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1
An intertemporal approach to measuring environmental performance with
directional distance functions: greenhouse gas emissions in the European Union
Andrés J. Picazo-Tadeo*, Juana Castillo and Mercedes Beltrán-Esteve
Departamento de Economía Aplicada II. Facultad de Economía. Universidad de Valencia.
Campus de Tarongers. 46022, Valencia. Spain.
* Corresponding author. Email: andres.j.picazo@uv.es
ABSTRACT. The impact of economic activity on the environment is a matter of growing concern for firm
managers, policymakers, researchers and society as a whole. Building on previous work by Kortelainen
[Kortelainen, M., 2008. Dynamic environmental performance analysis: A Malmquist index approach. Eco-
logical Economics 64, 701-715], we contribute an approach to assessing intertemporal environmental perfor-
mance at the level of the management of specific pollutants, as the result of change in eco-efficiency and envi-
ronmental technical change, which identify catching-up with best available environmental practices and eco-
innovation, respectively. In doing so, we use Data Envelopment Analysis techniques, directional distance
functions and Luenberger productivity indicators. Our approach is employed to assess environmental per-
formance in the emission of greenhouse gases in the European Union-28 over the period 1990-2011. The
main result is that environmental performance has been boosted by environmental technical change rather
than by increases in eco-efficiency, although with certain differences among air pollutants. Accordingly,
policy measures aimed at enhancing eco-efficiency are recommended to improve environmental perfor-
mance in European countries regarding greenhouse gas emissions.
KEYWORDS: Intertemporal environmental performance; directional distance functions; Data
Envelopment Analysis; greenhouse gases emissions; European Union.
JEL CLASSIFICATION: C61; O44; Q01; Q54.
FINAL MANUSCRIPT 2 February, 2014
1. Introduction
Economic performance is a recurrent matter of study in both theoretical and empirical eco-
nomics; as a result of this interest, many researchers have addressed the issue of assessing
performance using a wide range of measures of efficiency and productivity growth (see Balk
2008). In parallel, the traditional view of economic growth entirely focused on increasing the
quantity of goods and services available to satisfy human needs has given way in recent dec-
ades to a vision of growth based on sustainable development, understood as the ‘development that
meets the needs of the present without compromising the ability of future generations to meet their own
needs’ (WCED 1987, p.43). Sustainability is a multifaceted concept that involves, at least, two
strongly related dimensions, namely, the economic dimension and the environmental dimen-
2
sion. Furthermore, literature in the field of ecological economics has long recognised the need
to develop tools to assess the impact of productive activity on the environment, as a necessary
condition for environmental policies aimed at achieving sustainable development to be effec-
tive (Huppes and Ishikawa 2005a; 2009).
A strand of literature has approached the analysis of sustainability through the concept of eco-
efficiency that, according to the OECD (1998, p.7), ‘…expresses the efficiency with which ecological
resources are used to meet human needs (...) and can also be defined as a ratio of output and input so
that the output represents the value of the products or services that a company produces and the input
is the sum of environmental pressures caused by the production’. Eco-efficiency can be interpreted
then as a relationship between economic performance, measured by the value of products and
services produced, and an aggregate measure of environmental performance (see Schaltegger
and Synnestvedt 2002).1 Moreover, several international organisations have recognised that
the assessment of eco-efficiency is a powerful instrument capable of providing managers and
policymakers with helpful information to design better managerial strategies and environ-
mental policies (United Nations 2009).
In this line of research, Kuosmanen and Kortelainen (2005) developed a general framework to
measure relative eco-efficiency using Data Envelopment Analysis (DEA) techniques (Charnes et al.
1978). Based on the benefit of the doubt principle (Cherchye et al. 2007), DEA allows building an
aggregate score of environmental performance without resorting to prices, which is a noticea-
ble advantage for the purpose of assessing eco-efficiency in that pollutants and environmental
pressures have no market prices. Later on, Kortelainen (2008) generalised this approach to an
intertemporal setting using Malmquist indices (Malmquist 1953) and conventional Shephard’s
distance functions (Shephard 1970) to develop an overall proportional measure of dynamic
environmental performance. In the spirit of the seminal paper by Färe et al. (1994), environmental
1 This definition of eco-efficiency has the advantage of easiness of computation and straightforwardness of
interpretation for policymakers and the general public. However, other definitions can also be found in this
literature, e.g., taking production factors (labour and capital) and environmental pollution simultaneously
into account (see Korhonen and Lutpacik, 2004).
3
performance change was decomposed into the result of relative eco-efficiency change and environ-
mental technical change, as a natural way to identify, respectively, catching-up with best availa-
ble environmental practices and eco-innovation or progress in environmental technology.
Our paper extends the approach by Kortelainen (2008) to assessing intertemporal environmental
performance2 and its determinants at the level of the management of specific pollutants. In do-
ing so, we use Luenberger productivity indicators (Chambers et al. 1996), directional distance
functions (Färe and Grosskopf 2000) and the DEA-based approach to eco-efficiency measure-
ment by Picazo-Tadeo et al. (2012). Our foremost contribution to the state-of-the-art in this
literature, and particularly to the two aforementioned papers, is that we propose different
indicators of environmental performance growth, eco-efficiency growth and environmental
technical change, representing different sets of preferences regarding economic and ecological
performance. This methodological approach is employed to assess intertemporal environmen-
tal performance in greenhouse gas (GHG) emissions in the European Union-28 (EU-28) over
the period 1990-2011.
Global warming and climate change caused by rising concentrations of GHG are a matter of
increasing concern for policymakers, researchers and society around the world. Furthermore,
several studies have addressed the analysis of environmental performance in the European
Union (EU) regarding GHG emissions, in an attempt to provide scientific grounds to Europe-
an environmental policies against climate change. Without aiming to be exhaustive, Mahlberg
et al. (2011) employed Malmquist indices to analyse the driving forces of eco-productivity
change in 14 EU member countries for the period 1995-2004, using aggregate GHG emissions
to account for the impact of economic activity on the environment. The foremost result is that
eco-productivity growth was more driven by reduction in GHG emissions than by input sav-
ings. Camarero et al. (2014) assessed convergence in eco-efficiency during the period 1990–
2 By using the expression intertemporal environmental performance we depart from the terminology employed
by Kortelainen (2008), who refers to his measure of performance as a dynamic environmental performance indi-
cator. The reason is that this approach does not model the dynamics of the change in environmental perfor-
mance, but just compares scores of performance observed at different points of time.
4
2009 in the European Union-27 (EU-27) regarding aggregate GHG emissions as well as indi-
vidual emissions of carbon dioxide, nitrous oxide and methane. Although specific conver-
gence clubs were found for different pollutants, four groups of countries can roughly be de-
fined: the first two including core EU high-income countries, a third club mainly made up of
peripheral countries, and a final group involving most Eastern European countries. Accord-
ingly, the authors suggest that different environmental policies might be required for countries
showing different eco-efficiency convergence paths.
The contribution of our paper to existing empirical studies on environmental performance re-
garding GHG emissions, and particularly to those based in the use of DEA techniques, is that
we provide an assessment of the environmental performance of EU members and its determi-
nants at the level of the management of particular contaminant gases. Furthermore, beyond
the assessment of convergence in eco-efficiency as regards specific GHG emissions carried out
by Camarero et al. (2014), we assess intertemporal environmental performance and its deter-
minants, including environmental technical change and change in eco-efficiency. In our opin-
ion, these empirical contributions might provide European policymakers with sound infor-
mation to improve the design of their environmental policies.
Following this Introduction, Section 2 develops the methodology. Section 3 describes the data
and the empirical application. Section 4 discusses the results and highlights some policy rec-
ommendations, while a final Section concludes and suggests some avenues for future re-
search.
2. Methodology
2.1. Environmental performance, eco-efficiency and environmental technical change
Let us start by assuming that we observe a set of k=1,…,K producers to which we will refer as
decision-making units (DMUs) hereafter, which each year from a period t=1,…,T generate an
5
economic result represented by value added vt, and a series of n=1,…,N pollutants that dam-
age the environment denoted by the vector
pt=p1
t,..., pN
t
( )
3.
The Pollutant Generating Technology Set (PGTS), which represents all feasible combinations of
value added and pollutants in period t, is defined as (Kuosmanen and Kortelainen 2005; also
see Picazo-Tadeo et al. 2011):
PGTSt=vt,pt
( )
∈R+
N+1value added vt can be obtained with pollutants pt
⎡
⎣⎤
⎦
(1)
Environmental technology can also be represented by the Pollutant Requirement Set (PRS) (see
Beltrán-Esteve et al. 2014), which represents all the combinations of pollutants p that permit
obtaining at least value added v, and which in period t is defined as:
( ) ( )
⎡⎤
=∈
⎣⎦
pp
tt t tt t
PRS v v , PGTS
(2)
Following Picazo-Tadeo et al. (2012), we assume that environmental technology has the fol-
lowing properties: a) economic activity unavoidably dumps some pollutants on the environ-
ment, and the only way not to generate pollutants is not to produce; b) lower value added can
always be obtained dumping the same amount of pollutants on the environment; c) pollutants
can always be increased for any given value added; and, finally, d) any convex combination of
feasible (observed) pairs of value added and pollutants is also feasible. In accordance with earlier
papers by Korhonen and Luptacik (2004), Kuosmanen and Kortelainen (2005) and Zhang et al.
(2008), in this characterisation of the technology pollutants are formally treated as conventional
inputs.4
Let us now define environmental performance as the ratio between economic value added and a
composite indicator of the aggregate pollutant dumped on the environment (see Kortelainen
3 Vectors are in bold type throughout the paper to distinguish them from scalars.
4 Undesirable resultants of production processes are often considered as bad outputs that generate environ-
mental pressures, as it is the case with climate changing emissions, which might have not only contemporary
impacts on economy and society but also in later periods. Dyckhoff and Allen (2001) discuss different ap-
proaches to treating undesirables in the framework of DEA-based models.
6
2008). Accordingly, environmental performance would improve when the value added in-
creases with respect to the aggregate pollutant. Formally, environmental performance in peri-
od t is formulated as:
Environmental performancet=Economic value addedt
Aggregate pollutantt=vt
w1p1
t+w2p2
t+...+wNpN
t
(3)
In the computation of the aggregate pollutant score we follow the most common approach in
literature consisting of taking as aggregating function a linear weighted average of the partic-
ular harmful pollutants, wn being the weight awarded to pollutant n.
Furthermore, it is worth highlighting that here we interpret the ratio between economic value
added and the aggregate pollutant in a slightly different manner than Kuosmanen and Korte-
lainen (2005), where this ratio was used as a measure of relative eco-efficiency. The reason is
that, for the purpose of our intertemporal analysis, we want to unmistakably separate the con-
cept of eco-efficiency, which involves a relative evaluation of performance with respect to a
benchmark, from environmental performance that does not involve such comparison.5
Our next methodological building block is the directional distance function, represented by the
parameter β. This function models value added and pollutants jointly, providing a measure of
the extent to which value added could be increased in a direction gv and pollutants decreased
in a direction –gp, which is negative to pick up the fact that contaminants are being reduced,
while remaining within the PGTS.6 Formally, the directional distance function of an observa-
tion in period t with respect to the contemporaneous technology is (Färe and Grosskopf 2000):
Dtvt,pt;g=gv,−gp
( )
⎡
⎣⎤
⎦=Sup βpt−βgp
( )
∈PRStvt+βgv
( )
⎡
⎣
⎢⎤
⎦
⎥
(4)
( )
=−
v
g, p
gg
being the so-called direction vector.
5 Other papers have referred to this ratio as environmental productivity (Huppes and Ishikawa 2005b).
6 Picazo-Tadeo et al., 2005 highlight the usefulness of these functions for environmental analyses.
7
The directional distance function provides a complete representation of the PGTS and is lower
bounded to zero (other properties are in Chambers et al. 1998). Furthermore, as it measures
deviations from the boundary of the environmental technology, it constitutes a flexible and
powerful tool for assessing eco-efficiency. As mentioned above, directional distance functions
make it possible to assess potential increases in economic value added and/or reductions in
harmful contaminants along a particular direction vector defined by the researcher, which
might represent the preferences of policymakers, firm managers or society regarding the
trade-off between economic and ecological performance.
After defining the concepts of environmental performance and directional distance function,
following Kortelainen (2008), we suggest an approach to assessing the change in environmen-
tal performance and its determinants based on the calculation of Luenberger indicators (Cham-
bers et al. 1996). In order to assess the change in environmental performance of a given DMU
between adjacent periods 0 and 1, let us first set the technology of period 0 as the benchmark
and assess environmental performance change by the difference in the directional distance
functions of observations 0 and 1 to that technology. Formally:
Environmental performance change0=EPCh0=
D0v0,p0;g=gv,−gp
( )
( )
⎡
⎣
⎢
−
D0v1,p1;g=gv,−gp
( )
( )
⎤
⎦
⎥
(5)
Alternatively, the change in environmental performance can be measured regarding the tech-
nology of period 1:
Environmental performance change1=EPCh1=
D1v0,p0;g=gv,−gp
( )
( )
⎡
⎣
⎢
−
D1v1,p1;g=gv,−gp
( )
( )
⎤
⎦
⎥
(6)
Following Chambers et al. (1996), the Luenberger environmental performance change indicator as-
sessing the change in environmental performance over periods 0 and 1 is computed as the
8
arithmetic mean of the two indices of environmental performance change in expressions (5)
and (6):7
LEPCh 0,1 v0,p0,v1,p1;g=gv,−gp
( )
⎡
⎣⎤
⎦=1
2
D0v0,p0;g=gv,−gp
( )
( )
−
D0v1,p1;g=gv,−gp
( )
( )
⎡
⎣
⎢
+
D1v0,p0;g=gv,−gp
( )
( )
−
D1v1,p1;g=gv,−gp
( )
( )
⎤
⎦
⎥
(7)
In the spirit of the Malmquist productivity index decomposition (Färe et al. 1994) used by Kor-
telainen (2008), here we decompose the Luenberger indicator of environmental performance
change into two mutually exclusive elements representing, as noted in the Introduction, eco-
efficiency change, that measures catching-up with the technological frontier that represents best
contemporaneous available environmental practices, and environmental technical change that
measures how much the environmental frontier shifts as a result of eco-innovation.8
As already commented, flexibility is one of the primary advantages of directional distance
functions, enabling researchers to evaluate performance in different directions representing
either their own preferences or those of managers and policymakers. Thus, before proceeding
with the decomposition of environmental performance change, let us assume a scenario in
which our interest lies in evaluating the extent by which all pollutants can be proportionally
or radially reduced without decreasing value added. The directional distance function that
assesses this proportion in period t provides a measure of eco-efficiency and is computed as:
Eco −efficiencyt=EEfft=
Dtvt,pt;g=0, −pt
( )
⎡
⎣⎤
⎦=Sup β1− β
( )
pt
( )
∈PRStvt
( )
⎡
⎣⎤
⎦
(8)
( )
=−
t
0,gp
being the direction vector that represents the abovementioned preferences.
Furthermore, the change in eco-efficiency between periods 0 and 1 in this scenario can be
evaluated as the difference in the directional distance functions of observations 0 and 1 with
respect to their respective contemporaneous technologies:
7 A positive record for this indicator would point to an improvement in environmental performance, whereas
negative scores mean that environmental performance has worsened.
9
EEffCh0,1 v0,p0, v1,p1;g=0, −p
( )
⎡
⎣⎤
⎦=
D0v0,p0;g=0, −p0
( )
( )
−
D1v1,p1;g=0, −p1
( )
( )
⎡
⎣⎤
⎦
(9)
Accordingly, this indicator measures the increase/decrease in environmental pollutants due
to the difference of eco-efficiency between periods 0 and 1.
On the other hand, environmental technical change in this scenario is assessed by comparing
observed value added and pollutants in period 0 with respect to the technology of periods 0
and 1, respectively. Formally:
ETechCh0,1 v0,p0, v1,p1;g=0, −p0
( )
⎡
⎣⎤
⎦=
D1v0,p0;g=0, −p0
( )
( )
−
D0v0,p0;g=0, −p0
( )
( )
⎡
⎣⎤
⎦
(10)
or, alternatively, using the observation in period 1 as a basis of comparison:
ETechCh0,1 v0,p0, v1,p1;g=0, −p1
( )
⎡
⎣⎤
⎦=
D1v1,p1;g=0, −p1
( )
( )
−
D0v1,p1;g=0, −p1
( )
( )
⎡
⎣⎤
⎦
(11)
Taking the average of expressions (10) and (11) yields:
ETechCh0,1 v0,p0, v1,p1;g=0, −p
( )
⎡
⎣⎤
⎦=1
2
D1v0,p0;g=0, −p0
( )
( )
−
D0v0,p0;g=0, −p0
( )
( )
⎡
⎣
⎢
+
D1v1,p1;g=0, −p1
( )
( )
−
D0v1,p1;g=0, −p1
( )
( )
⎤
⎦
⎥
(12)
This indicator of environmental technical change measures the increase/decrease in pollu-
tants due to the shift in environmental technology between periods 0 and 1.
Joining together eco-efficiency change and environmental technical change in expressions (9)
and (12), respectively, yields what we call here the proportional Luenberger environmental per-
formance change indicator, which is formally expressed as:
LEPCh 0,1 v0,p0,v1,p1;g=0,−p
( )
⎡
⎣⎤
⎦=EEffCh0,1 v0,p0, v1,p1;g=0, −p
( )
⎡
⎣⎤
⎦
+ETechCh0,1 v0,p0, v1,p1;g=0, −p
( )
⎡
⎣⎤
⎦
(13)
This indicator measures the change in environmental performance as a result of eco-efficiency
change and environmental technical change, assessed in a direction that reduces all pollutants
8 Boussemart et al. (2003) compare the relative performance of Malmquist indices and Luenberger indicators.
10
proportionally while maintaining value added. This decomposition would be equivalent to
the dynamic decomposition of environmental performance proposed by Kortelainen (2008),
but computed using Luenberger indicators and directional distance functions instead of
Malmquist indices and conventional Shephard’s distances.9 Nonetheless, the assumption of
proportionality might be overly restrictive as it does not allow modelling some preferences
regarding the trade-off between economic performance and ecological performance, which
might be of interest to researchers, managers and/or policymakers.10
On the contrary, the use of directional distance functions and Luenberger indicators makes it
possible to assess environmental performance change in terms other than radial or propor-
tional measures. Let us therefore consider a scenario in which policymakers are interested in
assessing the change in environmental performance in a scenario in which only one pollutant
or group of pollutants, denoted by i, are reduced without decreasing economic value added
and with no increase in the remaining pollutants, which are denoted by –i. In this scenario, the
directional distance function that assesses eco-efficiency in period t is:
Eco −efficiencyi
t=EEffi
t=
Di
tvt,pt;g=0,(−pi
t,0)
( )
⎡
⎣⎤
⎦=Sup βi1− βi
( )
pi
t,p-i
t
( )
∈PRStvt
( )
⎡
⎣⎤
⎦
(14)
Furthermore, eco-efficiency change between periods 0 and 1 in this scenario is:
EEffChi
0,1 v0,p0, v1,p1;g=0, −pi,0
( )
( )
⎡
⎣⎤
⎦=
Di
0v0,p0;g=0, −pi
0,0
( )
( )
( )
⎡
⎣
⎢
−
Di
1v1,p1;g=0, −pi
1,0
( )
( )
( )
⎤
⎦
⎥
(15)
while environmental technical change between 0 and 1 is:
9 Briec et al. (2012) demonstrate the exact relationship that exists between Malmquist indices and Luenberger
indicators in the conventional case where all inputs are proportionally reduced, which is formally equivalent
to our proportional indicator of change in environmental performance.
10 Furthermore, slacks in value added and pollutants would not be accounted for under this assumption,
when they might be an important source of inefficiency (Mahlberg and Sahoo 2011).
11
ETechChi
0,1 v0,p0, v1,p1;g=0, −pi,0
( )
( )
⎡
⎣⎤
⎦=1
2
Di
1v0,p0;g=0, −pi
0,0
( )
( )
( )
−
Di
0v0,p0;g=0, −pi
0,0
( )
( )
( )
⎡
⎣
⎢
⎢
⎢
+
Di
1v1,p1;g=0, −pi
1,0
( )
( )
( )
−
Di
0v1,p1;g=0, −pi
1,0
( )
( )
( )
⎤
⎦
⎥
⎥
⎥
(16)
Finally, the indicator of environmental performance change between periods 0 and 1 for a pollu-
tant or group of pollutants i, which we will refer to as the pollutant-specific Luenberger environmen-
tal performance change indicator, can be defined as:
LEPChi
0,1 v0,p0, v1,p1;g=0, −pi,0
( )
( )
⎡
⎣⎤
⎦=EEffChi
0,1 v0,p0, v1,p1;g=0, −pi,0
( )
( )
⎡
⎣⎤
⎦
+ETechChi
0,1 v0,p0, v1,p1;g=0, −pi,0
( )
( )
⎡
⎣⎤
⎦
(17)
The main interest in assessing intertemporal environmental performance and its determinants
using directional distance functions and pollutant-specific directions is that both proportional
and non-proportional Luenberger indicators could yield different rates of environmental per-
formance change, eco-efficiency change and environmental technical change.11 What is more,
change estimates are also expected to be different depending on the specific direction chosen
for the reduction of pollutants. In our opinion, these features could yield worthwhile infor-
mation to policymakers, helping them to design better environmental policies; e.g., if policy-
makers are aware of scarce environmental performance progress regarding a particular pollu-
tant due to slow environmental technical change, policy measures particularly aimed at pro-
moting green technologies and eco-innovations in the management of this pollutant would
probably be put in practice. Figure 1 illustrates this assertion.
In the picture we consider a technology that generates an added value v and two contami-
nants, namely p1 and p2, and is represented by the PRS(v). For the sake of simplicity, we eval-
uate environmental technical change projecting the observation of DMU k in period 1, namely
11 Furthermore, our DEA-based approach could also model other scenarios involving, for example, im-
provements in economic performance while pollutants are maintained or simultaneous increases in value
added and decreases in pollutants.
12
k1, onto the eco-efficient frontiers of periods 0 and 1. Projecting in a direction that only reduc-
es p2 while maintaining value added and p1 at their observed levels allows us to assess the
potential saving achievable through environmental technical change. This potential is meas-
ured by the segment FE and comes from the difference between the directional distance func-
tions of observation k1 projected onto the eco-efficient frontiers of periods 1 and 0, respective-
ly. However, with a direction that only reduces pollutant p1, always maintaining value added
and p2, the potential saving due to the environmental technical change occurred between pe-
riods 0 and 1 is measured by DC. Figure 1 also shows the potential saving in pollutants p1 and
p2 due to the change in environmental technology in a scenario where directional distance
functions are computed assuming proportional reductions in both pollutants; in this case, BA
would represent environmental technical change. Noticeably, the contribution of environmen-
tal technical change to the change in environmental performance could be quite different de-
pending on the scenario considered, i.e., the direction vector.
2.2. Computing directional distance functions with Data Envelopment Analysis
Data Envelopment Analysis is a well-known non-parametric approach to efficiency measure-
ment initially proposed by Charnes et al. (1978) that has been used in hundreds of empirical
papers (see Cook and Seiford 2009 for a review). In essence, this technique permits simultane-
ously constructing frontier technology from data on best observed practices in a sample of
DMUs and calculating the distance that separates each DMU to that frontier in terms of a per-
formance indicator (see Cooper et al. 2007 for details). Given the absence of prices for pollu-
tants in our case study, an important advantage of DEA over other approaches to building
composite indicators12 is that the scheme of weightings used to aggregate contaminants is en-
dogenously generated at DMU level. Based on the so-called benefit of the doubt principle (Cher-
chye et al. 2007), DEA assigns to each DMU evaluated the set of weights that rates it in the
most favourable light when compared to all other DMUs in the sample using the same set of
weights.13
12 Zhou et al. (2006) compares several aggregating methods to construct composite environmental indicators.
13
Using a direction that reduces all pollutants proportionally, the DEA-based program required
to compute the directional distance function of an observation or DMU k’ on period 0 with
respect to its contemporaneous technology is:
Maximize βk' , zk
D0v0,p0;g=0, −p0
( )
⎡
⎣⎤
⎦=βk'
subject to:
vk'
0≤zkvk
0
k=1
K
∑(i)
1− βk '
( )
pk' n
0≥zkpkn
0
k=1
K
∑n=1,..., N (ii)
zk≥0 k =1,..., K (iii)
(18)
with zk standing for the weight of each DMU k in the composition of the virtual eco-efficient
observation on the technological frontier DMU k’ is compared to.
Furthermore, computing the directional distance function of DMU k’ in this scenario in period
0 with respect to the technology in period 1 requires solving the following linear program:
Maximize βk' , zk
D1v0,p0,v1,p1;g=0,−p0
( )
⎡
⎣⎤
⎦=βk'
subject to:
vk'
0≤zkvk
1
k=1
K
∑(i)
1− βk '
( )
pk' n
0≥zkpkn
1
k=1
K
∑n=1,..., N (ii)
zk≥0 k =1,..., K (iii)
(19)
On the other hand, with a direction vector that reduces one pollutant alone or a group of pol-
lutants i, the contemporaneous directional distance function of DMU k’ in period 0 and the
directional distance function in period 0 with respect to the technology in period 1 can be
computed, respectively, as:
13 In some cases the optimal set of weights can assign great importance (weights) to pollutants that are scarce-
ly relevant for managers or policymakers. Kuosmanen and Kortelainen (2005) proposed dealing with this
problem by imposing additional a priori restrictions on the relative importance of different contaminants.
Allen and Thanassoulis, 2004 reviews several techniques to incorporate weighting restrictions in DEA.
14
Maximize βik' , zk
!
Di
0v0,p0;g=0, −pi
0,0
( )
( )
⎡
⎣⎤
⎦=βik'
subject to:
vk'
0≤zkvk
0
k=1
K
∑(i)
1− βik '
( )
pik'
0≥zkpik
0
k=1
K
∑i∈n=1,..., N and i ∉−i (ii)
p−ik'
0≥zkp−ik
0
k=1
K
∑−i∈n=1,..., N (iii)
zk≥0 k =1,..., K (iv)
(20)
and
Maximize βik' , zk
!
Di
1v0,p0,v1,p1;g=0, −pi
0,0
( )
( )
⎡
⎣⎤
⎦=βik'
subject to:
vk'
0≤zkvk
1
k=1
K
∑(i)
1− βik '
( )
pik'
0≥zkpik
1
k=1
K
∑i∈n=1,..., N and i ∉−i (ii)
p−ik'
0≥zkp−ik
1
k=1
K
∑−i∈n=1,..., N (iii)
zk≥0 k =1,..., K (iv)
(21)
In programs (18) to (21) we have assumed that the technology exhibits constant returns to
scale by allowing the sum of the elements of the intensities vector to be free (Banker et al.
1984). Picazo-Tadeo et al. (2012, p.802) provides a detailed justification of this assumption in
the framework of eco-efficiency measurement. In essence, the size of production activity mat-
ters little in the assessment of eco-efficiency, as we are interested on the ratio of value added
to an aggregate pollutant, and in the literature of DEA this is interpreted as a constant returns
to scale model (see Kortelainen and Kuosmanen, 2004). Moreover, as noted by Beltrán-Esteve
et al. (2014), the non-radial nature of some of our eco-efficiency measures might cause difficul-
ties when measuring returns to scale (see Krivonozhko et al. 2012; Torgersen et al. 1996). Fur-
thermore, minor changes of notation are needed to formulate the programs required to obtain
the contemporaneous directional distance functions of observation k’ in period 1, as well as
the directional distance functions with respect to the technology in period 0, which is left to
the readers.
15
3. Intertemporal environmental performance in greenhouse gas emissions in the EU-28
3.1. Dataset and variables
In this paper, the environmental technology is constructed using data on EU-28 member state
emissions of the three main GHGs for which reduction targets were agreed in the Kyoto Proto-
col, namely, carbon dioxide (CO2), nitrous oxide (N2O) and methane (CH4), to account for en-
vironmental performance. Furthermore, economic performance is measured by real Gross
Domestic Product in purchasing power parity (GDP PPP) (constant 2005 international $).14 On
the one hand, figures on the above-mentioned air pollutants, which jointly represent around
98% of aggregate GHG emissions in the EU-28, come from the Annual European Union Green-
house Inventory 1990-2011 of the European Environmental Agency (EEA, 2013)15 and cover the
period 1990-2011. Concerning GHG-emitting sectors, our aggregates include emissions from
the sectors of energy, industrial processes, solvents and other product use, agriculture, waste
and, finally, others. Furthermore, emissions are measured in CO2 equivalent million tons. On
the other hand, data on EU-28 countries’ GDP in PPP come from the World Development Indica-
tors database of the World Bank.16,17 Table 1 displays the amount of emissions in 1990 and 2011.
14 As noted in the Introduction, there is no consensus regarding the definition of eco-efficiency and, thus, the
characterisation of the environmental technology. In addition to the already-mentioned arguments of easi-
ness of calculation and interpretation of the concept of eco-efficiency used in this paper, the inclusion of ad-
ditional variables, such as inputs labour and capital, would have introduced some difficulties in our empiri-
cal analysis. On the one hand, there are problems to obtain reliable data for some European countries on
input capital for the whole period 1990-2011. On the other hand, provided that our sample size is limited to
current members of the EU-28, involving more variables in our DEA-based models, in addition to GDP and
three air pollutants, would have noticeably decreased their capacity of discrimination (see Cooper et al. 2007
for details).
15 Accessed on 13th September 2013 through http://www.eea.europa.eu.
16 Accessed on 13th September 2013 through http://databank.worldbank.org.
17 This source does not provide data for some years in the 1990s for Estonia, Ireland and Croatia. In these
cases, the series have been extrapolated back by applying to available data growth rates of GDP at 2005 pric-
es from the Annual Macro-economic Database of the European Commission’s Directorate General for Economic and
Financial Affairs (AMECO) (accessed through http://ec.europa.eu/economy_finance/db_indicators/ameco
on 19th September 2013). Additionally, figures for Croatia in years 1990 and 1991 have been extrapolated back
using average growth rates of GDP PPP in 2005 international $ of Macedonia, Serbia and Slovenia, three of
16
Moreover, we have calculated the intensity of emissions as the ratio of GHG emissions to GDP
PPP, which in the EU-28 has dropped from an average of 0.56 CO2 equivalent tons per 1,000$
of GDP PPP in 1990-1992 to 0.33 in 2009-2011. Reductions are particularly significant in the
Eastern countries that joined the EU from 2004, which is highly relevant considering that the
intensity of GHG emissions in these economies was noticeably higher. Meanwhile, reductions
in countries from the former EU-15 are also significant, albeit to a lesser extent.18 The patterns
of behaviour for the intensity of emissions of individual GHG are rather similar.
3.2. Results: eco-efficiency change versus environmental technical change
Intertemporal environmental performance has been assessed for each member of the EU-28 in
four scenarios that contemplate different objectives regarding GHG reduction, namely, pro-
portional reduction of all three gases considered and specific reductions of CO2, N2O and CH4,
respectively. Results are in Table 2, which displays countries’ average growth rates in the Lu-
enberger environmental performance change indicator and its determinants, eco-efficiency change
and environmental technical change, over the period 1990-2011. Given the additive nature of
directional distance functions, it is worth remembering here that the growth rate of environ-
mental performance can be obtained as the sum of the growth rates of eco-efficiency and envi-
ronmental technical change.
Before commenting on these results, let us say that in some cross-period programs, i.e., pro-
grams in which the observation of one period is compared to the technology of a different
period, the observation under evaluation remained outside of the PGTS, so no feasible posi-
tive solution existed for directional distance functions in these super-efficient observations. In
the current countries that in the 1990s integrated the former Yugoslavia for which data are available. Finally,
we have obtained GDP PPP for Estonia in years 1990 to 1992 by applying the average of growth rates for
Latvia and Lithuania, the other two Baltic Republics. While allowing analysis of environmental performance
in the whole EU-28, these criteria impose, in our opinion, very little cost in terms of the accuracy of our re-
sults. The main reason is that Croatia, Estonia and Ireland never appear as eco-efficiency peers for other Eu-
ropean countries.
18 Figures on emission intensities for individual EU-28 members are available upon request.
17
particular, infeasibility has occurred for 346 out of 4,704 cross-period programs, i.e., 7.3%, in-
volving two countries usually located on the eco-efficient frontier, namely, Sweden and Malta,
in addition to some other few countries like Austria, France, Italy, Portugal and Spain in the
1990s, and Luxembourg in some years at the end of the period studied.
No easy solution in an economically meaningful way exists for infeasibility in the framework
of the Luenberger productivity indicator (Briec and Kerstens 2009). The more common solu-
tions used in literature to deal with this drawback are either assigning a value of no change to
infeasible observations, i.e., a value equal to zero in our case study, or simply omitting them
from the computation of averages. Notwithstanding, we have dealt with infeasibility using
the recent proposal by Mahlberg and Sahoo (2011), which consists of relaxing the assumption
of non-negativity in the empirical computation of the directional distance functions, in order
the underlying objective of projecting super-efficient observations on the eco-efficient frontier
to be achieved.19 This approach assures feasibility when the direction vector is of full dimen-
sion, as is the case with our proportional indicator of environmental performance change. Con-
versely, when the direction vector is not of full dimension, as in our three pollutant-specific
indicators, feasibility is not assured (see Briec and Kerstens 2009). By using this procedure,
problems with no solution have decreased to 161 (3.4% of total cross-period programs).20 Fur-
thermore, observations for which infeasibility still remained have been omitted from the com-
putation of the averages for the period 1990-2011 of pollutant-specific environmental perfor-
mance growth, eco-efficiency change and environmental technical change.21
19 These cross-period programs will yield feasible although negative solutions, implying that pollutants need
to be increased to achieve the technological frontier (see Mahlberg and Sahoo, 2011, p.723 for details).
20 Considering jointly both cross-period and contemporaneous programs involved in our analysis, infeasibil-
ity goes down to 2.2%, which is noticeably lower than figures reported in other similar studies (Chung et al.,
1997; Färe et al. 2001; Yoruk and Zaim, 2005).
21 In the case of CO2, averages for Luxembourg have been computed using 13 (out of 21) year-to-year growth
rates; for the pollutant N2O, averages of France, Italy and Luxembourg have been calculated using 16, 20 and
13 growth rates, respectively; furthermore, regarding CH4, averages for Austria, France, Italy, Portugal and
Spain have been calculated using, respectively, 15, 16, 20, 17 and 20 growth rates. Finally, due to insufficient
number of year-to-year growth rates (below 13), averages of environmental performance change and envi-
18
Moving on to the results, in the scenario where all GHG are reduced by the same proportion,
i.e., proportional GHG environmental performance, environmental performance in the EU-28 has
improved during the period 1990-2011 by an annual average rate of 1.86%. Moreover, with an
average annual growth of 1.68%, technical progress has been by far the main driving force
behind the increase in environmental performance, while eco-efficiency has scarcely grown at
an average rate of 0.18%. In other words, improvements in environmental technology explain
90% of the growth reached by environmental performance in the EU-28 from the 1990s, while
eco-efficiency gains, i.e., catching-up with best available environmental practices, explain just
the remaining 10%. This result is in line with the findings in Kortelainen (2008).22
The countries that display the highest growth rates in environmental performance are Lux-
embourg, Sweden, the United Kingdom and Germany, in addition to Lithuania and Latvia. At
the opposite end of the scale, the poorest performance growth is observed in some of the East-
ern countries more recently incorporated into the EU-28, particularly Croatia, Bulgaria and
Estonia, and also in some Southern European countries such Greece, Cyprus, Portugal and
Spain. Concerning countries driving environmental technical change23, Sweden and Malta are
identified as eco-innovators in most year-to-year periods (16 and 13 times, respectively, out of
21), while Luxembourg also appears as innovator at the end of the period analysed (6 times).
Furthermore, other countries like Austria and France are also innovators but just in a few
year-to-year periods at the beginning of the 1990s (only 3 times in both cases).24 Finally, re-
ronmental technical change have not been computed for Malta in the case of CO2, and Malta and Sweden for
pollutants N2O and CH4.
22 Furthermore, this result coincides with a recent work by Mahlberg and Luptacik (2014) that assesses eco-
efficiency and eco-productivity change in the Austrian economy over the period 1995-2007 within the
framework of an augmented Leontief’s input-output model. This paper also finds eco-technical progress as
the main driving force of eco-productivity change.
23 Following Färe et al. (1994, p.79), a country has been considered an eco-innovator between periods 0 and 1
when the following three conditions are achieved. First, the country has experienced positive environmental
technical change from period 0 to period 1; second, observed GDP and pollutants in period 1 are not achiev-
able with the technology of period 0; and, third and final, the country is fully eco-efficient in period 1.
24 Most of the countries identified as eco-innovators in our research, are also identified as innovators by Oh
19
garding changes in eco-efficiency, the greatest improvements correspond to Luxembourg, the
United Kingdom25 and Germany, in addition to Lithuania and the Slovak Republic, whereas
eco-efficiency has even deteriorated in South European economies such as Italy, Spain or Por-
tugal, as well as in several Eastern countries.
In the scenarios where eco-performance is assessed at specific GHG level, i.e., pollutant-specific
environmental performance, the overall result that environmental technical change has been the
main driving force behind environmental performance growth in the EU-28 holds. Notwith-
standing, some features are worth mentioning adding interest to the approach proposed in
this paper. In the case of CO2, the change in environmental performance has reached an annu-
al average of 2.04% and has been entirely driven by environmental technical change, insofar
as eco-efficiency has remained virtually stagnant and even deteriorated at an annual rate of
0.04%. Moreover, Sweden is by far the major eco-innovator moving up the environmental
technological frontier as far as this air pollutant is concerned. The results for N2O emissions
are quite similar in that eco-efficiency has remained stagnant and the only source of environ-
mental performance growth has been environmental technical change; in this case, innovative
countries are particularly Malta and Austria.
Finally, the results for pollutant CH4 are somewhat different insofar eco-efficiency change
makes a positive contribution to the progress reached by environmental performance in the
period, i.e., nearly 21% of total growth; conversely, the contribution of environmental tech-
nical change is lower than in the case of the other two abovementioned pollutants. The main
eco-innovator country is now Luxembourg.
In order to provide further insight into the relative levels of eco-efficiency among EU-28
member states, Table 3 displays the averages of eco-efficiency at both the beginning and also
(2010) in a paper that analyses environmentally sensitive productivity growth and its determinants in 26
OECD countries for the period of 1990–2003.
25 Recent studies have also found important improvements in environmental performance and/or eco-
efficiency in the United Kingdom (Kortelainen, 2008; Marrero, 2010).
20
the end of the period analysed. For the period 2009-2011, GHG proportional eco-efficiency
records an average across EU-28 member states of 0.326, indicating that a proportional reduc-
tion of all three emissions of 32.6% could be achieved while maintaining value added at ob-
served levels. Furthermore, averages of eco-efficiency scores for CO2, N2O and CH4 are 0.408,
0.640 and 0.535, respectively;26 hence, the best eco-efficiency average corresponds to pollutant
CO2 and the worst to emissions of N2O. Concerning individual countries, the eco-efficient
peers that under-performers are compared with are Malta, Sweden and, although to a much
lesser extent, some other countries like Luxemburg at the end of the period; other highly eco-
efficient economies are Austria and the United Kingdom. Conversely, the worst eco-efficiency
is observed, by far, in Eastern European economies that joined the EU-28 from 2004, such as
Bulgaria, Romania, Estonia and Poland.
The eco-efficiency profile observed in 1990-1992 is similar, with some core European countries
and some Nordic economies among the most eco-efficient and the most recent EU members
occupying the bottom of the ranking. Furthermore, it is worth commenting here that the sharp
GDP decline during the transition process of the former communist countries in Central and
Eastern Europe in the 1990s, and even after year 2000 in Southeast Europe, reduced their lev-
els of eco-efficiency.
4. Discussion and policy implications
Under the Kyoto Protocol, the members of the former EU-15 agreed to cut down their collective
GHG emissions by 2012 to 8% below the levels recorded in the base year 1990, an objective
that is on course to be overachieved as emissions in 2011 are estimated to have decreased by
14.7% (EEA, 2013). In addition, most of the newer Eastern members of the EU have also
agreed significant reduction targets so the combined reduction of GHG emissions in 2011 for
the EU-28 has already reached 18.2% (see Table 1). In addition, according to the EEA (2012),
26 These scores of eco-efficiency at the end of the period analysed and, above all, their evolution from the year
2008 should be interpreted in the context of the current financial and economic crisis in Europe.
21
most EU members forecast that in 2020 their emissions outside the EU Emissions Trading Sys-
tem27 will be lower than their national targets set under the EU Climate and Energy Package.
Beyond the reduction in GHG emissions achieved in the EU-28 since the 1990s, which has
resulted in a considerable enhancement of ecological performance, our results in this paper
show that when economic performance and ecological performance are jointly considered,
there has also been a clear improvement. Furthermore, environmental technological change
has been, definitely, the main driving force behind environmental performance enhancement,
while average eco-efficiency change has even been negative in regard to some particular air
pollutants. Accordingly, one policy conclusion from these results is that more effort is re-
quired on behalf of European environmental policymakers to encourage catching-up among
European members. In other words, research and development policies focused on investigat-
ing new emission saving technologies might not be enough if best practices are not later ap-
plied in full to production processes and generally to the management of air pollutants by
European countries, allowing them to approach the environmental technological frontier.28
Differences in eco-efficiency among European countries might be due to different capabilities
to jointly manage production processes and the environment, but also to other circumstances
such as different levels of development, differences in citizens’ environmental awareness or,
largely, different production structures.29 Among most eco-efficient countries in our case
study, Luxembourg is the richest economy in the EU-28 and has a productive structure highly
oriented towards services, particularly banking and finance. Sweden is also a highly devel-
oped European country where, as in other Nordic economies, citizens have traditionally
27 Launched in 2005, the Emissions Trading System is one of the cornerstones of EU policy against climate
change, which works on a cap and trade principle; i.e., there is a limit on the emission of certain greenhouse
gases, but companies receive emission allowances which they can sell to or buy from one another as needed.
28 Strengthening both eco-innovations and eco-efficiency was, in fact, already identified by the EU as a key
option to achieve the competitiveness targets in the Lisbon Agenda (EC 2010).
29 Production structures are, in turn, influenced by countries’ endowment of productive resources and, also,
by international trade and flows of foreign direct investment; i.e., some developed countries might reallocate
polluting activities in developing countries with lower environmental standards (pollution haven hypothesis).
22
shown a high level of environmental awareness.30 In contrast, less eco-efficient countries,
mostly the newer Eastern members of the EU-28, have production structures oriented to more
contaminating industrial activities31 and, moreover, environmental regulations and environ-
mental awareness on behalf of citizens are more recent than in other Western European coun-
tries.
Most of the aforementioned factors affecting countries’ eco-efficiency, including citizens’ con-
cern for the environment or production structures, only change in the longer term. However,
this does not necessarily mean that medium and short term environmental policies aimed at
boosting eco-efficiency cannot be effective. According to Ahtonen and Chiorean-Sime (2012),
environmental measures targeted at making eco-efficiency a driver for growth in the EU
should focus on five essential aspects, namely, building a bigger market for products and ser-
vices that contribute to a greener economy; establishing a system of prices of environmental
resources that reflects the true cost of using them; increasing public and private investment
for greener products and services; finding fresh approaches to meeting the 20/20/20 target;
and, finally, building a knowledge-base, educating stakeholders and empowering consumers.
Moving on to particular measures of environmental policy to encourage eco-efficiency in the
EU, pushing the consumption of eco-efficient goods and services within the European Single
Market, e.g., providing consumers with better and more transparent information on green
products, or including commitments in favour of trade liberalisation of green technologies in
trade agreements with third countries, would be highly recommended regarding the function-
ing of markets. Likewise, creating incentives for firms to invest in eco-efficient technologies,
e.g., providing loans and access to venture capital to small and medium enterprises (SMEs) or
promoting public-private partnerships as instruments in leveraging private capital, would
30 Results from several special editions of the Eurobarometer carried out by the European Commission support
this assertion (EC 2008; 2009).
31 According to the data from the Statistical Office of the European Communities (Eurostat), the share of industry
and energy activities in the aggregate value added in Eastern countries in the EU currently averages 22%,
while in the former EU-15 is about 18%.
23
also be warmly recommended. Harmonised implementation across EU members and better
enforcement of existing environmental legislation like the Waste Framework Directive or im-
provement of the current functioning of the Emissions Trade Scheme, perhaps extending it into
a global emissions trading system, are also advisable. Lastly, insofar as inefficiencies are more
than likely related to poor technical management of production factors, i.e., overuse of inputs,
including energy, more general policy measures based on promoting skills and managerial
capabilities would also be a welcome means of improving eco-efficiency.
Clearly, some of the abovementioned policy recommendations are not new, as they constitute
keystones of current environmental policymaking against climate change in the EU. Notwith-
standing, in our view, performing studies aimed at providing scientific grounds to European
environmental policies, particularly from renewed perspectives as we do in this paper by
combining economic and environmental performance, is a must for researchers.
5. Concluding remarks and suggestions for further research
After two decades of prolific work, researchers in the field of ecological economics still con-
tinue to ride a wave of literature aimed at studying the relationship between economic activi-
ty and the environment. Building on Kortelainen (2008), our paper contributes an approach to
assessing intertemporal environmental performance as the result of eco-efficiency change and envi-
ronmental technical change at the level of the management of specific pollutants generated by
economic activity. Data Envelopment Analysis techniques, directional distance functions and
Luenberger productivity indicators are used to assess performance under different sets of pref-
erences as regards the trade-off between economic performance and ecological performance.
Our approach is used to measure environmental performance in the emissions of greenhouse
gases in the European Union-28 over the period 1990-2011. The main findings are summarised
as follows. First, environmental performance has noticeably improved in the period. Second,
environmental performance growth has been almost entirely due to environmental technical
progress, while eco-efficiency has remained virtually stagnant. Third, some core European
24
economies such as Luxembourg, Austria, the United Kingdom and Germany, in addition
Sweden, display the highest growth rates in environmental performance, while the lowest
rates are observed in Eastern European countries, particularly Croatia, Bulgaria and Estonia,
and also in Southern European economies like Greece, Cyprus, Spain and Portugal. Fourth
and finally, while Sweden and Malta, in addition to Luxembourg at the end of the period
studied, are considered as eco-innovator countries, the former communist economies perform
the furthest away from their technological frontiers.
The main policy implication from these results is that further environmental policy measures
are needed in the European Union to boost catching-up. In other words, in addition to boost-
ing research and development policies on eco-innovations, measures aimed at facilitating the
use of the best available environmental technologies that reduce the emission of greenhouse
gases are required; particularly as regards nitrous oxide and methane pollutants, which rec-
ord the lowest levels of eco-efficiency, and also in most of the recent Eastern members of the
European Union-28 that perform further away from the environmental frontier.
As a final point, we would like to mention certain clarifications and limitations that should be
taken into account when interpreting the results of our empirical application, together with
some lines for future work. On the one hand, our results concerning potential greenhouse gas
reductions are not measures of absolute ecological performance, but rather measures of eco-
logical performance relative to economic performance, and this should be accounted for when
designing environmental policies aimed at boosting sustainability. In this sense, eco-efficiency
improvement does not necessarily boost countries’ sustainability, as the latter demands taking
into account the absolute value of emissions and the capacity of the environment to absorb
them. However, improving eco-efficiency is often the least costly way of reducing the envi-
ronmental pressures that jeopardise sustainability; also, policies aimed at improving eco-
efficiency are easier to implement than more drastic measures restricting the level of economic
activity. Accordingly, improving eco-efficiency could be seen an essential ingredient to obtain
the environmental improvements that society demands at a minimum cost.
25
On the other hand, future work in this burgeoning field of research should include methodo-
logical challenges such as assessing environmental performance while controlling for coun-
tries’ different production structures or foreign investment flows, or computing other non-
radial slack-based measures of environmental performance with directional distance func-
tions. Furthermore, from an empirical point of view, one avenue for research that, in our opin-
ion, could be of great interest to policymakers could be to extend our approach to the analysis
of broader notions of eco-performance including, in addition to economic and ecological per-
formance, other dimensions of sustainability such as social performance.
Acknowledgments
The authors gratefully acknowledge the thoroughgoing comments from three anonymous
referees, which have greatly contributed to improving the manuscript. This research has been
funded by the Spanish Ministry of Economy and Competitiveness (AGL2010-17560-C02-02,
ECO2011-30260-C03-01 and ECO2012-32189). The usual disclaimer applies.
References
Allen, R., Thanassoulis, E., 2004. Improving envelopment in data envelopment analysis. Euro-
pean Journal of Operational Research 154(2), 363–379.
Ahtonen, A., Chiorean-Sime, S., 2012, Green revolution: making eco-efficiency a driver for
growth. EPC Issue Paper, 68. European Policy Center.
Balk, B., 2008. Price and quantity index numbers. Cambridge University Press, Cambridge.
Banker, R., Charnes, R., Cooper, W., 1984. Some models for estimating technical and scale in-
efficiencies in Data Envelopment Analysis. Management Science 30(9), 1078-1092.
Beltrán-Esteve, E., Gómez-Limón, J.A., Picazo-Tadeo, A.J., Reig-Martínez, E., 2014. A meta-
frontier directional distance function approach to assessing eco-efficiency. Journal of
Productivity Analysis 41(1), 69–83.
Boussemart, J.P., Briec, W., Kerstens, K., Poutineau, J.C., 2003. Luenberger and Malmquist
productivity indices: theoretical comparisons and empirical illustration. Bulletin of Eco-
nomic Research 55, 391–405.
26
Briec, W., Kerstens, K., Peypoch, N., 2012. Exact relations between four definitions of
productivity indices and indicators. Bulletin of Economic Research 64, 265–274.
Briec, W., Kerstens, K., 2009. Infeasibility and directional distance functions with application
to the determinateness of the Luenberger productivity indicator. Journal of Optimization
Theory and Applications 141, 55–73.
Camarero, M., Castillo-Giménez, J., Picazo-Tadeo, A.J., Tamarit, C., 2014. Is eco-efficiency in
greenhouse gas emissions converging among European Union countries? Empirical Eco-
nomics, in press; DOI: 10.1007/s00181-013-0734-1.
Chambers, R., Chung, Y., Färe, R., 1998. Profit, directional distance functions and Nerlovian
efficiency. Journal of Optimization Theory and Applications 98(2), 351-364.
Chambers, R.G., Färe, R., Grosskopf, S., 1996. Productivity growth in APEC countries. Pacific
Economic Review, 1996, 1(3): 181-90.
Charnes, A., Cooper, W.W., Rhodes, E., 1978. Measuring the efficiency of decision making
units. European Journal of Operational Research 2, 429-444.
Cherchye, L., Moesen, W., Rogge, N., van Puyenbroek, T., 2007. An introduction to ‘benefit of
the doubt’ composite indicators. Social Indicators Research 82(1), 111–145.
Chung, Y., Färe, R., Grosskopf, S. 1997. Productivity and undesirable outputs: A directional
distance function approach. Journal of Environmental Management 51, 229-240.
Cook, W.D., Seiford, L.M., 2009. Data envelopment analysis (DEA)-Thirty years on. European
Journal of Operational Research 192, 1-17.
Cooper, W.W., Seiford, L.M., Tone, K., 2007. Data Envelopment Analysis. A comprehensive
text with models, applications, references and DEA-Solver software. Springer, New York.
Dyckhoff, H., Allen, K., 2001. Measuring ecological efficiency with data envelopment analysis
(DEA). European Journal of Operational Research 132, 312–325.
EC, European Commission, 2008. The attitudes of European citizens towards the environ-
ment. Special Eurobarometer 295. Directorate General for the Environment. Brussels.
EC, European Commission, 2009. Europeans’ attitudes towards the issue of sustainable con-
sumption and production. Flash Eurobarometer Series 256. Directorate General for the En-
vironment. Brussels.
EC, European Commission, 2010. Europe 2020: A European strategy for smart, sustainable
and inclusive growth. Communication COM(2010) 2020. Brussels.
27
EEA, European Environment Agency, 2012. Greenhouse gas emission trends and projections
in Europe 2012. Tracking progress towards Kyoto and 2020 targets. Technical report,
6/2012, Luxembourg.
EEA, European Environmental Agency, 2013. Annual European Union greenhouse gas inven-
tory 1990–2011 and inventory report 2013. Technical report, 8/2013. Luxembourg.
Färe, R., Grosskopf, S., Norris, M., Zhang, Z., 1994. Productivity growth, technical progress
and efficiency change in industrialized countries. American Economic Review 84, 66-83.
Färe, R., Grosskopf, S., 2000. Theory and application of directional distance functions. Journal
of Productivity Analysis 13, 93-103.
Färe, R., Grosskopf, S., Pasurka, C.A., 2001. Accounting for air pollution emissions in
measures of state manufacturing productivity growth. Journal of Regional Science 41(3),
381-409.
Huppes, G., Ishikawa, M., 2005a. Why eco-efficiency. Journal of Industrial Ecology 9(4), 2-5.
Huppes, G., Ishikawa, M., 2005b. A framework for quantified eco-efficiency analysis. Journal
of Industrial Ecology, 9, 25-41.
Huppes, G., Ishikawa, M., 2009. Eco-efficiency guiding micro-level actions towards sustaina-
bility: Ten basic steps for analysis. Ecological Economics 68, 1687–1700.
Korhonen, P.J., Luptacik, M., 2004. Eco-efficiency analysis of power plants: an extension of
data envelopment analysis. European Journal of Operational Research 154, 437-446.
Kortelainen, M., 2008. Dynamic environmental performance analysis: A Malmquist index ap-
proach. Ecological Economics 64, 701-715.
Kortelainen, M., Kuosmanen, T., 2004. Measuring eco-efficiency of production: A frontier ap-
proach. EconWPA Working Paper at WUSTL, No. 0411004. Department of Economics,
Washington University, St. Louis, MO.
Krivonozhko, V., Førsund, F., Rozhnov, A., Lychev, A., 2012. Measurement of returns to scale
using a non-radial DEA model. Doklady Mathematics 85, 144–148 (Published in Russian in
Doklady Akademii Nauk 442, 605–609).
Kuosmanen, T., Kortelainen, M., 2005. Measuring eco-efficiency of production with Data En-
velopment Analysis. Journal of Industrial Ecology 9, 59-72.
Mahlberg, B., Sahoo, B., 2011. Radial and non-radial decompositions of Luenberger productiv-
ity indicator with an illustrative application. International Journal of Production Economics
131, 721–726.
28
Mahlberg, B., Luptacik, M., Sahoo, B., 2011. Examining the drivers of total factor productivity
change with an illustrative example of 14 EU countries. Ecological Economics 72, 60–69.
Mahlberg, B., Luptacik, M., 2014. Eco-efficiency and eco-productivity change over time in a
multisectoral economic system. European Journal of Operational Research 234, 885-897.
Malmquist, S., 1953. Index numbers and indifference surfaces. Trabajos de Estadística 4, 209–
242.
Marrero, G., 2010. Greenhouse gases emissions, growth and the energy mix in Europe. Energy
Economics 32, 1356–1363.
OECD, Organization for Economic Co-operation and Development, 1998. Eco-efficiency,
OECD, Paris.
Oh, D. 2010. A global Malmquist-Luenberger productivity index. Journal of Productivity
Analysis 34, 183-197.
Picazo-Tadeo, A.J., Beltrán-Esteve, M., Gómez-Limón, J.A. 2012. Assessing eco-efficiency with
directional distance functions. European Journal of Operational Research 220, 798-809.
Picazo-Tadeo, A.J., Gómez-Limón, J.A., Reig-Martínez, E., 2011. Assessing farming eco-
efficiency: A Data Envelopment Analysis approach. Journal of Environmental Manage-
ment, 92, 1154-1164.
Picazo-Tadeo, A.J., Reig-Martínez, E., Hernández-Sancho, F., 2005. Directional distance func-
tions and environmental regulation. Resource and Energy Economics 27, 131-142.
Shephard, W., 1970. Theory of cost and production functions. Princeton University Press,
Princeton.
Schaltegger, S., Synnestvedt, T., 2002. The link between ‘green’ and economic success: envi-
ronmental management as the crucial trigger between environmental and economic per-
formance. Journal of Environmental Management 65, 339-346.
Torgersen, A., Førsund, F., Kittelsen, S., 1996. Slack-adjusted efficiency measures and ranking
of efficient units. Journal of Productivity Analysis 7, 379–398.
United Nations, 2009. Eco-efficiency indicators: Measuring resource-use efficiency and the
impact of economic activities on the environment. Greening of Economic Growth Series,
ST/ESCAP/2561.
WCED, World Commission on Environment and Development, 1987. Our common future.
Oxford University Press, Oxford.
29
Yörük, B., Zaim, O. 2005. Productivity growth in OECD countries: A comparison with
Malmquist indices. Journal of Comparative Economics 33, 401-420.
Zhang, B., Bi, J., Fan, Z., Yuan, Z., Ge, J., 2008. Eco-efficiency analysis of industrial system in
China: a data envelopment analysis approach. Ecological Economics, 68, 306–316.
Zhou, P., Ang, B.W., Poh, K.L., 2006. Comparing aggregating methods for constructing the
composite environmental index: an objective measure. Ecological Economics 59, 305–311.
30
Figure 1
Pollutant-generating technology and environmental technical change
•
0
eco-efficient frontier
1
eco-efficient frontier
( )
PRS v
C
D
E
F
1
pollutant
2
pollutant
1
k
A
B
D2
1v1,p1; g =0,(0,−p2
1)
( )
⎡
⎣⎤
⎦
D2
0v1,p1; g =0,(0,−p2
1)
( )
⎡
⎣⎤
⎦
D1
0v1,p1; g =0,(−p1
1,0)
( )
⎡
⎣⎤
⎦
D1
1v1,p1; g =0,(−p1
1,0)
( )
⎡
⎣⎤
⎦
D0v1,p1; g =0,−p1
( )
⎡
⎣⎤
⎦
D1v1,p1; g =0,−p1
( )
⎡
⎣⎤
⎦
31
Table 1
Emissions1 of GHG in the EU-28 (CO2 equivalent million tons)
1990
2011
Carbon dioxide (CO2)
4,430.3
3,764.3
Nitrous oxide (N2O)
521.0
334.8
Methane (CH4)
594.6
387.6
Sulphur hexafluoride (SF6)
11.0
6.4
Hydrofluorocarbons (HFCs)
27.9
81.8
Perfluorocarbons (PFCs)
21.3
3.6
Aggregated emission (GHG)
5,601.1
4,578.5
1 In addition to the three air pollutants considered in our empirical analysis, figures on SF6, HFCs and
PFCs emissions are also included to illustrate their lesser importance in total GHG emission in the EU-28.
32
Table 2
Intertemporal environmental performance in the EU-28: Eco-efficiency change versus environmental technical change
(Averages for the period 1990-2011)1
Proportional GHG environmental performance
Carbon Dioxide (CO2) environmental performance
Luenberger Environmental
Performance Change
Indicator (LEPCh)
Eco-efficiency
Change
(EEffCh)
Environmental
Technical Change
(ETechCh)
Luenberger Environmental
Performance Change
Indicator (LEPCh)
Eco-efficiency
Change
(EEffCh)
Environmental
Technical Change
(ETechCh)
Austria
0.0180
-0.0039
0.0219
0.0250
-0.0094
0.0345
Belgium
0.0211
0.0061
0.0150
0.0171
-0.0016
0.0187
Bulgaria
0.0112
0.0037
0.0075
0.0087
0.0010
0.0077
Croatia
0.0097
-0.0074
0.0171
0.0092
-0.0074
0.0166
Cyprus
0.0102
-0.0037
0.0139
0.0064
-0.0084
0.0148
Czech Republic
0.0154
0.0057
0.0097
0.0119
0.0023
0.0096
Denmark
0.0155
-0.0040
0.0195
0.0152
-0.0030
0.0181
Estonia
0.0122
0.0064
0.0058
0.0088
0.0025
0.0064
Finland
0.0165
0.0007
0.0158
0.0092
-0.0049
0.0141
France
0.0171
-0.0094
0.0265
0.0179
-0.0094
0.0272
Germany
0.0255
0.0084
0.0170
0.0238
-0.0014
0.0252
Greece
0.0093
-0.0041
0.0134
0.0053
-0.0088
0.0141
Hungary
0.0154
0.0003
0.0151
0.0151
0.0002
0.0149
Ireland
0.0247
0.0065
0.0182
0.0247
0.0065
0.0182
Italy
0.0139
-0.0079
0.0218
0.0223
-0.0126
0.0348
Latvia
0.0262
0.0082
0.0180
0.0259
0.0082
0.0177
Lithuania
0.0274
0.0104
0.0170
0.0275
0.0104
0.0171
Luxembourg
0.0376
0.0160
0.0216
0.0507
0.0343
0.0164
Malta
0.0197
0.0000
0.0197
-
0.0000
-
Netherlands
0.0239
0.0054
0.0185
0.0242
0.0024
0.0218
Poland
0.0156
0.0066
0.0090
0.0126
0.0035
0.0091
Portugal
0.0104
-0.0090
0.0194
0.0162
-0.0158
0.0320
Romania
0.0158
0.0051
0.0107
0.0162
0.0053
0.0108
Slovak Republic
0.0208
0.0092
0.0116
0.0178
0.0066
0.0111
Slovenia
0.0131
-0.0027
0.0158
0.0095
-0.0068
0.0162
Spain
0.0129
-0.0085
0.0214
0.0192
-0.0148
0.0340
Sweden
0.0312
0.0000
0.0312
0.0708
0.0000
0.0708
United Kingdom
0.0295
0.0111
0.0184
0.0387
0.0083
0.0304
Average EU-282
0.0186
0.0018
0.0168
0.0204
-0.0004
0.0208
33
Table 2 (continued)
Nitrous Oxide (N2O) environmental performance
Methane (CH4) environmental performance
Luenberger Environmental
Performance Change
Indicator (LEPCh)
Eco-efficiency
Change
(EEffCh)
Environmental
Technical Change
(ETechCh)
Luenberger Environmental
Performance Change
Indicator (LEPCh)
Eco-efficiency
Change
(EEffCh)
Environmental
Technical Change
(ETechCh)
Austria
0.0586
-0.0106
0.0692
0.0299
0.0072
0.0228
Belgium
0.0114
0.0017
0.0098
0.0266
0.0119
0.0146
Bulgaria
0.0048
0.0020
0.0028
0.0054
0.0033
0.0021
Croatia
0.0038
-0.0018
0.0056
0.0045
-0.0026
0.0071
Cyprus
0.0079
0.0000
0.0079
0.0060
0.0007
0.0053
Czech Republic
0.0072
0.0019
0.0053
0.0110
0.0060
0.0050
Denmark
0.0197
0.0068
0.0129
0.0124
0.0019
0.0105
Estonia
0.0060
0.0019
0.0040
0.0100
0.0049
0.0050
Finland
0.0057
0.0005
0.0052
0.0164
0.0078
0.0086
France
0.0466
-0.0019
0.0485
0.0230
-0.0104
0.0333
Germany
0.0012
-0.0062
0.0074
0.0253
0.0157
0.0096
Greece
0.0071
0.0005
0.0065
0.0069
0.0001
0.0068
Hungary
0.0056
0.0011
0.0044
0.0086
0.0027
0.0059
Ireland
0.0179
0.0083
0.0095
0.0090
0.0054
0.0036
Italy
0.0334
-0.0279
0.0612
0.0330
0.0017
0.0313
Latvia
0.0101
0.0022
0.0079
0.0104
0.0052
0.0052
Lithuania
0.0055
0.0012
0.0044
0.0084
0.0040
0.0044
Luxembourg
0.0182
0.0057
0.0125
0.0380
0.0160
0.0220
Malta
-
0.0000
-
-
0.0000
-
Netherlands
0.0290
0.0098
0.0192
0.0219
0.0117
0.0102
Poland
0.0060
0.0023
0.0037
0.0052
-0.0047
0.0099
Portugal
0.0202
-0.0207
0.0409
-0.0023
-0.0165
0.0142
Romania
0.0039
0.0009
0.0030
0.0048
0.0005
0.0043
Slovak Republic
0.0090
0.0042
0.0048
0.0078
0.0024
0.0054
Slovenia
0.0066
-0.0012
0.0078
0.0083
0.0014
0.0069
Spain
0.0286
-0.0196
0.0482
0.0097
-0.0204
0.0301
Sweden
-
0.0000
-
-
0.0000
-
United Kingdom
0.0427
0.0199
0.0228
0.0286
0.0199
0.0087
Average EU-282
0.0160
-0.0007
0.0167
0.0142
0.0029
0.0113
1 Due to problems of infeasibility, in a very few countries averages have been computed using less than 21 year-to-year growth rates; furthermore, averages for the change in environmental
performance and environmental technical change are not computed for Malta in the case of CO2, and Malta and Sweden for pollutants N2O and CH4. See footnote 21 for details.
2 In order to maintain the decomposition additive, averages for the EU-28 have been computed excluding Malta in the case of pollutant CO2, and Malta and Sweden for N2O and CH4.
34
Table 3
Eco-efficiency in GHG emissions in the EU-28
Average 1990-1992
Average 2009-2011
GHG
CO2
N2O
CH4
GHG
CO2
N2O
CH4
Austria
0.037
0.053
0.141
0.234
0.116
0.223
0.374
0.221
Belgium
0.300
0.418
0.764
0.519
0.200
0.480
0.732
0.274
Bulgaria
0.747
0.748
0.939
0.931
0.671
0.722
0.898
0.850
Croatia
0.265
0.265
0.798
0.653
0.488
0.488
0.881
0.738
Cyprus
0.355
0.425
0.768
0.738
0.414
0.584
0.741
0.715
Czech Republic
0.670
0.719
0.868
0.829
0.545
0.668
0.823
0.688
Denmark
0.325
0.369
0.862
0.606
0.383
0.409
0.767
0.550
Estonia
0.800
0.860
0.924
0.813
0.656
0.789
0.874
0.703
Finland
0.430
0.457
0.841
0.686
0.408
0.555
0.830
0.497
France
0.022
0.021
0.455
0.228
0.205
0.205
0.473
0.437
Germany
0.319
0.398
0.640
0.591
0.198
0.456
0.730
0.276
Greece
0.377
0.407
0.822
0.686
0.433
0.575
0.789
0.644
Hungary
0.499
0.505
0.870
0.813
0.464
0.483
0.857
0.740
Ireland
0.473
0.473
0.930
0.918
0.361
0.361
0.776
0.798
Italy
0.007
0.010
0.030
0.085
0.166
0.252
0.487
0.385
Latvia
0.643
0.643
0.935
0.878
0.428
0.428
0.874
0.753
Lithuania
0.628
0.628
0.932
0.858
0.407
0.407
0.900
0.770
Luxembourg
0.329
0.537
0.650
0.329
0.000
0.000
0.000
0.000
Malta
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
Netherlands
0.299
0.317
0.801
0.719
0.192
0.273
0.603
0.473
Poland
0.746
0.771
0.908
0.772
0.600
0.684
0.864
0.763
Portugal
0.012
0.013
0.044
0.160
0.175
0.296
0.433
0.732
Romania
0.694
0.697
0.916
0.881
0.570
0.570
0.896
0.870
Slovak Republic
0.639
0.703
0.886
0.748
0.441
0.546
0.818
0.663
Slovenia
0.334
0.407
0.757
0.738
0.335
0.506
0.746
0.669
Spain
0.006
0.009
0.029
0.063
0.160
0.269
0.398
0.459
Sweden
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
United Kingdom
0.359
0.384
0.758
0.738
0.124
0.195
0.346
0.300
Average EU-281
0.368
0.401
0.652
0.579
0.326
0.408
0.640
0.535
Standard deviation
0.261
0.270
0.343
0.306
0.198
0.214
0.285
0.264
1 Computed as the arithmetic mean of all countries in the EU-28.