Efficiency of activity of urban municipalities
in Poland versus their income level
Jarosław Olejniczak, PhD
Department of Finance
Wrocław University of Economics, Poland
Aim of presented research:
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 expences.
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 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):
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)
𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 =
𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑_𝑂𝑢𝑡𝑝𝑢𝑡𝑟
𝑠
𝑟=1
𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑_𝐼𝑚𝑝𝑢𝑡𝑖
𝑚
𝑖=1
Charnes, Cooper and 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 (1978), and BCC with variable output of scale (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.
Stages:
1. 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),
2. 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,
3. Analysis of their income (own and general) per capita.
4. Additionally, the Malmquist index for each DMU as well as its
average values for the whole collectivity throughout the years
have been calculated.
Results of study
Results of study
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
Tab.1:Variables set used in the research
Source: own elaboration
Results of study
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 were assessed
positively, and similar to the increase in output which, while
maintaining the stability of results, were assessed negatively.
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
Results of study
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
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
Source: own elaboration
Percentage of inefficient DMUs
Voivodeship 2009 2010 2011 2012 2013 2014 2015 2016
Dolnośląskie 88% 100% 96% 83% 88% 88% 88% 79%
Kujawsko-pomorskie 100% 100% 91% 100% 91% 91% 100% 91%
Lubelskie 75% 75% 75% 81% 75% 56% 75% 50%
Lubuskie 100% 100% 100% 100% 100% 100% 100% 100%
Łódzkie 73% 80% 80% 87% 93% 93% 80% 67%
Małopolskie 50% 50% 50% 83% 67% 67% 50% 50%
Mazowieckie 94% 88% 94% 88% 88% 82% 71% 100%
Opolskie 50% 100% 50% 100% 100% 50% 100% 100%
Podkarpackie 67% 75% 75% 75% 83% 67% 75% 75%
Podlaskie 70% 90% 60% 50% 50% 60% 60% 50%
Pomorskie 80% 87% 87% 87% 80% 80% 73% 80%
Śląskie 80% 75% 75% 85% 80% 85% 75% 65%
Świętokrzyskie 100% 100% 100% 75% 75% 75% 50% 50%
Warmińsko-mazurskie 86% 86% 100% 71% 86% 86% 79% 79%
Wielkopolskie 58% 42% 58% 58% 75% 58% 58% 58%
Zachodnio-pomorskie 100% 100% 88% 88% 88% 100% 100% 100%
Total : 81% 83% 82% 81% 82% 79% 77% 74%
Avg efficiency
Voivodeship 2009 2010 2011 2012 2013 2014 2015 2016
Dolnośląskie 0.82 0.77 0.82 0.85 0.86 0.89 0.91 0.93
Kujawsko-pomorskie 0.81 0.75 0.78 0.76 0.84 0.83 0.86 0.90
Lubelskie 0.89 0.85 0.85 0.84 0.88 0.91 0.87 0.94
Lubuskie 0.79 0.75 0.74 0.79 0.80 0.85 0.85 0.89
Łódzkie 0.90 0.87 0.85 0.90 0.92 0.92 0.94 0.93
Małopolskie 0.92 0.95 0.91 0.91 0.91 0.91 0.92 0.91
Mazowieckie 0.85 0.83 0.84 0.85 0.88 0.89 0.88 0.87
Opolskie 0.81 0.70 0.87 0.82 0.87 0.90 0.89 0.91
Podkarpackie 0.92 0.87 0.92 0.89 0.89 0.88 0.91 0.93
Podlaskie 0.91 0.88 0.90 0.93 0.93 0.92 0.91 0.96
Pomorskie 0.90 0.85 0.83 0.84 0.87 0.90 0.90 0.90
Śląskie 0.86 0.87 0.88 0.90 0.88 0.90 0.87 0.92
Świętokrzyskie 0.86 0.67 0.81 0.85 0.91 0.93 0.94 0.95
Warmińsko-mazurskie 0.90 0.81 0.85 0.87 0.91 0.90 0.93 0.92
Wielkopolskie 0.93 0.95 0.94 0.92 0.92 0.92 0.94 0.95
Zachodnio-pomorskie 0.88 0.87 0.86 0.89 0.89 0.88 0.89 0.89
Total : 0.87 0.84 0.85 0.87 0.88 0.90 0.90 0.92
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
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
Type H M N L Sum
A 2 10 26 7 45
B 2 15 37 7 61
C 9 23 20 4 56
D 16 4 8 2 30
Sum 29 52 91 20 192
Type H M N L Sum
A 2 6 28 3 39
B 7 19 35 4 65
C 5 16 33 4 58
D 12 9 8 1 30
Sum 26 50 104 12 192
Type H M N L Sum
A 6 5 35 4 50
B 2 17 38 2 59
C 5 23 27 1 56
D 10 7 5 5 27
Sum 23 52 105 12 192
Conclusions:
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.
Thank You for attention.
Jarosław Olejniczak, PhD
Wroclaw University of Economics
jaroslaw.olejniczak@ue.wroc.pl