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

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: />
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
/>

INTERNATIONAL JOURNAL OF WATER RESOURCES DEVELOPMENT
/>
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 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 nonparametric approaches, such as data envelopment analysis (DEA). In these approaches,
CONTACT Maria Molinos-Senante

© 2023 Informa UK Limited, trading as Taylor & Francis Group


2

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 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; 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

3

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 γgx ; yt ỵ gy 2 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 2 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 > 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):


4

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 þ 1 is defined as follows (Juo et al., 2015):
Profit LPIt;tỵ1 ẳ

1
2




t pt ; wt ị pt 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 Þ
(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 ỵ 1
(Juo et al., 2015). Productivity increases if Profit LPIt;tỵ1 > 0 and it decreases
if Profit LPIt;tỵ1 < 0.
Profit LPIt;tỵ1 can be split into the following parts:
t pt ; wt Þ ðpt yt wt xt Þ πt ðpt ; wt ị pt ytỵ1 wt xtỵ1 ị
pt gy ỵ wt gx
pt gy ỵ wt gx
tỵ1 tỵ1 tỵ1
tỵ1 t
tỵ1 t
1 π ðp ; w Þ ðp y
w xÞ
πt ðpt ; wt ị pt yt wt xt ị
ỵ
2
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 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).


INTERNATIONAL JOURNAL OF WATER RESOURCES DEVELOPMENT

5

PEC can be presented as follows:
tỵ1
t pt ; w t ị 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 þ wtþ1 gx

wtþ1 xtþ1 Þ

t
~
D ðxt ; 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

1 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 ẳ PEC ỵ PTC ẳ TEC þ AEC Þ þ ðTC 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 ẳ xk ; yk ị, where:
PT
xk ẳ

t
tẳ1 xkm

T

m ẳ 1; . . . ; MÞ

(12)


6

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


t;t
k xkm

XR

t
rẳ1 r

tr 0

"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 1 allows ~
Dtỵ1
xktỵ1 ; yktỵ1 ; xk ; yk to
k
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 ỵ 1.
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 � 0

"m ¼ 1; . . . ; M
"n ¼ 1; . . . ; N
¼1

"r ¼ 1; . . . ; R

Similarly, the maximum profit frontier of period t ỵ 1 is estimated by replacing period t

with period t ỵ 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.


INTERNATIONAL JOURNAL OF WATER RESOURCES DEVELOPMENT

7

Table 1. 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
4
0.882
0.379

SD
495,434
5979
75,299
130,007
33,999
2
0.076
0.130

Minimum
3304
83
1522

1782
293
1
0.771
0.234

Maximum
1,950,626
21,859
279,815
495,245
133,057
8
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 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


8

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
0
2010

2011

2012

2013

AIFF

2014
TIFF

2015

2016

2017

2018

PIFF

Figure 1. 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 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

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 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.


INTERNATIONAL JOURNAL OF WATER RESOURCES DEVELOPMENT

9

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 3. 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 4. 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 5. Evolution of drivers of Profit_LPI for Chilean concessionary water utilities.

Table 2. 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
/>Ramon Sala-Garrido
/>Maria Molinos-Senante
/>Alexandros Maziotis
/>
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 sector. Journal of Cleaner Production, 196,
1097–1105. />

INTERNATIONAL JOURNAL OF WATER RESOURCES DEVELOPMENT

15

Arocena, P., Saal, D. S., Urakami, T., & Zschille, M. (2020). Measuring and decomposing productivity
change in the presence of mergers. European Journal of Operational Research, 282(1), 319–333.
/>Berg, S., & Marques, R. (2011). Quantitative studies of water and sanitation utilities: A benchmarking
literature survey. Water Policy, 13(5), 591–606. />Cetrulo, T. B., Marques, R. C., & Malheiros, T. F. (2019). An analytical review of the efficiency of water
and sanitation utilities in developing countries. Water Research, 161, 372–380. />1016/j.watres.2019.05.044
Chambers, R. G., Chung, Y., & Färe, R. (1998). Profit directional distance functions and Nerlovian
efficiency. Journal of Optimization Theory and Applications, 98, 351–364. />A:1022637501082
Chen, X., & Wu, X. (2020). What factor contributes to productivity growth of Chinese city banks: The
role of regional difference. North American Journal of Economics and Finance, 54, 101259. https://
doi.org/10.1016/j.najef.2020.101259
Coelli, T. J., Rao, D. S. P., O’Donnell, C. J., & Battese, G. E. (2005). An introduction to efficiency and
productivity analysis. Springer Science & Business.
Correia, T., & Marques, R. (2011). Performance of Portuguese water utilities: How do ownership, size,
diversification and vertical integration relate to efficiency? Water Policy, 13(3), 343–361. https://
doi.org/10.2166/wp.2010.032
De Witte, K., & Marques, R. C. (2012). Gaming in a benchmarking environment. A nonparametric
analysis of benchmarking in the water sector. Water Policy, 14(1), 45–66. />wp.2011.087
De Witte, K., & Saal, D. S. (2010). Is a little sunshine all we need? On the impact of sunshine regulation
on profits, productivity and prices in the Dutch drinking water sector. Journal of Regulatory
Economics, 37(3), 219–242. />Färe, R., & Grosskopf, S. (2007). Theory and application of directional distance functions. Journal of
Productivity Analysis, 13(2), 93–103. />Färe, R., & Primont, D. (2003). Luenberger productivity indicators: Aggregation across firms. Journal

of Productivity Analysis, 20(3), 425–435. />Ferro, G., & Mercadier, A. C. (2016). Technical efficiency in Chile’s water and sanitation provides.
Utilities Policy, 43, 97–106. />Garcia, S., Moreaux, M., & Reynaud, A. (2007). Measuring economies of vertical integration in
network industries: An application to the water sector. International Journal of Industrial
Organization, 25(4), 791–820. />Garcia, S., & Reynaud, A. (2004). Estimating the benefits of efficient water pricing in France. Resource
& Energy Economics, 26(1), 1–25. />Goh, K. H., & See, K. F. (2021). Twenty years of water utility benchmarking: A bibliometric analysis of
emerging interest in water research and collaboration. Journal of Cleaner Production, 284, 124711.
/>Grifell-Tatje, E., & Lovell, C. A. K. (1999). Profits and productivity. Management Science, 45(9),
1177–1193. />Grosskopf, S. (2003). Some remarks on productivity and its decompositions. Journal of Productivity
Analysis, 20(3), 459–474. />Guerrini, A., Molinos-Senante, M., & Romano, G. (2018). Italian regulatory reform and water utility
performance: An impact analysis. Utilities Policy, 52, 95–102. />03.005
Juo, J. C., Fu, T. T., & Yu, M. M. (2015). Profit-oriented productivity change. Omega, 57, 176–187.
/>Kumbhakar, S. C., & Lien, G. (2009). Productivity and profitability decomposition: A parametric
distance function approach. Food Economics – Acta Agriculturae Scandinavica, Section C, 6(3–4),
143–155. />Lin, C., & Berg, S. V. (2008). Incorporating service quality into yardstick regulation: An application to
the Peru water sector. Review of Industrial Organization, 32(1), 53–75. />s11151-008-9160-5


16

M. MOCHOLI-ARCE ET AL.

Llanquileo-Melgarejo, P., & Molinos-Senante, M. (2021). Evaluation of economies of scale in
eco-efficiency of municipal waste management: An empirical approach for Chile. Environmental
Science and Pollution Research, 28(22), 28337–28348. />Marques, R. C. (2008). Comparing private and public performance of Portuguese water services.
Water Policy, 10(1), 25–42. />Marques, R. C., Simoes, P., & Pires, J. S. (2011). Performance benchmarking in utility regulation: The
worldwide experience. Polish Journal of Environmental Studies, 20(1), 125–132.
Maziotis, A., Saal, D. S., Thanassoulis, E., & Molinos-Senante, M. (2014). Profit change and its drivers in
the English and Welsh water industry: Is output quality important? Water Policy, 18(4), 1–18.
Maziotis, A., Sala-Garrido, R., Mocholi-Arce, M., & Molinos-Senante, M. (2021). Changes to the
productivity of water utilities: Comparison of fully private and concessionary water utilities.

Water Resources Management, 35(10), 3355–3371. />Mellah, T., & Ben Amor, T. (2016). Performance of the Tunisian water utility: An input distance
function approach. Utilities Policy, 38, 18–32. />Mocholi-Arce, M., Sala-Garrido, R., Molinos-Senante, M., & Maziotis, A. (2023). Profit productivity
change in the English and Welsh water sector: Impact of the price reviews. Utilities Policy, 82,
101544. />Molinos-Senante, M., Maziotis, A., & Sala-Garrido, R. (2014). The Luenberger productivity indicator in
the water industry: An empirical analysis for England and Wales. Utilities Policy, 30, 18–28. https://
doi.org/10.1016/j.jup.2014.07.001
Molinos-Senante, M., Maziotis, A., Sala-Garrido, R., & Mocholi-Arce, M. (2022). An investigation of
productivity, profitability, and regulation in the Chilean water industry using stochastic frontier
analysis. Decision Analytics Journal, 4, 100117. />Molinos-Senante, M., Porcher, S., & Maziotis, A. (2018). Productivity change and its drivers for the
Chilean water utilities: A comparison of full private and concessionary utilities. Journal of Cleaner
Production, 183, 908–916. />Munisamy, S. (2009). Efficiency and ownership in water supply: Evidence from Malaysia. International
Review of Business Research Papers, 5(6), 148–260.
Nerlove, M. (1965). Estimation and identification of Cobb–Douglas production functions. Rand
McNally.
Nyathikala, S. A., & Kulshrestha, M. (2017). Performance and productivity measurement of urban
water supply services in India. Water Science and Technology: Water Supply, 17(2), 407–421.
Pinto, F. S., Simoes, P., & Marques, R. C. (2017). Water services performance: Do operational
environmental and quality factors account? Urban Water Journal, 14(8), 773–781. https://doi.
org/10.1080/1573062X.2016.1254254
See, K. F. (2015). Exploring and analyzing sources of technical efficiency in water supply services:
Some evidence from Southeast Asian public water utilities. Water Resources Economics, 9, 23–44.
/>Sipilainen, T., Kumbhakar, S. C., & Lien, G. (2014). The performance of dairy farms in Finland and
Norway from 1991 to 2008. European Review of Agricultural Economics, 41(1), 63–86. https://doi.
org/10.1093/erae/jbt012
Walker, N. L., Norton, A., Harris, I., Williams, A. P., & Styles, D. (2019). Economic and environmental
efficiency of UK and Ireland water utilities: Influence of exogenous factors and rurality. Journal of
Environmental Management, 241, 363–373. />Walker, N. L., Styles, D., Gallagher, J., & Williams, A. P. (2021). Aligning efficiency benchmarking with
sustainable outcomes in the United Kingdom water sector. Journal of Environmental
Management, 287, 112317. />Walker, N. L., Williams, A. P., & Styles, D. (2020). Key performance indicators to explain energy &
economic efficiency across water utilities, and identifying suitable proxies. Journal of

Environmental Management, 269, 110810. />