Multivariate Analysis of the Sustainable Development of the Silver Economy in the European Union Countries
Abstract
:1. Introduction
2. Silver Economy
- Improving the health and quality of life of Europeans with a focus on older people;
- Supporting the long-term sustainability and efficiency of health and social care systems;
- Enhancing the competitiveness of EU industry through business and expansion in new markets.
3. Research Methodology and Data
3.1. The COPRAS Method in a Dynamic Approach
- Step 1
- Step 2
- Step 3
- Step 4
- Step 5
- ;
- —the best object in period t, for t = 1, …, T;
- —the worst object in period t, for t = 1, …, T.
3.2. Analysis of the Dynamics of the Synthetic Variable—The DTW Method
- Boundary, meaning that the first (last) element of the first sequence must be matched with the first (last) element of the second one;
- Monotonicity, meaning that warping path can move only right or up or right-up of its current position;
- Step size, meaning that every index from the sequence X must be matched with at least one index from the sequence Y.
3.3. Data Used in This Study
- x1—share of population aged 65+ in total population—destimulant;
- x2—old-age dependency ratio—destimulant;
- x3—activity ratio of persons aged 65+—stimulant;
- x4—employment ratio of persons aged 55–64—stimulant;
- x5—share of old age pensions in GDP—destimulant;
- x6—share of inactive persons aged 55–74 willing to work, but not seeking employment—destimulant;
- x7—at-risk-of-poverty rate for pensioners aged 65+—destimulant;
- x8—share of social protection benefits for elderly persons in GDP—destimulant.
4. Results of Empirical Analysis
4.1. Results of Cluster Analysis in 2009, 2015, 2019, 2021
- Czechia, Denmark, Finland, Germany, Ireland, The Netherlands, and Sweden.
- Austria, Belgium, Croatia, France, Greece, Italy, Luxembourg, Malta, Poland, Slovakia, Slovenia, Spain, and Romania.
- Bulgaria, Estonia, and Latvia.
4.2. Rankings of the EU Countries (2009–2021)
- The following countries were in the best situation in terms of selected variables compared to other EU countries in the period 2009–2021: Estonia (2011–2021), Cyprus (2009–2011), Portugal (2009–2014), Ireland (2015–2021), Romania (2009), and Sweden (2010, 2012–2021).
- The worst situation in terms of selected variables compared to other EU countries in the period 2009–2021 was observed in the following countries: Belgium (2009–2012, 2021), Greece (2012–2018), Spain (2013–2015), France (2009–2010), Croatia (2016–2021), Luxembourg (2016–2020), Hungary (2009–2015), Romania (2021), Slovenia (2019–2020), and Slovakia (2011).
- High percentage of elderly people,
- High burden on GDP with pensions, and
- Lower professional activity due to potentially higher pensions.
4.3. Clustering Countries According to the Dynamics of the Synthetic Variable
- The first cluster consisted of Romania, Croatia, Portugal, Luxembourg, Slovenia, Greece, Cyprus (Figure 5). In these countries, the value of the synthetic variable decreased or remained more or less constant in the years 2009–2021.
- The second cluster included the remaining EU countries in which the value of the synthetic variable increased in the years 2009–2021 (Figure 6).
5. Discussion
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
Descriptive Statistics | Variables | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
x2 | x3 | x4 | x5 | x6 | x7 | x2 | x3 | x4 | x5 | x6 | x7 | |
2009 | 2010 | |||||||||||
min | 16.00 | 1.40 | 29.10 | 4.10 | 0.66 | 4.20 | 16.50 | 1.50 | 29.30 | 3.90 | 0.72 | 3.70 |
max | 30.90 | 17.00 | 68.60 | 11.50 | 12.44 | 53.50 | 31.40 | 16.50 | 69.10 | 11.60 | 12.53 | 42.30 |
mean | 24.07 | 5.86 | 44.58 | 7.41 | 3.89 | 20.60 | 24.43 | 5.64 | 44.51 | 7.57 | 4.17 | 16.09 |
median | 25.20 | 4.90 | 43.00 | 7.00 | 3.04 | 19.40 | 25.60 | 4.70 | 42.80 | 7.00 | 3.43 | 16.20 |
standard deviation | 3.75 | 3.80 | 9.89 | 1.77 | 2.62 | 12.06 | 3.76 | 3.61 | 9.31 | 1.80 | 2.85 | 8.39 |
coefficient of variation | 0.16 | 0.65 | 0.22 | 0.24 | 0.67 | 0.59 | 0.15 | 0.64 | 0.21 | 0.24 | 0.68 | 0.52 |
skewness | −0.40 | 1.21 | 0.38 | 0.44 | 1.42 | 1.22 | −0.41 | 1.35 | 0.52 | 0.33 | 1.30 | 1.13 |
2011 | 2012 | |||||||||||
min | 17.20 | 1.80 | 29.30 | 4.00 | 0.72 | 3.50 | 17.80 | 1.80 | 30.90 | 4.10 | 1.04 | 4.40 |
max | 31.40 | 14.50 | 70.70 | 12.70 | 12.10 | 37.80 | 32.00 | 14.60 | 71.60 | 13.90 | 13.73 | 31.20 |
mean | 24.80 | 5.57 | 45.17 | 7.58 | 4.54 | 15.19 | 25.36 | 5.67 | 46.08 | 7.80 | 4.97 | 14.93 |
median | 25.90 | 4.90 | 42.70 | 7.00 | 3.57 | 14.50 | 26.50 | 5.00 | 44.20 | 7.30 | 4.24 | 14.80 |
standard deviation | 3.76 | 3.24 | 9.85 | 2.01 | 2.73 | 7.93 | 3.80 | 3.22 | 9.94 | 2.19 | 2.88 | 6.33 |
coefficient of variation | 0.15 | 0.58 | 0.22 | 0.27 | 0.60 | 0.52 | 0.15 | 0.57 | 0.22 | 0.28 | 0.58 | 0.42 |
skewness | −0.47 | 1.09 | 0.54 | 0.64 | 1.12 | 0.94 | −0.53 | 1.00 | 0.60 | 0.80 | 1.11 | 0.51 |
2013 | 2014 | |||||||||||
min | 18.40 | 1.70 | 31.50 | 4.20 | 1.38 | 4.30 | 19.00 | 1.70 | 33.00 | 4.40 | 1.14 | 4.40 |
max | 32.70 | 13.30 | 72.30 | 13.00 | 12.14 | 28.60 | 33.10 | 11.90 | 72.80 | 13.50 | 11.68 | 35.40 |
mean | 26.00 | 5.61 | 47.27 | 8.04 | 5.41 | 14.07 | 26.69 | 5.77 | 48.65 | 8.10 | 5.18 | 14.46 |
median | 26.90 | 5.10 | 45.20 | 7.70 | 4.67 | 13.50 | 27.40 | 5.40 | 46.00 | 7.20 | 4.81 | 13.90 |
standard deviation | 3.81 | 3.03 | 10.06 | 2.22 | 2.78 | 6.17 | 3.81 | 2.91 | 10.08 | 2.32 | 2.76 | 7.30 |
coefficient of variation | 0.15 | 0.54 | 0.21 | 0.28 | 0.51 | 0.44 | 0.14 | 0.50 | 0.21 | 0.29 | 0.53 | 0.50 |
skewness | −0.58 | 0.79 | 0.55 | 0.44 | 0.45 | 0.41 | −0.63 | 0.46 | 0.47 | 0.52 | 0.40 | 1.02 |
2015 | 2016 | |||||||||||
min | 19.70 | 1.90 | 32.70 | 4.60 | 1.30 | 4.30 | 20.20 | 1.40 | 35.30 | 4.60 | 1.18 | 5.70 |
max | 33.70 | 11.80 | 73.20 | 14.30 | 11.55 | 39.80 | 34.30 | 13.50 | 74.10 | 14.30 | 17.29 | 45.50 |
mean | 27.40 | 5.76 | 50.30 | 8.03 | 4.91 | 15.74 | 28.03 | 5.81 | 52.40 | 7.99 | 5.05 | 16.68 |
median | 27.90 | 5.30 | 48.30 | 7.30 | 4.14 | 14.00 | 28.30 | 5.00 | 50.50 | 7.00 | 4.56 | 14.20 |
standard deviation | 3.79 | 2.83 | 10.21 | 2.46 | 2.80 | 9.04 | 3.79 | 3.09 | 10.27 | 2.45 | 3.34 | 9.61 |
coefficient of variation | 0.14 | 0.49 | 0.20 | 0.31 | 0.57 | 0.57 | 0.14 | 0.53 | 0.20 | 0.31 | 0.66 | 0.58 |
skewness | −0.65 | 0.58 | 0.25 | 0.62 | 0.60 | 1.22 | −0.67 | 0.58 | 0.15 | 0.66 | 1.83 | 1.54 |
2017 | 2018 | |||||||||||
min | 20.50 | 2.10 | 36.90 | 4.40 | 1.35 | 7.00 | 20.60 | 1.90 | 38.60 | 4.20 | 1.40 | 6.40 |
max | 34.80 | 13.50 | 75.20 | 13.70 | 15.20 | 46.60 | 35.20 | 14.20 | 76.70 | 13.20 | 15.26 | 53.80 |
mean | 28.64 | 6.18 | 54.63 | 7.93 | 4.76 | 17.82 | 29.25 | 6.50 | 56.85 | 7.88 | 4.70 | 19.00 |
median | 28.70 | 5.50 | 53.50 | 7.60 | 4.08 | 14.60 | 29.60 | 5.80 | 55.90 | 7.50 | 3.58 | 15.40 |
standard deviation | 3.78 | 3.04 | 10.17 | 2.41 | 2.96 | 10.62 | 3.79 | 3.17 | 10.07 | 2.39 | 3.38 | 11.96 |
coefficient of variation | 0.13 | 0.49 | 0.19 | 0.30 | 0.62 | 0.60 | 0.13 | 0.49 | 0.18 | 0.30 | 0.72 | 0.63 |
skewness | −0.72 | 0.54 | 0.04 | 0.51 | 1.71 | 1.49 | −0.76 | 0.51 | −0.06 | 0.42 | 1.74 | 1.66 |
2019 | 2020 | |||||||||||
min | 20.70 | 2.30 | 40.40 | 4.10 | 1.02 | 7.40 | 20.90 | 2.80 | 41.50 | 4.00 | 1.04 | 7.10 |
max | 35.80 | 14.60 | 76.50 | 13.20 | 14.64 | 53.80 | 36.40 | 14.10 | 76.30 | 14.50 | 13.94 | 49.40 |
mean | 29.77 | 6.83 | 58.38 | 7.85 | 4.43 | 19.68 | 30.34 | 6.84 | 58.97 | 8.53 | 4.64 | 20.20 |
median | 30.40 | 6.60 | 58.50 | 7.50 | 3.70 | 15.60 | 31.10 | 6.30 | 59.60 | 8.30 | 3.72 | 16.10 |
standard deviation | 3.83 | 3.26 | 10.01 | 2.41 | 3.17 | 11.81 | 3.89 | 3.23 | 9.65 | 2.59 | 3.29 | 11.12 |
coefficient of variation | 0.13 | 0.48 | 0.17 | 0.31 | 0.72 | 0.60 | 0.13 | 0.47 | 0.16 | 0.30 | 0.71 | 0.55 |
skewness | −0.75 | 0.49 | −0.07 | 0.39 | 1.71 | 1.59 | −0.75 | 0.56 | −0.11 | 0.36 | 1.45 | 1.37 |
2021 | ||||||||||||
min | 21.00 | 2.40 | 43.80 | 3.60 | 0.89 | 9.10 | ||||||
max | 37.00 | 14.70 | 76.90 | 13.30 | 17.06 | 51.20 | ||||||
mean | 30.87 | 7.24 | 60.66 | 8.09 | 4.68 | 19.93 | ||||||
median | 31.60 | 6.20 | 62.80 | 7.90 | 3.35 | 15.80 | ||||||
standard deviation | 3.93 | 3.56 | 8.94 | 2.47 | 3.77 | 11.23 | ||||||
coefficient of variation | 0.13 | 0.49 | 0.15 | 0.31 | 0.81 | 0.56 | ||||||
skewness | −0.78 | 0.63 | −0.08 | 0.25 | 1.64 | 1.55 |
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Years | Cluster Number | ||||||
---|---|---|---|---|---|---|---|
1 | 24.127 | 5.147 | 37.060 | 7.547 | 3.391 | 16.407 | |
2009 | 2 | 24.013 | 5.938 | 54.275 | 7.825 | 3.450 | 16.100 |
3 | 23.975 | 8.400 | 53.400 | 6.100 | 6.646 | 45.350 | |
1 | 26.663 | 4.506 | 43.069 | 8.363 | 4.826 | 12.844 | |
2015 | 2 | 28.100 | 7.629 | 61.843 | 8.500 | 4.186 | 11.943 |
3 | 29.125 | 7.475 | 59.025 | 5.875 | 6.512 | 33.975 | |
1 | 29.114 | 4.250 | 50.164 | 8.129 | 3.520 | 15.014 | |
2019 | 2 | 30.000 | 9.256 | 66.978 | 8.411 | 4.980 | 16.167 |
3 | 31.575 | 10.425 | 67.775 | 5.625 | 6.361 | 43.925 | |
1 | 30.254 | 4.362 | 52.508 | 8.685 | 3.044 | 15.738 | |
2021 | 2 | 31.040 | 9.500 | 68.290 | 8.190 | 6.508 | 15.820 |
3 | 32.475 | 10.975 | 68.050 | 5.875 | 5.455 | 43.825 |
Countries | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Belgium | 26 | 25 | 26 | 26 | 23 | 24 | 23 | 24 | 23 | 23 | 22 | 24 | 25 |
Bulgaria | 18 | 19 | 20 | 19 | 16 | 17 | 15 | 14 | 14 | 13 | 13 | 13 | 13 |
Czechia | 14 | 13 | 13 | 13 | 13 | 13 | 13 | 12 | 11 | 11 | 11 | 11 | 12 |
Denmark | 8 | 7 | 7 | 6 | 5 | 5 | 5 | 5 | 6 | 7 | 8 | 8 | 6 |
Germany | 13 | 11 | 9 | 10 | 10 | 9 | 8 | 8 | 9 | 9 | 10 | 10 | 10 |
Estonia | 4 | 5 | 3 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Ireland | 5 | 6 | 6 | 7 | 4 | 4 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |
Greece | 17 | 17 | 19 | 25 | 26 | 27 | 27 | 25 | 25 | 25 | 23 | 23 | 21 |
Spain | 21 | 23 | 23 | 23 | 25 | 25 | 25 | 22 | 24 | 24 | 24 | 22 | 24 |
France | 25 | 26 | 24 | 22 | 22 | 21 | 19 | 19 | 20 | 22 | 21 | 21 | 23 |
Croatia | 12 | 15 | 14 | 15 | 21 | 23 | 22 | 26 | 26 | 26 | 26 | 26 | 26 |
Italy | 22 | 21 | 21 | 20 | 20 | 19 | 18 | 17 | 17 | 16 | 17 | 19 | 18 |
Cyprus | 2 | 2 | 2 | 4 | 7 | 11 | 11 | 10 | 10 | 10 | 9 | 9 | 8 |
Latvia | 7 | 9 | 10 | 9 | 8 | 8 | 6 | 7 | 7 | 6 | 4 | 5 | 4 |
Lithuania | 11 | 14 | 12 | 12 | 12 | 12 | 9 | 6 | 5 | 5 | 6 | 4 | 5 |
Luxembourg | 19 | 20 | 18 | 18 | 19 | 20 | 24 | 27 | 27 | 27 | 27 | 27 | 22 |
Hungary | 27 | 27 | 27 | 27 | 27 | 26 | 26 | 21 | 22 | 21 | 20 | 16 | 15 |
Malta | 24 | 22 | 22 | 21 | 18 | 16 | 16 | 18 | 19 | 18 | 15 | 14 | 14 |
The Netherlands | 9 | 8 | 8 | 8 | 9 | 6 | 7 | 9 | 8 | 8 | 7 | 7 | 7 |
Austria | 16 | 16 | 16 | 14 | 14 | 15 | 14 | 15 | 16 | 15 | 19 | 20 | 19 |
Poland | 20 | 18 | 17 | 16 | 15 | 18 | 17 | 16 | 15 | 17 | 18 | 17 | 16 |
Portugal | 1 | 1 | 1 | 1 | 2 | 3 | 4 | 4 | 4 | 4 | 5 | 6 | 11 |
Romania | 3 | 4 | 5 | 5 | 6 | 7 | 12 | 13 | 13 | 14 | 14 | 18 | 27 |
Slovenia | 10 | 10 | 15 | 17 | 17 | 14 | 20 | 23 | 21 | 20 | 25 | 25 | 20 |
Slovakia | 23 | 24 | 25 | 24 | 24 | 22 | 21 | 20 | 18 | 19 | 16 | 15 | 17 |
Finland | 15 | 12 | 11 | 11 | 11 | 10 | 10 | 11 | 12 | 12 | 12 | 12 | 9 |
Sweden | 6 | 3 | 4 | 3 | 3 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
2010 | 0.979 | 1 | ||||||||||
2011 | 0.965 | 0.982 | 1 | |||||||||
2012 | 0.929 | 0.949 | 0.980 | 1 | ||||||||
2013 | 0.875 | 0.911 | 0.937 | 0.971 | 1 | |||||||
2014 | 0.834 | 0.879 | 0.896 | 0.937 | 0.979 | 1 | ||||||
2015 | 0.767 | 0.808 | 0.846 | 0.900 | 0.955 | 0.967 | 1 | |||||
2016 | 0.709 | 0.746 | 0.789 | 0.841 | 0.903 | 0.910 | 0.969 | 1 | ||||
2017 | 0.723 | 0.759 | 0.792 | 0.841 | 0.905 | 0.915 | 0.968 | 0.993 | 1 | |||
2018 | 0.723 | 0.758 | 0.785 | 0.831 | 0.898 | 0.913 | 0.965 | 0.988 | 0.995 | 1 | ||
2019 | 0.669 | 0.702 | 0.736 | 0.780 | 0.851 | 0.866 | 0.937 | 0.970 | 0.974 | 0.976 | 1 | |
2020 | 0.604 | 0.634 | 0.675 | 0.717 | 0.787 | 0.809 | 0.893 | 0.949 | 0.951 | 0.954 | 0.984 | 1 |
2021 | 0.535 | 0.580 | 0.615 | 0.643 | 0.719 | 0.749 | 0.830 | 0.871 | 0.874 | 0.889 | 0.902 | 0.941 |
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Bieszk-Stolorz, B.; Dmytrów, K.; Frąckiewicz, E. Multivariate Analysis of the Sustainable Development of the Silver Economy in the European Union Countries. Sustainability 2024, 16, 10703. https://doi.org/10.3390/su162310703
Bieszk-Stolorz B, Dmytrów K, Frąckiewicz E. Multivariate Analysis of the Sustainable Development of the Silver Economy in the European Union Countries. Sustainability. 2024; 16(23):10703. https://doi.org/10.3390/su162310703
Chicago/Turabian StyleBieszk-Stolorz, Beata, Krzysztof Dmytrów, and Ewa Frąckiewicz. 2024. "Multivariate Analysis of the Sustainable Development of the Silver Economy in the European Union Countries" Sustainability 16, no. 23: 10703. https://doi.org/10.3390/su162310703
APA StyleBieszk-Stolorz, B., Dmytrów, K., & Frąckiewicz, E. (2024). Multivariate Analysis of the Sustainable Development of the Silver Economy in the European Union Countries. Sustainability, 16(23), 10703. https://doi.org/10.3390/su162310703