USE OF DEA APPROACH TO MEASURING EFFICIENCY TREND IN OLD EU
MEMBER STATES
Lukáš Melecký
Department of European Integration, Faculty of Economics, VŠB-Technical University of Ostrava
16. 9. 2013
CONTENT
I.
INTRODUCTION
II.
THEORETICAL FRAMEWORK OF EFFICIENCY CONCEPT
• Efficiency Analysis in the Context of Competitiveness and Performance
III. MEASUREMENT OF EFFICIENCY BY DEA APPROACH
• Theoretical Background of Data Envelopment Analysis
• Basis of DEA Model Specification
IV. EFFICIENCY ANALYSIS OF EU15 COUNTRIES
• Background of DEA Efficiency Analysis
• Characteristics of Data Base
• Specification of DEA models
V.
RESULTS AND DISCUSSION
VI. CONCLUSION
ACKNOWLEDGEMENT
„Macroeconomic Efficiency as a Factor of
Competitiveness in EU Member States in a Globalized
Economy“.
Project registration number:
SP 2013/45
Period of research:
1. 1. 2013 – 31. 12. 2013
Recipient:
VŠB–TU Ostrava, Faculty of Economics,
Department of European Integration
Supervisor:
Team Leader:
Team Members:
Ing. Boris Navrátil, CSc.
Ing. Michaela Staníčková
doc. Ing. Jana Hančlová, CSc.
Ing. Lukáš Melecký
Ing. Bohdan Váhalík
Bc. Nikol Pešlová
Bc. Karolína Popelářová
Bc. Tomáš Vyvial
Motivation
• Most of EU15 countries present one of the most developed
part of the world with high living standards.
X
• Nevertheless, there exist significant and huge economic,
social and territorial disparities having negative impact on
the balanced development across Member States and their
regions thus weaken EU’s performance and competitiveness
in a global context.
↓
• The process of achieving an increasing trend of performance
and a higher level of productivity and competitiveness is
significantly difficult by the heterogeneity of different areas
(countries, regions) in the European Union.
I. INTRODUCTION
• Aim of the paper:
– To measure efficiency level over the reference period (2000-2011) and to analyze a
level of productivity changes in individual EU15 countries based on the Malmquist
(productivity) index, and then to classify the old EU Member States to homogeneous
units (clusters) according to efficiency results based on the Cluster analysis.
• Research premises (assumptions):
−
−
−
The efficiency is perceive like a „mirror“ of competitiveness.
DEA method evaluates the efficiency of countries with regard to their ability to
transform inputs into outputs → countries achieving best (better) results in
efficiency coefficients are countries best (better) at converting inputs into outputs.
Countries achieving greater level of efficiency = better using of competitive
advantages = better competitive potential and perspectives.
• Research hypothesis:
– Advanced EU countries achieving best/better results in efficiency (e.g. Germany or
Scandinavian countries) are countries best/better at converting inputs into outputs
and therefore having greater performance and productive potential than less
developed EU countries (e.g. Mediterranean countries) within the group of EU15
evaluated countries, with regard to the economic crisis.
II. THEORETICAL FRAMEWORK OF EFFICIENCY CONCEPT (i)
•
In relation to competitiveness objectives, performance and efficiency
are complementary objectives, which determine the long-term
development of countries and regions, as it confirmed in many research
studies, e.g. (Farrell, 1957); (Molle, 2007); (Annoni, Kozovska, 2010); Mihaiu,
Opreana, Cristescu, 2010); (Melecký, Staníčková, 2012).
•
Measurement, analysis and evaluation of productivity changes,
efficiency and level of competitiveness are topics that acquire great
interest among researchers, because performance remains one of the
basic standards of efficiency evaluation and it is also seen as a
reflection of success of area (country/region) in a wider
(international/inter-regional) comparison (Hančlová, 2011); (Staníčková,
Skokan, 2013).
•
Efficiency is a central issue in analyses of economic growth, the effects
of fiscal policies, the pricing of capital assets, the level of investments,
the technology changes and production technology, and other
economic topics and indicators (Charnes, Cooper, Rhodes, 1978).
II. THEORETICAL FRAMEWORK OF EFFICIENCY CONCEPT (ii)
„Efficiency can be achieved under the conditions of maximizing
the results of an action in relation to the resources used,
and it is calculated by comparing the effects obtained in their efforts.“
(Charnes, Cooper, Rhodes, 1978)
Fig. 1 The triangle of the performance
Source: MIHAIU, D. M., OPREANA, A., and CRISTESCU, M. P., 2010
•
Efficiency and effectiveness analysis is based on the relationship between the inputs
(entries/actions), the outputs (results) and the outcomes (effects).
•
Efficiency (efektivita/účinnost) is given by the ratio of inputs to outputs, but there is
difference between the technical efficiency and the allocative efficiency.
•
Effectiveness (efektivita/účelnost) implies a relationship between outputs and
outcomes.
III. MEASUREMENT OF EFFICIENCY BY DEA APPROACH (i)
• Measurement of efficiency of EU countries (or regions), resp. their factors,
remains a conceptual challenge, because there are difficulties in efficiency
measuring:
• measurement of efficiency is highly sensitive to the data sets being
used. Good quality data are needed because the techniques available to
measure efficiency are sensitive to outliers and may be influenced by
exogenous factors,
• data used for international comparisons require a minimum level of
homogeneity.
•
Data Envelopment Analysis (DEA) is a mathematical quantitative approach for
providing a relative efficiency assessment and evaluating the performance of a
set of peer entities called Decision Making Units (DMUs).
III. MEASUREMENT OF EFFICIENCY BY DEA APPROACH (ii)
• An efficiency analysis by DEA approach compares the actual output of a
DMUs with the maximal output estimated by a production function.
• The best-practice units of a comparison group are used as a reference
for the evaluation of the other group units.
• DEA method examines DMUs on the effective and not effective by the
size and quantity of consumed resources by the produced output or
other type of output.
• The relative efficiency score in the presence of multiple input and
output factors is defined as:
III. MEASUREMENT OF EFFICIENCY BY DEA APPROACH (iii)
• Basis of DEA Models:
• Model selection:
• basic - CCR, BCC; additive – SBM; FDH, FRH; super efficiency models….)
• Shape of the Production possibility set:
• Constant Returns to Scale (CRS); Variable Returns to Scale (VRS)
• Orientation of the model:
• Input oriented model (I-O); Output oriented model ( O-O)
• Number of inputs and outputs (factors, items or performance measures):
•
•
•
The selection of performance measures is crucial for successful application
of DEA, e.g. (Cook, W.D., Zhu, J., 2007; Toloo, M., 2009, 2012, 2013).
Empirically, when the number of performance measures is high in
comparison with the number of DMUs, then most of DMUs are evaluated
efficient.
Copper et al. (2007) recommend a process of selecting a small set of input
and output items at the beginning and gradually enlarging the set to
observe the effects of the added items.
III. MEASUREMENT OF EFFICIENCY BY DEA APPROACH (iv)
• Basis of DEA Models:
• Number of performance measures: The rule of thumb:
n  max 3(m  s), m  s
where n is the number DMUs which consume m inputs to produce s
outputs.
• Statistically, in most of the empirical cases the number of inputs and
outputs do not exceed 6.
• A simple calculation shows that if m ≤ 6 and s ≤ 6, then 3(m+s) ≥ m×s.
Hence, the rule of thumb can be written as
n  3(m  s )
IV. EFFICIENCY ANALYSIS OF EU15 COUNTRIES (i)
• Basis of DEA Efficiency Analysis
•
•
•
•
Territorial definition: EU15 countries » 15 DMUs
Reference period: reference years 2000 (beginning of growth period), 2011 (last
year of complete data-base for all evaluated countries; post-crisis year)
Indicators: 61 selected indicators (m= 36 inputs, s = 25 outputs)
Measuring the efficiency level of EU15 countries is based on following
procedure:
Pre-processing phase – Input data analysis
Collection of indicators » Data analysis of indicators » Groups of indicators
for input and output
Data Envelopment Analysis
CCR I-O CRS model » efficiency evaluation;
Malmquist index » efficiency evaluation
Source: Own elaboration, 2013
• Data Envelopment Analysis method – developed DEA approach: Malmquist
(productivity) index based on input oriented Charnes-Cooper-Rhodes (IO CCR
CRS) model.
IV. EFFICIENCY ANALYSIS OF EU15 COUNTRIES (ii)
(ii)
• Database indicators:
• Based on Country Competitiveness Index (CCI) - pillars of CCI are grouped
according to the different dimensions (input versus output aspects) of national
competitiveness they describe. ‘Inputs’ and ‘outputs’ are meant to classify
pillars into those which describe driving forces of competitiveness, also in terms
of long-term potentiality, and those which are direct or indirect outcomes of a
competitive society and economy
• Eurostat, World Bank, Euro barometer, Organization for Economic Co-operation
and Development (OECD), European Cluster Observatory.
• 61 selected indicators (m = 36 inputs, s = 25 outputs).
• Appropriateness of the DEA model?
•
The thumb rule:
15  max 3(36  25), 36  25 → 15  max 61, 900
• How to deal with this issue?
•
Increasing the number of DMUs ? NO » »EU15 countries
•
Decreasing the number of performance measures? YES » » Factor analysis – using
extracted factors or Malmquist productivity index
IV. EFFICIENCY ANALYSIS OF EU15 COUNTRIES (iii)
• Specification of DEA model (i)
Dual version of input oriented CCR model assuming CRS:
min g   q - ε(eT s   eT s  ),
subject to:
X   s    q xq ,
Y   s   yq ,
 , s  , s   0,
where g is the coefficient of efficiency of DMUq; 𝜽𝒒 is radial variable indicates required rate of
reduction of input; ε is infinitesimal constant (usually 10-6 or 10-8) ; eT is vector; in the case of CRS
eT = (1, 1, …, 1); s+, and s− are vectors of slack variables expressing the difference between virtual
inputs/outputs and appropriate inputs/outputs of the observed DMUq; λ represent vector of weights
assigned to individual units; xq means vector of input of DMUq; yq means vector of output of DMUq;
X is input matrix; Y is output matrix.
In CCR I-O model the efficiency coefficient of efficient DMU equals 1, but the
efficiency coefficient of inefficient DMU is lower than 1.
IV. EFFICIENCY ANALYSIS OF EU15 COUNTRIES (iv)
• Specification of DEA model (ii)
The Malmquist index (M0) measures total efficiency change of production of unit
M0 between successive periods t and t+1
M0 (xt, yt, xt+1, yt+1)
We can decompose M0 , on the basis of maximization of production factors, into
two components:
M0 = TEC0 . TSF0 =
•
•
TEC0 = the change of technical efficiency = is change in the relative efficiency of unit DMU0
in relation to other units (i.e. due to the production possibility frontier) between time
periods t and t+1,
TSF0 = the change of technology efficiency = production frontier shift = describes the
change in the production possibility frontier as a result of the technology development
between time periods t and t+1.
IV. EFFICIENCY ANALYSIS OF EU15 COUNTRIES (v)
•TEC0 = the change of technical efficiency =
0t  x0t , y0t 
TEC0 
0t  x0t , y0t 

t 1
0
x
t 1
0
t 1
0
,y

,
= function that assigns for production unit 0 (DMU0) degree of effectiveness in time t with input x and output y
•TSF0 = the change of technology efficiency =
  x , y    x , y  
TSF0   t t 1 t 1  t t t 
 0  x0 , y0  0  x0 , y0  
t 1
0
TEC or TSF
<1
=1
>1
t 1
0
t 1
0
t 1
0
t
0
t
0
1
2
Efficiency meaning
Improving
Unchanging
Declining
V. RESULTS AND DISCUSSION (i) – CCR I-O CRS Model
Input-Oriented
CRS
DMU No. DMU Name Efficiency (2000)
1 BE0
2 DK0
3 DE0
4 IE0
5 EL0
6 ES0
7 FR0
8 IT0
9 LU0
10 NL0
11 AT0
12 PT0
13 FI0
14 SE0
15 UK0
1,00000
1,00000
1,00000
1,00000
1,00000
1,00000
1,00000
1,00000
1,00000
1,00000
1,00000
1,00000
1,00000
1,00000
1,00000
Input-Oriented
CRS
Efficiency (2011)
1,00000
1,00000
1,00000
1,00000
1,00000
1,00000
1,00000
1,00000
1,00000
1,00000
1,00000
1,00000
1,00000
1,00000
1,00000
Source: Own calculation and elaboration, 2013
S
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
RTS Benchmarks
Constant
1,000
Constant
1,000
Constant
1,000
Constant
1,000
Constant
1,000
Constant
1,000
Constant
1,000
Constant
1,000
Constant
1,000
Constant
1,000
Constant
1,000
Constant
1,000
Constant
1,000
Constant
1,000
Constant
1,000
BE0
DK0
DE0
IE0
EL0
ES0
FR0
IT0
LU0
NL0
AT0
PT0
FI0
SE0
UK0
The thumb rule:
15  3(36  25)
The thumb rule:
15  3(7  5)
V. RESULTS AND DISCUSSION (ii) – Malmquist index
Source: Own calculation and elaboration, 2013
V. RESULTS AND DISCUSSION (iii)
MI 2000-2011
Source: Own calculation and elaboration, 2013
V. RESULTS AND DISCUSSION (iv)
MI 2000-2011
‘Efficient’ countries‘
BE
4.5
UK
•
•
DK
4
3.5
SE
‘Highly efficient countries‘
DE
3
2.5
2
1.5
FI
Germany (DE)
Spain (ES)
IE
1
•
•
•
•
•
Sweden (SE)
France (FR)
Ireland (IE)
Italy (IT)
Portugal (PT)
0.5
‘Slightly inefficient countries’
0
PT
EL
AT
ES
NL
FR
LU
Source: Own calculation and elaboration, 2013
IT
•
•
•
•
•
•
Austria (AT)
Finland (FI)
Netherlands (NL)
Greece (EL)
Belgium (BE)
United Kingdom (UK)
‘Inefficient countries’
•
•
Denmark (DK)
Luxemburg (LU)
V. RESULTS AND DISCUSSION (v)
Country Cluster Profile
• Cluster Analysis has been used for defining clusters of countries based on the
results of efficiency analysis.
• The best interpretation of data ensures five-cluster solution in comparison years
2000 and 2011 by MI.
Clusters of EU15 countries
•
•
•
•
•
Cluster I is created by Ireland, Italy,
Portugal, France, Sweden, Germany
and Spain – increasing trend of
efficiency development.
Cluster II is characterized by
countries as Belgium, United
Kingdom and Greece – deteriorating
trend in efficiency.
Cluster III represents Austria,
Finland, and Netherlands – slight
efficiency deterioration
Cluster IV is created by Denmark –
highly declining efficiency trend.
Cluster V represents Luxemburg highly declining efficiency trend.
Source: Own calculation and elaboration, 2013
V. RESULTS AND DISCUSSION (vi)
• The initial hypothesis of efficiency being a mirror of competitive potential
has been „partly" confirmed through analysis by Malmquist productivity
index value:
• Some of advanced EU15 countries have recorded predominantly
total efficiency increase through the time period (Germany,
Ireland, Sweden)
• Most of advanced EU15 countries have reached predominantly
total efficiency decrease during reference years (Belgium,
Denmark, Netherlands, Austria, Finland and United Kingdom).
• Some of less developed EU15 countries have recorded
predominantly total efficiency increase through the time period
(Spain, Italy and Portugal).
• Only Greece (from the group of Mediterranean countries) have
reached predominantly total efficiency decrease during
reference years.
V. CONCLUSION
•
Applying advanced MI based on CCR I-O CRS model presents a possible way
of comparing efficiency across DMUs on national (country) level.
•
Based on the DEA analysis used IO CCR CRS MI has been found out:
•
there is a distinct gap between economic and social standards in terms of
evaluated countries, so differences still remain;
•
according to MI results, seven of EU15 countries has achieved noticeable
productivity decreases and performance deteriorating during reference
years;
•
EU15 countries experienced decline in their performance as a persistent
result of economic crisis in the year 2011.
•
The economic crisis has threatened the achievement of sustainable
development in the field of competitiveness. The crisis has underscored
importance of competitiveness-supporting economic environment to
enable economies better absorb shocks and ensure solid economic
performance going in future.
ACKNOWLEDGEMENT
Thank You for Your Attention
Q/A
Comments
Suggestions
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Lukáš Melecký
lukas.melecky@vsb.cz
Department of European Integration
Faculty of Economics, VŠB-Technical University of Ostrava
Katedra
evropské
integrace