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Глобальная экономика 2022 г. в индексах, не зависящих от размера страны. II. Двумерное распределение стран на плоскости {Индекс Восприятия Коррупции CPI, Масштабированная Экономическая Продуктивность П}
Сейдаметова Зарема Сейдалиевна, доктор педагогических наук, профессор
Темненко Валерий Анатольевич, кандидат физико-математических наук, доцент
Крымский инженерно-педагогический университет имени Февзи Якубова, Симферополь, Республика Крым
Цель исследования – построить и описать двумерное распределение стран на плоскости экономических индексов {CPI, П} по статистическим данным 2022 года, выделяя страны Глобального Периметра, находящиеся на периферии области, занятой странами, и выделяя страны, принадлежащие ядру каждой П-группы продуктивности; выделить страны, принадлежащие периметру ядер П-группы и внутренней области ядер П-групп. Научная новизна заключается в самом выявлении факта существования Глобального Периметра: не любое сочетание индексов CPI и П является допустимым («нулевой закон глобальной экономики»). Представленные данные позволяют в результате приблизиться к пониманию характера распределения стран на плоскости индексов {CPI, П} и к пониманию законов глобальной экономики, определяющим плотность этого распределения в разных группах Продуктивности.
Ключевые слова: мировая экономика; экономические индексы; масштабированный Индекс Продуктивности П; Индекс Восприятия Коррупции CPI; Глобальный Периметр; группа продуктивности.
Цитировать: Seidametova Z.S., Temnenko V.A. Global Economy 2022 in country-size-independent indices. II. Two-dimensional distribution of countries on the plane {the Corruption Perception Index CPI, the Scaled Economic Productivity П} // KANT. – 2024. – №1(50). – С. 91-98. EDN: FCWWUN. DOI: 10.24923/2222-243X.2024-50.15
Seidametova Zarema Seidalievna, DSc of Pedagogical sciences, Professor
Temnenko Valerii Anatolievich, Ph.D. of Physics and Mathematical sciences, Associate Professor
Fevzi Yakubov Crimean Engineering-Pedagogical University, Simferopol, RC
The purpose of the research is to construct and describe a two-dimensional distribution of countries on the plane of economic indices {CPI, П} according to statistical data for 2022, highlighting the countries of the Global Perimeter located on the periphery of the area occupied by countries, and highlighting the countries belonging to the nucleus of each П-group of productivity; highlight the countries belonging to the perimeter of the П-group nuclei and the inner region of the П-group nuclei. The scientific novelty lies in the very identification of the fact of the existence of the Global Perimeter: not any combination of the CPI and П indices is acceptable (“zero law of the global economy”). The presented data allows to make it possible, as a result, to come closer to understanding the nature of the distribution of countries on the plane of indices {CPI, П} and to understanding the laws of the global economy that determine the density of this distribution in different Productivity groups.
Keywords: world economy; economic indices; scaled Productivity Index П; Corruption Perception Index CPI; Global Perimeter; productivity group.
УДК 339.97:330.43
ВАК РФ 5.2.5
Seidametova Z.S., Temnenko V.A.
Global Economy 2022 in country-size-independent indices. II. Two-dimensional distribution of countries on the plane {the Corruption Perception Index CPI, the Scaled Economic Productivity П}
Introduction
The previous paper presents one-dimensional distributions of 2022 countries by four key economic indices. These four indices form two pairs, convenient for a minimal statistical description of the global economy [1]. The first pair is a pair of basic economic indices {the Corruption Perception Index CPI, the Scaled Economic Productivity П}.
The term “basic” here means that these indices are borrowed from international databases either unchanged (Index CPI, the source of which is the database [2]), or after a non-linear monotonic scaling transformation that does not change the ranking of countries on this index, but compresses index change interval (Economic Productivity Index П, the source of which is the database [3]).
Index CPI is a hybrid discrete expert index, determined in integer points on a hundred-point scale. This index provides an assessment of the level of corruption in a country: the higher the CPI value, the lower the level of corruption.
The second index in this pair of basic indices is the scaled Economic Productivity П, defined as follows [1]:
П=〖10〗^2∙∜((GDP/PC)/max{GDP/PC} ), (1)
where GDP/PC is the Gross Domestic Product per Capita, expressed in current US dollars, and max {GDP/PC} is the maximum value of GDP/PC achieved in the same year in some country in the world.
Purpose of the paper: to study and describe the two-dimensional distribution of countries in 2022 on the plane of indices {CPI, П}. This goal structures the following tasks: 1) construct the distribution of countries on the {CPI, П} plane; 2) define the concept of the “Global Perimeter” and provide a list of countries of the “Global Perimeter”; 3) determine the economic meaning of the existence of the Global Perimeter; 4) indicate Productivity Groups on the {CPI, П} plane; 5) define the concept of the nucleus of the Productivity Group and the concept of the “Framing Necklace” for the nuclei of the Productivity Groups; 6) provide a list of countries of the “Framing Necklace”; 7) provide a list of countries belonging to the nuclei of the Productivity Groups.
Electronic appendices № 1 (https://t.ly/Inpqj) and № 2 (https://t.ly/oZh5p) to this paper provide information on the Scaled Productivity П and the Corruption Perceptions Index CPI in 2022. Each list contains 169 countries. The first list is ordered in descending order by Productivity П, the second list is ordered in descending order by CPI. All figures and tables in the paper are based on these Appendices.
Main part.
Global Swarm and Global Perimeter. Fig. 1 shows the distribution of countries on the plane of indices {CPI, П}. We will call the entire set of countries represented by the dots in this figure the “Global Swarm”. The Global Swarm contains all countries for which the CPI and index П values are known in 2022.
The countries of the Global Swarm are not distributed over the entire square of size 100 100 on the plane {CPI, П}, but occupy some limited and clearly defined area. Let us introduce the concept of “Global Perimeter” (GP) for the Global Swarm of countries.
The Global Perimeter is a closed convex broken line on the plane {CPI, П}, passing through some countries-vertices of this broken line so that all countries of the Global Swarm are on one side of each segment connecting two adjacent vertices inside the area surrounded by the Global Perimeter or on the Global Perimeter itself.
Fig. 1. Distribution of countries on the plane of indices {CPI, П} in 2022: Countries of the Global Perimeter.
Countries belonging to GP in Fig. 1 are designated by their three-letter ISO-3 codes [4]. These GP countries are shown separately in Fig. 2, which shows the full name of each country, its ISO-3 code and the values of the indices П and CPI. In Fig. 2 GP countries are presented in the form of two lists, compiled in descending order of П, going through the GP from the country with the highest П value (Luxembourg) to the country with the lowest П value (Burundi) clockwise (right list) and counterclockwise (left list). On the right are countries that have excessively high CPI values for their productivity groups. On the left are countries that have extremely low CPI values for their Productivity groups.
Fig. 2. Global Perimeter Countries (2022)
What is the economic rationale for the existence of the Global Perimeter? This meaning can be formulated as the “zero law of the Global Economy”:
“Not any combination of indices CPI and П is acceptable for Global Swarm countries”. For example, the combination {CPI=70, П=20} or {CPI=20, П=80} is not allowed. Such combinations are outside the Global Perimeter.
Formulating this “zero law” we can say that:
For any CPI (〖CPI〗^-<CPI<〖CPI〗^+), where 〖CPI〗^-≃CPI (Somalia)=12 and 〖CPI〗^+≃CPI (Denmark)=90, there are two maximum possible values of П (П_min and П_max), depending on CPI, such that for any country with a given CPI value it is possible only the Productivity value П on the interval П_minП П_max.
In exactly the same way, this “zero law” can be formulated in the language of restrictions for CPI (above and below) for a given П.
In a more abstract form, the “zero law” of the Global Economy can be formulated as follows:
There is some “State Function” Φdepending on the indices CPI and П, such that, for any country in the Global Swarm Φ(CPI, П)>0, and the equation Φ(CPI, П)=0 defines a closed convex curve (Global Perimeter) on the plane {CPI, П}.
"Global Perimeter" in Fig. 1 is some approximation of this ideal smooth perimeter using a finite set of chords. But this perimeter in the form of a closed convex broken line is an empirical object, and an ideal smooth perimeter is some kind of theoretical abstraction.
Productivity groups on the {CPI, П} plane. In the previous paper, when discussing the one-dimensional distribution of countries by Productivity П, the entire interval of change in П was divided into six discrete levels of Productivity. These levels are named in descending order of П values: 1) “Hot”, 2) “Warm”, 3) “UpperCold”, 4) “MiddleCold”, 5) “LowCold”, 6) “LDC” (the “Least Developed Countries”). Countries that belong to the same level of Productivity in terms of П values are called “Productivity Group” or “П-Group”. The set of countries belonging to the “UpperCold”, “MiddleCold”, “LowCold” and “LDC” levels are called “cold economies”. Countries belonging to the “Hot” level are called “hot economies”. Countries belonging to the “Warm” level are called “warm economies”. The paper [5] notes that “hot” and “warm” economies together form the so-called. “Global North”, and “cold” economies form the so-called “Global South”.
In Fig. 3 shows the location of Productivity groups on the plane {CPI, П}. The broken line for each П-group shows its perimeter on this plane. In this figure the dotted line shows the regression line for the Global Swarm:
П=k∙CPI+d, (2)
where
k=0.8475; d=13.952. (3)
The coefficient of determination R^2 for the linear regression equation (2) is quite high:
R^2=0.6986. (4)
This coefficient value R^2 shows that the linear statistical relationship (2) is expressed quite confidently, but the statistical spread of points relative to line (2) is not small. For some П-groups (not all), the perimeter of the П-group is greatly stretched to the right and left by the countries of the Global Perimeter.
Fig. 3. Distribution of countries on the plane of indices {CPI, П}: Productivity Groups.
It should be noted that linear regression (2) with statistical parameters (3) and (4) is not uniformly suitable for all parts of the Global Swarm. According to our calculations for the “Top 100” subset, consisting of one hundred countries belonging to the top part of the productivity ranking, the linear regression equation (2) has the following statistical parameters:
k=0.6592; d=28.217; R^2=0.6433. (5)
The “tail” of the productivity distribution, i.e. countries that have in the electronic appendix №1 (https://t.ly/Inpqj) numbers n≥101have completely different statistical characteristics:
k=0.2433; d=26.426; R^2=0.1501. (6)
Statistical characteristics (5) and (6) show that the linear regression equation (2) is a very poor approximation of the statistical relationship between CPI and П for the “tail” of the distribution, but a fairly satisfactory approximation of such a relationship for the “upper” part of the distribution (“Top 100”).
Productivity Nuclei and Framing Necklace. We can try to isolate some compact nucleus from each Productivity group if, when constructing Fig. 3, we discard in each П-group the countries of the Global Perimeter, and then also those countries that, after discarding the countries of the Global Perimeter, turned out to be too far from the regression line (2), deviating to the right, towards excessively large CPIs, or to the left, towards excessively small CPIs. We will call these excessively far deviating countries “Framing Necklace”. Countries of the Global Perimeter are marked in Fig. 4 with a cross (), and the countries of the Framing Necklace are indicated by numbers. The country numbering of the left and right parts of the Framing Necklace are independent. Those countries that remained at the П-level after the separation of the GP and FN countries form the nucleus of the Productivity group. Fig. 4 shows the perimeter of each nucleus of the П-group. The names of the П-groups are inscribed. Table 1 provides a list of countries that belong to the left (L) and right (R) parts of the Framing Necklace. The country numbers in this table correspond to the country numbers of the Framing Necklace in fig. 4. The table shows the name of the countries, ISO-3 code, П-level (abbreviated name), index П, Index CPI.
Fig. 4. Distribution of countries on the plane of indices {CPI, П} in 2022. Nuclei of productivity groups and countries of the “Framing Necklace”.
– countries of the Global Perimeter.
Table 1. Countries of the Framing Necklace for the nuclei of Productivity groups 2022.
(L – left side of FN, R – right side of FN, country numbers correspond to Fig. 4))
L R
№ Country Name ISO-3 П-level П CPI № Country Name ISO-3 П-level П CPI
1 Israel ISR H 81.09 63 1 Finland FIN H 79.51 87
2 Bahrain BHR W 69.88 44 2 Japan JPN W 71.91 73
3 Guyana GUY W 62.25 40 3 Estonia EST W 68.80 74
4 Russia RUS UC 59.02 28 4 Uruguay URY W 63.84 74
5 Azerbaijan AZE UC 49.74 23 5 Seychelles SYC UC 59.53 70
6 Libya LBY UC 48.01 17 6 Chile CHL UC 59.03 67
7 Iraq IRQ UC 46.35 23 7 St.Vincent a. the Gren. VCT UC 51.83 60
8 Guatemala GTM MC 45.61 24 8 Botswana BWA UC 49.74 60
9 Iran IRN MC 43.16 25 9 Fiji FJI MC 45.28 53
10 Honduras HND MC 39.38 23 10 Cabo Verde CPV MC 41.92 60
11 Nicaragua NIC LC 36.55 19 11 Vanuatu VUT MC 39.28 48
12 Haiti HTI LC 34.29 17 12 Sao Tome a. the Prin. STP LC 37.14 45
13 Comoros COM LC 32.92 19 13 Ghana GHA LC 36.22 43
14 Yemen YEM LDC 27.05 16 14 Senegal SEN LC 33.53 43
15 Benin BEN LC 31.86 43
16 Burkina Faso BFA LDC 28.49 42
Countries belonging to the Productivity nuclei: the perimeter of the nucleus and the inner area of the nucleus. When presenting lists of countries belonging to the nuclei of П-groups, we will use the following scheme: we will consider separately the countries on the perimeter of the nucleus and the countries located in the inner region of the nucleus. It is convenient to present the perimeter countries in the form of two lists (left and right lists) in descending order of index П, from maximum value to minimum. Countries located within the nucleus will be presented in the form of a separate list in descending order of index П.
We do not know at the moment how useful this division of the nucleus countries into the perimeter and the central region is, but we hope that it can bring some order, some clarity to the chaos of the arrangement of countries on the plane {CPI, П}. “Bringing clarity to chaos” was once put by Voltaire in praise of Isaac Newton. This bringing of clarity is both a challenge and a delight for any researcher.
“Hot” nucleus countries. The countries of the hot nucleus perimeter are shown in Fig. 5. Countries located inside the “hot” nucleus are shown in table 2. For each country its ISO-3 code and indices П and CPI are given.
Fig. 5. Countries on the perimeter of the “hot” nucleus (2022).
Table 2. Countries belonging to the inner hot nucleus region (2022).
№ Country Name ISO-3 П CPI
1 Iceland ISL 87.14 74
2 Australia AUS 84.51 75
3 Netherlands NLD 81.58 80
4 Canada CAN 81.20 74
5 Austria AUT 80.13 71
6 Belgium BEL 79.14 73
7 Hong Kong SAR HKG 78.90 76
8 United Kingdom GBR 77.60 73
If we tried to construct the state function Ф(CPI, П) in the form of a quantity proportional to the number of countries per unit area of the plane {CPI, П}, then from fig. 4, fig. 5 and table 2, it can be estimated (by order of magnitude) that this density should decrease several times from a certain conventional center of the nucleus to its perimeter and decrease further to the FN and GP zone.
Countries of the “warm” nucleus. The countries of the perimeter of the “warm” nucleus are shown in fig. 6. Countries located in the inner region of the “warm” nucleus are shown in table 3. Croatia, given in table 3, is very close to the perimeter of the nucleus.
Fig. 6. Countries on the perimeter of the “warm” nucleus (2022).
Table 3. Countries belonging to the inner region of the “warm” nucleus (2022).
№ Country Name ISO-3 П CPI
1 Cyprus CYP 70.53 52
2 Saudi Arabia SAU 70.05 51
3 Slovenia SVN 69.48 56
4 Spain ESP 69.41 60
5 Czechia CZE 68.38 56
6 Lithuania LTU 66.57 62
7 Portugal PRT 66.20 62
8 Latvia LVA 64.48 59
9 Slovak Rep. SVK 64.04 53
10 Greece GRC 63.64 52
11 Croatia HRV 61.78 50
For the П-group Warm, according to these data, as well as for the П-group Hot, one can see that the density of countries per unit area falls from a certain conventional center of the nucleus to its Perimeter and then falls further towards the “Framing Necklace” and “Global Perimeter” zone.
Countries of the nucleus of the П-group “UpperCold”. The perimeter countries of the nucleus of the П-group “UpperCold” are presented in fig. 7. Countries located in the inner region of the nucleus of the П-group “UpperCold” shown in table 4.
Fig. 7. Countries on the perimeter of the nucleus of the П-group “UpperCold” (2022).
Table 4. Countries located in the inner nucleus of the “UpperCold” П-group (2022).
№ Country Name ISO-3 П CPI
1 Bulgaria BGR 57.45 43
2 Argentina ARG. 57.36 38
3 China CHN 56.32 45
4 Malaysia MYS. 55.47 47
5 Maldives MDV 55.29 40
6 Kazakhstan KAZ 54.61 36
7 Turkiye TUR 53.83 36
8 Mauritius MUS 53.32 50
9 Dominican Rep. DOM 53.19 32
10 Grenada GRD 53.05 52
11 Montenegro MNE 52.89 45
12 Serbia SRB 52.21 36
13 Brazil BRA. 51.54 38
14 Dominica DMA 50.79 55
15 Belarus BLR 50.00 39
16 Bosnia and Herzegovina BIH 49.49 34
17 Peru PER 48.72 36
18 Armenia ARM 48.53 46
19 Thailand THA 48.35 36
20 Albania ALB 48.16 36
21 South Africa ZAF 48.12 43
22 Colombia COL 47.85 39
23 North Macedonia MKD 47.78 40
24 Ecuador ECU 47.42 36
Dominica, shown in this table, is very close to the perimeter of the “UpperCold” П-group.
Countries of the nucleus of the П-group “MiddleCold”. This П-group is in a sense “almost hollow”: there are more countries on the perimeter of the group than inside the perimeter. Countries belonging to the perimeter of the П-group are shown in fig. 8, and the countries located inside the perimeter are given in table 5.
Fig. 8. Countries located on the perimeter of the nucleus of the П-group “Middle Cold” (2022).
It should be noted that the young state of Kosovo has different ISO-3 codes in different WB and IMF documents. The codes used are XKX, UVK and KSV. We use the code KSV.
Table 5. Countries located in the inner nucleus of the П-group “Middle Cold” (2022).
№ Country Name ISO-3 П CPI
1 Mongolia MNG 44.48 33
2 Indonesia IDN 44.11 34
3 Ukraine UKR 43.52 33
4 Algeria DZA 42.88 33
5 Vietnam VNM 42.60 42
6 Tunisia TUN 41.57 40
7 Bolivia BOL 40.86 31
8 Philippines PHL 40.79 33
In this П-group, only 5 countries have a CPIof 40, and of these, only 2 countries have a CPI>45. We noted earlier [6] that for low-productivity countries with EPI4 (i.e. П44.72) with high and even moderate corruption (CPI<45), the Index CPI may not be a good indicator of the state of society. In any case, the statistical trend of the relationship between the indices CPI and П for low-productivity countries differs significantly from the statistical relationship between these indices in the area of highly productive countries.
Countries belonging to the nucleus of the “LowCold” П-group (2022). Countries belonging to the perimeter of the П-group “LowCold” is shown in fig. 9, and the countries located in the inner region of this nucleus are shown in table 6.
Fig. 9. Countries located on the perimeter of the nucleus of the П-group “Low Cold” (2022).
Table 6. Countries located in the inner nucleus of the “Low Cold” П-group (2022).
№ Country Name ISO-3 П CPI
1 Uzbekistan UZB 36.54 31
2 Mauritania MRT 36.28 30
3 Nigeria NGA 36.26 24
4 Kenya KEN 35.90 32
5 Lao PDR LAO 35.85 31
6 Cambodia KHM 34.48 24
7 Kyrgyz Rep. KGZ 33.58 27
8 Pakistan PAK 33.52 27
9 Cameroon CMR 33.48 26
10 Guinea GIN 33.18 25
11 Zambia ZMB 32.94 33
12 Napal NPL 32.06 34
In this “LowCold” group, low economic productivity corresponds to low values of the Index CPI, i.e. very high level of corruption. Only three countries out of twelve nucleus countries, located on the right branch of the nucleus perimeter, have CPI40.
Nucleus countries of the LDC П-group. In total, there are 24 countries in the LDC П-group in 2022. Four of them belong to the Global Perimeter. Two countries belong to the Framing Necklace. There are 18 countries in the nucleus of this П-group. Eight of them are located on the perimeter of the LDC nucleus (fig. 10). Ten countries are located in the inner region of this nucleus (table 7).
Fig. 10. Countries belonging to the perimeter of the nucleus П-group LDC (2022).
Table 7. Countries located in the inner nucleus of the П-group LDC (2022).
№ Country Name ISO-3 П CPI
1 Myanmar MMR 30.51 23
2 Tajikistan TJK 30.22 24
3 Uganda U.G.A. 29.55 26
4 Togo TGO 29.19 30
5 Gambia, The GMB 28.55 34
6 Mali MLI 28.49 28
7 Guinea-Bissau GNB 27.99 21
8 Liberia LBR 27.79 26
9 Mozambique MOZ 25.58 26
10 Madagascar MDG 25.14 26
This list includes 8 poorest countries of Africa and 2 poorest countries of Asia. Another Asian country, Afghanistan, is usually present in the LDC group. But the GDP/PC value for 2022 is unknown for this country.
Conclusions
The paper describes in detail the distribution of the countries of the Global Swarm on the plane of economic indices {CPI, П}. This description pursued the goal of introducing some order, some clarity into the chaos of the two-dimensional distribution of countries on this plane. The Global Perimeter of country distribution is highlighted. The “zero law” of the global economy has been formulated: not any combination of the level of corruption and economic productivity is possible. The concept of the “Framing Necklace” is defined as a set of countries with excessively low and excessively high Index CPI values for each level of Productivity (П-level) after discarding the countries of the Global Perimeter. The concept of the nucleus of a productivity group is defined. Lists of countries belonging to the nuclei of all six productivity groups are provided. These lists are compiled separately for the countries on the perimeter of each nucleus and for the countries belonging to the inner region of each nucleus. All this painstaking classification work based on data from one year (2022) can create the basis for subsequent study of the dynamics of the structure of the Global Swarm and identifying the quantitative form of the empirical laws of the Global Economy.
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