USE OF DEA APPROACH TO MEASURING EFFICIENCY TREND IN OLD EU MEMBER STATESLukáš MeleckýDepartment of European Integration, Faculty of Economics, VŠB-Technical University of Ostrava16. 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 MeleckýIng. Bohdan VáhalíkBc. Nikol PešlováBc. Karolína PopelářováBc. 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.

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• 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.

• 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.

I. INTRODUCTION

• 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 (i)

„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)

• 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.

II. THEORETICAL FRAMEWORK OF EFFICIENCY CONCEPT (ii)

Fig. 1 The triangle of the performanceSource: MIHAIU, D. M., OPREANA, A., and CRISTESCU, M. P., 2010

• 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 (i)

• 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 (ii)

• 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 (iii)

• Basis of DEA Models:

• Number of performance measures: The rule of thumb:

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

III. MEASUREMENT OF EFFICIENCY BY DEA APPROACH (iv)

max 3( ),n m s m s

3( )n m s

• 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:

IV. EFFICIENCY ANALYSIS OF EU15 COUNTRIES (i)

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.

Pre-processing phase – Input data analysisCollection of indicators » Data analysis of indicators » Groups of indicators for input and output

Data Envelopment AnalysisCCR I-O CRS model » efficiency evaluation;

Malmquist index » efficiency evaluation

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:

• 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

15 max 3(36 25),36 25 → 15 max 61,900

IV. EFFICIENCY ANALYSIS OF EU15 COUNTRIES (iii)

• Specification of DEA model (i)Dual version of input oriented CCR model assuming CRS:

min - ε( ),T Tqg e s e s

subject to: ,

,

, , 0,

q q

q

X s x

Y s y

s s

where g is the coefficient of efficiency of DMUq; 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.

• 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 (iv)

• TEC0 = the change of technical efficiency =

• TSF0 = the change of technology efficiency =

IV. EFFICIENCY ANALYSIS OF EU15 COUNTRIES (v)

,,

,

t t t0 0 0

0 t 1 t 1 t 10 0 0

x yTEC

x y

,t t t0 0 0x y = function that assigns for production unit 0 (DMU0) degree of effectiveness in time t with input x and output y

, ,

, ,

12t 1 t 1 t 1 t 1 t t

0 0 0 0 0 0

0 t t 1 t 1 t t t0 0 0 0 0 0

x y x yTSF

x y x y

TEC or TSF Efficiency meaning

< 1 Improving

= 1 Unchanging

> 1 Declining

V. RESULTS AND DISCUSSION (i) – CCR I-O CRS Model

Source: Own calculation and elaboration, 2013

Input-Oriented Input-Oriented

CRS CRS

DMU No. DMU Name Effi ciency (2000) Effi ciency (2011) S RTS Benchmarks1 BE0 1,00000 1,00000 1,000 Constant 1,000 BE02 DK0 1,00000 1,00000 1,000 Constant 1,000 DK03 DE0 1,00000 1,00000 1,000 Constant 1,000 DE04 IE0 1,00000 1,00000 1,000 Constant 1,000 IE05 EL0 1,00000 1,00000 1,000 Constant 1,000 EL06 ES0 1,00000 1,00000 1,000 Constant 1,000 ES07 FR0 1,00000 1,00000 1,000 Constant 1,000 FR08 IT0 1,00000 1,00000 1,000 Constant 1,000 IT09 LU0 1,00000 1,00000 1,000 Constant 1,000 LU0

10 NL0 1,00000 1,00000 1,000 Constant 1,000 NL011 AT0 1,00000 1,00000 1,000 Constant 1,000 AT012 PT0 1,00000 1,00000 1,000 Constant 1,000 PT013 FI0 1,00000 1,00000 1,000 Constant 1,000 FI014 SE0 1,00000 1,00000 1,000 Constant 1,000 SE015 UK0 1,00000 1,00000 1,000 Constant 1,000 UK0

15 3(7 5)

15 3(36 25)

The thumb rule:

The thumb rule:

V. RESULTS AND DISCUSSION (ii) – Malmquist index

Source: Own calculation and elaboration, 2013

MI 2000-2011

V. RESULTS AND DISCUSSION (iii)

Source: Own calculation and elaboration, 2013

MI 2000-2011

V. RESULTS AND DISCUSSION (iv)

Source: Own calculation and elaboration, 2013

BEDK

DE

IE

EL

ES

FR

ITLU

NL

AT

PT

FI

SE

UK

00.511.522.533.544.5

‘Efficient’ countries‘• Germany (DE)• Spain (ES)

‘Highly efficient countries‘• Sweden (SE)• France (FR)• Ireland (IE)• Italy (IT)• Portugal (PT)

‘Slightly inefficient countries’• 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

• 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. RESULTS AND DISCUSSION (vi)

• 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.

V. CONCLUSION

ACKNOWLEDGEMENT

Lukáš Meleckýlukas.melecky@vsb.cz

Department of European Integration Faculty of Economics, VŠB-Technical University of Ostrava

€UR Katedra evropské integrace

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