Application of multivariate statistical analysis to assess the implementation of Sustainable Development Goal 8 in European Union countries

Abstract

Sustainable development should ensure a fair and balanced natural, social and economic environment. Sustainable Development Goal 8 (SDG 8) – decent work and economic growth – is of the greatest economic importance. The purpose of the study is to assess the implementation of SDG 8 in EU member states. The analysis covered the years 2002–2021 with a particular focus on two crises periods: the financial crisis of 2007–2009 and the COVID-19 pandemic in the years 2020–2021. The study uses Eurostat data and multivariate statistical analysis methods, i.e. cluster analysis – the k-means method and linear ordering – the TOPSIS method.
Denmark, Finland, the Netherlands and Sweden are the countries where the fulfilment of SDG 8 was the greatest, while the lowest was observed in Greece, Italy, Romania, Slovakia and Spain. The study also shows that the countries which joined the EU in 2004 generally demonstrated a much lower degree of SDG 8 implementation compared to the well-developed Western Europe. The influence of the crisis periods was more visible in the results of the cluster analysis than in the rankings.
The novelty of the research involves the application of multivariate statistical analysis methods to assess the overall situation of the studied countries in terms of their implementation of SDG 8 while taking into account both crisis periods.

Full text

Wiadomości Statystyczne. The Polish Statistician, 2023, 68(3), 22–43 DOI: 10.59139/ws.2023.03.2
Statystyka w praktyce / Statistics in practice
Zgłoszony/submitted: 20.01.2023, poprawiony/revised: 11.03.2023, zaakceptowany/accepted: 21.03.2023
Application of multivariate statistical analysis
to assess the implementation of Sustainable
Development Goal 8 in European Union countries1
Beata Bieszk-Stolorz,a Krzysztof Dmytrówb
Abstract. Sustainable development should ensure a fair and balanced natural, social and
economic environment. Sustainable Development Goal 8 (SDG 8) – decent work and economic
growth – is of the greatest economic importance. The purpose of the study is to assess the
implementation of SDG 8 in EU member states. The analysis covered the years 2002–2021 with
a particular focus on two crises periods: the financial crisis of 2007–2009 and the COVID-19
pandemic in the years 2020–2021. The study uses Eurostat data and multivariate statistical
analysis methods, i.e. cluster analysis – the k-means method and linear ordering – the TOPSIS
method.
Denmark, Finland, the Netherlands and Sweden are the countries where the fulfilment of
SDG 8 was the greatest, while the lowest was observed in Greece, Italy, Romania, Slovakia and
Spain. The study also shows that the countries which joined the EU in 2004 generally
demonstrated a much lower degree of SDG 8 implementation compared to the well-developed
Western Europe. The influence of the crisis periods was more visible in the results of the cluster
analysis than in the rankings.
The novelty of the research involves the application of multivariate statistical analysis
methods to assess the overall situation of the studied countries in terms of their
implementation of SDG 8 while taking into account both crisis periods.
Keywords: sustainable development, Sustainable Development Goal 8, decent work and
economic growth, EU member states, TOPSIS method, k-means method
JEL: C38, Q56
1 The article is based on a paper delivered at the 2nd International Conference on Renewable Economics –
ReECON, held on 20–22 September 2022 in Biograd na Moru, Croatia / Artykuł został opracowany na pod-
stawie referatu wygłoszonego na 2nd International Conference on Renewable Economics – ReECON, która
odbyła się w dniach 20–22 września 2022 r. w Biogradzie na Moru w Chorwacji.
a Uniwersytet Szczeciński, Instytut Ekonomii i Finansów, Polska / University of Szczecin, Institute of Economics
and Finance, Poland. ORCID: https://orcid.org/0000-0001-8086-9037.
Autor korespondencyjny / Corresponding author: beata.bieszk-stolorz@usz.edu.pl.
b Uniwersytet Szczeciński, Instytut Ekonomii i Finansów, Polska / University of Szczecin, Institute of Economics
and Finance, Poland. ORCID: https://orcid.org/0000-0001-7657-6063.
E-mail: krzysztof.dmytrow@usz.edu.pl.
© Beata Bieszk-Stolorz, Krzysztof Dmytrów
Artykuł udostępniony na licencji CC BY-SA 4.0 / Article available under the CC BY-SA 4.0 licence

B. BIESZK-STOLORZ, K. DMYTRÓW Application of multivariate statistical analysis to assess... 23
Zastosowanie wielowymiarowej analizy statystycznej
do oceny realizacji Celu Zrównoważonego Rozwoju 8
w krajach Unii Europejskiej
Streszczenie. Zrównoważony rozwój powinien zapewnić sprawiedliwe i zrównoważone śro-
dowisko naturalne, społeczne i gospodarcze. Godna praca i wzrost gospodarczy, czyli Cel
Zrównoważonego Rozwoju (Sustainable Development Goal – SDG) 8, ma największe znaczenie
gospodarcze. Celem badania omawianego w artykule jest ocena realizacji SDG 8 w krajach
członkowskich UE. Badanie obejmowało lata 2002–2021, ze szczególnym uwzględnieniem
okresów kryzysowych: kryzysu finansowego z lat 2007–2009 i pandemii COVID-19 panującej
w latach 2020–2021. W badaniu wykorzystano dane z bazy Eurostatu. Zastosowano metody
wielowymiarowej analizy statystycznej: analizę skupień metodą k-średnich i porządkowanie
liniowe metodą TOPSIS.
Krajami o najwyższym stopniu realizacji SDG 8 okazały się: Dania, Finlandia, Holandia i Szwe-
cja, natomiast najniższy stopień realizacji obserwowano w Grecji, we Włoszech, w Rumunii, na
Słowacji i w Hiszpanii. Również nowe kraje członkowskie, przyjęte do UE po 2004 r., ogólnie
charakteryzują się znacznie niższym stopniem realizacji SDG 8 niż wysoko rozwinięte kraje
Europy Zachodniej. Wpływ okresów kryzysowych był bardziej zauważalny w wynikach analizy
skupień niż w rankingach.
Wartością dodaną badania jest wykorzystanie metod wielowymiarowej analizy statystycznej
do oceny ogólnej sytuacji analizowanych krajów w zakresie realizacji SDG 8 przy uwzględnieniu
obu okresów kryzysowych.
Słowa kluczowe: zrównoważony rozwój, Cel Zrównoważonego Rozwoju 8, godna praca
i wzrost gospodarczy, kraje członkowskie UE, metoda TOPSIS, metoda k-średnich
1. Introduction
Sustainable development assumes the parallel development of the economy, society
and the environment. Many legal acts, political documents, development strategies
at all levels of aggregation, from local to global, refer to this concept. Its
implementation tends to be difficult as it is of a complex and interdisciplinary
character. Sustainable development has been defined as one which meets the needs
of people in the present without compromising the ability of future generations to
fulfil their needs. The achievement of sustainable development goals (SDGs)
depends on many factors. As research by Zioło et al. (2021) indicates, there is
a strong link between economic sustainability reflected in e.g. Sustainable
Development Goal 8 (SDG 8) and the sustainable finance model. SDG 8 relates to
well-being and quality of life and is impossible to attain through a sustainable public
financial system alone. It also requires the cooperation with and involvement of
a sustainable market financial system. Sustainable development requires a common
effort to build a sustainable and crisis-resilient future for people around the world
and for the planet.

24 Wiadomości Statystyczne. The Polish Statistician 2023 | 3
Crises which may interfere with the assumed goals can be of an economic (linked
to banking, currency, stock market, finances or overproduction), ecological, political
(e.g. war) or demographical (associated with migrations, decrease of fertility, etc.)
nature as well as health-related (e.g. pandemics). The spread of their effects is
influenced by any existing links between markets, systemic risks or faulty regulations
(Roszkowska & Prorokowski, 2014). In the last 20 years, the world faced two crises:
the financial one of 2007–2009 and the COVID-19 pandemic, which emerged in
early 2020 and whose consequences ensued in the years that followed. Both
phenomena had a great impact on the socio-economic development of countries
around the world due to their numerous and strong economic interconnections.
The impact of crises on individual economies tends to vary across countries and is
visible both in its first phase, i.e. during the emergence of its negative effects, and in
the post-crisis economic growth (Foo & Witkowska, 2017). Crises have been
analysed and researched by many scientists worldwide (Clemente-Suárez et al., 2021;
Sombultawee et al., 2022). It has been found that if a key sector of the economy
collapses during a crisis, the economic equilibrium of the entire country is disrupted.
For example, during the COVID-19 pandemic movement restrictions were
introduced which particularly affected transport and tourism. Hence, countries with
GDPs heavily dependent on these and the related industries were greatly affected by
the pandemic (Ružić & Popek Biškupec, 2021; Škare et al., 2020). Some sectors,
however, attempted to adapt to the new conditions: remote working and learning
became widespread, remote concerts took place and even online visits to museums
were possible (Domšić et al., 2021). Despite the measures taken, poverty and
unemployment rates increased (Jianu et al., 2021). Economic and social
development was particularly severely disrupted. Therefore, there is no doubt that
crises of all kinds, especially those of a global nature, pose a threat to the
achievement of SDGs. Preliminary research on the EU labour market (SDG 8.5, SDG
8.6) from the years 2018–2021 showed that the COVID-19 pandemic did not affect
the similarities of the labour markets in the EU countries, but rather influenced the
similarities of changes in those markets (Bieszk-Stolorz & Dmytrów, 2022).
The purpose of the study is to assess the implementation of SDG 8 in EU
countries. The analysis covered the years 2002–2021 with a particular focus on the
crisis periods: the financial crisis (2007–2009) and the COVID-19 pandemic (2020–
2021).

B. BIESZK-STOLORZ, K. DMYTRÓW Application of multivariate statistical analysis to assess... 25
2. Sustainable Development Goals
SDGs were established during the United Nations General Assembly in 2015
(Resolution adopted by the General Assembly on 25th September 2015). SDG 8 is to
‘promote sustained, inclusive and sustainable economic growth, full and productive
employment and decent work for all. SDG 8 is the aspiration that the economic
sector of each country should provide its citizens with the necessary needs for a good
life, regardless of their origin, race or culture’. SDG 8 has a total of 12 targets,
presented in Table 1.
Table 1. SDG 8 targets
Target no. Description
8.1 ..........................................
sustainable economic growth
8.2 ..........................................
to diversify, innovate and upgrade for economic productivity
8.3 ..........................................
to promote policies to support job creation and growing enterprises
8.4 ..........................................
to improve resource efficiency in consumption and production
8.5 ..........................................
full employment and decent work with equal pay
8.6 ..........................................
to promote youth employment, education and training
8.7 ..........................................
to end modern slavery, trafficking, and child labour
8.8 ..........................................
to protect labour rights and promote safe working environments
8.9 ..........................................
to promote beneficial and sustainable tourism
8.10 .......................................
universal access to banking, insurance and financial services
8.a ..........................................
to increase aid for trade support
8.b ..........................................
to develop a global youth employment strategy
Source: authors’ work based on United Nations (n.d.).
The progress towards achieving the 17 goals is measured, monitored and
evaluated by means of different sets of indicators, used at different levels of
sustainable development monitoring. The UN applies a global set of indicators,
while Eurostat provides a set of indicators for the EU. In addition, each country
monitors its own priorities with a different set of indicators, tailored to the specifics
of the country or region.
The Sustainable Development Goals Report 2021 (United Nations, 2021)
indicates that even before the pandemic began, global economic growth had already
faced a slowdown. However, the outbreak of the pandemic in 2020 severely
disrupted economic activity around the world. The recession that resulted from
COVID-19 was considered the worst since the Great Depression. The above-
mentioned report concluded the following with regard to the SDG 8 targets:
1. For many countries, the road to economic recovery may be long and bumpy.
2. COVID-19 has led to massive job losses, particularly among young people and
among women.

26 Wiadomości Statystyczne. The Polish Statistician 2023 | 3
3. The lack of a social safety net has left informal workers on their own to cope with
the COVID-19 fallout.
4. The worst year on record for international tourism disproportionally affected
small-island, developing states.
5. The pandemic has led to an increase in the number of young people who are not
employed, in school or in training.
3. Literature review
The implementation of SDGs is not an easy task. Modern economics must be re-
oriented from the direction of economic growth to the direction of sustainable
development. In many countries, along with Poland, mainstream economics did not
include the concept of sustainable development as the main theory of management
and a foundation for a rational policy (Kostka, 2011). In the years 2010–2015, the
‘Europe 2020’ strategy prevailed as one ensuring social equality. The analysis of the
key indicators of social equality outlined in this strategy showed a large diversity in
inequality patterns, as both an increase and decrease in inequality at the EU level
were observed. These changes are most often related to the business cycle, especially
to labour market access and income inequality (Stanickova, 2017).
Many studies stress that the leading EU economies are not only the drivers of
development within the EU, but also in other, non-EU countries. For example,
research by Radulović and Kostić (2021) shows a significant long-term relationship
between the real GDP of Germany and France and that of Serbia. Moreover, in the
case of France, it has a short-term positive impact on the Serbian economy. In
contrast, no short-term impact of the German economy is observed here.
As regards Poland, the last decade was characterised by positive changes in the
area of sustainable development. However, the scale of these changes was smaller
than the EU average. The COVID-19 pandemic in Poland caused a short-lived, yet
pronounced decline in macroeconomic performance and may have also affected the
scale of the economy’s impact on the environment (Główny Urząd Statystyczny
[GUS], 2022).
Pełka (2019) conducted a development analysis for 30 European OECD countries.
The analysis involved linear ordering and cluster analysis based on a symbolic-
numeric approach for linear ordering visualisation, and single and ensemble
clustering for symbolic interval-valued data. Two clusters of countries were
obtained. Cluster 1 included the most developed countries: Denmark, Finland,
France, Germany, Iceland, Italy, Norway, Sweden, and the United Kingdom, and
a pattern object. The objects from this cluster were most similar to one another.
Cluster 2 included the following countries: Austria, Belgium, Bulgaria, Croatia,

B. BIESZK-STOLORZ, K. DMYTRÓW Application of multivariate statistical analysis to assess... 27
Cyprus, Czechia, Estonia, Greece, Hungary, Ireland, Latvia, Lithuania, Luxembourg,
the Netherlands, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Switzerland,
and an anti-pattern object. These were highly and medium-highly developed states.
The countries in this cluster were the least similar to each other.
A number of studies related to sustainable development are being undertaken,
among which circular economy (CE) development is particularly promoted
(Skvarciany et al., 2021). In Europe, Scandinavian countries recorded the highest
level of CE in 2019, while Greece, Luxembourg and Poland the lowest. Similar
conclusions were reached by Zioło et al. (2019). Their study indicates that in the
case of Scandinavian countries, economic growth does not entail neglecting
environmental issues, while the opposite is observed in economically less developed
countries (Greece, Hungary, Poland and Portugal). The classification of EU
countries by Piwowarski et al. (2018) based on two methods: TOPSIS (Technique for
Order of Preference by Similarity to Ideal Solution) and VIKOR (VIseKriterijumska
Optimizacija I Kompromisno Resenje) showed that in 2016, Austria was the most
sustainable country and Romania was the least. The weak position of Romania as
well as Bulgaria was also confirmed by the study of Stanujkic et al. (2020). Both
countries are located in Eastern Europe and joined the EU in 2007. They have not
yet properly incorporated sustainability as a postulate in their policies.
This study uses the multiple-criteria decision-making approach (MCDM) in
defining the position of the EU countries relative to SDGs in the years 2015–2018.
The analysis indicated that Sweden was the leader in SDG implementation.
Observation of the input data for this country showed, however, that its
achievements were not the best in all segments. However, Sweden’s attainments
outlined in Agenda 2030 were always between average and the best, placing Sweden
as the country that made the most significant progress towards SDGs during the
period of 2015–2018.
Rocchi et al. (2022) presented the evolution of an existing sustainability index in
order to measure the progress of EU countries towards the achievement of the
objectives of Agenda 2030. They proposed the Sustainable Development Goals
Achievement Index (SDG-AI), which represents all the sustainability-related
information. The study showed that in 2019, in terms of SDG-AI among EU
countries, the Nordic countries (Denmark, Finland and Sweden) were the most
advanced. They were at the top of the ranking in all the verified dimensions, except
for the environmental one in the case of Denmark. In contrast, the EU Baltic States
and the former Eastern Bloc countries achieved the lowest scores. Good governance
and institutional effectiveness are associated with long-run development and
sustainability success (Barbier & Burgess, 2021), which explains the high position of
the Nordic countries in the context of SDGs implementation. On the other hand, the

28 Wiadomości Statystyczne. The Polish Statistician 2023 | 3
low position of the EU post-communist countries results from their later accession
to the EU. It should be noted, however, that it had a positive impact on their
economic development, including their labour markets (Bieszk-Stolorz & Dmytrów,
2020; Dmytrów & Bieszk-Stolorz, 2021).
4. Research method
The achievement of SDG 8 is monitored by means of indicators. The global set of
SDG 8 indicators defined by the UN consists of 16 of them (GUS, n.d. a), while the
example set of indicators for Poland contains 13 (GUS, n.d. b). This research is based
on the set of indicators provided by Eurostat for the needs of EU countries.
The empirical analysis involves two steps. In the first step, we assess the degree to
which particular countries achieved SDG 8 through the composite measure based on
the TOPSIS method. It is then used to create the rankings of countries. In the second
step, we divide the EU countries into homogeneous clusters using the -means
method. The research period covers the years 2002–2021. The first year is 2002, with
data available for at least half of the variables (indicators). All data come from
Eurostat and refer to the variables that describe the targets specified in SDG 8. There
are eight variables that we take into consideration (square brackets represent the
codes for the variables in the Eurostat database):
 – GDP per capita in constant prices from the year 2021 (in euro, available for the
whole period) [SDG_08_10],
 – investment share of GDP by institutional sectors (percentage of GDP, available
for the whole period) [SDG_08_11],
 – young people (aged 15–29) not in employment, nor in education or training,
by sex (NEET) (percentage of the total population, available for the whole
period) [SDG_08_20],
 – employment rate (for persons aged 20–64) (percentage of the total population,
available for the whole period) [SDG_08_30],
 – long-term unemployment rate (percentage of the total population in the labour
force, available for the period of 2009–2021) [SDG_08_40],
 – in work at-risk-of-poverty rate (percentage of the total employed persons, aged
18 and more, available for the period of 2005–2021) [SDG_01_41],
 – fatal accidents at work per 100,000 workers (available for the period of 2010–
2019) [SDG_08_60],
 – inactive population due to caring responsibilities (percentage of population
aged 20–64, outside the labour force and wanting to work, available for the
whole period) [SDG_05_40].

B. BIESZK-STOLORZ, K. DMYTRÓW Application of multivariate statistical analysis to assess... 29
Variables ,  and  are stimulants (variables, for which the highest values are
the most desirable), while the remaining ones are destimulants (variables, for which
the lowest values are the most desirable). We perform calculations in the years 2002–
2004 for four variables, in the years 2005–2008 for six variables, in the years 2009
and 2020–2021 for seven variables and in the years 2010–2019 for all eight variables.
The different number and different sets of variables in each year depended on their
availability. The European countries were not in all cases obliged to provide specific
data in their reports (due to the different periods of their accession to the EU).
Variables were analysed with respect to their variability. Most of them were
characterised by at least a 15% of coefficient of variation. Only one variable – 
(employment rate) – had the level of variability slightly lower than 10%. However, if
it was excluded from the analysis, the results were exactly the same. Nevertheless, as
the employment rate is a very important variable with respect to EU policy, the
decision was to leave it in the set of variables.
We perform the calculations in Microsoft Excel for Microsoft 365 and in R
language (R Core Team, 2022) with the use of two libraries: clusterSim (Walesiak
& Dudek, 2020) and factoextra (Kassambara & Mundt, 2020).
4.1. The TOPSIS method
There are many techniques of performing the linear ordering of objects. On the basis
of multivariate statistical analysis, one of the first proposals of constructing the
composite measure was the composite measure of development, proposed by
Hellwig (1969, 1972a, 1972b). TOPSIS is a multivariate technique created for the
need of multi-criteria decision-making. It is, however, also widely used in
multivariate statistical analysis. It is one of the methods of the linear ordering of
objects. It was devised by Hwang and Yoon (1981). Its idea is based on the weighted
distance of each object (in our case each EU country) from the best values in the
dataset (the pattern) and the worst ones (the anti-pattern). The starting point of
every multivariate statistical method is observation matrix :
=




 

   
   
   
, (1
)
where:
 – value of the -th variable in the -th object (= 1, … , , = 1, … , ),
 – number of variables,
 – number of objects.

30 Wiadomości Statystyczne. The Polish Statistician 2023 | 3
As the variables are in most cases measured in different units, the first step to the
further analysis is the normalisation of data. We use one of the quotient inversions:
=





 , (2
)
where  – normalised value of the -th variable in the -th object (= 1, … , ,
= 1, … , ).
The main reasons for using this method were as follows: it did not change the
measurement scale of the variables, the normalised variables differed with respect to
the level of the central tendency and variability, and it was the method that the
authors had applied when they had proposed the TOPSIS method.
In the next step, we apply weights to the variables, which is not an easy task. It is
difficult to discern which variables are more important than others. There are
various methods of assigning weights to the variables: the naïve method (assuming
equal weights), methods based on the variables’ variation, correlation coefficients,
Shannon’s entropy, ranks and expert methods. As the set of variables is different in
various years, we use the naïve method and assume equal weights imposed on
variables. The weight of every variable  equals 
 and the condition 

 = 1 is
satisfied. After the weighing, we obtain a weighed, normalised observation matrix:
=, = 1, … , , = 1, … , .
(3)
On the basis of the weighed observation matrix for every variable, we find the
pattern (the best value in the dataset, denoted by ) and anti-pattern (the worst
value in the dataset, denoted by ):
=󰇥󰇡max
|󰇢,󰇡min
|󰇢|= 1, … , 󰇦=
=

,…,

, … , 


,
(4
)
=󰇥󰇡min
|󰇢,󰇡max
|󰇢|= 1, … , 󰇦=
=

, … , 

, … , 


,
(5
)
where:
 – stimulants,
 – destimulants.

B. BIESZK-STOLORZ, K. DMYTRÓW Application of multivariate statistical analysis to assess... 31
In the subsequent step, we calculate the weighted distance of every object from the
pattern (
) and anti-pattern (
). The most popular distance measure is the
Euclidean measure, which we also use as follows:

=

 , = 1, … , , (6
)

=

 , = 1, … , . (7
)
The composite measure in the TOPSIS method is calculated by means of the
following equation:
=





+
, = 1, … , . (8
)
Measure  is normalised – it belongs to interval [0, 1]. The best object has the
highest value of  and the worst object the lowest.
4.2. The k-means method
The k-means method is a technique used in cluster analysis, proposed by MacQueen
(1967). Cluster analysis aims at the separation of homogeneous groups of objects
(,…,) from the set of all objects ={,, … , }, where  is the number of
clusters, and  represents the number of objects (). The obtained clusters
should satisfy two conditions: firstly, the objects within the cluster should be to the
highest degree similar with respect to the values of the variables, and secondly, the
objects in different clusters should be to the highest degree different with respect to
the values of the variables. The methods in cluster analysis are divided into two
groups. The first group consists of hierarchical clustering methods (agglomerative
and deglomerative). The second group is formed by methods optimising the initial
division of objects. The -means method belongs to the second group (Everitt et al.,
2011).
The initial steps of the -means method (or any other cluster analysis technique)
is the same as in the case of the linear ordering methods. In the first step we have the
observation matrix (1), which is then normalised. We use the same normalisation
method (2) as in the case of the TOPSIS technique. The distance between the objects
is calculated by means of the Euclidean metric. The steps of the -means method are
as follows:

32 Wiadomości Statystyczne. The Polish Statistician 2023 | 3
1. The division of the set of objects into  clusters (= 1, … , ,…,).
2. Calculation of the centre of gravity (centroid) and the distance of every object
from it for every cluster.
3. Change of the assignment of objects to clusters with the closest centroid.
4. Calculation of the new centroids.
5. Repeating steps 3–4, until the next relocation of objects will cease to improve the
general distances of the objects from the centroids.
6. Repeating steps 2–5 for various numbers of clusters.
The procedure above is very time-consuming; therefore, we can apply various
methods to determine the optimal number of clusters. These methods are divided
into two groups: graphical and those based on quality assessment indexes. One of
the most widely-used indexes is the Caliński and Harabasz index. It is calculated by
means of the following equation (Everitt et al., 2011):
()=
trace()
1
trace()

, (9
)
where:
 – number of clusters,
trace() – trace of the between-group dispersion matrix,
trace() – trace of the within-group dispersion matrix.
The optimal number of clusters is the one that maximises the value of ().
Having selected the number of clusters (), we chose the optimal division of objects
between them () by means of the cost, measured as the sum of squares of the
within-group distances from the centroids:
=argmin
 





 , (10
)
where:
={, … , } – set of homogeneous clusters,
 – distance of the -th object from the centroid for the -th cluster,
 – centroid for the -th cluster.
5. Empirical results
In the first step of the analysis, we perform the linear ordering of countries according
to the fulfilment of SDG 8 by means of the TOPSIS method. In order to ensure the

B. BIESZK-STOLORZ, K. DMYTRÓW Application of multivariate statistical analysis to assess... 33
comparability of the obtained composite measures , the anti-pattern and pattern
values of the variables were calculated for the whole period. They are presented in
Table 2.
Table 2. Anti-pattern and pattern values of variables presenting the SDG 8 indicators
Specification        
Anti
-pattern .........
1,704.78 10.58 31.00 52.50 17.50 19.80 6.37 75.
70
country .............
year ....................
Romania
2002
Greece
2019
Bulgaria
2002
Greece
2013
Greece
2014
Romania
2014
Romania
2011
Malta
2004
Pattern ...................
86,550.00
53.59
4.70
81.80
0.60
2.70
0.45
2.40
country .............
year ....................
Luxembourg
2021
Ireland
2019
Denmark
2006
Sweden
2018
Czechia
2019
Finland
2017
Malta
2017
Sweden
2002
Note.  – SDG_08_10,  – SDG_08_11,  – SDG_08_20,  – SDG_08_30,  – SDG_08_40,  –
SDG_01_41,  – SDG_08_60,  – SDG_05_40.
Source: authors’ work based on Eurostat data.
Generally, we can observe the highest values of the variables relating to the
implementation of SDG 8 in the Nordic countries, Czechia and Luxembourg. The
lowest values are in southern European countries: Bulgaria, Greece and Romania.
Quite an interesting situation can be observed in Malta, where one indicator
(inactive population due to caring responsibilities) is of the lowest value, while
a different one (fatal accidents at work) is the highest.
After applying the TOPSIS method, we calculate the synthetic variable presenting
the fulfilment of SDG 8. On its basis we create rankings of EU countries according to
the fulfilment of SDG 8 in the years 2002–2021. The rankings are presented
in Table 3.
We can observe that the best situation with respect to the fulfilment of SDG 8
during the whole period was in Austria, Belgium, Denmark, Finland, Luxembourg,
Sweden and the Netherlands. It is worth noting that the situation of these countries
was stable throughout the whole analysed period. An interesting situation appeared
in Ireland – until 2007, it was amongst the countries which achieved SDG 8 to the
greatest extent. However, its position deteriorated during the financial crisis, but
started to improve after 2011. In the final three years (2019–2021) of the analysis,
Ireland occupied the highest position in this respect. Until 2009, Germany was in the
middle in the ranking, but in 2010, the country reached the top ten and remained in
this position until the end of the observation period. On the other hand, the ranking
of France deteriorated after 2015. For most of the observation period, Italy ranked in
the middle, although following 2016 its position deteriorated considerably. From
that moment on, Italy was amongst the countries in the worst situation as far as the
fulfilment of SDG 8 is concerned. Greece, Latvia, Poland (until 2010), Romania,

34 Wiadomości Statystyczne. The Polish Statistician 2023 | 3
Slovakia, and Spain (starting 2012) occupied the lowest positions in the ranking. The
situation in Poland worsened again in 2020, which might have been the effect of the
COVID-19 pandemic. In 2002, Malta was one of the lowest-ranking countries with
respect to the implementation of SDG 8, but after 2008, its position started to
improve. Then, the COVID-19 pandemic caused the deterioration of its situation in
this regard.
Table 3. Ranking of EU countries according to the fulfilment of SDG 8 in the years 2002–2021
Country
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
Austria
11
11
7
9
8
9
9
6
9
6
7
7
7
7
8
9
9
9
7
7
Belgium
9
9
10
6
7
7
6
7
7
7
6
6
6
6
6
8
7
7
8
9
Bulgaria
17
18
19
16
15
13
13
14
18
18
17
18
22
17
21
21
23
24
21
24
Croatia
24
21
25
17
19
21
18
23
19
24
26
25
23
24
24
22
21
23
17
15
Cyprus
21
25
26
24
23
19
16
12
13
11
15
17
17
20
17
17
19
19
22
17
Czechia
15
16
18
12
11
11
11
11
10
10
10
10
11
11
11
10
10
10
11
11
Denmark
2
1
1
1
1
1
1
1
2
3
2
1
1
1
1
1
2
4
2
2
Estonia
13
12
13
14
13
14
15
18
23
17
14
14
14
13
16
13
14
15
13
14
Finland
5
5
5
4
5
5
5
5
4
4
4
4
4
4
4
4
4
5
6
5
France
6
6
9
7
9
10
7
8
6
9
9
9
9
10
10
11
11
13
10
10
Germany
14
14
16
11
12
12
12
13
8
8
8
8
8
8
7
7
6
8
9
8
Greece
25
19
23
27
27
27
27
25
21
26
27
27
27
27
27
27
27
27
27
27
Hungary
16
15
17
19
18
15
17
16
15
14
12
13
13
14
13
15
15
14
14
13
Ireland
8
7
6
3
4
6
10
10
12
15
13
11
10
9
5
6
5
1
1
1
Italy
20
22
15
15
16
18
19
15
14
13
16
16
16
18
20
25
26
26
26
25
Latvia
19
20
21
21
22
23
24
26
27
27
25
19
21
22
23
19
20
21
20
18
Lithuania
18
17
14
20
21
17
22
19
26
25
20
21
20
16
14
16
17
17
18
22
Luxembourg
4
4
4
8
6
4
2
4
5
5
5
5
5
5
9
5
8
6
4
6
Malta
27
27
27
25
24
25
25
21
17
16
19
15
15
15
15
12
13
12
15
21
Netherlands
3
3
3
5
2
3
3
2
1
2
3
3
3
3
3
3
3
2
3
3
Poland
26
26
22
26
26
26
26
24
24
19
18
20
18
19
19
20
18
18
23
20
Portugal
7
8
11
13
14
16
14
17
16
20
22
22
19
21
18
18
16
16
16
16
Romania
23
24
24
23
25
24
23
20
22
23
21
23
24
25
25
24
24
22
19
23
Slovakia
22
23
20
22
20
20
20
27
25
22
23
24
25
23
22
23
22
20
24
19
Slovenia
10
10
8
10
10
8
8
9
11
12
11
12
12
12
12
14
12
11
12
12
Spain
12
13
12
18
17
22
21
22
20
21
24
26
26
26
26
26
25
25
25
26
Sweden
1
2
2
2
3
2
4
3
3
1
1
2
2
2
2
2
1
3
5
4
Source: authors’ work based on Eurostat data.
Generally, Austria, the Benelux Union and the Nordic countries occupied the top
positions in the ranking illustrating the achievement of SDG 8. The lowest positions,
on the other hand, were taken by Latvia, Poland, Slovakia, and the southern
European countries. From among the post-communist countries, the closest to

B. BIESZK-STOLORZ, K. DMYTRÓW Application of multivariate statistical analysis to assess... 35
achieving SDG 8 was Czechia. The position of this country was very close to the top
10 and remained stable during the whole studied period. Estonia, Hungary and
Slovenia ranked in the middle. If we analyse the rankings during the crisis periods
(i.e. the financial crisis of 2007–2009 and the COVID-19 pandemic in 2020–2021),
no significant changes could be detected. It seems that the financial crisis influenced
the rankings slightly more (with regard to the earlier mentioned Ireland, as well as
Croatia and Slovakia). The COVID-19 pandemic did not change the rankings
dramatically, although the positions of Malta, Poland and Slovakia did change.
In the next step of the analysis, we grouped the countries showing a similar level
of SDG 8 achievement into homogeneous clusters. Since separate clusters can be
created for each year, the full presentation of the analysis in such a form would
exceed the capacity of the research. Therefore, the results of the cluster analysis refer
to three selected years: 2002 (beginning of the observation period), 2009 (peak of the
financial crisis) and 2020 (when the governments of European countries imposed
the most severe pandemic-related restrictions).
In 2002, the optimal number of clusters was set at 6. Figure 1 presents the results
of the cluster analysis, while the mean values of the indicators in each cluster are
shown in Table 4.

36 Wiadomości Statystyczne. The Polish Statistician 2023 | 3
Table 4. Mean values of SDG 8 indicators in each cluster in 2002
Cluster no. 1 2 3 4 8
1 .....................
3,851.28
22.54
23.00
61.04
21.17
2 .....................
9,166.41
26.27
13.92
69.22
18.55
3 .....................
25,518.72
21.17
10.02
73.23
12.20
4 .....................
50,705.60
21.30
7.50
68.40
47.60
5 .....................
20,787.99
22.19
13.62
67.93
40.95
6 .....................
9,763.08
16.71
18.50
58.20
65.80
Note. As in Table 2.
Source: authors’ work based on Eurostat data.
In 2002, the Nordic countries jointly with Belgium, France and the Netherlands
created one cluster (number 3) with the generally highest values of the analysed
indicators (with the exception of the GDP per capita and NEETs, whose values were
higher in cluster 4, which included only Luxembourg). Malta itself created one
cluster (number 6). Although most variables did not differ to a high degree across
clusters, two indicators (investment share of GDP and inactive population due to
caring responsibilities) were the worst for all analysed countries. Cluster 1 was the
largest and consisted only of post-communist countries. It was characterised by the
lowest GDP per capita, an average investment share, the largest share of NEETs,
quite a low employment rate and a low share of the inactive population due to caring
responsibilities. Cluster 2 mostly consisted of post-communist countries, together
with Portugal and Spain. Its main feature was the highest investment share of GDP.
Cluster 5 was internally the most heterogeneous. It was characterised by quite a high
average GDP per capita, an average investment share of GDP, an average share of
NEETs, a high employment rate and one of the highest shares of the inactive
population due to caring responsibilities.
During the peak of the financial crisis (year 2009), the optimal number of clusters
was set at 2. Figure 2 presents the clusters and Table 5 the mean values of the
indicators.

B. BIESZK-STOLORZ, K. DMYTRÓW Application of multivariate statistical analysis to assess... 37
Table 5. Mean values of SDG 8 indicators in each cluster in 2009
Cluster no.       
1 ........................
11,084.91
22.15
16.86
64.33
4.09
9.56
27.40
2 ........................
29,658.21
22.14
11.08
72.58
1.85
6.03
20.51
Note. As in Table 2.
Source: authors’ work based on Eurostat data.
In 2009, EU countries were almost equally divided into two clusters. Cluster 1
contained most post-communist countries (except for Czechia and Slovenia) and
most of the southern European states (Greece, Italy, Malta, Portugal and Spain). The
remaining countries created cluster 2. As expected, the average values of the
analysed indicators were higher in cluster 2 (except for the investment share of GDP,
which was virtually identical in both clusters). When comparing these results with
those of 2002, Czechia and Slovenia moved to the cluster of countries where the
situation regarding the fulfilment of SDG 8 was better.
Finally, we present the results of the cluster analysis in 2020. Figure 3 illustrates
our findings in this regard and the mean values of the indicators within each cluster
are presented in Table 6. The optimal number of clusters was set at 5.

38 Wiadomości Statystyczne. The Polish Statistician 2023 | 3
Table 6. Mean values of SDG 8 indicators in each cluster in 2020
Cluster no.       
1 ........................
15,411.12
22.55
12.65
75.55
1.77
7.03
37.15
2 ........................
15,546.27
19.88
17.26
67.94
3.38
11.32
16.20
3 ........................
36,717.02
23.33
9.75
76.11
1.46
6.28
11.73
4 ........................
70,486.25
28.24
10.95
72.10
1.55
8.95
22.45
5 ........................
16,083.50
11.66
18.70
58.30
10.50
10.10
29.20
Note. As in Table 2.
Source: authors’ work based on Eurostat data.
In 2020, clusters 3 and 4 consisted of countries which were most advanced in
terms of their fulfilment of SDG 8. Cluster 3 included Austria, most of the Benelux
Union (except for Luxembourg), France, Germany and the Nordic countries. There
were only two countries in cluster 4 – Ireland and Luxembourg. In cluster 3 most
indicators showed the highest values: the percentage of NEETs, the employment
rate, the long-term unemployment rate, the in work at-risk-of-poverty rate and the
share of inactive population due to caring responsibilities. Cluster 4, on the other
hand, was characterised by the highest average GDP per capita and investment share
of GDP. Most post-communist countries (except for Bulgaria and Romania, which
were in cluster 2) were grouped in cluster 1 together with Malta and Cyprus. The

B. BIESZK-STOLORZ, K. DMYTRÓW Application of multivariate statistical analysis to assess... 39
average values of the following indicators: investment share of GDP, percentage of
NEETs and long-term unemployment rate ranked third among all the clusters. It
had the lowest GDP per capita, second average employment rate and second in work
at-risk-of-poverty rate. It also had the highest mean value of the share of the inactive
population due to caring responsibilities. Cluster 2 (with the previously mentioned
Bulgaria and Romania jointly with Italy, Portugal and Spain) showed the second
lowest values of most indicators: GDP per capita, investment share of GDP,
percentage of NEETs, employment rate, long-term unemployment rate. It also had
the highest in work at-risk-of-poverty rate, but on the other hand, the second lowest
share of the inactive population due to caring responsibilities. Cluster 5 contained
only one country – Greece. Most indicators (investment share of GDP, percentage of
NEETs, employment rate and long-term unemployment rate) in this cluster were of
the lowest values, the in work at-risk-of-poverty rate and share of inactive
population due to caring responsibilities were the second highest, while the average
GDP per capita was the third best.
6. Conclusions
The aim of our research was to assess the extent to which EU countries fulfilled the
targets set by SDG 8. The rankings obtained through the TOPSIS method showed
that during the whole analysed period, Austria, the Benelux Union and the Nordic
countries occupied the highest positions in rankings showing the implementation of
SDG 8. The opposite situation was in the case of Greece, Latvia, Poland, Romania
and Slovakia, and also in the final years of the analysis in Spain and Italy. These
results were confirmed by the cluster analysis. The countries which proved most
advanced in achieving the SDG 8 targets were grouped into separate clusters from
those formed by countries which have a long road ahead towards reaching SDG 8.
Our research, showing that Denmark, the Netherlands and Sweden are the leaders in
SDG 8 achievement is consistent with the results of other research proving that these
countries are the most advanced in the attainment of not only SDG 8, but all SDGs
(Kuc-Czarnecka et al., 2023).
Our research demonstrates that despite the fact that less-developed regions of the
EU (Greece, southern Italy, Portugal, Spain and post-communist countries) receive
significant financial support for the achievement of the targets set by SDGs, the well-
developed Western European countries still maintain a large advantage in this
regard. The situation did not change much during the whole observation period.
Some exceptions, however, could also be observed – Czechia managed to strengthen
its position, while Slovenia had already held a high position, although at the end of
the analysed period it slightly declined.

40 Wiadomości Statystyczne. The Polish Statistician 2023 | 3
The crisis periods had little influence on the rankings. However, their impact on
the results of the cluster analysis was more visible. It was more evident during the
financial crisis of 2007–2009. The countries were separated into two clusters with
a lower and higher degree of SDG 8 implementation. The differences between the
countries within these clusters were so minor, that the further division into smaller
ones did not occur.
The main policy recommendation based on our research is that the less-
developed, post-communist and Southern European countries continue their efforts
to fully implement the SDG 8 targets. The improvement of the situation of less-
developed countries can be achieved particularly by means of increasing their GDP
per capita, decreasing their long-term unemployment rate, decreasing the fraction of
NEETs, and decreasing the number of inactive persons due to caring responsibilities
– the differences between the most and least advanced countries were the highest
with regard to the values of these indicators. The future area of research will also
include other SDGs with the purpose of obtaining a full picture of the degree of their
implementation in the EU, and especially in the post-communist, less-developed
countries.
Acknowledgements
The project was financed within the framework of the Minister of Science and
Higher Education programme ‘Regional Excellence Initiative’ in the years 2019–
2022; project number: 001/RID/2018/19; amount of financing: PLN 10,684,000.
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