Governance and Efficiency in Brazilian Water Utilities: An Analysis Based on Revenue Collection Efficiency

Abstract

This study analyzed the relevance of governance structure for efficient revenue collection by Brazilian water utilities (WUs). Data were collected from the National Information System on Sanitation (SNIS) for 127 Brazilian WUs, covering a balanced longitudinal panel from 2018 to 2022. The governance structures evaluated included ownership (public or private) and corporatization (publicly traded or not). We searched scientific databases and did not find any studies on the efficiency of specific WUs in collecting customer bills for services rendered and its relationship with this type of governance; thus, this is the main innovative contribution of this study to the literature. In the first stage, this study utilized the dynamic slack-based model (DSBM) to assess revenue collection efficiency. In the second stage, an econometric model with generalized estimating equation (GEE) was used to explain the efficiency. The findings revealed a global average inefficiency in revenue collection of 50.47%. Corporatization was linked to higher collection efficiencies, while ownership type was significantly linked with lower collection efficiency. Factors such as tariff accessibility, urbanization, and the COVID-19 pandemic also influenced efficiency. This study suggests that regulatory bodies should consider these insights to implement policies that prevent inefficiencies from affecting the tariff system for services.

1. Introduction

Efficiency considers the provision of water services at the lowest possible operational cost, and billions of dollars are needed to ensure the availability and sustainable management of water and sanitation for all, which is Sustainable Development Goal 6 of the 2030 Agenda. Therefore, reducing service inefficiency appears to be an effective strategy to save resources and expand access [1].

The efficiency of revenue collection measures how effectively a utility can convert its billed revenue into actual cash [2]. Moreover, from a broad perspective, public authorities see revenue collection as a way to stimulate and manage economic and social goals, aiming to aid in national development [3]. To achieve this objective, high revenue collection performance is necessary to promote efficiency in the provision of services and for national and organizational economic growth [4].

Regarding water utilities’ collection efficiency, the authors of [5] conducted a study to identify the factors affecting the financial efficiency and receivable collection of the Palestinian water sector under the dimensions of receivable collection (collected fees divided by billed sales), payment discounts, prepaid meters, dunning actions, water continuity, and payment methods. From another perspective, the authors of [4] evaluated the impact of on-the-spot billing systems, water costs, and revenue collection mechanisms on the revenue collection performance of public entities in Uganda. It aimed to determine how water costs and revenue collection mechanisms affect performance in the National Water and Sewerage Corporation (Mbarara Centre, Uganda) and to explore the relationship between the on-the-spot billing system and revenue collection performance.

In 2011, the UN Secretary-General Ban Ki-moon emphasized that governments need to recognize that the urban water crisis is a crisis of governance, characterized by weak policies and management, rather than a scarcity problem [6]. Therefore, an important aspect to consider is tariff revisions and how they affect other areas, such as revenues, with the aim of achieving higher-quality services [7].

Within the Brazilian context, water supply and sanitation services are primarily managed by public entities. However, this situation has been changing with the increasing number of concessions of these services to private entities [8]. Thus, understanding the organizational structure of the water supply service has been crucial to improving its efficiency [9].

As water supply and sanitation services are being provided by only one utility in each region of the country, a natural monopoly has been created. Typically, in markets with this configuration, investments tend to be high, costs are very low, and there is little to no rivalry [10]. This leads to a scenario of inefficiency since competitive pressures aimed at maximizing profits are absent [11]. However, the recent update of Law 11.445/07 [12] through the enactment of Law 14.026/20 [13] has brought forth incentives to open up competition, encouraging greater private capital investment in the sector’s concessions.

Governance is a term widely used to describe the institutional arrangements that affect organizations, with water governance being influenced by institutions, interests (stakeholders), and incentives [14]. Conceptually, it can be described in a model that distinguishes between (a) structural (endogenous) governance, which can be divided into the three dimensions of ownership form, practice standards, and enterprise autonomy, and (b) institutional (exogenous) governance, which is evident in the dimensions of market contestability, external review, and economic regulation. Each of these dimensions can be complementary or substitutive [15].

Brazilian water utilities have different institutional arrangements for service provision: (1) operated by the municipality itself through a government department or an autarchy; (2) provided by state-owned enterprises (public companies and mixed-capital corporations); and (3) granted to private companies. In the latter two cases, there are utilities with shares listed on the Brazilian stock exchange which are regulated by the Comissão de Valores Mobiliários (CVM) in terms of the disclosure of financial statements, accounting practices, and the monitoring of corporate governance, among other aspects.

Within this framework, the present study analyzed the association between governance structure and revenue collection efficiency, which was measured as the intertemporal dynamic efficiency of revenue collection. The scope of governance for this study focused on the structural and institutional fields, capturing the dimension of ownership form through the sector’s privatization process. The other dimensions were represented by a proxy for the utilities listed on the stock exchange, considering that these dimensions can be complementary or substitutive, along with the entire set of regulatory mechanisms practiced by the CVM for these utilities, which we refer to as corporatization.

Recent discussions about privatizations have been taking place around the world in recent years, and the water and sanitation sector is no exception. In this context, this topic has been widely debated [16]. Privatization, as highlighted by the authors, aims to enhance service efficiency through corporate governance. In developed countries, however, a different scenario emerges. A re-municipalization movement is occurring in various regions, particularly in European countries, where the return to public control has been driven by high tariffs imposed without corresponding improvements in service quality by private entities, as well as low transparency [17].

In Brazil, the discussion about the outsourcing and privatization of basic services was prominent in the 1990s and has returned to the political agenda due to the new regulatory framework for the sector, introduced by Provisional Measure 868/18, which amended the regulatory framework for basic sanitation—Law 11.445/2007 [12]. After losing validity, it was replaced by Bill 4.162/2019, which later became Law 14.026/2020 [13]. This new law creates ideal conditions for municipalities to promote the concession of sanitation services to the private sector. In this sense, the privatization of sanitation services contrasts with the global trend in re-municipalizing services [18].

Those who oppose the privatization process, including members of the Brazilian academia, sanitation sector experts, social movements, unions, and political parties, argue that privatization will not achieve the desired objectives. They claim that service improvement is incompatible with profit generation and that peripheral areas will be the most affected. As water becomes a commodity, the most vulnerable consumers will be unable to afford it. Additionally, there will be little investment in sanitation due to its low profitability [18].

According to Ref. [16], privatization aims to increase service efficiency through corporate governance. Conversely, Ref. [19] argues that the pro-(re-)municipalization movement seeks social justice by advocating for lower and more affordable tariffs, defending sustainability through investment in the system network to reduce losses, and promoting democratic management through greater financial transparency.

Given these conditions, to increase efficiency or send a “positive signal” to the market, it is expected that the utilities listed on the CVM will present better performance indicators than the non-listed utilities. Regarding privatization, despite the global discussion and movement towards re-municipalization in various countries, it is anticipated that services provided by private entities aim to enhance service efficiency [16].

Ref. [20] identifies ownership and regulatory mechanisms as key explanatory variables in the governance structure used in water utility benchmark studies. Additionally, other variables are considered, including the number of towns served (output), operational expenditure—OPEX (input), capital expenditures—CAPEX (input), chemical quality (quality), the region of operation (environmental factors), and gross domestic product (GDP) per capita (macroeconomic factors).

However, uncollectible receivables are part of OPEX, and previous studies did not structure the efficiency assessment model with variables specifically related to revenue collection and from an accounting perspective.

In this context, this study aims to analyze the relevance of governance structure for efficiency in revenue collection by Brazilian water utilities—WUs. The present work contributes to the scientific area by offering a novel perspective on the relevance of governance structure (ownership and corporatization) for efficiency, with a focus on revenue collection performance, which is not found in the existing efficiency literature or in Refs. [4,5]. The identification of these factors will provide valuable insights and support decision making by regulators aiming to enhance service efficiency.

Another important aspect to consider was the peak of the COVID-19 pandemic. According to Ref. [21], economies faced a supply and demand shock that triggered a global financial crisis due to pandemic-related factors. The authors also point out that this crisis incorporated the potential impacts of the pandemic, leading to a sharp decline in major stock market indices in March 2020, with values plummeting by nearly one-third within a few weeks.

2. Literature Review

With the framework established by Law 14.026/2020 [13], the Brazilian sanitation system has become quite similar to the French sanitation system in both institutional and regulatory models [22]. However, in the French context, the performance of private utilities did not meet expectations, with progressively increasing tariffs and, in some areas, unsatisfactory service quality, leading to the re-municipalization of water services in 2010 [23].

In that context, accurate billing and appropriate pricing are key to ensuring stable revenue [24]. Ref. [25] point out that public water utilities may suffer losses due to inefficient tariffs and billing, faulty metering, non-revenue water, and illegal connections.

For Spain, the authors of [26] found that privatization leads to higher prices, whereas the authors of [27] concluded that prices are lower when services are provided directly by local councils. Conversely, when services are outsourced, prices under public management are higher than those under private management.

In Italy, the authors of [28,29] found that water and sanitation utilities (WUs) under public management charge lower tariffs. These findings align with those of Ref. [30], which reported higher prices for public–private partnerships in France. Ref. [31] also found that in Germany, consumers pay more when utilities are privately managed. Other research supports this, showing that private utilities generally charge more than public ones. For example, in Chile, privatization led to short-term tariff increases Ref. [32], and in various developing countries, public–private partnerships resulted in higher tariffs [33].

These findings suggest that private management often results in higher prices, likely due to the focus on cost recovery and profitability. However, an empirical study in Argentina showed that privatization improved productivity and reduced tariffs [34]. Similarly, in Thailand, privatization lowered prices for poorer urban consumers [35], which aligns with Brazilian policies aimed at improving accessibility by reducing tariffs for low-income and low-consumption households [36].

Public inefficiency is linked to the independence of private utilities, as public providers face budgetary constraints. This situation resembles the French case, where significant modernization, such as the replacement of lead pipes and improvement of water quality, occurred in the early stages of the concession period. Despite these investments, which may have improved water quality, the sharp increase in public service tariffs and restricted access for poorer populations contributed to the re-municipalization process [22].

Various factors can influence the efficiency of services provided. Ref. [37] identified a positive influence of regulatory incentives on operator efficiency and divergent results concerning privatization, economies of scale, scope, and density. Ref. [38] found economies of scale, especially for small utilities, but ambiguous results for privatization. Ref. [39] indicated, in a meta-regression of 60 articles, a high likelihood that in developed countries, it is more common to find diseconomies of scale and scope among larger providers and those with public control. Ref. [40] analyzed the impact of privatization and regulation on efficiency.

In this context, the findings in Brazil identified only the economies of scale [41,42,43]. Regarding private control, results varied. In a survey in [37], 18 studies identified private control as more efficient, 17 found inconclusive results, and 12 indicated public control as more efficient. Additionally, the authors of [44] pointed out that the differences in provider efficiency are due to the methods or data sources used.

Considering the methods of the previous papers, the authors of [45] conducted a review of earlier studies on efficiency frontiers in the Brazilian water and sanitation sectors, finding that only two out of the six studies utilized data envelopment analysis (DEA). The authors of [46] explored the feasibility of implementing yardstick schemes to promote efficiency in the Brazilian sanitation sector, emphasizing the need for cost savings in the industry. The authors of [43] examined the impact of different types of water supply and sanitation service providers, considering aspects such as ownership and coverage. They used the Malmquist Index to analyze productivity trends and investigated the relationship between the lack of tariff regulation and reduced efficiency.

In addition to the studies reviewed in Ref. [45], several other works have applied DEA to assess the efficiency of water supply and sanitation (WU) providers. Ref. [47] used a DEA model to determine the efficiency scores of 26 WU providers and evaluated the average efficiency across different Brazilian regions. In [48], the efficiency of 57 WU providers in the state of São Paulo was analyzed, considering ownership and coverage, which contributed to the development of future tariff policies for the sector.

Ref. [49] presented the efficiency scores for 36 Brazilian WU providers and conducted a regional efficiency analysis. Additionally, Ref. [50] focused on the efficiency measurement of 26 WSS providers located in the capitals of Brazilian states.

One of the issues that initiated the privatization debate in Brazil was the poor management and indicators presented by public control. In this regard, the authors of [51] assert that losses and defaults were high.

Despite the empirical literature, three theories support the argument for superior private performance: the property rights theory, public choice theory, and agency theory [52].

Using the theoretical framework of Ref. [52], the property rights theory argues that under public management, managers cannot claim any generated savings, have no incentives for cost containment or launching new products/services, and, thus, do not act towards these goals.

The theory explores the conjunction between legal frameworks and economics, referred to as “economic analysis of law”, focusing on the relationship between property rights and external factors or externalities. These theoretical foundations allowed for verifying the importance of a system of property rights in the efficient performance of the economy, identifying the main elements that guide the allocation and formation of such legal systems [53].

In the early years of the 21st century, discussion of the theory of property rights has been specifically developed by Ref. [54] in the context of public water supply and sanitation services. The authors argue that one factor that could motivate owners to oversee managers’ actions is their capacity to fund enhancements in management efforts. According to the theory of property rights, private owners, as residual claimants, have more precisely defined incentives to encourage effective decision making by managers.

The public choice theory infers that bureaucrats seek to serve their own interests at the expense of the common interest, leading to patronage policies and other issues [52]. Thus, the notion that government economic management can be driven solely by public interest, relying on the capabilities of politicians and government experts to develop effective public policies to correct market failures, has been challenged by the public choice theory in its examination of political decision-making processes. This theory posits that politicians and bureaucrats, as well as business leaders and consumers within a neoclassical economic framework, act based on rational self-interest, with politicians primarily motivated by the pursuit and retention of power [55].

Finally, the agency theory suggests that principals (public managers) could exploit informational asymmetry for tariff collection that benefits them [52]. In summary, the theory focuses on economic outcomes at the institutional level based on the relationship established between two parties: a principal who delegates the pursuit of their interests and an agent responsible for managing economic activity.

According to [54], privately owned corporations craft contracts that incentivize managers to adopt strategies aligned with maximizing profits, consistent with the corporation’s goals. These private companies experience reduced political interference compared to their public counterparts.

Applying the aspects of agency theory to public water supply and sanitation services, the authors of [54] comment that the theory serves as a valuable foundation for understanding how ownership impacts the performance of water utility management. Within a principal–agent framework, the owner’s responsibility is to craft a contract that incentivizes the manager to select strategies that optimize their success.

Exploiting the theories mentioned before and considering that some empirical studies on the efficiency of Brazilian WUs, such as [56,57,58], have suggested that private control results in higher efficiencies, we posit the following hypothesis:

H1. 

Privately controlled utilities are more likely to achieve better efficiency in revenue collection.

The informational asymmetry in markets originates from the inherent uncertainty about the quality of products or services provided. According to [59], this uncertainty is the main driver for the products and services of varying quality being treated the same, devaluing higher-quality products and overvaluing lower-quality ones.

The signaling theory, formulated by [60], posits that an individual’s characteristics can be manipulated by the individual. The author suggests that in decision-making environments with uncertainty, these characteristics or parameters can guide decisions, thus acting as the potential mitigators of informational asymmetry [61].

According to [61], higher-quality companies adopt policies that allow their superiority to be perceived, while lower-quality companies tend to adopt policies that conceal their weaknesses. Therefore, presenting better signals with improved revenue collection efficiency indicators can be interpreted by the market as a sign of higher-quality service providers.

For the authors of [62], revenue evasion (or uncollected receivables) is related to economic efficiency. Thus, corporatized (with shares on the stock exchange) companies aim to present “good signals” (signaling theory) to the market, and a high inefficiency of revenue collection may indicate a failure in controls or practices to ensure resource inflows for services rendered. Revenue is crucial because it influences a business’s earnings and reflects its performance over a specific period [63]. Several factors impact business profitability. For instance, companies that cannot generate and collect sufficient revenue to cover operational costs may face economic failure [64]. The authors of [65] concurred with the authors of [64], noting that accelerated revenues are essential for business survival, as they can determine liquidity and profitability. Conversely, declining revenues coupled with rising costs can create a gap that negatively affects business profitability.

H2. 

Corporatized utilities with shares on the stock exchange are more likely to achieve greater efficiency in revenue collection.

3. Materials and Methods

3.1. Data Collection

Our sample selection included water utilities classified as state-owned enterprises, mixed-ownership state enterprises with public management, mixed-ownership state enterprises with private management, and privately owned enterprises listed in the Brazilian sanitation information system or Sistema Nacional de Informações Sobre Saneamento (SNIS) between 2018 and 2022. Initially, 180 utilities were selected. However, due to missing information, the absence of financial reports, and the presence of outliers, we excluded some utilities, resulting in a final sample of 127 utilities and 635 observations of a balanced panel. Figure 1 shows the distribution of the utilities studied by the Brazilian Federative Unit.

3.2. Model Specification for Efficiency Score Model

3.2.1. The Proposed Data Envelopment Analysis Model

Data envelopment analysis (DEA) is widely used, appearing in 68% of the publications in the literature on water and sanitation efficiency in developing countries. The majority of studies (9 out of 12) use the variable returns to scale (VRS) approach, which compares operators at the same scale level, whereas the constant returns to scale (CRS) approach assumes that all the operators function at an optimal level [44].

To choose between the models with CRS and VRS, we followed the logic presented in [66], using the t-test for the paired samples of two related groups: one group with efficiency scores generated with CRS and the other with the scores generated by VRS. If there was a significant difference between the means of the two groups, the VRS model was selected. However, if the efficiency scores did not exhibit normal distribution behavior, the non-parametric Wilcoxon two-related-sample test was used.

In addition to the scale choice, more concerns are described in [67] concerning the protocol for non-homogeneous units and non-homogeneous environments; homogeneity between the units was suggested, as all the information involved was from the same public utility service, and the recognition and measurement process followed the same accounting regulations. The issue of a non-homogeneous environment was expected to be verified with the explanatory model. Regarding the protocol of the number of inputs and outputs, there was no restriction, as there were 127 DMUs for one input, one output, and one carry-over, which can be considered an output. Furthermore, correlations were used to verify factor correlation (Kendall’s tau-b) and isotonicity.

In the Brazilian water and wastewater sector, tariff review processes cover a cycle of 4 to 5 years, often recognizing efficiencies by periods and overall cycles. In this case, an intertemporal dynamic analysis is an interesting proposal, especially when it is necessary to capture the effect of efficiency from one year being carried over to another year. However, the traditional DEA models only evaluate period efficiency scores independently. To address this, Ref. [68] introduced production frontiers with dynamic DEA. Following this perspective, the authors of [69,70,71,72,73,74,75,76,77] expanded the scope of the DEA additive model known as the slack-based model (SBM) to a dynamic model capable of estimating the production frontier over several periods: the dynamic slack-based model (DSBM).

Returning to the scope of the sector, some work is being developed concerned with intertemporal effects (dynamic efficiency). The authors of [78] aimed to measure efficiency dynamically, incorporating intertemporal capital links within the production function for the water and wastewater sector in England and Wales (1996–2011), concluding that ignoring the intertemporal effects can lead to the overestimation of allocative inefficiency.

Other studies evaluating the efficiency of the water and wastewater sector using dynamic models based on slack, including [41], which developed a score for the dynamic efficiency of water and sewerage utilities in Brazil, considered the universal access deficit to services as a bad carry-over, and explained their efficiency through the governance structure. The authors of [79] examined the pattern of water use efficiency and its potential relationship with urbanization and foreign direct investment between 2007 and 2016 in 11 West African countries (these two used the DSBM). Ref. [80] analyzed the impact of the Brazilian regulatory environment on the efficiency levels of water and sewerage utilities using the network approach described in [77], DNSBM.

Similarly concerned with the temporal influence on revenue collection efficiency, the DSBM was used in this study to observe only dynamic collection efficiency, which involves a small set of variables extracted from financial accounting.

3.2.2. Variable Selection for Efficiency Assessment

In Brazilian water utilities’ tariff review processes, losses due to uncollectible credits are tariff components and, in some cases, subject to certain regulatory limits. According to the Brazilian accounting standards, the [81] Pronunciamento Técnico CPC 48—Instrumentos Financeiros (correlation with International Accounting Standards—IFRS 9) determines that such expected losses may be calculated on accounts receivable from customers using a matrix of accruals. Unfortunately, the SNIS database does not have information on expenditures on losses in accounts receivable from customers, with credit balances in said accounts being the best proxy available in the system.

Customer accounts receivable occupy an important space and substantial representation in the current assets and working capital [82]. The cash flow does not necessarily reflect the profit disclosure resulting from the increased accounts receivable, and the failure in debt collection processes lead to bad debts and deep economic crises in entities [68]; in this sense, customer accounts receivable (RECEIVABLE) is considered as the primary variable for evaluating efficiency and is classified as “input”.

In the water sector, receivable collection and cost recovery represent critical references for financial sustainability and the continuity of water delivery [83,84]. These factors are especially important for enabling expansion and equity in the provision of services [84]. Low received collection rates result in insufficient cash to meet the challenge of providing water services in the necessary quantity and quality, renewing aging infrastructure, coverage of the growing population and urbanization, impacting human resources, and tariff issues [85]. Efficient receivables collection enhances the financial performance of water providers [5]; therefore, the collection received from customers (COLLECTION) variable, which represents the annual value effectively collected from all operational revenues, will be the “output” in the efficiency score assessment.

Considering that the “input” (RECEIVABLE) is working capital from operational revenues billed for the services provided to consumers, which have not yet entered the utility’s cash flow, and the “output” (COLLECTION) is the result of the same revenues added to the cash flow; regardless of the accrual period of the invoiced amounts, the moment in which such revenues enter the utilities’ cash flow is important for evaluating the efficiency of water services calculated by $Fi32=G38/G3\times H1$), where $Fi32$ represents the delay in the accounts receivable (in days equivalent); $G38$ is the accounts receivable from drinking water at the reference date; $G3$ is the sales revenues during the assessment period; and $H1$ is the assessment period [86]. For wastewater services, the importance is the same [87] and is calculated similarly, recognizing only revenues and receivables from wastewater services (performance indicator code $wFi32$).

The use of the DSBM is required to identify the connection components of the efficiency (carry-over), which carry the efficiency from one period to another according to their characteristics. Thus, it is possible to identify four categories of carry-overs: good carry-over (desirable and behavior similar to that of an output), bad carry-over (undesirable and behavior similar to that of an input), free carry-over (discretionary and freely controlled by the DMU), and fixed carry-over (non-discretionary and outside the control of the DMU) [77].

The collections for a period do not correspond to the same revenue period, considering that consumers will be charged at different due dates and that some customers delay payments (for a long or short time) or even fail to make them. To capture this phenomenon in the efficiency score, operating revenues are weighted considering the delay period and will be a good carry-over (REVENUE), as its increase is related to the increase in revenue collections within the existing receivables conditions. Considering that each utility has its own billing and recognition policy for probable losses, the hypothesis of a constant currency based on an inflationary index also requires careful consideration so that collections are more closely linked to the inflationary processes of their respective revenues.

Due to the limitation of data before 2017 (since the longitudinal panel began in 2018, there are collections billed in 2017, for example) for all the DMUs studied, we set the maximum delay period at 2 years.

If the delay was less than or equal to 365 days, the REVENUE values were those of the same COLLECTION period. If the delay was greater than or equal to 730 days, revenue from the immediate previous year was considered. If they did not fit into any of these situations, REVENUE was the result of the weighted average between the operating revenues of the reference period and the immediately previous period according to the time that exceeds 365 days, provided by the following:

$$\begin{array}{cc}\hfill {\mathit{REVENUE}}_{jt}=& \left[OPRE{V}_{jt}/365\times \left({\mathit{DELAY}}_{jt}-365\right)\right]\hfill \\ \hfill & +\left\{OPRE{V}_{jt-1}/365\times \left[365-\left({\mathit{DELAY}}_{jt}-365\right)\right]\right\}\hfill \end{array}$$

(1)

where $OPRE{V}_{jt}$ is the invoiced value of utility j in year t (term of DSBM) arising from the utility’s core activities and corresponds to the sum of direct and indirect operating revenue from water and wastewater services (FN005 of SNIS), and $DELA{Y}_{ji}$ is the delay in accounts receivable from utility j in period t, calculated according to the authors of [87,88]. This measurement procedure is justified because, in the sector, it is common for consumer debts to be paid in installments, sometimes over up to 24 months, and recorded in the accounts as receivables from noncurrent assets.

The efficiency model studied focuses on the effort to increase revenue collection considering the level of customer receivables observed for each utility (DMU). Therefore, the orientation of the data envelopment model is towards output. All the values were measured in BRL (Reais) and were adjusted to the constant currency of the year 2022 based on the Brazilian inflationary correction measured by the Índice Nacional de Preços ao Consumidor Amplo (IPCA) released by the Instituto Brasileiro de Geografia e Estatística (IBGE), accumulated retroactively up to each year. Figure 2 and

Table 1. DSBM variables for revenue collection efficiency assessment.

Variable	Description	DSBM Specification
$RECEIVABL{E}_{jt}$	Accumulated gross balance of the accounts receivable from utility j in year t, considering the last day of the reference year, as a result of billing for direct and indirect water and wastewater services (FN008 of the SNIS), and adjusted using the Brazilian price index IPCA/IBGE (measured in BRL).	$\mathrm{Input}$	$=x_{1jt}$
$COLLECTIO{N}_{jt}$	Value effectively collected from all the operating revenues of utility j in year t (FN006 of the SNIS), adjusted using the Brazilian price index IPCA/IBGE (measured in BRL).	$\mathrm{Output}$	$=y_{1jt}$
$REVENU{E}_{jt}$	Value of the revenue from the direct and indirect provision of water and wastewater services proportional to the delay in the accounts receivable of utility j in year t. Adjusted using the Brazilian price index IPCA/IBGE (measured in BRL).	$\mathrm{Good}\mathrm{carry}-\mathrm{over}$	$=z_{1jt}^{good}$

present the structure and description of the variables used in calculating efficiency based on DSBM, respectively. In [77], the DSBM is described extensively and in detail using 27 mathematical notations. The DSBM specification column of Table 1 presents the descriptions of the variables observed in these notations (see the paper for more details).

3.3. Explanatory Econometric Model Construction and Variable Measurement

To analyze these variables, we employed the generalized estimating equation (GEE) regression, an extension of generalized linear model (GLM) suitable for longitudinal panel data [88]. This method was chosen due to the time-dependent nature of the dependent variable.

The authors of [89] used GEE with a second stage to explain the most important factors affecting DEA efficiencies in the Iranian insurance market. In [90], it was used to explain the relationship between DEA-based performance of hospitals in the Netherlands and managed competition components. In [41], it was used to explain the relevance of governance in DSBM-based cost efficiency and universal access for Brazilian water utilities, highlighting the use of the model in evaluating the second stage of the literature based on DEA.

In GEE models, it is necessary to choose the distribution family (the random component for the response variable, which follows a distribution from the exponential family), the link function (the connection between the random component and the systematic component), and the within-group correlation structure or working correlation matrix (exchangeable, independent, autoregressive, stationary, and unstructured). The model with the smallest quasi-likelihood under the independence model criterion (QIC) is suggested as the most robust choice in GEE [91].

The econometric model has assumed that the option family follows a binomial distribution where the results can only be grouped into two categories: inside and below the optimal efficiency frontier, as explained in [41]. For the DSBM scores, two link functions were considered: identity and logit. In this sense, we used the lowest QIC criterion for a more robust link and correlation matrix choice.

The following panel data model was constructed to analyze the association between governance structure and efficiency:

$$EF{F}_{jt}={\beta }_{1}COR{P}_{jt}+{\beta }_{2}OW{N}_{jt}+{\beta }_{3}REPCUS{T}_{jt}+{\beta }_{4}DENSIT{Y}_{jt}+{\beta }_{5}SIZECUS{T}_{jt}+{\beta }_{6}UR{B}_{jt}+{\beta }_{7}AFFO{R}_{jt}+{\beta }_{8}JOIN{T}_{jt}+{\beta }_{9}COVID{19}_{jt}+{\epsilon }_{jt}$$

(2)

Table A1. Description of the model’s explanatory variables.

Variable	Description	Expectation a priori and Hypothesis	Reference Literature
$EF{F}_{jt}$	The revenue collection efficiency score of utility j in year t, calculated using the DSBM under the premises of VRS and input-oriented considering customer accounts receivables (input), revenue collections (output), and revenue (good carry-over). Source: DSBM score.	Dependent Variable
$OW{N}_{jt}$	The ownership structure of utility j in year t. Was collected through the SNIS platform using the information of “Natureza juridica”; 1 for the utilities with private control (“Empresa Privada” and “Sociedade de economia mista com gestão privada”), and 0 for the utilities with public control (“Empresa Pública” and “Sociedade de economia mista com gestão pública”).	+ (H1)	[43,45]
$COR{P}_{jt}$	The corporatization of utility j in year t. This variable captures whether a utility is publicly listed; 1 for utilities listed with the CVM, 0 otherwise. Source: CVM.	+ (H2)	[45]
$REPCUS{T}_{jt}$	The proportion of residential customers per economies of utility j in year t. Thus, the number of active residential water (AG013 of the SNIS) and wastewater (ES008 of the SNIS) units that were fully operational on the last day of the reference year proportional to active water (AG003 of the SNIS) and wastewater (ES003 of the SNIS) economies. This refers to the number of units connected to the water supply network and provided with water for user consumption in the reference year.	+	[41,91]
$DENSIT{Y}_{jt}$	The density of the service area of utility j in year t. Therefore, the total population served with water (AG001 of the SNIS) and wastewater (ES001 of the SNIS) services by the service provider on the last day of the reference year proportional to active water (AG003 of the SNIS) and wastewater (ES003 of the SNIS) economies. This refers to the number of units connected to the water supply network and provided with water for user consumption in the reference year.	−/+	[41,46]
$AFFO{R}_{jt}$	Average per capita consumption (IN022 from the SNIS) multiplied by the average applied tariff (IN004) divided by GDP per capita. On this portal, the GDP per municipality, the population attended per municipality, and the GDP per capita per municipality can be found. For this work, the GDPs per municipality were summed to calculate the GDP per company. Then, the GDP per capita per company was obtained by dividing this total by the sum of the total population served per company. Average tariff and GDP were adjusted using the Brazilian price index IPCA/IBGE.	−	[36,43]
$SIZECUS{T}_{jt}$	The size of utility j in year t. Total assets relative to the number of economies served. Thus, the annual value of the sum of current assets, long-term receivables, and permanent assets (BL002 of the SNIS) divided by active water (AG003 of the SNIS) and wastewater (ES003 of the SNIS) economies. This refers to the number of units connected to the water supply network and provided with water for user consumption in the reference year. Then, the number is adjusted using the Brazilian price index IPCA/IBGE (measured in BR/Econ).	−	[45]
$UR{B}_{jt}$	The proportion of the urban population served in relation to the total active economies of utility j in year t. It represents the value of the urban population served with water supply by the service provider on the last day of the reference year in proportion to the total population served with water (AG001 from the SNIS) and wastewater (ES001 from the SNIS) services by the service provider on the last day of the reference year.	+	[8]
$JOIN{T}_{jt}$	The joint provision of water and wastewater of utility j in year t. Was collected through the SNIS platform using the information of “Tipo de serviço”; 1 for the utilities providing both water and wastewater services (“Água e Esgoto”), and 0 for the utilities providing either water or wastewater services (“Água”; “Esgoto”).	−/+	[45]
$COVID{19}_{jt}$	Effect of COVID-19 on utility j in year t 2020 onwards.	−/+	[104]

(Appendix A) describes all the variables of the explanatory econometric model. The dependent variable was obtained from DSBM efficiency. The independent variables included in the study model were corporatization (CORP) and ownership (OWN), both of which are dummy variables. The first variable was assigned a value of 1 for the utilities listed (with shares on the stock exchange) on the Comissão de Valores Mobiliários (CVM) and 0 for the non-listed utilities. The second variable was assigned a value of 1 for the utilities with private control (mixed capital utilities with private control or private utilities) and 0 for the utilities with public control (mixed capital utilities with public control). The corporatization variable was manually collected from the CVM website, while the ownership variable was collected from the SNIS using Juridical Nature (Natureza Jurídica) data.

The control variables included in the model were the proportion of residential customers (REPCUST), network density (DENSITY), tariff affordability (AFFOR), provider size (SIZECUST), urban population served (URB), utilities working with both services water and wastewater (JOINT), and the COVID-19 pandemic period.

The tariff affordability variable (AFFOR) was added to capture the effect of elasticity on the payment of fees. It was derived from three variables: two collected from the SNIS and one from the IBGE database. The first two variables did not require specific treatment. However, the variable obtained from the IBGE database needed to be processed as follows: The GDP per municipality was obtained from the platform, as well as the population it served. The GDP per municipality was summed by the utility responsible for the supply to find the GDP per municipality per utility. This value was then divided by the total population served by the utility to obtain the GDP per capita per utility, which was finally updated using the IPCA index.

According to the findings of Ref. [41], performance and GDP have a negative relationship. However, Ref. [92] found a positive impact of GDP on operator efficiency, while [93] did not identify any statistical significance. Regarding tariffs, Ref. [43] found that tariffs have a negative relationship with productivity. In the Brazilian scenario, the authors of [36] concluded that private management in Brazil leads to greater accessibility. The study measured accessibility by calculating the ratio between the average per capita value of the service (consumption per capita multiplied by the average tariff) and the GDP per capita.

Additionally, the authors of [36] pointed out that affordability presents a critical issue, as lower-income families spend a higher percentage of their monthly budget on water supply and sanitation services compared to higher-income families. The author noted that families earning up to two minimum wages spent 1.46% of their monthly budget on these services, whereas families earning more than 30 minimum wages spent only 0.29% of their monthly budget on the same services.

According to Ref. [94], economies of scale lead to significant cost savings that greatly surpass any possible differences in costs specific to individual firms. Thus, when associating this with the variable SIZECUST, as was carried out in Ref. [45], the variation in relative efficiency between state-level companies and municipal or micro-regional companies is linked to the literature on the economies of scale.

The variable for the share of residential connections (REPCUST) was collected from the SNIS database. The treatment performed to obtain this variable involved summing the residential water and sewage connections and dividing this by the total water connections plus the total sewage connections to determine the share of residential connections in relation to the whole. Another variable included to capture the share of a specific stratum of the total was the urban population share (URB), obtained by dividing the ratio of the urban population served by water and sewage treatment by the total water and sewage connections.

In this context, according to the findings of Ref. [95], less-populous cities exhibit better relative performance. The authors of [96] indicated that the number of measured consumers is negatively associated with performance, while in [97], it was suggested that rural operators have higher productivity values. In addition, Ref. [94] demonstrates that in Brazil, residential water consumption is negatively associated with performance.

The density variable was also collected from the SNIS platform and was included in the model to measure the extent of water and sewage connections divided by the total population served. In the Brazilian context, the literature indicates that increasing network density enhances the efficiency of providers by reducing costs [98]. Further, regarding the densities of water supply and sewage networks in Brazil, the authors of [46] found that the density of the water supply network negatively impacted performance, while the density of the sewage network positively impacted performance. However, the coefficient for the sewage network was not statistically significant.

A single variable was included in the model to capture the type of service, which was treated as a dummy variable. The utilities providing both water and sewage services were coded as 1, while the utilities providing either water or sewage services were coded as 0. In developing countries, the presence of economies of scope has yielded different results. While the authors of [41,57] found evidence of economies of scope, the authors of [96,99] did not. The former found no significant results, and the latter found diseconomies of scope.

Economies of scope relate to the provision of two services or the production of two products that, when produced or provided together, reduce the associated costs, thereby making businesses more efficient or productive.

The last variable inputted was a dummy variable to categorize the COVID-19 pandemic period from 2020 onwards. Brazil is one of the low- and middle-income countries (LMICs) where the COVID-19 pandemic has intensified pre-existing trends in the water sector. By the end of 2021, Brazil had recorded over 22 million COVID-19 cases and 619,056 deaths, ranking third in the world for confirmed cases and second for reported deaths [100].

Regarding water and sanitation services, 84% of the Brazilian population had access to the water supply system, while only 55% had access to the sewerage system in 2020 [101]. The population most affected by the lack of these services resides in low-income areas, such as indigenous villages, urban peripheries, and informal settlements, making this population more vulnerable to infectious diseases [102].

Figure 3 presents the methodological stages of the Efficiency Score Model (first stage) and the explanatory econometric model (second stage).

4. Results and Discussion

4.1. Revenue Collection Efficiency Assessment

For an analysis of the revenue collection efficiency, at first, the efficiency scores (calculated according to Section 3.3) are assessed year by year and consolidated throughout the entire panel using descriptive analyses. This approach outlines the panorama of the efficiency (and respective frontier) of Brazilian WUs and provides a diagnosis of the variability in the respective efficiency of the utilities (DMUs) over the years, subsequently verifying in the explanatory model.

Table 2. Panel of descriptive statistics of DSBM variables for revenue collection efficiency assessment.

Variable		Obs.	Mean	Std. Dev.	Min.	Max.
RECEIVABLE (Input)	2018	127	165.869.467,21	657.283.064,94	74.646,46	6.897.348.366,50
	2019		167.374.566,76	561.457.858,19	30.585,57	5.530.197.982,14
	2020		158.014.639,85	491.273.835,81	79.843,79	4.591.003.333,72
	2021		157.639.908,21	504.144.089,44	124.037,10	4.810.883.363,14
	2022		163.443.068,09	533.186.618,26	15.745,76	5.071.957.155,28
COLLECTION (Output)	2018	127	471.691.116,07	1.749.687.069,82	692.011,06	17.226.245.956,49
	2019		492.783.587,21	1.806.613.058,97	731.916,37	17.697.395.904,04
	2020		488.928.181,88	1.777.387.685,86	781.831,46	17.223.734.191,47
	2021		471.055.305,68	1.692.515.241,82	738.760,91	16.353.129.233,29
	2022		496.094.613,70	1.810.782.140,01	984.241,22	17.821.953.434,74
REVENUE (Good carry-over)	2018	127	502.398.538,08	1.835.741.403,66	686.753,62	18.093.571.779,99
	2019		532.450.227,00	1.983.504.112,52	726.061,35	19.634.345.685,23
	2020		513.724.131,31	1.829.264.675,43	775.733,16	17.648.578.345,92
	2021		499.887.041,02	1.779.251.733,57	754.463,03	17.248.220.283,74
	2022		529.384.479,57	1.912.209.670,65	1.013.075,30	18.837.156.721,07

presents the descriptive statistics of the variables established to evaluate the efficiency of revenue collections by panel year. Notably, the average value of collections was higher in 2022, while the average receivables from consumers were the lowest, signaling possible general improvements in collections in that year. This understanding is strengthened by the observation that the average revenues and receivables in 2019 were higher than in 2022, while the average collections were lower, indicating lower cash conversion in 2019.

Regarding isotonicity, all of the efficiency variables in all the years did not allow for the possibility of normal distribution in the Kolmogorov–Smirnov and Shapiro–Wilk tests. Therefore, the correlation test used was the non-parametric Kendall’s tau-b test.

Table 3. Panel with Kendall’s tau-b correlation coefficient between revenue collection efficiency variables.

Variable		REVENUE (Good Carry-over)	COLLECTION (Output)
RECEIVABLE (Input)	2018	0.845 (***)	0.827 (***)
	2019	0.836 (***)	0.815 (***)
	2020	0.847 (***)	0.830 (***)
	2021	0.851 (***)	0.827 (***)
	2022	0.837 (***)	0.821 (***)
COLLECTION (Output)	2018	0.973 (***)
	2019	0.964 (***)
	2020	0.971 (***)
	2021	0.964 (***)
	2022	0.977 (***)

Note: *** significance at 1%.

shows that all the correlation coefficients between the revenue collection efficiency variables were significant, at 1%, with 0.821 being the lowest among all the coefficients. This proves that the isotonicity verification protocol was followed and that a proportional increase in inputs generates a proportional increase in outputs.

Considering that the output orientation had already been defined, the return to scale issue was decided by the Wilcoxon two-related-sample test, which disproved the hypothesis of the equality of means between the efficiency scores reproduced under the premise of CRS and VRS. Therefore, VRS was chosen following the understanding described in [66].

Table A2. DSBM efficiency scores.

DMU	Overall Score	2018	2019	2020	2021	2022	DMU	Overall Score	2018	2019	2020	2021	2022
35503000-SABESP(1st)	1.000	1.000	1.000	1.000	1.000	1.000	35298011-AMT(65th)	0.457	0.392	0.463	0.574	0.499	0.400
51055811-AMA(1st)	1.000	1.000	1.000	1.000	1.000	1.000	35284011-SM(66th)	0.453	0.399	0.398	0.452	0.536	0.513
43149000-CORSAN(1st)	1.000	1.000	1.000	1.000	1.000	1.000	23044000-CAGECE(67th)	0.429	0.444	0.430	0.407	0.436	0.433
51083011-AUS(1st)	1.000	1.000	1.000	1.000	1.000	1.000	35407011-BRK(68th)	0.428	0.375	0.418	0.501	0.474	0.395
51013011-AA(5th)	0.996	0.982	1.000	1.000	1.000	1.000	35467011-BRK(69th)	0.424	0.366	0.364	0.493	0.493	0.443
51062511-SETAE(6th)	0.994	1.000	1.000	1.000	1.000	0.971	35385011-AP(70th)	0.419	0.305	0.424	0.539	0.512	0.404
31062000-COPASA(7th)	0.994	0.979	0.990	1.000	1.000	1.000	50027011-AG(71st)	0.414	0.376	0.417	0.410	0.423	0.450
33033011-CAN(8th)	0.986	0.935	1.000	1.000	1.000	1.000	42125012-AP(72nd)	0.403	0.366	0.384	0.395	0.413	0.477
35334011-CODEN(9th)	0.961	0.925	1.000	1.000	1.000	0.891	41182011-PS(73rd)	0.401	0.425	0.430	0.400	0.385	0.372
41069000-SANEPAR(10th)	0.960	1.000	1.000	0.968	0.949	0.894	51026711-ACV(74th)	0.399	0.317	0.374	0.432	0.439	0.474
52087000-SANEAGO(11th)	0.960	0.901	0.916	0.994	1.000	1.000	35177011-GUARA(75th)	0.398	0.318	0.390	0.508	0.428	0.390
33034011-CANF(12th)	0.952	1.000	1.000	0.985	0.943	0.850	43224011-BRK(76th)	0.394	0.411	0.388	0.400	0.391	0.383
17210000-SANEATINS(13th)	0.941	0.912	0.987	1.000	0.947	0.871	31039011-SANARJ(77th)	0.391	0.269	0.396	0.497	0.479	0.408
24081000-CAERN(14th)	0.938	1.000	1.000	0.967	0.926	0.821	51041011-AG(78th)	0.389	0.330	0.356	0.439	0.419	0.426
32053000-CESAN(15th)	0.875	0.867	0.883	0.879	0.868	0.878	33024012-BRK(79th)	0.374	0.181	0.569	0.492	0.497	0.493
35475012-COMASA(16th)	0.869	0.703	0.826	1.000	1.000	0.892	21122013-AT(80th)	0.373	0.355	0.393	0.392	0.351	0.381
35184011-SAEG(17th)	0.834	0.958	1.000	0.840	0.709	0.739	51070411-APL(81st)	0.370	0.371	0.380	0.401	0.363	0.340
33042011-CAAN(18th)	0.824	0.751	0.805	0.872	0.860	0.846	33038011-CAPY(82nd)	0.367	0.337	0.362	0.385	0.410	0.351
42024012-BRK(19th)	0.785	0.739	0.749	0.803	0.860	0.786	35294012-BRK(83rd)	0.363	0.483	0.411	0.362	0.323	0.293
35095011-SANASA(20th)	0.769	0.799	0.811	0.756	0.704	0.784	51002511-AAF(84th)	0.360	0.300	0.320	0.403	0.412	0.399
35144011-EMDAEP(21st)	0.756	0.676	0.951	1.000	0.764	0.565	25075000-CAGEPA(85th)	0.347	0.353	0.345	0.336	0.349	0.352
33039011-CAI(22nd)	0.747	0.794	0.815	0.760	0.737	0.651	35110011-EAC(86th)	0.337	0.302	0.334	0.403	0.361	0.303
35028011-SAMAR(23rd)	0.738	0.711	0.749	0.802	0.758	0.681	51056011-AM(87th)	0.334	0.243	0.318	0.406	0.349	0.417
42054000-CASAN(24th)	0.737	0.747	0.730	0.740	0.717	0.754	51064211-APA(88th)	0.330	0.261	0.342	0.406	0.353	0.322
35452012-SANESALTO(25th)	0.733	0.627	0.678	0.919	0.773	0.732	51030511-AC(89th)	0.316	0.249	0.325	0.358	0.342	0.333
50027000-SANESUL(26th)	0.723	0.728	0.767	0.742	0.734	0.653	33007011-PROLAGOS(90th)	0.314	0.300	0.309	0.303	0.321	0.342
35356012-CAEPA(27th)	0.721	0.515	0.714	0.892	0.864	0.763	15014000-COSANPA(91st)	0.307	0.277	0.283	0.307	0.287	0.413
29274000-EMBASA(28th)	0.718	0.756	0.750	0.702	0.697	0.691	11002812-ARM(92nd)	0.300	0.172	0.279	0.407	0.406	0.427
42062012-GS(29th)	0.697	0.375	0.908	0.902	0.876	0.867	42187012-TBSSA(93rd)	0.300	0.236	0.282	0.299	0.358	0.366
29148011-EMASA(30th)	0.696	0.538	0.723	0.815	0.791	0.688	51034011-CBA(94th)	0.297	0.305	0.292	0.284	0.293	0.310
33002011-CAJ(31st)	0.689	0.647	0.631	0.693	0.744	0.744	35293011-AM(95th)	0.290	0.259	0.262	0.319	0.324	0.299
35570011-CAV(32nd)	0.677	0.609	0.672	0.736	0.725	0.657	11000212-AA(96th)	0.284	0.180	0.261	0.374	0.357	0.364
53001000-CAESB(33rd)	0.673	0.667	0.723	0.685	0.655	0.639	15050311-PMNP/ANP(97th)	0.281	0.221	0.254	0.320	0.335	0.307
35269011-BRKL(34th)	0.665	0.768	0.686	0.636	0.635	0.620	11001812-APB(98th)	0.271	0.233	0.266	0.287	0.307	0.275
31471011-CAPAM(35th)	0.664	0.545	0.631	0.722	0.742	0.727	51067511-APL(99th)	0.267	0.223	0.250	0.315	0.302	0.265
31367011-CESAMA(36th)	0.654	0.740	0.720	0.691	0.632	0.533	51063711-SBPP(100th)	0.264	0.231	0.247	0.317	0.280	0.261
42084512-IS(37th)	0.650	0.500	0.574	0.775	0.765	0.739	51033511-ACO(101sh)	0.264	0.180	0.252	0.316	0.323	0.319
51072411-ASC(38th)	0.647	0.295	0.770	0.985	1.000	0.978	51073011-ASJ(102th)	0.261	0.222	0.240	0.315	0.287	0.262
42020712-GS(39th)	0.646	0.279	0.961	1.000	0.978	0.913	51085011-AVE(103th)	0.250	0.185	0.237	0.295	0.292	0.284
42091012-CAJ(40th)	0.641	0.629	0.624	0.637	0.684	0.635	51035012-ADI(104th)	0.242	0.212	0.218	0.294	0.275	0.233
51027011-AC(41st)	0.641	0.448	0.592	0.767	0.774	0.775	15013012-ASF(105th)	0.236	0.165	0.194	0.277	0.291	0.340
35253012-CAJA(42nd)	0.637	0.544	0.615	0.681	0.701	0.671	51027911-AGUASCAR(106th)	0.231	0.135	0.244	0.313	0.291	0.284
14001000-CAER(43rd)	0.637	0.515	0.594	0.653	0.710	0.779	51049011-SBJ(107th)	0.226	0.178	0.225	0.268	0.243	0.235
35259011-DAE Jundiaí(44th)	0.583	0.548	0.582	0.592	0.587	0.609	51063012-APA(108th)	0.222	0.197	0.195	0.272	0.248	0.214
31472011-COSÁGUA(45th)	0.580	0.470	0.535	0.704	0.635	0.612	51065011-APO(109th)	0.219	0.181	0.206	0.257	0.237	0.227
42032012-AC(46th)	0.561	0.445	0.502	0.622	0.650	0.658	15061312-BRK(110th)	0.217	0.287	0.257	0.228	0.202	0.158
35190512-AH(47th)	0.544	0.448	0.563	0.592	0.582	0.562	51050011-AJ(111th)	0.216	0.144	0.210	0.256	0.273	0.262
42162012-ASFS(48th)	0.538	0.460	0.503	0.530	0.606	0.627	28003000-DESO(112th)	0.214	0.220	0.215	0.204	0.217	0.216
32012011-BRK(49th)	0.537	0.577	0.561	0.522	0.541	0.490	23042011-SAAEC(113th)	0.203	0.161	0.205	0.218	0.239	0.210
51079211-AS(50th)	0.536	0.433	0.512	0.605	0.599	0.574	29307711-EMSAE(114th)	0.202	0.150	0.164	0.262	0.245	0.243
35029011-CAA(51st)	0.520	0.435	0.445	0.638	0.603	0.546	13026011-MA(115th)	0.180	0.161	0.174	0.187	0.177	0.205
35021011-AA(52nd)	0.513	0.461	0.527	0.596	0.564	0.448	51068211-APE(116th)	0.177	0.145	0.188	0.237	0.135	0.227
51032011-AC(53rd)	0.511	0.455	0.482	0.561	0.538	0.532	33018511-FSSG(117th)	0.175	0.208	0.181	0.188	0.158	0.152
35524012-BRK(54th)	0.508	0.559	0.536	0.516	0.484	0.459	11002000-CAERD(118th)	0.170	0.179	0.181	0.174	0.167	0.154
35350011-ESAP(55th)	0.505	0.370	0.493	0.640	0.581	0.533	27043000-CASAL(119th)	0.168	0.178	0.187	0.205	0.162	0.130
42083011-CIA de Águas(56th)	0.501	0.472	0.468	0.493	0.509	0.578	21112012-BRK(120th)	0.156	0.169	0.141	0.161	0.159	0.152
51018012-ABG(57th)	0.498	0.461	0.472	0.539	0.520	0.507	11004512-ABU(121st)	0.139	0.092	0.114	0.152	0.200	0.214
33010011-CAP(58th)	0.491	0.504	0.501	0.482	0.492	0.478	51060011-ANOR(122th)	0.109	0.110	0.107	0.114	0.106	0.108
51079011-AS(59th)	0.491	0.382	0.445	0.508	0.568	0.632	22110000-AGESPISA(123th)	0.102	0.120	0.095	0.098	0.099	0.103
22110011-AT(60th)	0.489	0.428	0.496	0.509	0.501	0.525	21075012-BRK(124th)	0.089	0.073	0.096	0.099	0.092	0.089
51033011-AC(61st)	0.486	0.350	0.455	0.617	0.577	0.530	21113000-CAEMA(125th)	0.077	0.084	0.080	0.086	0.077	0.063
26116000-COMPESA(62nd)	0.470	0.486	0.474	0.461	0.471	0.460	33045511-FABZO(126th)	0.069	0.072	0.068	0.069	0.068	0.068
35303011-SANESSOL(63rd)	0.460	0.418	0.453	0.540	0.489	0.423	13026000-COSAMA(127th)	0.033	0.039	0.012	0.075	0.079	0.072
42024511-AB(64th)	0.458	0.378	0.420	0.477	0.519	0.540

(Appendix B) and Figure 4 present the results of the efficiency scores in revenue collection using the DSBM and using input-oriented and variable returns to scale approaches.

The results revealed an overall average efficiency in revenue collection for all the years of 49.53% (overall score), indicating a general average inefficiency of 50.47%. In the annual observation, the least inefficient period was 2020, with a global average inefficiency of 45.92%, and 2018 was the worst year in the panel, with 55.07% inefficiency. Only four utilities were efficient across the entire panel. In 2022, four fewer utilities reached the efficiency frontier compared to 2021, which also slightly increased overall inefficiency.

In the analysis of inefficiencies by clusters (classified according to Tukey’s hinges, excluding the efficient clusters in the sample, into extreme inefficiencies, high inefficiencies, and lowest inefficiencies (25% of the total)), it is possible to observe that 30 utilities were classified as such in the overall score, with 2018 being the worst year, showing 32.28% of the utilities in the extreme inefficiency zone.

The dispersions reproduced by the different efficiency scores obtained by each utility over the years of the panel can be seen in Chart 1.

Chart 1 illustrates how the revenue collection efficiencies of the utilities fluctuate from year to year, indicating a certain level of independence in the scores from one year to the next, signaling the behavior of an independent correlation structure in the GEE model. These fluctuations highlight significant gains and losses in efficiency for various utilities over different years, drawing attention to the cases of 35475012-NASA(16th), 351840 11-SAEG(17th), and 35144011-EMDAEP(21st), which were in the efficiency zone in some periods in the panel and fell to the percentages of 89.2%, 73.9%, and 56.5% (see Appendix B—Table A2), respectively, in the year 2022. The next section will present the results of the explanatory model.

4.2. Econometric Explanatory Model

Table 4. Descriptive statistics of econometric explanatory model variables.

Variable	Obs.	Mean	Std. Dev.	Min.	Max.
EFF	635	0.5057	0.2686	0.0115	1.0000
				Mann–Whitney tests
Utilities on the stock market	71	0.4767	0.2545	Prob > |z| = 0.0000
Other utilities	564	0.7361	0.2562
Privately owned utilities	475	0.4761	0.2439	Prob > |z| = 0.0000
Publicly owned utilities	160	0.5934	0.3162
Water and sewage utilities	487	0.5224	0.2554	Prob > |z| = 0.0003
Utilities water or wastewater	148	0.4505	0.3024
Pre-COVID-19 period	254	0.4741	0.2715	Prob > |z| = 0.0072
COVID-19 period	381	0.5267	0.2649
CORP	635	0.1118	0.3154	0.0000	1.0000
OWN	635	0.7480	0.4345	0.0000	1.0000
REPCUST	635	0.9166	0.0436	0.6025	1.0000
DENSITY	635	245.6764	112.1077	53.1081	728.0620
SIZECUST	635	10,117.78	109,895.70	0.0017	1,647,134.00
URB	635	2.5378	0.6100	0.5278	5.3328
AFFOR	635	0.1944	0.1415	0.0021	1.9383
JOINT	635	0.7669	0.4231	0.0000	1.0000
COVID-19	635	0.6000	0.4903	0.0000	1.0000

presents the descriptive statistics of the variables analyzed. For the dependent variable, we observe a mean revenue collection efficiency of 50% with a standard deviation of 26%.

Regarding the variables of interest in the study, the sample shows that, on average, 11% of the utilities are corporatized, and 74% are controlled by private agents. Other factors analyzed indicate that 47% of the utilities are listed on the stock market, while 53% are not; 52% of concessionaries provide both water and wastewater services; and 60% of the period analyzed includes the pandemic period.

It is worth noting that the sample studied represents, over the panel, the averages of 73% of the active water connections, 72% of the active sewage connections, 76% of the revenue from services, and 77% of the revenue collection of all the Brazilian utilities registered in the SNIS database. This includes those considered as direct provision, where municipalities themselves, through government agencies or their own government departments (usually infrastructure departments), manage the services. These were not considered within the scope of our study due to the lack of corporatization characteristics.

4.3. Explanatory Econometric Analysis

Table 5. Econometric results of the GEE regression models after marginal effects.

	Model 1—Exchangeable		Model 2—Independent		Model 2—AR (1)
	Binomial Logit	Binomial Identity	Binomial Logit	Binomial Identity	Binomial Logit	Binomial Identity
OWN	−0.061651900	−0.050723000	−0.111411700	−0.111236400	−0.087367800	−0.081416900
	−0.97 (0.332)	−0.84 (0.404)	−1.82 (0.069) *	−1.98 (0.047) **	−1.45 (0.147)	−1.37 (0.171)
CORP	0.130064000	0.108718100	0.207300200	0.188442800	0.095203100	0.074438700
	1.74 (0.082) *	1.68 (0.093) *	2.52 (0.012) **	2.49 (0.013) **	1.66 (0.097) *	1.7 (0.089) *
REPCUST	0.001722000	−0.009210100	−0.272000200	−0.313330100	0.110811400	0.094847600
	0.01 (0.993)	−0.04 (0.964)	−0.67 (0.504)	−0.78 (0.434)	0.48 (0.628)	0.43 (0.668)
DENSITY	0.000220000	0.000215300	−0.000016300	−0.000045500	0.000219000	0.000219400
	1.43 (0.152)	1.5 (0.133)	−0.07 (0.944)	−0.22 (0.825)	0.94 (0.350)	0.98 (0.329)
SIZECUST	−0.000000065	−0.000000038	0.000000009	0.000000041	−0.000000011	−0.000000004
	−3.72 (0.000) ***	−2.07 (0.038) **	0.11 (0.914)	0.65 (0.517)	−1.12 (0.261)	−0.3 (0.763)
URB	−0.016778700	−0.014840200	−0.168176000	−0.153196900	−0.021120200	−0.018322600
	−0.81 (0.418)	−0.74 (0.461)	−3.87 (0.000) ***	−4.48 (0.000) ***	−0.94 (0.348)	−0.83 (0.406)
AFFOR	0.067605200	0.065856700	−0.419747600	−0.377515900	0.089764100	0.088255400
	0.83 (0.404)	0.89 (0.373)	−2.5 (0.012) **	−3.85 (0.000) ***	0.86 (0.388)	0.94 (0.348)
JOINT	0.069453100	0.074361500	0.037114700	0.036536300	0.060850500	0.063340200
	3.3 (0.001) ***	3.88 (0.000) ***	0.68 (0.497)	0.74 (0.459)	4.74 (0.000) ***	5.58 (0.000) ***
COVID19	0.053706100	0.052483800	0.031000500	0.029180300	0.042980300	0.041824700
	6.31 (0.000) ***	6.21 (0.000) ***	2.63 (0.008) ***	2.86 (0.004) ***	7.39 (0.000) ***	7.36 (0.000) ***
Robustness analysis
Wald chi2(9)	196.91	260.77	421.87	414.02	201.38	242.71
Prob > chi2	0.000 ***	0.000 ***	0.000 ***	0.000 ***	0.000 ***	0.000 ***
QIC	875.447	878.636	851.644	849.911	877.857	884.791
QICu	884.913	886.591	853.405	853.37	887.421	892.179
Number of observations: 635
Number of groups: 127
Variance inflation factor (mean): 1.2

Note: *** significance at 1%; ** significance at 5%; * significance at 10%.

shows that the variance inflation factor (VIF) is low, ruling out the possibility of multicollinearity. Among the combinations of link functions (logit and identity) and within-group correlation structures, the models with stationary and unstructured structures did not converge. Among the remaining combinations (exchangeable, independent, and autoregressive), the model with the identity link function and independent correlation structure obtained the lowest QIC, making it the most robust; therefore, this model was selected for the explanatory analyses.

In terms of public or private ownership, the results showed that being controlled by private owners is associated with lower revenue collection efficiency. Some studies have observed that private utilities tend to lead to higher prices, such as in Chile [32] and in various developing countries with public–private partnerships that have increased tariffs [33], possibly aiming to recover costs and enhance profitability. In the Brazilian scenario, studies such as [56,57,58] suggest that structural governance originating from privately owned water utilities results in greater efficiencies.

Based on the results presented in Model 2—Independent (binomial—identity), the variable OWN obtained an elasticity of −0.111236400 and was significant at 5%. In other words, this means that the publicly owned water utilities are more linked to efficiency in revenue collection than the privately owned water utilities by 11.11%, resulting in the rejection of H1. This finding is divergent from the findings presented in [56,57,58] and suggests that the structural governance originating from the privately owned water utilities is degrading the efficiency of revenue collection. A possible explanation may be based on the findings of [8], which suggest that tariffs for private utilities are 27.97% higher.

Regarding corporatization, the results revealed that the utilities listed on the Brazilian stock exchange are more efficient in collecting revenue by 18.84%. Therefore, hypothesis H2 (corporatized utilities with shares on the stock exchange are more likely to achieve greater efficiency in revenue collection) cannot be rejected. This is possibly due to the stricter enforcement of service cutoffs for late payments, making these utilities more efficient in revenue collection. Another explanation might be related to stakeholder pressure, which can influence managers to be more efficient. In other words, these external stakeholder groups could positively impact revenue collection efficiency through their vigilance.

Additionally, being corporatized (publicly listed) is positively associated with revenue collection efficiency. This reinforces the presented framework and supports the hypothesis (H2). In summary, it can be pointed out that publicly listed utilities generally implement policies that showcase their strengths, whereas lower-quality utilities often employ strategies to hide their shortcomings [61].

A theoretical argument supporting this is the signaling theory, formulated in [60], which posits that individuals can manipulate their characteristics to guide decision making in uncertain environments. These characteristics can mitigate informational asymmetry [61]. Furthermore, according to this author, higher-quality utilities adopt policies to showcase their superiority, while lower-quality utilities conceal their weaknesses. Therefore, presenting better signals through improved revenue collection efficiency can be interpreted by the market as an indicator of higher-quality service providers, suggesting that this type of institutional governance, triggered by corporatization (listing on the stock exchange), is beneficial for improving revenue collection efficiency.

The urbanization factor is associated with lower efficiency, likely because in rural areas, a cheaper tariff, known as the “social tariff” [8], is commonly applied, making it easier for people to pay. The findings also align with those of the authors of [97], who indicated that rural operators are more productive.

The tariff affordability variable (AFFOR) was added to capture the effect of elasticity on the payment of fees. The findings can be explained by the behavior of public institutions, which have high consumption but also high rates of default on payments. It is very common for Brazilian utilities to mention difficulties in collecting revenue from public consumers in their integrated reports. For example, [103] reports a high number of uncollected bills linked to public consumers.

The last significant variable was the COVID-19 pandemic. At first glance, it may seem strange to observe better revenue collection efficiency during a crisis period. However, various social policies were implemented to protect and support informal workers with financial aid during this time. The most significant policy was the emergency aid established by Law 13.982/2020 [104]. This law provided a fixed amount of money to help individuals, with an additional amount and three times more for women who are the primary breadwinners of their households.

5. Conclusions

This work focused on analyzing a more specific problem, which is the relevance of governance structure (ownership and corporatization) for efficiency in revenue collection for water utilities in the Brazilian scenario, an innovative contribution to the existing literature.

Regarding the findings corresponding to the efficiency assessment, the following highlights are presented:

• The overall average inefficiency in revenue collection is 50.47%, with at least 17% of the water utilities being extremely inefficient.

In other words, there is a significant gap in inefficiencies within the sector that needs to be addressed with systemic productivity gains in collection efficiency year after year.

Some contextual factors such as urbanization, tariff accessibility, and the COVID-19 period proved important for the comparative assessments of efficiencies in revenue collection from water utilities. The level of urbanization supported the existing framework, which indicated that rural utilities are more productive and that urban utilities tend to apply more expensive tariffs compared to rural utilities. Affordability is negatively related to collection performance, as public institutions with high bills also tend to have high default rates. The COVID-19 pandemic period was associated with better efficiency. Contrary to common sense, this crisis period may have resulted in more efficiency, possibly due to government political aid in Brazil, especially emergency aid.

Concerning the relevance of governance for efficiency in revenue collection, the following can be highlighted:

• Ownership is relevant to efficiency; however, privately controlled water utilities are more likely to face inefficiency in revenue collection, challenging the prevailing belief that private management is more productive and efficient than public management;
• Corporatization is also relevant to efficiency in revenue collection, with water utilities with shares on the stock exchange being more likely to achieve greater efficiency.

The findings of this work may indicate some practical implications, such as alerting regulatory bodies about the importance of imposing regulatory limits for recognizing losses with uncollectible receivables, putting pressure on utilities to improve collection practices with a focus on reducing losses, and providing fairer tariffs under an efficiency regime.

Finally, regarding suggestions for future research, work could be carried out considering the influence of some regulatory contexts such as tariff regimes, consumption-based fixed-rate billing, and the level of uncollected receivables recognized by the regulator in price reviews. This work could also be expanded to water utilities in Latin American countries.