A DEA approach to regional development

Abstract

Our research is based on the effect of fiscal policies on the Greek prefectures. Using DEA methodology we compare the efficiency of the prefectures over the last three decades. Moreover, we determine where the resources are distributed in an efficient way and /or have been used efficiently by the local authorities in order to stimulate regional development and provide quality of life to the Greek citizens. The efficient prefectures seem to have definite and strong characteristics, which are determined and discussed in detail. Our empirical results imply that the resources of a prefecture don’t necessarily ensure the efficiency of this prefecture.

Full text

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MPRA
Munich Personal RePEc Archive
A DEA approach to regional
development
Halkos, George and Tzeremes, Nickolaos
University of Thessaly, Department of Economics
2005
Online at http://mpra.ub.uni-muenchen.de/3992/
MPRA Paper No. 3992, posted 07. November 2007 / 03:35

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A DEA approach to regional development


By
George Emm. Halkos and Nickolaos G. Tzeremes
Department of Economics, University of Thessaly
Argonavton and Filellinon st., 38221, Volos, Greece



Abstract
Our research is based on the effect of fiscal policies on the Greek prefectures. Using DEA
methodology we compare the efficiency of the prefectures over the last three decades.
Moreover, we determine where the resources are distributed in an efficient way and /or
have been used efficiently by the local authorities in order to stimulate regional
development and provide quality of life to the Greek citizens. The efficient prefectures
seem to have definite and strong characteristics, which are determined and discussed in
detail. Our empirical results imply that the resources of a prefecture don’t necessarily
ensure the efficiency of this prefecture.


JEL Classification Codes: O18, P25

Keywords: Data Envelopment Analysis; Regional Development; Living Standards; Greek
Prefectures

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1. Introduction
It is generally accepted that the level of economic development is not uniform
across regions. On the contrary, it substantially differs. This plays an important role and
stimulates internal migrations from less developed prefectures too more developed ones.
As human activities are related to economic development and are affected by regional
development, the way of measurement of the conditions of regional development is really
essential and important in the determination of a country’s socio-economic policies.
In many countries, governments have tried to establish policies able to reduce
regional economic discrepancies. Georgiou (1992) and Karkazis and Thanassoulis (1998)
assess the effectiveness of regional development policies of the Greek Governments.
Greece used the Development Act 1262 of 1982 in order to make the differentiations and
disparities in economic development more uniform. The main target behind those policies
was the economic development of the prefectures with a direct impact on the citizens’
living standards. In the case of Greece different policies and implications for economic
development of the prefectures have been observed, due to the entrance of Greece into the
European Union.
Similar policies can be found in other countries like Italy (facing migration moves
from South to North parts of the country) and the UK. Mishan (1988) assesses the
performance of public expenditure policies using cost-benefit analysis (CBA). Meen and
Andrew (2004) analysed the impact of fiscal policies on UK’s regional development from
the perspective of population distribution. In a similar way, Newton (1972) applied CBA to
assess the performance of specific types of public investment on a regional basis. But CBA
due to its additive nature limits its ability in measuring performance on a comparative
basis, as we are interested in the benefits relative to costs and not to the absolute net
benefits.

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In this paper a non-parametric analytic technique for the evaluation of prefectures’
performance is applied. Specifically, the Data Envelopment Analysis (hereafter DEA)
technique is employed, which is a non-statistical method relying on linear programming. It
provides a measure of relative technical efficiency of different decision-making units
(hereafter DMUs) operating and performing in the same or similar tasks. The technique’s
main advantage is that it can deal with the case of multiple inputs and outputs as well as
factors, which are not controlled by individual management.
Another advantage of this non-parametric technique, and in general of all the non-
parametric techniques, is that we skip most of the usual difficulties, which arise by the use
of parametric methods in the analysis of ratios. That is, we skip problems like the necessity
to determine the functional form1 or to determine the statistical distribution of the ratios.
Additionally, when we refer to the analysis of ratios problems arise if the numerator or the
denominator takes negative values, while the manipulation of outliers is not clear. On the
contrary, using the proposed technique these difficulties can be overcome and the most
efficient prefectures can be found in relation to the empirical data in use. Then the less
efficient prefectures can be compared to the most efficient ones.
Thus, in this study applying DEA to the Greek prefectures, we obtain the efficiency
scores and the optimal output (ratios) levels for inefficient prefectures for the last three
decades (1980, 1990, 2000). For the first time, we use a number of inputs and outputs in a
DEA framework formulation seeking efficiency comparisons with the simultaneous use of
multiple criteria, which determine efficiency for each DMU, forming a rounded judgment
on DMU efficiency taking into consideration a variety of efficiency dimensions and
combining them into a single performance measure.
Specifically, DEA provides us with an overall objective numerical score, ranking,
and efficiency potential improvement targets for each one of the inefficient units. The

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comparison of relative efficiency of all prefectures is carried out, relying on the derived
efficiency ratio for every prefecture, as the solution of the mathematical model. The higher
a prefecture’s efficiency ratio in relation to the corresponding ratio of another prefecture
the higher is the efficiency of this prefecture.
This paper is organized a follows. Section 2 presents a review of the existing
literature. In section 3 the various variables that are used in the formulation of the proposed
model are presented and discussed. In section 4 the technique adopted both in its theoretical
and mathematical formulation is presented. In section 5 the empirical findings of our study
are obtained. The final section concludes the paper discussing the derived results and the
implied policy implications.
2. Literature Review
DEA is a very important tool for analysing efficiency gains and provides a way for
multidimensional measure. Charnes et al. (1989, 1994) have developed DEA models
analysing the efficiency in terms of economic development of 28 Chinese cities. An
extensive use of the models provided by Charnes et al. (1989) can be found in Sueyashi
(1992) and Macmillan (1986, 1987) who measured the regional economic planning in the
USA. Byrnes and Storbeck (2000) applied a multi-unit DEA analysis to regional
economic development policy to Chinese cities. They used the data from Charnes et al.
(1989), but in their model they had one output (value of gross industrial output) and two
inputs (size of labour force and level of investment/ capital) recorded for the years 1983
and 1984. Moreover, in their study they measure the efficiency of the city with different
types of measurement models introduced by Färe and Primont (1984). All of these studies
were output based DEA models with variable returns.
Karkazis and Thanassoulis (1998) measured the effectiveness of policies for
economic development in terms of private investment in Northern Greece. They used an

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output based DEA model with variable returns to scale and data for five years 1987-1991
with two inputs (public investments and investment incentives) and one output (private
investment into service industry and agriculture). Chang et al. (1995) used DEA combined
with Malmquist productivity index approach expressed by Färe et al. (1992). They
evaluated the change of regional development in Taiwan area using indicators2 for two
years (1983 and 1990). They found that the larger the value of their indicators, the greater
was the degree of development in that region.
Zhu (2001) used similar indicators for 15 US domestic cities and 5 international
cities in order to demonstrate how DEA can be used for measuring the quality of life. High-
and low-end housing monthly rental, cost of loaf of French bread, cost of martini, class A
office rental (US $ / ft2) and number of violent crimes were used as inputs while median
household income, number of population with bachelor’s degree, number of doctors,
number of museums, number of libraries and number of 18-hole golf courses were used as
outputs. The purpose was to measure the quality of life across cities using the CCR model
(Charnes et al., 1978). Without a priori knowledge of factor relationship, a multi
dimensional quality of life measure was demonstrated.
Other approaches measure living standards by several economic development
indexes (Quality of Life indexes) by satisfying a set of parameters. By using GDP and
other indicators such as life expectancy and literacy rates economists have developed a
methodology based on a technical literature measuring QOL (Atkinson and Bourguignon
1982, Dasgupta 1988, Kakwani 1993, Dowrick et al. 1998, Dowrick et al. 2003, Ditlevsen
2004). However this methodology has been criticised due to the fact that indexes most of
the time don’t have multidimensionality, thus an ideal index does not exist. The advantage
deploying DEA methodology is exactly the fact that it measures multidimensional

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relationships among several inputs and outputs without an a priori underlying functional
form assumption (Zhu 2001).
Previous research on efficiency and productivity of municipalities consists of
studies which vary widely in their results and methodologies adopted. A number of studies,
close related to ours, has been expressed, amongst others, by Weber and Domazlicky
(1999), De Borger and Kerstens (1996), De Borger et al. (1994), Hayes and Chang (1990),
Deller (1992), Domazlicky and Webber (1997) and Raab and Lichty (2002). DEA has the
advantage of evaluating municipalities’ efficiencies as well as their determinants. Most of
the studies lack explanation of the estimated inefficiencies in a more systematic way (De
Borger et al., 1994).
Domazlicky and Webber (1997) measured the growth rate of total factor
productivity for forty-eight US states. Using public and private outputs and private and
public sectors labor and capital as inputs, they constructed a Malmquist productivity index,
which then was decomposed to changes of technical and scale efficiency as well as
technological change. They found that the innovative states tended to use more private and
less public capital, and less public labor compared to non-innovative firms.
Moreover, Raab and Lighty (2002) based on the identification of three distinct sub-
regions comprising a metropolitan area, emphasize the role of the central urban core in
regional economic development through stronger development initiatives between the core
and its surrounding areas. Instead of explaining urban growth through cross metropolitan
comparisons they explained it through intra-regional transactions. Furthermore, using a
DEA additive model, with five inputs (employee compensation, proprietor’s income, other
proprietary income, indirect business taxes and intermediate imports) and four outputs
(household consumption, business investment, government spending and exports) they
tested the efficiency levels of counties both within and outside of the urban core. They

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found support indicating that core counties showed greatest levels of robust efficiency
when applying DEA analysis and efficiency drops along with decreasing population
densities and income levels as research moves away from the urban core.
Huges and Edwards (2000) using county-level data, tried to capture inter-
jurisdictional spillover effects. Using the total property value as an output and fiscal policy
as an input (expressed by government expenditure on education, social services,
transportation etc.), they evaluated the efficiency of government performance using DEA.
They noticed that larger land area tend to be less efficient, probably as a result of
diseconomies of scale. This implies that decentralization and decreased spending by the
public sector increase efficiency.
Our, work is among these lines using inputs and outputs, which are fundamental
elements of regional development as well as of quality of life. Next the data used and the
proposed methodology are presented.
3. Data

The implementation of uniform regional development needs an enormous amount
of money and most of all the most effective use of resources. This, in turn, requires the
knowledge of the relative conditions of the regional development of each area before we
proceed to a long run sustainable planning. Information on indices of urban and regional
development such as population density, urban planned area as a percentage of total area,
number of telephone lines per 1000 people, number of doctors per 1000 people, average
income per capita etc is substantial in formulating the regional development plans (Council
for Planning and Development, 1990). The knowledge of this information helps authorities
to understand the conditions of each area and plan accordingly its development.
The various indicators of each region differ as one indicator may be high and
another may be low. This implies that it is important to weight the various indicators in

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order to obtain an indicator, which will help us to understand the current conditions of the
regional development of each area. The main issue is how to weight these indicators in a
realistic and representative way.
The National Statistical Service of Greece has recorded the data used here. They
refer to the Census of the last three decades (1980, 1990, and 2000) for all Greek
prefectures (see Fig. 1a). For the purpose of the analysis we code each of the 51 prefectures
as shown in Table 1. This table also provides information on key characteristics of the
prefecture (population, area in km2, area in miles2). These prefectures form thirteen
administrative regions, whose basic characteristics are also presented in Table 1.
For our research we use four inputs: 1) Number of hospital beds per 1000 citizens
(NHO), 2) Number of doctors per 1000 citizens (NDO), 3) Number of public schools per
1000 students (NPUS), 4) Number of public busses per 1000 citizens (NPB) and three
outputs: 1) GDP as a percentage of the mean GDP of the country (GDP), 2) Difference of
urban rural population (DUR) and 3) Number of new Houses per 1000 citizens (NNH).
These variables have been used, measured and criticised by several economists in
order to formulate, analyse and explain quality of life and economic/regional development3.
Correlations and descriptive statistics are also presented in tables 2-3. The indicators can be
categorized into four main areas: Health (NHO, NDO), Education (NPUS), Living
Standards (NPB, DUR, NNH) and Economic and Regional Development (GDP).

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Table 1: Codes, names and general information of Greek prefectures and regions
Map
Code
Prefecture Code Prefectures Population Area(km.²) Area(mi.²)
Administrative
region
Population Area(km.²) Area(mi.²)
C1 AIT
Aitolokarnanias
230,688 5,447 2,103
Aegean North
(C51, C31, C42)
Aegean South (C9)
Attica (C37, C45)
Crete (C50, C40,
C16, C30)
Epirus (C4, C19,
C39, C17)
Greece Central
(C11, C12, C48,
C46, C6)
Greece West (C5,
C1, C14)
Ionian Islands
(C23, C32,
C24,C13)
Macedonia
Central (C49, C15,
C25, C36, C38,
C43, C18)
Macedonia East
and Thrace (C8,
C10, C20, C41,
C35)
Macedonia West
(C47, C7, C22)
Peloponnese (C2,
C3, C26, C28, C34)
Thessaly (C21,
C29, C33, C44)
13 regions





































198,241
257,522
3,522,769
3,836
5,286
3,808
1,481
2,041
1,47
C2
C3
ARG
ARK
Argolidas
Arkadias
97,25
103,84
2,214
4,419
855
1,706
C4 ART
Artas
78,884 1,612 622
536,98 8,336 3,219
C5 AHA
Axaias
297,318 3,209 1,239
339,21 9,203 3,553
C6 BOI
Boiotias
134,034 3,211 1,24
578,881 15,549 6,004
C7 GRE/KOZ
Grebenon/
Kozanis
37,017/
150,159
2,338/3,562 903/1,375
702,027 11,35 4,382
C8 DRA
Dramas
96,978 3,468 1,339
191,003 2,307 891
C9 DOD
Dodekanisou
162,439 2,705 1,044
1,736,066 18,811 7,263
C10 EVR
Evrou
143,791 4,242 1,638
570,261 14,157 5,466
C11 EVI
Euvias
209,132 3,908 1,509
292,751 9,451 3,649
C12 EVT
Euritanias
23,535 2,045 790
605,663 15,49 5,981
C13 ZAK
Zakinthou
32,746 406 157
731,23 14,037
131,621
5,42
50,82
C14
C15
C16
C17
C18
C19
C20
C21
C22
C23
C24
C25
C26
C27
C28
C29
C30
C31
C32
C33
C34
C35
C36
C37
C38
C39
C40
C41
C42
C43
C44
C45
C46
C47
C48
C49
C50
C51
ILI
HMA
HRA
THP
THE
IOA
KAV
KAR
KAS
KER
KEF
KIL
KOR
KYK
LAK
LAR
LAS
LES
LEF
MAG
MES
XAN
PEL
ATT
PIE
PRE
RET
ROD
SAM
SER
TRI
ATT
FTH
FLO
FOK
HAL
HAN
HIO
Ileias
Imathias
Irakleiou
Thesproteias
Thessalonikis
Ioanninon
Kavalas
Karditsas
Kastorias
Kerkiras
Kefallonias
Kilkis
Korinthias
Kikladon
Lakonias
Larisas
Lasithiou
Lesvou
Leukadas
Magnisias
Messinias
Xanthis
Pellas
Region Attikis
Pierias
Prebezas
Rethimnon
Rodopis
Samou
Serron
Trikalon
Rest of Attiki
Fdiotidas
Florinas
Fokidas
Halkidikis
Xanion
Xiou
174,021
138,068
263,868
44,202
977,528
157,214
135,747
126,498
52,721
105,043
32,314
81,845
142,365
95,083
94,916
269,3
70,762
103,7
20,9
197,613
167,292
90,45
138,261
3,522,769
116,82
58,91
69,29
103,295
41,85
191,89
137,819
3,522,769
168,291
52,854
43,889
91,654
133,06
52,691
2,681
1,712
2,641
1,515
3,56
4,99
2,109
2,576
1,685
641
935
2,614
2,29
2,572
3,636
5,351
1,823
2,154
325
2,636
2,991
1,793
2,506
3,808
1,506
1,086
1,496
2,543
778
3,97
3,367
3,808
4,368
1,863
2,121
2,945
2,376
904
1,035
661
1,02
585
1,375
1,927
814
995
651
247
361
1,009
884
993
1,404
2,066
704
832
125
1,018
1,155
692
968
1,47
581
419
578
982
300
1,533
1,3
1,47
1,686
719
819
1,137
917
349
10,262,604

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Table 2: Descriptive Statistics of the selected variables































Table 3: Correlation coefficients

Correlations: 1980
NHO NDO NPUS NPB GDP DUR
NDO 0,501
NPUS -0,255 -0,376
NPB 0,453 0,387 -0,167
GDP -0,060 0,029 -0,372 0,344
DUR -0,298 -0,632 0,341 -0,118 -0,028
NNH -0,128 -0,239 -0,111 0,265 0,340 0,073
Correlations: 2000
NHO NDO NPUS NPB GDP DUR
NDO 0,642
NPUS -0,380 -0,421
NPB 0,117 0,217 -0,127
GDP 0,207 0,110 -0,258 0,296
DUR -0,341 -0,599 0,292 -0,229 -0,143
NNH -0,159 -0,016 -0,110 0,245 0,011 0,101


Correlations: 1990
NHO NDO NPUS NPB GDP DUR
NDO 0,636
NPUS -0,293 -0,412
NPB 0,490 0,403 -0,230
GDP 0,131 0,099 -0,352 0,278
DUR -0,405 -0,689 0,336 -0,503 -0,151
NNH -0,013 -0,094 -0,008 0,227 0,315 0,099









1980
Variable N Mean StDev Minimum Maximum
NHO 51 4,260 2,725 0,519 15,792
NDO 51 1,2694 0,6831 0,4741 4,5592
NPUS 51 11,787 4,699 3,046 28,201
NPB 51 1,4668 0,4728 0,6465 3,0852
GDP 51 95,14 22,33 64,17 201,86
DUR 51 8201 95001 -624367 65575
NNH 51 13,515 6,960 5,650 45,144
1990
Variable N Mean StDev Minimum Maximum
NHO 51 3,391 1,929 0,607 9,647
NDO 51 2,017 1,086 0,902 6,349
NPUS 51 10,358 3,899 3,251 27,419
NPB 51 2,421 0,820 0,872 5,313
GDP 51 93,26 18,06 67,40 174,73
DUR 51 -61530 442539 -3072922 57620
NNH 51 11,52 7,24 2,82 38,37
2000
Variable N Mean StDev Minimum Maximum
NHO 51 3,229 1,594 0,977 6,692
NDO 51 2,946 1,280 0,760 7,480
NPUS 51 9,868 3,347 4,363 24,292
NPB 51 1,936 0,808 1,118 6,322
GDP 51 100,00 30,23 60,41 227,94
DUR 51 -61530 442539 -3072922 57620
NNH 51 9,452 5,363 4,056 30,142

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Figure 1: Maps of Greece and Greek prefectures illustrating efficient prefectures per
decade, according to their efficient scores.



F1a


F1b

F1c


F1d

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4. The Technique
We may think of DEA as measuring the technical efficiency of a given prefecture
by calculating an efficiency ratio equal to a weighted sum of outputs over a weighted sum
of inputs. For each DMU these weights are derived by solving an optimization problem
which involves the maximization of the efficiency ratio for that DMU subject to the
constraint that the equivalent ratios for every DMU in the set is less than or equal to 1.
That is, DEA seeks to determine which of the N DMUs determine an envelopment
surface or an efficient frontier. DMUs lying on the surface are deemed efficient, while
DMUs that do not lie on the frontier are termed inefficient, and the analysis provides a
measure of their relative efficiency. As mentioned, the solution of the model dictates the
solution of (N) linear programming problems, one for each DMU. It provides us with an
efficiency measure for each DMU and shows by how much each of a DMU’s ratios should
be improved if it were to perform at the same level as the best performing prefectures in the
sample. In this way we extract an efficiency ratio for each prefecture, which shows us by
how much the ratios of each prefecture could be improved so as to reach the same level of
efficiency with that of the most efficient prefectures in the sample.
The fundamental feature of DEA is that technical efficiency score of each DMU
depends on the performance of the sample of which it forms a part. This means that DEA
produces relative, rather than absolute, measures of technical efficiency for each DMU
under consideration. DEA evaluates a DMU as technically efficient if it has the best ratio
of any output to any input and this shows the significance of the outputs/inputs taken under
consideration.
4.1 DEA models (CRS vs VRS)

Under the restriction of Constant Returns to Scale (hereafter CRS), Charnes et al.
(1978) specify the linear programming problem representing the fitting of an efficient

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production surface to the data. An extension allowing for Variable Returns to Scale
(hereafter VRS) is provided by Banker et al. (1984). The latter assumption requires an
additional constraint on the solution, compared with the constant returns to scale case and
the resulting efficiency estimate will be greater than that obtained under constant returns to
scale. Thus, where the methods yield different values, the index obtained under variable
returns takes account of scale related effects and therefore represents pure technical
efficiency alone, whereas the constant returns to scale measure represents overall technical
efficiency, in which pure technical and scale efficiency are combined.
Banker et al. (1984) show that the index of overall efficiency is equal to the product
of the scale and pure technical efficiency indices. Hence, an index of scale efficiency can
be obtained by manipulating the DEA results obtained under the assumption of constant
and variable returns. Moreover, following Banker (1984), a measure of the local returns to
scale properties of the technology can be obtained by aggregating the weights applied to
the peer DMUs in constructing the hypothetical DMU used in the calculation of overall
efficiency. Given the assumption of constant returns to scale (CRS), the size of the
prefecture is not considered to be relevant in assessing its efficiency. Under the assumption
of constant returns to scale (CRS) introduced by Charnes et al. (1978) small prefectures (in
terms of population), can produce outputs with the same ratios of input to output, as can
larger prefectures. This is because the assumption implies that there are no economies (or
diseconomies) of scale present, so doubling all inputs will generally lead to a doubling in
all outputs.
However, this assumption may be inappropriate for regional development and
policy implications on quality of life amongst the Greek prefectures, because economies of
scale (or increasing returns to scale, IRS) may exist. Based on this assumption doubling all
inputs should lead to more than a doubling of output in terms or higher rates of regional

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development. For other prefectures, might become too large (in terms of population and
absorption of resources) and diseconomies of scale (decreasing returns to scale, DRS)
could set in. In this case, a doubling of all inputs will lead to less than doubling of outputs.
It would be to the local administrations’ advantage to ensure that its development (through
the efficient use of the resources) is of optimal size -neither too small if there are increasing
returns nor too large if there are decreasing returns to scale.
4.2 Advantages and limitations of DEA methodology

DEA modelling can incorporate multiple inputs and outputs. In order to calculate
technical efficiency, information on output and input is required. This makes it particularly
suitable for analysing the efficiency of fiscal policies on regional development. Possible
sources of inefficiency can be determined as well as efficiency levels. The technique, gives
the ability to decompose economic inefficiency into technical and allocative inefficiency.
Furthermore, it allows technical inefficiency to be decomposed into scale effects. By
identifying the ‘peers’ for the prefectures, which are not efficient, DEA provides a set of
potential role models that the policy makers of the prefectures can look at, for ways of
improving the effect of their fiscal policies on regional development and quality of life.
However, some major disadvantages when using this technique have to be
mentioned. Having a deterministic nature DEA produces results that are particularly
sensitive to measurement error. If one prefecture’s inputs are understated or its outputs
overstated, then that prefecture can distort the shape of the frontier and reduce the
efficiency scores of nearby prefectures. It only measures efficiency relative to best practice
within the particular sample. Thus, it is not meaningful to compare the scores between two
different studies because differences in best practice between the samples are unknown.
DEA scores are sensitive to input and output specification and the size of the
sample. There are different rules as to what the minimum number of prefectures in the