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Measurement of Revenue Efficiency in European Union Countries: A Comparison of Different Approaches

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This paper analyses revenue efficiency of the banking sectors in the European Union (EU) countries in 2015. The Data Envelopment Analysis (DEA) and traditional method of ratios were applied. The results of the DEA, by country, indicate that the revenue efficiency ranged from 34.47% in case of Greece to 100% in case of Germany, Denmark, Estonia, United Kingdom, Luxembourg, Malta, Netherland and Sweden. When we measured revenue efficiency by ratios we can see that the most efficient were banking sectors in Latvia and Romania, and the last efficient was banking sector in Greece. The revenue efficiency was also analysed in 3 groups of banking sectors, categorised according to the volume of total assets. According to the DEA, the large banking sectors appears to be most efficient and the least efficient were banking sectors within the small sized group. The situation was different when the method of ratios was applied, where the most efficient were banking sectors within the medium-sized group. In the last part of our analysis, four main European “regions” were determined, and average revenue efficiency was analysed within them. According to the DEA, the levels of average efficiencies in the case of the Northern and Western European banking sectors were above the average for the whole sample. In the case of Southern and Eastern European banking sectors efficiencies were under the total average. In the case of ratios, the levels of average efficiencies were under the total average only in Southern European banking sectors. Comparing traditional financial ratios and DEA, we found that each method brings different results. Therefore, when analysing banks respectively banking sectors, it is appropriate to use more methods simultaneously.
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Measurement of Revenue Efficiency in European Union Countries...
31 International Journal of Applied Business and Economic Research
Measurement of Revenue Efficiency in European Union Countries:
A Comparison of Different Approaches
Kristína Kočišová
1 Technical University of Košice, Faculty of Economics, Department of Banking and Investments, Nemcovej 32, 04001 Košice,
Slovakia, Email: Kristina.Kocisova@tuke.sk
Abstract: This paper analyses revenue efficiency of the banking sectors in the European Union (EU) countries in
2015. The Data Envelopment Analysis (DEA) and traditional method of ratios were applied. The results of the DEA,
by country, indicate that the revenue efficiency ranged from 34.47% in case of Greece to 100% in case of Germany,
Denmark, Estonia, United Kingdom, Luxembourg, Malta, Netherland and Sweden. When we measured revenue
efficiency by ratios we can see that the most efficient were banking sectors in Latvia and Romania, and the last
efficient was banking sector in Greece. The revenue efficiency was also analysed in 3 groups of banking sectors,
categorised according to the volume of total assets. According to the DEA, the large banking sectors appears to be
most efficient and the least efficient were banking sectors within the small sized group. The situation was different
when the method of ratios was applied, where the most efficient were banking sectors within the medium-sized
group. In the last part of our analysis, four main European “regions” were determined, and average revenue efficiency
was analysed within them. According to the DEA, the levels of average efficiencies in the case of the Northern and
Western European banking sectors were above the average for the whole sample. In the case of Southern and Eastern
European banking sectors efficiencies were under the total average. In the case of ratios, the levels of average efficiencies
were under the total average only in Southern European banking sectors. Comparing traditional financial ratios and
DEA, we found that each method brings different results. Therefore, when analysing banks respectively banking
sectors, it is appropriate to use more methods simultaneously.
JEL Classification:G21, C14, C6
Keywords: Data Envelopment Analysis; Ratios; Revenue Efficiency; European Banking Sector
1. INTRODUCTION
In the economic system of the country that works in accordance with the principles of the market mechanism,
there are carried out economic activities of individual economic entities. One of the conditions for the effective
functioning of the economic system is functioning financial system. Significant changes that have affected the
financial sector in recent years have included changes in deregulation, globalisation of markets, innovation and
technological progress. Changes mentioned above are the main factors that will gradually reduce the cost of
capital and significantly affect the performance and competitiveness of the banking sector in the international
Kristína Koèišová
International Journal of Applied Business and Economic Research 32
context. Just a gradual process of globalisation significantly affects the structure of the financial and banking
system, their performance, efficiency and stability.
In modern society, there are many ways how to define efficiency. We used definition presented by Farrell
(1957), who stated that the efficiency of a firm consists of two components: technical and allocative efficiency.
Technical efficiency describes the ability of a bank to gain maximal output from anexisting set of inputs. On the
other hand, allocative efficiency indicates the competency of a bank to use the inputs in optimal proportions,
given input prices and the production technology. Technical and allocative efficiency could bemerged into an
overall economic efficiency. The overall efficiency could be analysed from the input point of view, then we can
talk about overall cost efficiency. It could be also analysed from an output point of view, which results in overall
revenue efficiency. Farrell´s (1957) paper led to the development of several approaches to measuring the input
and output efficiency. Greatest importance was assigned to a Stochastic Frontier Approach and Data Envelopment
Analysis.
The process of efficiency measurement and identification the source of inefficiency are an important
condition for increasing the competitiveness of production units. Under the term production unit, we can
understand a unit that produces some outputs, using some inputs. It could be any homogeneous units, which
perform the same or similar activities. According to this definition, the production units can be for example and
banks, hospitals, schools, agricultural entities, banking, economics, etc.The efficiency of banks is a very important
question in the financial system, as their efficiency can affect the stability of banking industry and thus the
efficiency of a whole monetary system.
We can assess the banks´ efficiency from a different perspective. In our paper, we will discuss the efficiency
in the form of revenue efficiency. Revenue efficiency demonstrates how a bank (or banking system) couldpredict
their performance in terms of revenue relative to other units in the same period for producing the same range of
outputs.
The aim of this study is to compare the select approaches in the evaluation of efficiency. This paper deals
with DEA method and traditional method of ratios and describes its application in measuring revenue efficiency
in European banking. The structure of the study is as followed. The review of relevant literature is described in
part 2. Used methodology is discussed in detail in part 3. Part 4 contains the practical application of selected
methods for measuring revenue efficiency in European banking sector in 2015 using the R software. Finally, the
paper ends with some concluding remarks.
2. LITERATURE REVIEW
The earliest techniques usually measure the efficiency through the financial ratios, examined financial statements
of individual banks and compared them with a benchmark. Probably the best-known ratios used to measure the
efficiency of commercial banks are Return on assets, Return on equity, Capital adequacy ratio, Cost to income
ratio, Non-performing loans ratio, Loan to deposit and so on. Ratios are traditional tools for assessing the
efficiency when comparing economies, economic sectors, entities operating in the relevant markets, etc. This
method is also used to assess the efficiency of the banking sector. Application of classical ratios in the banking
area can be found in the work of Kumbirai and Webb (2010), Said and Tumin (2011), Bičo and Ganić (2012),
Kaur et al. (2015), Sriyana (2015), Dasuki et al. (2016), and Kumar and Selvan (2016).
More recent methods are labelled as methods of the multi-criteria decision, the Balanced Scorecard (BSC)
method, parametric methods and non-parametric methods. BSC method and methods of the multi-criteria
decisionare used in evaluating the efficiency in various sectors of the national economy. For example,Gavurová
(2011), Šoltés and Gavurová (2013), in their works describe the use of the BSC method in evaluating the efficiency
of the private and public sectors in Slovakia. Shaverdi et al. (2011) in their work describe the possibility of using
the BSC method and methods of the multi-criteria decision in evaluating the efficiency of private banks in Iran.
Measurement of Revenue Efficiency in European Union Countries...
33 International Journal of Applied Business and Economic Research
As well asSpronk et al. (2005), Akkoc andVatansever (2013) Lou and Denesh (2015) used methods of the
multi-criteria decision in evaluating in the sector of services.
Next in the group of modern methods for efficiency measurement are parametric methods and non-parametric
methods. Parametric methods count the Stochastic Frontier Approach, the Thick Frontier Approach, and the
Distribution-Free Approach. Non-parametric methods count the Data Envelopment Analysis and the Free Disposal
Hull. Also, these methods could be used for evaluation of efficiency in various sectors of the national economy.
For example besides the banking area in Slovakia was the DEA method used for evaluation of e.g. health
services (Koróny and Gavurová 2013; Stefko et al. 2016), education, transport (Klieštik 2009; Kráľ and Roháčová
2013), and agriculture (Bielik and Hupková 2011).
DEA is a non-parametric linear programming approach to frontier estimation. Sherman and Gold (1985)
were first who applied this method to banking. They evaluated technical efficiency of 14 saving bank branches
and defined how to eliminate inefficiency by setting input and output of inefficient bank branches.
In the case of Indian banks, the DEA was used by Karimzadeh (2012) who examined the efficiency of 8 big
commercial banks throughout 2000-2010. He found out that the average CCR efficiency in 2000 was 100%,
decreasing to 98% in 2002, remained volatile from 2003 to 2009 till 2010-2011, which reached to 100% again.
The growth in efficiency was positively affectingby many economic and financial reforms, which was implemented
during the evaluated period, innovation, higher competition, better supervision, and enhanced investment in new
IT.
Pančurová and Lyócsa (2013) measured bank cost and revenue efficiencies using DEA. They estimated
efficiencies and their determinants for a sample of 11 CEE countries during the 2005-2008. They adopted the
intermediation approach and assumed that banks produce 2 outputs: loans and other earning assets. The prices
of those outputs were represented by the ratios of interest received on loans to total performing loans and
noninterest income to other earning assets, respectively. Total deposits and total costs represented the two inputs.
The prices of those inputs were interest expenses to deposits and costs to total assets, respectively. They found
out no dramatic changes in the average cost and revenue efficiencies during the analysed period, although cost
efficiency declined slightly and revenue efficiency increased. The average cost efficiency was higher for the
Baltic countries and the Czech Republic. Lower values were observed for Romania and Hungary.
Boďa and Zimková (2015) used three approaches: the services-oriented, intermediation and the profit-
oriented approach to investigated efficiency of the Slovak banks over the 2000-2011.They applied DEA models
to evaluate technical efficiency of eleven commercial banks in 3 sub-periods: 2000-2003, 2004-2008 and 2009-
2011. In each of these periods, banks were pooled together in one data frame.
The second method, Stochastic Frontier Approach is a parametric approach to frontier estimation. This
method was employed by Bos and Kolari (2005) to measure cost and profit efficiency of large European and
American banks between the 1995 and 1999. They identified that the big U.S. banks had higher average profit
efficiency than European ones. They applied intermediation approach. As the bank outputs were defined loans,
investments and off-balance sheet activities. As the input variables were used a number of employees, interest
expenses and operating expenses.
Řepková (2013) estimated the cost and profit efficiency of commercial banks in the Czech Republic using
SFA. The average cost efficiency moved between the values 78-91% and the average profit efficiency between
64-99%. The highest average cost efficiency was reached by the group of the medium-sized banks following by
the small-sized group and the highest average profit efficiency was reached by the group of small banks. The
largest banks reached the lowest efficiency in the case of both approaches.
Most studies have focused on the input side, estimating cost efficiency. Only a few studies have examined
the output side evaluating revenue and profit efficiency, but they preferred to use SFA methodology. Therefore
Kristína Koèišová
International Journal of Applied Business and Economic Research 34
in this study, we decide to apply output-oriented DEA model to measure revenue efficiency and compare the
results of DEA with traditional ratios like ROA and ROE.
3. METHODOLOGY
The basic DEA model designed by Charnes, Cooper and Rhodes (1978) is based on the theorem of a constant
return to scale. The basic model was adjusted by Banker, Charnes, and Cooper (1984), beingbased on the
theorem of a variable return to scale. Both these DEA models were created in form of the input and output-
oriented.
In this paper, we discuss some extensions of basic output-oriented DEA model under the theorem of
variable return to scale. If price data are available then we can measure allocative, output-oriented technical
efficiency as well as overall revenue efficiency. To calculate these main types of efficiency, a set of linear
programs should be solved.
The output-oriented model under the theorem of variable return to scale could be written in the next form
(Coelli et al., 2005):
Max
q
(1)
s.t.
1
1, 2, ...,
n
ij j iq
j
x x i m
 
1
1, 2, ...,
n
rj j q rq
j
y y r s
 
 
1
1
n
j
j
0 1, 2, ...,
j
j n
 
Where q is output-oriented technical efficiency (TEq) of the Decision Making Unit (DMUq) in the output-
oriented DEA model, yrq is produced amounts of rth output for DMUq, xiq is consumed amounts of ith input for
DMUq, yrj is produced amounts of rth output for DMUj, xij is consumed amounts of ith input for DMUj, j is weight
assigned to theDMUj.
For calculation of revenue efficiency the following revenue maximisation DEA problem is necessary to
solve (Coelli et al., 2005):
Max
*
1
s
rq rq
r
p y
(2)
s.t.
1
1, 2, ...,
n
ij j iq
j
x x i m
 
*
1
1, 2, ...,
n
rj j rq
j
y y r s
 
Measurement of Revenue Efficiency in European Union Countries...
35 International Journal of Applied Business and Economic Research
1
1
n
j
j
0 1, 2, ...,
j
j n
 
Where prq is a vector of output prices of DMUqand
is the revenue maximising vector of output quantities
for DMUq, given the output prices prqand the input levels xiq.
The overall revenue efficiency (REq) is defined as the ratio of observed revenue to maximum revenue for
the DMUq (Coelli et al., 2005):
1
*
1
s
rq rq
r
qs
rq rq
r
p y
RE
p y
(3)
The overall revenue efficiency can be formulated as a product of technical and allocative efficiency.
Therefore, the allocative efficiency (AEq) of the DMUq can be calculated as the ratio of revenue efficiency (REq)
to output-oriented technical efficiency (TEq) of the DMUq:
q
q
q
RE
AE
TE
(4)
These three measures (technical, allocative and overall revenue efficiency) can take values ranging from
zero to one, where a value of one in a case of TE, AE and RE indicates full efficiency. If the production unit is
fully technically efficient (TEq=1) and displays allocative efficiency (AEq=1); it is also overall revenue efficient
(REq=1). This production unit achieves the maximum possible outputs at given inputs, while the proportion of
outputs will guarantee the maximum possible revenues. If the production unit is technically efficient (TEq=1)
but doesn’t demonstrate allocative efficiency (AEq<1), it isn’t also overall revenue efficient (REq<1). This
production unit achieves the maximum possible outputs using a given inputs, but the proportion of inputs will
not guarantee the maximum possible revenues. If the production unit fails to demonstrate any of these three
types of efficiency (TEq<1; AEq<1; REq<1), then the value of overall revenue efficiency can be interpreted as a
potential revenue increasing that can be achieved if the production unit uses the outputs in optimal combination.
Potential revenues increasing can be calculated by subtracting the value of overall revenue efficiency from the
number one.
Besides the DEA method, the traditional method of ratios was applied. As the traditional indicators for
measurement of revenue efficiency were used two probability ratios: Return on Assets or Return on Equity. The
theoretical definition of these indicators is described in the works of many authors (e.g.Kumbirai and Webb
2010;Bičo and Ganić 2012; Sriyana 2015) therefore in this part of the paper these indicators will not be described
separately.
4. EMPIRICAL ANALYSIS AND RESULTS
This section describes the practical application of DEA method and traditional method of ratios for measuring
revenue efficiency in the European banking sector in 2015. For the calculation of revenue efficiency through
DEA the R software (R core team, 2013) was used, specifically the package “Benchmarking”. This package
includes methods to calculate efficiency using DEA while supporting different technology assumptions (free
Kristína Koèišová
International Journal of Applied Business and Economic Research 36
disposability hull, variable or constant return to scale, decreasing or increasing return to scale), and using various
efficiency measures (input or output based, hyperbolic graph, additive, super-efficiency, directional).
The study evaluates a cross-country level data of 28 European Union (EU) banking sectors in 2015 compiled
from the database of European Central Bank. To evaluate banking sectors the intermediation approach was used.
This approach investigates bank as an intermediary of financial services and supposes that banks gather funds
(deposits and purchases funds) with the support of labour and capital and convert them into loans and other
earning assets.
For each banking sector in the sample, it was necessary to select inputs, outputs, and output prices. Input
and output variables and selected types of revenues are measured in thousands of EUR. We consider three
inputs, namely, deposits (x1), the number of employees (x2) and fixed assets (x3). On the output side, we consider
two types of outputs: loans (y1) and other earning assets (y2), which refer to non-lending activities. Each of these
outputs generates revenues. Therefore, we can easily calculate prices for each output as a ratio of the particular
revenue to the selected output. The first price (p1) is defined as the ratio of interest income to loans, and the
second price (p2) is defined as the ratio of total non-interest income to other earning assets.
To solve the revenue maximisation problem using R, we first load the data from MS Excel file that must be
saved in the comma-separated values format. The solution of the revenue maximisation DEA model requires
using the procedure revenue.opt from the Benchmarking package. This command estimates the optimal output
vector that maximises revenues in the context of the DEA technology. The part of the command is to define
which variables will act as inputs (the matrix of inputs, x), outputs (the matrix of outputs, y), output prices (as a
matrix, p) and used technology (variable return to scale “vrs”) of applied model. To calculate overall revenue
efficiency, we have to find the actual revenues and the optimal revenues. By dividing these values we obtain
overall revenue efficiency of evaluated production units.
Figure 1 shows the level of revenue efficiency calculated through the DEA model in EU banking sector in
2015. We can see notable differences among observed countries. The results of the DEA, by country, indicate
that the revenue efficiency ranged from 34.47% in case of Greece to 100% in case ofGermany, Denmark,
Estonia,United Kingdom, Luxembourg, Malta, Netherland, and Sweden. The average revenue efficiency in
2015 was 68.76% indicating that on average banking sectors could increase their potential revenues by 31.24%
by producing the outputs in optimal combination while maintaining a given output prices.
As the benefits of DEA analysis is that it provides recommendations on how banks should adjust the
structure of their inputs or outputs, taking into account output prices, which should result in a shift to the
efficiency frontier. It can be illustrated by the example of an individual banking sector. Consider banking sector
Figure 1: Revenue efficiency calculated through the DEA in EU banking sectors; 2015
Source: Author´s calculations
100%
0%
20%
40%
60%
80%
Germany
Denmark
Estonia
United Kingdom
Luxembourg
Malta
Netherlands
Sweden
France
Finland
Lithuania
Italy
Sp[ain
Ireland
Austria
Belgium
Slovenia
Latvia
Slovakia
Croatia
Poland
Hundary
Bulgaria
Czech Republic
Portugal
Romania
Cyprus
Greece
Measurement of Revenue Efficiency in European Union Countries...
37 International Journal of Applied Business and Economic Research
in Slovakia, which reached a value of revenue efficiency equal to 52.07%. This means, that banking sector in
Slovakia didn’t reach the maximum possible outputs using existing inputs, and the proportion of outputs didn’t
guarantee the maximum possible revenues. So there existed the space for potential revenue increasing equal to
47.93%. When we looked at revenues of Slovakia we can see, that the observed value of revenues was EUR 3.03
billion and the optimal value of revenue was EUR 5.81 billion. It indicates that optimal combination of inputs,
outputs and their prices could increase the revenues in Slovak banking sector in the real term by 92.03% (which
is in real term higher than potential value). This increase in revenues could be achieved by increasing total loans
by 98.95% and by increasing of other earning assets by 71.08% while maintaining optimal values of inputs
andgivenoutput prices. This optimal combination of variables allowed achieving maximum revenue and shift on
the efficiency frontier.
The results of efficiency analysis using DEA was compared with traditional ratios like ROA and ROE. The
comparison per country isdisplayed in Table 1. As can be seen, the revenue efficiency measured by DEA (RE)
Table 1
Revenue efficiency calculated through the different approaches in EU banking sectors in 2015, per country, (%)
Country RE ROA ROE
Austria 59.2573 0.5633 7.5611
Belgium 57.5161 0.6968 10.2722
Bulgaria 42.6611 1.0262 8.0113
Cyprus 37.0882 -0.6267 -7.5639
Czech Republic 40.5309 1.1137 10.3003
Germany 100.0000 0.0918 1.6892
Denmark 100.0000 0.4085 6.8103
Estonia 100.0000 1.0772 6.7903
Spain 72.9233 0.4664 6.5914
Finland 90.4960 0.4663 8.3298
France 94.7564 0.3955 6.8255
United Kingdom 100.0000 0.2028 3.1705
Greece 34.4698 -2.8226 -24.2172
Croatia 46.1043 -0.8538 -6.7969
Hungary 42.9588 -0.0938 0.2679
Ireland 65.6383 0.8701 6.8076
Italy 77.6118 0.2394 3.1431
Lithuania 78.2972 0.9186 7.4803
Luxembourg 100.0000 0.5523 7.2235
Latvia 54.4516 1.1951 10.7459
Malta 100.0000 0.8983 6.3406
Netherlands 100.0000 0.4005 7.0933
Poland 45.3700 0.8626 7.7433
Portugal 40.4743 0.0908 0.9354
Romania 37.7692 1.1694 11.2984
Sweden 100.0000 0.6154 11.1914
Slovenia 54.7882 0.4057 3.5012
Slovakia 52.0730 0.9295 9.6894
Source: Author´s calculations
Kristína Koèišová
International Journal of Applied Business and Economic Research 38
ranged from 34.4698% to 100%. The highest revenue efficiencies (RE) were recorded in case of countries like
the Germany, Denmark, Estonia, United Kingdom, Luxembourg, Malta, Netherland, and Sweden. These banking
sectors were identified to be overall efficient. Other remaining 20 banking sectors were declared revenue inefficient.
Only one banking sector, in Finland, were inefficient only due to its allocative inefficiency. Other banking
sectors were inefficient due to both technical and allocative inefficiencies. The lowest revenue efficiency (RE)
scores were observed in the case of countries like Greece, Cyprus, Romania, Portugal and the Czech Republic.
In the case of thirteen countries, the average revenue efficiency was higher than the average in the whole sample
(68.7584%), in other fifteen countries, the average revenue efficiency was lower.
When we measured revenue efficiency by traditional indicators like Return on Assets (ROA) or Return on
Equity (ROE) we can see various results. As we know the banking sector (or bank) can be considered as profitable
(efficient) if ROA is greater as 1%. According to this criterion, as the efficient banking sectors can be considered
banking sectors in Latvia, Romania, Czech Republic, Estonia and Bulgaria. On the other hand, the last efficient
were banking sectors in Greece, Croatia, Cyprus, Hungary and Portugal. According to ROE, the most efficient
banking sectors were in Romania, Sweden, Latvia, Czech Republic and Belgium. On the other hand, the last
efficient were banking sectors in Greece, Cyprus, Croatia, Hungary and Portugal. We can see that these results
are more comparable, as they used the same methodology and both are based on the same variable, the banking
sectors net profit.
In the next part of our study, we calculated average revenue efficiency scores for 3 groups of banking
sectors categorised according to the value of total assets. We adopt part of the methodology to determine significant
banking sectors applied by the European Central Bank. We divided banking sectors into three groups: large,
medium-sized, and small banking sectors. Large banking sectors are defined as the three most significant banking
sectors in the EU. It means, that these three banking sectors have three highest shares of total assets in the
European banking sector. Medium-sized banking sectors are defined as banking sectors with a share of total
assets on the total assets of the European banking sector higher than 1%, but not involved in the group of large
banking sectors. The last group of small banking sectors is defined as the banking sectors with a share of total
assets on the total assets of the European banking sector less than 1%. In the first group, there are three banking
sectors: in Germany, France, and in the United Kingdom. In the second group, there were involved ten banking
sectors: Austria, Belgium, Denmark, Spain, Finland, Ireland, Italy, Luxembourg, Netherlands, and Sweden. In
the last group, there were banking sectors of Bulgaria, Cyprus, Czech Republic, Estonia, Greece, Croatia, Hungary,
Lithuania, Latvia, Malta, Poland, Portugal, Romania, Slovenia, and Slovakia. Large banking sectors appear to
be the most revenue efficient, where the average RE in 2015 was 98.2521% (see Table 2). On the second place,
there was average revenue efficiency within the medium-sized banking sectors, where the RE reached 82.3442%.
The least efficient were banking sectors in the last group, where the average RE in 2015 was only 62.0797%.
The situation was different when the method of ratios was applied. According to this method, the most efficient
banking sectors were within the medium-sized group (average ROA 0.4962%; ROE 6.9903%).
In the last part of our analysis, there were determined the four main European “regions” (Northern, Western,
Southern and Eastern Europe) and we analysed the revenue efficiency within them. The United Nations defines
Northern Europe as consisting of the following eight EU countries: Denmark, Estonia, Finland, Ireland, Lithuania,
Table 2
Revenue efficiency of the European Union banking sector in 2015, by size, (%)
Size RE ROA ROE
Large 98.2521 0.2300 3.8951
Medium-sized 82.3443 0.4962 6.9903
Small 62.0797 0.4069 3.4251
Source: Author´s calculations
Measurement of Revenue Efficiency in European Union Countries...
39 International Journal of Applied Business and Economic Research
Latvia, Sweden and the United Kingdom. The Western Europe is created of next six EU countries: Austria,
Belgium, France, Germany, Luxembourg, and Netherlands. Countries that are part of the Southern Europe are
Croatia, Greece, Italy, Malta, Portugal, Slovenia and Spain. The Eastern Europe is defined as consisting of seven
countries: Bulgaria, Cyprus, Czech Republic, Hungary, Poland, Romania, and Slovakia. In Table 3 could be
seen, that levels of average revenue efficiency measured by DEA in case of Northern (RE 81.4805%) and
Western European (RE 85.2549%) banking sectors were above the average for the whole sample (RE 68.7584%);
on the other hand, the average revenue efficiencies in Southern (RE 63.3779%) and Eastern European (42.6359%)
banking sectors were under the total average. Under the DEA method, the Western European banking sectors
appeared as the most efficient, and the last place was occupied by banking sectors from Eastern Europe. The
understanding of the generally lower efficiency of Eastern European banking sectors could be explainedin a
number of factors. Mainly, unpremeditated mortgage lending, increasing value of non-performing loans, lack of
transparency and accountability in mortgage financing, shadow banking activities, failure of management of
risks, lack of regulation of systematic risks and other factors which led to the financial crisis in American and
European financial markets.
In the case of ratios, the most efficient banking sectors were within the countries from Northern Europe
(ROA 0.6681%; ROE 7.7908%). The level of efficiencies was under the total average (ROA 0.4021%; ROE
4.6869%) only in case of Southern European banking sectors (ROA -0.1203%; ROE -0.6176%).
Table 3
Revenue efficiency of the European Union banking sector in 2015, by region, (%)
Region RE ROA ROE
Northern Europe 81.4805 0.6681 7.7908
Western Europe 85.2550 0.4500 6.7775
Southern Europe 63.3779 -0.1203 -0.6176
Eastern Europe 42.6359 0.6258 5.6781
Source: Author´s calculations
As shown in the previous tables the efficiency scores have wide dispersion. In the case of DEA, the values
moved approximately from 30% to 100%, in the case of ROA from -3% to 2% and in the case of ROE from -25%
to 12%. When we would like to compare the results from different methods which have different variance it is
better to make a normalisation of values to have the same variance.For example, if one variable is 100 times larger
than another, then the comparison may be better behave if we normalise the two variables to be approximately
equivalent. In literature, there are two main methods for normalisation: statistical and empirical normalisation.
Statistical normalisation converts indicators to a common scale with an average of zero and standard
deviation of one. In this approach, the extreme values of variable could have a bigger effect on the composite
indicator. Therefore we prefer to use empirical normalisation which places all indicators on the same scale in the
interval from 0 to 1. Through this process, every indicator is compared to its limit values in the analysed period
and its normalised value represents the deviation from them. According to the empirical normalisation, the
approximation of the index value to 1 (max), means lower risk, while movement towards 0 (min) means higher
risk. The formula that presents this method is as follows (Petrovska and Mihajlovska, 2013):
( )
( ) ( )
nit i
it
i i
I Min I
I
Max I Min I
(5)
Where: Iit
n is normalized value of indicator i in period t; Iit is value of indicator i in period t; Min(Ii) and
Max(Ii) are the minimum and maximum of the indicator i in the analysed period.
Kristína Koèišová
International Journal of Applied Business and Economic Research 40
The advantage of empirical normalisation is that the different values of indicators are located within the
same interval which increases the explanatory power of index.
Figure 2 displays a box-plot of normalised values of revenue efficiencies in European Union countries measured
by different methods. As can be seen, the normalised values of revenue efficiency measured by DEA were skewed
towards lower values, which reflected in Figure 2 by moving the median values (horizontal line in the rectangle a
restrictive value of 25th percentile and 75th percentile) down. The gap between the median value and the 25th
percentile value was lower than the gap between the median value and the 75th percentile value. In the case of RE,
the level of volatility was higher than in the case of ROA and ROE, which can be seen by the box size limited by the
value of 25th percentile and 75th percentile. The values of ratios were more centred on the median values.
The normalised values were also compared by correlation analysis, the Pearson correlation coefficient was
used. On the basis of results, we can say, that between both methods there exist a positive correlation. An almost
perfect correlation was found between the indicators ROA and ROE but in consequence of the nature of their
calculation. More interesting for as are values of correlation coefficients between revenue efficiency measured
by DEA and calculated by ratios. We found out that even among these values exist positive correlation, but
according to the methodology presented by Cohen (1988), there exist only a small (between RE and ROA),
respectively moderately strong correlation (between RE and ROE). This suggests that DEA and financial ratios
had the same trend but the relation was really small. The correlation analysis, therefore, suggests that financial
ratios and DEA should generally be viewed as complementary rather than competing, and should be used together
when evaluating performance (efficiency) of production units since they answer different questions. DEA takes
into account the performance of production unit on several inputs and outputs at the same time and thus it
expresses a broader view of the bank´s performance. On the other hand, the advantage of financial ratios is the
simplicity of their calculation and these indicators bring information how efficient is the management of bank at
usage its assets or capital brought by shareholders to generate earnings.
5. CONCLUSION
This paper analyses revenue efficiency of the banking sectors in the EU countries in 2015. The DEA method and
traditional method of ratios are applied. The results of the DEA, by country, indicate that the revenue efficiency
Figure 2: Box-plot of normalised values of revenue efficiencies in EU banking sectors; 2015
Source: Author´s calculations
1.0
0.0
0.2
0.4
0.6
0.8
ROA REROE
Measurement of Revenue Efficiency in European Union Countries...
41 International Journal of Applied Business and Economic Research
measured by DEA ranged from 34.47% in case of Greece to 100% in case of Germany, Denmark, Estonia,
United Kingdom, Luxembourg, Malta, Netherland and Sweden. When we measured revenue efficiency by
traditional indicators like ROA or ROE we can see that the most efficient banking sectors were in Latvia and
Romania, and the last efficient was banking sector in Greece. The revenue efficiency was also analysed in 3size
groups of banking sectors and in 4 main European “regions”.
Comparing traditional method of ratios and DEA method, we found that each method brings different
results. Therefore, when analysing efficiency, it is appropriate to use more methods simultaneously. As the
benefits of DEA over ratios is that it provides recommendations on how banks should adjust the structure of
their inputs and outputs, taking into account output prices, which should resultin a shift to the efficiency frontier.
On the other hand, the disadvantage is that DEA method is used to calculate relative efficiency, it means within
the selected group of decision-making units (DMUs) under the selected group of variables (input, output, prices).
Each change in a group of DMUs or used variables can lead to a change in efficiency frontier and this way can
influence the level of efficiency of each one.
ACKNOWLEDGEMENTS
This study is a part of the research project VEGA 1/0446/15 financed by the Slovak Scientific Grant
Agency.
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