Measuring and decomposing profit efficiency changes of water utilities a case study for chile

Changes to profit efficiency differed among full private and concessionary utilities, with averages of 0.021 and 0.002, respectively.ARTICLE HISTORY Received 22 March 2023 Accepted 6 Jul

International Journal of Water Resources Development ISSN: (Print) (Online) Journal homepage: www.tandfonline.com/journals/cijw20 Measuring and decomposing profit efficiency changes of water utilities: a case study for Chile Manuel Mocholi-Arce, Ramon Sala-Garrido, Maria Molinos-Senante & Alexandros Maziotis To cite this article: Manuel Mocholi-Arce, Ramon Sala-Garrido, Maria Molinos-Senante & Alexandros Maziotis (18 Aug 2023): Measuring and decomposing profit efficiency changes of water utilities: a case study for Chile, International Journal of Water Resources Development, DOI: 10.1080/07900627.2023.2235438 To link to this article: https://doi.org/10.1080/07900627.2023.2235438 Published online: 18 Aug 2023 Submit your article to this journal Article views: 59 View related articles View Crossmark data Full Terms & Conditions of access and use can be found at https://www.tandfonline.com/action/journalInformation?journalCode=cijw20 INTERNATIONAL JOURNAL OF WATER RESOURCES DEVELOPMENT https://doi.org/10.1080/07900627.2023.2235438 Measuring and decomposing profit efficiency changes of water utilities: a case study for Chile Manuel Mocholi-Arce a, Ramon Sala-Garrido and Alexandros Maziotis b a , Maria Molinos-Senante b a Departament of Mathematics for Economics, University of Valencia, Valencia, Spain; bDepartamento de Ingeniería Hidráulica y Ambiental, Pontificia Universidad Católica de Chile, Santiago, Chile ABSTRACT ARTICLE HISTORY Estimating profit inefficiency and its drivers is highly relevant for water utilities and water regulators to reduce water tariffs We employed a novel methodological approach to compute profit inefficiency and changes to profit efficiency based on the Luenberger productivity indicator This empirical application focused on the water industry in Chile from 2010 to 2018 Estimated average profit inefficiency was 43.6%, with the main contributor being allocative inefficiency (35.7%) In contrast, the effect of technical inefficiency was more limited (7.9%) Changes to profit efficiency differed among full private and concessionary utilities, with averages of 0.021 and 0.002, respectively Received 22 March 2023 Accepted July 2023 KEYWORDS Profit efficiency; productivity change; Luenberger productivity indicator; directional distance functions; water utilities Introduction The water sector contributes to the economy, environment and peoples’ health Over the years, globally water utilities have made substantial investments to increase access to water and wastewater services to as many people as possible Evaluating the performance of these utilities over time has been conducted from both production and profit perspec­ tives (Goh & See, 2021; Sipilainen et al., 2014) Reducing production costs could have dual benefits in lowering tariffs for customers and raising the profits of utilities (Marques, 2008; Marques et al., 2011) Thus, understanding the factors driving change to the performance of water utilities could facilitate appropriate policy decisions, especially as resources in the economy are scarce in most of the countries (Kumbhakar & Lien, 2009) Therefore, to complete a thorough performance assessment over time, productivity change and profit efficiency must be evaluated Changes to productivity in the water industry have been previously evaluated using both parametric (econometric) and non-parametric (linear programming) techniques Econometric techniques, such as stochastic frontier analysis (SFA), are beneficial because they include both noise and inefficiency in the analysis However, such techni­ ques must specify a functional form (e.g., Cobb–Douglas, translog) for production technology (Coelli et al., 2005) In contrast, this specification is not required by nonparametric approaches, such as data envelopment analysis (DEA) In these approaches, CONTACT Maria Molinos-Senante mmolinos@uc.cl © 2023 Informa UK Limited, trading as Taylor & Francis Group M MOCHOLI-ARCE ET AL the frontier is constructed by the most efficient utilities in the sample, and is not statistically estimated (as in econometrics) Most existing studies evaluating the productivity change of water utilities used the traditional Malmquist productivity index (MPI) (Arocena et al., 2020; Maziotis et al., 2021; Nyathikala & Kulshrestha, 2017) In this approach, productivity change is usually separated (decomposed) into efficiency change and technical change (Lin & Berg, 2008; De Witte & Marques, 2012) MPI is mainly limited in that it must be input or output orientated In other words, water utilities must choose between maximizing outputs or minimizing inputs, but cannot both simultaneously To overcome this limitation, the Luenberger productivity indicator (LPI) was proposed by Chambers et al (1998) It allows the simulta­ neous expansion of production and contraction of inputs This indicator can also be separated into efficiency change and technical change Several studies have used this indicator to evaluate productivity change and its determinants in several sectors of the economy, including the water utilities (Ananda, 2018; Guerrini et al., 2018; MolinosSenante et al., 2014) However, these studies did not integrate the concept of profit efficiency in their analyses Profitability change and its determinants have received considerable interest because profit changes are related to the prices charged to customers Grifell-Tatje and Lovell (1999) provided a detailed analysis of profit decomposition for several banks in Spain They evaluated several factors driving changes to profits, including productivity change, price and scale effects De Witte and Saal (2010) and Maziotis et al (2014) subsequently used this approach to assess the effect of regulating the financial performance of the urban water sector These studies were primarily limited in that they did not incorporate the concept of profit efficiency in the approach Also, distance functions were used to measure efficiency, in which it was assumed that all inputs for a given level of output would contract In other words, directional distance functions were not used, which would allow efficiency to be measured by increasing outputs and reducing inputs in parallel These previous studies only focused on measuring changes to the profits of sectors in developed countries (such as Spain, the Netherlands, England and Wales; Mocholi-Arce et al., 2023) To date, comparative research in developing and middle-income countries remains limited (Cetrulo et al., 2019) To address the identified issues, we evaluated the performance of water utilities in Chile, a middle-income country, by integrating the concepts of profit efficiency and productivity change in a unified manner The water industry in Chile has both full private and conces­ sionary water utilities Hence, our analyses took the ownership of utilities into account We used Profit_LPI, which allowed us to evaluate what factors drive changes to the profit efficiency of water utilities (Juo et al., 2015) Profit_LPI could be separated into several factors associated with productivity growth, including technical and allocative efficiency change, technical change, and price effect This study contributes to the current vein of literature by evaluating the financial and productivity performance of water utilities in a middle-income country which has achieved almost universal coverage in the provision of water and wastewater services in urban areas The Chilean water industry embraces full private and concessionary utilities and, therefore, this study also contributes to the literature by shedding light on the influence of ownership on the profitability of water companies The remainder of the paper is structured as follows The methodology section presents the methodological approaches used to estimate profit inefficiency and profit efficiency INTERNATIONAL JOURNAL OF WATER RESOURCES DEVELOPMENT change In the case study description section the sample of water companies evaluated and data are then described The results and discussion section presents and discusses the results Finally, the paper highlights the main conclusions Methodology This section outlines the methodological approach used to derive profit inefficiency (PIFF) and Profit_LPI for water utilities Profit inefficiency (PIFF) estimation Based on the PIFF concept of Nerlove (1965), profit inefficiency is decomposed into technical inefficiency (TIFF) and allocative inefficiency (AIFF) To estimate these para­ meters, it is assumed that, at any time, t, a water company produces a set of N total outputs, yt , using a set of M total resources (inputs), xt Production technology (PT t ) is presented as follows: � � � PT t ¼ xt ; yt : xt can produce yt (1) Based on PT t , technical efficiency is the ability of a firm to reduce its inputs for a given level of outputs (input oriented) or the ability of a firm to increase its outputs for a given level of inputs (output oriented; Coelli et al., 2005) The technical efficiency of a water company is estimated using directional distance functions These functions allow for the simultaneous contraction of inputs and expansion of outputs The directional distance function is defined as follows (Chambers et al., 1998): !t t t � � � � D x ; y ; gx ; gy ¼ sup γ : xt gx ; yt ỵ gy PT t (2) !t t t � where TIFF is measured by D x ; y ; gx ; gy , and g presents the direction at which products expand and inputs contract (Chambers et al., 1998) If we denote the set of prices for outputs as p and the set of prices for inputs as w, then we can define profits (π) as the difference between revenue and costs The PIFF of production technology is defined as follows (Juo et al., 2015): � � � � PIFF t pt ; wt ¼ sup pt yt wt xt : xt ; yt PT t (3) This equation can be rewritten as follows: PIFF t ; � πt ðpt ; wt Þ ðpt yt wt xt Þ ~t t t � D x ; y ; gx ; gy t t p gy ỵ w gx (4) where PIFF is measured by πt ðpt ; wt Þ, which is defined as the difference between max­ imum (frontier) and observed (actual) profit (Chambers et al., 1998) PIFF is an indepen­ dent of unit of measurement (Juo et al., 2015) PIFF > indicates high profit inefficiency, whereas PIFF = means that the water company is profit efficient AIFF measures the ability of a water company to allocate resources and outputs efficiently for a given level of inputs and outputs, respectively Thus, AIFF is defined as follows (Chambers et al., 1998): M MOCHOLI-ARCE ET AL AIFF ẳ t pt ; wt ị pt yt wt xt ị pt gty ỵ wt gtx ~ Dt xt ; yt ; gx ; gy � (5) Based on equation (5), PIFF is estimated as the sum of TIFF and AIFF (Chambers et al., 1998) This is presented as: PIFF ẳ AIFF ỵ TIFF (6) Profit efficiency change estimation PIFF is integrated with productivity change by using LPI, which decomposes into profit efficiency change (PEC) and profit technical change (PTC) The former, further decom­ poses into: technical efficiency change (TEC) and allocative efficiency change (AEC) The latter further decomposes into: technical change (TC) and price effect (PE) Profit_LPI between t and t ỵ is defined as follows (Juo et al., 2015): Profit LPIt;tỵ1 ẳ �� � πt ðpt ; wt Þ ðpt yt wt xt ị pt gy ỵ wt gx tỵ1 ptỵ1 ; wtỵ1 ị ptỵ1 yt pt gy ỵ wt gx t pt ; wt ị pt ytỵ1 wt xtỵ1 ị pt gy ỵ wt gx wtỵ1 xt ị tỵ1 ptỵ1 ; wtỵ1 ị ptỵ1 yt pt gy ỵ wt gx wtỵ1 xt ị (7) where changes to profit and productivity are measured relative to profit boundaries The first term in this equation captures changes to the productivity of water utilities’ with respect to the ratio differential of PIFF based on the profit frontier in period t In a similar manner, the second term of equation (7) presents changes to the productivity of water utilities regarding the ratio differential of PIFF based on the profit frontier in period t þ (Juo et al., 2015) Productivity increases if Profit LPIt;tỵ1 > and it decreases if Profit LPIt;tỵ1 < Profit LPIt;tỵ1 can be split into the following parts: πt ðpt ; wt Þ ðpt yt wt xt Þ t pt ; wt ị pt ytỵ1 wt xtỵ1 ị pt gy ỵ wt gx pt gy ỵ wt gx tỵ1 tỵ1 tỵ1 tỵ1 t tỵ1 t ðp ; w Þ ðp y w xÞ πt ðpt ; wt ị pt yt wt xt ị ỵ ptỵ1 gy ỵ wtỵ1 gx pt gy ỵ wt gx Profit LPIt;tỵ1 ẳ ỵ tỵ1 ptỵ1 ; wtỵ1 ị ptỵ1 ytỵ1 ptỵ1 gy ỵ wtỵ1 gx wtỵ1 xtỵ1 ị t pt ; wt ị pt ytỵ1 wt xtỵ1 ị pt gy ỵ wt gx (8) The first part of equation (8) is defined as PEC It measures how water utilities improve their profit efficiency over time (catch-up in profits) Positive values of this component mean that water utilities moved closer to the profit frontier, whereas negative values mean that there were losses in profit efficiency (Chen & Wu, 2020) The latter implies that less profitable water utilities not improve their performance towards the most profit­ able ones in the industry The second part of equation (8) is defined as PTC and captures how the profit frontier shifts over time Positive values of PTC imply progress, whereas negative values mean that the profit frontier regresses (Juo et al., 2015) INTERNATIONAL JOURNAL OF WATER RESOURCES DEVELOPMENT PEC can be presented as follows: tỵ1 t pt ; w t Þ ð p t y t w t x t ị ~ D xtỵ1 ; ytỵ1 ; gx ; gy ị ỵ pt g y ỵ w t g x t PEC ẳ ẵ~ D xt ; yt ; gx ; gy Þ t ~ D x t ; y t ; gx ; gy tỵ1 ptỵ1 ; wtỵ1 ị ptỵ1 ytỵ1 ptỵ1 gy ỵ wtỵ1 gx wtỵ1 xtỵ1 ị t ~ D xt ; yt ; gx ; gy Þ (9) The first part of equation (9) measures traditional TEC It captures how the technical efficiency of water utilities improves or deteriorates over time (catch-up in efficiency) Positive values of TEC imply gains in efficiency In other words, less technically efficient water utilities improve their efficiency relative to the most efficient ones in the industry If TEC > 0, then it has been improved, whereas if TEC < 0, a deterioration of technical change occurred AEC corresponds with the second part of equation (9) and informs about the catch-up required to the optimal use of resources and outputs (Juo et al., 2015) Positive and negative values of AEC indicate improvement and deterioration, respectively PTC is further decomposed into the following parts: t tỵ1 tỵ1 n~tỵ1 t t t tỵ1 tỵ1 tỵ1 ~ D x ; y ; gx ; gy x ; y ; gx ; gy ~ D x t ; yt ; gx ; gy ỵ ~ D D x ; y ; gx ; gy 2� � � � tỵ1 t t tỵ1 ptỵ1 ; wtỵ1 ị ptỵ1 y t wtỵ1 x t ị t pt ; wt ị pt y t wt x t ị ~ D ỵ x ; y ; gx ; gy tỵ1 tỵ1 t t p gy ỵ w gx p gy ỵ w gx tỵ1 tỵ1 tỵ1 t p ; w ị ptỵ1 ytỵ1 wtỵ1 x tỵ1 ị t pt ; wt ị pt ytỵ1 wt x tỵ1 ị ~ D x t ; y t ; gx ; gy ỵ tỵ1 tỵ1 t t p gy ỵ w gx p gy ỵ w gx tỵ1 o t tỵ1 tỵ1 tỵ1 tỵ1 ~ ~ x ; y ; gx ; gy D x ; y ; gx ; gy D PTC ¼ (10) The first part of equation (10) is the traditional TC, which is the shift of the benchmark technology over the two time periods Positive values in TC indicate improvements to technology (e.g., technical progress), whereas negative values of TC indicate deterioration of technology (e.g., technical regression) The second part of equation (10) is PE, which captures how changes to the prices of inputs and outputs affect the maximum (frontier) profit Positive and negative PE values positively and negatively (deterioration) impact profit productivity, respectively The decomposition of the Profit_LPI is presented as: Profit LPI ¼ PEC ỵ PTC ẳ TEC ỵ AEC ị ỵ TC þ PEÞ (11) The Profit_LPI decomposition presented in equations (7) to (10) requires several direc­ tional distance functions to be calculated using DEA techniques Following past practices (e.g., Fare & Grosskopf, 2007; Fare & Primont, 2003; Grosskopf, 2003; Juo et al., 2015), the directional vector for each water company k is set to be equal to the mean value of its own inputs and outputs over the whole study period Thus, the directional vector takes the � following form: g ¼ gx ; gy ¼ ðxk ; yk Þ, where: PT xk ¼ t t¼1 xkm T ðm ¼ 1; ; MÞ (12) M MOCHOLI-ARCE ET AL PT t t¼1 ykn yk ¼ T ðn ¼ 1; ; NÞ (13) To calculate the directional distance functions of period t, the following DEA model is then solved: � ~ Dtk xkt ; ykt ; �xk ; �yk ¼ max δt;t (14) k XR λt r¼1 r XR λt r¼1 r t t � � yrn ykn ỵ t;t k ykn t t � xrm � xkm � δt;t k � xkm XR λt r¼1 r λtr � "n ¼ 1; ; N "m ¼ 1; ; M ¼1 "r ¼ 1; ; R where λ are scalar variables that are used to build the efficient frontier and δ measures � inefficiency The replacement of period t by period t ỵ allows ~ Dtỵ1 xktỵ1 ; yktỵ1 ; xk ; yk to k be calculated, which measures the TIFF of a water company with respect to period t ỵ technology using data from period t ỵ Similarly, we calculate the cross-period directional distance functions by interchanging the data and technology of time periods t and t ỵ To calculate the PIFF of each water company in period t, the following DEA model is solved: XK XK � � t � πtk ptk ; wkt ¼ max ptk y� ; wkt x� ¼ max p y wt x� (15) km m k¼1 k¼1 kn n XR λt r¼1 r XR t � � yrm � ym λt r¼1 r t � xrn � xn� XR λt r¼1 r λtr � "m ¼ 1; ; M "n ¼ 1; ; N ¼1 "r ¼ 1; ; R Similarly, the maximum profit frontier of period t ỵ is estimated by replacing period t with period t ỵ in equation (15) Case study description We measured PIFF and Profit_LPI for several water utilities in Chile that provided water and sewerage services over the period 2010–18 The water industry in Chile was privatized between 1998 and 2004 Currently, there are full private utilities and concessionary utilities (Ferro & Mercadier, 2016) The water regulator is the Superintendencia de Servicios Sanitarios (SISS), which monitors the economic and managerial performance of all water utilities Data are available from the SISS’s weblink INTERNATIONAL JOURNAL OF WATER RESOURCES DEVELOPMENT Table Averages for Chilean water utilities, 2010–18 Variables Number of customers Network length Operating expenditure Total turnover Capital expenditure Price for network length Price for operating inputs Price for customers Units Number km 000s US$/year 000s US$/year 000s US$/year 000s US$/year Index US$/customer Mean 294,415 4056 55,442 84,762 19,786 0.882 0.379 SD 495,434 5979 75,299 130,007 33,999 0.076 0.130 Minimum 3304 83 1522 1782 293 0.771 0.234 Maximum 1,950,626 21,859 279,815 495,245 133,057 1.000 0.884 Note: Observations = 99 Costs, turnover and prices are in 2018 prices Inputs and outputs, and their related prices, are selected based on a review of the published literature on the water industry and available data (Berg & Marques, 2011; Cetrulo et al., 2019; Goh & See, 2021; Pinto et al., 2017; See, 2015; Walker et al., 2019, 2020, 2021) We used one output, which is defined by the number of water and sewerage customers per year served by water utilities The price of this output is defined as turnover for water and sewerage services divided by the number of customers Turnover is measured in thousands of Chilean pesos per year (CLP/year) Two inputs were used in our analysis The first input is water and sewerage network length defined as the sum of water and sewerage networks’ length (km) (Garcia et al., 2007; Garcia & Reynaud, 2004; Mellah & Ben Amor, 2016; Molinos-Senante et al., 2018; Munisamy, 2009) The price for network length is defined ‘as the ratio of capital expenditure measured in thousands of CLP/year and network length’ (Correia & Marques, 2011; Molinos-Senante et al., 2022) The second input is the expenditure of operating inputs, which is measured in thousands of CLP/year The price for the second input is defined by the producer price index taken from the national statistics of Chile (Coelli et al., 2005; Mellah & Ben Amor, 2016; Molinos-Senante et al., 2022) Descriptive statistics are shown in Table Results and discussion Profit inefficiency The evolution of the average PIFF, and its drivers, in the period 2010–18 for the water utilities assessed in Chile is shown in Figure During 2010–18, the water industry in Chile showed considerable high levels of PIFF, which was mainly attributed to AIFF Profit loss (43.6%) was attributed to a considerable loss in allocative efficiency (35.7%), and a smaller loss in technical efficiency (7.9%) Thus, the allocation of capital, operating expenditure and customers was inefficient, causing PIFF to increase PIFF was volatile over the years, and followed the trend of AIFF, which declined during 2011–13 at a rate of 8%/year However, in 2014–17, AIFF considerably increased, which was mainly attributed to an average increase in operating expenditure (by 3.4%/year), and an average increase in network length (by 0.8%/year) During this period, the number of customers increased by 2.64%/year This trend was interrupted in the final year of our study, with profit loss due to AIFF being 24% TIFF also contributed towards explaining PIFF in the industry A TIFF of 0.079 showed that, on average, the operating costs and capital of the water industry in Chile could be reduced by M MOCHOLI-ARCE ET AL Profit inefficiency and its drivers 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 2010 2011 2012 2013 AIFF 2014 TIFF 2015 2016 2017 2018 PIFF Figure Evolution of profit inefficiency (PIFF) and its drivers: technical inefficiency (TIFF) and allocative inefficiency (AIFF) for Chilean water utilities 7.9%, while expanding its customer base by the same value TIFF rose from 2012 onwards; thus, a rise in operating expenditure and network length offset any increases in the number of customers Consequently, it negatively contributed to profit efficiency In 2018, PIFF was lowest, because the allocation of inputs and outputs improved, whereas TIFF peaked Figure shows the degree of inefficiency in terms of profits, allocation and technology based on the type of water company ownership (fully private versus concessionary) Overall, concessionary utilities were considerably less efficient than full private ones The mean PIFF of concessionary water utilities (0.618) was almost three times higher compared with that of fully private utilities (0.225) Thus, on average, fully private utilities were closer to the maximal profit benchmark compared with concessionary utilities, performing better in terms of profit efficiency On average, the profit losses of fully private water utilities were Profit inefficiency and its drivers 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 2010 AIFF_FP 2011 2012 TIFF_FP 2013 AIFF_C 2014 2015 TIFF_C 2016 PIFF_FP 2017 2018 PIFF_C Figure Evolution of profit inefficiency (PIFF) and its drivers: technical inefficiency (TIFF) and allocative inefficiency (AIFF) for full private (FP) and concessionary (C) Chilean water utilities INTERNATIONAL JOURNAL OF WATER RESOURCES DEVELOPMENT attributed to a loss in allocative efficiency (17.8%) and technical efficiency (4.7%) (Figure 2) In contrast, on average, high levels of PIFF were reported for concessionary utilities This phenomenon was mainly attributed to AIFF (51.1%) TIFF was smaller compared with AIFF, but was two times higher compared with that of fully private utilities When evaluating the temporal evolution, in 2010, the average PIFF for fully private utilities was low based on allocative and technical inefficiencies (0.079 and 0.047, respec­ tively) Over the next two years, expenditure increased to operate and upgrade the network to provide water and sewerage services to more customers This action could have led to higher levels of inefficiency from an allocation perspective AIFF increased (from 0.079 to 0.159), whereas TIFF remained at similar levels The inefficient allocation of resources was evident from 2015 onwards, mainly due to an average increase in operating expenditure (6.2%/year on average), whereas network length stably increased (0.8%/year on average) This trend was interrupted in 2018 when AIFF declined During the same period, TIFF rose, peaking in 2018 Thus, fully private utilities might have primarily improved profit efficiency by improving how resources were allocated The rise in TIFF over time shows that daily operations must be managed better to improve technical and profit efficiency The PIFF for concessionary water utilities showed average profit losses in 2010 due to a substantial loss in allocative efficiency (41%) and a loss in technical efficiency (8.7%) (Figure 2) AIFF then increased in 2011, but then decreased in 2012–13 at an annual rate of 11% However, TIFF remained high In 2012, on average concessionary utilities could further reduce their inputs by 11.5% and expand their customer base by the same magnitude to improve technical efficiency Inefficiency levels were high in 2014–17 for both allocation and technology High expenditure to run businesses led to an inefficient allocation of resources, causing concessionary utilities to shift away from maximal profit benchmark Simultaneously, high increases in inputs offset any increase in the number of customers, leading to higher TIFF, negatively contributing to profit efficiency This trend changed in 2018, when a better allocation of resources reduced PIFF; however, TIFF remained high Thus, concessionary utilities need to make substantial efforts to improve resource allocation, which is the main source of PIFF Better managerial practices could also be adopted as shown by the upward trend of TIFF over time Profit efficiency change (Profit_LPI) On average, fully private utilities improved at reducing profit inefficiency The average Profit_LPI for fully private water utilities between 2010 and 2018 was 0.021 (Figure 3) This value was attributed to PTC, which had an average of 0.028 In contrast, average PEC was negative (−0.008) PEC was negative throughout most of the study period; however, small gains were evident in 2012–13, 2015–16 and 2017–18 In contrast, PTC was positive throughout most of the study period Thus, the profit efficiency of the most profitable utilities continued to improve over time, contributing favourably towards reducing the profit inefficiency of the industry Concessionary water utilities (Figure 3) had low and positive average Profit_LPI (0.002) Thus, there were some small gains at reducing inefficiency from a profit perspective On average less profitable concessionary utilities caught up with the most profitable ones in the industry, whereas the most profitable utilities reduced profit efficiency over time Both components of Profit_LPI were volatile over time Less profitable utilities moved closer to M MOCHOLI-ARCE ET AL 0.80 0.05 0.60 0.04 Drivers of Profit_LPI 0.40 0.03 0.20 0.02 0.00 0.01 -0.20 0.00 -0.40 Profit_LPI 10 -0.01 -0.60 -0.80 -0.02 2010-11 2011-12 2012-13 2013-14 2014-15 2015-16 2016-17 2017-18 PEC_FP PTC_FP PEC_C PTC_C Profit_LPI_FP Profit_LPI_C Figure Evolution of Profit_LPI and its components: profit efficiency change (PEC) and profit technical change (PTC) for full private (FP) and concessionary (C) water utilities the frontier during 2012–14, with the profit frontier shifting downwards over the same period In subsequent years the most profitable utilities appeared to be more efficient than less profitable utilities, thus reducing any profit inefficiency in the industry Therefore, profit inefficiency among concessionary water utilities could be reduced by improving the profit efficiency of the most profitable utilities To elucidate key factors driving profit change in the water industry of Chile, we analysed the components of PEC and PTC within utilities (Figure 4) PEC was retarded due to the deterioration of both TEC and AEC Thus, managers should focus on adjusting the combination of inputs–outputs to improve profits Profits could be improved by reducing costs when trying to expand production such as by eliminating any technical 0.3 Drivers of Profit_LPI 0.2 0.1 0.0 -0.1 -0.2 -0.3 2010-11 2011-12 2012-13 TEC AEC 2013-14 TC 2014-15 PE 2015-16 PEC 2016-17 PTC Figure Evolution of drivers of Profit_LPI for Chilean full private water utilities 2017-18 INTERNATIONAL JOURNAL OF WATER RESOURCES DEVELOPMENT 11 inefficiencies During 2011–14, TEC was mainly small and positive Thus, fully private utilities managed to make some improvements in the production process However, these improvements did not continue in subsequent years because TEC became negative In contrast, AEC was quite volatile over time During 2011–15, there was an inefficient allocation of resources, on average, which negatively impacted the productivity and profits of utilities In subsequent years, the situation improved, with AEC remaining positive during the final period of our study Thus, on average, less efficient full private utilities were able to improve productivity and increase profits by managing their opera­ tions better, and moving to an efficient allocation of resources such as substituting capital with operating expenditure PE was the dominant source of PTC when decomposing it for fully private water utilities (0.028) (Figure 4) On average, TC showed a small but positive change for fully private utilities (0.003) Thus, utilities generally experienced technical progress, allowing produc­ tivity and profits to increase PE was also positive, but its magnitude was larger (0.025) This phenomenon was attributed to higher increases in the price of customers offsetting any changes in the price for capital and operating expenditure Throughout the study period the price of customers increased at an annual rate of 8%, on average, whereas the price for inputs increased at a rate of 1.1%/year TC was negative at the beginning of the study period However, the adoption of best practices by the industry positively impacted productivity and profits during 2012–14 Technical regress was evident for the following year but in the following years it mainly remained positive PE was mainly positive until 2014–15, except for 2012–13 Thus, over this period high increases in turnover and the price of outputs offset any changes to inputs and associated prices Consequently, profits increased PE adversely impacted the productivity and profits of fully private water utilities during the last period of our study Thus, fully private water utilities in Chile could mainly improve profits by improving technology The profits of less efficient concessionary utilities mainly improved through improve­ ments to AEC (average = 0.021) (Figure 5) TEC was small but negative (−0.04) Thus, improving the efficiency of the production process was challenging for concessionary utilities In particular, concessionary utilities had some technical inefficiencies during the first two years of the study, which were also present in 2013–14 In subsequent years, less efficient utilities achieved some small gains in their TEC contributions, enhancing profits In contrast, concessionary utilities appeared to be efficient at making decisions on how to allocate resources during 2011–13 However, this was not the case for the subsequent years when a misallocation in the combination of inputs–outputs mix reduced profits During 2017–18 this pattern was reserved, with changes to allocation efficiency positively contributing to productivity and profits Thus, less efficient concessionary utilities could improve their performance by enhancing managerial practices There is also notable room for improving decision making processes when allocating inputs and outputs Thus, the business plans of concessionary utilities should focus on both technical and allocative efficiency to improve performance The positive TC (0.011) of concessionary utilities was offset by negative PE (−0.026) (Figure 5) TC was positive throughout the entire period, indicating that the adoption of new technologies improved productivity and profits Technical progress peaked during 2011–14 However, its impact on profits declined in subsequent years PE contributed negatively to profits during 2011–13 and 2017–18 Increases in inputs and associated prices 12 M MOCHOLI-ARCE ET AL 0.7 Drivers of Profit_LPI 0.5 0.3 0.1 -0.1 -0.3 -0.5 -0.7 2010-11 2011-12 2012-13 TEC AEC 2013-14 TC 2014-15 PE 2015-16 PEC 2016-17 2017-18 PTC Figure Evolution of drivers of Profit_LPI for Chilean concessionary water utilities Table P-values of the Mann–Whitney test Variable p-value PIFF 0.035 AIFF 0.048 TIFF 0.049 Profit_LPI 0.718 PEC 0.045 PTC 0.215 TEC 0.038 AEC 0.050 TC 0.437 PE 0.573 were offset any increases in turnover and the number of customers Thus, PE negatively contributed to productivity and profits Concessionary water utilities could increase profits by further improving their technology, which could help overall production costs In parallel, these utilities could expand their customer base to increase overall turnover To verify whether profitability differences among full private utilities and concessionary utilities are statistically significant or not, the non-parametric Mann–Whitney test was applied The null hypothesis tested was that concessionary and full private utilities are derived from the same population If p ≤ 0.05, then the null hypothesis could be rejected at a 95% of significance (Llanquileo-Melgarejo & Molinos-Senante, 2021) According to the p-values shown in Table 2, PIFF differences among Chilean full private utilities and concessionary utilities are statistically significant By contrast, the Mann–Whitney test did not lead us to reject the hypothesis of equality of means for profit efficiency change (Profit_LPI) with 95% significance Focusing on the components of the Profit_LPI, differ­ ences among both types of water companies are statistically significant for TEC and AEC but not for TC and PE drivers Conclusions Understanding to what extent a company is profit efficient and inefficient, and what drives profit change over time, could help managers to enhance performance Changes to profit could be attributed to changes in the way resources are allocated over time, improvements in technology, and/or changes to the prices of inputs and outputs Understanding these INTERNATIONAL JOURNAL OF WATER RESOURCES DEVELOPMENT 13 factors and how they impact productivity and profit could help water utilities to manage operations better and provide services to customers at minimum expenditure This study estimated PIFF and profit efficiency change of a sample of Chilean water utilities in Chile from 2010 to 2018 The water industry in Chile had high PIFF (average = 0.436), which was mainly attributed to AIFF (average = 0.357) TIFF was also clearly evident, but had a lower impact (average = 0.079) Thus, the inefficient allocation of combinations of inputs–outputs, along with the inability of water utilities to reduce costs and expand production, led to profit inefficiencies Fully private water utilities were more profit efficient compared with concessionary utilities The mean PIFF of concessionary utilities was almost three times higher compared with that of fully private utilities (−0.008 versus 0.017) Average profit efficiency change (i.e., Profit_LPI) of fully private and concessionary utilities was 0.021 and 0.002, respectively PTC positively contributed to Profit_LPI for fully private utilities (average = 0.028), but negatively contributed for concessionary utilities (average = −0.016) The PTC drivers of fully private and concessionary water utilities also differed PE was the main contributor (average 0.025) to the PTC of fully private utilities In contrast, the average PE was −0.026 for concessionary utilities From a management perspective, water utilities in Chile could adopt some actions to improve their profitability Some examples are as follows: (1) implement effective cost management practices by analysing and reducing operational costs, optimizing energy consumption, and implementing maintenance strategies to minimize repair and replace­ ment expenses; (2) explore opportunities to increase revenue by implementing water pricing mechanisms that reflect the true value of water, encouraging water conservation measures, and identifying new customer segments; (3) conduct regular assessments of infrastructure assets, prioritize investments based on asset condition and criticality, and develop long-term asset management plans to ensure optimal utilization and longevity of assets; (4) embrace innovation and technology to identify and implement smart water solutions, such as real-time monitoring systems, data analytics, and predictive mainte­ nance, to optimize operations and reduce costs; and (4) develop robust long-term financial plans and investment strategies to balance short-term profitability goals with sustainable growth and infrastructure development needs The estimation of profit efficiency change also provides relevant information for the water regulator It provides insights into the overall financial viability of the water sector and allows the regulator to evaluate whether companies are operating efficiently and sustainably or not In Chile, and in many other countries, the regulator has established a maximum profitability threshold Consequently, profitability information aids the reg­ ulator in determining fair and reasonable pricing structures By analysing the profitability of water companies, the regulator can assess the need for tariff adjustments, considering factors such as operational costs, capital investment requirements, and the need for maintaining adequate financial reserves By tracking profitability trends, the regulator can identify potential financial risks, inefficiencies, or underperformance, and take appro­ priate actions, such as regulatory interventions or performance improvement initiatives Moreover, profitability information can be used by the regulator to design incentive mechanisms that reward efficient and financially sustainable behaviour By utilizing profitability information effectively, the water regulator can ensure the financial sustain­ ability of the sector, protect consumer interests, promote efficient operations, and sup­ port the long-term development of water services 14 M MOCHOLI-ARCE ET AL Although this study contributes to literature in the framework of productivity change and profitability of water utilities, it is not exempt from some limitations First, the number of inputs and outputs integrated in the assessment was limited by the number of units (water companies) analysed In particular, the evaluation did not involve any quality of service variables such as drinking water quality, wastewater treatment quality, water supply interruptions or non-revenue water Thus, future research on this topic might focus on extending the number of utilities and/or years analysed and to integrate additional outputs related to quality of service variables Second, the analysis of the influence of ownership on water companies´ profitability was preliminary because it was based on a hypothesis test, and it did not consider any public water company Hence, a further assessment of the influence of ownership by employing more advanced methods such as DEA metafrontier and integrating other types of water companies could be also considered in future studies Authors contributions A Maziotis and M Molinos-Senante contributed to the study’s conception and design Material preparation and data collection were performed by A Maziotis Data analysis was undertaken by Mocholi-Arce and R Sala-Garrido The first draft of the manuscript was written by A Maziotis and M Molinos-Senante R Sala-Garrido and M Mocholi-Arce commented on previous versions of the manuscript All authors read and approved the final manuscript Disclosure statement No potential conflict of interest was reported by the authors Ethical approval The authors undertake that this article has not been published in any other journal and that no plagiarism has occurred ORCID Manuel Mocholi-Arce http://orcid.org/0000-0003-3574-503X Ramon Sala-Garrido http://orcid.org/0000-0002-4693-3944 Maria Molinos-Senante http://orcid.org/0000-0002-6689-6861 Alexandros Maziotis http://orcid.org/0000-0001-9817-1470 Data availability statement The data are available from the corresponding author upon reasonable request References Ananda, J (2018) Productivity implications of the water–energy–emissions nexus: An empirical analysis of the drinking water and wastewater 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