Water Supply Services in Spanish Cities and the Debate on Private Participation in Their Management: Which Model is Most Ecient?

Supplying water to the population is one of the fundamental services of any Spanish city given the importance of the good itself, regardless of how it is managed. However, it is sometimes seen more as a source of extra nance for the municipality, and, in recent years, as an issue of political debate in terms of the adequacy of one form of management or another: public or private. Currently, 35% of Spain's population is supplied by public specialised entities, 33% by private companies under a concession contract, 22% by mixed companies and 10% by undifferentiated municipal services. In simple terms, 45% corresponds to public management and 55% is fully or partially managed by the private sector. By analysing the annual accounts of the companies that operate in the Spain's principal municipalities, this study seeks to determine the role played by the private sector in the management of the mixed companies. Due to the diversity of services provided by these companies and the lack of differentiated statistics for each of them, we have used the Annual Accounts presented to the Central Mercantile Register or the data submitted to the Ministry of Finance in order to assess the inuence of private participation on the results of the companies.


Introduction
The public supply of certain services is justi ed by the essential nature of the activity. Article 128.2 of the Spanish Constitution establishes that "Public initiative in economic activity is recognised. Essential resources or services may be restricted by law to the public sector, especially in the case of monopolies [...]". And the services of urban water supply, which falls under municipal jurisdiction, is one such service. However, the law also stipulates the different ways through which these services can be provided: from direct management by the municipality itself or public entities or companies to public-private collaboration formulas that enable the creation of synergies between the Public Administration and private companies. According to the most recent available data, 35% of Spain's population is supplied by public entities, 33% by private companies, 22% by mixed companies and 10% by municipal services (AEAS 2018). In other words, 55% of the population receives water through companies that are fully or partially owned by private capital that have been granted the corresponding concessions. The rest is supplied through purely municipal companies or direct management by the municipalities.
This study seeks to analyse the in uence of the private sector in the management of the urban water supply services, through its participation in mixed supply service companies. To do this, we will compare the accounting data of the pro t and loss accounts and balance sheets of public and mixed companies in order to determine the relevance of private capital in the development of their activities. We should bear in mind that the accounting of the of public service concessions is not performed separately. Therefore, this service cannot be compared.

Literature Review
An adequate supply of water and sanitation services for the population requires a huge amount of resources, in terms of both investments to construct the infrastructures and operating expenses for their maintenance. The major nancial shortages of the public sector, the lack of stability in part of the revenue received and the di culty in undertaking investment commitments in long-term infrastructures with very long amortisation periods have given rise to the participation of private capital in the provision of this essential service, traditionally attributed to public management.
Furthermore, in such a relevant issue such as the human right to drinking water and sanitation, the United Nations, in Objective number 17 of its 2030 Agenda for sustainable development, establishes that it is necessary to encourage and promote effective public, public-private and civil society partnerships in order to ful l the SDGs. This re ects an acknowledgement of the di culties of an exclusively public management and promotes private participation. We should also remember that the presence of the incentives inherent in the private sector in the management of such an important service can give rise to other types of problems. These can include the complexity of supervising their action from the public sphere within a context in which asymmetric information can prevail or even di culty in aligning the objectives of the private agents with the levels of service demanded by the consumers.

Private participation in water supply services
The participation of private companies in the provision of public services has been widely examined in many studies from different disciplines ( This partnership also has a lower impact in terms of public-sector accounting, thanks to the treatment of non-public assets. Therefore, PPP enables a signi cant turnover of public works to be maintained with less short-term nancial effort, optimising the economic ows through the capture of private assets but without ruling out vigorous public However, the research does not only analyse the participation of the private sector but also the preference for one or another of the different models of service provision (concessions to private companies, provision through public companies or public-private collaboration through mixed companies), although these studies are not conclusive conclude that private management is more e cient in the use of the labour input, mainly due to the technological restrictions faced by public management and the legal and institutional restrictions and that private management seems to be less e cient in managing operating costs. Bhattacharyya et al. (1995) nd that the opposite is the case and that from a technical point of view and in terms of the use of inputs such as labour, energy and materials, private companies are less e cient. The existence or not of relevant differences in the management model of water services can also vary between areas. While Estache and Kouassi (2002) indicate that privatisation has had a positive effect on the water services in the African context, the results obtained by Estache and Rossi (2002) do not reveal any signi cant differences. Lobina (2013), meanwhile, suggests that institutional adaptability explains the e ciency and effectiveness of the public sector in relation to the private sector. Lobina and Hall (2000) conclude that public companies are more e cient in achieving social and development objectives. Frone and Frone (2013) show several successful PPP models used to manage and mitigate risks and improve performance in the provision of public water supply and sanitation services. Voorn et al. (2017) argue that municipally-owned corporations are a feasible way of providing certain local public services, including water management, and are capable of initiating and managing complex contracts. In line with other studies, González-Gómez et al. (2010) a rm that the economic literature has not shown that private management is more e cient than public management and, as a result, other reasons should be sought by governments to privatise the service. Meanwhile, Bel (2020) identi es the concern for excessively high prices and the corruption in private management as factors that in uence remunicipalisation, while ideological pressures seem to play a much less relevant role. Although it is well known that these factors are not exclusive to private management, aspects such as limitations to public borrowing and the problems of scal consolidation or budgetary stability facilitate the transition from public management models to public-private participation, or the provision of the services exclusively by private companies.
Spain has a long tradition of creating mixed companies which, unlike public companies or concessions to private companies for providing this service, are based on a unique public-private collaboration model in which the company's capital and governing bodies are mixed. The operational management is undertaken by the private partner, with the public partner playing a marginal role [1].
[1]It is interesting to examine the case of Aguas de La Habana S.A. formed by the Cuban government and the company Aguas de Barcelona S.A., in which the Cuban government has had a high level of in uence in the management despite having a mixed structure. Aguas de La Habana (2019).

The Sample / Data
It is important to note the di culties involved in obtaining data related to companies providing public services in general and water services in particular. Theoretically, as provided by articles 1, 2 and 3 of Law 27/2006, of 18 July, regarding access to information, public participation in decision-making and access to justice in environmental matters (it incorporates Directives 2003/4/EC and 2003/35/EC), and in accordance with the provisions of Law 19/2013 of 9 December on transparency, access to public information, and good governance, the access to economic data of companies that in some way participate with public capital should be available. But this is not always the case. After making requests to the companies and city councils (directly or through the transparency portals), there are municipalities for which we do not have information, even though they should be included in the sample due to their characteristics: Aguas de Valencia, Aguas de Albacete, Aguas de Alcalá, Aigües de Girona, Consorcio de Aguas de la Rioja, Empresa Mixta de Aguas de las Palmas, Aguas de Zaragoza [2], Aigües de Reus, EMMASA de Santa Cruz de Tenerife, EMATSA in Tarragona or Aguas de Telde.
In addition, the lack of clear and homogeneous accounting criteria has given rise to annual accounts with incomplete items and general notes with no details with which to compare the different companies. Furthermore, the lack of separate accounts for the activities developed by a public service company hinders their analysis. Another cause for confusion is that the data of the annual accounts submitted to the Ministry of Finance in the budgets of the local entities do not always coincide with the gures provided by the companies in the audit reports or annual reports.
On the other hand, the di culty entailed in conducting this analysis, together with the lack of concern of the public administration about evaluating such an important service as this, explains why the only exhaustive study on the In spite of all of this, and given the that our objective is to determine the e ciency of the participation of private capital in the provision of water supply services, the data for this study have been obtained from the annual accounts (balance sheets and pro t and loss accounts) of 2018 for the companies that provide the service in the towns and cities of more than 100,000 inhabitants and in the provincial capitals of Spain, only in the case of public or mixed companies. The nal sample is made up of 24 companies, 10 mixed and 14 public (table 1), that supply a total of 16.5 million people, employing more than 8,000 direct workers and distributing 1,200 mh3 per year through 163,700 km of pipes.  Sometimes, depending on the technique used for the analysis, the conclusions can vary. The study by Kirkpatrick et al (2006) shows that, while the results of the DEA tentatively indicate the superiority of the private sector, the stochastic frontier analysis (SFA) provides some evidence, although statistically insigni cant, that public service companies are more cost effective. The descriptive statistics suggest statistically signi cant differences.
For our case, and given the characteristics of the data, a two-stage methodology has been used. First, we have estimated the e ciency of the group of companies analysed through the non-parametric technique of data envelopment analysis (DEA). Introduced by Farrel (1957) and subsequently developed by Charnes et al. (1978), this is the non-parametric test that is most used in empirical studies on e ciency. DEA essentially calculates the economic e ciency of a company in relation to the performance of other companies that produce the same type of services, instead of against an idealised performance standard. It is a non-stochastic method in the sense that it assumes that all of the deviations from the frontier are ine cient results.
Speci cally, for this study, we have estimated e ciency through the two most widely used models; constant returns to scale (CRS) and variable returns to scale (VRs), using the package Benchmarking (Bogetoft and Otto 2020) for the programming language R.4.0.4 (R Core Team 2021). The "input" orientation has been used in both models.
In the second stage, the e ciency ratios have been compared for the different types of company (public or mixed/private) using the Tobit regression in order take into account the delimited nature of the e ciency ratio This study considers the following variables, referring to each company for the year 2018. From the pro t and loss account we have considered sales (Ventas), procurements (Aprovisionamiento), personnel costs (Cpersonal), amortizations (Amortiza), operating income (Rdoexpl) and the nancial result of the company (Rdo n). From the balance sheet, we have used the non-current assets of the company (Acnocorr). Finally, through the business reports, other relevant variables have been included such as the population supplied (Población), the workers employed (Trabajadores), the production of water in cubic metres (M3factu) and the supply network in kilometres of pipes (Kmtube).
In order to calculate the e ciency of each company, the variables of procurements and the number of workers in the company have been used. With respect to output, the sales of the company and the cubic metres of water produced have been used. Table 2 compares the variables considered between the different types of company. Taking into account the small size of the sample, the two-sample t-test does not reveal any signi cant differences in any of the variables considered. For this reason, we have calculated the standardised mean difference (SMD), also known as Cohen's d or effect size as a control value to observe the differences. Cohen (1988) proposed the following guidelines to interpret the magnitude of the SMD in the social sciences: small, DMS = 0.2; average, DMS = 0.5; and large, DMS = 0.8. Therefore, based on a value of 0.2 we can consider that there is a difference, although small, between the two types. As we can see in the table, the largest differences between the different types of companies can be observed in their procurements, amortizations and non-current assets. In the rest of the variables, the differences between the companies are considered as being small. Table 3 shows the e ciency ratios obtained for each company for both the CRS and VRS models. The most e cient companies are those with a value of 1 and, in the CRS version are: the Consorcio de Aguas de Bilbao, Aguas del Añarbe, San Sebastián and EMASESA Sevilla. All of these are public companies. In the VRS version, in addition to these, we can add Canal de Isabel II to the public companies and Aigües de Barcelona and Aguas de León to the mixed companies. The average e ciency of the public companies in the CRS version (0.62) is higher than that of the mixed companies (0.49). This difference in means has been calculated through the Welch Two Sample t-test, which is close to reaching statistical signi cance (t=-1.5 and p-value=0.16) for an exploratory study such as this one. Meanwhile, the average e ciency of the public companies in the VRS version (0.69) is also higher than that of the mixed companies (0.40) but in this case the difference does not reach statistical signi cance (t=-0.87 and p-value=0.4).

Results
As the sample size is small, it is advisable to calculate ratios and bootstrap con dence intervals for the differences in means. The mean bootstrap e ciency ratio of the public companies in the CRS version (0.49) is higher than that of the mixed companies (0.41), but the difference is not signi cant. Meanwhile, the average e ciency of the public companies in the VRS version (0.55) is also higher than that of the mixed companies (0.49) and does not reach statistical signi cance either.
The calculation of the con dence interval for the difference in means of the bias corrected bootstrap e ciency ratio based on 200 replications in the CRS model is (-0.20, 0.05). The lower limit of the interval reveals that a difference of up to 20% in e ciency with respect to the mixed companies is compatible with the data. In the case of the VRS version, the interval is (-0.20, 0.08), so a difference of up to 26% would be compatible.   The above tables once again show that there are no differences in e ciency between mixed and public companies once the population supplied has been controlled for, although the positive coe cient of the type of public company indicates a possible improved performance of the former, which we cannot con rm with the results of the analysis.

Discussion And Conclusions
This study seeks to establish empirical evidence which would enable us to determine the in uence of the presence of private companies in the management of urban water supply. We have compared the data of the pro t and loss accounts and balance sheets of the public and mixed companies of a representative sample of rms that provide the service in towns and cities of over 100,000 inhabitants and in the provincial capitals of Spain, (only public or mixed companies) which, together, supply a total of 16.5 million people. As it is impossible to nd the data in a single source, we have gathered them from each individual company and homogenised them to carry out the empirical analysis.
Given that the two-sample t-test does not generate signi cant differences in any of the variables considered, we have used other alternatives to attempt to determine the existence of signi cant differences. We have found relevant values for procurements, which have higher value in the mixed companies and amortizations and non-current assets which have higher gures in the public companies.
The e ciency ratios obtained for each company through the two models are higher for public companies, although the differences do not reach statistical signi cance (in the CRS model they are very close).
As the size of the sample is small, we have calculated ratios and bootstrap con dence intervals for the differences in mean, which reveal a mean e ciency that is slightly higher in public companies, although neither of the models reach statistical signi cance.
The calculation of the con dence interval for the difference in means of the bias corrected bootstrap e ciency ratio based on 200 replications in the CRS model is (-0.20, 0.05). The lower limit of the interval reveals that a difference of up to 20% in e ciency with respect to the mixed companies is compatible with the data. In the case of the VRS version, the interval is (-0.20, 0.08), so a difference of up to 26% would be compatible.
The Tobit regressions subsequently conducted reveal that there are no differences in e ciency between mixed and public companies once the population supplied has been controlled for, although the positive coe cient of the type of public company indicates a possible improved performance of the former, which we cannot con rm with the results of the analysis.
In short, the results of our analysis do not generate signi cant evidence that one type of company or another is capable of operating with a higher level of e ciency. This means that private participation in the management, as opposed to exclusively publicly managed cases, does not constitute a relevant contribution.

Declarations
Ethics approval and consent to participate.
Not Applicable.

Consent for publication.
Not Applicable.
Availability of data and materials.
The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.