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Published in revised form in Int. J. Oil, Gas and Coal Technology 2010:3(2):182-200

Page 1 of 17

Is there a cointegrating relationship between Australia’s fossil-fuel based carbon dioxide

emissions per capita and her GDP per capita?

Rajaratnam Shanthini# and Kanthi Perera1

Department of Chemical & Process Engineering

1Department of Engineering Mathematics

University of Peradeniya, Peradeniya 20400, Sri Lanka

Abstract: Carbon dioxide (CO2) emission per capita of Australia, a high-income economy

with a fossil fuel-rich fuel-mix, is proven to have a strong cointegrating relationship with her

gross domestic product (GDP) per capita. A conditional equilibrium correction model

(ECM) has been developed to quantify the relationship between the two variables by

employing the autoregressive distributed lag bound-testing approach to cointegration. The

long-run income elasticity is estimated to be as high as 0.7, and 36% of any deviation from

the long-run equilibrium is corrected within a year. In the short-run, 1% increase in GDP per

capita growth in the previous year leads to 0.33% increase in the current growth in CO2

emission per capita. The conditional ECM developed is robust against functional form

misspecification and have stable regression coefficients over the sample period studied.

Thus, it could be used to reliably predict the future CO2 emissions in Australia.

Keywords: ARDL; Australia; carbon dioxide; cointegration; ECM; emission modelling;

equilibrium correction; GDP per capita; long-run equilibrium; short-run dynamics.

1 Introduction

Incipient research studies on carbon dioxide (CO2) emission modelling (Shafik, 1994;

Shafik and Bandyopadhyay, 1992) found the CO2 emission to monotonically increase with

rising income. Schmalensee, Stoker, and Judson (1998), however, contradicted the above and

showed that the relationship between per capita CO2 emission and per capita income describes

an ‘inverse-U-shaped’ (quadratic) relationship, known as the Environmental Kuznets Curve

(EKC). They located falling per capita CO2 emission with rising income at per capita income

levels reached in high-income economies during the 1970s. The ‘inverse-U-shaped’

relationship was foreseen by de Bruyn, van den Bergh, and Opschoor (1998) as a temporary

phenomenon that was on its way to grow into an ‘N-shaped’ (cubic) relationship.

Econometric evidence was found for the existence of ‘N-shaped’ relationship between CO2

and income for a single country (Friedl and Getzner, 2003) as well as for a group of countries

(Galeotti and Lanza, 2005).

In explaining the ‘N-shaped’ relationship between emission and income, de Bruyn (2000)

observed that pollution reduction initiatives taken by some economies may have ceased ‘once

the technological opportunities for further reductions have been exhausted or have become

too expensive’. Carrying out a comprehensive survey of the empirical evidence and of

# Email: rshanthini@pdn.ac.lk

Published in revised form in Int. J. Oil, Gas and Coal Technology 2010:3(2):182-200

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possible causes of the EKC, Lieb (2003) concluded that ‘for a given pollutant an EKC will

only exist when policy measures are taken with respect to this pollutant’. Lieb also observed,

however, that the emission-income relationship monotonically rises for global pollutants, such

as CO2.

The phase diagram analysis of Unruh and Moomaw (1998) showed that the reduction in

the rate of increase in per capita CO2 emissions in some of the high-income economies during

the 1970s was caused by the ‘oil shocks of the 1970s’, during which the economically

prosperous countries looked for alternatives to raise their per capita incomes either in the

increase use of non-fossil fuel sources of energy, or in adapting innovative emission-reduction

technologies, or in the relatively less energy-intensive service sector.

The impact of the ‘oil shocks of the 1970s’ upon the fuel-mix of a number of high-income

economies was such that it has negated the otherwise strong relationships prevailed between

the CO2 emission of a country and her economic prosperity in high-income economies such as

Austria, France, Japan, Sweden, and United States (Aldy, 2005; Friedl and Getzner, 2003;

Lanne and Liski, 2004; Lindmark, 2002; Managi, 2006; Shanthini and Perera, 2007; Unruh

and Moomaw, 1998).

In case of Australia, however, the place of fossil-fuel in its fuel-mix has been so strong

that it has never fallen below 94% of the total energy consumption since 1965 (British

Petroleum, 2009). In 2006, for instance, about 44% of Australia’s total energy consumption

was met by coal, 33.6% by petroleum, 19% by natural gas, 2.8% by hydroelectricity, and

about 0.6% by other renewable energy sources (Energy Information Administration, 2008). It

is therefore highly likely that the fossil-fuel based CO2 emissions in Australia and her

economic prosperity may move together describing a cointegrating relationship (Engle and

Granger, 1987) between them.

The primary objective of this study is to seek for the probable existence of a cointegrating

relationship between Australia’s fossil-fuel based CO2 emission per capita and her gross

domestic product (GDP) per capita measured in market exchange rates, which is the proxy

used for economic prosperity. In case of firmly establishing a cointegrating relationship, the

next step is to develop a robust statistical model describing the long-run equilibrium

relationship and the short-run dynamic equation prevailing between the emission per capita

and GDP per capita for Australia. The existence of statistically significant long-run

equilibrium relationship and short-run dynamic equation would pave the way for forecasting

Australia’s fossil-fuel based CO2 emission per capita for hypothetical growth scenarios of her

GDP per capita (Amarawickrama and Hunt, 2008).

The econometric methodology used is the cointegration testing procedure advocated in the

autoregressive distributed lag (ARDL) bound-testing approach (Pesaran, Shin, and Smith,

2001). ARDL approach is adopted in this study since it is known to be better suited for

regressors of different order of integration (Pesaran, Shin, and Smith, 2001) and for small

sample sizes (Pesaran and Shin, 1999).

Cointegration is not new for the CO2 emission versus income research literature. Friedl

and Getzner (2003) showed evidence for the existence of cointegration between the Austrian

annual emission and income time series in the range of 1960 to 1999. They used the

augmented Dickey-Fuller test in the sense of Engle and Granger (1987) to arrive at the

conclusion, and then reverted back to ordinary least square (OLS) regression approach to

estimate the parameters of a simple linear model with a dummy variable accounting for

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structural break in 1974, of an EKC model, and of an ‘N-shaped’ model. Aldy (2005) tested

for cointegration among the emission, income, and income-squared state-specific time series

using the Engle-Granger type augmented Dickey-Fuller test for United States using the state-

level annual data spanning 1960 to 1999. Aldy found evidence for cointegration in 8 of the 48

states for production-based CO2 emissions and in 7 states for consumption-based CO2

emissions, and estimated the parameters of the EKC-type models of these states using the

state-specific dynamic OLS regression. Both Friedl and Getzner (2003) and Aldy (2005),

however, failed to complement their cointegration analyses with the standard equilibrium-

correction modelling approach which combine the long-run equilibrium relationship with the

short-run dynamic equation (Engle and Granger, 1987; Pesaran, Shin, and Smith, 2001).

In this paper, for the first-time to the best of our knowledge, the ARDL modelling

approach has been employed to capture the long-run equilibrium relationship between the

CO2 emission and income time series. The rest of the paper is organized in the following

manner. Time series data used for developing the model and their characteristics are presented

in Section 2 along with the rationale behind the model developed. A brief account of the

ARDL bound-testing approach used to develop the model is presented in Section 3. Section 4

presents the results and discussion and Section 5 concludes.

2 Data characteristics

2.1 Data used

Historic time series data on the Australian annual CO2 emission estimates are available in two

independent sources which are the Carbon Dioxide Information Analysis Center (Marland,

Boden, and Andres, 2008), abbreviated CDIAC, and the International Energy Agency (2009),

abbreviated IEA. CDIAC uses the ‘Reference Approach’ which is based on the supply of

energy in a country and IEA uses the ‘Sectoral Approach’ which includes emissions only

when the fuel is actually combusted (International Energy Agency, 2009, pp.31-32).

Figure 1 shows the cumulative CO2 emissions stemming from the burning of solid, liquid

and gaseous fossil fuel obtained from both sources. It is evident in Figure 1 that the emissions

from the two sources somewhat differ from each other since 1980 and that a decline in

emission during 1998 to 2001 has been reported by CDIAC and not by IEA. CDIAC

emissions estimates are based on the fuel consumption data available in the Energy Statistics

Database of United Nations Statistics Division, which reports a 9.2% decline in Australia’s

gross production of coal during 1998 to 1999 coupled with the 5.9% increase in her coal

exports during the same period. This fact explains the decline in emission in 1998 reported by

CDIAC (private communication with Tomas A. Boden, CDIAC Director). However, such

decline in Australia’s coal production has not been reported in any data sources of Australian

origin or in the IEA database. It is therefore IEA data source was chosen as the primary

emission data source of this study with the emission data from CDIAC added to cover the

range of 1960 to 1973.

The CO2 emission per capita time series data used in this study were derived from

dividing the aforementioned CO2 emission data by the mid-year population data obtained

from World Development Indicators (World Bank, 2008). Time series data on the Australian

annual GDP per capita were obtained from the same source as well. Unit of CO2 emission per

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capita used in this study is tonne of CO2 (which is equivalent to 1000 kg of CO2) and that of

GDP per capita is thousand of constant 2000 US$. It can be observed in Figure 2 that the data

used for model development, spanning the period 1960 to 2007, exhibit a tendency to move

together suggesting the probable existence of a cointegrating relationship between CO2

emissions per capita and GDP per capita. It is also to be noted in Figure 2 that both the CO2

emissions per capita growth and the GDP per capita growth slow down during the 1970s,

which is the decade of two major oil shocks, and that the emission appear to flatten out since

2000.

50

100

150

200

250

300

350

400

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

Year

CO

2

emissions

(million tonnes of CO

2

)

CDIAC

IEA

Figure 1 Australia’s estimated annual carbon dioxide emissions stemming from the burning of solid, liquid

and gaseous fossil fuel, obtained from CDIAC (Carbon Dioxide Information Analysis Center) and IEA

(International Energy Agency).

5

10

15

20

25

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Year

CO2

emissions

per capita

5

10

15

20

25

GDP per capita

GDP per capita

CO2 emissions per capita

Figure 2 Australia’s annual carbon dioxide emission per capita (in tonnes of CO2) and her annual GDP per

capita (in thousands of constant 2000 US$).

Figure 3 shows that the annual average marker crude oil price (British Petroleum, 2009)

experienced very little fluctuations till 1973, then a sharp increase during 1973 to 1974, and

another increase during 1978 and 1979. This decade of two major oil shocks is followed by a

general decline in oil price till 1998. From 1998 to 2008, oil price has increased once again.

The impact of the oil shock decade on Australian CO2 emission is such that the percentage

shares of CO2 emissions stemming from coal and oil burning switched their roles (Figure 4).

Emission from oil burning has been on the decline and that from coal burning has been on the

Published in revised form in Int. J. Oil, Gas and Coal Technology 2010:3(2):182-200

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increase since the oil-shock decade. It is therefore the influence of oil price upon the

relationship between CO2 emissions per capita and GDP per capita is also researched into in

this study.

0

20

40

60

80

100

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

Year

Annual Average Crude Price

(constant 2008 $ per barrel)

Arabian Light

Brent

Figure 3

Figure 3 Variation in the marker crude price during 1960 to 2008.

0%

10%

20%

30%

40%

50%

60%

70%

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

Year

Percentage share of

CO2 emissions

Coal

Oil

Gas

Figure 4 Percentage shares of carbon dioxide emissions stemming from burning of solid, liquid and gas fossil

fuels.

2.2 Model rationale

The study of the data presented in Section 2.1 led us to hypothesize that there exists a

cointegrating relationship between CO2 emissions per capita and GDP per capita, and that

these two variables must be strongly tied up in a long-run relationship. We also hypothesize

that the inclusion of oil price might strengthen the long-run equilibrium relationship, even

though the impact of oil price on CO2 emissions per capita would be many folds smaller than

the impact of GDP per capita on it. Since we are interested in the temporal growths of the

variables concerned, we use natural logarithms of the variables for model development.

Natural logarithms of CO2 emissions per capita, GDP per capita, and oil price are denoted by

C(t), G(t), and O(t), respectively, where t represents the time in years.

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2.3 Stationary tests

Since the landmark contribution of Engle and Granger (1987) in the regression analyses of

time series, it has become a routine procedure to test if the time-series concerned are

stationary or not. It is because an OLS regression model developed with non-stationary time

series data violate the standard assumptions for asymptotic analyses such as hypothesis tests

about the regression parameters (Granger and Newbold, 1974). Time series data on C, G and

O were thus subjected to augmented Dickey-Fuller test (ADF), GLS-detrended Dickey-Fuller

test (DF-GLS), Phillips-Perron test (PP), Ng and Perron test (NP-MZt), and Kwiatkowski,

Phillips, Schmidt, and Shin test (KPSS) of Dickey and Fuller (1979), Elliott, Rothenberg, and

Stock (1996), Phillips and Perron (1988), Ng and Perron (2001), and Kwiatkowski et al.

(1992), respectively. All tests except the KPSS test have the null hypothesis that the data

series tested contains a unit root, i.e. the tested series is non-stationary. The KPSS test has the

null of the tested series being stationary. The test statistics obtained at levels and at first

differences of C, G and O, using the statistical package EViews6 from Quantitative Micro

Software LLC, are listed in Table 1. All test statistics confirm that C and G are non-stationary

at level and stationary at first difference. That is, C and G are I(1) series. All tests but the

KPSS test point out that O is an I(1) series. When considering the KPSS test statistics, O must

be taken as an I(0) series. Since O is used as a regressor in the ARDL procedure used in this

study, whether O is an I(1) series or an I(0) series does not effect the analyses (Pesaran, Shin,

and Smith, 2001).

Table 1 Unit root / Stationary test statistics for C, G, and O (which are the respective natural logarithms of

CO2 emissions per capita, GDP per capita, and oil price) and their first differences.

Variable ADF test DF-GLS test PP test NP-MZt test KPSS test

C -1.91 [0] 0.94 [0] -2.06 2.48 0.73**

ΔC -6.72 [0]*** -6.44 [0]*** -6.72*** -3.34*** 0.27

G -0.89 [0] 2.46 [0] -0.86 4.52 0.74***

ΔG -5.72 [0]*** -5.77 [0]*** -5.71*** -3.34*** 0.13

O -1.23 [0] -0.85 [0] -1.38 -0.90 0.29

ΔO -6.47 [0]*** -6.39 [0]*** -6.48*** -3.41** 0.09

Note: Symbol Δ denotes first difference. Symbols *** and ** indicate significance at the 1% and 5% levels,

respectively. Given within the brackets are the respective lag lengths of the ADF and DF-GLS test statistics,

selected automatically based on Hannan-Quinn Criterion with the user specified maximum lag of 9. The PP,

NP-MZt and KPSS test statistics are based on the automatically selected Newey-West bandwidth using Parzen

kernel.

3 Econometric methodology

In the ARDL bound-testing approach (Pesaran and Shin, 1999; Pesaran, Shin, and Smith,

2001), testing of cointegration among a dependent variable Y and regressors Xj (j = 1, 2, …, k)

begins with the unrestricted equilibrium correction model (ECM), given by Eq. (1), in which

the regressors Xj may be I(0) or I(1) series.

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ε(t)(t-i) Xb(t)Xb

Y(t-i)a)(tX)Y(tY(t)

j

p

i

k

jijj

k

jj

p

iij

k

jjy

+++

+−+−+=

∑∑∑

∑∑

= ==

==

ΔΔ

Δ11Δ

1 11

11

0

ββα

(1)

where Δ symbolizes the first difference, α0 is the unrestricted intercept, βy is the coefficient of

the lagged level dependent variable Y and βj (j = 1, 2, …, k) are the coefficients of the lagged

level regressors Xj, t is time in year, ai are the coefficients of lagged ΔY, bj are the coefficients

of current ΔXj, bij are the coefficients of lagged ΔXj, k denotes the maximum number of

regressors used, p denotes the maximum lag length used, and ε(t) are the serially uncorrelated

residuals.

The first step in the ARDL bound testing approach is to determine the optimal value for

the lag length p in Eq. (1) so as to maintain the balance between mitigating the residual serial

correlation problem in Eq. (1) and refraining from over-parameterizing Eq. (1). This is done

by estimating Eq. (1) using the OLS procedure for different values of lag length p. For each

regression, Akaike’s Information Criterion (AIC) is determined. The lag length corresponding

to the regression with extreme value for AIC is chosen as the maximum lag length. The above

choice is further fortified by the determination of the Breusch-Godfrey Lagrange multiplier

test statistics for testing the null hypothesis of no residual serial correlation.

Having chosen the appropriate lag length p, the probable existence of a cointegrating

relationship in Eq. (1) is tested in the ARDL bound-testing procedure by calculating the F-

statistic under the null hypothesis that βy = βj (j = 1, 2, …, k) = 0 (that is, no cointegration)

against the alternative hypothesis that they are not. The F-statistic is then compared with the

asymptotic critical value bounds provided in Pesaran, Shin and Smith (2001) that are

reproduced in Table 2 for the cases of (i) a single regressor and (ii) two regressors.

If the F-statistic falls on the right-hand side of the upper bound critical value then the null

of no cointegration is rejected and cointegration among the variables is firmly established.

Consequently, a long-run equilibrium relationship among the dependent variable Y and the

regressors Xj shall be established in which the Xj are regarded as forcing Y. If the F-statistic

falls on the left-hand side of the lower bound critical value then the null cannot be rejected

and no cointegration among the variables is firmly established. Finally, if the F-statistic falls

between the lower and upper bound critical values, no conclusive decision could be reached.

Table 2 Asymptotic critical value bounds for F-statistic and t-ratio at 5% level of significance for the cases of

(i) a single regressor and (ii) two regressors.

Asymptotic critical value bounds at 5% level of significance

(i) with a single regressor (ii) with two regressors

Test

statistic Lower bound

I(0) Upper bound

I(1) Lower bound

I(0) Upper bound

I(1)

FIII 4.94 5.73 3.79 4.85

tIII -2.86 -3.22 -2.86 -3.53

Note: FIII is the F-statistic for testing βy = βj (j = 1, 2, …, k) = 0 in Eq. (1) and tIII is the t-ratio for testing βy = 0 in

Eq. (1). Critical values for FIII and tIII, are obtained from Tables CI(iii), and CII(iii) of Pesaran, Shin and Smith

(2001), respectively.

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The above test is complemented by the calculation of t-ratio under the null hypothesis of

βy = 0 in Eq. (1) against the alternative hypothesis that it is not. The t-ratio is then compared

with the asymptotic critical value bounds tabulated in Table 2. If the t-ratio falls on the right-

hand side of the upper bound critical value then the null of βy = 0 is rejected. If it falls on the

left-hand side of the lower bound critical value then the null cannot be rejected. If it falls

within the bounds then no conclusive decision could be reached.

Once the non-rejection of cointegration among the variables concerned are established,

the long-run equilibrium relationship is estimated using the ARDL approach detailed in

Pesaran and Shin (1999). First, the numerical values of the lag orders m and nj (j = 1, 2, … k)

of the ARDL(m,nj) model, expressed by Eq. (2), are estimated using the OLS procedure for

different combinations of m and nj (j = 1, 2, … k).

(t)(t-i)XY(t-i)Y(t) j

k

j

n

iij

m

ii

j

υτγσ

+++= ∑∑∑ = == 1 01

0 (2)

where σ0 is the constant term, γi are the coefficients of the lagged level dependent variable Y,

τij are the coefficients of the current and lagged level regressors Xj, k denotes the maximum

number of regressors used, m and nj denote the maximum lag lengths of Y and Xj,

respectively, and υ(t) are the serially uncorrelated residuals.

The lag lengths corresponding to the regression with minimum value for AIC or for

Schwarz Criterion (SC) give the ARDL(m,nj) model representing the long-run equilibrium

relationship. The coefficients of the long-run equilibrium relationship are estimated using the

OLS procedure, and the corresponding standard errors and t-statistics are estimated using the

Delta method as suggested in Pesaran and Shin (1999).

The residuals of the long-run equilibrium relationship is known as the equilibrium

correction term, which paves the way for estimating the short-run dynamic equation among Y

and Xj by setting up a conditional ECM corresponding to the ARDL(m,nj) model representing

the long-run equilibrium relationship. In the conditional ECM, the first difference of Y is

regressed on a one period lag of the equilibrium correction term, lagged first differences of Y

and current and lagged first differences of Xj using OLS regression (Pesaran, Shin, and Smith,

2001).

The short-run dynamic equation is considered statistically significant only if the residuals

of the model do not reject the null hypotheses of no residual serial correlation, no

heteroskedasticity among the residuals, and normally distributed residuals. These hypotheses

tests were carried out in this study using the Breusch-Godfrey Lagrange multiplier test,

Jarque-Bera normality test, and ARCH heteroskedasticity test, respectively. The stability of

the estimated parameters of the short-run dynamic equation is tested by employing the

Ramsey regression specification error test (RESET), which would reveal any misspecification

in the short-run dynamic equation such as non inclusion of all relevant variables. The stability

was further verified using the cumulative sum of recursive residuals (CUSUM) test (Brown,

Durbin, and Evans, 1975).

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4 Results and discussion

4.1 Cointegration test results

Cointegration was first tested with C as the dependent variable and G as the regressor. Eq. (1)

with k = 1 was estimated using the OLS regression for different values of lag length p. Since a

limited number of annual data were used for the analyses, maximum value of p was limited to

3. For each regression, AIC statistics, P-values of Breusch-Godfrey Lagrange multiplier test

statistics at prescribed lag orders 1 and 4, F-statistic, and t-ratio were estimated. All statistics,

except the AIC statistics, for the cases of p = 0, 1, 2, and 3 were evaluated using the data sets

spanning the periods 1961-2007, 1962-2007, 1963-2007, and 1964-2007, respectively. In

estimating the AIC statistics for all values of p, the data set spanning the period 1964-2007

was used, which was a necessity to aid comparison among the AIC values estimated.

The results, tabulated in Table 3, show that the AIC statistic is at its minimum at p = 3.

The corresponding P-values of the Breusch-Godfrey Lagrange multiplier test statistics are

large enough to not reject the null hypothesis of no residual serial correlation even at 10%

level of significance. The corresponding F-statistic listed in Table 3 falls on the right-hand

side of the respective upper bound critical value (listed in Table 2) resulting in the rejection of

the null of no cointegration at 5% level of significance. The t-ratio given in Table 3 reveals

that the null of βy = 0 in Eq. (1) is also rejected at 5% level of significance. It is therefore the

existence of cointegration among the variables C and G for Australia is strongly established

with G forcing C. That is, GDP per capita forces CO2 emissions per capita.

Table 3 Statistics for testing the existence of a cointegrating relationship between C and G in Eq. (1) with k =

1, with C as the dependent variable and G as the regressor.

Maximum lag length p = 0 p = 1 p = 2 p = 3

AIC -4.545 -4.522 -4.436 -4.726

Probability )1(

2

SC

χ

0.605 0.493 0.564 0.375

Probability )4(

2

SC

χ

0.667 0.761 0.038 0.404

FIII 6.48right 5.49mid 6.21right 8.32right

tIII -3.27right -2.77left -3.02mid -3.96right

Note: Probability )1(

2

SC

χ

and Probability )4(

2

SC

χ

denote the P-values of the Breusch-Godfrey Lagrange

multiplier test statistics for the null of no residual serial correlation at pre-specified lag orders 1 and 4,

respectively. Superscripts right, left, and mid denote that the statistic concerned falls on the right-hand side of the

upper critical bound, on the left-hand side of the lower critical bound, and in the middle of the critical bounds

tabulated in Table 2, respectively.

When the above analyses were repeated with G as the dependent variable and C as the

regressor, the F-statistics and t-ratios of all cases studied fell on the left-hand side of the

respective lower bound critical values, and thereby resulting in the non-rejection of the null of

no cointegration. It can therefore be concluded that, in case of Australia, GDP per capita

forces CO2 emissions per capita and CO2 emissions per capita does not force GDP per capita.

The results of the tests carried out in search of a cointegration relationship among C, G

and O with C as the dependent variable, tabulated in Table 4, show that p = 3 was chosen.

However, the corresponding F-statistic and t-ratio fall within the critical bound values (listed

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in Table 2) resulting in neither the rejection nor the non-rejection of the null of no

cointegration at 5% level of significance. It is therefore the existence of a long-run

relationship among C, G and O for Australia is not firmly established.

Table 4 Statistics for testing the existence of a cointegrating relationship among C, G and O in Eq. (1) with k

= 2, with C as the dependent variable and G and O as the regressors.

Maximum lag length p = 0 p = 1 p = 2 p = 3

AIC -4.571 -4.541 -4.417 -4.627

Probability )1(

2

SC

χ

0.498 0.247 0.853 0.395

Probability )4(

2

SC

χ

0.849 0.473 0.060 0.352

FIII 4.48mid 4.27mid 4.36mid 4.84mid

tIII -3.06mid -2.74low -2.82low -3.05mid

Note: Same as in Table 3.

4.2 Long-run equilibrium relationships

Since cointegration between the dependent variable C and the forcing variable G was firmly

established, as discussed in Section 4.1, as the next step, the long-run equilibrium relationship

between C and G was estimated. First the AIC and SC statistics were estimated for different

combinations of the lag orders m and n1 in the ARDL(m,n1) model, given by Eq. (2) with k =

1. Since we deal with annual data, the maximum lag length was limited to 3. We therefore

carried out 16 (= [3+1]2) regressions. Of which, the minimum AIC value was found to

correspond to the ARDL(1,2) model whereas the minimum SC value corresponded to the

ARDL(1,0) model. The coefficients of the levels relationship given by the ARDL(1,2) and

ARDL(1,0) models were estimated using the OLS procedure, and the corresponding standard

errors and t-statistics were estimated using the Delta method. The results are tabulated in

Table 5.

Table 5 shows that the coefficients and the standard errors of the ARDL(1,2) and

ARDL(1,0) models are very similar, and therefore the ARDL(1,2) model is chosen to represent

the long-run equilibrium relationship between C and G, and is expressed by Eq. (3).

ARDL(1,2): (t)tGC(t) 1

]5.13[]1.5[ ˆ

)(7020.07468.0

ν

++= (3)

where the numerical values given within the brackets are the t-statistics of the corresponding

coefficients and the residual (t)

1

ˆ

ν

is the equilibrium correction term.

Table 5 Coefficients and related statistics of the long-run equilibrium relationship between C and G.

Regressor Coefficient Standard Error t-statistic

ARDL(1,2):

Constant 0.7468 0.1473 5.07

G 0.7020 0.0519 13.5

ARDL(1,0):

constant 0.7070 0.1517 4.66

G 0.7202 0.0525 13.73

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Page 11 of 17

Since the null of no cointegration among the dependent variable C and the forcing

variables G and O was not rejected, as discussed in Section 4.1, the long-run equilibrium

relationship between C, G and O, given by Eq. (4), was also estimated following a procedure

similar to that described in the preceding paragraphs.

ARDL(1,2,0): (t)tOtGC(t) 2

]8.2[]6.19[]2.7[ ˆ

)(0396.0)(6842.06399.0

ν

+++= (4)

where the t-statistics are given within the brackets below the corresponding coefficients and

the residual (t)

2

ˆ

ν

is the equilibrium correction term.

The t-statistics in Eq. (3) and (4) prove that the coefficients of the forcing variables G and

O are statistically significant. Moreover, the long-run equilibrium relationships show that 1%

increase in GDP per capita causes about a 0.7% increase in CO2 emissions per capita, whereas

1% increase in oil price causes only an insignificant 0.04% increase in CO2 emissions per

capita.

4.3 Short-run dynamic equations

The short-run dynamic equation estimated from the conditional ECM corresponding to

ARDL(1,2), using the OLS procedure, is given in Table 6 along with the estimated essential

statistics. It is evident from the tabulated results that the coefficient of the equilibrium

correction term )(t 1

ˆ1−

ν

, known as the adjustment parameter, not only has the expected

negative sign, but also is highly significant, which can be taken as further proof of the

existence of a stable long-run equilibrium relationship (Bannerjee, Dolado, and Mestre, 1998).

The numerical value of the adjustment parameter reveals that any deviation from the long-run

equilibrium following a short-run disturbance is corrected by about 36% in a year. Tabulated

P-values also show that the coefficient of ΔG(t-1) is statistically significant at 10% level and

that the coefficients of ΔG(t) and ΔG(t-2) must be taken as zero. Therefore, we conclude that

the impact of GDP per capita growth upon the CO2 emissions per capita growth is such that

1% increase in the GDP per capita growth in the previous year would lead to about 0.33%

increase in the CO2 emissions per capita growth in the current year.

Table 6 Equilibrium correction form of the ARDL(1,2) model of Eq. (3).

Regressor Coefficient Standard Error t-Statistic P-value

)(t 1

ˆ1−

ν

-0.3640 0.0947 -3.84 0.0004

ΔG(t) -0.0116 0.1634 -0.07 0.9439

ΔG(t-1) 0.3247 0.1768 1.84 0.0736

ΔG(t-2) -0.0772 0.1570 -0.49 0.6256

adjusted R2 = 32.4%; Durbin-Watson statistic = 2.06

)4(

2

SC

χ

= 3.45 [0.49]; )2(

2

N

χ

= 0.49 [0.78]; )1(

2

H

χ

= 0.24 [0.62]; )1(

2

FF

χ

= 1.79 [0.18]

Note: The equilibrium correction term )(t 1

ˆ1−

ν

is the residual of Eq. (3). )4(

2

SC

χ

, )2(

2

N

χ

, )1(

2

H

χ

and )1(

2

FF

χ

denote chi-squared statistics of Breusch-Godfrey serial correlation LM test, Jarque-Bera normality test, ARCH

heteroskedasticity test, and RESET, respectively. The corresponding P-values are given within the brackets.

Published in revised form in Int. J. Oil, Gas and Coal Technology 2010:3(2):182-200

Page 12 of 17

P-values corresponding to the chi-squared statistics of the residual tests, tabulated in Table

6, show that none of the test statistics was significant even at 10% level of significance. We

therefore concluded that the parameter estimates of the short-run dynamic equation are

statistically significant. P-values corresponding to the RESET ruled out any model

misspecification in the short-run dynamic equation.

In order to further verify the stability of the short-run dynamic equation, we subjected it to

the CUSUM test. Figure 5 reveals that CUSUM confines itself within the 5% critical lines and

that the departure of CUSUM from the zero line is insignificant since 1980. It is therefore we

conclude that the estimated coefficients have remained nearly constants from one sample

period to the other providing further verification for the stability of the short-run dynamic

equation considered.

-20

-15

-10

-5

0

5

10

15

20

1970 1975 1980 1985 1990 1995 2000 2005

CUSUM

5% Significance

CUSUM

Year

Figure 5 Cumulative sum of recursive residuals (CUSUM) of the conditional ECM given in Table 6. The

broken lines represent the 5% critical limit.

The short-run dynamic equation estimated from the conditional ECM corresponding to

ARDL(1,2,0) is given in Table 7. The adjustment parameter is highly significant and its

numerical value reveals that any deviation from the long-run equilibrium following a short-

run disturbance is corrected by about 51% in a year. Moreover, the coefficient of ΔG(t-1) is

statistically significant at 5% level, the coefficients of ΔG(t) and ΔG(t-2) must be taken as

zero, and the coefficient of ΔO(t) is statistically significant at 10% level,. Therefore, we

conclude that 1% increase in the GDP per capita growth in the previous year would lead to

about 0.33% increase in the CO2 emissions per capita growth in the current year and that 1%

increase in the growth in oil price would lead to a negligible 0.02% increase in the CO2

emissions per capita growth in the same year. The P-values corresponding to the chi-squared

statistics confer statistical significance of the parameter estimates of the short-run dynamic

equation considered as well as the absence of any model misspecification.

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Page 13 of 17

Table 7 Equilibrium correction form of the ARDL(1,2,0) model of Eq. (4).

Regressor Coefficient Standard Error t-Statistic P-value

)(t 1

ˆ2−

ν

-0.5109 0.1205 -4.24 0.0001

ΔG(t) 0.1364 0.1528 0.89 0.3773

ΔG(t-1) 0.3353 0.1651 2.03 0.0489

ΔG(t-2) 0.0560 0.1476 0.38 0.7064

ΔO(t) 0.0230 0.0121 1.90 0.0642

adjusted R2 = 38.9%; Durbin-Watson statistic = 1.88

)4(

2

SC

χ

= 4.59 [0.33]; )2(

2

N

χ

= 0.55 [0.76]; )1(

2

H

χ

= 0.019 [0.89]; )1(

2

FF

χ

= 0.17 [0.68]

Note: The equilibrium correction term )(t 1

ˆ2−

ν

is the residual of Eq. (4). Chi-squared statistics are described in

Table 6.

4.4 CO2 emissions forecast

From the results presented in the preceding three subsections, it could be firmly concluded

that there exists a strong cointegrating relationship between CO2 emissions per capita and

GDP per capita and that the impact of oil price on CO2 emissions per capita is negligible.

Therefore, for forecasting purposes, we would consider only the long-run equilibrium

relationship given by Eq. (3) and the corresponding short-run dynamic equation given in

Table 6. Subjecting the latter for further statistical testing, we find that it has a Theil

inequality coefficient of 0.39 in the scale of 0, indicating perfect fit, to 1. The bias and the

variance proportions of the mean squared forecast error were estimated to be 0.0015 and

0.2075, respectively. The near zero bias proportion indicates that the mean of the forecast is

exactly the same as the mean of the actual series, and the 21% variance proportion indicates

that there is only a very small difference between the variations of the forecast and of the

actual series. Such small bias and variance proportions testify the forecasts of the short-run

dynamic equation considered are reliable.

The forecast equation is derived by substituting the equilibrium correction term from the

long-run equilibrium relationship given by Eq. (3) into the corresponding short-run dynamic

equation given in Table 6 as follows:

[

]

)(t.)G(t-.)-C(t-.(t) 1ΔG324707468.0170200136400ΔC −+−−= (5)

Figure 6 shows the CO2 emissions per capita obtained by dynamically simulating Eq. (5),

along with the actual co2pc values used for developing the model. Dynamical simulation of

Eq. (5) is carried out with the actual values of GDP per capita and with the actual value of

CO2 emissions per capita at 1960 as the initial emission input. The match between the model

predictions and the actual emissions seen in Figure 6 is commendable. Eq. (5) could therefore

be used for reliably forecasting Australia’s future CO2 emissions.

In forecasting CO2 emissions per capita after 2007, which is the end year of the data set

used, we used four different hypothetical GDP per capita growth rate scenarios, which were

the low-growth, reference-growth, average-growth, and high-growth scenarios. In these

scenarios, GDP per capita was assumed to grow at the rates of 0.7%, 1.4%, 2.5%, and 4.1%,

respectively, from 2007 onwards. The low, average and high GDP per capita growth rates

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Page 14 of 17

were the respective minimum, average and maximum GDP per capita growth rates prevailed

during the period 1992-2007. The reference growth scenario assumes current trends in

economic activity continue into the future (Commonwealth of Australia, 2008, pp.17).

8

12

16

20

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

Year

CO2 emissions per capita

(tonnes of CO2)

Actual

Dynamical simulation

Figure 6 Dynamically simulated CO2 emissions per capita using the forecast equation, Eq. (5), compared

with the actual values used for model development.

Forecasts of cumulative CO2 emissions in 2010, 2020 and 2030 were calculated by

multiplying the forecasted CO2 emissions per capita values for these years by the respective

medium variant population projections of United Nations (2009), which were 21,512,000 in

2010, 23,675,000 in 2020, and 25,656,000 at 2030, respectively. The results are tabulated in

Table 8.

Gurney et al. (2007) observed that in the absence of any major regional or global climate

change initiatives and without any significant technological breakthroughs, greenhouse gas

(GHG) emissions in Australia would reach 549, 638, and 695 million tonnes of CO2

equivalent in 2010, 2020, and 2030, respectively. The composition of CO2 emissions in the

total GHG emissions of Australia was about 70% in 1990 (Australian Bureau of Statistics,

2007) and about 74% on 2005 (Australian Bureau of Statistics, 2007). If this composition is

assumed to vary in the range of 74% to 80% during 2010 to 2030, the CO2 emissions would

fall in the range of 406 to 439 million tonnes of CO2 in 2010, 472 to 510 million tonnes of

CO2 in 2020, and 514 to 556 million tonnes of CO2 in 2030.

Table 8 Forecast of cumulative CO2 emissions stemming from the burning of solid, liquid and gaseous fossil

fuel at hypothetical growth rates of GDP per capita since 2007 and at United Nations predicted

medium variant population projections.

Fossil-fuel based CO2 emissions

projection (in million tonnes of CO2)

Hypothetical

scenario

GDP per capita

growth rate

since 2007

(in %)

2010 2020 2030

Low-growth 0.7 425 492 560

Reference-growth 1.4 429 521 622

Average-growth 2.5 434 568 732

High-growth 4.1 443 644 925

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Page 15 of 17

Retuning to the results tabulated in Table 8, it could be seen that the projected CO2

emissions in 2010 for the low, reference and average-growth scenarios fall in the range of 406

to 439 million tonnes of CO2. Projected CO2 emission in 2020 falls in the range of 472 – 510

million tonnes of CO2 only in the low-growth scenario. Projected CO2 emission in 2030 is

slightly larger than 556 million tonnes of CO2 in the low-growth scenario. As it is highly

likely that the GDP per capita growth rate of Australia during 2008 to 2030 lie below the

reference-growth rate considered in this study, we conclude that the CO2 emissions forecasts

made by the model developed are comparable with the emissions predicted by Gurney et al.

(2007).

The cumulative CO2 emissions stemming from the burning of solid, liquid and gaseous

fossil fuel in 2000 was 337 million tonnes of CO2. Percentage growths in cumulative CO2

emissions at 2010, 2020 and 2030 over 2000 level would, therefore, become 26%, 36%, and

46%, respectively, for the low-growth scenario and 27%, 40% and 55%, respectively, for the

reference-growth scenario. It should be borne in mind that such high forecasted percentage

increases of CO2 emissions over the 2000 level would be realized only if the economic growth

and energy consumption paths pursued by Australia since 1960 undergo no appreciable

changes in the future.

5 Conclusion

Existence of a strong cointegrating relationship between Australia’s CO2 emission per

capita and her GDP per capita is firmly established in this study. It is also proven that growing

GDP per capita forces the CO2 emissions per capita to grow, whereas the reverse is not true.

Inclusion of oil price as a forcing variable is found to have insignificant impact on CO2

emissions per capita which is not surprising because of the persistent high place of fossil-fuel

in her fuel-mix owing to perhaps her indigenous fossil-fuel reserves.

In the long-run, 1% increase in Australia’s GDP per capita causes about 0.7% increase in

her CO2 emission per capita. In the short-run, 1% increase in GDP per capita growth in the

previous year leads to about 0.33% increase in the current growth in CO2 emission per capita.

Moreover about 36% of any deviation from the long-run equilibrium is corrected within a

year. These results clearly prove that Australia’s current economic development path is CO2

emission intensive.

Such a strong tie between income and CO2 emissions results in the projection of the

cumulative CO2 emissions stemming from the burning of solid, liquid and gaseous fossil fuel

to grow by 36 to 40% in 2020 over the 2000 level for GDP per capita growth rates in the

range of 0.7 to 1.4%. It should be borne in mind that such high forecasted percentage

increases in CO2 emissions would become a reality only in the absence of proactive actions

taken by the Australian government to weaken the strong cointegrating relationship existing

between CO2 emissions and economic prosperity, measured by GDP per capita.

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