1 Introduction

The efficiency of water utilities is a highly debated issue, because reducing the cost for a cubic meter of water delivered could decrease tariffs or improve investments and service quality. Furthermore, the financial context demands excellent performance by service providers; the economic crisis affecting EU countries implies that the only viable alternative for utilities, rather than cutting services or raising taxes, is reducing costs. According to new public management and new public governance paradigms (Osborne 2006), input and output control and performance evaluation techniques, as have been traditionally adopted in the private sector, could enhance the efficiency and effectiveness of public services (Hood 1991; Clark 2000; Osborne 2006).

To achieve efficiency, water utilities might adopt various routes, only some of which are discretionary and under their control. This cluster of activities includes technological innovations, job training, improved procurement policies, and the development of an internal control system dedicated to achieving effective, efficient corporate processes. Other tactics depend on the context in which the utility operates, such that they cannot be controlled fully by the firm, such as firm size, the degree of investment diversification, and network density. Economies of scale, scope, and density thus can be achieved only partially through manager decisions; more frequently, they arise from the characteristics of the area served by a firm, agreements made with municipalities involved in the water management, and normative frameworks in the industry. Thus these various economies are worthy of investigation, because they depend on decisions by various stakeholders: firm managers, private owners, municipalities, local authorities, and national governments. This article aims to identify the impacts of scale, scope, and customer density on the efficiency of water utilities.

Economies of scale exist when a unit increase in output results from a less than proportional increase in input (Silvestre 1987). Economies of scope occur when the unit average cost to produce two or more articles is lower than when they are produced by separated entities (Panzar and Willig 1981). In the water industry, economies of density pertain to two main types: (1) output or production density, which refers to the extent of the change in the cost if the total volume of water produced or wastewater treated increase, holding the number of customers and network length constant, and (2) customer density, which indicates how much the cost would change if the number of customer increased, with a constant network length (Nauges and Van Den Berg 2008).

Many scholars have attempted to highlight the existence of economies of scale and scope in this industry, to develop a comprehensive framework that can facilitate managerial and municipal decision making. Yet the results do not converge (Berg and Marques 2011; Carvalho et al. 2012): Most studies of firm size indicate the presence of economies of scale, but others suggest that the water industry is affected by diseconomies of scale. Furthermore, researchers have not come to an agreement about the “optimal scale” (Kim and Clark 1988; Bhattacharyya et al. 1995; Fabbri and Fraquelli 2000). Another group of studies considers the integration of various activities related to water services (production and distribution) and segments (water and wastewater), again with contrasting results (Saal and Parker 2000; Stone and Webster Consultants 2004; Garcia et al. 2007). For Italy in particular, Fraquelli et al. (2004) and Guerrini et al. (2011) observe economies arising from the integration of drinking water and wastewater services with other public services, such as energy, gas, or waste management.

The literature on the existence of economies of density is quite scarce (Berg and Marques 2011) and for this reason further empirical contributions are required.

Starting from these conflicting results, we investigate the potential presence of economies of scale, scope, and customer density in water utilities operating in the developed nation of Italy. It provides an appealing setting for comparing the performance of water utilities, because it features the coexistence of small, medium, and large companies serving different areas and populations, as either mono-utilities or multi-utilities. Romano and Guerrini (2011) cite, with a sample of 43 Italian firms, similar percentages of small, medium, and large companies, operating in high densely areas (Milan, Rome, Naples) and sparsely populated areas (Alps and Apennines). Furthermore, by focusing on a single country, we can eliminate cross-cultural noise and thereby specify the optimal size, degree of investment diversification, and population density that will produce the maximum level of efficiency in this particular setting (Tasman 2007; Carvalho et al. 2012).

The method chosen is made of two main stages. Stage 1 includes outliers detection on a population of 64 Italian water utilities, applying the super-efficiency approach proposed by Banker and Gifford (1988). Then, DEA scores were obtained: constant return to scale technical efficiency (CRSTE), variable return to scale technical efficiency (VRSTE) and scale efficiency (SE). Next, we regressed the efficiency scores obtained through standard DEA on our explanatory variables: the degree of investment diversifications, population density, and firm size. With these methods, we contribute to the ongoing debate regarding the best organizational choices of water utilities by providing clear policy directions, relevant to the implementation of carefully chosen strategies.

In the next section, we review literature related to our research goals and applied methodologies; Section 3 details our Italian study context. After we describe our methodologies, we outline the results in Section 5. Finally, we conclude with some implications and suggestions for further research.

2 Literature Review

Since Ford and Warford’s (1969) pioneering study of the U.K. water industry, empirical research conducted all over the world has addressed the relationship of the performance of water utilities with their size and diversification, as well as the possible existence of economies of scale, scope, and density. This type of studies is consistent with the new public management and new public governance paradigm (Osborne 2006) which have promoted the use of efficiency evaluation techniques as effective instruments for enhancing the performance and effectiveness of public actors, as it has always been in the private sectors (Hood 1991; Clark 2000).

The following table (Table 1) updates and extends the work of Abbott and Cohen (2009) and Guerrini et al. (2011) by summarizing the findings of the most relevant research papers that have investigated the effects of size on performance of water utility companies.

Table 1 Effects of size on water utilities’ performance: Prior research findings
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The results clearly are not consensual. Most studies confirm economies of scale in water utilities, but several others highlight diseconomies of scale in various countries (Ford and Warford 1969; Bhattacharyya et al. 1995; Aida et al. 1998; Saal and Parker 2000; Antonioli and Fillipini 2001; Mizutani and Urakami 2001; Saal et al. 2007; Alsharif et al. 2008; Baranzini and Faust 2009). Furthermore, some contributions suggest a positive relationship between size and efficiency in every segment (Kim and Lee 1998), whereas others specify their existence only in specific segments (e.g., wastewater, Knapp 1978), processes (e.g., distribution, Fox and Hofler 1985), or clusters of customers (e.g., non-residential, Kim 1987; Kim and Clark 1988).

Furthermore, many researchers propose that only small and medium-sized utilities can improve their efficiency by growing, whereas for big firms growth processes cannot produce benefits and sometimes even cause diseconomies. Kim and Clark (1988) indicate no significant economies of scale in the industry’s overall operations, but small utilities exhibit economies of scale, while large utilities exhibit moderate diseconomies of scale. Similarly, Filippini et al. (2008) posit that the optimal size for water utilities is close to the sample median, noting that economies of scale exist for small utilities, but large companies (above the third quartile in the distribution) exhibit diseconomies. According to Bhattacharyya et al. (1995), water utilities that produce 5–10 billions of gallons per year (BGY) are the least inefficient, and their inefficiency increases with their size. Marques and De Witte (2011) similarly identify 10 million m3 of water delivered per year as an optimal size, corresponding to 160,000–180,000 inhabitants. They also find diseconomies of scale for the largest utilities (see also De Witte and Marques 2011). Torres and Morrison-Paul (2006) demonstrate that through consolidation, small utilities can generate cost efficiencies, assuming a concurrent expansion of the network, but the consolidation of already large utilities without corresponding increases in output density is unlikely to be cost effective. Finally, Martins et al. (2006) show that large utilities (more than 20 million m3 provided) appear to suffer moderate diseconomies of scale.

In Italy, Fabbri and Fraquelli (2000) also find high economies of scale for firms that deliver around 350,000 m3 (minimum point) and diseconomies at the maximum point of 393,960,000 m3. Romano and Guerrini (2011) demonstrate that economies of scale in Italy exist and apply to firms in the medium size cluster too (more than 50,000 customers). With a focus on multi-utilities, Fraquelli et al. (2004) uncover economies of scale only for firms with output levels lower than those that characterize a median firm. Those that are bigger than the median indicated neither economies nor diseconomies of scale.

Another approach compares community instead of firm sizes: Garcia and Thomas (2001) indicate that merging local French communities into a water district of up to five communities is a profitable option, though for districts with more than two local communities, economies of scale decrease in magnitude. Furthermore, they report an unclear gain from merging more municipalities, but neither were any significant diseconomies of scale observed in larger water districts. According to Tynan and Kingdom’s (2005) international comparison among 33 countries, economies of scale exist. Nauges and Van den Berg (2008) concur in their international comparison of the economies of scale that emerge for small and medium-sized utilities in Colombia, Moldova, and Vietnam (cf. Brazil). In Switzerland though, Baranzini and Faust (2009) find diseconomies of scale for multi-utilities.

Another relevant topic in water industry research pertains to the existence of economies of scope. As highlighted by González-Gómez and García-Rubio (2008) and Guerrini et al. (2011), no consensus exists in this field either (see Table 2). The vast majority of existing research pertains to vertical integration in the water industry value chain (i.e., production and distribution, water and wastewater, water and sewerage). Very few studies (e.g., Lynk 1993; Hunt and Lynk 1995; Fraquelli et al. 2004; Carvalho and Marques 2011; Guerrini et al. 2011) have analyzed the effects of diversification in other industries related to water, such as electricity, gas, or urban waste. Carvalho and Marques (2011) show that the provision of water supply and wastewater simultaneously hinders performance, compared with the sole provision of water supply services. Yet they observe scope economies in Portugal, where a positive influence results from the joint provision of water supply, wastewater, and urban waste services.

Table 2 Effects of diversification on water utilities’ performance: Prior research findings
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In Italy in particular, with an analysis of 90 Italian utilities operating in the gas, water, and electricity sectors during 1994–1996, Fraquelli et al. (2004) find significant scope economies in multi-utilities with output levels lower than the median; they highlight how small, specialized firms might benefit from cost reductions by transforming into multi-utilities that provide more than one service, such as gas, water, and electricity concurrently. The highest cost advantage stemmed from the joint provision of water and gas. Guerrini et al. (2011) also identify economies of scope, though they depended on factors other than labor costs, such as energy costs, overhead, or discretionary costs. In addition, Italian multi-utilities incur higher labor costs per capita than mono-utilities, likely because they are more complex than mono-utilities and require more highly skilled managers and employees.

Finally, a relevant body of literature addresses a concept related to scale economies, namely, economies of density (Caves et al. 1981). According to Fabbri and Fraquelli (2000), density affects not just water utilities’ costs but also definitions of an optimal size. In the water industry, economies of density exist when the unit costs decrease with a greater population density or water provided per km of mains, because it lowers the costs of the infrastructure required to provide the service. That is, water utilities have significant economies of both customer and output density (Berg and Marques 2011), as we show in Table 3.

Table 3 Effects of density on water utilities’ performance: Prior research
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In the Italian water industry, Fabbri and Fraquelli (2000) find that greater customer density leads to cost savings, an effect confirmed by Antonioli and Fillipini (2001). Although Torres and Morrison-Paul (2006) find customer and spatial density economies, they arise only for smaller firms. For larger enterprises, output density economies instead fail to counterbalance the deleterious effects of vertical and horizontal expansion when the network expands proportionally. In contrast, Anwandter and Ozuna (2002) find that population density does not affect the use of operating inputs, and Renzetti and Dupont (2009) and Zschille and Walter (2012) demonstrate diseconomies of customer and output density, respectively.

Starting from these conflicting results, we inquire into the presence of economies of scale, scope, and customer density in water utilities operating in the developed country of Italy, using a method that consists of two main stages: a standard DEA approach and the regression of the efficiency scores obtained through DEA on the explanatory variables.

A minority of studies has adopted DEA to investigate the existence of economies of scale, scope and density (see Tables 1, 2 and 3). However the use of DEA for performance measurements has increased substantially, as reported by Gattoufi et al. (2004), including in water industry research (González-Gómez and García-Rubio 2008). Berg and Marques (2011) even indicate, in their literature review, that most non-parametric studies use DEA.

The reasons for the increasing popularity of the DEA non-parametric approach are several. It requires no assumptions about the functional relationship between costs and outputs, and it uses data related to multiple inputs and outputs (Stolp 1990; Cubbin and Tzanidakis 1998) that are reliable, readily available, and well-defined (Byrnes et al. 1986), usually based on minimal, defensible assumptions (Marques and De Witte 2011). However, we acknowledge that DEA exhibits greater sensitivity to measurement errors, because no error terms control for the effect of unobserved factors, and it is not possible to incorporate the exogenous environment or exogenous variables without imposing a separability condition between the inputs and outputs (De Witte and Marques 2010).

3 The Italian Context

The Italian water industry, known as the Sistema Idrico Integrato (SII), includes water utilities that operate as monopolists in specific areas of the country. Comprehensive water reforms, begun in 1994 with Law 36, have progressively modified the industry’s features. Each region is defined according to optimal geographic portions (Ambiti Territoriali Ottimali), in accordance with the locations of natural water basins, to avoid excessive service fragmentation. The relationship between the local regulatory authorities (Autorita‘d’Ambito Territoriale Ottimale [AATOs]) and the regulated utilities is characterized by information asymmetry, which prompted the implementation of a transparent reporting system to summarize companies’ performance and benchmark competition (Massarutto et al. 2008; Guerrini et al. 2011).

The reforms also sought to integrate water-related (water and wastewater) services, in an attempt to exploit economies of scope; merge water utilities to exploit economies of scale; apply tariffs that could cover both current costs and investments; and overcome the monopoly on the in-house supply of services by municipalities, by granting water-related service contracts to independent firms. Since the 1990s, the Italian water industry has been undergoing a “corporatization” process (Shleifer and Vishny 1994), including the creation of private companies, publicly owned corporations, and mixed public–private entities, to fulfill the general interest need for water services. However, corporatizing water services does not necessarily lead to more efficient services (Cruz and Marques 2011), nor have the advantages of privatizing water services been confirmed by empirical evidence (Anwandter and Ozuna 2002; González-Gómez et al. 2013). In Italy, empirical studies demonstrate that publicly owned firms are more efficient than private and mixed ones (Romano and Guerrini 2011); moreover, public-owned companies invest more than mixed ownership firms but still demand lower tariffs (Guerrini et al. 2011; Romano et al. 2013).

Approximately 20 years after the reforms went into effect, their purposes still have not been completely achieved. Recent studies instead indicate the potential for efficiency improvement (Cruz et al. 2012; Romano and Guerrini 2011), despite some progress. For example, many firms now integrate water and wastewater services (Co.n.vi.r.i. 2009) or function as multi-utility firms (Fraquelli et al. 2004) and provide gas, electrical energy, and/or waste services too. Publicly owned companies coexist with mixed and privately owned firms, with contracts appointed through a competitive tendering process by local water authorities. Finally, aggregation process has led to the emergence of several large utilities, in terms of both population and area served, that seek economies of scale, even as many small firms that serve only one municipality or a few remain in the market.

4 Data and Methods

4.1 Data Collected

The AATOs assigned responsibility for providing water and wastewater services to 114 Italian water utilities. Using Co.n.vi.r.i. and the Bureau Van Dijk AIDA databases, as well as information available from corporate websites, we collected data on the populations these utilities served, their main lengths, and financial statements. The number of inhabitants served by each company was available in the Co.n.vi.r.i. database. The length of the mains was generally available from websites or corporate financial statements; otherwise, we solicited this information directly from company technical staff. The financial data referred specifically to items related to water and wastewater management; thus, we obtained segmental reports for multi-utility companies, from financial statements, websites, or the company’s financial department directly. For the mono-utilities, we could simply gather financial statements from the AIDA database, because the water and wastewater segmental reports coincided with the operating areas in the published financial statements. These statements provided us with data pertaining to revenues, depreciation and interest paid, staff costs, and other costs (e.g., services, maintenance, materials). Finally, the number of employees was collected.

In gathering these data, we were able to obtain complete information about 64 companies that provide water services to approximately 72 % of the Italian population who purchased water from privately or publicly owned companies rather than directly from municipalities. That is, our central data set accounts for the majority of Italy’s water industry. In contrast to a previous article (Romano and Guerrini 2011), this study included both mono-utilities and multi-utilities in order to identify the existence of economies of scope.

Table 4 contains the data statistics, which reveal the notable differences in the sizes of the populations being served. Small utilities, with few employees, provide services for tens of kilometers and operate alongside massive corporations providing water and wastewater services across several regions of Italy.

Table 4 Descriptive statistics of the collected data
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We divided this data set into different groups, according to three criteria. First, we categorized companies into clusters of mono- versus multi-utilities. The former consisted of units that provided only water and wastewater services; the latter featured companies offering more than one service, in addition to water management, such as waste management, energy, and gas distribution. Second, considering the ratio of the population service to the kilometers of mains, we identified four approximately equally sized groups, based on their customer densities: very high density (VHD; > 182 inab./km), high density (HD; 122 inab./km < > 182 inab./km), low density (LD; 57 inab./km < > 122 inab./km), and very low density (VLD; <57 inab./km). Third, we distinguished large, medium, and small firms on the basis of their revenues. Adopting European Union parameters, utilities with more than 50 million Euros in sales were large, those that earned between 50 and 10 million Euros represented medium companies, and those with less than 10 million Euros in revenue were small utilities.

In Table 5 we provide an overview of the clusters, along with their descriptive statistics. The clusters differ substantially and effectively represent the Italian context. In terms of size, some firms are 12 times smaller than others when measured by mains length, 25 times smaller in terms of average population served, and 39 times smaller with regard to the number of employees. Such wide differences also emerge for the average value of revenues. As expected, multi-utilities are larger than mono-utilities on each indicator considered, because firms that provide a wide range of public services usually operate on a larger scale. The VLD cluster includes firms with a wide mains network that serves few customers. In terms of number of employees, the average size of these firms is medium.

Table 5 Main features of each cluster
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4.2 DEA Analysis

To detect economies of scale, scope, and density in the Italian water industry, we applied a two-stage method, based on DEA and regression analysis. Unlike previous research (Cubbin and Tzanidakis 1998), we do not use regression analysis solely as a control method to confirm the DEA results. Instead, after creating a ranking based on the DEA scores, we applied a regression model to determine the influences of the three independent variables (i.e., degree of investment diversification, customer density, and firm size). This two-stage method has applied previously to study the water sector (Estache and Kouassi 2002; Anwandter and Ozuna 2002; Kirkpatrick et al. 2006; Garcia-Sanchez 2006; Renzetti and Dupont 2009).

As a non-parametric technique, DEA can determine a frontier and calculate an efficiency ratio for each unit. Through a linear programming approach, DEA identifies an efficient virtual producer for each unit; the efficiency ratio is the distance separating the virtual from the real unit. Charnes et al. (1978) use this linear programming method to build a production frontier, in which decision-making units (DMUs) can linearly scale inputs and outputs without any variation in efficiency. However, this assumption is valid only for a limited range of production, when all units operate on an optimal scale. Banker et al. (1984) therefore remove the constant return to scale (CRS) assumption and instead determine a scale effect (SE) and a pure technical efficiency (VRSTE), which in combination yield a global efficiency index (CRSTE). Specifically, the VRSTE measures the real capability of a company to purchase, mix, and consume inputs; its SE indicates the effectiveness of the decision to operate at a certain production scale. To evaluate SE, we must consider the distance between the variable return scale (VRS) frontier and the CRS frontier for each DMU. In line with most DEA research (Berg and Marques 2011), we opt for the VRS assumption and thereby highlight the real determinants of global efficiency in water utilities by distinguishing pure from scale efficiency.

If efficiency is the capability to reduce consumption of inputs at a given level of output, we must choose the measures to use as inputs and outputs in the DEA model carefully. According to two analyses (Berg and Marques 2011; De Witte and Marques 2010) the most frequently adopted inputs are staff cost, operational expenditures, energy, and mains length. The leading output measures are distributed water volume and the number of customers. Consistent with this evidence and the data available, we consider four inputs—the sum of amortization, depreciation, and interest paid; staff costs; other operating costs; and the length of the mains—and two outputs—population served and total revenues.

After we collected all the data, we applied a super-efficiency approach (Banker and Gifford 1988) to detect outliers. Nonparametric models such as DEA yield some advantages compared with parametric methods, in that they issue no a priori hypothesis about the functional form of the data. However, they suffer from outliers, due to errors or atypical DMUs. To avoid this problem, the super-efficiency method identifies as outliers any observations whose super-efficiency score exceeds a prespecified screening level, set in this study to 1.4 (see Zschille and Walter 2012). Above this level, scores are less densely distributed and show higher dispersion. Next, we removed six observations identified as outliers and then ran our chosen DEA model.

To solve the chosen linear programming model we used DEAP Version 2.1 (Coelli 1996), a freely downloadable software for efficiency analysis developed by the Centre for Efficiency and Productivity Analysis (CEPA). With this software, users can define their own linear programming model by choosing the kind of return scale (constant or variable), as well as the orientation toward input or output and the number of stages needed to solve the problem. We have already addressed the choice of the return scale assumption; we discuss the other two aspects here.

Input-oriented models identify an efficiency improvement as a proportional reduction in the consumption of inputs with the same amount of outputs; output-oriented models instead view efficiency as an increase in the production of outputs, given a certain amount of input. Scholars use the output orientation model when the DMUs observed have a certain amount of resources and must maximize outputs; if DMUs need to produce a fixed level of output but aim to reduce their consumption of inputs, an input-oriented model is more appropriate. For water utilities, outputs (measured by cubic meter of water delivered or inhabitants served) remain fairly constant over time, but inputs depend on price fluctuations and internal efficiency. Therefore, most articles in this realm and in our literature review use input-oriented models (Berg and Marques 2011; De Witte and Marques 2010).

We adopted the following linear programming model, with the assumption of a VRS and input orientation:

$$ \begin{array}{ll} Min\kern0.5em \varPhi \hfill & \hfill \\ {}{\displaystyle \sum_{\mathrm{j}}{\lambda}_{\mathrm{j}}{x}_{\mathrm{j}\mathrm{m}}\le \varPhi {x}_{{\mathrm{j}}_0\mathrm{m}}}\hfill &; \kern0.5em \mathrm{m}=1,2,\dots, \mathrm{M}\hfill \\ {}{\displaystyle \sum_{\mathrm{j}}{\lambda}_{\mathrm{j}}{y}_{\mathrm{j}\mathrm{n}}\ge {y}_{{\mathrm{j}}_0\mathrm{n}}}\hfill &; \kern0.5em \mathrm{n}=1,2,\dots, \mathrm{N}\hfill \\ {}{\lambda}_{\mathrm{j}}\ge 0\&{\displaystyle \sum_{\mathrm{j}}{\lambda}_{\mathrm{j}}=1}\hfill &; \kern0.5em \mathrm{j}=1,2,\dots, \mathrm{J}\hfill \end{array} $$

Finally, with DEAP 2.1 we can choose between a one- or multi-stage model. The efficient projected points determined by a one-stage DEA model (Charnes et al. 1978) may not comply with the criterion of Pareto optimality, in which case they should not be classified as efficient points—a problem due to the input/output slacks that arise when it is still possible to increase outputs or reduce inputs beyond an efficient projected point on the frontier. In response, according to Coelli (1998), we adopted a multi-stage linear programming model that can set aside slacks and give a Pareto-optimal set of projected points.

4.3 Statistical Analysis

The final part of this section provides a description of the statistical analysis applied to DEA scores (CRSTE, VRSTE, SE).

Existing DEA studies seek to group DMUs using exogenous and operational variables, such as geographical localization or size, to identify influences on efficiency (Brockett and Golany 1996; Anwandter and Ozuna 2002; Romano and Guerrini 2011; Garcia-Sanchez 2006). To achieve a similar objective, we conducted a statistical analysis to compare the means, medians, and variances of the DEA scores for the created clusters, also applying nonparametric rank statistics. If the differences are statistically significant, the variable used to group firms is a relevant determinant of performance.

We thus applied Mann–Whitney, median, and t-tests to reveal the differences between the two clusters created on the basis of the degree of diversification (i.e., mono and multi-utilities); Bartlett’s test indicated the differences across groupings based on size (small/medium/large) and density (VHD/HD/LD/VLD). Non-parametric rank statistics, such as the Mann–Whitney test, are particularly appropriated for testing DEA outcomes, because the distribution of efficiency scores is generally unknown (Brockett and Golany 1996).

Next, we used a regression model to verify the findings of these tests and explore the causal relationship further. The model related each DEA score to three independent variables:

  • Degree of investment diversification (DID), a dummy variable that may correspond to the mono- or multi-utility cluster, such that it verifies the presence of scope economies for the firms observed.

  • Customer density (CD), which indicates the presence of economies of density in the Italian water industry, measured by the ratio of population served to kilometers of mains length.

  • Size (SIZE), to show the presence of scale economies, measured by the total amount of revenue collected for water services.

Thus we ran the model three times, once for each DEA score (CRSTE, VRSTE, SE), as follows:

$$ \mathrm{DEA}\kern0.5em \mathrm{SCORES}=\beta 0+\beta 1\mathrm{DID}+\beta 2\mathrm{CD}+\beta 3\mathrm{SIZE}+\epsilon . $$

We chose a Tobit regression function, because of its ability to describe the relationship between a non-negative dependent variable and the independent variables. Scholars frequently associate Tobit functions with DEA models when studying performance across several industries, because the dependent variable value, measured by DEA scores, is restricted between 0 and 1, (Aly et al. 1990; Chirkos and Sears 1994; Dietsch and Weill 1999; Ray 1991; Sexton et al. 1994; Stanton 2002). However, this two-stage approach has been criticized (Simar and Wilson 2004, 2007) for failing to account for serial correlation in DEA scores. Because DEA scores may be biased, and the environmental variables correlate with output and input variables, bootstrapping techniques can better reveal the impact of exogenous and operational variables on efficiency scores (Peda et al. 2013).

Despite the limits of our chosen two-stage method, it offers an appropriate means to answer our research question, considering its widespread prior use (Tupper and Resende 2004; Garcia-Sanchez 2006; Renzetti and Dupont 2009) and its effectiveness compared with alternative approaches, such as ordinary least squares, the Papke–Wooldridge Method, and the unit inflated beta model (Hoff 2007).

5 Results and Discussion

As Fig. 1 shows, the DEA efficiency scores for water and wastewater utilities in Italy reveal that more than half of the firms are near the efficient frontier with VRS, with VRSTE scores between 0.9 and 1. Regarding the distance between the VRS and CRS frontiers (as measured by SE), the number of efficient firms increases, such that 76 % of the observed DMUs operate at a potentially optimal scale. Only 16 % of firms fall well below the average CRSTE (0.78), with scores between 0.30 and 0.50. This inefficiency is due to their poor capabilities to purchase, mix, and consume inputs. These underperforming DMUs mainly include small and medium firms and mono-utilities that serves less densely populated areas. These findings provide brief insights into the weaknesses of Italian water utilities.

Fig. 1
figure 1

Efficiency distribution, Italian context

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To identify the real determinants of water utilities’ performance, we compared the CRSTE, VRSTE, and SE scores for the clusters of utilities, according to the degrees of investment diversification, density, and size. With the Tobit regression model, we then inferred the unique impact of these three variables on efficiency scores. In Table 6, we provide the average global efficiency, technical pure efficiency, and scale efficiency score for each cluster.

Table 6 DEA scores and differences across clusters
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First, the degree of investment diversification does not appear significant in terms of efficiency. The multi-utility cluster obtained higher scores than the mono-utility cluster, but the difference was not significant, as confirmed across all three statistical tests. These results require further consideration with a regression function, to verify the presence of economies of scope. Second, the level of population density per kilometer of mains length offered clear, robust evidence: utilities operating in high or very high density regions are more efficient in terms of technical pure efficiency and scale. That is, economies of density help reduce costs for purchasing inputs and consumption.

Third, size exerted a statistically notable effect on two measure of efficiency. Large companies were most efficient in terms of technical pure efficiency, followed by small and then medium-sized companies. That is, large companies have the greatest capacity to purchase, combine, and deploy production factors. When it collects at least 50 million Euros in revenues, a firm performs well. Companies operating below this threshold should pursue a growth strategy to improve their efficiency. In terms of SE, the results are less dispersed than those for VRSTE, and the ranking is reversed: Firms collecting revenues of between 10 and 50 million Euros indicate the best organizational scale, followed by large and small firms, whose SE score matches (0.89).

This evidence indicates that a medium size is probably the best suited scale for water utilities operating in Italy. However, some problems affect this cluster, in that its firms exhibit the lowest VRSTE. Therefore, the scale advantages of this cluster are only supposed, since a poor purchasing, mixing, and consumption capabilities dramatically decrease the global efficiency of its firms.

To confirm these results, we ran the regression model; in Table 7, we list the beta coefficient of each function and its related p-value.

Table 7 Beta coefficients and p-values of the three Tobit functions
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In contrast with prior tests, the regression confirms the presence of economies of scope. The multi-utility attribute related positively to CRSTE and SE. This evidence is partially coherent with the results of a previous study in which diversified Italian utilities obtained higher returns on sales and investment productivity than companies operating only in the water and wastewater sector (Guerrini et al. 2011; see also Fraquelli et al. 2004). In other European countries, Lynk (1993) and Hunt and Lynk (1995) demonstrate the presence of scope economies for U.K. regional authorities when they also provide environmental services related to water (e.g., water quality regulation, pollution alleviation, river maintenance); Carvalho and Marques (2011), with evidence from Portugal, note a positive influence of the joint provision of drinking water, wastewater services, and urban waste activities.

Customer density positively affects all the efficiency scores, though VRSTE is particularly influenced by greater density. Firms operating in small, densely populated areas, such as cities, achieve the lowest costs for delivering a cubic meter of water and often can apply higher rates. This cost advantage depends on ability to deliver a cubic meter of water with fewer resources (mains and electricity) and limit water loss per customer. These evidence also is consistent with prior research (Fabbri and Fraquelli 2000; Tupper and Resende 2004; Garcia-Sanchez 2006). However, unlike Carvalho and Marques (2011), we find no threshold value for customer density; as the graph in Fig. 2 indicates, higher customer density implies greater efficiency.

Fig. 2
figure 2

Relationship between population density and VRSTE

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Our findings also confirm previous results related to size. That is, even though we found no differences in the CRSTE across large, medium, and small companies, greater efficiency in purchasing, combining, and consuming input to deliver a cubic meter of water increases significantly with a firm’s size. Figure 3 also contains a graph of the relationship between revenues collected and VRSTE. Diseconomies appear for DMUs that operate while collecting less than 60 million Euro in revenues; beyond this threshold, each firm records a maximum VRSTE. The biggest players in this sector, with revenues of 100–400 million Euro, such as Hera, AQP, AcegasAps, and Metropolitana Milanese, achieved optimal efficiency levels, probably because of their excellent pipeline capacity, skilled staff, and better purchasing power for strategic inputs (electricity and services).

Fig. 3
figure 3

Relationship between sales and VRSTE

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In contrast, the findings regarding scale economies are not consistent with the results of prior research that indicates growth advantages accrue only to small firms, whereas similar strategies followed by large companies would lead to diseconomies (Fraquelli and Giandrone 2003; Torres and Morrison-Paul 2006; Tynan and Kingdom 2005; Sauer 2005; Martins et al. 2006; Filippini et al. 2008; Marques and De Witte 2011). As was the case for customer density, our study indicated no threshold value for scale economies.

6 Conclusions

This study addressed the performance of water utilities, with the aim of contributing to the ongoing scientific debate about the most efficient way to organize and manage such firms. Our research extends existing literature on performance measures for water utilities by applying a combined DEA and regression analysis method to the Italian context. Evidence from this study highlights significant differences across groups of firms in terms of the degree of investment diversification, customer density, and firm size.

Companies with a high degree of investment diversification are more efficient than those that concentrate their investments in the water sector only. Multi-utilities achieve relevant synergies by providing additional public services, beyond water and wastewater, such as energy, gas, and waste management. The major cost advantages likely result from the reduction of administrative and commercial costs due to the sale of distinct services to the same customers. Another cause could be cross-subsidization among services; for example, the costs of the water business unit could be attributed partially to other company divisions. Further cost advantages accrue to firms operating in regions with high population density, because the presence of many customers per kilometers of mains decreases the costs for delivering a cubic meter of water, due to the lower unit costs for energy and infrastructure. Finally, the Italian water sector is characterized by economies of scale. The lowest unit cost results when companies earn more than 60 million Euros. Greater bargaining power with suppliers and customers and relevant economies of experience likely ensure these benefits.

The implications of this study are of interest for both policy makers and utility managers. Following the principles of new public management, utilities can achieve synergies and cost savings by providing a wide range of services while also increasing their size. Such objectives might be achieved through mergers and acquisition or by targeting areas still served directly by municipalities. The new national regulator (AEEG) is developing a new method for cost and tariff estimations; we recommend that this authority should consider the specific characteristics of each area served, in terms of size and density, and the company’s strategy, such as its degree of investment diversification, to define an effective competition model for water utilities and account for all the exogenous and operational variables that affect efficiency.