The 21st century being marked by the transition to green energies and to the 2020 and 2050 milestones set by global meetings on climate changes, our current transition pace is far too low when taking into account the expected progression of the GDP, and countries' carbon footprint instead of their carbon emission.

1. 1
MEMOIRE
Présenté en vue de l'obtention du Master en science de
gestion - Année académique 2015-2016
The evolution of the GDP resulting from a
diminution of the natural resources.
Par Efraim CHABABE
Directeur: Professeur Yves DOMINICY
Codirecteur: Professeur Bruno KESTEMONT
Assesseur: Professeur Julien RAVET
Expert: Benjamin RAUSCH

2. 2
1. Introduction 3
2. Data and methods 5
3. Analysis and Results 7
3.1 The Kaya equation 7
3.2 Cobb-Douglas 8
3.2.1 Restrained model with CO2 10
3.2.2 Restrained Model with Carbon Footprint 17
4. Discussion 24
5. Conclusion 24
6. References 27
7. Appendix 30

3. 3
1. Introduction
The scarcity of the natural resources has always been ignored because it was seen as
having no impact on the economy. For this reason, it has become since a couple of
years one of the major problems in our world.
Indeed, as announced by Global Footprint Network, the world has entered in the last
century in a situation where its consumption of natural resources has exceeded its
capacity of production, and hence we are facing the growing scarcity of these
resources. The European Commission came to the same conclusion in 2011, when it
communicated that we cannot maintain our current way of growth, based on the
extraction of natural resources. We know that after 2050, most of our resources will be
in a critical state of scarcity (Sverdrup et al., 2013), which will generate increasingly
important price fluctuations in the coming years and conflicts to have these resources.
In addition to this, if we do not change our habits, we will need two planets like Earth
to please everyone (Townsend & Burke, 2002).
Becoming conscious of the need to depend less on these major decreasing resources,
all countries present at the 2010 Cancun Climate Change Conference agreed on a
precise objective of limiting the rise of the global temperature to maximum two degrees
compared to pre-industrial times. The rise of the temperature being influenced by our
emissions of CO2 and by our consumption of natural resources, European Union’s
goal of reducing the Greenhouse Gases (GHG) emissions by at least 80% should help
the rich countries to progressively decrease their consumption of CO2 and scarce
resources (Cancun: une étape clé pour un accord international sur le climat., 2010). In
order to attain this goal, the European Union established for the developed countries
another goal, of reducing their greenhouse gas emissions by 80% to 95% by 2050, in
comparison to 1990 levels. Each developed country has established its own ‘Low
Carbon Development Strategies’, to reduce its greenhouse gas emissions, which are
easier to measure and to control than the global temperature rise. Since the conference
of 2010, ‘Low Carbon Economy’ roadmaps have also been linked to other roadmaps,
as the Energy roadmap or the Transport roadmap, in order to increase the efficiency
of this low carbon transition (VITO and Co., 2013).

4. 4
The issue is, as stated by Jan-Erik Lane in 2013, that the accumulation of GHG in the
atmosphere is still today strongly positively linked with economic growth and with the
Gross Domestic Product (GDP) indicator. There is in addition to that an intermediating
positive link between total GDP and total emissions, which is linked to the energy
consumption, which has increased dramatically since 1970. The energy consumption
has indeed more than doubled between 1970 and 2007, following exactly the same
growth rate than the global GDP (Akan et al.; 2010). Diminution of the GHG is so set
up actually that if nothing happens, the scarcity of these resources, which causes a
forced reduction of the use of natural resources, will force the GDP to follow the same
path and to decrease as well. It is true that the energy consumption per GDP unit has
decreased, due to technological innovations, but our necessity to grow is more than
enough to push our total energy consumption to continue to rise anyway (Lane; 2013).
Reducing emissions of CO2 and our energy consumption today would actually mean
decreasing economic growth, as overall energy consumption determines GDP, which
in turn determines to a large extent the total emissions of CO2 (Lane; 2013).
And as any other developed country, Belgium has also accepted to reduce significantly
its use of fossil fuels and its GHG emissions by 80-95% for 2050. In its report made by
VITO and Climact (2013), Belgian authorities have already noticed that this was an
achievable goal for our world, but that it will require important changes in all the sectors
that constitute our society and in all the habits that we have in our daily life. According
to the ‘Scenarios for a low carbon Belgium by 2050’, that we can take as reference
since it is one of the most documented reports of the situation in the world, we know
that there are solutions and opportunities linked to this forced shift to a low carbon
society. Some countries, regions and industries have already implemented their low
carbon roadmap to anticipate future threats and to foresee future opportunities, for
example in the field of innovation, green jobs, lower energy bills (Arievoorburg; 2015),
and waste management (OECD; 2015). As said by VITO and Climact (2013), investing
in a low carbon society can even be linked to less total system costs, as the
investments are compensated by lower fuel use and expense.
This report also puts the emphasis on the urgency of the change. ‘As an economy is
never static, it goes along with changes, and the cost that goes with it. Economies have
however a tendency to be 'locked-in' to paths determined by past investment decisions,

5. 5
and so to respond slowly when it comes to changes’ (European Commission; 2011).
Over the last century, the use of renewable resources has declined while the extraction
of non-renewable resources has grown, reflecting the trend to move from an
agricultural economy to an industrial one (OECD; 2013). Our current industrial
economy is also a temporary one moving to something else, and as for every period,
innovation, politics and competition will let the best adapted firms grow at the expense
of others (European Commission; 2011). The problem with this is that the current pace
of change is not fast enough and has to evolve quickly, and the longer we wait the
higher our pace will have to be (Toossi; 2007). As we already reduced our GHG
emissions by 0.3% per year from 1990 to 2010 thanks to innovations, and political
decisions, we have to have an average reduction of around 5% per year from now until
2050, if we want to attain our goal (Climact and VITO; 2013).
The topic of this paper is to find the decoupling factor between the energy use and the
CO2 emissions, and between the GDP and the CO2. This two factors will be calculated
for one country, Belgium, and they will help to explain if the country can continue to
grow economically of it reduces its use of natural resources.
2. Data and methods
In order to respond to the research question, a first analyze will be done using the
equation of Kaya (1997). This method being a good first step, because of its simplicity,
as it restrains the CO2 of being only determined by to the world population, the GDP
and by the energy consumption. This method is as well a good way to have a first look
to the difficulties linked to this challenge. Kaya’s equation will give an idea of the
precise decoupling factor that would be needed to continue to grow and in the same
time to reduce Belgian’s GHG emissions to stay under the 2°C increase in the global
temperature, as compared to pre-industrial levels. Comparing this factor to our current
pace of change will help us to have a first insight of the project’s feasibility and of the
effort that needs to done.
After that, a deeper investigation will be required in order to confirm the first trend. For
this we will use the equation of Cobb-Douglas, the linear multiple regression and an
ordinary least squares (OLS) approach. In the complete version of the Cobb-Douglas

6. 6
equation, we already know the expected average GDP growth of 1,7% per year until
2060 (OECD; 2012), the CO2 reduction expected by 2050, which is a 80% reduction
compared to the 1990 level (Climact & VITO; 2013).
As independent variables to explain the GDP growth, we use the CO2 consumptions,
the energy consumptions, the flows of foreign direct investments and the levels of
capital formations, that we found on the internet site of Eurostat and of OECD-stat, to
predict the future. Cobb-Douglas’ equation, completed with the real values of the
parameters alpha (α) will allow a predictive analysis of the evolution of the different
variables with the evolution of the GDP, and an analysis of the future values of these
variables in a neoclassical framework (with all the hypothesis of a “perfect market’’).
The parameters will be calculated with the multiple regression analysis tool on Excel,
and if it is not possible, the ordinary least squares approach will be used. The GDP will
here be the dependent variable, explained, with the Excel's multiple regression tool or
with an OLS calculation, by the dependent variables which are the CO2 consumptions
(CO2), the energy consumptions (ENC), the foreign direct investments inflows (FDI)
and the capital (K). The needed energy consumption will then be calculated, and will
give an idea of the feasibility of the objective. This will help to calculate the energetic
mix (CO2/ENC) and GHG intensity (GDP/CO2) that enables our economy to continue
to grow, by reducing our CO2 emissions by 80 percent for 2050.
In comparison to the equation of Kaya, the analysis done with the Cobb-Douglas
formula adds the influence of foreign direct investment inflows and of the capital. It is
more precise in a way that each variable’s value is weighted according to the
importance of its role in the GDP growth. This method will be useful in the research,
because after having analyzed the relationship between the GDP and the C02
emissions, with the current link that exist between them, it will be possible to see if, as
VITO and Climact did it in their review « Scenarios for a Low Carbon Belgium by
2050 », the importance of the CO2 emission in the determination of the GDP will really
decrease, and if the energy efficiency will by higher in the future.
This research paper will be concluded by a link between the results of the Kaya and
the Cobb-Douglas analysis, and the solutions brought by VITO and Climact in their
analysis. In their paper, they provide solutions for a fast change, after having insisted

7. 7
on the necessity of a behavioral change, and of an increase in the pace of technological
improvements. This paper will put figures on the needed changes announced, to see
the compatibility of our calculated numbers with their possible solutions.
3. Analysis and Results
3.1 The Kaya equation
The Kaya equation, developed by Yoichi Kaya, a Japanese economist specialized in
the energy sector, has the objective of providing a link between CO2 emitted by an
economy or by the world, its population, its GDP, and the energy it used to generate
the GDP.
The equation is:
(1) CO2= Population X (GDP/population) X (Energy/GDP) X (CO2/Energy).
In this equation, the ratio (GDP/Population) represents the bargaining power, the ratio
(Energy/GDP) represents the energy efficiency, and (CO2/Energy) represents the
energetic mix.
By using the simplification of the Energy, in the two last terms of equation (1), and of
the population in the two first terms of the same equation, we obtain:
(2) CO2 = GDP x (CO2/GDP).
To calculate the changes needed by 2050, this equation (2) however needs to be
changed to:
(3) δCO2= δGDP x δ(CO2/GDP),
where delta (δ) represents the factor of change, between 2010 and 2050.
δCO2 is known, and is equal to 0,2 (as Belgium wants to reduce its reductions by at
least 80% based on the levels of 1990, which are nearly the same as the levels of
2010). δGDP can be calculated easily. The expected growth of the GDP for the coming
years, partially based on past figures, is at 1,7% per year. We know as well that the
GDP has to be multiplied by 1,96 from 2010 to 2050.

8. 8
By replacing the real figures in the equation (3), we have:
(4) 0,2= 1,96 x δ(CO2/GDP).
In order to grow by 1.7% per year, and knowing that Belgium, as many of the European
countries, wants to reduce its GHG emissions by at least 80 percent, the equation of
Kaya shows that δ(CO2/GDP) has to be divided by at least 10,2. This means that by
2050, Belgians will have to be able reject 10.2 times less CO2 for the same amount of
production as today.
As we now come back to the equation (2), the factor (CO2/GDP) has been found by a
simplifying two factors of the equation (1), the energy efficiency (ENC/GDP) and the
energetic mix (CO2/ENC). The values of these two factors were, in 2005, respectively
at 130% and 110% from their levels of 1970. The ratio (CO2/GDP), which is found by
the multiplication of the energy efficiency and the energetic mix, was so, in 2005, at
145% of its 1970’s level. It has been multiplied by 1,43 in 35 years, in the world (OECD;
2013), while it now needs to be multiplied by 10 in the next 40 years.
The European government has planned to improve by 20% its energy efficiency by
2020, this objective is part of the 20-20-20 objectives that aims to cut by 20% the GHG
emissions, from 1990 levels, to have 20% of the EU energy from renewables, and to
improve the energy efficiency by 20%. This is a good start, but the simple equation of
Kaya shows that it is far from being enough.
3.2 Cobb-Douglas
In order to not restrain the GDP of being only influenced by the CO2 emissions, the
population and the energy, this paper will use a modified version of the Cobb-Douglas
equation, as a lot of other researches on this topic did. So, as Kais Saidi and Sami
Hammami did it in their paper of 2015, the starting model will be:
(5) GDP= f (ENC; CO2; K; L; FDI).
The gross domestic product (GDP) is here the dependent variable, influenced by the
energy consumption (ENC), the CO2 consumption (CO2), the capital stock (K), the

9. 9
population (L) and the foreign direct investment inflows (FDI), which are the
independent variables. In order to facilitate the calculation of the real impact of the
energy and the CO2 consumption on the GDP, and to better analyze their
relationships, the GDP per capita will be used in our calculation, and the population
will be eliminated from the previous model.
We so have:
(6) GDP/ Capita = f (ENC/c; CO2/c; K/c; FDI/c).
And with the multiple linear regression, this model becomes:
(7) ln(GDP/c)= α0 + α1*ln(ENC/c) + α2*ln(CO2/c) + α3*ln(FDI/c) + α4*ln(K/c) + ε,
with the αi representing the ponderation of the influence of the different dependent
variables on the GDP, α0 being a constant. The little ‘c', in the ratios (…./c) represents
the values per capita of the different variables.
Before predicting the future values, each factor will first of all to be analyzed separately
according to the literature review, to see to the relevance of its potential to predict the
future of the GDP.
The ENC/c is supposed to evolve and to contribute positively, in the future, to the
evolution of the GDP. The continuous improvements of the living conditions in Belgium
indeed always require more energy. The nature of the energy is however unknown,
but the part of the fossil fuel is supposed to lower in favor of the renewable energies.
The CO2/c is expected to evolve negatively, and to contribute negatively to the GDP.
To limit the rise of the temperature of the earth by less than 2 degrees Celsius, and as
planned by the European-Union and explained by VITO and Climact in their research:
’Scenarios for a low carbon Belgium by 2050’, the CO2 emissions have to decrease
by at least 80%, in comparison to the level of 1990, for 2050. Knowing that the levels
of 2010 were higher than the ones of 1990, and that the population is expected to grow
by a factor 1.36, from 2010 to 2050, according to the data of Eurostat, the CO2 per
capita has to decrease by a factor 7,46 in Belgium in order to respect its objective. This

10. 10
factor has been calculated according the levels of CO2 emissions of 1990, of 2010,
and the increase of the population between 1990 and 2010. This is supposed to reduce
the GDP that will have to be increased by other variables, those having a positive
influence.
FDI inflows are expected to evolve independently from the GDP in the future. FDI are
indeed influenced by the investment rates by the world citizens, and the investments
are influenced by the age of the people investing. Young people tend to invest while
older people tend to use their money previously invested. The OECD countries see
their population becoming older and older, so the money invested tends to lower, but
the poor and the developing countries have high birth rates, high young people so high
investment rates. These two contrary movements will stabilize the FDI, independently
of the GDP which is expected to continue to increase, until 2030. After 2030 and at
least until 2050, the FDI inflows will decrease, because even in the poor countries, the
population will become older (OECD; 2012).
And finally, K, the capital, is expected to have a limited positive impact of the GDP in
the future, as the theory of diminishing returns limits the possible influence that capital
can have on the growth of the GDP.
Due to the fact that FDI and K is expected to evolve independently on the GDP and
that the two other terms, in the future, will not be present anymore in the Cobb-Douglas
equation which is destined to predict the future relations of the GDP, the CO2, and the
energy consumption.
3.2.1 Restrained model with CO2
The equation that we will use to predict the future is different from the equation used
by Saïdi in 2015 to described the past. The predictive equation is:
(8) GDP/ Capita = f (ENC;CO2)
(9) ln(GDP/c) = α0 + α1*ln(ENC/c) + α2*ln(CO2/c) + ε
To calculate the values of the parameters α, the past figures of the table 1 will be used,
but this time without FDI and K, which will be independent from the GDP in the future.

11. 11
Table 1: past values of ln(GDP/c), ln(ENC/c) and ln(CO2/c). To have real values without 'ln', see appendix 11.
ln(GDP/c) ln(ENC/c) ln(CO2/c)
1990 10,00 8,40 9,19
1991 10,02 8,46 9,24
1992 10,03 8,46 9,25
1993 10,02 8,44 9,21
1994 10,05 8,49 9,24
1995 10,07 8,50 9,23
1996 10,09 8,56 9,28
1997 10,12 8,56 9,25
1998 10,14 8,57 9,30
1999 10,17 8,58 9,28
2000 10,21 8,58 9,25
2001 10,22 8,58 9,25
2002 10,23 8,54 9,20
2003 10,23 8,59 9,23
2004 10,26 8,57 9,19
2005 10,28 8,57 9,17
2006 10,30 8,55 9,15
2007 10,32 8,52 9,13
2008 10,32 8,54 9,13
2009 10,28 8,49 9,10
2010 10,30 8,55 9,15
2011 10,30 8,51 9,03
2012 10,29 8,44
Using the excel multiple regression tool, the program provides the results in the form
tables of values, that gives the probable estimates of the parameters, and the
probability that the estimates can be taken as right.

12. 12
Regression Statistics
Multiple R 0,963
R Square 0,928
Adjusted R Square 0,921
Standard Error 0,032
Observations 22
df SS MS F Significance F
Regression 2 0,244 0,122 122,714 0,00000000001
Residual 19 0,019 0,001
Total 21 0,263
Coefficients Standard
Error
t Stat P-value Lower 95% Upper 95%
Intercept 8,649 1,342 6,446 0,0000035250 5,841 11,458
ln(ENC/c) 1,571 0,132 11,912 0,0000000003 1,295 1,847
ln(CO2/c) -1,289 0,106 -12,217 0,0000000002 -1,510 -1,068
The adjusted R^2 of 0,92 shows that 92% of the variability of the GDP can be explained
by the energy consumption and the CO2 emissions. The other 8% of the variability
being influenced by factors that are not analyzed in this research paper. The adjusted
R^2 when the equation was containing the variables FDI and K, in addition of the
energy consumption and the CO2 emissions, was equal to 0,88, meaning that
eliminating K and FDI was right.
The critical value of F of 10^(-12), means that the probability that these estimations are
wrong is equal to 0,000000001%, so nearly equal to 0.
In addition of the analysis of the adjusted R^2 and the critical value of F, P value can
be analyzed to show the reliability of the results. As we check it for a significance level
of 0.05, the P values of the constant, ln(ENC/c) and ln(CO2/c) have to be lower than
0,05 in order to be accepted.

13. 13
P value represents the probability, according to the data encoded, that an independent
variable has no effect on the dependent variable. All the P values are here much lower
than 0,05, so we have enough evidence here to reject the hypothesis that they have
no effect on the GDP.
As the 3 reliability tests were positive, the proposed coefficients can be considered,
and the equation becomes:
(10) lnGDP/c = 8,65+ 1,57*ln(ENC/c) - 1,28*ln(CO2/c) + ε.
Now, predicting the future becomes possible, as values of the parameter α’s and the
desired values of GDP and CO2 are already known, the energy consumption is the
only unknown factor. The expected growth of the GDP per capita is indeed of 1,7% per
year, and the expected CO2 level for 2050, is one fifth of the 1990’s one. The GDP per
capita has thus to be multiplied by a factor 1,96 between 2010 and 2050. The CO2 has
to be divided by a factor 5,5, as the CO2 level has increased from 1990 to 2010. In
2011 and 2012, the level of CO2 has however decreased drastically, and it was in 2012
already lower than in 1990 (see appendix). Concerning the levels per capita, they are
decreasing since 1998 for the CO2, and since 2003 for the energy consumption. Using
the formula above (10), and the known future values of the GDP/c and the CO2/c, we
have:
Table 2: future values of ln(GDP/c), ln(ENC/c) and ln(CO2/c). See appendix 3.
ln(GDP/Capita) ln(ENC/Capita) ln(CO2/Capita)
2013 10,30 8,33 8,93
2014 10,32 8,30 8,88
2015 10,34 8,27 8,83
2020 10,42 8,13 8,59
2025 10,50 7,98 8,34
2030 10,59 7,84 8,10
2035 10,67 7,69 7,85
2040 10,76 7,55 7,61
2045 10,84 7,40 7,37

14. 14
2050 10,93 7,27 7,14
where ln(ENC/c) = (ln(GDP/c) - 8,65 - ( -1,28*ln(CO2/c)) / 1,57.
Table 3: Future values ln(GDP/c), ln(ENC/c) and ln(CO2/c), transformed in their real values
(GDP/Capita)
(EURO)
(ENC/Capita)
(EURO)
(CO2/Capita)
(Kg of Oil
equivalent)
CO2/ENC
(Kg of oil
per
EURO)
GDP/CO2
(EURO
per Kg of
oil)
2013 29.807 4.159 7.555 1,82 3,95
2014 30.314 4.036 7.187 1,78 4,22
2015 30.829 3.917 6.836 1,75 4,51
2020 33.540 3.398 5.378 1,58 6,24
2025 36.490 2.925 4.188 1,43 8,71
2030 39.699 2.537 3.294 1,30 12,05
2035 43.190 2.184 2.566 1,17 16,83
2040 46.988 1.895 2.018 1,07 23,28
2045 51.120 1.644 1.588 0,97 32,20
2050 55.615 1.438 1.261 0,88 44,09
The exponential is then used to return to the values without the logarithm, and to
analyze the results easier.
To achieve its objectives concerning the increase of the GDP and the decrease of the
CO2 emissions, in the same time, the energy consumption per capita in Belgium has
to decrease according to the current link between the GDP, the ENC and the CO2. As
the CO2 is negatively linked to the GDP, a higher GDP means a lower CO2 level. The
demanded diminution of the CO2 is, in this scenario, enough to guarantee on its own
the expected increase of the GDP. The desired CO2 reduction also permits to diminish
the ENC/c, which is positively linked with the GDP, which means that a diminution of
the ENC/c is generally linked to a diminution of the GDP. The ENC/c can diminish here,
because the diminution of the CO2 is so important, having a positive impact on the
GDP/c, that the negative impact of a diminution of the ENC/c can still be linked with a
increase of the GDP per capita of 1,7% per year.

15. 15
Even if the diminution of ENC/c can seem uninteresting, because it is linked with a
diminution of the GDP/c, it is however important in a technological way. The diminution
of the ENC/c, following a forced diminution of the CO2/c, can lighten the effort that
needs to be done concerning the CO2/ENC ratio. The energetic mix, in this scenario
has only to move from 1,82 to 0,88. This move, minimized to the lowest possible in this
case, has still an increase by a factor of 2,14 for 2050. Even if it is known that reducing
the CO2 emissions by 80% will be difficult and will require a lot of changes in the
political and in the technological world, decreasing the energetic mix will require much
less efforts. The CO2/ENC (energetic mix) has to evolve by a factor 2,5 from 2010 to
2050, while the ratio already evolved by a factor 1,2 from 1990 to 2010.
Here is the graph showing the past and the expected future value of the energetic mix.
There is however a bigger problem with the GDP/CO2 ratio, which represents the
productivity of the CO2. This ratio, linking the demanded decrease of the CO2 with the
desired growth of the GDP shows the effort that needs to be done in a cultural or
technological way. As the graph below clearly shows it, some quick changes have to
occur in order to separate our production from our CO2 emissions. As the GDP/CO2
ratio improved by 1,42 from 1990 to 2010, it now needs to grow by a factor 14 from
2010 to 2050. Even the needed shift for the energetic mix (CO2/ENC) is clearly
achievable, the needed progression of the CO2 productivity (GDP/CO2) is only
achievable if there is an immediate and sharp change in the way we build our GDP.
0
0,55
1,1
1,65
2,2
2,75
1990 2000 2010 2020 2030 2040 2050
CO2/ENC
Figure 1: graph representing the evolution of the ratio CO2/ENC across the time. Own calculations, see appendix 3.

16. 16
In addition to that, Belgium, as all the countries of the OECD, have a lower CO2
productivity growth rate compared to the world average; poor and developing countries
having however higher productivity growth rates as they progress thanks to the
technological progress and thanks to their catch up phenomena. Belgium progress in
CO2 productivity, as the productivity of all the leading countries, is only influenced by
the technological progress, which is around 1,3% per year according to the OECD.
(OECD, 2012). This percentage needs to change and to be followed by behavioral
changes, as said by VITO and Climact in 2013. They indeed came to the same
conclusion in their study, when they claimed that the only hope for Belgium would be
to combine technological improvements in strategic sectors with general behavior
changes.
In this research about the Belgian values, an issue occurs. Even if all the values used
come from serious sources, as Eurostat, OECD-stat,… , the analysis is biased by the
way the calculation of the CO2 is done. This analysis is done according to the link
between the GDP and the CO2, which is not counting all the CO2 we generate. As we
look only at the CO2 emissions, it can be seen that since 1998, there is an absolute
decoupling between GDP and CO2 in Belgium. This was only possible because big
companies started to outsource most of their polluting activities to developing countries
(Herald; 2014). The CO2 figures that are published and used in this paper, are so not
counting all the CO2 consumption but the CO2 emitted by the Belgian territory. All the
imported products are not counted in this analysis, and as suspected by Lisa Medearis
in 2011, rich countries have found a solution to decrease their CO2 emissions by
outsourcing all the activities that are too polluting. They can so claim that they reduce
their CO2 levels. It is good for them, but these activities would then be made by low
0
12,5
25
37,5
50
1990 2000 2010 2020 2030 2040 2050
GDP/CO2
Figure 2: graph of the evolution of the CO2 productivity (GDP/CO2) across the time.

17. 17
technological countries that pollute more to do the same activities (Muradian; 2002, Xu
and Dietzenbacher; 2014). From 1995 to 2007, developed countries maintained a high
growth of “consuming” emissions but having a relatively low growth of their territorial
emissions, at the expense of environmental conditions elsewhere (Xu and
Dietzenbacher, 2014). As shown by the following graph provided by Carbon Dioxide
Analysis Center, global pollution is in this scenario not decoupled with the GDP, and
still rising today.
To solve this biased vision, the CO2 consumption has to be analyses instead of the
CO2 production. Even if the figures therefore are more difficult to find, ecological
companies have mostly used the Carbon Footprint to calculate the total CO2
consumption, so we will take it as the most suitable indicator here.
3.2.2 Restrained Model with Carbon Footprint
We replace CO2 Carbon Footprint (CF) in the equation (8)
(11) GDP/ Capita = f (ENC/c; CF/c)
(12) ln(GDP/c) = α0 + α1*ln(ENC/c) + α5*ln(CF/c) + ε
Figure 3: the evolution of the emissions of carbon per capita cross the time.

18. 18
α5 is here a new parameter, supposed to correct and to show the real relationship
between GDP and the CO2, here represented by the carbon footprint (CF).
A new calculation so needs to be done, to calculate ln(CF/c), to reestimate the future values
of the different parameters, thanks to the multiple linear regression analysis tool.
Table 4: past figures of ln(GDP/c), ln(ENC/c) and ln(CF/c). see appendix 4
Ln (GDP/c) Ln(ENC/c) Ln(CF/c)
1990 10,00 8,40 9,68
1991 10,02 8,46 9,70
1992 10,03 8,46 9,84
1993 10,02 8,44 9,70
1994 10,05 8,49 9,71
1995 10,07 8,50 9,75
1996 10,09 8,56 9,75
1997 10,12 8,56 9,78
1998 10,14 8,57 9,82
1999 10,17 8,58 9,87
2000 10,21 8,58 9,90
2001 10,22 8,58 9,88
2002 10,23 8,54 9,92
2003 10,23 8,59 9,88
2004 10,26 8,57 10,00
2005 10,28 8,57 9,89
2006 10,30 8,55 9,98
2007 10,32 8,52 9,99
2008 10,32 8,54 10,05
2009 10,28 8,49 9,95
2010 10,30 8,55 10,01
2011 10,30 8,51 No data

19. 19
Ln (GDP/c) Ln(ENC/c) Ln(CF/c)
2012 10,29 8,44 No data
As for the former analysis, with the CO2, the excel software proposes new results to
the different elements analyzed by its multiple linear regression tool. This will give the
values of the parameters α that will help for the calculation of the future values.
Regression Statistics
Multiple R 0,953
R Square 0,909
Adjusted R Square 0,899
Standard Error 0,035
Observations 21
df SS MS F Significance F
Regression 2 0,225 0,113 89,836 0,0000
Residual 18 0,023 0,001
Total 20 0,248
Coefficients Standard
Error
t Stat P-value Lower 95% Upper 95%
Intercept -0,646 1,242 -0,520 0,609 -3,256 1,963
ln(ENC/c) 0,304 0,177 1,715 0,103 -0,068 0,676
ln(CF/c) 0,835 0,084 9,960 0,000 0,659 1,011
Due to the results of P value, ln(ENC/c) has to be excluded. Perhaps this is just a
model where ln(GDP/c) = constant + ln(CF/c), but we need to compare the variation of
carbon and the variation of the GDP, which are known, with the resulting variation of
energy consumption. So, another model has to be found. The model chosen was the

20. 20
method of least squares (OLS). It goes with our formula (12) «GDP/c = α0 + α1*ENC/c
+ α5*CF/c», as it is based on the overall function (7).
First of all, this table has to be filled in. The values of Y, x1 and x2 being known, the
rest has been calculated.
Table 5: OLS: Values and calculations to find ᾱ and β.
Y (=Ln
(GDP/c)
(yi-
ym)
x1 (=
Ln(EN/c
))
(x1-
x1m)
(x1-x1m)
^2
(x1-
x1m)(yi-
ym)
x2 (=
LN(CF/c)
)
(x2-
x2m)
(x2-
x2m) ^2
(x2-
x2m)(yi
-ym)
1990 10,00 -0,18 8,40 -0,13 0,02 -0,003 9,68 -0,18 0,03 0,032
1991 10,02 -0,15 8,46 -0,07 0,01 -0,001 9,70 -0,16 0,03 0,024
1992 10,03 -0,14 8,46 -0,07 0,00 -0,001 9,84 -0,02 0,00 0,003
1993 10,02 -0,15 8,44 -0,09 0,01 -0,001 9,70 -0,16 0,03 0,025
1994 10,05 -0,12 8,49 -0,04 0,00 -0,000 9,71 -0,15 0,02 0,018
1995 10,07 -0,10 8,50 -0,02 0,00 -0,000 9,75 -0,11 0,01 0,012
1996 10,09 -0,09 8,56 0,03 0,00 -0,000 9,75 -0,11 0,01 0,009
1997 10,12 -0,05 8,56 0,03 0,00 -0,000 9,78 -0,08 0,01 0,004
1998 10,14 -0,04 8,57 0,04 0,00 -0,000 9,82 -0,04 0,00 0,001
1999 10,17 0,00 8,58 0,05 0,00 0,000 9,87 0,01 0,00 0,000
2000 10,21 0,03 8,58 0,06 0,00 0,000 9,90 0,04 0,00 0,002
2001 10,22 0,04 8,58 0,05 0,00 0,000 9,88 0,02 0,00 0,001
2002 10,23 0,05 8,54 0,01 0,00 0,000 9,92 0,06 0,00 0,003
2003 10,23 0,06 8,59 0,06 0,00 0,000 9,88 0,02 0,00 0,001
2004 10,26 0,09 8,57 0,05 0,00 0,000 10,00 0,14 0,02 0,013
2005 10,28 0,10 8,57 0,04 0,00 0,000 9,89 0,03 0,00 0,003
2006 10,30 0,12 8,55 0,02 0,00 0,000 9,98 0,12 0,01 0,014
2007 10,32 0,14 8,52 -0,01 0,00 0,000 9,99 0,13 0,02 0,019
2008 10,32 0,15 8,54 0,02 0,00 0,000 10,05 0,19 0,04 0,028
2009 10,28 0,11 8,49 -0,04 0,00 0,000 9,95 0,09 0,01 0,010
2010 10,30 0,12 8,55 0,02 0,00 0,000 10,01 0,15 0,02 0,019
TOTA
L
213,65 -0,00 179,10 -0,00 0,06 -0,01 207,05 -0,00 0,26 0,24
MOYE
NNE
10,17 -0,00 8,53 -0,00 0,00 -0,00 9,86 -0,00 0,01 0,01

21. 21
Y being considered as representing ln(GDP/c), X1 representing ln(ENC/c) and X2 for
ln(CF/c). This table indeed contains all the data that will be used for the OLS. ym, x1m
and x2m being the average value of y, x1, and x2, respectively.
The second step is then to find β1 and β2.
The general formula of B being:
(13) β =
β1 is so equal to covxyVarx
= Σ(x1i-x1m)*(yi-ym) / Σ((x1i-x1m)^2)
and β2 = covxyVarx
= Σ(x2i-x2m)*(yi-ym) / Σ((x2i-x2m)^2).
Third step: finding ᾱ.
The general formula of ᾱ is:
(14) ᾱ = ym- β1*x1m- β2*x2m.
According to this formulas and to the table, β1 is equal to 1,30; β2 = 0,92; and ᾱ = -
10,00.
The fourth and final step is then to construct the predicting formula, which is:
(15) y= ᾱ + β1*x1+ β2*x2.
And after replacing y, ᾱ, β1, x1, β2, x2 by its real values, the final equation is:
(16) ln(GDP/c) = -10,00 + 1,30*ln(ENC/c) + 0,92*ln(CF/c).

22. 22
After that, thanks to the equation (16) it is possible to create future predictions. Knowing
the relationships between the different elements influencing the GDP, and the
expected future values of the GDP and the carbon footprint, it is indeed possible to
recreate a table with the predictions of the values of these elements.
The Belgian GDP/c is expected to grow by 1,7% per year according the OECD, and
as the carbon footprint (CF) is taken as independent variable to know the real value of
the CO2 consumption, it has to decrease by 80% at least, as stated by Climact and
VITO (2013), and according to the European directive.
A new table has been done with the equation (16), and the known values of ln(GDP/c)
and ln(CF/c) that have been calculated with the already known future values of GDP/c
and CF/c.
Table 6: results of the OLS
ln(GDP/c) ln(ENC/c) ln(CF/c)
2013 10,30 8,16 9,82
2014 10,32 8,27 9,76
2015 10,34 8,37 9,70
2020 10,42 8,88 9,41
2025 10,50 9,40 9,11
2030 10,59 9,92 8,81
2035 10,67 10,44 8,51
2040 10,76 10,94 8,22
2045 10,84 11,45 7,93
2050 10,93 11,94 7,65
After that, to facilitate the analysis, the exponential of these values have been
calculated.

23. 23
Table 7: Results of the OLS with the exponential of the ln..
GDP/c
(EURO)
ENC/c (EURO) CF/c (Kg of oil
equivalent)
CF/ENC (Kg of
oil per EURO)
GDP/CF
(EURO per Kg
of oil)
2013 29733 3510 18398 5,24 1,62
2014 30031 3894 17327 4,45 1,73
2015 30333 4321 16318 3,78 1,86
2020 32533 7163 12210 1,70 2,66
2025 34201 12045 9045 0,75 3,78
2030 36316 20255 6701 0,33 5,42
2035 38561 34061 4964 0,15 7,77
2040 40946 56466 3715 0,07 11,02
2045 43915 93609 2779 0,03 15,80
2050 47099 152988 2101 0,01 22,42
Knowing the GDP/c and the CF/c, only the ENC/c was the only term which needed to
be calculated. Contrary to the previous predictive table containing the national CO2
emissions, this time, to support a GDP per capita growth of 1,7% per year, and a
decrease of the carbon footprint by 80% for 2050, the Energy consumption need to
increase. The carbon footprint and the energy consumption being positively linked with
the GDP, the decrease of the Carbon footprint per capita causes a diminution of the
GDP/c. To increase the GDP per capita, the energy consumption per capita has thus
to rise a lot to cover the negative effect of the decrease of the CO2/c and to create a
positive effect of 1,7% per year on the GDP/c. In this scenario, the GDP/CF should be
increased by a factor 14, which is the same factor as when the calculation was done
with the CO2, but this is normal since the increase of the GDP and the diminution of
the carbon is the same and given in both scenarios. The CF/ENC, however needs to
be reduced by a factor 524, between 2010 and 2050, which is clearly impossible! In
addition to the fact that such a progression is impossible, both factors are even not
going in the right direction. The energetic mix (CF/ENC), grow by a factor 1,27 between
1990 and 2010, as it has theoretically to decrease to 0,01 in 2050, and the carbon
efficiency (GDP/CF) has decreased from 1,37 (level of the year 1990) to 1,34 (level in
2010), as it has to be at 22,42 in 2050.

24. 24
The main preoccupations that companies and politicians have so to focus on is on a
radical change and the the greening of the energy. If they manage to reduce the
Carbon footprint per unit of energy consumed, so the energetic mix (CF/ENC), this
would mean that the energy used to produce the GDP is greener, and so that the
carbon efficiency (GDP/CF) is better. Reducing the CF/ENC ratio by greening the
energy can be the solution to come as close as possible from the objectives, but
attaining them is nearly impossible.
4. Discussion
The limits of this study are that this research paper is based only on a mathematical
and an econometric world. Even if the results show an impossibility to reach the goal,
there might be solutions or levers, in the real and more complex world, that might make
this goal not so impossible to reach. The data used to make all the calculations of this
study are also taken from a short period of time (1990-2010). This may not show the
real trend and may have influenced the study in a bad way.
This study is also based on predictions of the future, which is never sure. Even if the
predictions are made by the world's most serious organizations like the United Nations
or the OECD, they are based on on linear future, without wars, economic crisis or
technological revolutions. These things can change behavior the pace of the
technological pace drastically, but they are not predictable, so not counted in this study.
The results of this study however seems to show an impossibility to reach our goal
unless drastic changes.
5. Conclusion
Our results suggest that the goal set at the Cancun Climate Change Conference and
modified for the European countries by the European Union, of reducing the CO2
emissions by at least 80% in comparison to the 1990's level, and in the same time to
grow our GDP by 1,7%, seems too optimistic when compared to our current
consumption of CO2, the current link between CO2 and GDP, and the current pace of

25. 25
progression of both values. Only an immediate and radical change in the way we live
and work would make it possible. An energetic mix divided by a factor 524 and a CO2
productivity increased by a factor 14 are indeed requiring sharp changes, if achievable.
It is therefore that Vito and Climact (2013) started their review with the hypothesis that
technological and behavioral improvements are both needed to be able to limit the rise
of the temperature by 2 degrees, compared to preindustrial times. Limiting the average
global temperature of the earth, if possible, requires the effort of everybody, and each
Belgian citizens have to diminish their CO2 consumption by at least 80% for 2050. But
during the same time, the Belgian GDP, usually positively linked with the CO2, will
have to grow. Governance and financing structures will have to find new possibilities
to grow greenly, but the needed change will not be possible without the complete
involvement of the Belgian citizens. The effort to do is so big that technological
progression, which improves the energy efficiency by 1,5% per year currently, is not
fast enough to achieve that goal, and not enough focussed on the CO2 productivity.
Even if improvements have been planned to make the energy greener, this cannot
have the needed impact on the greening of the economy unless the whole population
makes the same effort. And even if every Belgian would join the challenge, reaching
the goal would be very hard to do.
This paper also rejoins the analysis done by Climact and VITO (2013) in a sense that
the move towards greener energy has to be drastic, and has to be made now, because
the more we wait, the more difficult it will be. Belgium has to decrease its CF/ENC ratio
by a factor 524 in 37 years, when the average world has only progressed by a factor
1,1 in the last 35 years, and its CO2 productivity (GDP/CO2 ratio) by a factor 14 when
it has evolved by a factor 1,4 between 1990 and 2010. This will only be possible if we
change our habits soon and drastically.
In this paper, there were calculations in order to quantify the effort to do, while in the
‘Scenarios for a Low Carbon Belgium by 2050’ have analyzed the most polluting
activities and proposed solutions to lever the impact of the changes. Starting with the
same hypothesis, this a complementary paper as it focuses on the problem and
‘Scenarios for a Low Carbon Belgium by 2050’ on the solutions. A behavioral or a

26. 26
technological change indeed modify the elasticity between components of the GDP
and lever the positive impact of changes. Even the results of this papers show goals
impossible to reach, Low Carbon Belgium claims that strategic changes, leveraging
the positive impact of changes can maybe make it possible.

27. 27
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30. 30
7. Appendix
1. Population projections graphs available on Eurostat
2. Data+ linear regression GDP/c = F(ENC/c, CO2/c, FDI/c, K/c)
Belgium (Per
capita)
population
(million)
GDP (million
EURO)
ENC (million
EURO)
GHG
emissions (K
tonnes of oil
equivalent)
FDI Inflows
(million
EURO)
K (million
EURO)
1990 9,948 218.172,2 44.214,61 97.184 18.719
1991 9,987 225.151,9 46.975,55 103.158 -9.321
1992 10,022 228.580,6 47.457,51 104.729 2.469
1993 10,068 226.317,4 46.382,32 100.812 -5.703
1994 10,101 233.799,0 49.101,65 104.145 8.884
1995 10,131 239.548,2 49.979,17 103.657 8.121
1996 10,143 243.443,3 52.781,98 108.441 3.919
1997 10,170 252.796,7 52.916,84 106.172 14.966
1998 10,192 257.955,9 53.819,74 111.622 8.642
1999 10,214 267.866,9 54.372,29 109.093 7.072
2000 10,239 277.870,3 54.743,88 106.094 14.171
2001 10,263 280.393,8 54.732,70 107.057 2.860
2002 10,310 284.953,1 52.712,17 101.545 18.081 -12.709
2003 10,356 287.540,9 55.447,48 106.126 34.544 201
2004 10,396 297.661,4 55.063,04 102.285 44.415 23.277
2005 10,446 303.426,5 54.853,83 100.404 33.684 7.616
2006 10,512 311.526,2 54.386,75 99.120 58.828 19.502
2007 10,585 320.508,2 53.113,38 97.899 96.588 6.090
2008 10,667 323.665,7 54.777,84 98.863 184.842 -25.634
2009 10,753 314.601,2 52.134,50 96.094 65.835 -2.580
2010 10,840 321.956,1 55.977,26 102.438 78.185 16.806
2011 11,001 327.604,0 54.788,65 91.727 117.161

31. 31
2012 11,162 327.132,9 51.527,48 -30.828,71
2013 327.776,1 51.821,20 -3.268,51
GDP/capita
(EURO)
ENC/capita
(EURO)
GHG/capita (Kg
of oil
equivalent)
FDI
Inflows/capita
(EURO)
K/capita
(EURO)
1990 21931,70 4444,66 9769,37 1881,74
1991 22544,50 4703,67 10329,26 -933,34
1992 22807,88 4735,33 10449,93 246,33
1993 22478,22 4606,77 10012,81 -566,45
1994 23147,04 4861,26 10310,73 879,59
1995 23646,00 4933,49 10232,05 801,60
1996 24001,11 5203,78 10691,17 386,42
1997 24856,61 5203,13 10439,55 1471,51
1998 25308,90 5280,43 10951,61 847,85
1999 26225,98 5323,41 10680,90 692,37
2000 27138,15 5346,55 10361,62 1384,05
2001 27319,78 5332,80 10430,96 278,66
2002 27639,32 5112,87 9849,44 1753,74 -1232,71
2003 27766,17 5354,24 10248,02 3335,71 19,44
2004 28631,20 5296,36 9838,51 4272,17 2238,96
2005 29047,43 5251,23 9611,85 3224,60 729,09
2006 29636,70 5174,02 9429,66 5596,51 1855,26
2007 30280,90 5018,03 9249,24 9125,41 575,34
2008 30343,00 5135,31 9268,21 17328,56 -2403,17
2009 29256,79 4848,32 8936,43 6122,37 -239,91
2010 29701,02 5164,00 9450,12 7212,73 1550,39
2011 29780,56 4980,51 8338,38 10650,42
2012 29308,78 4616,50 -2762,03
2013

32. 32
3. Data+ linear regression GDP/c = F(ENC/c & CO2/c) + projections
Population
(million)
GDP (million
EURO)
ENC (million
EURO)
CO2 (K tonnes of
oil equivalent)
1990 9,948 218.172,2 44.214,61 97.184
1991 9,987 225.151,9 46.975,55 103.158
1992 10,022 228.580,6 47.457,51 104.729
1993 10,068 226.317,4 46.382,32 100.812
1994 10,101 233.799,0 49.101,65 104.145
1995 10,131 239.548,2 49.979,17 103.657
1996 10,143 243.443,3 52.781,98 108.441
1997 10,170 252.796,7 52.916,84 106.172
1998 10,192 257.955,9 53.819,74 111.622
1999 10,214 267.866,9 54.372,29 109.093
2000 10,239 277.870,3 54.743,88 106.094
2001 10,263 280.393,8 54.732,70 107.057
2002 10,310 284.953,1 52.712,17 101.545
2003 10,356 287.540,9 55.447,48 106.126
2004 10,396 297.661,4 55.063,04 102.285
2005 10,446 303.426,5 54.853,83 100.404
2006 10,512 311.526,2 54.386,75 99.120
2007 10,585 320.508,2 53.113,38 97.899
2008 10,667 323.665,7 54.777,84 98.863
2009 10,753 314.601,2 52.134,50 96.094
2010 10,840 321.956,1 55.977,26 102.438
2011 11,001 327.604,0 54.788,65 91.727
2012 11,162 327.132,9 51.527,48 88.150
GDP/Capita (EURO) ENC/Capita (EURO) CO2/Capita (Kg of oil
equivalent)

33. 33
1990 21.931,70 4.444,66 9.769,37
1991 22.544,50 4.703,67 10.329,26
1992 22.807,88 4.735,33 10.449,93
1993 22.478,22 4.606,77 10.012,81
1994 23.147,04 4.861,26 10.310,73
1995 23.646,00 4.933,49 10.232,05
1996 24.001,11 5.203,78 10.691,17
1997 24.856,61 5.203,13 10.439,55
1998 25.308,90 5.280,43 10.951,61
1999 26.225,98 5.323,41 10.680,90
2000 27.138,15 5.346,55 10.361,62
2001 27.319,78 5.332,80 10.430,96
2002 27.639,32 5.112,87 9.849,44
2003 27.766,17 5.354,24 10.248,02
2004 28.631,20 5.296,36 9.838,51
2005 29.047,43 5.251,23 9.611,85
2006 29.636,70 5.174,02 9.429,66
2007 30.280,90 5.018,03 9.249,24
2008 30.343,00 5.135,31 9.268,21
2009 29.256,79 4.848,32 8.936,43
2010 29.701,02 5.164,00 9.450,12
2011 29.780,56 4.980,51 8.338,38
2012 29.308,78 4.616,50 7.897,59
ln(GDP) ln(ENC/c) ln(CO2)
1990 9,99568835778731 8,39945865458377 9,18700725984614
1991 10,0232464127428 8,4560983340564 9,24273592353609
1992 10,0348613692668 8,46280669696148 9,25435055880593
1993 10,0203021193779 8,43528223966102 9,2116205521957
1994 10,0496221895683 8,48905294255193 9,24094037954809

34. 34
1995 10,0709492464231 8,50380192733662 9,23328022987692
1996 10,0858553582606 8,55714056356583 9,27717344611241
1997 10,12087899213 8,55701564656341 9,25335675705937
1998 10,1389113915121 8,57176281277824 9,30124175639998
1999 10,1745058014891 8,579869354441 9,27621237862662
2000 10,2086957659955 8,58420677206545 9,24586387424523
2001 10,2153662609437 8,58163170755348 9,2525335859452
2002 10,2269946755529 8,5395161693705 9,19516987975808
2003 10,231573652172 8,58564404937372 9,23483979517498
2004 10,2622523112899 8,57477507113741 9,19405955581649
2005 10,2766852902082 8,56621761385934 9,17075199124146
2006 10,2967687371793 8,55140522821976 9,15161531983434
2007 10,3182724296988 8,52079270538598 9,13229666496881
2008 10,3203211273815 8,5438954905502 9,13434554390584
2009 10,2838669624726 8,48638753217147 9,0978914595555
2010 10,2989366676354 8,54946675196653 9,15378271881986
2011 10,301611110628 8,51328757441374 9,02862423188055
2012 10,2856424088195 8,43739212121268
SUMMARY
OUTPUT
Regression Statistics
Multiple R 0,96340367
6391682
R Square 0,92814664
3685009

35. 35
Adjusted R
Square
0,92058313
2493958
Standard
Error
0,03155538
77640113
Observatio
ns
22
ANOVA
df SS MS F Significance
F
Regression 2 0,2443825
44868876
0,1221912
72434438
122,71372
6500873
0,00000000
0013685071
2083028
Residual 19 0,0189191
074418052
0,0009957
424969371
17
Total 21 0,2633016
52310681
Coefficients Standard
Error
t Stat P-value Lower 95% Upper
95%
Intercept 8,64936800
358131
1,3417154
4954756
6,4464995
2156245
0,0000035
249568819
4179
5,84112529
3507
11,457610
7136556
Ln(ENC/c) 1,57058911
349694
0,1318518
55540666
11,911771
0331542
0,0000000
002934506
98038834
1,29462000
823196
1,8465582
1876193
Ln(CO2/c) -
1,28901954
674736
0,1055090
83148402
-
12,217142
9064009
0,0000000
001912706
6368624
-
1,50985259
573553
-
1,0681864
9775919
RESIDUAL
ANALYSIe
Observatio
n
Predictions
for Y
Residual
1 9,99923439
168668
-
0,0035460
338993722
5
2 10,0163567
188479
0,0068896
938948714
8

36. 36
3 10,0119213
087048
0,0229400
605620143
4 10,0237715
09467
-
0,0034693
900890996
3
5 10,0704293
594881
-
0,0208071
699197774
6 10,1034680
370832
-
0,0325187
906601574
7 10,1306619
047764
-
0,0448065
465158543
8 10,1611658
892205
-
0,0402868
970905335
9 10,1226029
277864
0,0163084
637257107
10 10,1675983
310628
0,0069074
704262330
8
11 10,2135304
473267
-
0,0048346
813311521
7
12 10,2008886
902852
0,0144775
706584941
13 10,2086854
23055
0,0183092
524979251
14 10,2299980
728266
0,0015755
793454310
7
15 10,2654938
995879
-
0,0032415
882979552
9
16 10,2820975
56672
-
0,0054122
664638658
3
17 10,2835009
28545
0,0132678
086342786
18 10,2603233
571842
0,0579490
725146865
19 10,2939672
950558
0,0263538
323256469
20 10,2506359
489731
0,0332310
13499476
21 10,2776625
59187
0,0212741
084483969
22 10,3821716
728934
-
0,0805605
622654113

37. 37
GDP/Capita (EURO) ENC/Capita (EURO) CO2/Capita (Kg of oil
equivalent)
2013 29807,02926 4420,23 7.521,52
2014 30313,74875742 4312,03 7.163,35
2015 30829,0824862961 4211,55 6.822,24
2016 31353,1768885632 4118,43 6.497,37
2017 31886,1808956687 4032,37 6.187,97
2018 32428,2459708951 3953,06 5.893,31
2019 32979,5261524003 3880,21 5.612,67
2020 33540,1780969911 3851,18 5.377,97
2021 34110,36112464 3783,96 5.116,80
2022 34690,2372637588 3722,56 4.868,31
2023 35279,9712972427 3666,73 4.631,89
2024 35879,7308092959 3616,23 4.406,96
2025 36489,6862330539 3570,82 4.192,94
2026 37110,0108990158 3530,29 3.989,32
2027 37740,8810842991 3494,42 3.795,59
2028 38382,4760627321 3463,03 3.611,26
2029 39034,9781557986 3435,92 3.435,89
2030 39698,5727844471 3429,59 3.278,47
2031 40373,4485217827 3416,20 3.122,35
2032 41059,7971466531 3406,57 2.973,67
2033 41757,8136981462 3400,57 2.832,06
2034 42467,6965310146 3398,04 2.697,20
2035 43189,6473720419 3398,88 2.568,76
2036 43923,8713773666 3402,95 2.446,44

38. 38
2037 44670,5771907818 3410,15 2.329,95
2038 45429,9770030251 3420,35 2.219,00
2039 46202,2866120765 3433,47 2.113,33
2040 46987,7254844818 3468,99 2.019,48
2041 47786,516817718 3496,41 1.926,18
2042 48598,8876036192 3526,56 1.837,19
2043 49425,0686928807 3559,34 1.752,31
2044 50265,2948606597 3594,71 1.671,35
2045 51119,8048732909 3632,58 1.594,14
2046 51988,8415561368 3672,91 1.520,49
2047 52872,6518625912 3715,62 1.450,24
2048 53771,4869442552 3760,68 1.383,24
2049 54685,6022223075 3808,03 1.319,34
2050 55615,2574600868 3895,94 1.266,13
ln(GDP/Capita) ln(ENC/Capita) ln(CO2/Capita)
2013 10,30 8,33 8,93
2014 10,32 8,30 8,88
2015 10,34 8,27 8,83
2020 10,42 8,13 8,59
2025 10,50 7,98 8,34
2030 10,59 7,84 8,10
2035 10,67 7,69 7,85
2040 10,76 7,55 7,61
2045 10,84 7,40 7,37
2050 10,93 7,27 7,14

39. 39
(GDP/Capita) (ENC/Capita) (CO2/Capita) CO2/ENC GDP/CO2
2013 29.807 4.159 7.555 1,82 3,95
2014 30.314 4.036 7.187 1,78 4,22
2015 30.829 3.917 6.836 1,75 4,51
2020 33.540 3.398 5.378 1,58 6,24
2025 36.490 2.925 4.188 1,43 8,71
2030 39.699 2.537 3.294 1,30 12,05
2035 43.190 2.184 2.566 1,17 16,83
2040 46.988 1.895 2.018 1,07 23,28
2045 51.120 1.644 1.588 0,97 32,20
2050 55.615 1.438 1.261 0,88 44,09
4. Datas + Linear regression GDP/c = F(ENC/c; CF/c)
GDP/Capita (EURO) ENC/Capita (EURO) CF/capita (Kg of oil
equivalent)
1990 21.931,70 4.444,66 16.000,00
1991 22.544,50 4.703,67 16.300,00
1992 22.807,88 4.735,33 18.700,00
1993 22.478,22 4.606,77 16.300,00
1994 23.147,04 4.861,26 16.500,00
1995 23.646,00 4.933,49 17.100,00
1996 24.001,11 5.203,78 17.200,00
1997 24.856,61 5.203,13 17.700,00
1998 25.308,90 5.280,43 18.400,00
1999 26.225,98 5.323,41 19.300,00
2000 27.138,15 5.346,55 20.000,00
2001 27.319,78 5.332,80 19.600,00
2002 27.639,32 5.112,87 20.300,00
2003 27.766,17 5.354,24 19.600,00

40. 40
GDP/Capita (EURO) ENC/Capita (EURO) CF/capita (Kg of oil
equivalent)
2004 28.631,20 5.296,36 22.100,00
2005 29.047,43 5.251,23 19.800,00
2006 29.636,70 5.174,02 21.500,00
2007 30.280,90 5.018,03 21.800,00
2008 30.343,00 5.135,31 23.200,00
2009 29.256,79 4.848,32 20.900,00
2010 29.701,02 5.164,00 22.200,00
2011
2012
Ln (GDP) Ln(ENC LN(CF)
1990 10,00 8,40 9,68
1991 10,02 8,46 9,70
1992 10,03 8,46 9,84
1993 10,02 8,44 9,70
1994 10,05 8,49 9,71
1995 10,07 8,50 9,75
1996 10,09 8,56 9,75
1997 10,12 8,56 9,78
1998 10,14 8,57 9,82
1999 10,17 8,58 9,87
2000 10,21 8,58 9,90
2001 10,22 8,58 9,88
2002 10,23 8,54 9,92
2003 10,23 8,59 9,88
2004 10,26 8,57 10,00
2005 10,28 8,57 9,89

41. 41
Ln (GDP) Ln(ENC LN(CF)
2006 10,30 8,55 9,98
2007 10,32 8,52 9,99
2008 10,32 8,54 10,05
2009 10,28 8,49 9,95
2010 10,30 8,55 10,01
2011 10,30 8,51
2012 10,29 8,44
SUMMARY
OUTPUT
Regression
Statistics
Multiple R 0,953383513
R Square 0,908940123
Adjusted R
Square
0,898822359
Standard
Error
0,035403494
Observation
s
21
ANOVA
df SS MS F Significance
F
Regression 2 0,225202372 0,1126011
86
89,8360
6598
4,30471E-
10
Residual 18 0,022561332 0,0012534
07
Total 20 0,247763705
Coefficients Standard Error t Stat P-value Lower 95% Upper
95%
Intercept -0,646406008 1,242223807 -
0,5203619
54
0,60915
2932
-
3,25622138
4
1,9634093
68
Ln(ENC/c) 0,303642289 0,177008882 1,7154070
76
0,10343
3446
-
0,06823957
3
0,6755241
5
Ln(CF/c) 0,834803053 0,083814841 9,9600863
09
9,49756
E-09
0,65871460
6
1,0108915
01

42. 42
RESIDUAL
ANALYSIS
Observation Predictions for
Y
Residual
1 9,985205574 0,010482784
2 10,0179114 0,005335014
3 10,13461557 -0,099754197
4 10,01159075 0,008711367
5 10,03809846 0,011523727
6 10,07239444 -0,001445196
7 10,09345798 -0,00760262
8 10,11734154 0,003537449
9 10,1541981 -0,015286707
10 10,19652513 -0,022019331
11 10,22758383 -0,018888067
12 10,20993665 0,005429608
13 10,22644294 0,00055174
14 10,21115497 0,020418683
15 10,30807116 -0,045818849
16 10,21373151 0,062953778
17 10,27799741 0,018771331
18 10,28027004 0,038002385
19 10,3392451 -0,018923969
20 10,23462721 0,049239757
21 10,30415535 -0,005218685
5. OLS avec GDP = F( ENC/c & CF/c) + predictions
Tableau 1
Ln
(GDP)
(yi-ym) Ln(EN
C
(xi-xm) (x1-
x1m)^2
(x1-
x1m)(yi
-ym)
LN(CF) (x2-
X2m)
(x2-
x2m)^2
(x2-
x2m)(yi
-ym)
1990 10,00 -0,18 8,40 -0,13 0,02 0,02 9,68 -0,18 0,03 0,03
1991 10,02 -0,15 8,46 -0,07 0,01 0,01 9,70 -0,16 0,03 0,02
1992 10,03 -0,14 8,46 -0,07 0,00 0,01 9,84 -0,02 0,00 0,00 a1 1,31

43. 43
Tableau 1
Ln
(GDP)
(yi-ym) Ln(EN
C
(xi-xm) (x1-
x1m)^2
(x1-
x1m)(yi
-ym)
LN(CF) (x2-
X2m)
(x2-
x2m)^2
(x2-
x2m)(yi
-ym)
1993 10,02 -0,15 8,44 -0,09 0,01 0,01 9,70 -0,16 0,03 0,02 a2 0,92
1994 10,05 -0,12 8,49 -0,04 0,00 0,00 9,71 -0,15 0,02 0,02 b -10,00
1995 10,07 -0,10 8,50 -0,02 0,00 0,00 9,75 -0,11 0,01 0,01
1996 10,09 -0,09 8,56 0,03 0,00 -0,00 9,75 -0,11 0,01 0,01
1997 10,12 -0,05 8,56 0,03 0,00 -0,00 9,78 -0,08 0,01 0,00
1998 10,14 -0,04 8,57 0,04 0,00 -0,00 9,82 -0,04 0,00 0,00
1999 10,17 0,00 8,58 0,05 0,00 0,00 9,87 0,01 0,00 0,00
2000 10,21 0,03 8,58 0,06 0,00 0,00 9,90 0,04 0,00 0,00
2001 10,22 0,04 8,58 0,05 0,00 0,00 9,88 0,02 0,00 0,00
2002 10,23 0,05 8,54 0,01 0,00 0,00 9,92 0,06 0,00 0,00
2003 10,23 0,06 8,59 0,06 0,00 0,00 9,88 0,02 0,00 0,00
2004 10,26 0,09 8,57 0,05 0,00 0,00 10,00 0,14 0,02 0,01
2005 10,28 0,10 8,57 0,04 0,00 0,00 9,89 0,03 0,00 0,00
2006 10,30 0,12 8,55 0,02 0,00 0,00 9,98 0,12 0,01 0,01
2007 10,32 0,14 8,52 -0,01 0,00 -0,00 9,99 0,13 0,02 0,02
2008 10,32 0,15 8,54 0,02 0,00 0,00 10,05 0,19 0,04 0,03
2009 10,28 0,11 8,49 -0,04 0,00 -0,00 9,95 0,09 0,01 0,01
2010 10,30 0,12 8,55 0,02 0,00 0,00 10,01 0,15 0,02 0,02
Total 213,65 -0,00 179,10 -0,00 0,06 0,08 207,05 -0,00 0,26 0,24
avera
ge
10,17 -0,00 8,53 -0,00 0,00 0,00 9,86 -0,00 0,01 0,01
ln(GDP/c) (EURO) ln(ENC/c) (EURO) ln(CF/c) (tons of
CO2)
2013 10,30 8,16 9,82
2014 10,32 8,27 9,76
2015 10,34 8,37 9,70
2020 10,42 8,88 9,41

44. 44
ln(GDP/c) (EURO) ln(ENC/c) (EURO) ln(CF/c) (tons of
CO2)
2025 10,50 9,40 9,11
2030 10,59 9,92 8,81
2035 10,67 10,44 8,51
2040 10,76 10,94 8,22
2045 10,84 11,45 7,93
2050 10,93 11,94 7,65
GDP/c
(EURO)
ENC/c
(EURO)
CF/C
(Kg of oil
equivalent)
CF/ENC (Kg of
oil per EURO)
GDP/CF
(EURO
per Kg
of oil)
2013 29733 3510 18398 5,24 1,62
2014 30031 3894 17327 4,45 1,73
2015 30333 4321 16318 3,78 1,86
2020 32533 7163 12210 1,70 2,66
2025 34201 12045 9045 0,75 3,78
2030 36316 20255 6701 0,33 5,42
2035 38561 34061 4964 0,15 7,77
2040 40946 56466 3715 0,07 11,02
2045 43915 93609 2779 0,03 15,80
2050 47099 152988 2101 0,01 22,42