Radojko Lukic, PhD

Economic Performance of Balkan Countries
DOI: https://doi.org/10.55707/eb.v11i1.136
Original scientific article

Izvirni znanstveni članek

UDK 338.123+519.8(497)

UDK 338.123+519.8(497)

KEYWORDS: economy, performance, Balkan countries, LMAW-DNMA method.

KLJUČNE BESEDE: gospodarstvo, zmogljivost, balkanske države, metoda LMAW-DNMA.

ABSTRACT - The issue of analyzing the factors of the
dynamics of the economic performance of each economy, which means the countries of the Balkans (Albania, Bosnia and Herzegovina, Bulgaria, Croatia,
Kosovo, North Macedonia, Montenegro, Romania,
Serbia, Slovenia, Greece and Turkey), Southeastern
Europe, is continuously very current, challenging,
significant and complex. Adequate control of key
factors can have a significant impact on the achievement of the target economic performance of each
economy, including the Balkan countries. The application of multi-criteria decision-making methods
enables adequate control of the key factors of the economic performance of the economies of the Balkan
countries. In terms of economic performance, Serbia
is in a better position than Croatia and Slovenia.
Kosovo is in the worst economic position. The target economic performance of the countrymen of the
Balkans can be achieved by managing inflation, and
unemployment, and receiving personal remittances
as effectively as possible.

POVZETEK - Problematika analize dejavnikov dinamike gospodarske uspešnosti posameznega gospodarstva, kar pomeni države Balkana (Albanija,
Bosna in Hercegovina, Bolgarija, Hrvaška, Kosovo,
Severna Makedonija, Črna gora, Romunija, Srbija,
Slovenija, Grčija in Turčija), jugovzhodna Evropa, je
vseskozi zelo aktualna, zahtevna, pomembna in kompleksna. Ustrezen nadzor ključnih dejavnikov lahko
pomembno vpliva na doseganje ciljne gospodarske
uspešnosti vsakega gospodarstva, tudi balkanskih
držav. Uporaba večkriterijskih metod odločanja
omogoča ustrezen nadzor nad ključnimi dejavniki
gospodarske uspešnosti gospodarstev balkanskih
držav. Srbija je po gospodarski uspešnosti v boljšem
položaju kot Hrvaška in Slovenija. Kosovo je v najslabšem gospodarskem položaju. Ciljno gospodarsko
uspešnost balkanskih državljanov je mogoče doseči s
čim bolj učinkovitim obvladovanjem inflacije in brezposelnosti ter prejemanjem osebnih nakazil.

1 Introduction
The motivation for researching the problem addressed in this paper is to use a
mathematical approach to assess the economic performance of Balkan countries as
accurately as possible. The goal of this is to improve the economic performance of
Western Balkan countries in the future by taking appropriate measures based on this
knowledge. The basic research hypothesis of the problem discussed in this study is
based on the fact that only the continuous control of key factors contributes to the
improvement of the economic performance of Balkan countries. The function of this
is the application of the LMAW–DNMA method.
Researching the factors of the dynamics of the economic performance of each
economy, which also includes the countries of the Balkans (Albania, Bosnia and
Prejeto/Received: 3. 1. 2024
Sprejeto/Accepted: 22. 3. 2024

Besedilo/Text © 2024 Avtor(ji)/The Author(s)
To delo je objavljeno pod licenco CC BY Priznanje avtorstva 4.0 Mednarodna.
/ This work is published under a CC BY Attribution 4.0 International license.
https://creativecommons.org/licenses/by/4.0/

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Herzegovina, Bulgaria, Croatia, Kosovo, North Macedonia, Montenegro, Romania,
Serbia, Slovenia, Greece, and Turkey) in Southeastern Europe, is very challenging, significant, complex, and continuously topical. It indicates the critical factors and what
measures should be taken to achieve the target economic performance. Bearing that in
mind, this paper comparatively analyzes the economic performance of the economies
of Balkan countries using the LMAW–DNMA (Logarithm Methodology of Additive
Weights – Double Normalization-based Multiple Aggregation) method. Based on a
complex comparative analysis using the given methodology, the real situation in terms of the achieved economic performance of the economy of Balkan countries can
be viewed, and relevant measures for future improvement can be proposed, such as
effective management of the growth of the gross domestic product, inflation, industry,
agriculture, import, export, income, taxes, etc.
Permanent control of key factors is a basic assumption for improving the economic performance of the economies of Balkan countries. In addition to the application
of ratio analysis, a significant role is played by statistical analysis, DEA (Data Envelopment Analysis), and the use of multi-criteria decision-making methods, including the
LMAW–DNMA method. In contrast to classical analysis, their integrated application
gives more accurate results of the achieved economic performance of the economies
of Balkan countries as a basis for future improvement by applying adequate measures. In this paper, the comparative analysis of economic performance factors of the
economy of Balkan countries is based on ratio analysis, statistical analysis, and, in
particular, on the use of the LMAW–DNMA method, which enables the ranking of
alternatives (in this particular case, the alternatives are the Balkan countries) based on
the simultaneous use of several selected criteria. Knowing the positioning of individual Balkan countries is a prerequisite for future improvement by applying relevant
economic and other measures.
The literature devoted to the analysis of the economic performance of each economy is very rich. In classical literature, the analysis of the economic performance
of the economy is mainly based on financial analysis, ratio analysis, and statistical
analysis. In contemporary literature, DEA (Data Envelopment Analysis) models are
increasingly used in the world when analyzing the efficiency of companies from all
countries and economic sectors (Park & Kim, 2022; Zohreh Moghaddas et al., 2022;
Amirteimoori et al., 2022; Alam et al., 2022; Photos Čiković & Lozić, 2022; SalaGarrido, 2023; Andersen & Petersen, 1993; Banker et al., 1984; Chen et al., 2021;
Chang et al., 2020; Guo & Cai, 2020; Lee et al., 2011; Lin et al., 2020; Pendharkar
et al., 2021; Tone, 2002; Dobrović et al., 2021; Podinovski et al., 2021; Rostamzadeh
et al., 2021; Fenyves & Tarnóczi, 2020; Amini et al., 2019; Tsai et al., 2021; Cooper
et al., 1999; Amin & Hajjami, 2021; Chen et al., 2018, 2020, 2021a, 2021b; Stević et
al., 2022; Rasoulzadeh et al., 2021). This is the case, for example, with the analysis of
the efficiency of companies in Serbia (Đurić et al., 2020; Mandić et al., 2017; Martić
& Savić, 2001; Radonjić, 2020; Lukic et al., 2017, 2020; Lukic, 2018, 2022a, 2022b,
2022c, 2023c; Lukic & Kozarevic, 2019; Lukic & Hadrovic Zekic, 2019; Vojteški
Kljenak & Lukić, 2022). DEA models give a realistic picture of which domestic or

Radojko Lukic, PhD: Economic Performance of Balkan Countries

5

foreign companies are efficient and which are not, and what measures should be taken
to increase efficiency.
Recently, in world literature, multi-criteria decision-making methods (ARAS –
Additive Ratio Assessment, TOPSIS – Technique for Order Preference by Similarity
to Ideal Solution, WASPAS – Weighted Aggregates Sum Product Assessment, etc.) are
increasingly applied when analyzing the performance of companies from all countries
of the world and economic sectors (Ayçin & Arsu, 2021; Popović et al., 2022; Ecer &
Aycin, 2022; Mishra et al., 2022; Nguyen et al., 2022; Rani et al., 2022; Toslak et al.,
2022). The situation is the same, for example, with literature in Serbia (Stojanović et
al., 2022; Lukic, 2021, 2023a, 2023b, 2023e, 2023f, 2023g, 2023h, 2023j, 2023k). Because multi-criteria decision-making methods (DCDM) lead to more realistic results
compared to classical methods (such as financial analysis and ratio analysis) as a basis
for future improvement by applying relevant eco-friendly and other measures. Based
on that, in this paper, the economic performance factors of the economies of Balkan
countries are comparatively analyzed using, in addition to ratio analysis and statistical
analysis, especially the LMAW–DNMA method. LMAW–DNMA is a newer multi
-criteria decision-making method. Compared to the classical methods, for example,
ratio analysis, this method gives more accurate results as they simultaneously integrate several indicators. This enables the selection of adequate economic and other
measures to improve the economic performance of the economies of Balkan countries
in the future.

2 Methodology
In this paper, the required empirical data from the World Bank is used, for the
reason that they fully correspond to the researched aspect of economic performance
factors of the economies of Balkan countries.
Using the LMAW and DNMA methods, we will evaluate the economic performance factors of the economies of Balkan countries, based on statistical data from the
World Bank. In the following, we will present the basic characteristics of the given
methods.
The LMAW (Logarithm Methodology of Additive Weights) method is the latest method used to calculate criteria weights and rank alternatives (Liao & Wu,
2020; Demir, 2022). It takes place through the following steps: m alternatives
A={A1,A2,…,Am } are evaluated in comparison with n criteria C={C1,C2,…,Cn } with
the participation of k experts E={E1,E2,…,Ek } and according to a predefined linguistic
scale (Pamučar et al, 2021).
Step 1: Determination of weight coefficients of criteria
Experts E={E1,E2,…,Ek } set priorities with criteria C={C1,C2,…,Cn } in relation to
the previously defined values of the linguistic scale. At the same time, they assign a
higher value to the criterion of greater importance and a lower value to the criterion of

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lesser importance on the linguistic scale. Thus, the priority vector is obtained. The label
represents the value of the linguistic scale that the expert e(1 ≤ e ≤ k) assigns to the
criterion Ct (1 ≤ t ≤ n)
Step 1.1: Defining the absolute anti-ideal point γAIP
The absolute ideal point should be less than the smallest value in the priority vector. It is calculated according to the equation:

where γemin is the minimum value of the priority vector and S should be greater
than the base logarithmic function. In the case of using the function Ln, the value of S
can be chosen as 3.
Step 1.2: Determining the relationship between the priority vector and the
absolute anti-ideal point
The relationship between the priority vector and the absolute anti-ideal point is
calculated using the following equation:

So, the relational vector Re=(neC1, neC2,... neCn) is obtained, where neCn represents the
value of the relational vector derived from the previous equation, and represents the
relational vector e (1 ≤ e ≤ k).
Step 1.3: Determination of the vector of weight coefficients
The vector of weight coefficients w= (w1,w2,…,wn )T is calculated by the expert
e(1 ≤ e ≤ k) using the following equation:

where wej represents the weighting coefficients obtained according to expert evaluations eth and the neCn elements of the realization vector R. The obtained values for the
weighting coefficients must meet the following condition: ∑n(j=1)wej=1.
By applying the Bonferroni aggregator shown in the following equation, the
aggregated vector of weight coefficients w= (w1,w2,…,wn)T is determined:

The values of p and q are stabilization parameters and p,q ≥0. The resulting weight
coefficients should fulfill the condition that ∑n(j=1)we =1.

Radojko Lukic, PhD: Economic Performance of Balkan Countries

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The DNMA (Double Normalization-based Multiple Aggregation) method is a
newer method for showing alternatives (Demir, 2022). Two different normalized (linear and vector) techniques are used, as well as three different coupling functions
(Complete Compensatory Model – CCM, Uncompensatory Model – UCM, and Incomplete Compensatory Model – ICM). The steps for applying this method are as
follows (Liao & Wu, 2020; Ecer, 2020):
Step 1: Normalized decision matrix
The elements of the decision matrix are normalized with linear
normalization using the following equation

The vector

is normalized using the following equation:

The value rj is the target value for the cj criterion and is considered
for both
utility and
cost criteria.
Step 2: Determining the weight of the criteria
This step consists of three phases:
Step 2.1: In this phase, the standard deviation (σj ) for the criterion c1is determined
with the following equation, where m is the number of alternatives:

Step 2.2: Values of the standard deviation calculated for the criteria are
normalized with the following equation:

Step 2.3: Finally, the weights are adjusted with the following equation:

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Step 3: Calculating the aggregation model
Three aggregation functions (CCM, UCM, and ICM) are calculated separately for
each alternative.
The CCM (Complete Compensatory Model) is calculated using the following
equation:

The UCM (Uncompensatory Model) is calculated using the following equation:

The ICM (Incomplete Compensatory Model) is calculated using the following
equation:

Step 4: Integration of utility values
The calculated utility functions are integrated with the following equation using
the Euclidean distance principle:

In this case, the means r1(ai) and r3(ai) represent the ordinal number of the alternative ai sorted by CCM and ICM functions in descending value (higher value first).
On the other hand, r2(ai) shows the sequence number in the obtained order according
to the increasing value (smaller value first) for the UCM function used. The label
φ is the relative importance of the child value used and is within the range [0.1]. It
can be considered as φ=0.5. The coefficients w1,w2,w3 are the obtained weights of
the used functions CCM, UCM, and ICM, respectively. The sum should be equal to
w1 + w2 + w3=1. When determining the weights, if the decision maker attaches importance to a wider range of performance alternatives, he or she can set a higher value
for w1. In case the decision maker is not willing to take risks, i.e., to choose a poor

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Radojko Lukic, PhD: Economic Performance of Balkan Countries

alternative according to some criterion, he or she can assign a higher weight to w2.
However, the decision maker may assign a greater weight to w3, if he or she simultaneously considers overall performance and risk. Finally, the DN values are sorted in
descending order, with the higher-value alternatives being the best.

3 Empirical results and discussion
The key issue in the application of the LMAW–DNMA method to the evaluation
of the economic performance of the economies of Balkan countries is the selection of
appropriate criteria and the determination of their weighting coefficients (weights).
In this paper, the choice of criteria (C1 – GDP (current US$) – billion; C2 – GDP per
capita (current US$); C3 – GDP growth (annual %); C4 – Unemployment, total (% of
total labor force) – modeled ILO estimate; C5 – Inflation, consumer prices (annual %);
and C6 – Personnel remittances, received (% of GDP)) was carried out according to
the nature of the research of the problem in question. The criteria are shown in Table
1 and fully correspond to the nature of the problem of a comparative analysis of economic performance factors of the economies of Balkan countries. The alternatives are
the Balkan countries (A1 – Albania, A2 – Bosnia and Herzegovina, A3 – Bulgaria, A4
– Croatia, A5 – Kosovo, A6 – North Macedonia, A7 – Montenegro, A8 – Romania, A9
– Serbia, A10 – Slovenia, A11 – Greece, and A12 – Turkey), which are also shown in
the same table. Figure 1 shows a ratio analysis of the observed economic performance
indicators of the economies of Balkan countries for 2022.
Table 1
Initial data, 2022

A1
A2
A3
A4
A5
A6
A7
A8
A9
A10
A11

Albania
Bosnia and
Herzegovina
Bulgaria
Croatia
Kosovo
North Macedonia
Montenegro
Romania
Serbia
Slovenia
Greece

GDP (current US$)
(billion)

GDP per
capita (current US$)

GDP
growth
(annual
%)
C3
4.8
3.9

Unemployment,
total (% of total
labor force)
(modeled ILO
estimate)
C4
11.8
14.1

Inflation,
consumer
prices
(annual
%)
C5
6.7
14.0

Personal
remittances received (% of
GDP)
C6
9.2
10.1

C1
18.88
24.53

C2
6,802.2
7,585.4

89.04
70.96
9.43
13.56

13,772.5
18,413.2
5,351.4
6,591.5

3.4
6.3
3.5
2.1

4.4
6.7
0
15.1

15.3
10.8
11.6
14.2

2.3
7.6
17.1
3.4

6.1
301.26
63.5
62.12
219.07

9,893.5
15,892.1
9,393.6
29,457.4
20,732.1

6.1
4.8
2.3
5.4
5.9

15.4
5.4
9.5
4.2
12.2

13.0
13.8
12.0
8.8
9.6

13.6
2.9
8.8
1.1
0.3

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Revija za ekonomske in poslovne vede (1, 2024)
Turkey
Statistics
Mean
Median
Std. Deviation
Minimum
Maximum

Note: Author's statistics

905.99

10,616.1

5.6

10.0

72.3

0.1

148.7033
62.8100
255.18936

12875.0833
10254.8000
7162.70570

4.5083
4.8000
1.45005

9.0667
9.7500
4.92587

16.8417
12.5000
17.64408

6.3750
5.5000
5.54406

6.10
905.99

5351.40
29457.40

2.10
6.30

.00
15.40

6.70
72.30

.10
17.10

Source: The World Bank. https://data.worldbank.org/country
Figure 1
Economic performance indicators of the Balkan countries

Source: Author's picture
In the specific case, the gross domestic product per capita is the highest in Slovenia, and the lowest in Kosovo. The growth rate of the gross domestic product is the
highest in Croatia and the lowest in North Macedonia. The unemployment rate is the
highest in Montenegro (there is no data for Kosovo). Inflation is the highest in Turkey
and the lowest in Albania. Received personal remittances are the highest in Kosovo
and the lowest in Turkey. The differences are caused by the different levels of economic development of these Balkan countries.
In this case, therefore, there is a strong statistically significant correlation between
the criteria C1 (Gross domestic product) and C5 (Inflation). In other words, this me-

Radojko Lukic, PhD: Economic Performance of Balkan Countries

11

ans that the target gross domestic product can be achieved in the Balkan countries by
adequately managing inflation, for example, through the interest rate.
The Friedman Test is shown in Table 2 and Figure 2.
Table 2
Friedman test
NPar Tests
Friedman Test
Ranks
Mean Rank
4.38
6:00
1.63
3.25
3.58
2.17

C1
C2
C3
C4
C5
C6
Test Statistics a
N
Chi-Square
df
Asymp. Sig.

Note: Author's statistics

12
42.542
5
.000
a. Friedman Test

Figure 2
Friedman Test

Source: Author's picture
Therefore, there is a significant statistical difference between the analyzed variables in this particular case ( Asymp. Sig. .000).
Table 3 shows the prioritization scale.

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Revija za ekonomske in poslovne vede (1, 2024)

Table 3
Prioritization scale
Prioritization Scale
Linguistic Variables
Low
Very Low
Low
Medium
Equal
Medium High
High
Very High
High

Abbreviation
AL
VL
L
M
E
MH
H
VH
AH

Prioritization
1
1.5
2
2.5
3
3.5
4
4.5
5

Source: Demir, 2022
Table 4 and Figure 3 shows the evaluation and weight coefficients of the criteria.
Table 4
Evaluation and weight coefficients of the criteria
KIND
E1
E2
E3
E4
ϒAIP
R1
R2
R3
R4

1
C1
H
VH
E
MH
0.5
C1
8
9
6
7

1
C2
AH
VH
MH
E
C2
10
9
7
6

1
C3
H
MH
VH
E
C3
8
7
9
6

1
C4
E
H
AH
VH
C4
6
8
10
9

1
C5
MH
H
AH
AH
C5
7
8
10
10

Weight Coefficients Vector
W1j
W2j
W3j
W4j

C1
0.171
0.177
0.142
0.165

C2
0.190
0.177
0.154
0.152

C3
0.171
0.156
0.174
0.152

C4
0.148
0.167
0.182
0.186

Aggregated Fuzzy Vectors
W1j
W2j
W3j
W4j
SUM
Aggregated Weight Coefficient Vectors

C1
0.007
0.007
0.006
0.007
0.027
0.1634

C2
0.008
0.007
0.007
0.007
0.028
0.1677

C3
0.007
0.006
0.007
0.006
0.027
0.1632

C4
0.007
0.007
0.008
0.008
0.029
0.1705

Note: Author's statistics

1
C6
MH
MH
H
E
C6
7
7
8
6

LN(Πη)
12.145
12.445
12.620
11.821

C5
0.160
0.167
0.182
0.195

C6
0.160
0.156
0.165
0.152

C5
0.007
0.007
0.008
0.008
0.031
0.1760

C6
0.006
0.006
0.006
0.006
0.025
0.1582

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Radojko Lukic, PhD: Economic Performance of Balkan Countries

Figure 3
Aggregated Weight Coefficient Vectors

Source: Author's picture
In this specific case, therefore, the most important criterion is inflation (C5). In
other words, this means that effective management of inflation can influence the achievement of the target economic performance of Balkan countries.
We will rank the countries of the Balkans according to their economic performance in 2022 using the LMAW–DNMA method. All the calculations and results of the
LMAW–DNMA method are shown in further presentations of the studied problem
(Tables 5–11, Figure 4). The meaning of individual symbols in the tables shown below
is given in the analysis of the methods themselves.
Table 5
Initial Matrix
INITIAL
MATRIX

KIND
Weight
A1
A2
A3
A4
A5
A6
A7
A8
A9
A10

1
0.1634
C1
18.88
24.53
89.04
70.96
9.43
13.56
6.1
301.26
63.5
62.12

1
0.1677
C2
6,802.20
7,585.40
13,772.50
18,413.20
5,351.40
6,591.50
9,893.50
15,892.10
9,393.60
29,457.40

1
0.1632
C3
4.8
3.9
3.4
6.3
3.5
2.1
6.1
4.8
2.3
5.4

1
0.1705
C4
11.8
14.1
4.4
6.7
0
15.1
15.4
5.4
9.5
4.2

1
0.1760
C5
6.7
14
15.3
10.8
11.6
14.2
13
13.8
12
8.8

1
0.1582
C6
9.2
10.1
2.3
7.6
17.1
3.4
13.6
2.9
8.8
1.1

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A11
A12
MAX
MIN

219.07
905.99
905.9900
6.1000

Note: Author's calculation

20,732.10
10,616.10
29457.4000
5351.4000

5.9
5.6
6.3000
2.1000

12.2
10
15.4000
0.0000

9.6
72.3
72.3000
6.7000

0.3
0.1
17.1000
0.1000

Table 6
Linear Normalization Matrix
Linear
Normalization A1
A2
MATRIX
A3
A4
A5
A6
A7
A8
A9
A10
A11
A12

C1
0.0142
0.0205
0.0922
0.0721
0.0037
0.0083
0.0000
0.3280
0.0638
0.0623
0.2367
1.0000

Note: Author's calculation

C2
0.0602
0.0927
0.3493
0.5418
0.0000
0.0514
0.1884
0.4373
0.1677
1.0000
0.6380
0.2184

C3
0.6429
0.4286
0.3095
1.0000
0.3333
0.0000
0.9524
0.6429
0.0476
0.7857
0.9048
0.8333

C4
0.7662
0.9156
0.2857
0.4351
0.0000
0.9805
1.0000
0.3506
0.6169
0.2727
0.7922
0.6494

C5
0.0000
0.1113
0.1311
0.0625
0.0747
0.1143
0.0960
0.1082
0.0808
0.0320
0.0442
1.0000

C6
0.5353
0.5882
0.1294
0.4412
1.0000
0.1941
0.7941
0.1647
0.5118
0.0588
0.0118
0.0000

MAX
0.7662
0.9156
0.3493
1.0000
1.0000
0.9805
1.0000
0.6429
0.6169
1.0000
0.9048
1.0000

C6
0.7638
0.7907
0.5574
0.7159
1.0000
0.5903
0.8953
0.5754
0.7518
0.5215
0.4976
0.4916
0.1802

MAX
0.9144
0.9663
0.8344
1.0000
1.0000
0.9922
1.0000
0.9144
0.8472
1.0000
0.9772
1.0000

Table 7
Vector Normalization Matrix
Vector
Normalization A1
A2
MATRIX
A3
A4
A5
A6
A7
A8
A9
A10
A11
A12
Adj Wj

C1
0.3392
0.3435
0.3915
0.3780
0.3322
0.3353
0.3297
0.5496
0.3725
0.3715
0.4884
1.0000
0.1707

Note: Author's calculation

C2
0.6127
0.6261
0.7318
0.8112
0.5879
0.6091
0.6655
0.7681
0.6570
1.0000
0.8508
0.6779
0.1606

C3
0.9144
0.8630
0.8344
1.0000
0.8401
0.7602
0.9886
0.9144
0.7716
0.9486
0.9772
0.9600
0.1542

C4
0.9068
0.9663
0.7151
0.7747
0.0000
0.9922
1.0000
0.7410
0.8472
0.7099
0.9171
0.8601
0.1694

C5
0.4025
0.4690
0.4809
0.4399
0.4472
0.4708
0.4599
0.4672
0.4508
0.4217
0.4289
1.0000
0.1649

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Radojko Lukic, PhD: Economic Performance of Balkan Countries

Table 8
CCM (Complete Compensatory Model)
CCM (Complete
Compensatory
Model)

u1(ai)
A1
A2
A3
A4
A5
A6
A7
A8
A9
A10
A11
A12

C1
0.0032
0.0038
0.0450
0.0123
0.0006
0.0014
0.0000
0.0871
0.0176
0.0106
0.0446
0.1707

C2
0.0126
0.0163
0.1606
0.0870
0.0000
0.0084
0.0303
0.1093
0.0437
0.1606
0.1133
0.0351

Note: Author's calculation

C3
0.1294
0.0722
0.1366
0.1542
0.0514
0.0000
0.1468
0.1542
0.0119
0.1211
0.1542
0.1285

C4
0.1694
0.1694
0.1386
0.0737
0.0000
0.1694
0.1694
0.0924
0.1694
0.0462
0.1484
0.1100

C5
0.0000
0.0200
0.0619
0.0103
0.0123
0.0192
0.0158
0.0278
0.0216
0.0053
0.0081
0.1649

C6
0.1259
0.1158
0.0667
0.0795
0.1802
0.0357
0.1431
0.0462
0.1495
0.0106
0.0023
0.0000

SUM
0.4405
0.3975
0.6095
0.4170
0.2445
0.2342
0.5055
0.5169
0.4137
0.3545
0.4709
0.6092

Table 9
UCM (Uncompensatory Model)
UCM (Unu2(ai)
compensatory A1
A2
Model)
A3
A4
A5
A6
A7
A8
A9
A10
A11
A12

C1
0.1675
0.1669
0.1256
0.1584
0.1700
0.1692
0.1707
0.0836
0.1530
0.1600
0.1260
0.0000

Note: Author's calculation

C2
0.1480
0.1444
0.0000
0.0736
0.1606
0.1522
0.1304
0.0514
0.1170
0.0000
0.0474
0.1256

C3
0.0248
0.0820
0.0176
0.0000
0.1028
0.1542
0.0073
0.0000
0.1423
0.0330
0.0000
0.0257

C4
0.0000
0.0000
0.0309
0.0957
0.0000
0.0000
0.0000
0.0770
0.0000
0.1232
0.0211
0.0594

C5
0.1649
0.1448
0.1030
0.1546
0.1526
0.1456
0.1490
0.1371
0.1433
0.1596
0.1568
0.0000

C6
0.0543
0.0644
0.1134
0.1007
0.0000
0.1445
0.0371
0.1340
0.0307
0.1696
0.1778
0.1802

MAX
0.1675
0.1669
0.1256
0.1584
0.1700
0.1692
0.1707
0.1371
0.1530
0.1696
0.1778
0.1802

Table 10
ICM (Incomplete Compensatory Model)
ICM (Incomplete
Compensatory Model)

u3(ai)
A1
A2
A3

C1
0.8443
0.8382
0.8788

C2
0.9377
0.9326
0.9791

C3
1.0000
0.9827
1.0000

C4
0.9986
1.0000
0.9742

C5
0.8735
0.8876
0.9131

C6
0.9681
0.9645
0.9299

MAX
0.6685
0.6577
0.7118

A4
A5
A6
A7
A8

0.8470
0.8285
0.8310
0.8275
0.9168

0.9669
0.9182
0.9246
0.9367
0.9724

1.0000
0.9735
0.9598
0.9982
1.0000

0.9577
0.0000
1.0000
1.0000
0.9650

0.8734
0.8757
0.8844
0.8798
0.8952

0.9416
1.0000
0.9107
0.9803
0.9199

0.6450
0.0000
0.5939
0.6673
0.7084

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Revija za ekonomske in poslovne vede (1, 2024)
A9
A10
A11
A12

0.8691
0.8445
0.8884
1.0000

0.9600
1.0000
0.9780
0.9395

Note: Author's calculation

0.9857
0.9919
1.0000
0.9937

1.0000
0.9436
0.9893
0.9748

0.9012
0.8673
0.8731
1.0000

0.9787
0.8893
0.8855
0.8799

0.7254
0.6096
0.6645
0.8007

Table 11
Rank Order
w1
0.6
CCM

φ

UCM

φ

ICM

φ

w2 w3
0.1 0.3

Utility Values

Rank
Order

u1(ai) Rank 0.5
Albania

u2(ai) Rank 0.5

u3(ai) Rank 0.5

A1

0.4405 6

0.6567 0.1675 6

0.7465 0.6685 5

0.7555 0.6953

0.6953

6

Bosnia and A2
Herzegovina

0.3975 9

0.5179 0.1669 5

0.7181 0.6577 8

0.6512 0.5779

0.5779

9

Bulgaria

A3

0.6095 1

1.0000 0.1256 1

0.4966 0.7118 3

0.8616 0.9081

0.9081

2

Croatia

A4

0.4170 7

0.5992 0.1584 4

0.6647 0.6450 9

0.6164 0.6109

0.6109

8

Kosovo

A5

0.2445 11

0.3072 0.1700 9

0.8524 0.0000 12

0.0589 0.2872

0.2872

12

North Mace- A6
donia

0.2342 12

0.2780 0.1692 7

0.7818 0.5939 11

0.5375 0.4063

0.4063

11

Montenegro

A7

0.5055 4

0.7907 0.1707 10

0.8921 0.6673 6

0.7193 0.7794

0.7794

4

Romania

A8

0.5169 3

0.8407 0.1371 2

0.5509 0.7084 4

0.8201 0.8056

0.8056

3

Serbia

A9

0.4137 8

0.5632 0.1530 3

0.6260 0.7254 2

0.9113 0.6739

0.6739

7

Slovenia

A10

0.3545 10

0.4477 0.1696 8

0.8156 0.6096 10

0.5666 0.5201

0.5201

10

Greece

A11

0.4709 5

0.7216 0.1778 11

0.9525 0.6645 7

0.6851 0.7337

0.7337

5

Turkey

A12

0.6092 2

0.9589 0.1802 12

1.0000 0.8007 1

1.0000 0.9754

0.9754

1

MAX 0.6095

Note: Author's calculation

0.1802

0.8007

Radojko Lukic, PhD: Economic Performance of Balkan Countries

17

Figure 4
Rank Order

Source: Author's picture
In this case, therefore, the ranking of the Balkan countries by economic performance according to the LMAW–DNMA method is as follows: Turkey, Bulgaria, Romania, Montenegro, Greece, Albania, Serbia, Croatia, Bosnia and Herzegovina, Slovenia, North Macedonia, and Kosovo. In terms of economic performance, Serbia is in
a better position than Croatia and Slovenia.
The target economic performances of Balkan countries can be achieved, among
other things, by managing inflation and unemployment, and by receiving personal
remittances as efficiently as possible. Another method is adequate control of the key
factors of economic performance, such as geopolitical and economic climate, foreign
direct investments, energy crisis, climate change, the concept of sustainable development, digitalization of the company's entire business, etc.
The research in this paper, using the LMAW–DNMA method, has demonstrated
that applying the multi-criteria decision-making method and the DEA model, in addition to classical methodology, to the evaluation of the economic performance of the
economies of Balkan countries is justified, as they give more accurate results. Therefore, it is recommended that they be used as much as possible in the analysis of the
economic performance of the economies of Balkan countries.

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4 Conclusion
Empirical research of the problem discussed in this paper, using the LMAW–
DNMA method, has shown that the ranking of Balkan countries according to economic performance is as follows: Turkey, Bulgaria, Romania, Montenegro, Greece,
Albania, Serbia, Croatia, Bosnia and Herzegovina, Slovenia, North Macedonia, and
Kosovo. In terms of economic performance, Serbia is in a better position than Croatia
and Slovenia. Kosovo is in the worst economic position.
The target economic performances of Balkan countries can be achieved, among
other things, by managing inflation and unemployment, and by receiving personal
remittances as efficiently as possible. Another method is adequate control of the key
factors of economic performance, such as geopolitical and economic climate, foreign
direct investments, energy crisis, climate change, the concept of sustainable development, digitalization of the company's entire business, etc.
The comparative application of multi-criteria decision-making methods (including the LMAW–DNMA method) with other relevant methods to the evaluation of
the economic performance of Balkan countries gives more accurate results in terms of future improvements by applying relevant measures. That is why, along with
the classical methodology, it is recommended to use multi-criteria decision-making
methods for these purposes.
Dr. Radojko Lukić

Gospodarska uspešnost Balkanskih držav
Raziskovanje dejavnikov dinamike gospodarske uspešnosti posameznega gospodarstva, kar pomeni tudi držav Balkana oz. jugovzhodne Evrope (Albanija, Bosna
in Hercegovina, Bolgarija, Hrvaška, Kosovo, Severna Makedonija, Črna gora, Romunija, Srbija, Slovenija, Grčija in Turčija) je zelo zahtevno, pomembno in nenehno aktualno. Navaja kritične dejavnike in ukrepe, ki jih je treba sprejeti za dosego
ciljne gospodarske uspešnosti. Prispevek primerjalno analizira ekonomsko uspešnost
gospodarstev balkanskih držav z metodo LMAW-DNMA (Logarithm Methodology of
Additive Weights ‒ Double Normalization-based Multiple Aggregation). Na podlagi kompleksne primerjalne analize po podani metodologiji je mogoče videti realno
stanje dosežene gospodarske uspešnosti gospodarstev balkanskih držav in predlagati
ustrezne ukrepe za izboljšanje v prihodnosti, kot je učinkovito upravljanje rasti bruto
domačega proizvoda, inflacije, industrije, kmetijstva, uvoza, izvoza, dohodka, davkov
itd.
Stalna kontrola ključnih dejavnikov je osnovna predpostavka za izboljšanje gospodarske uspešnosti gospodarstev balkanskih držav. Poleg ratio analize, statistične
analize, DEA analize in uporabe večkriterijskih metod odločanja smo vključili tudi

Radojko Lukic, PhD: Economic Performance of Balkan Countries

19

metodo LMAW-DNMA, ki ima pri tem pomembno vlogo. Glede na klasično analizo
daje njihova celostna uporaba natančnejše rezultate o doseženi gospodarski uspešnosti gospodarstev balkanskih držav in osnovo za izboljšave v prihodnosti z uporabo
ustreznih ukrepov. Primerjalna analiza dejavnikov ekonomske uspešnosti gospodarstev balkanskih držav v prispevku temelji na racio analizi, statistični analizi, predvsem pa na uporabi metode LMAW-DNMA, ki omogoča razvrščanje alternativ (v
konkretnem primeru so alternative balkanske države) na podlagi hkratne uporabe več
izbranih kriterijev. Poznavanje položaja posameznih balkanskih držav je predpogoj
za izboljšanje gospodarstva v prihodnosti z uporabo ustreznih ekonomskih in drugih
ukrepov.
Literatura, namenjena analizi gospodarske uspešnosti posameznega gospodarstva, je zelo bogata. V klasični literaturi analiza ekonomske uspešnosti gospodarstva
temelji predvsem na finančni analizi, analizi razmerij in statistični analizi. V sodobni literaturi se v svetu vedno pogosteje uporabljajo modeli DEA (Data Envelopment
Analysis) pri analizi učinkovitosti podjetij iz vseh držav in gospodarskih sektorjev
(Park in Kim, 2022; Zohreh Moghaddas idr., 2022; Amirteimoori idr., 2022; Alam
idr., 2022; fotografije Čiković in Lozić, 2022; Sala-Garrido, 2023; Andersen in Petersen, 1993; Banker idr., 1984; Chen idr., 2021, Chang idr., 2020; Guo in Cai, 2020;
Lee idr., 2011; Lin idr., 2020; Pendharkar idr., 2021; Tone, 2002; Dobrović idr.,
2021; Podinovski idr., 2021; Rostamzadeh idr., 2021; Fenyves in Tarnóczi, 2020;
Amini idr., 2019; Tsai idr., 2021; Cooper idr., 1999; Amin in Hajjami, 2021; Chen
idr., 2018, 2020, 2021a, b; Stević idr., 2022; Rasoulzadeh idr., 2021). Tako je na
primer pri analizi učinkovitosti podjetij v Srbiji (Đurić idr., 2020; Mandić idr., 2017;
Martić in Savić, 2001; Radonjić, 2020; Lukic idr., 2017, 2020; Lukic, 2018, 2022a,
b, c, 2023c; Lukic in Kozarevic, 2019; Lukic in Hadrovic Zekic, 2019; Vojteški Kljenak in Lukić, 2022). Modeli DEA dajejo realno sliko o tem, katera domača ali tuja
podjetja so učinkovita in katera ne ter kakšne ukrepe je treba sprejeti za povečanje
učinkovitosti.
V zadnjem času se v svetovni literaturi vse pogosteje uporabljajo večkriterijske
metode odločanja (ARAS ‒ Additive Ratio Assessment, TOPSIS ‒ Technique for Order Preference by Similarity to Ideal Solution, WASPAS ‒ Weighted aggregates sum
product assessment itd.) pri analizi uspešnosti podjetij iz vseh držav sveta in gospodarskih sektorjev (Ayçin in Arsu, 2021; Popović idr., 2022; Ecer in Aycin, 2022;
Mishra idr., 2022; Nguyen idr., 2022; Rani idr., 2022; Toslak idr., 2022). Enako je
na primer z literaturo v Srbiji (Stojanović idr., 2022; Lukic, 2021, 2023a, b, e, f, g,
h, j, k), ker večkriterijske metode odločanja (DCDM) vodijo do realnejših rezultatov
v primerjavi s klasičnimi metodami (kot so finančna analiza in racio analiza) kot
podlago za izboljšave v prihodnosti z uporabo ustreznih okolju prijaznih in drugih
ukrepov. Na podlagi tega so v tem prispevku primerjalno analizirani dejavniki gospodarske uspešnosti gospodarstev balkanskih držav z uporabo metode LMAW-DNMA,
poleg analize razmerij in statistične analize. LMAW-DNMA je novejša večkriterijska
metoda odločanja. V primerjavi s klasično metodo, na primer racio analizo, daje ta
metoda natančnejše rezultate, saj hkrati integrira več indikatorjev. To omogoča izbor

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Revija za ekonomske in poslovne vede (1, 2024)

ustreznih ekonomskih in drugih ukrepov za izboljšanje gospodarske uspešnosti gospodarstev balkanskih držav v prihodnosti.
V prispevku so uporabljeni potrebni empirični podatki Svetovne banke iz razloga,
ker v celoti ustrezajo opazovanemu vidiku raziskave dejavnikov ekonomske uspešnosti
gospodarstev balkanskih držav.
Z metodo LMAW in DNMA bomo na podlagi statističnih podatkov Svetovne banke
ocenili dejavnike gospodarske uspešnosti gospodarstev balkanskih držav.
Ključno vprašanje pri uporabi metode LMAW-DNMA pri vrednotenju gospodarske uspešnosti gospodarstev balkanskih držav je izbira ustreznih kriterijev in določitev njihovih utežnih koeficientov (uteži). V tem prispevku je bila izbira kriterijev (C1
– BDP, trenutni USD) (milijardi), C2 ‒ BDP na prebivalca (trenutni USD), C3 ‒ rast
BDP (letna v %), C4 ‒ brezposelnost, skupaj (% celotne delovne sile) (modelirana
ocena ILO), C5 ‒ inflacija, cene življenjskih potrebščin (letno v %) in C6 ‒ prejeta
nakazila osebja (% BDP)) izvedena po naravi raziskave obravnavanega problema.
Prikazani so v tabeli 1 in v celoti ustrezajo naravi problematike primerjalne analize dejavnikov gospodarske uspešnosti gospodarstev balkanskih držav. Alternative so
balkanske države (A1 ‒ Albanija, A2 ‒ Bosna in Hercegovina, A3 ‒ Bolgarija, A4 ‒
Hrvaška, A5 ‒ Kosovo, A6 ‒ Severna Makedonija, A7 ‒ Črna gora, A8 ‒ Romunija,
A9 ‒ Srbija, A10 ‒ Slovenija, A11 ‒ Grčija in A12 ‒ Turčija). Slika 1 prikazuje racio analizo opazovanih kazalnikov gospodarske uspešnosti gospodarstev balkanskih
držav za leto 2022.
V tem primeru torej obstaja močna korelacija med kriterijema C1 in C5 na ravni
statistične pomembnosti. To z drugimi besedami pomeni, da je ciljni bruto domači
proizvod v balkanskih državah mogoče doseči z ustreznim obvladovanjem inflacije, na
primer z obrestno mero.
V konkretnem primeru imamo najvišji bruto domači proizvod na prebivalca v Sloveniji, najmanjši pa na Kosovu. Razlike so posledica različne stopnje gospodarskega
razvoja balkanskih držav.
Zato obstaja pomembna statistična razlika med analiziranimi spremenljivkami v
tem konkretnem primeru (Asymp. Sig.:,000).
V konkretnem primeru je torej najpomembnejši kriterij inflacija. To z drugimi besedami pomeni, da lahko učinkovito obvladovanje inflacije vpliva na doseganje ciljne
gospodarske uspešnosti balkanskih držav.
Države Balkana bomo razvrstili po gospodarski uspešnosti v letu 2022 z metodo
LMAW-DNMA.
V tem primeru je torej razvrstitev držav Balkana po gospodarski uspešnosti po
metodi LMAW-DNMA naslednja: Turčija, Bolgarija, Romunija, Črna gora, Grčija,
Albanija, Srbija, Hrvaška, Bosna in Hercegovina, Slovenija, Severna Makedonija in
Kosovo. Srbija je po gospodarski uspešnosti v boljšem položaju, kot sta Hrvaška in
Slovenija.

Radojko Lukic, PhD: Economic Performance of Balkan Countries

21

Ciljno gospodarsko uspešnost balkanskih držav je mogoče doseči med drugim z
obvladovanjem inflacije in brezposelnosti ter čim bolj učinkovitim prejemanjem osebnih nakazil. Pomemben pa je tudi ustrezen nadzor nad ključnimi dejavniki gospodarske uspešnosti, kot so geopolitična in gospodarska klima, neposredne tuje investicije,
energetska kriza, podnebne spremembe, koncept trajnostnega razvoja, digitalizacija
celotnega poslovanja podjetja itd.
Raziskava v prispevku je na primeru metode LMAW-DNMA pokazala upravičenost uporabe, poleg klasične metodologije, tako večkriterijske metode odločanja pri
ocenjevanju gospodarske uspešnosti gospodarstev držav Balkana kot tudi modela
DEA, ker dajeta natančnejše rezultate. Zato je priporočljivo, da se ju čim bolj pogosto
uporablja pri analizi gospodarske uspešnosti gospodarstev balkanskih držav.
Empirična raziskava, ki v prispevku obravnava problematiko z metodo LMAW
-DNMA, je pokazala, da je razvrstitev balkanskih držav glede na gospodarsko uspešnost naslednja: Turčija, Bolgarija, Romunija, Črna gora, Grčija, Albanija, Srbija,
Hrvaška, Bosna in Hercegovina, Slovenija, Severna Makedonija in Kosovo. Srbija je
po gospodarski uspešnosti v boljšem položaju, kot sta Hrvaška in Slovenija. Kosovo je
v najslabšem gospodarskem položaju.
Ciljno gospodarsko uspešnost balkanskih držav je mogoče doseči med drugim z
obvladovanjem inflacije in brezposelnosti ter čim bolj učinkovitim prejemanjem osebnih nakazil. Pomemben je tudi ustrezen nadzor nad ključnimi dejavniki gospodarske uspešnosti, kot so geopolitična in gospodarska klima, neposredne tuje investicije,
energetska kriza, podnebne spremembe, koncept trajnostnega razvoja, digitalizacija
celotnega poslovanja podjetja itd.
Primerjalna uporaba večkriterijskih metod odločanja (vključno z metodo LMAW
-DNMA) z drugimi relevantnimi metodami pri vrednotenju gospodarske uspešnosti
balkanskih držav daje natančnejše rezultate v smislu prihodnjih izboljšav z uporabo
ustreznih ukrepov. Zato je poleg klasične metodologije za te namene priporočljiva
uporaba večkriterijske metode odločanja.
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2. Amini, A., Alinezhad, A., & Yazdipoor, F. (2019). A TOPSIS, VIKOR, and DEA integrated
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IJAOM.2019.100708
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Radojko Lukic PhD, full profesor at the Faculty of Economics, University of Belgrade, Serbia
E-naslov: radojko.lukic @ekof.bg.ac.rs