Performance, a method that allows us to distinguish between the impact of changes in the productivity of production factors and the impact of change on profitability (Saal & Parker, 2001). The criticism of this method derives from the need for extensive use of price indices to determine the value of inputs and outputs, when in the water sector the majority of the prices are controlled (Bosworth & Stoneman, 1998). Another method is the Stochastic Frontier Measures, this method builds an index measuring the effectiveness of the utility with respect to a utility that operates in an optimal manner (Cubbin & Tzanidakis, 1998; Estache & Rossi, 2002). Another method used for examining the effectiveness of water utilities, is Data Envelopment Analysis. In this method, for each firm, the ratio of the sum of outputs to inputs is measured and compared to the rest of the firms in the sample. This method was mostly used in studies to compare the relative effectiveness of privately and governmentally owned firms (Abbott & Cohen, 2009). The most commonly used method for examining the economies of scale is econometric analysis of production function (Abbott & Cohen, 2009). By using an econometric analysis, insight can be obtained regarding the various components of the cost function, and it is possible to find the areas in which a utility enjoys economies of scale (Tsagarakis, 2013). When the range in which economies of scale exist is defined, water utilities executives and policy decision makers will be able to create an optimal utility structure.

Methodology and model specification

Research on estimating the cost function of firms in general, and of water utilities in particular, has been the subject of numerous studies from the 1960s until today. Most studies have a common research method. The first common denominator is the economic theory which focuses on reducing the cost function under the constraint of the production function. The cost function can be defined as follows: 
formula
1
where C is total cost, Q is the amount of water, K, L and B are the production factor prices (K – capital; L – labor; B – billing cost), t is the technological improvements between the years, and D is the population density within the utility's area. The function in Equation (1) is different from a standard cost function. Since the main outputs are determined exogenously, the utility is committed to provide the amount of water required by the consumers without the ability of the utility to determine the quantity, unlike a standard cost function in which the quantity produced is determined endogenously to maximize the firm's profits. In this study the authors estimated the cost function using these two models in a logarithmic transformation in order to obtain the robustness of the results.
The elasticity is the relative change in the variable cost, with respect to the relative change in the production factors. The Cobb-Douglas fixed effects logarithmic cost function can be displayed as follows: 
formula
2
where and are the elasticity of the inputs and outputs relative to the cost C. To cope with the utilities’ various sizes, dummy variables were added to the model for large utilities that supply above 8,195 thousand cubic meters per year. measures the average differences between the two size groups and measures the difference in slope effects between the two groups. is the estimator of the special characteristics (e.g., fixed effect) of utility i.
The second model we estimated is a Translog model (for convenience we omitted the indices i and t): 
formula
3
This model contains the variables of the Cobb-Douglas function, without the size dummy variable. The function is more flexible and should be homogeneous of the first degree in inputs, linear homogeneous, and symmetric. These conditions can be enforced by the following constraints: 
formula
4
As noted above, multiplicity of variables in general, and of the interaction variables in particular, may create an issue of multicollinearity that results in insignificant estimates. To deal with this problem, the authors applied Shephard's lemma (Diewert, 1974) and estimated Equation (3) by using Zellner's effective iterative method (Zellner, 1962), Seemingly Unrelated Regression (SUR). Applying Shephard's lemma on Equation (3) gives us the cost-share equations: 
formula
5
 
formula
6
 
formula
7
where . The SUR estimation method, which includes Equation (3), is preferable to estimating the cost function alone, as it adds information by enabling simultaneous correlation between the random disturbances in the various equations (Berndt, 1991). In our case, it is not possible to estimate the cost equation alone due to the small sample size.

Data description

This study is based on panel data of 51 municipal water utilities in Israel and includes 153 observations, and combines two databases. The main database is the utility's financial statements as published on the Water Authority's site. The second database is from the Israeli Central Bureau of Statistics (CBS). Six utilities were omitted in total, due to either a lack of financial statement or the fact that the utilities were established during the study period.

The utility's costs, C, represents the overall financing costs, services costs, collection costs, trade payables, administrative and general expenses, minus the cost of the national water sector (purchasing water from Mekorot).

The output variables are: Q – the total amount of water consumed by consumers in thousands of cubic meters, according to data from the Water Authority (Antonioli & Filippini, 2001). Variable K represents the capital in the model, the fixed asset value after deducting the accumulated depreciation (Antonioli & Filippini, 2001; Mizutani & Urakami, 2001). The property value is determined according to a property survey held by the authorities, which may be biased due to a lack of reliability of the data. Variable W represents an estimate of labor cost, calculated as a sum of the salary sections in the financial statements. This variable was selected due to a lack of official data on the number of personnel in the utilities and differences in the employee wages between the various utilities. Payroll expenses range between 7.7%–27% of the total utility costs, as the variance in the workers’ wages can be explained by the amount of ‘Borrowed employees’ (Adlia, 2011). ‘Borrowed employees’ are former municipal employees who receive better wages than the rest of the new employees.

Many studies dealing with cost function analysis of water utilities consider additional inputs, energy and materials. The difficulty in introducing these variables to the model stems from the manner in which these sections are reported in the financial statements. The Water Authority requires a uniform format for the publication of the financial statements, with a separation of the different operating segments (self-production, distribution and sewage). Some of the utilities do not separate properly between the various costs (particularly self-production and distribution) and the costs of the production factors cannot be associated with the investments of the relevant section. The lack of uniformity in reporting and the difficulty of analyzing the data derived from it were also noted by Adlia (2011).

Variable D represents the density per square kilometer in the utility's area. The density calculation is carried out by dividing the population which receives services, by the utility's area as published by the CBS.

Many studies have examined the relationship between the topographic characteristics in which the utility operates and the production costs. In Israel, an index for characterizing the topography for the municipalities and local authorities is published by the CBS. The correlation between the weighted average rating of the utility and the variable cost is very low (the correlation between the topographic characterizations of CBS and the cost is 0.023). The authors of these studies conducted several robustness tests on the results of the model, which included inter alia, adding variables of topographic and socio-economic characteristics in the jurisdiction of the utility, on the basis of the indicators published by the CBS.

The authors did not include in the model a number of variables which were found significant in other studies (such as water source, water quality, ownership structure, regulation, chemical costs, etc.) for several reasons. One of the reasons is the consistency between the utilities regarding most of the excluded variables (e.g., water source, water quality, ownership structure, regulation). The other excluded variables, in which there is a variance between the utilities (e.g., water production, chemical costs), are expressed by the method of standardizing the changes in the purchase price from Mekorot by the regulator. Since we omitted the cost of purchase from Mekorot from the total cost, these variables have no meaning in the proposed model.

All of the variables in the model are logarithmic transformations in order to introduce the elasticity ratio between the independent variables and the dependent variables. Table 1 presents descriptive statistics of the various variables.

Table 1.

Descriptive statistics of the variables.

Variable Average Minimum Maximum 
Q – Amount of water consumed (thousands of cubic meters) (N = 153) 8,195.067 ( − 9,156.718) 827.534 54,613.4 
D – Density of population per kilometer 4,191.244 (4,314.992) 172.88 22,916.99 
K – Capital (NIS thousands) 163,477.3 ( − 142,099.1) 19,769 862,290 
W – Labor cost (NIS thousands) 5,597.69 ( − 9,440.65) 988.3 66,513 
B – Collection costs 7,542.14 ( − 7,994.54) 165 41,832 
  Number 0. Number 1. 
T11 - Dummy for 2011  102 51 
T12 - Dummy for 2012  102 51 
Variable Average Minimum Maximum 
Q – Amount of water consumed (thousands of cubic meters) (N = 153) 8,195.067 ( − 9,156.718) 827.534 54,613.4 
D – Density of population per kilometer 4,191.244 (4,314.992) 172.88 22,916.99 
K – Capital (NIS thousands) 163,477.3 ( − 142,099.1) 19,769 862,290 
W – Labor cost (NIS thousands) 5,597.69 ( − 9,440.65) 988.3 66,513 
B – Collection costs 7,542.14 ( − 7,994.54) 165 41,832 
  Number 0. Number 1. 
T11 - Dummy for 2011  102 51 
T12 - Dummy for 2012  102 51 

Results

In this study, we estimated two main models and conducted a few robustness tests. Their results are shown in Table 2. The estimation results of the Fixed Effects model (FE), suggest that the elasticity of the output () is positive and a 1% increase in the quantity of water supplied is associated with a 0.49% increase in the utility's cost. The labor () and billing () cost estimators are positive and significant, and the function increases monotonically to the production factors cost. The utility size dummy (), capital () and density () estimators are not significant in the fixed effect model.

Table 2.

Estimation results.

  Coefficient
 
Variable Annotation FE Translog 
Constant – 2.678 (1.843) −1.397*** (0.010) 
Q Output 0.488*** (0.170) 0.494*** (0.056) 
D D-Density ratio −0.087 (0.093) −0.225** (0.104) 
K Capital 0.069̇̇ (0.062) 1.097*** (0.051) 
W Labor cost 0.219*** (0.082) 0.337*** (0.057) 
B Collection cost 0.183*** (0.031) 0.435-*** (0.034) 
Dummy size Large utility 3.198* (1.739)  
Dummy Q  −0.395* (0.204)  
QQ Output*Output  −0.024*** (0.007) 
DD Density*Density  0.067*** (0.022) 
KK Capital*Capital  −0.089*** (0.005) 
WW Labor cost*Labor cost  0.104*** (0.006) 
BB Collection cost*Collection cost  −0.015*** (0.004) 
QK Output*Capital  −0.012 *** (0.000) 
QW Output*Labor cost  0.012 *** (0.000) 
QB Output*Collection cost  3.211 (1.264) 
QD Output*Density  −0.012 ** (0.006) 
KW Capital*Labor cost  −0.065 *** (0.001) 
KB Capital*Collection cost  0.071 *** (0.001) 
KD Capital*Density  −0.0004 *** (0.000) 
WD Labor cost*Density  0.00009 (0.000) 
WB Labor cost*Collection cost  6.94* (1.19) 
BD Collection cost* Density  −0.00008 (0.000) 
T11 Dummy for 2011 −0.033 (0.0241) −0.002 (0.047) 
T12 Dummy for 2012 0.080 *** (0.0269) −0.059 (0.046) 
  Coefficient
 
Variable Annotation FE Translog 
Constant – 2.678 (1.843) −1.397*** (0.010) 
Q Output 0.488*** (0.170) 0.494*** (0.056) 
D D-Density ratio −0.087 (0.093) −0.225** (0.104) 
K Capital 0.069̇̇ (0.062) 1.097*** (0.051) 
W Labor cost 0.219*** (0.082) 0.337*** (0.057) 
B Collection cost 0.183*** (0.031) 0.435-*** (0.034) 
Dummy size Large utility 3.198* (1.739)  
Dummy Q  −0.395* (0.204)  
QQ Output*Output  −0.024*** (0.007) 
DD Density*Density  0.067*** (0.022) 
KK Capital*Capital  −0.089*** (0.005) 
WW Labor cost*Labor cost  0.104*** (0.006) 
BB Collection cost*Collection cost  −0.015*** (0.004) 
QK Output*Capital  −0.012 *** (0.000) 
QW Output*Labor cost  0.012 *** (0.000) 
QB Output*Collection cost  3.211 (1.264) 
QD Output*Density  −0.012 ** (0.006) 
KW Capital*Labor cost  −0.065 *** (0.001) 
KB Capital*Collection cost  0.071 *** (0.001) 
KD Capital*Density  −0.0004 *** (0.000) 
WD Labor cost*Density  0.00009 (0.000) 
WB Labor cost*Collection cost  6.94* (1.19) 
BD Collection cost* Density  −0.00008 (0.000) 
T11 Dummy for 2011 −0.033 (0.0241) −0.002 (0.047) 
T12 Dummy for 2012 0.080 *** (0.0269) −0.059 (0.046) 

Significance level *90%, **95%, ***99%.

An initial comparison of the results of the Q estimator between small () and big water utilities (), shows that economies of scale exist in both estimations and in all of the examined parameters. This result indicates that the amounts of water supplied by the utilities are not quantities which maximize economic efficiency. Increasing the amount of water in each of the examined utilities’ sizes, will lead to improved efficiency.

The Translog model was estimated using the SUR method and the estimation results indicate that economies of scale exist from an increase in output (Q, ) for the average firm in the sample. The coefficient value is close to the coefficient value of the fixed effect estimation in Equation (2).

The coefficient received a negative value that approaches zero, thus, as the firm provides a greater amount of water, the utility's cost per cubic meter will decrease. This result of an equilibrium edge was obtained due to the sample structure, which contains a small number of observations of large water utilities. If the sample was ‘balanced’ in terms of the utilities’ sizes, we would have received a different optimum point and not necessarily an edge point. The sample contains approximately 90% of the existing utilities, therefore we can clearly assume that up to the size of the ‘Gihon’ utility, which is the largest utility in Israel, economies of scale exist. This result is conservative due to the limitations of the model, as we cannot predict beyond the maximum observation. However, according to the obtained results, it is most likely that the optimal utility size is larger.

The density coefficient () received a negative value, while the squared density variable () received a positive value smaller than 1. It can be concluded from these results that when the density ratio is small, an increase in this ratio will lead to a substantial improvement in the utility's efficiency, however the intensity of the improvement in efficiency will decline as the density rises. It is important to note that these results indicate that even in relatively crowded cities, economies of scale exist as a result of an increase in density, but at a smaller effect than in areas with low density.

The capital coefficient () received an exceptional value that is greater than 1, while the squared capital coefficient () received a negative value that approaches zero. The exceptional result was obtained due to the structure of the sample and to the large variance between the utilities. The standard deviation of the parameter log (k) is 0.752, while the standard deviation of log (k)2 is 8.83. In addition, following the incentives (shareholder loans from the municipal authorities) of the utilities reform, a direct relationship exists between the total assets and the scope and debt costs of the utility. An additional reason for the exceptional result is constraint (6) which is required for the implementation of Shephard's lemma.

Table 3 shows the robustness tests for the main models’ result (columns 1 and 6). By adding environmental variables (such as topographic and socio-economic conditions) we tested how the main estimator changes. Columns 1–4 show that topographic (altitude) and socio-economic conditions do not have an impact on the output estimator. This can be explained by the regulation in Israel which standardizes the difference in the purchase price from Mekorot. In column 5 we omitted the utilities fixed effect and the results indicate higher levels of economies of scale.

Table 3.

Robustness tests.

  Fixed effect
 
Cobb-Douglas Translog 
Model/Estimator 
Output – β(q) 0.488*** 0.488*** 0.488*** 0.488*** 0.298*** 0.494*** 
(0.170) (0.170) (0.170) (0.170) (0.059)  (0.056) 
Density – β(d) −0.087 −0.079 −0.015 −0.178 0.038* −0.225** 
(0.093) (0.092) (0.354) (0.174) (0.020) (0.104) 
Dummy size  – 
Dummy output  – 
Fixed effect  – 
Topographic – – 0.097 −0.151 – – 
– – (0.492) (0.163) – – 
Socio-economic – −0.003 – −0.041 – – 
– (0.0162) – (0.088) – – 
Adj -R-sq 0.974 0.974 0.974 0.974 0.941  
  Fixed effect
 
Cobb-Douglas Translog 
Model/Estimator 
Output – β(q) 0.488*** 0.488*** 0.488*** 0.488*** 0.298*** 0.494*** 
(0.170) (0.170) (0.170) (0.170) (0.059)  (0.056) 
Density – β(d) −0.087 −0.079 −0.015 −0.178 0.038* −0.225** 
(0.093) (0.092) (0.354) (0.174) (0.020) (0.104) 
Dummy size  – 
Dummy output  – 
Fixed effect  – 
Topographic – – 0.097 −0.151 – – 
– – (0.492) (0.163) – – 
Socio-economic – −0.003 – −0.041 – – 
– (0.0162) – (0.088) – – 
Adj -R-sq 0.974 0.974 0.974 0.974 0.941  

Significance level *90%, **95%, ***99%.

To sum up, in all estimations (Table 3, 1–6) β(q) < 1, i.e., an increase in the amount of water supplied by the utility will lead to a proportionally lower increase in the utility's costs.

Examination of utilities' consolidation

As noted, in Israel today there are 57 utilities that provide relatively small amounts of water to a small population. In 2013, the last amendment to the Water and Sewage Law – Government Resolution No. 161 dated May 13, 2013 – was published, which stated that the existing utilities will be merged into 15 regional utilities that take advantage of economies of scale in the distribution segment. This section shall estimate the expected impact from the transition to a reduced deployment of 15 water and sewage utilities.

The structure of the cost function which contains the density elasticity and the output elasticity, allows us to examine the case of an increase in output in economies of output density (EOD) and economies of scale (ES). According to previous studies (Caves et al., 1981; Roberts, 1986; Filippini, 1996, 1998; Antonioli & Filippini, 2001; Mizutani & Urakami, 2001), advantages of the increase in output are defined as the relative increase in the utility's costs due to the increase in the output volume (EOD). That is, when the quantity proportion increases more than the cost.

We define an advantage of an increase in output when EOD is larger than 1 and a disadvantage of an increase in output when EOD is less than 1. In the case that EOD = 1, the change is unitary and there are no advantages or disadvantages resulting from a change in output. An advantage to an increase in output exists as long as the average cost of the water corporate decreases as a result of an increase in output. Economies of scale will be defined when the relative increase in the average cost is lower than the increase in the output and in the density of the utility's consumers.

Table 4 presents an examination of economies of scale for the deployment of 15 spatial water and sewage utilities. This utilities’ deployment is based on a study published by the Water Authority (Israel Water Authority, 2013), which formulated a map of 15 spatial utilities as a replacement for the current layout. Table 4 displays the examination results of EOD and ES for the optional spatial utilities calculated as the sum of the parameters of the various utilities. According to Table 4, the result for each spatial utility is greater than 1, thus, increasing the amount of water supplied by the utilities and increasing the density will inevitably lead to improved efficiency and to a decrease in the cost of production per cubic meter of water, and thus to the utilization of economies of scale. The gap between the benefits of an increase in output (EOD) and economies of scale (ES) derives from the density effect on the total cost of the utility.

Table 4.

Examination of economies of scale results – Translog estimation (Equation (3)), spatial corporations.

Spatial corporation New water quantity (thousands of cubic meters per year) Number of customers per kilometer   
Judea and Samaria region 1,681 93 2.193 4.537 
Arava region 10,100 191 2.004 3.655 
Eastern Galilee region 14,103 123 1.972 3.523 
Western Galilee region 16,465 112 1.958 3.462 
Shfela region 24,616 239 1.922 3.444 
Nazareth region 26,766 158 1.914 3.357 
Southern region 30,915 204 1.902 3.363 
Haifa and its surroundings region 31,388 149 1.900 3.303 
Petah-Tikva region 32,294 211 1.898 3.360 
Northern Sharon region 32,524 185 1.897 3.334 
Central region 35,895 173 1.889 3.296 
Negev region 36,094 181 1.888 3.303 
Sharon region 42,645 110 1.874 3.161 
Tel-Aviv region 44,350 260 1.871 3.332 
Jerusalem region 52,974 168 1.856 3.194 
Spatial corporation New water quantity (thousands of cubic meters per year) Number of customers per kilometer   
Judea and Samaria region 1,681 93 2.193 4.537 
Arava region 10,100 191 2.004 3.655 
Eastern Galilee region 14,103 123 1.972 3.523 
Western Galilee region 16,465 112 1.958 3.462 
Shfela region 24,616 239 1.922 3.444 
Nazareth region 26,766 158 1.914 3.357 
Southern region 30,915 204 1.902 3.363 
Haifa and its surroundings region 31,388 149 1.900 3.303 
Petah-Tikva region 32,294 211 1.898 3.360 
Northern Sharon region 32,524 185 1.897 3.334 
Central region 35,895 173 1.889 3.296 
Negev region 36,094 181 1.888 3.303 
Sharon region 42,645 110 1.874 3.161 
Tel-Aviv region 44,350 260 1.871 3.332 
Jerusalem region 52,974 168 1.856 3.194 

At the spatial layout, the density of the customer connections is greater and the amount of water that the utility is required to provide is larger. Unlike competitive firms, the customer density and quantity of water supplied (output) for a water utility is determined exogenously; therefore it is up to the regulator to determine the amount and location (customer density) which will maximize economic efficiency. As a result of the consolidation and spatial layout, the average utility density will increase, but for some utilities the consolidation will lead to a decrease in density. Nevertheless, even in this case we can say with certainty that the growth in output will lead to improved economic efficiency and to a decrease in the utility's total costs.

Discussion

The study's results show that significant economies of scale exist in Israel's water utilities and the current division of the urban water sector is not exploiting its full advantage. All examined utilities, even the largest ones, do not exploit the full potential of economies of scale. The different estimations showed that an increase in the quantity of water supplied by a utility of 1% would lead to an increase of 0.5% in the utility's costs. This can be achieved by reducing the number of utilities. According to the findings of the study, it is proposed to increase the quantities of water in all existing utilities, except for the utilities that provide approximately 5 million cubic meters per year. These small utilities may be increased by ten-fold and still be within the range of economies of scale.

In the literature review, the authors mentioned that the function cost per cubic meter is U-shaped, and that certain studies had found an optimum size for a utility, a deviation from which would lead to diseconomies of scale. In Israel, however, the situation is different. As mentioned, all examined utilities do not exploit the full benefits of economies of scale and therefore any increase in the existing utilities will lead to improved efficiency. The optimum point was not found in the sample, therefore we can say that up to 54 million cubic meters (the maximum point), economies of scale exist in the urban water sector in Israel. Figure 3 illustrates the situation in Israel, but in practice it is not possible to know how the function ‘behaves’ over the observation edge (the point of the large utilities).
Fig 3.

Equilibrium edge of the sample.

Fig 3.

Equilibrium edge of the sample.

As a result of a corporate consolidation, the socio-economic rating and the topographic structure of some utilities may vary. The findings indicate that the effects of these changes on the total corporate costs are not significant, meaning we cannot say with certainty that these effects will take place. Allegedly, a corporate consolidation of the more efficient utilities with the less efficient utilities will lead to an average efficiency in all parameters, and thus will seemingly cause damage to the more efficient utilities. Nevertheless, according to the findings of this study, the improvement inherent in the corporate consolidation is significantly greater than the effect on the efficiency of the more efficient corporate, and therefore the impact on them will also be positive. In addition, it should be noted that the policy is supportive of utilities with high costs and weak opening figures, a fact that eases such a consolidation among the efficient utilities.

Summary and conclusions

The objective of this study was to examine, by econometric tools, the effectiveness of the current deployment of the water and sewage utilities in Israel's urban sector, and to find the optimal deployment model that will maximize the efficiency in urban water management. Using an econometric analysis of the cost function, the authors attempted to find the optimal size for the water and sewage utilities in Israel, based on the panel data of 51 existing utilities. The results indicate that there is a significant advantage to economies of scale in Israel's water utilities and that the existing distribution of the urban water sector in Israel is not taking full advantage of it. All examined utilities do not exploit the full advantage of economies of scale. It was found that the production costs per cubic meter of water decrease as the amount of production increases, thus it is proposed to increase the water quantities in all of the existing utilities. A transition to a layout of 15 spatial utilities will result in an increase of 3.5 times the amount of water supplied by the average utility, and 6 times the quantity of water provided by the median utility. Such a transition may lead to a decrease of 6–8% in the utilities’ total costs of water manufacturing. The empirical results of this study can serve the Water Authority in the process of future regulation in the municipal water sector, reduce the number of existing water utilities and increase the utilities’ efficiency.

Acknowledgements

The authors would like to thank the Water Authority for funding the research. Special thanks go to Matan Raz for his assistance in this study and to Hadas Joseph-Ezra for comments and editing.

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