Statistical Modelling of CO 2 Emissions in Malaysia and Thailand

Abstract

Carbon dioxide (CO 2) emissions is an environmental problem which leads to Earth's greenhouse effect. Much concerns with carbon dioxide emissions centered around the growing threat of global warming and climate change. This paper, however, presents a simple model development using multiple regression with interactions for estimating carbon dioxide emissions in Malaysia and Thailand. Five indicators over the period 1971-2006, namely energy use, GDP per capita, population density, combustible renewables and waste, and CO 2 intensity are used in the analysis. Progressive model selections using forward selection, backward elimination and stepwise regression are used to remove insignificant variables, with possible interactions. Model selection techniques are compared against the performance of eight criteria model selection process. Global test, Coefficient test, Wald test and Goodness-of-fit test are carried out to ensure that the best regression model is selected for further analysis. A numerical illustration is included to enhance the understanding of the whole process in obtaining the final best model.

Full text

Vol. 2 (2012) No. 5
ISSN: 2088-5334
Statistical Modelling of CO2 Emissions in Malaysia and Thailand
Tay Sze Hui1, Shapiee Abd Rahman2 and Jane Labadin3
Department of Computational Science and Mathematics,
Faculty of Computer Science and Information Technology,
Universiti Malaysia Sarawak, 94300 Kota Samarahan, Sarawak, Malaysia.
E-mail: 1shtay1011@gmail.com, 2sar@fit.unimas.my, 3ljane@fit.unimas.my
Abstract— Carbon dioxide (CO2) emissions is an environmental problem which leads to Earth’s greenhouse effect. Much concerns
with carbon dioxide emissions centered around the growing threat of global warming and climate change. This paper, however,
presents a simple model development using multiple regression with interactions for estimating carbon dioxide emissions in Malaysia
and Thailand. Five indicators over the period 1971-2006, namely energy use, GDP per capita, population density, combustible
renewables and waste, and CO2 intensity are used in the analysis. Progressive model selections using forward selection, backward
elimination and stepwise regression are used to remove insignificant variables, with possible interactions. Model selection techniques
are compared against the performance of eight criteria model selection process. Global test, Coefficient test, Wald test and Goodness-
of-fit test are carried out to ensure that the best regression model is selected for further analysis. A numerical illustration is included
to enhance the understanding of the whole process in obtaining the final best model.
Keywords— CO2 emissions; multiple regression; model selection techniques
I. INTRODUCTION
Carbon dioxide (CO2) is defined as a colourless,
odourless, incombustible and non-poisonous gas produced
during combustion of carbon, decomposition of organic
compounds and in the respiration of living organisms, as
referring to [1]. Carbon dioxide emissions happen when
carbon dioxide is released into the atmosphere over a
specified area and period of time through either natural
processes or human activities. Scientifically, carbon dioxide
is a chemical compound that composed of one carbon atom
and two oxygen atoms. Much concern with carbon dioxide
in particular is that its amount being released has been
dramatically increased in the twentieth century. Scientists
have found that greenhouse gas emissions such as carbon
dioxide possibly contribute to global warming, as pointed
out in [2]. CO2 emissions could aggravate global warming
and result in environmental deteriorations and public health
problems, as stated in [3]. In the year 2007, the
Intergovernmental Panel on Climate Change (IPCC) stated
that global average temperatures is likely to increase by
between 1.1 and 6.4 ⁰C during the 21st century [4]. To date,
mathematical modelling of carbon dioxide emissions in
Malaysia and Thailand is still lacking. Therefore, this study
focuses on the modelling of CO2 emissions in Malaysia and
Thailand based on socio-economic and demographic
variables using regression analyses.
II. LITERATURE REVIEW
At least until recently, there is clearly a rising awareness
about global warming due to man-made mechanical
emissions. Thus, there are several efforts being made to
analyze CO2 emissions in different countries or regions of
the world. Patterns in CO2 emissions and its related
determinants of many countries or regions of the world have
been analyzed in the literature. Reference [5] demonstrated a
newly developed dataset involving more than one hundred
countries around the world to study the reduced-form
relationship between per capita CO2 emissions and per capita
GDP, known as the Environmental Kuznets Curve (EKC).
Reference [6] had employed regression models to estimate
and compare fuel consumption and CO2 emissions from
passenger cars and buses. Meanwhile, [7] suggested
applying decomposition analysis (DA) method on energy-
related CO2 emissions in Greece as well as Arithmetic Mean
Divisia Index (AMDI) and Logarithmic Mean Divisia Index
(LMDI) techniques on a period-wise and time-series basis.
In [8] research, they scrutinized the environmental
convergence hypothesis and the stationarity property of
relative per capita CO2 emissions in 21 OECD countries
from 1960 to 2000 by using the seemingly unrelated
regressions augmented Dickey–Fuller (SURADF) test.
Reference [9] examined the relationships between carbon
10

dioxide emissions, energy consumption and economic
growth in China by using multivariate co-integration
Granger causality tests. On the other hand, [10] had used a
panel vector error correction model to investigate the
relationship between carbon dioxide emissions, electricity
consumption and economic growth of five ASEAN countries.
Reference [3] research had studied on various energy
efficiency efforts and carbon trading potential in Malaysia to
fight against global warming through reducing greenhouse
gases emissions. Based on [11] research, the consumer
lifestyle approach of different regions and income levels was
used to analyze and explain the impact of carbon dioxide
emissions and energy consumption by urban and rural
households in China. Reference [12] proposed a dynamic
panel data model to examine the determinants of carbon
dioxide emissions for a global panel involving 69 countries
with the dataset from the year 1985 to 2005. Reference [13]
pointed out that applying time series data of a single country
only into an investigation may be able to determine and
explain past experiences such as energy policies,
environmental policies and exogenous shocks.
It is remarkable that most studies are concerned with
analyzing the patterns of changes in energy consumption,
income and global emissions with those of CO2 in particular
for a range of countries using various methodologies.
Despite the increasing sophistication of applications and
methodologies employed on a variety of researches, the
interrelationship between CO2 emissions and other variables
in Malaysia and Thailand is still lacking and has not been
examined extensively up to date. Therefore, this study
attempts to provide such an analysis using multiple
regression approache. According to [14], multiple regression
is the widely used technique when a prediction is needed and
where the data on several relevant independent variables are
available.
III. DATA AND METHODOLOGY
The data used in this paper are the annual time series data
for Malaysia and Thailand from 1971 to 2006. The data were
obtained from World Bank’s World Development Indicators,
as in [15]. The variables employed are CO2 emissions
(metric tons per capita), energy use (kg of oil equivalent per
capita), GDP per capita (constant 2000 US$), population
density (people per sq. km of land area), combustible
renewables and waste (% of total energy), and CO2 intensity
(kg per kg of oil equilavent energy use).
Multiple regression (MR) model is a statistical method
used to examine the relationship between a dependent
variable and a set of independent variables. Suppose that the
value of a dependent variable, Y is influenced by k
independent variables, X1, X
2, X
3, ..., X
k. In general, the
multiple regression model is defined as:
Y = β0 + β1X1 + β2X2 + β3X3 + ... + βkXk + ε (1)
where β0 is the intercept term, βj denotes the j-th coefficient
of independent variable Xj and ε is the random error term.
The j-th variables, Xj where j = 1, 2, 3, …, k, can be single
independent variables, interaction variables, generated
variables, transformed variables or dummy variables. The
regression coefficients were estimated using ordinary least
square (OLS) method in order to obtain a model that would
describe the data, as stated in [16].
There are some basic assumptions of multiple regression
which must be statisfied so that the results will not be biased.
The assumptions are:
a) The error term, ε has a zero mean value for any set of
values of the independent variables such that E(ε) = 0.
b) Homoscedasticity, that is the variance of ε, is constant
such that var(ε) = σ².
c) The error term, ε follows the normal distribution with
zero mean and variance σ² such that ε ~ N(0, σ²).
d) The error term, ε is uncorrelated with one another such
that their covariance is zero, cov(εi, εj) = 0 for ݅≠݆. It
means that there is no autocorrelation exists between the
error terms.
e) No exact collinearity or no multicollinearity exists
between the k independent variables.
The regression model with k variables and k+1
parameters including the constant term as expressed in
equation (1) is one of the possible models. All the possible
models are listed out based on single independent variables
and all possible interactions of related single independent
variables either generated or transformed. If multicollinearity
phenomenon exists, then the source variables in the
regression models are removed. In order to obtain
appropriate regression models, Global test and Coefficient
test are conducted to test the overall statistical siginificance
of the independent variables on the dependent variable, as in
[17]. Then the regression models after the final elimination
are the selected models free from problems of
multicollinearity and insignificance. This process is known
as data-based model simplification.
The process of selecting a subset of original predictive
variables is by means of removing variables that are either
redundant or with little predictive information, as in [18].
Thus, it is useful to enhance the comprehensibility of the
resulting models so as to generalize better. There are three
popular optimization strategies employed in model selection,
namely forward selection, backward elimination and
stepwise regression. In this study, the model selection
algorithm is performed by using PASW Statistics Software.
Forward selection starts with an empty set of variable and
gradually adds in variables that most improve the model
performance until there is no additional variable that satisfies
the predetermined significance level. By contrast, backward
elimination method begins with a full set of all individual
variables and sequentially eliminates the least important
variable from the model. The process ends when an optimum
subset of variables is found. As for stepwise regression, it is
a combination of forward selection and backward
elimination that determines whether to include or exclude
the individual variables at each stage. The variable selection
terminates when the measure of all variables in the variable
set is maximized.
Reference [16] had also explained in detail the statistical
procedures of obtaining the best model based on model
selection criteria. The model selection criteria are Akaike
information criterion (AIC), finite prediction error (FPE),
generalised cross validation (GCV), Hannan and Quinn
criterion (HQ), RICE, SCHWARZ, sigma square (SGMASQ)
and SHIBATA. The whole selection criteria is based on the
11

residual sum of squares (RSS) multiplied by a penalty factor
which would depend on the model complexity. Model with
higher complexity generally will decrease the RSS but
increase the penalty. These criteria thus allow trade-offs
between goodness-of-fit and model complexity. The model
with the lowest values for most of the criteria statistics is
preferable and chosen as the best model. The joint
significances of regression coefficients are examined by the
Wald test, followed by the goodness-of-fit test so as to
investigate the suitability of the final model.
IV. RESULTS AND DISCUSSIONS
CO2 emissions (Y) as the dependent variable was related
to energy use (X1), GDP per capita (X2), population density
(X3), combustible renewables and waste (X4), and CO2
intensity (D). In this study, only the data for population
density was normally distributed in its level form. Since the
data for other variables were not normally distributed, they
were transformed into natural logarithms prior to analysis
because this helps to induce normality. Meanwhile, CO2
intensity was generated into dummy variable since it was
still not normal after several transformations.
Table I demonstrates the relationship between CO2
emissions and the determinants that are related. There is a
significant relationship between the variable X1, X2, X4 and D.
It is obvious that the energy use (X1), GDP per capita (X2)
and combustible renewables and waste (X4) are highly
correlated with the carbon dioxide emissions (Y).
Furthermore, a positive significant relationship exists
between Y and X1 (r = 0.9773, p-value < 0.01), Y and X2 (r =
0.9806, p-value < 0.01) as well as Y and D (r = 0.6166, p-
value < 0.01). From the highlighted triangle shown in Table
I, there exists multicollinearity such that the absolute value
of the correlation coefficient is greater than 0.95 among the
independent variables. Hence, the multicollinearity source
variables have to be removed from the model. After
resolving the multicollinearity problem, further analysis can
then be carried out.
All the possible models are subjected to Global test and
Coefficient test. For illustration purpose, model BM31.10,
the backward elimination model 31 after 10 times of the
multicollinearity source variable removals, was considered.
Table II represents the ANOVA table for Global test. The
hypothesis of Global test for model BM31.10 is as follows:
H0: β4 = β12 = β34 = β123 = β124 = β1D = β3D = β4D = 0
H1: At least one of the β’s in H0 is nonzero.
From Table II, the Fcal is 2726.85 and the Fcritical is F0.05, 8,
63 = 2.10. Since Fcal is greater than Fcritical, the decision is to
reject the null hypothesis where all the regression
coefficients in model BM31.10 are zero.
TABLE I
A PEARSON CORRELATION TABLE BETWEEN CO2 EMISSIONS AND ITS DETERMINANTS
Y X1 X
2 X
3 X
4 D
Y 1 0.9773(**) 0.9806(**) -0.0147 -0.9039(**) 0.6166(**)
0.0000 0.0000 0.9026 0.0000 0.0000
X1 0.9773(**) 1 0.9707(**) -0.0059 -0.9189(**) 0.4973(**)
0.0000 0.0000 0.9608 0.0000 0.0000
X2 0.9806(**) 0.9707(**) 1 -0.1551 -0.9542(**) 0.5078(**)
0.0000 0.0000 0.1934 0.0000 0.0000
X3 -0.0147 -0.0059 -0.1551 1 0.3845(**) 0.1873
0.9026 0.9608 0.1934 0.0009 0.1151
X4 -0.9039(**) -0.9189(**) -0.9542(**) 0.3845(**) 1 -0.3875(**)
0.0000 0.0000 0.0000 0.0009 0.0008
D 0.6166(**) 0.4973(**) 0.5078(**) 0.1873 -0.3875(**) 1
0.0000 0.0000 0.0000 0.1151 0.0008
** Correlation is significant at the 0.01 level (2-tailed).
TABLE II
THE ANOVA TABLE FOR GLOBAL TEST
Source of
Variations
Sum of
Squares df Mean
Square F
Regression 7.3431 8 0.9179 2726.85
Residual 0.0212 63 0.0003
Total 7.3643 71
12

The best model for CO2 emissions estimation is selected
by first applying the backward elimination method. Then,
the Coefficient test is carried out for all the coefficients in
the model where Table III shows the coefficient for each
variable of the model BM31.10.3 with the last digit is the
number of insignificant variables being eliminated.
The criteria condition used in this regression analysis is
by dropping the variable with the p-value > 0.05. From the
observations in Table III, the variable X3, X34 and X1D are
removed from the regression model since their p-values are
greater than 0.05. It indicates that the corresponding
variables are insignificant at α = 0.05. The resulting model
contains only significant variables with all the p-values less
than 0.05. Similar procedures are applied to the forward
selection and stepwise regression method for model
selection. After progressive eliminations, the final model is
thus obtained and expressed as in equation (2).
Y = -0.3728 - 0.6769X4 + 0.0885X12 + 0.0001X123
+ 0.0481X124 - 0.0006X3D + 0.1029X4D (2)
The Wald test is performed on the final model where the
unrestricted model denoted as (U) and the restricted model
denoted as (R) are expressed respectively in the equation (3)
and (4) as follows:
(U): Y = β0 + β4X4 + β12X12 + β34X34 + β123X123 + β124X124
+ β1DX1D + β3DX3D+ β4DX4D + ε (3)
(R): Y = β0 + β4X4 + β12X12 + β123X123 + β124X124 + β3DX3D
+ β4DX4D + ε (4)
The hypothesis of Wald test is:
H
0: β34 = β1D = 0
H
1: At least one of the β’s in H0 is nonzero.
As shown in Table IV, Fcal is 1.5753 and Fcritical is F0.05, 2,
63 = 3.15. The decision is not to reject the null hypothesis
where all the eliminated regression coefficients are zero
since Fcal is less than Fcritical. Thus, this justifies the removal
of the insignificant variables in the coefficient test. In order
to select the best model from forward, backward and
stepwise selection method, the model selection criteria
process is conducted. The models to be compared with are
shown in Table V, namely forward selection model
(FM26.8.3), backward elimination model (BM31.10.3) and
stepwise regression model (SM31.10.3). Majority of the
criteria indicates that BM31.10.3 and SM31.10.3 are the two
best models for CO2 emissions as both models show similar
findings with the same regression equation as expressed in
(2).
TABLE III
THE COEFFICIENTS IN MODEL BM31.10.3
Model
BM31.10.3
Unstandardized Coefficients t-values p-values
B Std. Error
Constant -0.3728 0.2602 -1.4329 0.1567
X4 -0.6769 0.0993 -6.8187 0.0000
X12 0.0885 0.0198 4.4709 0.0000
X123 0.0001 0.0000 4.2676 0.0001
X124 0.0481 0.0049 9.8776 0.0000
X3D -0.0006 0.0002 -2.7122 0.0085
X4D 0.1029 0.0130 7.8870 0.0000
Excluded Variables(b)
Model
BM31.10.3 Beta In t-values p-values Partial
Correlation
Collinearity Statistics
Tolerance
X3 -0.0071(a) -0.0624 0.9504 -0.0078 0.0036
X34 -0.0129(a) -0.1674 0.8676 -0.0209 0.0080
X1D 0.0635(a) 1.6631 0.1012 0.2035 0.0310
a. Predictors in the Model: Constant, X4D, X12, X124, X3D, X123, X4
b. Dependent Variable: Y
TABLE IV
THE WALD TEST
Source of
Variations
Sum of
Squares df Mean
Square F
Differences 0.0011 2 0.0005 1.5753
Unrestricted (U) 0.0212 63 0.0003
Restricted (R) 0.0223 65
13

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[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
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ORRESPONDIN
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RICE
S
0.0006
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GDP per ca
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ractions, the
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electricity
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OECD. 2011
.
http://stats.oe
c
M. Lanne an
d
Dioxide Emis
s
T. H. Oh an
d
Potential in
M
vol. 14, pp. 2
0
Intergovernm
e
Change 2007:
M. Galeottia
Kuznets,” En
v
1388, 2005.
J. A. Parav
a
Consumption
Buses,” Tech
n
2007.
E. Hatzigeor
g
Emissions in
G
Comparison o
Logarithmic
M
492–499, 200
8
C. C. Lee an
d
Per Capita
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G
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ODELS
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CHWARZ
S
0.0008
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0.0005
e
siduals
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e renewable
s
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lution. Othe
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e
ffect variabl
e
ff
ect on the
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to indicate
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occurrence o
X
2
indicates th
a
p
ita. Since th
e
polynomial
r
s
. Besides th
a
p
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c
onsumption
c
R
EFE
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Glossary of S
t
c
d.org/glossary
/
[
2
d
M. Liski, “Tr
e
s
ions,” Energy J
o
S. C. Chua, “E
n
M
alaysia,”
R
enew
a
0
95–2103, 2010.
e
ntal Panel on
Synthesis Repor
t
and A. Lanza,
v
ironmental Mo
d
a
ntis and D. A
and Carbon Dio
x
n
ology Forecast
g
iou, H. Polati
d
G
reece for 1990
–
f Results Using
t
M
ean Divisia In
d
8
.
d
C. P. Chang, “
N
C
arbon Dioxide
S
GMASQ S
H
0.0006
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0.0003
s
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sions will be
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t
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re exists effe
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egression co
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a
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c
apita income
could also b
e
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