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Efficiency ranking of economic growth toward sustainable growth with grey system theory: the case of small countries in advanced and emerging economies

Marcin Nowak
Marcin Nowak
 et 
Małgorzata Kokocińska
Małgorzata Kokocińska
   | 30 sept. 2023
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Article Category: Empirical Paper
Publié en ligne: 30 sept. 2023
Pages: 183 - 196
Reçu: 21 déc. 2022
Accepté: 29 avr. 2023
DOI: https://doi.org/10.2478/ijme-2023-0013
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© 2023 Marcin Nowak et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1.

Graphic presentation of the SEI-EG index for Estonia (2020). SEI-EG, Synthetic Efficiency Indicator for Economic Growth.
Graphic presentation of the SEI-EG index for Estonia (2020). SEI-EG, Synthetic Efficiency Indicator for Economic Growth.

Matrix of scaled inputs for 2020

o1 (BEL) o2 (CZE) o3 (DEN) o4 (EST) o5 (LAT) o6 (LIT) o7 (HUN) o8 (NET) o9 (AUT) o10 (SLO) o11 (FIN) o12 (SWE)
r1 0.986 0.564 0.858 0.507 0.201 0.329 0.456 0.649 0.907 0.258 0.833 1.000
r2 0.925 0.782 0.920 0.706 0.668 0.670 0.769 0.842 0.774 0.794 0.893 1.000
r3 0.967 0.730 1.000 0.459 0.333 0.476 0.595 0.817 0.864 0.384 0.959 0.853
r4 0.488 0.045 0.972 0.100 0.037 0.042 0.026 0.857 0.606 0.023 0.804 1.000
r5 0.637 0.863 0.599 0.547 0.580 0.274 1.000 0.467 0.915 0.887 0.613 0.755
r6 0.349 0.352 0.167 0.597 0.873 1.000 0.527 0.739 0.495 0.495 0.405 0.461
r7 0.764 0.681 0.864 0.680 0.690 0.690 0.705 1.000 0.728 0.676 0.821 0.881
i1 0.740 0.377 1.000 0.369 0.290 0.331 0.264 0.854 0.795 0.315 0.805 0.868
i2 1.000 0.334 0.373 0.168 0.384 0.413 0.706 0.481 0.738 0.529 0.612 0.351

Standardized partial efficiency matrix E for 2020

o1 (BEL) o2 (CZE) o3 (DEN) o4 (EST) o5 (LAT) o6 (LIT) o7 (HUN) o8 (NET) o9 (AUT) o10 (SLO) o11 (FIN) o12 (SWE)
e1∗$$e_1^ * $$ 0.415 0.765 0.506 1.000 0.000 0.222 0.266 0.290 0.453 0.010 0.449 0.808
e2∗$$e_2^ * $$ 0.034 0.735 0.205 1.000 0.602 0.489 0.357 0.156 0.000 0.539 0.156 0.390
e3∗$$e_3^ * $$ 0.178 1.000 0.479 0.700 0.069 0.325 0.280 0.276 0.191 0.000 0.390 0.430
e4∗$$e_4^ * $$ 0.320 0.046 0.858 0.202 0.035 0.037 0.000 0.775 0.464 0.001 0.682 1.000
e5∗$$e_5^ * $$ 0.019 1.000 0.100 0.774 0.592 0.021 0.790 0.000 0.286 0.811 0.096 0.312
e6∗$$e_6^ * $$ 0.065 0.306 0.000 0.809 0.961 1.000 0.345 0.353 0.164 0.380 0.134 0.210
e7∗$$e_7^ * $$ 0.000 0.626 0.229 1.000 0.708 0.590 0.349 0.374 0.043 0.436 0.169 0.343

SEI-EG index values for all countries analyzed for 2016–2020

o1 (BEL) o2 (CZE) o3 (DEN) o4 (EST) o5 (LAT) o6 (LIT) o7 (HUN) o8 (NET) o9 (AUT) o10 (SLO) o11 (FIN) o12 (SWE)
SEI-EG2020 0.012 0.338 0.116 0.633 0.188 0.146 0.097 0.078 0.042 0.069 0.082 0.234
SEI-EG2019 0.005 0.261 0.115 0.714 0.149 0.122 0.062 0.057 0.028 0.054 0.055 0.162
SEI-EG2018 0.006 0.262 0.127 0.758 0.147 0.146 0.059 0.058 0.028 0.053 0.062 0.141
SEI-EG2017 0.006 0.255 0.126 0.781 0.142 0.124 0.058 0.057 0.025 0.065 0.070 0.118
SEI-EG2016 0.008 0.236 0.139 0.754 0.146 0.136 0.050 0.055 0.024 0.063 0.078 0.119

T01

2016 2017 2018
1 Estonia 0.754 1 Estonia 0.781 1 Estonia 0.758
2 Czech Rep. 0.236 2 Czech Rep. 0.255 2 Czech Rep. 0.262
3 Latvia 0.146 3 Latvia 0.142 3 Latvia 0.147
4 Denmark 0.139 4 Denmark 0.126 4 Lithuania 0.146
5 Lithuania 0.136 5 Lithuania 0.124 5 Sweden 0.141
6 Sweden 0.119 6 Sweden 0.118 6 Denmark 0.127
7 Finland 0.078 7 Finland 0.070 7 Finland 0.062
8 Slovakia 0.063 8 Slovakia 0.065 8 Hungary 0.059
9 Netherlands 0.055 9 Hungary 0.058 9 Netherlands 0.058
10 Hungary 0.050 10 Netherlands 0.057 10 Slovakia 0.053
11 Austria 0.024 11 Austria 0.025 11 Austria 0.028
12 Belgium 0.008 12 Belgium 0.006 12 Belgium 0.006

T02

2019 2020
1 Estonia 0.714 1 Estonia 0.633
2 Czech Rep. 0.261 2 Czech Rep. 0.338
3 Sweden 0.162 3 Sweden 0.234
4 Latvia 0.149 4 Latvia 0.188
5 Lithuania 0.122 5 Lithuania 0.146
6 Denmark 0.115 6 Denmark 0.116
7 Hungary 0.062 7 Hungary 0.097
8 Netherlands 0.057 8 Finland 0.082
9 Finland 0.055 9 Netherlands 0.078
10 Slovakia 0.054 10 Slovakia 0.069
11 Austria 0.028 11 Austria 0.042
12 Belgium 0.005 12 Belgium 0.012

Input data matrix for 2020

o1 (BEL) o2 (CZE) o3 (DEN) o4 (EST) o5 (LAT) o6 (LIT) o7 (HUN) o8 (NET) o9 (AUT) o10 (SLO) o11 (FIN) o12 (SWE)
r1 3.48 1.99 3.03 1.79 0.71 1.16 1.61 2.29 3.2 0.91 2.94 3.53
r2 54.4 46.0 54.1 41.5 39.3 39.4 45.2 49.5 45.5 46.7 52.5 58.8
r3 2.0548 1.5497 2.1242 0.9746 0.7068 1.0117 1.2646 1.7361 1.8359 0.815 2.0365 1.8121
r4 208.52 19.26 414.99 42.87 15.79 17.89 11.18 366.14 258.61 9.89 343.43 427.10
r5 13.5 18.3 12.7 11.6 12.3 5.8 21.2 9.9 19.4 18.8 13.0 16.0
r6 22.6 22.8 10.8 38.6 56.5 64.7 34.1 47.8 32.0 32.0 26.2 29.8
r7 107.7 120.9 95.3 121.0 119.2 119.3 116.7 82.3 113.0 121.8 100.3 93.4
i1 39,560 20,170 53,480 19,720 15,500 17,710 14,100 45,670 42,540 16,860 43,030 46,420
i2 112.8 37.7 42.1 19.0 43.3 46.6 79.6 54.3 83.3 59.7 69.0 39.6

SEI-EG index values for all countries analyzed 2020

o1 (BEL) o2 (CZE) o3 (DEN) o4 (EST) o5 (LAT) o6 (LIT) o7 (HUN) o8 (NET) o9 (AUT) o10 (SLO) o11 (FIN) o12 (SWE)
SEI-EG 0.012 0.338 0.116 0.633 0.188 0.146 0.097 0.078 0.042 0.069 0.082 0.234

Selected macroeconomic indicators 2020

Country Total population Total employment From 15 years to 64 years percentage of total population GDP pc In PPS UE = 100 General government gross debt Labor productivity, GDP per person employed
2020 2020 2020 2020 2019/2020
Austria 8,916,864 72.4 124.9 82.3 −4.9
Belgium 11,538,684 64.7 119.0 112.0 −5.4
Denmark 5,834,404 74.4 132.7 42.2 −0.9
Finland 5,529,543 72.1 114.1 74.8 −0.5
Netherlands 17,441,500 77.8 130.5 54.7 −3.4
Sweden 10,353,442 75.5 122.4 39.5 −0.8
Czech Rep. 10,697,858 74.4 93.4 37.7 −3.9
Estonia 1,329,522 73.2 86.1 18.5 2.2
Hungary 9,750,149 69.7 74.5 79.3 −3.5
Lithuania 2,794,885 71.6 87.6 46.3 1.6
Latvia 1,900,449 71.6 72.0 42.0 0.8
Slovakia 5,458,827 67.5 71.8 58.9 −1.5

Partial efficiency matrix E for 2020

o1 (BEL) o2 (CZE) o3 (DEN) o4 (EST) o5 (LAT) o6 (LIT) o7 (HUN) o8 (NET) o9 (AUT) o10 (SLO) o11 (FIN) o12 (SWE)
e1 0.567 0.792 0.625 0.944 0.299 0.442 0.471 0.486 0.591 0.305 0.588 0.820
e2 0.532 1.100 0.670 1.314 0.992 0.900 0.793 0.630 0.504 0.940 0.630 0.820
e3 0.556 1.026 0.728 0.854 0.494 0.640 0.614 0.612 0.563 0.454 0.677 0.700
e4 0.281 0.063 0.708 0.187 0.055 0.056 0.027 0.642 0.395 0.027 0.568 0.820
e5 0.366 1.213 0.436 1.019 0.861 0.368 1.032 0.350 0.597 1.050 0.433 0.619
e6 0.201 0.495 0.122 1.111 1.296 1.344 0.544 0.553 0.322 0.586 0.286 0.378
e7 0.439 0.957 0.629 1.266 1.025 0.927 0.728 0.749 0.475 0.800 0.579 0.723
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