Several methodological approaches have traditionally been used to evaluate the efficiency of water supply and sanitation services (Fuentes et al. 2017; Molinos-Senante and Sala-Garrido 2016; Fuentes et al. 2015; Worthington 2014; Abbott et al. 2012; Berg and Marques 2011; Byrnes et al. 2010; Abbott and Cohen 2009; Walter et al. 2009; Marques and Garzón 2007), each with their advantages and limitations. The most used are the frontier efficiency measurement techniques (Worthington 2014; Berg and Marques 2011), although other non-frontier approaches, principally the estimation of production and cost functions using minimum least square regression, have also been used. Within the non-parametric methods, the majority of studies use the Data Envelopment Analysis (DEA) (Cheng et al. 2020; Molinos-Senante et al. 2018; Romano et al. 2017; Molinos-Senante and Sala-Garrido 2016; See 2015; Guerrini et al. 2013; Mahmoudi et al. 2012; Gupta et al. 2006, Woodbury and Dollery 2004) and, to a lesser extent, other techniques such as the Malmquist productivity index, the Full Disposal Hull (FDH), the Stochastic Frontier Analysis (SFA), directional distance functions or total factor productivity and partial productivity measures (Molinos-Senante and Maziotis 2020; Suárez-Varela et al. 2016; Berg and Marques 2011, Vishwakarma et al. 2010; Belchior et al. 2005 )
As we have already mentioned, one of the problems that we encounter when analysing these companies is their heterogeneity; aspects that should be taken into account range from the different services provided (Guerrini et al. 2013) to the different concepts included in their economic accounts, among other elements (Fried et al. 2008).
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 insignificant, that public service companies are more cost effective. The descriptive statistics suggest statistically significant differences.
For our case, and given the characteristics of the data, a two-stage methodology has been used. First, we have estimated the efficiency 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 efficiency. DEA essentially calculates the economic efficiency 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 inefficient results.
Specifically, for this study, we have estimated efficiency 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 efficiency 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 efficiency ratio between 0 and 1 and controlling for the variable of the population supplied.
The correct choice of inputs and outputs in the model is highly relevant and varies considerably between studies. See (2015), Berg and Marques (2011) and De Witte and Marques (2010) compile the variables most widely used in many studies, indicating that the most frequent outputs are the volume of water supplied, followed by the number of clients and the population served. The inputs used include operating costs, the number of workers, personnel costs and the kilometres of network of the company.
This study considers the following variables, referring to each company for the year 2018. From the profit and loss account we have considered sales (Ventas), procurements (Aprovisionamiento), personnel costs (Cpersonal), amortizations (Amortiza), operating income (Rdoexpl) and the financial result of the company (Rdofin). 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 efficiency 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.