Natural Resources, 2011, 2, 191-196
doi:10.4236/nr.2011.23025 Published Online September 2011 (http://www.SciRP.org/journal/nr)
191
New Vision on the Relationship between Income
and Water Withdrawal in Industry Sector
Abdolnaser Hemati1, Mohsen Mehrara1, Ali Sayehmiri1,2*
1Department of Economics, Faculty of Economics, University of Tehran, Tehran, Iran; 2Department of Economics, Faculty of Hu-
manities, Ilam University, Ilam, Iran.
Received July 5th, 2011; revised August 18th, 2011; accepted August 28th, 2011.
ABSTRACT
This paper investigates the relationship between industrial water withdrawal (IWW) and income in selected world
countries. The issue is addressed by means of a smooth transition regression (STR) model on cross section data of 132
countries in 2006. The results confirm the nonlinearity of the link between IWW and income. According to the results,
the income elasticity of IWW is a bell-shaped curve. Therefore, the policies and management processes in water sector
including water allocation between activities and reigns should take into account the development degree and also fo-
cus on income level, water scarcity and the economic, social and ecological structure in each country.
Keywords: Water-Income, STR, NRBEKC, Elasticity, Socio-Economic Structure
1. Introduction
Freshwater resources are vital for maintaining human life,
health, agricultural production, economic activities as
well as critical ecosystem functions. As populations and
economies grow, new constraints on freshwater resources
are appearing, raising problems for limits of water
availability. Accordingly, the analysis of the national
water withdrawal intensity measurement becomes an
important policy issue. To serve these purposes, some
water withdrawal efficiency indicators have been devel-
oped and applied to explain differences in performance
between countries and international benchmarking [1]. It
should be noted that the income elasticity of IWW is one
solution used in this paper.
In recent years, the relationship between income
elasticity of natural resources use and income has attracted
an increasing attention among academic, non-governmen-
tal organizations, and the media. A notable empirical
finding of the recent environmental economics literature
has been the existence of an inverted U-shaped
relationship between per capita income and pollution (per
capita emissions) of many local air pollutants [2]. Since
this relationship bears a resemblance to the Kuznets
relationship between income and income inequality, it is
known as the Environmental Kuznets Curve (EKC) and
has spawned a vast number of papers in recent years. In
addition, attempts have been made to estimate EKCs for a
wide range of environmental indicators, including energy
use, deforestation and municipal waste [3-6,7].
The shape of the EKC, attributed to scale, composition
and technique effects (SCTE) as discussed below, would
also seem to apply to (income elasticity of) water
consumption. The main reason to disregard water use in
EKC studies would appear to be a lack of socioeconomic-
hydrological data, although some recent investigations and
dataset have now resolved somewhat this problem [8-12].
In this paper, we examine the relationship between
IWW per capita and GDP per capita using Smooth
Transition Regression (STR) model for 132 countries
across the world based on cross section data in 2006. The
following section will provide a brief review of the
related literature. Section 3 introduces the econometric
methodology and empirical results, and the final section
presents the conclusions of the present study.
The majority of EKC literature examines pollution
levels as a function of income. This has led to the criticism
that such research ignores the natural resource component
of environmental quality [2,13-16]. These studies tend to
treat resource use identical to pollution as an indicator of
environmental quality pointing to natural resources based
on environmental Kuznets curve (NRBEKC). Like
pollution, resource use can provide an economic benefit
coupled with an undesired environmental impact. Thus,

New Vision on the Relationship between Income and Water Withdrawal in Industry Sector 192
many of the theoretical explanations for the existence of
EKCs for natural resources mirror those for pollution.
The inverted U relationship between income and
pollution is typically explained in terms of the interaction
of scale, composition and technique effects (SCTEs). The
scale effect (SE) implies that as the scale of the economy
grows (ceteris paribus), IWW will do so. The composition
effect (CE), however, refers to the fact that as economies
develop, there is totally a change in emphasis from heavy
industry to light manufactures and services sectors, and
also from high water intensity to low water intensity in
industrial, agriculture and domestic sectors. Since the latter
are typically less resource intensive than the former, the
composition effect of growth, ceteris paribus, will reduce
water use. Finally, there is the technique effect (TE). As
incomes rise there is likely to be an increased demand for
environmental regulations [5]. The effect of these regula-
tions must be considered to reduce water intensity due to
improved techniques of production and consumption.
2. Methodology
2.1. Smooth Transition Regression (STR)
The smooth transition regression (STR) model is a
nonlinear regression model that may be viewed as a
further development of the switching regression model
introduced by [17]. The STR model originated as a
generalization of a particular switching regression model
in the work of [17]. These authors considered two
regression lines and devised a model in which the
transition from one line to the other is smooth. The
earliest references in the econometrics literature are [18]
and [19]. Recent accounts include [20-25]. The standard
STR model is defined as follows:
 


'' ',,,, ,
t
z
tttttt t
yzzGcsuGcs u    

''
z,
ttt
Wx


(1)
where is a vector of explanatory variables
and 1are a
vector of exogenous variables. Furthermore,
'( )'p1, 1,,wyt yt

01
,,...,m
k
x '(,...,)'
tt
tx x

 

and

01
,,..., m

 

,,
K
c


are
parameter vectors and ut  iid (0, σ2) are
given. Transition function G (γ, c, st) is a bounded function
of the continuous transition variable st , continuous
everywhere in the parameter space for any value of st, γ is
the slope parameter and which is a vector
of location parameters, 1

 
m
1
cc
 
11
K
cc. The last expression
in equation (1) indicates that the model can be interpreted
as a linear model with stochastic time-varying coefficients
φ + θG (γ, c, st). In this paper it is assumed that the
transition function is a general logistic function:


1
1
,,1 exp{(c)}
K
tt
k
Gcs s 


 
  k
(2)
where γ > 0 is an identifying restriction. Equations (1)
and (2) jointly define the logistic STR (LSTR) model.
The most common choices for K are K = 1 and K = 2.
For K = 1, the parameters φ + θG (γ, c, st) change
monotonically as a function of st from φ to φ + θ. For K =
2, it change symmetrically around the midpoint


12
2cc, where this logistic function attains its
minimum value. The minimum lies between zero and 1/2.
It reaches zero when γ→∞ and equals 1/2 when c1 = c2
and γ < ∞. Slope parameter γ controls the slope and c1
and c2 the location of the transition function. Transition
function (2) with K = 1 is also the one that proposed,
whereas [18] favored the cumulative distribution
function of a normal random variable. In fact, these two
functions are close substitutes.
The LSTR model with K = 1(LSTR1 model) is capable
of characterizing asymmetric behavior. As an example, it
is supposed that st measures the phase of the business
cycle. Then the LSTR1 model can describe processes
whose dynamic properties are different in expansions
from what they are in recessions, and the transition from
one extreme regime to the other is smooth. On the other
hand, the LSTR2 model (K = 2) is appropriate in
situations in which the local dynamic behavior of the
process is similar at both large and small values of st and
different in the middle (For further work on
parameterizing the transition in the STR framework, see
[18]. When γ = 0, the transition function G (γ, c, st) ≡ 1/2,
and thus the STR model (1) nests the linear model. At the
other ends, when γ → ∞, the LSTR1 model approaches
the switching regression model with two regimes that
have equal variances. When γ → ∞ in the LSTR2 model,
the result is another switching regression model with
three regimes in which the outer regimes are identical
and the mid regime is different from the other two. It is
noteworthy that an alternative to the LSTR2 model exists,
the so-called exponential STR (ESTR) model. It is
Equation (1) with the follow transition function:



2
*
,,1 expt
Et t
Gcs sc    (3)
This function is symmetric around st = c*1 and has at
low and moderate values of slope parameter γ,
approximately the same shape, albeit a different minimum
value (zero), as (2). Because this function contains one
parameter less than the LSTR2 model, it can be regarded
as a useful alternative to the corresponding logistic
transition function. For more discussion [19].
2.2. The Modeling Cycle
In this section we consider modeling nonlinear relation-
ships using STR model (1) with transition function (2). We
present a modeling cycle consisting of three stages:
specification, estimation, and evaluation. The specification
stage entails two phases. First, the linear model forming

New Vision on the Relationship between Income and Water Withdrawal in Industry Sector 193
the starting point is subjected to linearity tests, and then
the type of STR model (LSTR1 or LSTR2) is selected.
Economic theory may give an idea of which variables
should be included in the linear model but may not be
particularly helpful in specifying the dynamic structure of
the model. Linearity is tested against an STR model with a
predetermined transition variable. If economic theory is
not explicit about this variable, the test is repeated for each
variable in the predetermined set of potential transition
variables, which is usually a subset of the elements in zt.
Testing linearity against STAR or STR has been discussed,
for example, in [20,21].
Figure 1. Observations of the logarithmic x-axis, and the
logarithm of the y-axis.
The resulting test is more powerful than both the
LSTR1 (K = 1) and LSTR2 (K = 2) models. Assume now
that the transition variable st is an element in zt and let zt
= (1, )’, where is an (m × 1) vector. The appro-
ximation yields, after merging terms and parameterizing,
the following auxiliary regression:
'
t
z'
t
z
'
'*
01,1
tj
tt jttt
j
yx xsutT 

 
 (4)
where tt

*
t3
'
uuR,,z
t
cs

  with the remainder
R3(γ ,c ,st).The null hypothesis is H0: β1 = β2 = β3 = 0
because each βj, j = 1, 2, 3, is of the form βj where,
0
j


*
t
uu
is a function of θ and c. This is a linear
hypothesis in a linear (in parameters) model. Because
under the null hypothesis, the asymptotic distribu-
t
Figure 2. Residuals of (1) (x-axis: the value ofi
x
; y-axis:
residualt

).
tion theory is not affected if an LM-type test is used.
An STR model is fitted to the logarithmic data. The
transition function is defined as a logistic function.
Where
y

 equals the residual standard deviation
and
R
ESET
p is the p-value of the RESET test. The test
does indicate serious misspecification of (5). On the
other hand, the residuals arranged according to iin
ascending order and graphed in Figure 2 show that the
linear model is not adequate. It can be seen in
Lx
R
ESET
plarge value in Equation (5).
3. Empirical Results
The basis of our empirical approach is exactly the same
as that used by many authors in literature. The observa-
tions in this modeling experiment come from AQUSTAT
FAO and WDI database of the [22]. The purpose of the
study is to investigate the effect of GDP per capita on the
annual water withdrawal (IWW). The IWW is assumed
to be a nonlinear function of the GDP per capita. Figure
1 demonstrates a clearly nonlinear relationship between
the logarithmic values of GDP per capita (x-axis) and the
IWW (y-axis) as long as kernel fitting curve.
The results of the linearity tests appearing in Table 1
p-values are remarkably small. Hypothesis H0 is the gen-
eral null hypothesis based on the third-order Taylor ex-
pansion of the transition function. Hypotheses H04, H03,
and H02 are the ones discussed in the Section of method-
ology. Because the p-value of the test of H03 is much
larger than the ones corresponding to testing H04 and H02,
The sample consisted of industrial water withdrawal
(IWW) per capita in cubic meter and GDP per capita in
2000 constant dollar for 132 countries of the world. Fit-
ting a linear model to the data yields:
The choice of K = 1 in Equation (6) (the LSTR1 model)
is quite clear. This is also obvious from Figure 1, for there
appears to be a single transition from one regression line to
the other. The next step is to estimate the LSTR1 model,
which yields:
LY =5.9901.070LX 
(–6.115) (9.418)
2
1.946,132,0.4055,(1,129) 0.1808
RESET
ynR p
  

(5)

 

1
ˆ 7.427 1.260(58.490075.6400) 1 exp2036.0894/x9.7948
ii ii
Ly LxLxLx 


  

(–5.928) (8.215) (–4.548) (4.464) (0.0002) (0.8008)
T = 132, R2 = 0.512, 1.3916


, L x 1.1582.,/1 2015





(6)

New Vision on the Relationship between Income and Water Withdrawal in Industry Sector 194
Table 1. p-Values of the linearity tests of model (5).
Hypothesis p-Value
H0 5.6223e-03
H2 1.8076e-01
H3 3.5337e-02
H4 1.1866e-02
where, σlx is the sample standard deviation of Lxi, σ is the
residual standard deviation of linear model and σL is that
of non-linear one. It should be noted that there are two
large standard deviations, which suggests that the full
model may be somewhat over parameterized. This is
often the case when the STR model is based on the linear
model without any restrictions. Model (6) is an example
of such a situation. It may appear strange that the need to
reduce the size of the model is obvious in this model al-
ready because it only has a single explanatory variable.
The first reaction of the model would perhaps be to
tighten the specification by removing the nonlinear in-
tercept, Restriction φ = 0 or G (Lxi,  , c) = 0. Another
possibility would be to restrict the intercepts by imposing
the other exclusion restriction φ0 = θ0. In fact, the first
alternative yields a model with a slightly better fit than
the latter one. The model estimated with this restriction is,
see Equation (7):
The estimated standard deviations of all estimates in (6)
are now appreciably small, and thus further reduction of
the model size is not necessary. The fit of both (6) and (7)
is vastly superior to that of (5), whereas there is little
difference between the two LSTR1 models. The residual
standard deviation of these models is only about
one-tenth of the corresponding figure for (2). Such an
improvement is unthinkable when economic time series
are being modeled. The graph of the transition function
as a function of the observations in Figure 3 shows that
the transition is indeed smooth.
The test of no additive nonlinearity [H0: β1 = β2 = β3 =
0 in (transition function)] has the p-value of 0.0010. In
testing [H02: β1 = 0 | β2 = β3 = 0, a test based on a first
order Taylor expansion of H (γ2, c2, x2i)] and thus one
against another LSTR1component, we find that the
p-value of the test equals 0.017. These results show that
nonlinearity in this data set has been adequately charac-
terized by the LSTR1 model. The tests of no error auto-
correlation and parameter constancy are not meaningful
here in the same way as they are in connection with time
series models, and they have therefore not been applied
to model (7).
We modify this approach by using STR model re-
cently developed by Gonzalez et al. [31].

01 ,, iiiii
LyLxLxG Lxci

 

  (8)
where εi is i.i.d


2
0,
x

and the transition function G is:
 
1
(,,), 0
1exp
i
i
GLx cLx c 


 (9)
4. Analysis
According on empirical result the relationship between
industrial water use and income is nonlinear model so we
can calculate the elasticity of water use. In STR model,
income elasticity of IWW per capitai depends on
(log GDP per pita) level (i). So it allows the parame-
ters to change smoothly as a function of the threshold or
transition variable. Indeed, the elasticity of income is
explained by the weighted average of parameters includ-
ing 0 and 1. The income elasticity for country ith
is:
(E )
i
(E )
Lx
 
i01
,
E,,
,
i
i
ii
ii
g
Lx c
Ly gLx cLx
Lx Lx

 


 

(10)
In this specification, a negative value of 1 may also
lead to the increase of elasticity. The estimated parame-
ters in this part could not be interpreted as elasticity. In
Equation (11), the income elasticity of IWW i has
been presented. All calculations are computed with Mat-
lab and JMULTI software’s. The equation used to calcu-
late elasticity is given as the following:
(E )


  

 


i
2
E 0.35460
6.22198
1 exp34.08179.8327
34.0817 6.2219862.5861
1
exp 34.08179.83274
1 exp34.08179.83274
i
i
i
i
i
i
Ly
Lx
Lx
Lx
Lx
Lx







 







 


 (11)
 
1
ˆ 0.35460(62.586106.22198) 1exp34.08176Lx9.83274
ii ii
Ly LxLxLx 


  


(18.3850) (-3.0463) (3.1094) (0.5366) (60.4258)
21.5909T, Lx1.1582,1.3132, R 0.3577361,
Lx
σ
σσ σ  (7)

New Vision on the Relationship between Income and Water Withdrawal in Industry Sector 195
Figure 3. Transition function of model (3) as a function of
the transition variable.
On the Figure 4, this elasticity is displayed for all
possible values of the transition variable (GDP per cap-
ita). Elasticity is increased slightly according to the in-
come level. Moreover, there is strong evidence that the
relationship between per capita income and elasticity of
IWW is bell-shaped.
5. Conclusions
In this paper, STR model based on cross section data was
used to estimate the relationship between IWW and in-
come for 132 countries throughout the world. It does
seem that it is an inverse U-shaped curve for world coun-
tries. The results suggest an importance to search for
alternative ways of water use to reduce the demand for
additional water in the process of industrialization. Ac-
cording to the results, the income elasticity of IWW in
selected countries is bell-shaped curve. These results
justify ideas of (NRBEKC), (STCE) and (OVW) con-
cepts that are combining ecological and social benefit as
Figure 4. The relationship between GDP per capita and
IWW’s elasticity.
a whole. The findings suggest that income and socio-
economic criteria along with water scarcity can have an
effect on industrial water withdrawal in water-scarce
countries and water intensity of use.
This line of thinking also has important implications
for the models of water use and economic growth devel-
oped by [33], and the other issues of water-income rela-
tionship by [1,5,8,35,11]. One way to accomplish this is
by estimating the water savings attributable to the struc-
tural transformation of an economy.
6. Acknowledgements
This paper was funded by grant from the University of
Tehran submitted to the author.
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