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

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International Journal of Water Resources Development

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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.

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

Manuel Mocholi-Arce a, Ramon Sala-Garrido a, Maria Molinos-Senante b

and Alexandros Maziotis b

a Departament of Mathematics for Economics, University of Valencia, Valencia, Spain; b Departamento de Ingeniería Hidráulica y Ambiental, Pontificia Universidad Católica de Chile, Santiago, Chile

ABSTRACT

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.

ARTICLE HISTORY

Received 22 March 2023 Accepted 6 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 non- parametric approaches, such as data envelopment analysis (DEA) In these approaches,

CONTACT Maria Molinos-Senante mmolinos@uc.cl

https://doi.org/10.1080/07900627.2023.2235438

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 do 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; Molinos- Senante 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

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, y t , using a set of M total resources (inputs), x t Production technology (PT t) is presented as follows:

PT t ¼� x t ; y t�: x t can produce y t� (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):

D t

!

x t ; y t; g x ; g y

�

¼sup γ : x t γg x ; y tþγg y

�

2PT t

(2)

where TIFF is measured by D!t x t ; y t; g x ; g y

�

, 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 p t ; w t�¼sup p� t y t w t x t: x t ; y t�2PT t� (3) This equation can be rewritten as follows:

PIFF t;π tðp t ; w tÞ ðp t y t w t x tÞ

p t g yþw t g x � ~ D

t x t ; y t; g x ; g y

�

(4)

where PIFF is measured by π tðp t ; w tÞ, 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 > 0 indicates high profit inefficiency, whereas PIFF = 0 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):

AIFF ¼ π

tðp t ; w tÞ ðp t y t w t x tÞ

p t g t

yþw t g t x

~

D t x t ; y t; g x ; g y

�

(5)

Based on equation (5), PIFF is estimated as the sum of TIFF and AIFF (Chambers et al., 1998) This is presented as:

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 þ 1 is defined as follows (Juo et al., 2015):

Profit LPI t;tþ1 ¼ 1

2

π tðp t ; w tÞ ðp t y t w t x tÞ

p t g yþw t g x

π tðp t ; w tÞ ðp t y tþ1 w t x tþ1Þ

p t g yþw t g x

�

π tþ1ðp tþ1 ; w tþ1Þ ðp tþ1 y t w tþ1 x tÞ

p t g yþw t g x

π tþ1ðp tþ1 ; w tþ1Þ ðp tþ1 y t w tþ1 x tÞ

p t g yþw t g x

(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 1

(Juo et al., 2015) Productivity increases if Profit LPI t;tþ1>0 and it decreases

if Profit LPI t;tþ1 <0

Profit LPI t;tþ1 can be split into the following parts:

Profit LPI t;tþ1 ¼ π tðp t ; w tÞ ðp t y t w t x tÞ

p t g yþw t g x

π tðp t ; w tÞ ðp t y tþ1 w t x tþ1Þ

p t g yþw t g x

þ 1 2

π tþ1ðp tþ1 ; w tþ1Þ ðp tþ1 y t w tþ1 x tÞ

p tþ1 g yþw tþ1 g x

�

�

π tðp t ; w tÞ ðp t y t w t x tÞ

p t g yþw t g x

þ π tþ1ðp tþ1 ; w tþ1Þ ðp tþ1 y tþ1 w tþ1 x tþ1Þ

p tþ1 g yþw tþ1 g x

π tðp t ; w tÞ ðp t y tþ1 w t x tþ1Þ

p t g yþw t g x

��

(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 do 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)

PEC can be presented as follows:

PEC ¼ ½~ D tðx t ; y t; g x ; g yÞ ~ D tþ1ðx tþ1 ; y tþ1; g x ; g yÞ� þπ tðp t ; w tÞ ðp t y t w t x tÞ

p t g yþw t g x

~

D t x t ; y t; g x ; g y� π

tþ1ðp tþ1 ; w tþ1Þ ðp tþ1 y tþ1 w tþ1 x tþ1Þ

p tþ1 g yþw tþ1 g x

~

D tðx t ; y t; g x ; g yÞ

(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:

PTC ¼ 1

2 ~ D

tþ1

x t ; y t; g x ; g y� ~ D t x t ; y t; g x ; g y�þ ~ D tþ1 x tþ1 ; y tþ1; g x ; g y�

n

~

D t x tþ1 ; y tþ1; g x ; g y�

þ π tþ1ðp tþ1 ; w tþ1Þ ðp tþ1 y t w tþ1 x tÞ

p tþ1 g yþw tþ1 g x

π tðp t ; w tÞ ðp t y t w t x tÞ

p t g yþw t g x

~

D tþ1 x t ; y t; g x ; g y�

�

~

D t x t ; y t; g x ; g y�� þ π tþ1ðp tþ1 ; w tþ1Þ ðp tþ1 y tþ1 w tþ1 x tþ1Þ

p tþ1 g yþw tþ1 g x

π tðp t ; w tÞ ðp t y tþ1 w t x tþ1Þ

p t g yþw t g x

~ D tþ1 x tþ1 ; y tþ1; g x ; g y

�

~

D t x tþ1 ; y tþ1; g x ; g y

�

(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 þ PTC ¼ TEC þ AECð Þ þðTC 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 g x ; g y

�

¼ðx k ; y kÞ, where:

x k¼

PT

t¼1 x t km

y k¼

PT

t¼1 y t kn

To calculate the directional distance functions of period t, the following DEA model is

then solved:

~ D t k x t k ; y t k ; �x k ; � y k�¼max δ t;t k (14)

XR

r¼1 λ t r�y t rn�y kn t þδ t;t k � �y kn "n ¼ 1; ; N

XR

r¼1 λ t r�x t rm�x t km δ t;t k � �x km "m ¼ 1; ; M

XR

r¼1 λ t r ¼1

λ t r�0 "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 þ 1 allows ~ D tþ1 k x k tþ1 ; y tþ1 k ; �x k ; � y k�to

be calculated, which measures the TIFF of a water company with respect to period t þ 1 technology using data from period t þ 1 Similarly, we calculate the cross-period directional distance functions by interchanging the data and technology of time periods t and t þ 1.

To calculate the PIFF of each water company in period t, the following DEA model is

solved:

π t k p t k ; w k t�¼max p t k y�; w k t x��¼maxXK k¼1 p t km y m� XK k¼1 w t kn x n� (15)

XR

r¼1 λ t r�y t rm�y�m "m ¼ 1; ; M

XR

r¼1 λ t r�x t rn�x�n "n ¼ 1; ; N

XR

r¼1 λ t r ¼1

λ t r �0 "r ¼ 1; ; R Similarly, the maximum profit frontier of period t þ 1 is estimated by replacing period t with period t þ 1 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

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 1

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 1 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

Table 1 Averages for Chilean water utilities, 2010–18

Number of customers Number 294,415 495,434 3304 1,950,626

Operating expenditure 000s US$/year 55,442 75,299 1522 279,815 Total turnover 000s US$/year 84,762 130,007 1782 495,245 Capital expenditure 000s US$/year 19,786 33,999 293 133,057 Price for network length 000s US$/year 4 2 1 8 Price for operating inputs Index 0.882 0.076 0.771 1.000 Price for customers US$/customer 0.379 0.130 0.234 0.884 Note: Observations = 99

Costs, turnover and prices are in 2018 prices.

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 2 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

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

2010 2011 2012 2013 2014 2015 2016 2017 2018

Figure 1 Evolution of profit inefficiency (PIFF) and its drivers: technical inefficiency (TIFF) and allocative inefficiency (AIFF) for Chilean water utilities

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

AIFF_FP TIFF_FP AIFF_C TIFF_C PIFF_FP PIFF_C

Figure 2 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

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