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Acta Polytechnica Hungarica Vol. 14, No. 7, 2017
– 51 –
Non-Parametric Approach to Measuring the
Efficiency of Banking Sectors in European
Union Countries
Adam P. Balcerzak1, Tomas Kliestik2, Dalia Streimikiene3,
Luboš Smrčka4
1 Nicolaus Copernicus University, Department of Economics, ul. Gagarina 13, 87-
100 Toruń, Poland, e-mail: adam.balcerzak@umk.pl
2University of Zilina, Faculty of Operation and Economics of Transport and
Communications, Univerzitna 1, 010 26 Zilina, Slovakia, E-mail:
tomas.kliestik@fpedas.uniza.sk
3 Vilnus University, Kaunas Faculty, Muitines 8, Kaunas, LT-42280, Lithunia, E-
mail: dalia.streimikiene@khf.vu.lt
4 University of Economics, Prague, Faculty of Business Administration, W.
Churchill Sq. 4, 130 67 Prague 3, Czech Republic, E-mail: smrckal@vse.cz
Abstract: The European banking sector has been in the center of interest for the last ten
years. There are several reasons for this: An impact of global financial crisis on banks
stability; Fundamental influence of banking sector on the effectiveness of governments’
anti-crisis actions, Vulnerability of banking institutions to the crisis of the Euro currency
and last, but not least, the problems of the biggest banks in Italy and Germany, which for
the last decades have been considered as the most efficient. The financial crisis and its
negative influence, not only on the small national banks, but also on the strongest
International Institutions, has shown that the problem of measurement of efficiency of the
banking sector is still a current topic, important not only from the perspective of academic
research, but also form the point of view of National and International Regulators. In this
context, the objective of this study is to propose a methodology for a comprehensive
evaluation of operational efficiency of the banking sectors in EU countries. The pointed
problem is often discussed in a nonlinear fashion. Thus, the potential methodological
proposal should be based on the interaction of multiple inputs with multiple outputs,
without the knowledge of the functional relationships between them. In the research, Data
Envelopment Analysis, is given as a suitable instrument for this purpose. Thanks to this
methodology we measured the degree of (in)efficiency of banking sectors in the EU
countries. Additionally, we proposed measures to increase their efficiency. We found that
there are differences between the efficiency of banking sectors of “old” fifteen and “new”
EU member countries. We also confirmed that there is a noticeable difference between the
efficiency of banking sectors within the European Monetary Union members and Countries
which do not belong to the Euro-zone.
Keywords: efficiency; banking sector; Data Envelopment Analysis; Malmquist Index
A. P. Balcerzak et al. Nonparametric Approach to Measuring Efficiency of Banking Sectors
in European Union Countries
– 52 –
1 Introduction
Banks are business entities, but they have a special meaning and role in national
economies. Banking institutions can be classified as financial intermediaries,
which are involved in allocation of excess liquidity among entities. They take
deposits from entities with excess liquidity and they provide these resources to the
deficient entities, in the form of loans, which is crucial, both from a micro and a
macroeconomic perspective. During “normal” times, it significantly influences
financial effectiveness and growth potential of enterprises, but what is more
during the periods of market turbulence or crisis, the liquidity of the banking
system determines an effectiveness measure of monetary authorities,
governments’ stabilization and anti-crisis actions [8, 21]. However, from the
perspective of measuring efficiency of banking institutions, the range of banking
services is currently much more diverse than simple financial intermediation. This
is the reason why it is very difficult to define or to measure the bank “production”
outcomes.
The logical consequence of the fact, that banks and banking sectors, have an
extremely important role in National Economies, is the interest of the professional
public in this issue, which is presented in many studies dedicated to the problem
of measurement and evaluation of the efficiency of banks [6, 7, 15, 25, 34, 24].
The fundamental trends in recent years, such as deregulation; increased
competition due to the globalization process; the global financial crisis of the
years 2007-2008 and its long term consequences, have resulted in higher pressure
in the sector and have forced banks to reduce costs and increase the efficiency of
operational activities. In the past, ratio indicators such as liquidity, profitability,
capital adequacy and so on, depending on the needs of the specific analysis, were
treated as standard instruments for measuring of the banks performance. The
results were usually a subject of comparison for a given bank in different time
points or they were used as a benchmark tool with other banks.
These traditional indicators are attractive, as they have a quite easy interpretation
and are simple from a methodological perspective. However, they have several
limitations which should be considered. One is the assumption that all the rated
banks are comparable, it means they should operate under conditions of similar
returns of scale [39]. Another disadvantage is that each group of indicators is
devoted to measurement of just a part of the banking activities. For this reason,
these indicators often provide contradictory results, which can be confusing and
provide inappropriate assessment of overall performance. Therefore, the simplistic
analytical methods cannot offer an objective identification of ineffective banks,
which could enable to separate them from the effective once. Simple financial
indicators cannot capture the multiple natures of inputs and outputs, thus, the
multivariate nature of efficiency phenomenon [2, 3]. These factors decrease the
usefulness of standard financial ratios as tools for assessing the effectiveness of
the group of banks.
Acta Polytechnica Hungarica Vol. 14, No. 7, 2017
– 53 –
The limitations which we mentioned above, led to the application of more
sophisticated instruments for detecting single bank efficiency or the efficiency of
whole banking sectors, which enable the measurement of the relative effectiveness
of individual bank against to effectiveness of the best banks within examined
group. For the case of all the methods, an objective problem relates to the
determination of "the best" bank benchmark, which should be empirically pointed,
as a theoretical "the best" bank model has not yet been developed. However,
analysis of the production boundary enables to determine the comprehensive
banks performance, and then divide them into the effective and ineffective groups.
Subsequently, this analysis enables discovery of the causes of inefficiency. At the
same time, the methods can provide specific recommendations which lead to the
fact that an ineffective bank moves to the boundary of efficiency. We can divide
the sophisticated methods for determining the efficiency into the following
categories [14]: (i) parametric methods (Stochastic Frontier Analysis (SFA),
Distribution-Free Approach (DFA)); (ii) nonparametric methods (Data
Envelopment Analysis (DEA)), which will be applied in the article.
Therefore, the objective of the current research is to propose a methodology for a
comprehensive evaluation of operational efficiency of the banking sectors in EU
countries, which is based on the Data Envelopment Analysis and Malmquist
index. From the strictly empirical perspective, the aim of the study is to measure
the degree of (in)efficiency of European banking sectors and to verify potential
differences between the efficiency of banking sectors of the “old” fifteen and the
“new” EU member countries, the banking sectors in the European Monetary
Union States and the “once outside” the Euro area.
The application of the DEA methodology to analysis of sectorial efficiency – also
in the case of banking sector – is not a novel idea. However, in relation to the
research on banking sector efficiency most of recent papers concentrate on single
countries or even the micro-cases of single banks [1, 5, 14, 20, 23, 26, 31, 33, 37,
38, 41, 42]. The actuality and empirical contribution of this article to the current
state of the art relates to the scope and scale of the research. To our best
knowledge, in recent years, it is unique research that is devoted to the efficiency
of the banking sector in the entire EU, with special consideration to the
differences between the original countries of the EU and the new member states
and member and non-member countries of the Euro zone.
2 Theoretical Framework
Efficiency is defined as a condition, where it is not possible to produce additional
unit of a good with current resources, unless one reduces production of another
good. It can be related to the microeconomic production frontier framework. Thus,
under the mentioned condition an entity is on the edge of its production
capabilities. Evaluation of efficiency is an integral part of rational behavior of the
A. P. Balcerzak et al. Nonparametric Approach to Measuring Efficiency of Banking Sectors
in European Union Countries
– 54 –
production units that aims to survive in a challenging competitive environment in
a long term. In practice it is possible to apply several methods to verify the level
of efficiency [7, 22, 27, 28], namely: (i) financial ratios; (ii) indexes; (iii) multi-
criteria evaluation of variants; (iv) statistical-econometric methods; (v) simulation.
The advantage of the first two instruments is their simple design and
measurability. Other advantages are the clear explanatory power for a wide range
of users and easy identification of deviations from targets or planned values.
However, these instruments also have some important disadvantages, for example,
they work with only two factors, or just with a few factors. It means that they are
not useful for identifying simultaneous presence of several factors. From the
quantitative perspective, a common problem is attributed to the fact that they are
often not measurable together and they cannot be aggregated. The mentioned
problems can be solved to some extent with application of many multi-criteria
evaluation methods. But these methods are also far from perfect. Their important
disadvantage is usually seen in the complicated interpretability of the obtained
results [35].
However, econometric methods have also several drawbacks. One of them is
defining inefficiency as the random variable that follows a certain probability
distribution, which must be specified a priori, as well as the form of dependence
transformation of input to the output. In the case of baking sector it is often
stressed that the form of transformation of an input to an output is often nonlinear
and difficult to specify [30]. Thus, the assumptions about the form of dependence
and probability distribution of inefficiency are not usually known in practice. As a
result, incorrect estimation of these parameters can lead to a situation, where the
model has no relation to reality [6]. That problem was especially visible during the
last global financial crisis.
Conversely, simulations can also have an important disadvantage – they are an
application for one specific example. It means that simulation does not offer the
rating for the set of several production units. This approach compares reading
frame of one unit in the system and not the system of units as a whole [28].
2.1 Data Envelopment Analysis
Data Envelopment Analysis (DEA) enables to reduce the mentioned
disadvantages of the traditional approaches. This is a group of methods which
represents a special area of application of linear programming. DEA measures the
efficiency of the various entities or organizational units. Investigation of
efficiency is not only related to profitability of entity in a private sector. In
general, one can examine the effectiveness of any entity that transforms an input
to an output in some way. In a study [16] authors state that DEA analysis is most
often applied in the following sectors: agriculture, banking, supply chain
management, transportation, and public policy. The popularity of the method has
Acta Polytechnica Hungarica Vol. 14, No. 7, 2017
– 55 –
increased significantly in recent years. In the mentioned study the authors show
that to 2016 there were 9881 scientific papers with DEA applications registered in
Scopus and WoS databases. In the first phase, 1978-1994, only several dozen of
papers per year were published. In the second phase, 1995-2003 the average
number of published papers was about 134 per year. Interesting is the last phase
2004-present, where there is an exponential increase of published articles. Even
within the three year period of 2014, 2015 and 2016, about 1,000 scientific
applications of the method per year were published.
Although DEA method was originally created to evaluate the effectiveness of non-
profit organizations, it began to be intensively used for an evaluation of business
entities including banking institutions. As the first the possibility of measuring the
efficiency of banks based on DEA investigated [39]. However, as a pioneering
study in the area of measuring the efficiency of banks one can point [6], who
analyzed the efficiency of 14,000 US banks. First, who carried the analysis of
efficiency of bank branches were [9]. Detailed analysis of the historical
development and application of DEA for analyzing banking sector was carried by
[36], where 80 published studies from 24 countries were analyzed. Another study
is [22] who verified 196 studies, which concentrated on the efficiency of banks
and banking sectors of which 151 were based on DEA applications.
The aim of DEA method is to eliminate or exclude subjectivity of using output
measurements in relation to input. The process of output and input selection,
which are intended for comparison, changes the process of analysis to objectivity
and eliminates subjectivity. Through the linear mathematical model weights to the
input and output of individual production units (Decision Making Units DMU) –
for example banks – are assigned, which reflect the efficiency of the bank. Models
relating to the relevant banks have the same shape, but with the different
efficiency they will have a different value of weights. According to these weights,
banks will be compared and sorted. Given that, weights are the index numbers, it
does not matter in which units they are expressed.
Basic ideas come from Farel [18] and later they were reformulated by Charnes,
Cooper & Rhodes [10] (model DEA CCR) and Banker, Charnes & Cooper [4]
(model DEA BCC). Because the method has few easily attainable assumptions,
the proposals have opened new possibilities in the evaluation of DMU. Especially,
when it is impossible to evaluate the DMU, mainly because of a complex and the
unknown nature of the relationship between inputs and outputs. Cooper, Seiford &
Ton [12] state that DEA models can be also applied in the cases, where other than
DEA models are used for evaluation of efficiency.
All models can be oriented either to the input (input oriented) or to the output
(output oriented), or they can use a combination of the two previous options and
an additive model (slack-based models) can be constructed.
In models which are input oriented, one detects efficiency of bank or banking
systems based on the input variables (the number of banks, total assets, number of
A. P. Balcerzak et al. Nonparametric Approach to Measuring Efficiency of Banking Sectors
in European Union Countries
– 56 –
employees, etc.). Banks whose optimal value of objective function is equal to one
is considered as operating effectively within the observed group. Banks whose
optimal value of objective function is less than one, are treated as inefficient. This
value shows the need for a proportional reduction of inputs (improvement), so that
ineffective bank became effective. It means that thanks to DEA models we are
able to determine the degree of bank efficiency and also we obtain information
how banks should "improve" their activities in order to become effective.
Output oriented models detect bank efficiency based on the output variables (the
number of served customers, loans, interest income, and the volume of deposits).
Banks whose optimal value of objective function is equal to one are considered as
effective within the observed group, and banks whose optimal value of objective
function is greater than one are inefficient. In output oriented models an increase
of some or all of the output variables is considered as "improvement" of banks
activities. Nowadays, there are a lot of modification of basic DEA models and Zhu
[43] made their detailed description.
In the current research we propose to apply CCR DEA model. The model for
DMU Uq can be formulated as the task for linear refracted programming:
1
1
1
1
,
1, 1,2,3, , ,
, 1,2,3, , ,
, 1,2,3, , ,
r
i iq
im
j jq
j
r
i iq
im
j jq
j
i
j
uy
maximize z vx
uy
subject to k n
vx
u i r
v j m
(1)
Where z is a measure of efficiency of the unit Uq, e is infinitesimal constant by
which the model ensures that all weights of inputs and outputs will be positive and
will be then involved in the model on at least a certain minimum level.
In the research we propose to apply output and input oriented CCR DEA model
because we assume a constant returns to scale. A comparative study provided by
[36] was a main argument for choosing that model. In this study authors state that
from 80 DEA models which were applied in the area of measuring the efficiency
of banks and banking sectors in more than 50 CCR was applied. Noulas [29]
shows special advantages of applying CCR model in the context of the possibility
of comparison of big and small banks or banking sectors, which is especially
important form the perspective of current research. However, it should be noted
Acta Polytechnica Hungarica Vol. 14, No. 7, 2017
– 57 –
that there are also contradictory propositions. For example, in the summary [19],
based on the 151 observed DEA models, the authors recommend to use the BCC
DEA model (variable returns to scale). There are also some studies [11, 12, 40],
where the simultaneous application of both CCR and BCC DEA is considered as a
possible compromise.
2.2 Malmquist Index
An ineffective DMU can become effective, thanks to implementation of various
rationalization measures. DMU which underrate the situation can be moved from
effective category to the ineffective category, vice versa. However, we are not
able to quantify this important fact with application of the basic DEA models. We
can consider basic DEA models as static models which do not take into account
the development or change in effectiveness of DMU in time. Fortunately, we are
able to eliminate this problem by using Malmquist index [4]. Färe, Grosskopf,
Lindgren and Roos [17] adjusted Malmquist index to measure changes in
effectiveness of DMU in time. We can also formulate Malmquist index in various
versions: oriented on inputs or outputs, with fixed, variables, not increasing or not
decreasing returns of scale.
Malmquist input oriented index quantifies the change in effectiveness of
production units q between successive periods t and t+1 and this model has
following form:
11
( , , , )
t t t t
q q qM x y x y E P
(2)
Term Mq (xt+1, yt+1, xt, yt) is also called “Total Factor Productivity Index TFP“. Eq
is given as the change in relative efficiency of unit q in comparison with other
DMU between period’s t and t+1, Pq quantifies the change in production
possibilities boundary, which is caused by the technology development between
periods t and t+1. These components are defined as follows:
1 1 1
,
,
t t t
q
qt t t
q
D x y
ED x y
(3)
12
11
1 1 1 1
,,
,,
t t t t t t
qq
qt t t t t t
qq
D x y D x y
PD x y D x y
(4)
Then:
12
1 1 1 1 1
11
1 1 1 1
, , ,
( , , , ) , , ,
t t t t t t t t t
q q q
t t t t
qt t t t t t t t t
q q q
D x y D x y D x y
M x y x y D x y D x y D x y
(5)
A. P. Balcerzak et al. Nonparametric Approach to Measuring Efficiency of Banking Sectors
in European Union Countries
– 58 –
The term in front of brackets is called the change of relative efficiency E and
measures the distance from boundary between period’s t and t+1. The section in
square brackets is the technical change T or technological progress. It is the
geometric average of change in production technologies between the two period’s
t and t+1. Färe in his paper showed how we can calculate the function of distance
and Malmquist index by using DEA. This fact again lead to the task of linear
programming, where for each of DMU we have to calculate four functions of
distance in time periods t and t+1. This situation requires solving four tasks of
mathematical programming. According to the value of Eq, Pq and mainly
according to the value of Malmquist index M achieved results can be interpreted
as follows: for the all indexes (technological progress, changes in economic
efficiency and M index) valid if they are less than one, it means that the position
of DMU in the area is worse (wrong decision), if they are equal to one (decision
were neutral), greater than one, DMU made good decisions that lead to
improvement of status for this DMU.
3 Application of DEA for Measuring of Efficiency of
European Banking Sectors
The objective of this study is to quantify the efficiency of banking sectors in
European Union Countries by application of Data Envelopment Analysis for the
years 2014 and 2015 and also quantify the interaction between them through the
Malmquist index. The short time span of the analysis was restricted by the data
availability for the whole panel of the EU countries.
In this study we determined three hypotheses:
H1: Banking sectors in the European Union countries are not enough consolidated
after the strong impact of the financial crisis. As a result, banking sectors in most
of the countries are ineffective.
H2: Banking sectors in “old” EU members countries are working more effectively
than the banking sectors in “new” EU members.
H3: Banking sectors of European Monetary Union countries are working more
efficient than the sectors of countries which do not apply the euro.
Providing proper definition of inputs and outputs is usually considered as the most
difficult operation in the process of DEA model constricting. Defining of inputs
and outputs of commercial banks is not an exception. Their definition is based on
the three basic bank models [9, 39]: (i) intermediation model, (ii) production
model), (iii) asset model. It should be noted that except of these basic models
there are also other possibilities such as a model of cost per user (User cost model)
or a model of value added (Value added model).
Acta Polytechnica Hungarica Vol. 14, No. 7, 2017
– 59 –
We took into account three models mentioned above and studies [15, 37] in the
process of determining the input and output characteristics. In accordance with the
extent of the group (28 countries) we chose six as an appropriate number of inputs
and outputs, as the number of factors involved in the analysis significantly
influences the results in the application of the DEA methodology. An excessive
number of variables artificially increases the number of efficient DMU and then
reduces the discriminatory power and explanatory power of the analysis. Thus, it
is recommended that the number of variables should not be greater than one third
of the range of the group [22]. In our study we used following input variables:
assets, staff, Herfindahl-Hirschman index and number of banks. In addition, we
used following output variables: deposits and loans. Tables 1 and 2 show the data
for 2015 and 2014. The data was obtained from the annual report of the European
Central Bank and the European Banking Federation.
Table 1
Input and output variables of bank sectors in 2015
Country
INPUT
OUTPUT
Assets
[€ mil.]
Staff
HHI
Number
of
banks
Deposits
[€ mil.]
Loans
[€ mil.]
Belgium
1102000
56611
998
103
619965
479513
Germany
7802346
647300
273
1808
4525100
4368244
Estonia
21455
4860
2409
37
14751
18582
Ireland
1079754
28871
679
446
349325
324808
Greece
397801
45654
2254
40
243789
236027
Spain
2973124
201643
896
226
2001535
1725788
France
8176956
411012
589
496
3985954
4375305
Italy
4022863
299684
435
670
2339704
2410291
Cyprus
91151
10956
1443
57
48866
65177
Latvia
30855
9374
1033
59
13945
19598
Lithuania
25487
8952
1939
89
16345
20938
Luxembourg
962871
25816
321
148
450633
387075
Malta
56872
4427
1621
27
26562
15341
Netherlands
2451308
94000
2104
218
1145010
1324449
Austria
879996
74110
397
707
503959
528696
Portugal
469053
53888
1159
150
284994
259468
Slovenia
43557
10682
1077
24
30095
28779
Slovakia
64238
18656
1250
28
46470
43118
Finland
579309
22019
2730
271
186249
273221
Bulgaria
47370
31715
2433
28
31573
31328
Croatia
57793
21190
1726
33
35788
43323
Czech Republic
195513
40334
1100
56
126154
114838
Denmark
1082400
37201
328
119
304283
639331
A. P. Balcerzak et al. Nonparametric Approach to Measuring Efficiency of Banking Sectors
in European Union Countries
– 60 –
Hungary
113460
39456
982
189
63777
78105
Poland
379577
175972
411
679
241341
259129
Romania
90492
57732
1992
39
54825
61182
Sweden
1247067
54644
592
159
404193
697069
United Kingdom
8997563
402561
318
361
3819623
4080962
Source: European Banking Federation & European Central Bank
Table 2
Input and output variables of bank sectors in 2014
Country
INPUT
OUTPUT
Assets
[€ mil.]
Staff
HHI
Number
of
banks
Deposits
[€ mil.]
Loans
[€ mil.]
Belgium
1021568
58233
982
103
617928
469940
Germany
7528947
651250
301
1842
4482598
4429237
Estonia
19951
4861
2445
31
13449
16385
Ireland
1016950
31776
667
458
386260
360963
Greece
407407
51242
2195
40
266776
246206
Spain
3150735
215663
839
290
2046168
1828885
France
7881631
415953
584
623
3908181
4334755
Italy
4047885
306313
424
694
2301355
2382174
Cyprus
90198
11142
1303
101
52635
63581
Latvia
29258
10029
1001
63
13747
20434
Lithuania
24035
8392
1818
91
13873
18348
Luxembourg
914817
26237
329
147
430624
393022
Malta
50333
4197
1648
27
19636
14922
Netherlands
2250131
96423
2131
253
1041558
1268028
Austria
915105
75980
412
731
511214
553294
Portugal
515328
57556
1164
151
308545
284089
Slovenia
46354
11218
1026
23
32216
32313
Slovakia
61129
18540
1221
28
44873
41109
Finland
525312
22402
3310
303
183439
263833
Bulgaria
47410
32756
2305
30
31150
32987
Croatia
57944
21646
1596
35
35145
44864
Czech Republic
190868
39742
1059
56
128863
114914
Denmark
1048300
36367
335
161
285992
634588
Hungary
116064
40750
1006
189
62437
65896
Poland
361627
179385
395
691
230311
250302
Romania
91396
58612
1854
39
51459
64675
Sweden
1214496
53594
572
168
395313
693523
United Kingdom
8895348
421508
315
358
3977473
4315786
Source: European Banking Federation & European Central Bank
Acta Polytechnica Hungarica Vol. 14, No. 7, 2017
– 61 –
Capital represents the total average value of fixed assets of all banks in the
country. The staff is expressed by the average number of employees in a given
banking sector. Herfindahl-Hirschman index is used in the context of antitrust
policy to measure the concentration of the sector in the national market. Low
value of the index indicates low level of sector concentration, which can be
interpreted as the sign of higher competition in the sector. Punt & Van Rooij [36]
provide also other possibilities of measurement the concentration in banking
sector such as Lerner index, Theil coefficient of entropy or concentration ratio.
The last input variable is the total number of domestic banks and foreign banks or
their branches. Deposits are measured as the total amount of current and term
deposits, which banks obtained from individual clients and from other financial
institutions. Loans are measured as the net value of loans to population, business
sector and other financial institutions.
4 Results and Discussion
As it was pointed, the main aim in this paper was to measure the efficiency of
banking sectors of the European Union member countries. The results of output
oriented analysis are presented in Table 3 and the results of input oriented analysis
are given in Table 4. We can conclude, that from the point of view of our analysis
the banking sectors are effective in 15 countries in 2015 (the rate of efficiency is
equal to one) and in 13 countries they are not effective (the rate of efficiency in
output oriented models is higher than one and in input oriented models is lower
than one, vice versa). In 2014, 18 banking sectors were effective and only 10
sectors were not effective. Compared to 2015 the rate of efficiency of banking
sectors fell from 64.29% to 53.57%.
As it was mentioned, the advantage of DEA is the ability to measure the efficiency
of DMU. In addition, DEA has another important advantage, which is the ability
to detect the reserves. It means in the input oriented models DEA provide
information on the necessary reduction of the inputs. In the output oriented models
information on the possibilities to increase the outputs is given.
The degree of inefficiency in the banking sector will be illustrated with an
example of Malta, which was rated as the least efficient banking sector in 2015.
As the first step we will do the analysis of output oriented models. The rate of
relative inefficiency of the sector was 0.6914 (1/1.44625). The banking sector in
Malta would be considered as effective if the original value of deposits was
increased from 26562 million € to 38415 million € (it must be increased by 11853
million €). Furthermore, the sector should increase the volume of lending from 15
341 million € to 33244 million € (the difference is 17903 million €). In the
analysis for Malta, the Spanish banking sector is used as a benchmark.
A. P. Balcerzak et al. Nonparametric Approach to Measuring Efficiency of Banking Sectors
in European Union Countries
– 62 –
Table 3
The efficiency of banking sectors in 2015 - output oriented model
Country
Efficiency
Benchmarks
OUTPUT
Deposits
[€ mil.]
Loans
[€ mil.]
Belgium
1.01704
Spain
10561
112288
Germany
1.00000
---
0
0
Estonia
1.00000
---
0
0
Ireland
1.35501
Luxembourg
124013
115309
Greece
1.00000
---
0
0
Spain
1.00000
---
0
0
France
1.00000
---
0
0
Italy
1.00000
---
0
0
Cyprus
1.00000
---
0
0
Latvia
1.18413
Cyprus
4636
3609
Lithuania
1.00000
---
0
0
Luxembourg
1.00000
---
0
0
Malta
1.44625
Spain
11853
17903
Netherlands
1.00000
---
0
0
Austria
1.00434
Italy
8108
2294
Portugal
1.09048
Spain
25786
23476
Slovenia
1.02310
Estonia
695
665
Slovakia
1.00000
---
0
0
Finland
1.20294
Spain
37798
55448
Bulgaria
1.06088
Estonia
1922
1907
Croatia
1.00000
---
0
0
Czech Republic
1.04639
Spain
5853
5328
Denmark
1.00000
---
0
0
Hungary
1.01642
Cyprus
4685
1282
Poland
1.00000
---
0
0
Romania
1.03857
Greece
2115
2360
Sweden
1.06255
Italy
25454
43605
United Kingdom
1.00000
---
0
0
Table 4 shows the results of input oriented analysis. The number of efficient
banking sectors must be the same as the benchmark for ineffective sectors. But the
rate of inefficiency is expressed directly. When we use the example of Malta, it is
0.69144. It means that the banking sector has to reduce the following inputs: the
assets must fall by 17 548 million €, from the amount of 56872 million € to 39324
million €. The number of employees must be reduced from the original amount of
4427 by 1366, which means that the employment level in the sector should be
equal to 3 061. The degree of concentration of banking sector in Malta, which is
Acta Polytechnica Hungarica Vol. 14, No. 7, 2017
– 63 –
expressed by Herfindahl-Hirschman index, must fall by 1575, it means from the
amount of 1621 to the final amount 46. Finally, the number of banks should fall
by 13, it means from the original amount of 27 to 14.
Table 4
The efficiency of banking sectors in 2015 - input oriented model
Country
Efficiency
INPUT
Assets
[€ mil.]
Staff
HHI
Number
of
Banks
Belgium
0.98325
18458
948
473
2
Germany
1.00000
0
0
0
0
Estonia
1.00000
0
0
0
0
Ireland
0.73800
305042
7564
423
330
Greece
1.00000
0
0
0
0
Spain
1.00000
0
0
0
0
France
1.00000
0
0
0
0
Italy
1.00000
0
0
0
0
Cyprus
1.00000
0
0
0
0
Latvia
0.84450
4798
1458
161
32
Lithuania
1.00000
0
0
0
0
Luxembourg
1.00000
0
0
0
0
Malta
0.69144
17548
1366
1575
13
Netherlands
1.00000
0
0
0
0
Austria
0.99568
3802
320
2
521
Portugal
0.91703
38918
4471
96
32
Slovenia
0.97742
983
241
24
3
Slovakia
1.00000
0
0
0
0
Finland
0.83130
97732
3715
2463
224
Bulgaria
0.94261
2719
18649
1061
2
Croatia
1.00000
0
0
0
0
Czech Republic
0.95566
8668
13317
49
2
Denmark
1.00000
0
0
0
0
Hungary
0.98385
1833
637
16
44
Poland
1.00000
0
0
0
0
Romania
0.96286
3361
32894
87
1
Sweden
0.94113
73417
3217
35
9
United Kingdom
1.00000
0
0
0
0
In 2015, 15 banking sectors were effective, it means that there are no specific
recommendations for changes in inputs and outputs in their case. This does not
mean that it is not necessary to optimize their business continuously, as they can
become ineffective in the future. Eventually, the results in 2014 were worse than
A. P. Balcerzak et al. Nonparametric Approach to Measuring Efficiency of Banking Sectors
in European Union Countries
– 64 –
in 2015. We reviewed the change in efficiency between the two years by using
Malmquist index. We investigated the development of the rate of efficiency in
individual banking sectors in 2015 compared to 2014. In addition, we investigated
whether the decisions of bank management, regulators or other uncontrollable
exogenous factors had a positive, negative or neutral influence.
Table 5
Malmquist index in time 2014-2015
Country
Efficiency
Malmquist
INDEX
2014
2015
Belgium
1.00000
1.01704
1.01319
Germany
1.00000
1.00000
1.03165
Estonia
1.00000
1.00000
1.05003
Ireland
1.25519
1.35501
0.93079
Greece
1.00000
1.00000
0.98142
Spain
1.00000
1.00000
1.07352
France
1.00000
1.00000
1.00630
Italy
1.00000
1.00000
1.01858
Cyprus
1.00000
1.00000
1.02416
Latvia
1.10606
1.18413
0.91714
Lithuania
1.04542
1.00000
1.07547
Luxembourg
1.00000
1.00000
1.02479
Malta
1.67847
1.44625
1.20013
Netherlands
1.00000
1.00000
1.06005
Austria
1.00000
1.00434
0.99585
Portugal
1.08703
1.09048
1.00622
Slovenia
1.00000
1.02310
0.96794
Slovakia
1.00000
1.00000
0.99288
Finland
1.16184
1.20294
0.96327
Bulgaria
1.04074
1.06088
0.97850
Croatia
1.00000
1.00000
0.97598
Czech Republic
1.00000
1.04639
0.96515
Denmark
1.00000
1.00000
1.05840
Hungary
1.20889
1.01642
1.18109
Poland
1.00000
1.00000
0.99206
Romania
1.00998
1.03857
0.95625
Sweden
1.04995
1.06255
0.98773
United Kingdom
1.00000
1.00000
0.96846
The first two columns of Table 5 express the efficiency of banking sectors in 2014
and 2015 separately. The third column presents the quantified change of
effectiveness over time. Based on the Malmquist index we are able to downwardly
classify the banking sectors of individual countries. The values of Malmquist
Acta Polytechnica Hungarica Vol. 14, No. 7, 2017
– 65 –
index, which are higher than one show the increasing rate of efficiency against
other DMU. The values of Malmquist index lower than one show decreasing rate
of efficiency. The value of index equal to one or around one expresses that the
effects of endogenous and exogenous factors on the bank sector were neutral.
Starting again with the example of Malta, the banking system achieved the highest
value of Malmquist index 1.20013. Despite of the fact that in 2014 (1.67847) and
2015 (1.44625) it was ineffective, this system achieved the most significant
increase in efficiency. This situation can be considered as a positive phenomenon.
The banking sector of Latvia was also ineffective in both years 2014 (1.10606)
and 2015 (1.18413). However, unlike Malta, this sector had decreasing
effectiveness, the value of Malmquist index was at the level of 0.91714. Banking
sector of Poland was effective in both years and the value of Malmquist index
equal to one informs us about this situation. Interesting is that Malmquist index of
Czech Republic (0.96515) and Great Britain (0.96846) was almost the same.
However, in the case of Czech Republic this situation expresses the inclusion of
its banking sector into the category of ineffective bank sectors.
In regard to our findings, the rate of efficiency of banking sectors in the EU
member countries was in 2015 at the level of 53.57%, whereas in 2014 it was at
the level of 64.29%. According to papers [22, 36] we considered as effective these
banking sectors which work with the rate of effectiveness higher than 70%.
Based on the obtained results we can state that the hypothesis H1 was confirmed,
which means that the banking sectors of the EU member countries are still not
sufficiently consolidated. Taking into consideration the pre-crisis research
conducted by Pastor [32], when the banking sector of the EU members achieved
an average rate of effectiveness equal to 86%, we can state that our results confirm
the negative long term consequences of the financial crisis.
In regard to the H2 hypothesis, we divided our sample into two groups. The first
group consists of “old” EU member states and in the second group the countries
that joined the EU after 2004 are found. From the 15 original member countries
the banking sectors in Germany, Greece, Spain, France, Italy, Luxembourg,
Netherlands, Denmark and United Kingdom can be considered as efficient, and
this situation reflects the rate of effectiveness at the level of 60%. From the
countries that joined to the EU after 2004 the banking sectors were effective in
Poland, Croatia, Slovakia, Lithuania, Cyprus and Estonia and this situation
reflects the rate of effectiveness at the level of 46.15%. Based on these results it
should be noted that the second hypothesis H2 was confirmed – the banking
sectors of the old EU members were more effective from the operational point of
view.
Finally, with regard to the H3 hypothesis we investigated whether the banking
sectors of the Eurozone members are more efficient than banking sectors of
countries, which have not applied the euro. For this reason we again divided our
sample into two groups. From the 18 countries in the Eurozone the banking
A. P. Balcerzak et al. Nonparametric Approach to Measuring Efficiency of Banking Sectors
in European Union Countries
– 66 –
sectors in Germany, Estonia, Greece, Spain, France, Italy, Cyprus, Lithuania,
Luxembourg, Netherlands and Slovakia worked effective and this situation
reflects the rate of effectiveness at the level of 57.89%. From the 9 countries
outside the euro area the banking sectors of Croatia, Denmark, Poland and United
Kingdom worked effective and this situation reflects the rate of effectiveness at
the level of 44.44%. Therefore, it should be noted that the hypothesis H3 was
confirmed – the banking sectors of the Eurozone members can be considered as
more efficient than the once outside euro area.
In the end the obtained results especially pointing to the efficiency of such
banking sectors as the once in Greece, Spain or Italy should be also commented
form the perspective of banking sector stability. It should be stressed that in the
present research the problem of undesirable output – for example, in the case of
banking sector, the share of non-performing loans in the portfolio, which is
important from the perspective of banking sector stability and capital adequacy
requirements – was deliberately omitted, which is considered as a standard
approach form the perspective of the objectives of the article [compare 40], and
still present controversies of data interpretation in this regard. So the obtained
results should be interpreted from the perspective of operational efficiency of the
banking sectors not form the perspective of their stability.
Conclusion
This paper was focused on the issue of measuring the efficiency of banking
sectors, especially on the issue of measuring the operational effectiveness of
banking sectors in the European Union member countries. The objective of this
paper was to suggest a relevant methodology for measuring bank efficiency based
on the Data Envelopment Analysis and Malmquist index.
The conducted empirical research confirms that the banking sectors in the EU
countries are characterized with relatively low levels of efficiency in 2015.
Empirical evidence suggests that the banking sectors are not enough consolidated.
The research confirms still visible negative impact of the last global financial
crisis, and probable negative implications of some other exogenous factors, where
one can point relatively low effectiveness of monetary stabilization policy of the
European Central Bank and the National Central Banks, and low effectiveness of
regulation efforts at the European Union level.
With regard to the comparative analysis of efficiency of banking sectors in the
Euro Area and outside the Monetary Union, we confirm that the banking sectors
of the Eurozone members are more efficient than the banking sectors of countries
which have not yet applied for the euro. In the case of comparison of banking
sector efficiency of the old 15 EU members and the member states admitted to the
EU after 2004, the first group can be considered as more efficient.
In the end, one should also point the restrictions of the research, the potential
applications of the proposed methodology and areas of possible future studies.
Acta Polytechnica Hungarica Vol. 14, No. 7, 2017
– 67 –
When we tried to create a model for measuring the efficiency of banking sectors,
we encountered several objective problems. This is the reason why we did not
include all the variables for which we planned. For example, we were not able to
obtain an average rate of profitability, the volume of non-performing loans, capital
adequacy for the whole set of countries. In our opinion, the achievement of the
assumption concerning homogeneity of DMU can be questionable, in the case of
banking sectors. It should be also remembered that explanatory power of some
variables, which we also used in the research, can also be questioned. For
example, loans are commonly accepted and designated as outputs of banking
activity, which is expressed in monetary units in the net value. However, this
value itself does not provide information on the quality of loans, that is important
from the perspective of sectors stability, which has been already stressed in a
previous section.
Despite the barriers and the problems we can state that obtained results can be
used for a variety of purposes, starting with continuous monitoring of the rate of
efficiency of banking sectors, in the EU countries and comparative research
between the countries. Interesting results, especially form a managerial
perspective, could be obtained at the lower aggregation level – if we were able to
assess for example the rate of effectiveness of individual banks within each
country of the EU. Another important area of future research would involve
addressing the problems with the development of technical, cost and overall
efficiency. As it has been already stressed, the validity of the model could be also
increased after expansion, including the undesirable output or the uncontrollable
variables.
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