Carbon Emission Allocation and Efficiency of EU Countries

doi:10.4236/me.2012.35078

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Modern Economy, 2012, 3, 590-596

http://dx.doi.org/10.4236/me.2012.35078 Published Online September 2012 (http://www.SciRP.org/journal/me)

Carbon Emission Allocation and Efficiency of EU

Countries*

Ming-Chung Chang

Department of Banking and Finance, Kainan University, Taiwan, China

Email: changmc@mail.knu.edu.tw

Received June 2, 2012; revised July 1, 2012; accepted July 10, 2012

ABSTRACT

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

allowance.

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

Protocol.

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

approval.

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-).

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

jsigr

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,,

,0for,,

jj jj

kk kk

uy uy

estir

vx vx

uv jk









 (1)

where uj and vk are the weights of output and input, re-

spectively.

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:

zz

max. .1,1,,

0for .

jj jj

ig ig

uy uy

estir

zz zz















(2a)

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

0,1,,

0for .

gg i

euystzz

uy zzir











 





  (2b)

M.-C. CHANG

592

=1,, 25;=1:ij3. 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

Model

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

max

..=10,0.

ii i

ig ig

sthz zyhzzh







 

 



 

 

 



(3)

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

Emission

Allowance

DEA CCR

Efficiency

Optimal Reallocation

on CO2

Emission

Allowance

ZSG-DEA

Efficiency Trading and

Adjustment

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.

M.-C. CHANG

594

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

igi

qcc



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:

igig

















gg i







 (4)

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

DEA CCR

Efficiency in the CA

Model Efficiency ChangeDEA CCR

Efficiency before

Forming an Alliance

DEA CCR

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.

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

regulation.

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

agreement.

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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