Modern Economy, 2012, 3, 590-596 Published Online September 2012 (
Carbon Emission Allocation and Efficiency of EU
Ming-Chung Chang
Department of Banking and Finance, Kainan University, Taiwan, China
Received June 2, 2012; revised July 1, 2012; accepted July 10, 2012
Reduction of CO2 emissions is increasingly important among countries that want to protect the environment against
global warming and climate change. This study examines two methods of CO2 emission reduction—CO2 emission allow-
ance and an internationa l agree ment—by applying th e Zero Sum Gains Model an d th e Coop eration an d Alliance Model.
We conclude that all DMUs reach 100% efficiency after trading on the CO2 emission allowance. The international
agreement also improves the average efficiency of all DMUs, but its effect is inferior to the trad ing of the CO2 emission
Keywords: CO2 Emission Allowance; International Agreement
1. Introduction
An excess of greenhouse gas (GHG) emissions has caus ed
the global climate change that is now threatening global
ecosystems and impacting human existence. For the sus-
tainability of earth and human life, restoring and safeg u a r d -
ing the environment has received much attention recently.
Carbon dioxide (CO2) is one GHG and controlling its
emissions has been ardently regulated by the mechanisms
of Clean Development Mechanism (CDM), Joint Imple-
mentation (JI), and Emission Trading (ET) in the Kyoto
The European Union has established the European
Union Emission Trading Sche me (EU ETS) by Directive
2003/87/EC for GHG emission allowanc e trading. The f i r s t
phase of the scheme was from 1 January 2005 to 31 De-
cember 2007 and set up CO2 emission regulation in the
EU’s 25 member states. Under the scheme, energy-incen-
tive industries and industries with a thermal capacity of
20 MW or more must hold a GHG emission permit to
legally emit GHG. Each member state’s National Alloca-
tion Plan (NPA) draws up an emission amount of GHG
and submits the draft to the European Commission for
The feature of the EU ETS allowanc e in the first phase
includes a grandfathering principle, a benchmarking prin-
ciple, and an auctioning principle. In the grandfathering
principle, the member states obtain an emission allow-
ance based on a post emission record. In the benchmark-
ing principle, the EU ETS allocation rules consider the
member states’ production technology and specific pro-
duction inputs and outputs. The auctioning principle is
for member states to bid on a CO2 emission allowance.
Sijm et al. analyze and compare the advantages and dis-
advantages among the three regulations for carbon credit
allocation and conclude that the auctioning regulation is
the best rule to fit economic efficiency [1].
The main objective of our paper is to propose two al-
ternative CO2 emission allowance allocation models. We
introduce the Zero Sum Gains Data Envelopment Analy-
sis (ZSG-DEA) model and the Cooperation and Alliance
(CA) model to reallocate the CO2 emission allowance.
Both models are applied in our paper to estimate the
performances of decision making units (DMUs) given the
total amount of CO2 emission required by the European
Commission. Based on the data provided by the Commu-
nity Independent Transaction Log (CITL), the approved
CO2 emission allowances are about 200 million tons
from 2005 to 2007.
The most seminal DEA model, popularly known as
DEA CCR, is proposed by Charn es et al. [2]. It applies a
non-parametric analysis method for evaluating the rela-
tive efficiency of DMUs based on the proportion of in-
puts and outputs. The DEA method has been applied in
many various fields such as education, health care, and
banking for improving and monitoring DMUs’ perform-
ance. It is widely-known that an efficiency estimation is
usually based on the assumptions that 1) Inputs need to
*The author appreciates the part of financial support from National
Science Council (NSC 100-2410- H -424-019-).
opyright © 2012 SciRes. ME
M.-C. CHANG 591
be minimized and outputs need to be maximized; and 2)
Inputs and outputs are isotonic variables; which means
that inputs and outputs are “good” or called desirable
variables [3]. However, both desirable (good) and unde-
sirable (bad) variables may be simultaneously present.
The concept of an undesirable output has been already
mentioned in the seminal work of Koopmans in that pol-
lutants (bad) may be generated in an inefficient produc-
tion process when the final products (good) are manu-
factured [4]. The output of pollutants is undesirable and
it is an anti-isotonic variab le.
An undesirable output, which is an inefficient produc-
tive result, should be minimized to improve performance.
Scheel uses DEA models that include undesirable outputs
to discuss issues surrounding environmental performance
[5]. There are three approaches to treat the undesirable
output variables in a DEA context: 1) Let the reciprocal
of the undesirable output be the DEA output [5-7]; 2)
Transform the undesirable output to be the negative num-
bers and then use th em as the DEA input; [5,8]; 3 ) View
the undesirable output as the input variable [9-11]. How-
ever, w e must str ess th at the th ird appro ach is not app r o v e d
by Seiford and Zhu since “if one treats the undesirable
outputs as inputs, the resulting DEA model does not re-
flect the true production process (S eiford and Zhu, 2002,
p. 17)” [12]. Similarly, Färe and Grosskopf also point out
some drawbacks when treating undesirable outputs as
inputs [13]. Although the CO2 emission is an undesirable
output, the CO2 emission allowance, which is the key
role in our study, is an indispensible input factor in the
regime of EU ETS whereby the amount of CO2 emission
allowance is also limited by the European Commission.
In this paper we propose the ZSG-DEA model to analyze
the issue of CO2 emission allowance.
Marcos et al. provide a theoretical framework of the
ZSG-DEA model to analyze the performance of partici-
pant countries in the Olympics in accordance with the
number of medals they have won [14]. The ZSG-DEA
model requires that the total number of medals to be won
is constant. The ZSG-DEA model is also applied in the
field of environmental economics. Sachs uses the ZSG-
DEA model in an ecological economy that provides a
limitation on pollutants’ emission [15]. Gomes and Lins
use the ZSG-DEA model to consider CO2 emission trade
in which CO2 emissions are viewed as an undesirable
output [10]. In our paper we also apply the ZSG-DEA
model and view the CO2 emission allowance as a desir-
able input. Moreover, we propose examining the alloca-
tion of CO2 emission allowance for the 25 member states
in the EU.
2. Model Set-Up
To formally present our calculation process, we consider
a set with r DMUs. Each DMU uses t inputs to manufac-
ture s outputs. We define k
as the amount of input k
and i
1, ,,1, ,,and1, ,,.kt
as the amount of input j for DMU i, where
 
2.1. DEA CCR Model
According to the classical DEA CCR model, a measure
of the relative efficiency of DMU g is defined as the ratio
of a weighted sum of its outputs to a weighted sum of its
inputs. The optimal efficient value is obtained by treating
weights as variables and by maximizing the efficiency
ratio of DMU g subject to th e constraint that other D MUs’
efficiency ratio is larger than 1 given the same set of
weights. The following model is the relative efficiency
value of DMU g under input orientation:
max. .1,1,,
jj jj
kk kk
uy uy
vx vx
uv jk
where uj and vk are the weights of output and input, re-
2.2. ZSG-DEA Model
In the regime of EU ETS, the CO2 emission allowance is
viewed as “good” and as a limited input factor. We de-
fine zi as the amount of CO2 emission allowance for
DMU i, and 1i. Based on the framework of the
DEA CCR model, the relative efficiency of DMU g un-
der the input orientation is obtained from the ZSG-DEA
model as follows:
max. .1,1,,
0for .
jj jj
ig ig
uy uy
zz zz
The fractional model in Equation (2a) can be rewritten
as a linear programming model by scaling the denomina-
tor in the objective function to be 1. The linear program-
ming model in the inpu t orientation is:
max. .=1
0for .
gg i
uy zzir
 
 (2b)
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Copyright © 2012 SciRes. ME
=1,, 25;=1:ij3. A Reallocation of CO2 Emission
Allowance in the EU for 25 member states in the EU is given
3.1. Data Description
In the previous literature, Gomes and Lins use CO2 emis-
sions as the input, while popu lation , energy con sumption ,
and gross domestic product (GDP) are used as outputs
[10]. In order to follow the isotonicity in classical DEA
models, we consider here the CO2 emission allowance as
the input and the GDP as the output to reallocate the CO2
emission allowance for 25 member states in the EU. We
refer to the 2007 data published by the CITL for the CO2
emission allowance (in ton3 of equivalent carbon) and the
World Bank Database for GDP (in USD).
3.2. CO2 Emission Allowance Model: ZSG-DEA
The reason for proposing the use of the ZSG-DEA model
is to have an efficient allocation on the CO2 emission
allowance while having all countries be on the efficiency
frontier. By refining Equation (2b), the ZSG-DEA model
25 25
ii i
ig ig
sthz zyhzzh
 
 
 
 
 
 
From Equation (3), we obtain a DEA frontier that
represents a fair allocation of the CO 2 emission allowa nc e
in which all countries lie uniformly on the DEA frontier.
In Table 1 there is only one efficient DMU in the D EA
CCR model: Sweden allocates 1.099% to the total CO2
emission allowance. The average efficiency value for all
DMUs is 36.3%. Consider the cas e between Denmark a nd
Greece in that they have almost the same GDP, but the
CO2 emission allowance of Denmark is less, which cre-
ates a higher efficiency value relative to Greece. Simila rly,
Poland and Sweden both have almost the same GDP, but
the CO2 emission allowance of Sweden is far less than
that of Poland, which causes a higher efficiency value
relative to Sweden.
Table 1. Data, DEA CCR efficiency, and optimal allocation by the ZSG-DEA model.
Country Country Code GDP CO2
Optimal Reallocation
on CO2
Efficiency Trading and
Austria AUT 372,291,309,787 32,729,289 0.562 46,896,844 1.000 14,167,555
Belgium BEL 458,619,726,869 60,428,821 0.375 57,771,474 1.000 –2,657,347
Cyprus CYP 21,835,946,095 5,899,493 0.183 2,750,634 1.000 –3,148,859
Czech Republic CZE 174,214,9 43,907 96,919,971 0.089 21,945,533 1.000 –74,974,438
Denmark DNK 310,721,016,955 27,902,895 0.550 39,140,949 1.000 11,238,054
Estonia EST 21,383,914,641 21,343,525 0.049 2,693,692 1.000 –18,649,833
Finland FIN 245,952,167,831 44,620,371 0.272 30,982,137 1.000 –13,638,234
France FRA 2,594,012,356,324 149,775,970 0.856 326,762,914 1.000 176,986,944
Germany DEU 3,329,145,212,814 497,302,479 0.331 419,366,233 1.000 –77,936,246
Greece GRC 309,916,787,520 71,162,432 0.215 39,039,642 1.000 –32,122,790
Hungary HUN 138,757,191,935 30,236,166 0.227 17,478,985 1.000 –12,757,181
Iceland ISL 20,428,032,019 19,240,229 0.052 2,573,281 1.000 –16,666,948
Italy ITA 2,116,201,719,593 203,255,077 0.514 266,573,996 1.000 63,318,919
Latvia LVA 28,765,687,042 4,035,018 0.352 3,623,560 1.000 –411,458
Lithuania LTU 39,103,973,051 10,318,307 0.187 4,925,855 1.000 –5,392,452
Luxembourg LUX 51,278,197,958 3,229,321 0.784 6,459,419 1.000 3,230,098
Malta MLT 7,547,856,389 3,048,394 0.122 950,789 1.000 –2097605
Netherlands NLD 778,311,557,844 86,476,714 0.445 98,042,460 1.000 11,565,746
Poland POL 425,321,393,718 237,542,720 0.088 53,576,945 1.000 –183,965,775
Portugal PRT 230,944,735,970 36,908,808 0.309 29,091,679 1.000 –7,817,129
Slovak Republic SVK 84,241,814,947 30,486,829 0.136 10,611,785 1.000 –19,875,044
Slovenia SVN 47,314,863,050 8,245,914 0.283 5,960,165 1.000 –2,285,749
Spain ESP 1,440,836,638,664 159,739,872 0.446 181,499,513 1.000 21,759,641
Sweden SWE 462,512,853,670 22,846,480 1.000 58,261,884 1.000 35,415,404
United Kingdom GBR 2,799,040,362,405 215,875,184 0.640 352,589,910 1.000 136,714,726
Total 2,079,570,279 2,079,570,279 0
EU state is in the G8.
M.-C. CHANG 593
Using the ZSG-DEA model, we redistribute the CO2
emission allowance (Table 1, Column 6) to make all
DMUs become 100% efficient (Table 1, Column 7). The
numbers in the final column of Table 1 can be seen as
the feasible trade quota of CO2 emission allowance. If
some countries aim to become 100% efficient, then they
can purchase or sell their CO2 emission allowance. For
example, France, Italy, and the United Kingdom in the
Group of Eight (G8) need more CO2 emission allowance
to improve performance1; however, Germany is also a
member of G8, ret needs to decrease CO2 emissions to
increase efficiency. Under the restricted CO2 emission
allowance, countries that can increase thei r emissions must
trade with others that need to reduce their emissions. We
also see that CO2 emissions are allowed to increase in
only 9 countries among t he 25 EU members. From a social
regulator’s viewpoint, a country with a high (low) GDP
should be allocated more (less) CO2 emission allowance.
In Figure 1 we find the DEA CCR frontier is located
on the right of the ZSG-DEA frontier. The reason for the
frontier in the DEA CCR model shifting to the right is
that the restriction in the ZSG-DEA model is more than
that in the DEA CCR model. Many EU member states
are concentrated in the southwest part of Figure 1. This
means these countries have a lower GDP and less CO2
emission allowance. On the contrary, a few EU member
states are located in the northeast part of Figure 1, such
as the United Kingdom, Germany, Fr ance, and Italy, w h i c h
all belong to the G8. These countries have a higher GDP
and more CO2 emission allowance. This phenomenon
shows that a country with a higher GDP will be allocated
more CO2 emission allowance. However, the amount of
CO2 emission allowance held by each state before trad-
ing cannot result in 100% efficiency. Hence, only Swe-
den is located on the DEA CCR frontier before trading.
A surplus or deficit CO2 emission allowance can be re-
spectively sold or obtained in the reg ime of the EU ETS.
After trading and reallocating the CO2 emission allow-
ance, each state shifts to the frontier of the ZSG-DEA
model, which means that each state reaches 100% effi-
ciency after the reallocation of CO2 emission allowance.
3.3. CO2 Emission Allowance Model: CA Model
There were 15 EU members in 1995. Based on the objec-
tive of the Kyoto Protocol, these 15 countries received a
more serious GHG emission reduction target, which is
called the European Bubble. The burden sharing agree-
ment (Council Decision 2002/358/EC) required these 15
countries to reach the GHG emission reduction target by
the triptych approach , which is a sector-based CO2 emis-
sion allowance allocation principle that includes power
sectors, energy intensiv e ind ustries, and domestically-o ri-
ented sectors. Hence, we now examine whether it is help-
ful to improve the performances of these 15 countries
through a cooperation and alliance.
Figure 1. Efficiency in the DEA CCR model and the ZSG-DEA model.
1The G8 is a forum for the governments of eight of the world’s largest economies including France, Germany, Italy, Japan, the United Kingdom, the
United States, Canada, and Russia. The forum is organized by the former six countries above mention in1975, thus leading to the name Group of Six
(G6). The forum became the Group of Seven (G7) in the following year when Canada joined the forum. In 1997, Russia was added to group which
then became known as the G8.
Copyright © 2012 SciRes. ME
The concept of performance by considering cooperation
and alliance among DMUs origi nates from the ideal model
in Gomes and Lins [10]. We let be the cooperative
DMUs’ set, q
is the proportionality factor
based on the proportional strategy, and cg and ci are the
respective classical efficiency values of DMU g and DMU
i tha t come f rom th e DE A CCR mod el. In the regime s of
the European Bubble and the burden sharing agreement,
we assume that these 15 countries form a cooperation
and alliance group. The efficiency values considering
such cooperation among DMUs are presented as follows:
gg i
Equation (4) implies that the more states there are in a
non-cooperation group, the lower their DMUs’ efficiency
values are. We next estimate all DMUs’ efficiency values
when 15 DMUs form an alliance. The results are in col-
umns 4 and 5 in Table 2. After forming an alliance, the
average performance in the CA model is superior to that
in the DEA CCR model. We also see from the results of
the CA model that the efficiency values of the DMUs
increase in more than half of the 25 EU member states.
However, the efficiency values of four countries in the
alliance group decrease. It is rather surprising that the
performance of Sweden decreased from 100% efficiency
to becoming inefficient after forming an alliance. Altho ugh
an alliance induces some countries’ performances to de-
teriorate, it is still helpful to improve the average effi-
ciency values no matter for all EU countries or for coun-
tries in the alliance. This result comes from comparisons
between columns 3 with 4 and between columns 6 with 7.
Table 2. DEA CCR efficiency in the CA model.
Country CO2 Emission
Allowance DEA CCR
Efficiency in the CA
Model Efficiency ChangeDEA CCR
Efficiency before
Forming an Alliance
Efficiency after
Forming an Alliance
Austria 32,729,289 0.562 0.653 + 0.562 0.653
Belgium 60,428,821 0.375 0.746 + 0.375 0.746
Cyprus 5,899,493 0.183 0.645 + -- --
Czech Republic 96,919,971 0.089 0.384 + -- --
Denmark 27,902,895 0.550 0.660 + 0.550 0.660
Estonia 21,343,525 0.049 0.222 + -- --
Finland 4,4620,371 0.272 0.742 + 0.272 0.742
France 149,775,970 0.856 0.500 0.856 0.500
Germany 497,302,479 0.331 0.754 + 0.331 0.754
Greece 71,162,432 0.215 0.694 + 0.215 0.694
Hungary 30,236,166 0.227 0.708 + -- --
Iceland 19,240,229 0.052 0.235 + 0.052 0.235
Italy 203,255,077 0.514 0.681 + 0.514 0.681
Latvia 4,035,018 0.352 0.752 + -- --
Lithuania 10,318,307 0.187 0.652 + -- --
Luxembourg 3,229,321 0.784 0.533 0.784 0.533
Malta 3,048,394 0.122 0.496 + -- --
Netherlands 86,476,714 0.445 0.718 + 0.445 0.718
Poland 237,542,720 0.088 0.381 + -- --
Portugal 36,908,808 0.309 0.753 + 0.309 0.753
Slovak Republic 30,486,829 0.136 0.537 + - - --
Slovenia 8,245,914 0.283 0.747 + -- --
Spain 159,739,872 0.446 0.718 + 0.446 0.718
Sweden 22,846,480 1.000 0.443 1.000 0.443
United Kingdom 215,875,184 0.640 0.609 0.640 0.609
Average 0.363 0.599 0.490 0.629
EU state is in the European Bubble and the burden sharing agreement.
Copyright © 2012 SciRes. ME
M.-C. CHANG 595
3.4. Market-Based Tool and
Command-and-Control Regulation
In previous subsection, we introduce the concept of CO2
emission allowance reallocation. Surplus or deficit allow-
ances can be respectively sold or purchased based on the
rule of the EU ETS, which requires a cap-and-trade pro-
gram. The EU ETS regime makes CO2 emission allow-
ance a tradable commodity. Thus, CO2 emission allow-
ance is viewed as a market-based tool for reducing CO2
emissions. The previous subsection introduces coopera-
tion and alliance among countries based on some interna-
tional agreements in which the member states have to
strictly comply to emission standards or implement par-
ticular technologies. Thus, cooperation and alliance is
viewed as a command-and-control type regulation.
We now examine the effect of an environmental policy
between the tradable allowance and the alliance among
countries. By Figure 1, we have represented that the ef-
ficiencies of all DMUs can reach 100% through trading
of CO2 emission allowance. Although cooperation and
alliance also improves the average efficiency values of
all DMUs and the DMUs in the alliance, from Table 2 it
cannot make the efficiency of all D MUs reach 100%. Thus,
we conclude that the environmental effect of a market-
based tool is superior to that of command-and-control
4. Conclusions
Environmental issues are not only becoming more and
more important, but should also not be neglected, becaus e
many countries are conscious about global warming re-
sulting from an increase in CO2 emissions. Both environ-
mental researchers and social regulators have been using
DEA to understand and solve the problem of global wa rm-
ing and climate change.
The EU has adopted both the CO2 mission allowance
and an international agreement as two methods of CO2
emissions’ reduction. In the EU ETS regime that requires
a cap-and-trade program, surplus or deficit CO2 emission
allowances can be respectively sold or purchased in a
carbon market. Under the international agreement, some
EU member states have formed a cooperation and alli-
ance group, such as the European Bubble, to decrease
CO2 emissions. Both of their aims are to reduce CO2
emissions and to prevent the global warming and climate
change. We employ the ZSG-DEA model and the CA
model to estimate the environmental effects of CO 2 emis-
sion allowance and the international agreement, respec-
tively. The result of this paper shows that the efficiencies
of all DMUs can reach 100% after CO2 emission allow-
ance reallocation by trading. Conversely, the internation al
agreement only improves the average efficiency of all
DMUs, but cannot make the efficiencies of all DMUs
reach 100%. Thus, the environmental effect of CO2 emis-
sion allowance is superior to that of the international
We lastly suggest a future improvement that con siders
a restricted undesirable output, such as the amount of CO2
emissions regulated by the social planner. One should note
that how to model an undesirable output in a DEA contex t
is presented in Dyckhoff and Allen as a reference [3].
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