Analysis of the Trend of 𝐂𝐎𝟐 Emissions in China, Korea, Japan, UAS,
Canada, Australia using an Environmental Kuznets Curve Approach

Lin Yi Jun1, Yongsung Cho1, 2, Guangyi Jin1
12

Department of Food and Resource Economics, Korea University

KU-KIST Green School, Graduate School of Energy and Environment, Korea University

1. Introduction
After China opened its economy to the world in 1978, it has a rapid development and growth in theeconomic sphere. Especially, it is obvious that there is a great advanced in the industrial economic, which brings
the high consumption of fossil energy and serious pollution problems. In order to develop and keep a highgrowth rate of GDP, it seems that, no matter China or other countries, it must spend its environment as externalcosts. The consumption of coal, that covers a half of the total fossil consumption, induces serious air pollution
in China. For example, recently it is getting worse in air pollution which is affected by fine dust; however, italso has a deep relationship with CO2 emissions, especially in Beijing and Shanghai. He et al. (2010) proposedthat CO2 emission in 2020 will be about 40% higher than prevailing in 2005 because of rapid growth of GDP.
It implies that the CO2 emission will increase because the heavy industry, energy-intensive business, will play
an important role on the economic growth. In addition, the CO2 pollution is not only problems for one country
but also global problems.
This study focuses on the relationship between per-capita real GDP growth and CO2 emissions. As
known, there are many kinds of previous literatures regarding the Environmental Kuznets Curve (EKC) to
explain the relationship between GDP growth and pollutions such as SO2, CO2 and NOX. This study will also
use the EKC theory to show if the curve (between the change of per-capita CO2 emission and per-capita realGDP) has an inverted-U-shaped or different shaped by the influence of the final fossil energy (coal and gas) andnon-fossil energy (renewable energy). This study chooses China and 5 OECD countries such as Korea, Japan,
USA, Canada, and Australia. Korea and Japan are the nearest countries to China which are playing importantroles on solving global CO2 pollution issue in Asia relatively. USA, Canada and Australia have rich fossil
energy resource and great size of land. USA, Canada and Australia also have high technology on producing
non-fossil energy. There is an obvious phenomenon (Fig. 1) that China, Korea, and Japan show the increase
trends of per-capita CO2 emission, while USA, Canada, and Australia show a relative decrease trend. So, it ispossible to get comparison results among 6 countries.
Most previous literatures used linear model or logarithm model to analysis the relationship between
CO2 emissions and GDP growth, and also summarized results about how endogenous factors (such as trade,1pollution emission, etc.) influence the change of CO2 emissions. However, they do not explain why they choose
specific functional formula. Wooldridge (2010) denoted that there are advantages on using the logarithm model.
Firstly, the logarithm can be used to overcome the heteroskedasticity problem; secondly, many variables violate
the normal distribution condition in econometrics, however the logarithm can make these variable obey thenormal distribution condition; thirdly, since the basic variables are all the macroeconomic data, the logarithm isable to make sure these variables are stable. However it is known that, the basic theory of EKC is using the nonlinear model to analysis the relationship between CO2 emissions and GDP growth; at the same time, there arestill a lot of studies which just used the non-linear model of EKC. This study has two objectives. The first one
is to test whether both a non-linear model and a logarithm model will have similar results or not. Additionally,
it will be tested whether or not an inverted U-shaped or an inverted-N-shaped is proper to each countries. The
second one is to use the vector auto regression (VAR) to test how the CO2 emission is affected by theendogenous factors, which are coal consumption, gas consumption, and renewable energy consumption. For
example, as known, the coal consumption has a positive effect on CO2 emissions; while this study will
estimates how much power does it take to affect CO2 emissions. Meanwhile, the renewable resource will play
an important role on reducing the CO2 emissions in the further. It is necessary to know that, even though the
EKC model also concludes the energy factors which affect the result of the relationship between CO2 emissionsand GDP growth, it is difficult to know how much affection each energy takes to increase or decrease the CO2
emissions. The VAR model seems more useful to estimate this kind of affection where does not consider the
GDP growth.
It is necessary to mention that coal, gas and renewable consumptions are the only influence factors to
be considered. As known, the coal is still playing an important role on the heavy industry and its consumption
almost charges the half of total final energy consumption in China; its chemical component is the direct reason
to produce CO2 which induces the global greenhouse effect. The gas consumption is the second factor to bechosen. Even though gas is the fossil energy, one of its characteristics is that it can induce relatively low levelof CO2 emissions. The last factor to be considered is renewable resource. As known, the using of non-fossil
energy instead of fossil energy is an inevitable trend in the further.

22. Literature Review
The Basic Theory of Environmental Kuznets Curve
The environmental Kuznets curve (EKC) shows the relationship between pollution emissions and GDP
growth (or economic development) and the general EKC function is as following;
Ei = α + β1 Yi + β2 Yi 2 + β3 Yi 3 + β4 Q i + δ(1)Where, E means the per-capita emission; Y means the per-capita real GDP growth; i is the number of country.
Q i indicates a vector of variables such as coal, gas, and non-fossil energy consumption. δ denotes an error
term. If β1 >0 (or β1 <0) and β2 =β3 =0, then there is a monotonically increasing (or decreasing) relationshipbetween variable E and variable Y. If β1 >0, β2 >0 and β3 =0, then it matches with the basic theory ofenvironment Kuznets curve (EKC) which means an inverted U shaped of EKC between GDP growth andpollution emissions (Orubu and Omotor, 2011). Finally, if β1 <0, β2 >0 and β3 <0, it comes up with an invertedN-shaped relationship (Kijima et al., 2010).

3

Besides equation (1), there is a popular equation formula of EKC. That is a logarithm function as following
the equation (2).
lnE = γ + θ1 lnYi + θ2 lnYi 2 + θ3 lnYi 3 + θ4 lnQ i + ε(2)Where, variables E, Y and Q are same notation of the equation (1). If θ1 >0 (or θ1 <0) and θ2 =θ3 =0, thenthere is a monotonically increasing (or decreasing) relationship; if θ1 <0, θ2 >0 and θ3 =0, then it can bedenoted by an inverted-U-shaped relationship, the original EKC pattern; if θ1 >0, θ2 <0 and θ3 >0, then it
shows an N-shaped relationship.

Environmental Kuznets Curve and VAR model
Apergis and Payne (2009) used the basic and original equation of EKC which is:
Cit = αit + βit Eit + β2i Yit + β3i Yit2 + εit .

(3)

Where, C is the CO2 emissions per capita; E is the energy consumption per capita; Y is the real output.
Apergis and Payne (2009) extended CO2 emissions, energy consumption, and output within a panel vector
error correction model for six Central American countries over the period 1971-2004. It showed that energy
consumption and real output exhibits the inverted U-shape pattern in long-run equilibrium.
Wang et al. (2011) used the basic formula of EKC to examine the causal relationships between carbon dioxide
emissions, energy consumption and real economic output using a panel cointegration and a panel vector error
correction modeling techniques based on the panel data for 28 provinces in China over the period 1995–2007.
2
Cit = αit + β1i Eit + β2i Git + β3i Git
+ εit

(4)

Where, C denotes the CO2 emission per capita; E denotes the energy consumption per capita and G means
4the economic growth. It has also been found that energy consumption and economic growth are the long-run
causes for CO2 emissions. The CO2 emissions and the economic growth are long-run causes for energy
consumption. The results indicate that China’s CO2 emission will not decrease in a long period of time, andreducing CO2 emission may handicap China’s economic growth to some degree. Jalil and Mahmud (2009) also
used this basic equation to get a similar result on the case of China.
Tao (2008) investigated the relationship between environmental pollution and economic growth in China
using Chinese provincial data over 1985–2005. Waste gas, waste water and solid wastes are used asenvironmental indicators and GDP is used as the economic indicator. The formula of EKC of this study is asfollowing:
S
P it

2
3
GDP
GDP
GDP
) + β2 [ln ( ) ] + β3 [ln ( ) ] + μit
P it
P it
P it

ln ( ) = αi + θt + β1 ln (S

Where, P and

(5)

GDP
mean per capita each pollution and per capita GDP respectively, denoting the population
P

by P. This study applied a panel co-integration test in order to check whether or not there exists a long-run cointegrating relationship between the per capita emissions and the per capita GDP.
Orubu and Omotor (2011) investigated the relationship between per capita income and environmental
degradation in Africa, using longitudinal data on suspended particulate matter and organic water pollutants. The
specific objective was to estimate EKC for two indicators of environmental quality, and to establish whether theestimated relationships conform to the inverted U-shape hypothesis. The basic equation is:ln(ED)t = β1 + β2 ln(PCGDP)t + β3 ln(PCGDP)2 + et

(6)

Where, variable ED and PCGDP denote a environmental pollution and a per capita GDP respectively. This
study also did not tell the reason why it used the logarithm formula. While the results of the empiricalinvestigation generally suggest the existence of EKC for a suspended particulate matter.
Baek et al. (2009) used a cointegration analysis to check a relationships among sulfur emissions (SO2),
income, and trade for the developed and the developing countries. They compiled annual time-series data on
SO2, income, and trade openness for 50 countries for the period 1960–2000. Baek et al. (2009) used thecointegrated vector auto regression (CVAR) model developed by Johansen in order to examine a dynamic
interrelationship between trade, income and SO2 emission. The Johansen method (Johansen, 1988; Johansen
and Juselius, 1992) uses a statistical model involving up to k lags as following;yt = μ + A1 yt−1 + ⋯ + Ak yt−k + μt

(7)

Its results suggest that trade and income growth tend to increase environmental quality in developed countries,
whereas they have detrimental effects on environmental quality in most developing countries.

5Cui and Wang (2010) also mentioned that there are relationships of mutual influence, mutual constraints
among energy system, economic system, and environmental system. VAR model has always been used forforecasting the relevant time-series and the random perturbation of variables that affect the dynamics of one
system. Therefore, they established a VAR model of China’s Energy-Economy-Environment based on the dataof China’s energy consumption, GDP and SO2 from1995 to 2006, and then forecast the years from 1995 to 2015.
The results confirm that the relationship among Energy-Economy-Environment based on VAR Model is reliable.

3. Estimation of EKC of China and other Countries
Logarithm model and Non-linear Model of EKCFirst of all, this study used a logarithm formula to test a relationship between the per-capita CO2 emissions
and a per-capita real GDP in the whole data and the different data of each countries. The functional form applied
to estimate is showed as:ln(CO2𝑖 ) = γ + θ1 ln(GDPi )1 + θ2 ln(GDPi )2 + ⋯ + θα ln(GDPi )α + θα+1 ln(Coali ) + θα+2 ln(Gasi )+θα+3 ln(Renewablei )(8)

As known, the basic theory of EKC denotes that ‘α=3’ denotes N-shaped of EKC, and ‘α=2’ means Ushaped of EKC. This study analyzed all the datasets of these 6 countries together. Meanwhile, when testing thedata of all countries, there are several problems such as a cross-sectional correlation (correlation with different
country in same year) and a heteroskedasticity with different country in same year. To handle those problems,
we used the Random-effect Generalized Least Squares model.
Meanwhile, this study also focus on the analysis of original formula. In fact, compared to the logarithm value,
the original data has a better explanatory power to denote how the growth of real GDP affects the CO2 emission
and what affection of the endogenous factors are positive or negative for CO2 emissions. In addition, since theresults of non-linear formula in this study are not so much clear, we establishes the non-linear equation where
the estimation on per-capita real GDP is not just square and cubic. It is estimated by η in equation (9) whichmeans that, if η=0, then the per-capita CO2 emission and the per-capita real GDP have no relationship at all;however, if η=1, 2 or 3, then the relationship between CO2 emission and the per-capita real GDP matches thebasic theory of Kuznets Curve; if η>3, it means the theory of Kuznets Curve in the situation of this study is notfounding and the non-linear formula can reject the hypothesis theoretically.
CO2 i = α + β1 GDPi1 + β2 GDPi 2 + ⋯ + βη GDPi η + βη+1 Coali + βη+2 Gasi + βη+3 Renewablei + δ(9)Description of Data
It is necessary to introduce the basic information of the data in order to understand the meaning of different
6factor and some basic characteristics such as mean, median, maximum and minimum of all the data of China
and other 5 OECD countries (USA, Korea, Japan, Canada, and Australia). This study compiles annual timeseries data on carbon emission (CO2 ), real GDP (measured by PPP) and final energy consumption (coal, gas
and renewable) for China and 5 countries for the period 1980–2013 year. All the data is calculated into percapita. Table 1 summaries the value of mean, median, maximum and minimum. Meanwhile, CO2 per means
the CO2 emission per capita which is measured by “tonne”; GDP means per-capita real GDP ($) which ismeasured by parity power price (PPP); coal means coal per capita, gas means gas per capita and renewablemeans renewable per capita, which are all measured by “toe”. It is easy to know that the usage of non-fossil
energy is still very low, especially the usage of renewable in China and Korea are very low. It also confirms theserious situation where the fossil energy is still the main energy resource being used into the second industry.
Table 1. Description of data by country from 1980 to 2013
(Unit: $1,000 USD, toe)Country

ALL

CHINA

USA

KOREA

JAPAN

Variable

MeanMedian

Max

Min

GDP

21.02720.25353.0010.302

CO211.941

13.67

20.78

1.46

Coal

2.687

1.976

7.507

0.684

Gas

1.532

1.226

4.134

0.001

Renewable

0.03

0.011

0.148

0.001

GDP

3.389

2.11

11.867

0.302

CO2

3.3

2.69

7.4

1.46

Coal

1.439

1.132

3.165

0.684

Gas

0.041

0.02

0.156

0.016

Renewable

0.003

0.002

0.011

0.001

GDP

32.07530.8

53.001

12.576CO2

19.17819.565

20.78

16.3

Coal

3.502

3.615

3.842

2.693

Gas

2.87

2.861

3.229

2.503

Renewable

0.017

0.016

0.023

0.012

GDP

14.96313.29633.791

2.308

CO2

6.811

5.61

12.7

3.53

Coal

1.527

1.291

2.814

0.807

Gas

0.501

0.405

1.482

0.001

Renewable

0.001

0.001

0.002

0.001

GDP

23.08923.94936.654

8.539

CO2

9.129

9.42

10.8

7.82

Coal

1.214

1.127

1.644

0.831

Gas

3.458

3.625

4.134

2.689

Renewable

0.01

0.01

0.012

0.008

GDP

24.91523.09339.54411.115CO2

16.27416.175

17.46

14.78

CANADA
7

AUSTRALIA

Coal

1.941

1.992

2.263

1.288

Gas

3.458

3.625

4.134

2.689

Renewable

0.138

0.139

0.148

0.126

GDP

26.13624.52445.13810.36

CO216.954

17.06

19.4

14.64

Coal

6.444

6.271

7.534

3.988

Gas

1.545

1.464

2.283

0.831

Renewable

0.011

0.011

0.015

0.009

Note that “CO2” variable means CO2 emission per capital (tone), “GDP” means GDP per capital measured by PPP ($). “Coal”,“Gas”, “Renewable” denote the coal consumption per capita (toe), the gas consumption per capita (toe), and the renewableconsumption per capita (toe), respectively.

Results of EKC estimation
Table 2 denotes that the empirical results of equation (8). It is obvious that the biggest power of GDP is just
3 (that is, α=3) and the sign of ln(GDP), ln(GDP)2 and ln(GDP) 3 are negative(-), positive(+) and negative(-),
respectively. This results indicates that the emission of CO2 will decrease with the increase of GDP, and thenit will increase with the increase of GDP, at last it still decrease with the GDP growth after arriving the second
turning point.
After analyzing the whole data, this study also uses the logarithm formula to analysis different data of eachcountry, independently. In the table 2, it shows that all the results of these countries match with the basic theoryof Kuznets Curve except the result of U.S. The results of China, Japan, Canada and Australia have the similar
inverted-N-shaped with the result of the whole data. Meanwhile the result of Korea shows that the coefficientsθ1 =-2.665012<0, θ2 = 0.151324>0 and θ3 =0, which means Korea has a normal-U-shaped in this situation.
With the affection of coal consumption, gas consumption and renewable consumption, the CO2 emission will
decrease with the growth of real GDP, and then it will increase again. While, the result of USA denotes that thecoefficient θ1 =-0.068937<0, and both θ2 = θ3 = 0. It can be understood as the growth of real GDP still has anegative effect on the CO2 emission. So it is very easy to know that the logarithm formula cannot reject thefirst stage hypothesis. It means even though the endogenous factors are final fossil and non-fossil energy
consumption, the results of each coefficient are able to construct a U-shaped or N-shaped, Kuznets theory.
Table 2. The Empirical Results of Logarithm Model
FactorLog(GDP)

Log(GDP)2

Log(GDP)3

Log(Coal)

Log(Gas)Log(Renewable)

ALL-7.0559***

0.89***-0.0349***0.3647***-0.0127***

0.1374***(Random effect)(0.759)(0.0896)(0.0034)(0.0121)(0.0041)(0.0055)ALL-0.9707***0.1376***-0.0058***

0.5093***0.0119***0.1851***R2Countries

8

0.942
0.984

(Fixed effect)
CHINA

USA

KOREA

JAPAN

CANADA

AUSTRALIA(0.9968)(0.1221)(0.0048)(0.0514)(0.0049)(0.0479)-2.9615**0.3575**-0.0136*

1.1652***-0.3165***

0.1111**(1.1114)(0.153)(0.0074)(0.0975)(0.1094)(0.0919)--0.5088***0.3559***-0.0471(0.0415)(0.0625)(0.0297)

0.6067**0.01390.1211(0.2441)(0.0625)(0.1396)-0.0689***(0.0082)-2.665*0.1513*(1.5564)(0.0836)-60.1031*

6.1159*-0.2074*0.04020.2088*0.0871(30.6326)(3.1187)(0.1057)(0.1148)(0.1135)(0.094)-113.588**

11.2272**-0.3695**

0.1724***0.1722-0.3302**(47.0981)(4.7339)(0.1583)(0.0622)(0.1621)(0.1569)-38.411***3.9398***-0.1339***0.035***-0.0255***

0.0862***(3.58E-05)(3.60E-06)(1.20E-07)(8.32E-08)(6.62E-08)(3.45E-09)

-

0.997

0.906

0.889

0.860

0.709

0.082

Note: ***, ** and * denote rejection of the null hypothesis of weak exogeneity at the 1%, 5% and 10% levels, respectively.

Table 3 carried out the Hausman test estimated the null hypothesis of this model existing random effect iscorrect or not. If H0 = 0, it can reject the null hypothesis and vice versa . It showed that the P-value is 0.0000
which is smaller than 0.01 in 99% confidence interval, so this null hypothesis can be rejected. It confirmed that
there existed a fixed effect on all the data of different country. Therefore, after adjusting the test equation, thisstudy got a relative accurate analysis of the total countries’ data.

Meanwhile, table 4 shows the results of equation (9) using all countries (η=3), USA (η=1) and Canada(η=3) are according with the basic concept of Kuznets Curve. USA and Canada seem to have similar trend withthe logarithm results on the relationship between CO2 emission and GDP growth, while the result of all
countries is opposite with the logistical results which shows a normal-N-shaped. Meanwhile, these three results
are all denoting that the CO2 emission will increase with the increasing of coal consumption; it will decrease
with the increasing of renewable consumption significantly. However, there is a normal relationship between
CO2 emission and gas consumption insignificantly. Thus, the Kuznets theory is not established in other 4
countries. The η of Korea and Australia are all equal to 5, the η of Japan is 4 and the η of China is 7 which isso much far away with the basic theory of Kuznets Curve.
Since this study is mainly focusing on the result of China1, it will use the data of China as an example to proof
1

These variety kinds of analysis on other countries will also be made and be showed in the appendix part. All of thesefour countries (China, Korea, Japan and Australia) can reject the null hypothesis H0 = 0 by Wald test and H1 = 0 by9

some countries’ model can reject the theory of Kuznets Curve in this situation. The coefficient β4 is 1.89E-13,
β5 is -2.25E-17, β6 is 1.35e-21 and β7 is -3.22E-26, all of them are so much small to be conjectured if they
are founded in this analysis. So it has to uses the likelihood ratio to test if variables (GDP4, GDP5, GDP6, GDP7)
are thought as redundant variables to be omitted, will the model be founded or not? If the null hypothesis H1 =0,
this null hypothesis can be rejected and vice versa. In the table 5, it denotes that the null hypothesis is rejectedby the P-value of likelihood ratio what is 0.0005 in the 99% confidence interval. These 4 variables2 should not
be omitted. The likelihood test reject their own null hypothesis which means the non-linear formula design on
the data of China is reasonable; and it also can reject the hypothesis of first stage, which can be said that not all
the non-linear formula results are similar with logarithm formula. In the non-linear model, it always has somespecial cases where the Kuznets theory cannot be adopted into when considering the endogenous variables tobe the data of final fossil and non-fossil energy consumption.
Table 4. The Empirical Results of Non-linear Model Estimation
Factor
GDP

GDP2

GDP3

GDP4

GDP5

-

-

Coal

Gas

Renewable

1.0428***4.2614***-31.6958***(0.0473)(0.1401)(2.8836)

1.4359**2.0132***-93.664***(0.1594)(0.3486)(20.955)

R2CountryALL

0.0005***-2.04E-08

2.15E-13***(Random)(4.46E-05)(2.11E-09)(2.87E-14)

ALL

0.0002***-9.80E-09***

9.10E-14***(Fixed)(4.84E-05)(1.94E-09)(2.61E-14)-0.0022***

1.97E-06***-8.45E-10***

1.89E-13***-2.25E-17***2.8957***-36.0201**394.559***(0.0007)(6.20E-07)(2.56E-10)(5.38E-14)(6.05E-18)(0.3322)(16.3041)(108.6313)

2.4972***2.4665***-69.5866*(0.2364)(0.4232)(34.4197)

-

0.971

-

0.986

0.998
CHINA
1.35E-21***GDP6-3.22E-26***GDP7(3.48E-22)(8.03E-27)-4.14-05***
USA

-

-

-

-

(5.33E-06)

0.896

0.0032***-5.23E-07***

3.39E-11***-9.42E-16***

9.45E-21***-0.9572

5.1556

1629.86*(0.001)(1.61E-07)(1.03E-11)(3.03E-16)(3.35E-21)(1.2874)(4.7897)(839.5343)

0.0006***-3.49E-08***

6.75E-13***-4.61E-18**

1.0269***4.3077***-32.7515***(0.0475)(0.1406)(2.9025)

1.3795*1.6591**-51.9866***(0.6809)(0.6978)(18.6489)

KOREA

0.952

JAPAN

(0.0006)(7.22E-09)(1.54E-13)-0.001***

3.69E-08***-4.28E-13***

CANADA(2.19E-18)

-

0.972

-

0.661

(0.0003)(1.21E-08)(1.54E-13)-0.1201***

1.05E-06***-4.26E-11***

8.14E-16***-5.92E-21***0.50860.445976.0072(0.0026)(2.13E-07)(8.21E-12)(1.51E-16)(1.07E-21)(0.442)(1.6625)(122.101)

AUSTRALIA

0.917

Note: ***, ** and * denote rejection of the null hypothesis of weak exogeneity at the 1%, 5% and 10% levels, respectively.

likelihood test.
.2 If 5 variables (GDP3, GDP4, GDP5, GDP6, GDP7) are omitted, the estimated null hypothesis also can be rejected by the
P-value of likelihood ratio be 0.0003 in the 99% confidence interval.

10

Table 5. Results of Likelihood Test for Redundant Variables

Box-Cox Transformation
When comparing the result of logarithm analysis and non-linear analysis, it is difficult to give a conclusion
about which one is better to be used in the EKC. Therefore, it has to use the Box-Cox Transformation to test
which model is better to be used or both them can be used. Box-Cox Transformation is a very good method todecide to choose a logarithm model or a non-linear model when establishing a model. There are three steps to
do in the Box-Cox Transformation.
a)Calculating the geometric mean of the dependence variable P;
̂ = (P1 P2 … Pn )1⁄n = exp(1 ∑ lnPi )
P
n

b)

(10)

Getting the new order of the dependence variable P∗ , which is form the dependence variable divided by
the geometric mean;̂P∗ = P/Pc)(11)

Instead of P, using the P∗ enter in to the logarithm model and non-linear model, then comparing thedifference of their residual sum of squares (RSS) to estimate which model is better. Zarembka (1968)
noted the testing statistic is
1
RSS2
n ∗ ln(RSS1)
2(12)Where RSS2 is the bigger residual sum of squares and RSS1 is the smaller residual sum of squares, n is
the sample size. Meanwhile the degrees of freedom are n-1-k, where k is the number of independent
variable. If the result of testing statistic is smaller than the critical value, it has no difference to choose
logarithm model or non-linear model at all; if the result is greater than the critical value, it is better tochoose the model which has a small residual sum of squares.
Following these three steps, this study also gets the result of testing statistic in table 6. It is easy to see thatthe results of testing statistic of China and U.S are 37.865 and 38.239 which are smaller than the critical
2 (29)
value X 0.05
= 42.5569 (n-1-k=29). The theory of the Box-Cox Transformation denotes when the value

11

1

RSS2

of the test statistic (2 n ∗ ln(RSS1)) is bigger than the critical value, the formula which has a small value of RSS
should be chosen, relatively. So for the case of China and U.S, there is no difference to choose logarithm modelor non-linear model. While, in order to make sure the analysis result being more appropriate, the logarithm
model is better to be used. On the other hand, the results of other countries are all greater than the critical value.
So they have to use logarithm model to get a better EKC estimation result because their RSS1, which belongs
to logarithm model, are smaller than RSS2.
Table 6. The result of Box-Cox Transformation
Country
Value

China

U.S

Korea

Japan

CanadaAustralia

RSS (1)0.01534

0.009378

0.674861

0.037120.018565

0.03121

RSS (2)0.141289

0.088913

13.84575

1.313556

4.842116

3.46995

𝟏
𝐑𝐒𝐒𝟏
𝐧 ∗ 𝐥𝐧()
𝟐
𝐑𝐒𝐒𝟐

37.86574

38.23960.57735

58.08469

94.58509

80.08967

the critical value

2 (29)
X0.05= 42.5569 (n-1-k=29)

Compared to non-linear formula, logistic formula is more appropriate to estimate if relationship between
CO2 emission and GDP growth matches the Kuznets theory in this study. Even though the cases of China andU.S have no difference to choose logarithm model or non-linear model, the logarithm result can show an Ushaped or N-shaped model which matches with the basic theory of EKC. When using the Kuznets curve toestimate the relationship between CO2 emission and GDP growth, it is necessary to test which model, logarithm
formula or non-linear formula, should be chosen in the analysis process and explain a simple reason about it.
Because for some cases, it has no problem to use either logarithm model or non-linear model to make a research;while for some other cases, an appropriate model will show a better result.

4. Vector Auto Regression (VAR) Analysis
Vector auto regression (VAR)3 is used to capture the linear interdependencies among multiple timeseries. VAR models generalize the univariate auto regression (AR) models by allowing for more than one
evolving variable. Although the estimated quantitative response coefficients will not in general be thesame, all variables in a VAR are treated symmetrically in a structural sense; each variable has an equation
explaining its evolution based on its own lags and the lags of the other model variables. VAR model
describes the evolution of a set of k variables (called endogenous variables) over the same sample period(t = 1, 2, ..., T) as a linear function of only their past values. The variables are collected in a k × 1 vector Zt,
which has as the i th element, Zi,t, the observation at time "t" of the i th variable. A ρ-th order VAR,
denoted VAR (ρ), is3

The source of this concept is from Wikipedia, the free encyclopedia.
12Zi, t = Ci + Ai, 1 Zi, t-1 + Ai, 2 Zi, t-2 + … + Ai, pZi, t-p + µ t(13)Where, the l-periods back observation Z t−l is called the l-th lag of Zi; C is a k × 1 vector of constants; Ai is
a time-invariant k × k matrix; µ t is a k × 1 vector of error terms. It takes CO2 emission, GDP, the ratio of
the primary coal consumption, the ratio of the gas consumption and the ratio of the primary renewable
as endogenous variables into the VAR model. There is a 2nd order VAR in which the lag p is 2, denoted
VAR (2), and the function will be shown as a matrix form:
𝐂𝐂,𝟏
𝐀𝐂,𝟏
𝐀𝐂,𝟐
μ𝐂,𝐭
𝐂𝐎𝟐,𝐭
𝐂𝐎𝟐,𝐭−𝟏
𝐂𝐎𝟐,𝐭−𝟐
𝐂𝐠𝐝,𝟏
𝐀𝐠𝐝,𝟏
𝐀𝐠𝐝,𝟐
𝛍𝐠𝐝,𝐭
𝐆𝐃𝐏𝐭
𝐆𝐃𝐏𝐭−𝟏𝐆𝐃𝐏𝐭−𝟐𝐜𝐨𝐚𝐥𝐭= 𝐂𝐜𝐨,𝟏 + 𝐀𝐂𝟎,𝟏 ∗ 𝐜𝐨𝐚𝐥𝐩𝐞𝐫𝐭−𝟏 + 𝐀𝐂𝟎,𝟐 ∗ 𝐜𝐨𝐚𝐥𝐩𝐞𝐫𝐭−𝟐 + μ𝐂𝟎,𝐭
μ𝐠,𝐭
𝐠𝐚𝐬𝐭
𝐀𝐠.𝟏
𝐀𝐠.𝟐
𝐂𝐠,𝟏
𝐠𝐚𝐬𝐩𝐞𝐫𝐭−𝟏
𝐠𝐚𝐬𝐩𝐞𝐫𝐭−𝟐[𝐫𝐫𝐞𝐧𝐞𝐰𝐚𝐛𝐥𝐞𝐭 ] [ 𝐂𝐫,𝟏 ] [ 𝐀𝐫,𝟏 ] [ 𝐫𝐞𝐩𝐞𝐫𝐭−𝟏 ] [ 𝐀𝐫,𝟐 ] [ 𝐫𝐞𝐩𝐞𝐫𝐭−𝟐 ] [ μ𝐫,𝐭 ](15)

Results of VAR
In a VAR model, if the roots of AR are smaller than 1 and their points are nearly staying in the unit circle,
it means that this VAR model is stable. The AR roots graph is used to test if the lag structure is stable andreasonable or not. In table 7, it just chooses three countries (Korea, Canada and Australia) to be used tocompare with China in order to make compare the difference between the developing countries and thedeveloped countries simply and intuitively. The graphs denote that these countries are relative stablebecause their roots are almost smaller than 1. Meanwhile, even though the countries, such as China, Korea,
Canada, has one point being out of the unit circle, the other points all stay in the unit circle. What’s more,
Engle and Granger (1987) show that, even in the case that all the variables in a model are non-stationary,
it is possible for a linear combination of integrated variables to be stationary. So it proofs that the designof this VAR model is reasonable relatively. It also denotes that the fossil and non-fossil energy
consumption have sustainable equilibrium relations with CO2 emission in long run. In short run, maybe
the variable will deviate with the equilibrium value. However, it is just a transient phenomenon, it will
return to the equilibrium value finally.

13

Table 7. The AR root of VAR model

14

Then, it carries on the VAR variance decomposition to estimate how much influence each energy takes toaffect the trend of CO2 emission. Fig. 3 shows the response of different primary energy consumption to CO2emission. The Horizontal axis means the period. In this part, the period is set as 35 (year) which is tending toconjecture how different energy consumption affects CO2 emission in the next 35 years. It is easy to know ifevery country can do a positive active on reducing the consumption of coal and increase the gas and renewableconsumption, there will have a great change on the emission of CO2 .
In the case of China, after coal consumption takes a peak point in the next 5 years, coal consumption willshow a decreasing affection on CO2 emission. From the 10th period to the 35th period, the coal consumption
will reduce sustainably to affect the CO2 emission. It means that because of the reduction of coal consumption,
it will have a weak affection on the CO2 emission in the further. The gas consumption at first will take a low
property to affect CO2 emission until 10th period, then, the property will rise up rapidly. From 15th period therise of this property will tend to slow down and at last the ratio of primary gas consumption will reducing CO2
emission significantly. Meanwhile, the response of the ratio of primary renewable consumption to CO2emission has a similar trend with the ratio of primary gas consumption. In the next 35 years, both of gas andrenewable will play an important role on reducing the CO2 emission.
The other three countries also show some other different trends in this graph. In the case of Korea, which isthe nearest countries to China, it shows the coal consumption will take a low level to affect the CO2 emission
and it has no so much difference in the further 35 years. It means that with the decreasing of coal consumption,
its affection on CO2 emission will also become weaker. The renewable resource and the gas will play similarroles on the CO2 abatement. Then in the case of the least developed countries, the trend of coal to CO2 emission
is decreasing and float in Canada; the trends of the primary coal consumption and primary renewableconsumption seem to be negative correlation when the coal consumption is decreasing, the renewableconsumption is increasing, otherwise. This phenomenon can be understood very easily, because Canada is the
only one country which uses the clear primary energy more than the fossil primary energy in these six countries,
which can affect the change of response of coal to CO2 by the clear primary energy easily. Australia seems tohave similar trend with that of China, while the gas play a more important role than the renewable.
Fig. 3. Percent 𝐂𝐎𝟐 Variance to different Energy Consumption

15

Note: Horizontal Axis is the further 35 years

5. Conclusion
All above the analysis of those results, it confirms that most countries show an N-shaped or U-shaped in thelogarithm formula which matches with the theory of EKC. For the case of Korea and U.S, it has an increase
relationship between CO2 emission and GDP growth. However, in the non-linear formula, not all the data of
every country can show a U-shaped or N-shaped relationship between CO2 emission and GDP growth, suchas China, U.S, Korea and Japan. The results of table 2 and table 4 confirm that by the different formulas,sometimes the result will be so much different. Actually, when just analyzing the results of the logarithm formulaand non-linear formula, it is difficult to say which one is better because they all match with basic theory of EKC.
16

𝟏

However, in the test of Box-Cox Transformation, all the cases of these countries show the test statistic 𝟐 𝐧 ∗𝐑𝐒𝐒𝟏𝐥𝐧(𝐑𝐒𝐒𝟐) is so much greater than the critical value which suggests the logarithm formula is better to be used toestimate the relationship between CO2 emission and GDP growth in this study relatively. But it does not mean
the non-linear model cannot be used in some other cases. As known, the basic theory of EKC is established bya non-linear model and the non-linear model is also very widely to be used in the other previous studies.
Therefore, there is a suggestion that when writing a paper about EKC, a simple explanation on which formula(logarithm or non-linear formula) should be used is so much necessary. Because in some cases, maybe it has noproblem to use either logarithm model or non-linear model to make a research; but in some other cases, only if
the right formula is chosen, the result will be accurate.
The second contribution this study does is that it conjectures the affection each energy resource takes on theCO2 emission in a hypothesis situation. For all the VAR model result of these 6 countries, it implies that,
although gas and renewable still do not show a significant effective action on reducing CO2 emission in recent
years, they will have a great positive effect on reducing the CO2 emission in the further 35 years. In the
hypothesis situation, all the energy resources construct can have some change in the next 35 years; especially,it shows that in China the gas and renewable resource can take a greater effect on reducing the CO2 emission,
only if Chinese government takes a positive and effective policy on changing the construct of fuel consumption,and the second industry also takes the advanced technology to improve the usage rate of fossil energy. At thesame time it is necessary to study or bring in the advanced technology from developed countries which are goodat protecting their environment. These can be used to enhance the increasing of non-fossil energy consumption
which will play a very great role on reducing the CO2 emission. What’s more, in order to solve the more andmore serious global pollution issue, it will be an inevitable trend in the further energy construct. This appearance
can give some countries, which still do not take care of environmental issue so much, an incentive to change
their idea of the using of the fossil and non-fossil energy consumption.
However, there is a limitation that this trend will only appear in a prefect hypothesis in which the usage of
non-fossil energy will increase rapidly without thinking about the natural limitation on the non-fossil energy orsome other unpredictable event. Meanwhile, it is a little difficult to estimate how much gas or renewable should
increase to reach this kind of trend. However, because the global green effect becomes more and more serious,
a relative explicit mass or property of different energy consumption is necessary to be estimated, which will
also be an important issue to be studied in the further.

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Appendix[Fig. A] Scatter Plot of GDP per capita and CO2 emissions for all 6 countries[Fig. B] Scatter Plot of GDP per capita and CO2 emissions for China

19[Fig. C] Scatter Plot of GDP per capita and CO2 emissions for USA[Fig. D] Scatter Plot of GDP per capita and CO2 emissions for Japan20

[Fig. E] Scatter Plot of GDP per capita and CO2 emissions for Canada[Fig. F] Scatter Plot of GDP per capita and CO2 emissions for S. Korea

21

[Fig. G] Scatter Plot of GDP per capita and CO2 emissions for Australia

22