XXI. MEZINÁRODNÍ KOLOKVIUM O REGIONÁLNÍCH VĚDÁCH. SBORNÍK
PŘÍSPĚVKŮ.
21ST
INTERNATIONAL COLLOQUIUM ON REGIONAL SCIENCES.
CONFERENCE PROCEEDINGS.
Place: Kurdějov (Czech Republic)
June 13-15, 2018
Publisher: Masarykova univerzita, Brno
Edited by:
Viktorie KLÍMOVÁ
Vladimír ŽÍTEK
(Masarykova univerzita / Masaryk University, Czech Republic)
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o regionálních vědách. Sborník příspěvků. Brno: Masarykova univerzita, 2018. s. 1–5.
ISBN 978-80-210-8969-3.
AUTHOR, A. Title of paper. In Klímová, V., Žítek, V. (eds.) 21st
International Colloquium
on Regional Sciences. Conference Proceedings. Brno: Masarykova univerzita, 2018. pp. 1–
5. ISBN 978-80-210-8969-3.
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Sborník příspěvků XXI. mezinárodní kolokvium o regionálních vědách Kurdějov 13.–15. 6. 2018
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DOI: 10.5817/CZ.MUNI.P210-8970-2018-54
EFFICIENCY OF ACTIVITY OF URBAN MUNICIPALITIES
IN POLAND VERSUS THEIR INCOME LEVEL
JAROSŁAW OLEJNICZAK.
Katedra Finansów
Wydział Nauk Ekonomicznych
Uniwersytet Ekonomiczny we Wrocławiu
Department of Finance
Faculty of Economic Sciences
Wroclaw University of Eonomics
 Komandorska 118/120, 53-345 Wroclaw, Poland
E-mail: jaroslaw.olejniczak@ue.wroc.pl
Annotation
The conducted research aimed to verify the hypothesis about the existence of a relationship between income
potential of municipalities and the (relative) efficiency of their expanses. The variables used in examination of
relative efficiency with the DEA CCR-O method. Those variables were supposed to reflect the main areas of
municipal activity. To reflect income potential of municipalities the level of own and total revenues p.c. was taken
into consideration. Time period covered 2009-2016 years. On a national scale, the percentage of ineffective
DMU’s in voivodeships fluctuated between 82 and 74%, showing a decreasing trend. It is also reflected in the
systematic increase in the average DMU effectiveness in some voivodeships - in particular in those where in the
beginning the average efficiency was lower (0.7 to 0.8). It can be concluded that there is a moderate negative
correlation between the level of own revenues per capita and the indicators of technical efficiency obtained from
the analysis - correlation factors between -0.37 and -0.24 (decreasing tendency). A much stronger relationship
occurs between their total revenues per capita and the mentioned indicators - between correlation factors -0.62
and - 0.38 (also decreasing).
Key words
DEA, local government, revenues
JEL classification: C14, H70
1. Introduction
The research on the efficiency of local government units’ activity is conducted in many countries and there are
various factors which trigger it, whilst, the main objective being the desire to impact the officials and limit their
inefficiency (Balaguer-Coll, Prior, Tortosa-Ausina, 2007). The discussion on the subject of the need to measure
the efficiency itself reaches back to the 30’s; while „in the last 20 years, nearly three dozen articles were published
in reputed scientific journals with the purpose of measuring the efficiency of local governments using different
methodologies”(da Cruz, Marques, 2014). Literature analysis conducted by da Cruz and Marques up to 2012
indicates that only a small percentage of publications are devoted to measuring of the global efficiency of local
governments. As indexed in the Web of Science or Scopus, also in later years the amount of publications analysing
this topic has been relatively small. There are practically no articles devoted to the efficiency of Polish
municipalities. The issue of efficiency is mainly addressed from the perspective of a certain field (activity of public
offices (Czarnecki, Szarota, Wozniak, 2015) (Lizińska et al., 2017); waste management (Przydatek, 2016), cultural
institutions management (Gałecka, Smolny, 2017), efficiency of subsidies and grants (Kańduła, 2017; Olejniczak,
2015; Olejniczak, Bednarska-Olejniczak, 2013; Sekula, 2015). Few authors attempt to evaluate global efficiency
(Czaplak, 2016; Gendzwill, Swianiewicz, 2016; Swianiewicz, Lukomska, 2016). There are significantly more
publications on the matter perceived from a local perspective, however, even here works focusing on global
efficiency are rare, despite the fact that the practical efficiency measurement is often said to be one of the most
important issues of public finances research (Guziejewska, 2008; Jastrzębska, 2016). One of the first studies of
this subject area in Polish scientific literature is the NBP (National Central Bank) study (Karbownik, Kula, 2009),
in which three areas of efficiency measurement have been proposed ( environment protection, education,
administration). The matter related to the ways of measuring expenditure efficiency of municipalities has also
been discussed by K. Owsiak (Owsiak, 2014), although the main focus was placed by this author on reviewing
the available research tools. Additionally, some studies explored only specific groups of municipalities (Kobiałka,
Kubik, 2017; Łękawa 2012) or specific types of municipalities(Sekuła, Julkowski, 2015).
Sborník příspěvků XXI. mezinárodní kolokvium o regionálních vědách Kurdějov 13.–15. 6. 2018
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From the point of view of the selected experimental method, the issue of efficiency can be considered in a number
of ways. Studies pointed out by da Cruz and Marquez employ both the methods of parametric and nonparametric
analysis. In the subsequent years as well, one of the most frequently used methods has been Data Envelopment
Analysis (DEA). It is worth highlighting that different varieties of DEA are used depending on the study’s
objective. Quite frequently in one article the author compares discrepancies between results obtained from many
varieties. In publications devoted to global efficiency of Polish municipalities (indexed in WoS) parametric
methods prevail (Gendzwill, Swianiewicz, 2016). One of the few works which apply nonparametric methods is
the article of Czarnecki, Szrota, and Woźniak mentioned before. Polish authors cited above (from outside WoS or
Scopus) also attempted using nonparametric methods in their studies in order to estimate the relative efficiency of
local governments’ activity, in particular DEA. Nevertheless, the gap in research on the matter of expenditure
efficiency using nonparametric methods is still noticeable. Therefore, it is justifiable to carry out research on the
existence of a relationship between income potential of municipalities and (relative) efficiency of their activity.
One of the reasons behind the above mentioned research are also the doubts concerning the accepted system of
funding of local governments in Poland that has been mentioned in literature, in particular, in the area of fiscal
transfers (Kańduła, 2017; Poniatowicz, Wyszkowska, 2015; Sekula, 2015).
2. Aim and method
The assessment of efficiency of the public finance sector units can be conducted with the use of either onedimensional
or multidimensional methods. In the case of the undertaken assessment of the local government units’
efficiency, comparison of many inputs and outputs of their activity is necessary, which in turn requires the usage
of methods allowing the possibility of aggregation of criteria. The essence of the DEA model is, as it has been
already mentioned, the possibility of taking into account various inputs and outputs characterizing the activity of
one unit (DMU Decision Making Unit) and depiction of their empirical layout, as well as the choice of data
envelope applying the best practice frontier. This method thus enables us to find the theoretical frontier of
production potential. In general terms, efficiency in DEA model can be defined in the following way (Cooper et
al. 2007):
=
∑ ℎ _
∑ ℎ _
where:
j – subsequent DMU
i – subsequent input
r – subsequent output
n – the number of researched objects (j=1,...,n)
m – the number of used input (i=1,...,m)
s – the number of activity output (r=1,...,s)
Charnes, Cooper and Rhodes (Charnes, Cooper, Rhodes, 1978) analysed the issue of comparison of the outputs of
different systems. The starting point was defining efficiency as the proportion of the sum of weighted output to
the sum of weighted input. This approach does not require any knowledge about the efficiency functions. By using
empirical numbers of input and output, one searches for weights maximizing efficiency of an object. This leads to
the formulation of a mathematic programming problem, the aim of which is to estimate efficiency of specific
objects in regard of the entire group of objects. Effectiveness of a given unit is measured in regard to other objects
in the group – therefore to maintain comparability of changes in efficiency in subsequent periods, the stableness
of the studied group’s structure is important. Basic models of DEA include: CCR which assumes stable output of
scale (Charnes, Cooper, Rhodes, 1978), and BCC with variable output of scale (Banker, Charnes, Cooper, 1984).
Both models can be either input or output oriented. It is important to note that in Polish conditions, a characteristic
feature of local government units is a significantly higher possibility of shaping the output (directions and effects
of expenses) than the mere amount of expanses. Thus the output oriented model is the most appropriate one.
In the basic form of DEA CCR model it is assumed that units (DMU) which can be placed on a curve are effective,
and their efficiency amounts to θ = 1. DMUs placed beneath the curve of efficiency are ineffective, their level of
inefficiency being 1 - θ . Efficiency is here understood in the Farrell’s sense, so the changes in input/output are
proportional. For each object it is determined whether its current technology enables the most beneficial realization
of its tasks. The primary issue is to establish the model’s orientation and taking or not taking into consideration
the scale’s effects. The abovementioned assumptions are characteristic for the input oriented model, which means
that the object being examined can decrease input while at the same time maintaining the existing output. In the
case of local government units, the amount of input is usually determined by law regulations, whereas
municipalities can work towards the maximization of output. Thus, with such a DMU orientation, for which
Sborník příspěvků XXI. mezinárodní kolokvium o regionálních vědách Kurdějov 13.–15. 6. 2018
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efficiency is greater than one these will be ineffective. It is to be noted that in the DEA model for which the
assumption is made of stable benefits of the scale, relative efficiency of a unit is the same in case of input
orientation, as it is in case of output orientation (Ćwiąkała-Małys, Nowak, 2009).
The conducted research aimed to verify the hypothesis about the existence of a relationship between income
potential of municipalities and the (relative) efficiency of their expanses. Test procedure comprised of: the analysis
of scientific literature with the purpose of establishing criteria which could be used as “input“ and “output“ (taking
into account local specificity), isolation from the group of all urban municipalities in Poland of those
municipalities, for which data was available for the whole experimentation period (2009-2016), correlation
analysis proposed on the basis of the analysed literature on the topic of “output” (“O”) – in order to avoid using
variables which would be closely correlated, their income (own and general) per capita. Additionally, the
Malmquist index for each DMU as well as its average values for the whole collectivity throughout the years have
been calculated. The variables used in examination of relative efficiency with the DEA CCR-O method were taken
from the Local Databases of CSO (Central Statistical Office) and from the System of Local Government Analyses.
Those variables were supposed to reflect the main areas of municipal activity (table 1).
Tab.1:Variables set used in the research
Area Symbol Category
Education and upbringing O1
O2
O3
Children at the age from 3 to 5 years per 1 place in the kindergarten
(opposite)
Gross solarisation coefficient (primary schools)
Percentage of chartered teachers
Health protection O4
O5
Medical centres per 10 thousand inhabitants
Relation between births and deaths within the municipality
Residential economy O6 Number of persons per chamber (opposite)
Social assistance O7 Percentage of inhabitants using social environmental assistance (opposite)
Communal economy and
environment protection as well
as Administration
O8
O9
O10
O11
O12
Number of inhabitants using the water supply network
Number of inhabitants using sewage network
Share of terrains covered by local spatial management plans in the general
area
Unemployment coefficient within the territory of the municipality
(opposite)
Number of economic entities per 10 thousand Inhabitants
Culture and protection of
national heritage
O13 Library book collections per 1 inhabitant
Source: own elaboration
Due to the lack of available data at the NUTS-5 level regarding the structure of the communication network (the
structure of municipal roads in the studied period was no longer reported in the CSO bases) the total expenditure
per capita of particular municipalities was adjusted for this expenditure item. Adequate to the partition
classification and the share of individual expenditure groups in the municipalities' budgets, 14 variables describing
the effects were selected, which enabled the creation of 13 measures. According to the assumptions of the model,
all measures meet the assumption of uniform direction of preferences, i.e. the increase of results from the point of
view of the objective will be assessed positively, and similar to the increase in output which, while maintaining
the stability of results, will be assessed negatively(Guzik, 2009). For this purpose, in the case of 4 variables, their
inverses were used in the calculations. Out of 241 municipalities with city status in 2009, 4 municipalities were
rejected due to their missing data. In addition, due to the sensitivity of the method of outliers, 45 municipalities
were excluded from the group of studied entities for whom the value of at least one of the effects (Ojr) did not
meet the quartile test condition (Chromiński , Tkacz, 2010), that is:
Qr1-1,5*(Qr3-Qr1)≤Ojr≤Qr3+1,5*(Qr3-Qr1)
where:
n - number of examined objects (DMU) (j = 1, ..., n)
s - number of activity outputs (r = 1, ..., s)
j – subsequent DMU
r - subsequent output
Ojr - the value of observation for j-th DMU and r-th output
Qr1 - the first quartile for the r-th output
Qr3 - third quartile for the r-th output
Sborník příspěvků XXI. mezinárodní kolokvium o regionálních vědách Kurdějov 13.–15. 6. 2018
413
3. Results and discussion
The first stage of research using the DEA CCR-O method showed that in the case of the studied municipalities a
gradual increase in both the average value and the median relative effectiveness of these DMUs can be observed
(Table 2). This means a relative decrease in discrepancies in the efficiency of the researched units.
Tab. 2: Basic descriptive statistics of the DEA CCR-O results in studied municipalities
2009 2010 2011 2012 2013 2014 2015 2016
Average 0.873 0.839 0.854 0.868 0.884 0.897 0.900 0.919
Median 0.887 0.843 0.868 0.877 0.893 0.914 0.916 0.934
Standard deviation 0.112 0.132 0.126 0.114 0.102 0.098 0.098 0.080
Variance 0.013 0.017 0.016 0.013 0.010 0.010 0.010 0.006
Kurtosis 0.017 0.271 0.228 0.016 1.126 0.164 0.840 1.649
Minimum 0.514 0.339 0.378 0.465 0.440 0.587 0.562 0.559
Source: own elaboration
Tab. 3: Share of inefficient DMUs in the population and average efficiency value among the voivodeships
Percentage of inefficient DMUs
Average DMU efficiency
Voivodeship 2009 2010 2011 2012 2013 2014 2015
2016
2009 2010 2011 2012 2013 2014 2015 2016
Dolnośląskie 88% 100% 96% 83% 88% 88% 88% 79% 0.82 0.77 0.82 0.85 0.86 0.89 0.91 0.93
Kujawsko-
pomorskie
100% 100% 91% 100% 91% 91% 100% 91% 0.81 0.75 0.78 0.76 0.84 0.83 0.86 0.90
Lubelskie 75% 75% 75% 81% 75% 56% 75% 50% 0.89 0.85 0.85 0.84 0.88 0.91 0.87 0.94
Lubuskie 100% 100% 100% 100% 100% 100% 100% 100% 0.79 0.75 0.74 0.79 0.80 0.85 0.85 0.89
Łódzkie 73% 80% 80% 87% 93% 93% 80% 67% 0.90 0.87 0.85 0.90 0.92 0.92 0.94 0.93
Małopolskie 50% 50% 50% 83% 67% 67% 50% 50% 0.92 0.95 0.91 0.91 0.91 0.91 0.92 0.91
Mazowieckie 94% 88% 94% 88% 88% 82% 71% 100% 0.85 0.83 0.84 0.85 0.88 0.89 0.88 0.87
Opolskie 50% 100% 50% 100% 100% 50% 100% 100% 0.81 0.70 0.87 0.82 0.87 0.90 0.89 0.91
Podkarpackie 67% 75% 75% 75% 83% 67% 75% 75% 0.92 0.87 0.92 0.89 0.89 0.88 0.91 0.93
Podlaskie 70% 90% 60% 50% 50% 60% 60% 50% 0.91 0.88 0.90 0.93 0.93 0.92 0.91 0.96
Pomorskie 80% 87% 87% 87% 80% 80% 73% 80% 0.90 0.85 0.83 0.84 0.87 0.90 0.90 0.90
Śląskie 80% 75% 75% 85% 80% 85% 75% 65% 0.86 0.87 0.88 0.90 0.88 0.90 0.87 0.92
Świętokrzyskie 100% 100% 100% 75% 75% 75% 50% 50% 0.86 0.67 0.81 0.85 0.91 0.93 0.94 0.95
Warmińsko-
mazurskie
86% 86% 100% 71% 86% 86% 79% 79% 0.90 0.81 0.85 0.87 0.91 0.90 0.93 0.92
Wielkopolskie 58% 42% 58% 58% 75% 58% 58% 58% 0.93 0.95 0.94 0.92 0.92 0.92 0.94 0.95
Zachodnio-
pomorskie
100% 100% 88% 88% 88% 100% 100% 100% 0.88 0.87 0.86 0.89 0.89 0.88 0.89 0.89
Total : 81% 83% 82% 81% 82% 79% 77% 74% 0.87 0.84 0.85 0.87 0.88 0.90 0.90 0.92
Source: own elaboration
Looking at the differences in the effectiveness of municipalities in the regional system, it should be emphasized
that there were voivodeships in case of which all surveyed units were ineffective in the selected years (tab. 3),
namely- Kujawsko-Pomorskie and Zachodniopomorskie. It should be noted that in certain voivodeships
(Opolskie, Lubuskie, Świętokrzyskie), due to the low number of researched DMUs, generalization on the basis of
percentage of municipalities should be treated with great caution. On a national scale, the percentage of ineffective
DMU’s in voivodeships in the analysed period fluctuated between 82 and 74%, showing a decreasing trend. It is
also reflected in the systematic increase in the average DMU effectiveness in some voivodeships - in particular in
those voivodeships where in the first two years the average efficiency fluctuated within the range between 0.7 and
0.8 (Dolnośląskie, Kuyavian-Pomeranian, and Lubuskie). In the case of voivodeships where the average efficiency
at the beginning of the analysed period approached 0.9, one may speak of maintaining the original average despite
periodic fluctuations (usually relatively small decreases of the efficiency ratio).
Sborník příspěvků XXI. mezinárodní kolokvium o regionálních vědách Kurdějov 13.–15. 6. 2018
414
At the same time, it should be pointed out that due to the calculated level of efficiency indicators DMU can be
divided into four categories (Table 4). On the basis of ordered values of efficiency indicators, the following groups
of municipalities were distinguished (e ́- the arithmetic mean, and δ_e- standard deviation of the DEA CCR-O
efficiency indicator):
 group A (high efficiency): ≥ ́ + ,
 group B (average efficiency): ́ ≤ < ́ + ,
 group C (low efficiency): ́ − ≤ < ́
 group D (very low efficiency): < ́ − .
Tab. 4: Division of DMU into groups based on the value of performance indicators
Efficiency groups 2009 2010 2011 2012 2013 2014 2015 2016
A 45 42 43 44 39 44 44 50
B 61 55 60 56 65 62 66 59
C 56 66 57 62 58 56 53 56
D 30 29 32 30 30 30 29 27
Source: own elaboration
As can be seen within the proposed classification method, there are slight differences in the quantity of some DMU
groups. In the analysed period the number of high efficient municipalities ranged from 39 to 50, with the lowest
number recorded in 2013 and the highest in 2009 and 2016. In turn, in the group of municipalities with very low
efficiency, the changes were insignificant (except 2011 and 2016). An analysis of the municipalities' affiliation to
particular groups indicates that only 16 DMUs in the period under examination were permanently included in
group C or D, and only three were included in group D (Nowy Dwór, Hel, Mikołów). This shows the changes in
the activities of some DMUs affecting their relative efficiency. On the other hand, it should be noted that 6 DMUs
(Bielsk Podlaski, Siemiatycze, Reda, Wodzisław Śląski, Chodzież, Luboń) were included in the high efficiency
group of DMU. At the same time, 31 municipalities were indicated in the analysed period only in the group of
municipalities with high or average efficiency.
The next additional stage of the investigation was to determine the Malmquist index for the studied DMUs. The
basic data is contained in table 5. As can be seen, the average value of TFP_CH (total factor productivity change)
was below 1 in all years and the average values of PE_CH (pure technical efficiency) SE_CH (scale efficiency
change) were slightly positive in most periods, while TECH_CH (technological change) indicators were below 1.
Detailed analysis of Malmquist indexes for particular units reaches beyond the scope of this publication.
Tab. 5: Malmquist index for annual means (output oriented DEA)
Year EFF_CH TECH_CH PE_CH SE_CH TFP_CH TFP_CH minimum TFP_CH maximum
2 0.957 0.979 1.000 0.957 0.936 0.416 1.494
3 1.019 0.978 1.001 1.018 0.997 0.546 1.926
4 1.019 0.979 0.999 1.02 0.997 0.642 1.534
5 1.021 0.964 1.001 1.02 0.984 0.712 2.372
6 1.016 0.938 1.001 1.015 0.953 0.731 1.619
7 1.003 0.981 1.000 1.003 0.984 0.517 1.495
8 1.024 0.863 0.999 1.025 0.883 0.604 1.503
mean 1.008 0.954 1.000 1.008 0.961 - Source:
authors’ own calculation
According to the assumptions of the work the research was carried out to verify the hypothesis that there is a
relationship between the income potential of municipalities and the (relative) efficiency of their expenses. The
basic research problem is to determine the correlation between the income of particular DMUs and their technical
efficiency indicators. In accordance with the results of calculations presented in Table 6, it can be concluded that
there is a moderate negative correlation between the level of own revenues per capita and the indicators of technical
efficiency obtained from the analysis. A much stronger relationship occurs between their total revenues per capita
and the mentioned indicators. In the case of the former, there are fluctuations correlation factors between -0.37
and -0.24 (with a decreasing tendency) while in the case of the latter the values range between -0.62 and - 0.38
(here also a decreasing tendency is present).
Sborník příspěvků XXI. mezinárodní kolokvium o regionálních vědách Kurdějov 13.–15. 6. 2018
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Tab. 6: Correlation between technical efficiency indicators from the DEA CCR-O model and particular income
aggregates in the studied DMU group
correlations 2009 2010 2011 2012 2013 2014 2015 2016
TR_DEA -0.48665 -0.62479 -0.51396 -0.50347 -0.37828 -0.51751 -0.48142 -0.39833
OR_DEA -0.36942 -0.36483 -0.33134 -0.28651 -0.23849 -0.27884 -0.31334 -0.23991
Source: authors’ own calculation
The obtained values of correlation indices make the thesis more probable to some extent for the effectiveness of
expending funds of financially weaker local governments. Of course, there is no option for uncritically accepting
the results obtained primarily due to the arbitrariness and selectivity adopted as comparison criteria of variables
and external effects affecting the obtained results. The aspect of DMU's acceptance of a certain level of
inefficiency resulting from the specific preferences of the residents of these units is also significant.
Conclusion
In closing, it should be stated that the conducted research has shown the existence of a relationship between the
level of income per capita of the studied municipalities and their relative technical efficiency measured by the
DEA CCR-O method. However, the obtained results should be treated with great caution due to both the
imperfection of the method, the limited scope of the data to be obtained, exogenous factors that may influence the
effects of the municipalities' activities and the specific preferences of the residents of particular municipalities.
From the point of view of future research the possibility of using other DEA models and changes in their direction
should be considered.
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