The World in economic indices depending on a country's size. IX. The Military levels Текст научной статьи по специальности «Экономика и бизнес»

Мир в экономических индексах, зависящих от размера страны.

IX. Милитарные уровни

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 – разработать понятийный аппарат и метод для сопоставления милитарных возможностей стран с их экономическими и демографическими возможностями. Для достижения этой цели выполнена шестиуровневая дискретизация оси Милитарного Индекса MI на дискретные уровни милитарного потенциала. Эта дискретизация учитывает особенности и детали одномерного распределения стран по Милитарному Индексу MI. Научная новизна заключается в конструировании Глобальной Матрицы Связи милитарного потенциала с экономическим потенциалом 〖МР〗_αβ и Глобальной Матрицы Связи милитарного потенциала с демографическим потенциалом 〖МD〗_αβ. Изучение этих матриц выявляет в результате фундаментальный закон доминирования главной диагонали матрицы 〖МР〗_αβ и менее четко выраженный закон диагонального доминирования матрицы 〖МD〗_αβ. Эти законы означают, что для большинства стран милитарный потенциал определяется экономическим потенциалом (и, в меньшей степени – демографическим потенциалом).

Ключевые слова: мировая экономика; экономические индексы; Милитарный Индекс MI; милитарный потенциал; Продуктовый Индекс PI; экономический потенциал; Демографический Индекс DI; демографический потенциал.

Цитировать: Seidametova Z.S., Temnenko V.A. The World in economic indices depending on a country’s size. IX. The Military levels// KANT. – 2023. – №1(46). – С. 80-85. EDN: POEJPR. DOI: 10.24923/2222-243X.2023-46.14

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 study is to develop a conceptual apparatus and a method for comparing the military capabilities of countries with their economic and demographic capabilities. To achieve this goal, a six-level discretization of the Military Index MI axis into discrete levels of military potential was performed. This discretization takes into account the features and details of the one-dimensional distribution of countries according to the Military Index MI. The scientific novelty of the research lies in the construction of the Global Matrix of Relationship between military potential and economic potential 〖МР〗_αβ and the Global Matrix of Relationship between military potential and demographic potential 〖МD〗_αβ. The study of these matrices reveals, as a result, the fundamental law of dominance of the main diagonal of the matrix 〖МР〗_αβ and a less clearly expressed the law of the diagonal dominance of the matrix 〖МD〗_αβ. These laws mean that for most countries, military potential is determined by economic potential (and, to a lesser extent, demographic potential).

Keywords: world economy; economic indices; the Military Index MI; military potential; the Product Index PI; economic potential; the Demographic Index DI; demographic potential.

УДК 339.97:330.43

5.2.5

Seidametova Z.S., Temnenko V.A.

The World in economic indices depending on a country’s size.

IX. The Military levels

Introduction

In the papers [1], [2] the concept of the Military Index MI was introduced and the distribution of countries according to this index was studied.

The purpose of this study is to develop a conceptual apparatus and method for comparing the military capabilities of countries with their economic and demographic capabilities, treating the Military Index MI as one of the economic indices, just as important as the Product Index PI or the Demographic Index DI. This goal structures the following tasks: 1) to discretize the continuous index MI into discrete levels of military potential, taking into account the details and features of the one-dimensional distribution of countries according to the index MI and taking into account the previously performed discretization of the Product Index PI and the discretization of the Demographic Index DI into discrete levels of demographic potential; 2) to construct the Global Matrix of Relations between military potential and economic potential 〖МР〗_αβ, presenting the matrix 〖МР〗_αβ as a numeric object and as a “list of lists” of countries belonging to each element of the matrix; 3) identify and describe the properties of the matrix 〖МР〗_αβ (the law of dominance of the main diagonal); 4) to construct the Global Matrix of Relations between military potential and demographic potential 〖МD〗_αβ, presenting the matrix 〖МD〗_αβ as a numeric object and as a “list of lists”; 5) identify and describe the properties of the matrix 〖МD〗_αβ (the law of diagonal dominance). The theoretical basis of this study is the papers [1] and [2] and the materials used in them. The practical significance of this study is to identify the global laws of connection between the country’s military potential and its economic and demographic potentials and to identify countries that are insufficiently or excessively militarized according to economic or demographic criteria.

Main part.

The description of military levels. When we thinking about the global economy, it is convenient to associate each country with a group of such countries that have relatively similar economic indices – for example, the Economic Productivity Index EPI, or the Product Index PI, or the Demographic Index DI. Countries that are similar in terms of the index EPI, we combined into EPI-groups, or “levels of productivity”. The names of these productivity levels, in descending order of characteristic EPI values, are as follows: 1) Hot, 2) Warm, 3) UpperCold, 4) MiddleCold, 5) LowCold, 6) LDC. The abbreviation LDC stands for the Least Developed Countries. All countries that are not included in the Hot and Warm EPI groups are referred to as “cold” economies. A detailed description of the EPI-groups of the global economy in pre-Covid 2019 is presented in papers [3], [4], [5]. Changes in the EPI groups of the global economy caused by the 2020 pandemic shake-up are described in [6]. The method of “interval classification” of countries according to the levels of the Product Index PI and the Demographic Index DI is described in [7], [8]. For each of these indices, six discrete levels were introduced in [7]. These levels, in descending order of these indices, have the following names in [7]: 1) SuperGiant, 2) Giant, 3) Big, 4) Medium, 5) Small, 6) VerySmall. Product Index PI is determined by the country’s GDP. Demographic Index DI is determined by the population of the country. Formulas for calculating these indices are given in [7]. To calculate these indices, we used data for 2021 from the IMF database [9].

It is convenient to use such terminology. We will talk about countries that are at the same discrete level of the Product Index PI as countries that have the same economic potential; the name of this level of economic potential will coincide with the name of the discrete Product Level. We will talk about countries that are at the same discrete level of the Demographic Index as having the same demographic potential; the name of this potential level will be identified with the name of the corresponding discrete level of the Demographic Index DI. In other words, we use the term “potential” (economic or demographic) as a descriptive, qualitative, discrete term. The Product Index PI is a continuous quantitative characteristic of a country, determined from annual WB or IMF statistics. Economic potential is a discrete qualitative characteristic of a country, determined by the index PI using the discretization procedure by the level PI [7].

Papers [7] and [8] noted that for any country, the level of the size of the economy (i.e., economic potential) and the level of the size of the country (i.e., demographic potential) may or may not coincide. If these levels do not match, then the difference between the level numbers is small (1 or 2 levels). This statement is called in [6] the law of diagonal dominance of the Global Matrix of Scales.

Developing the descriptive idea of discrete levels of economic and demographic potentials, here we introduce the same six-step interval scale of the levels of the Military Index (or military levels, or levels of the Military Potential) with the preservation of the names of the levels adopted in papers [7] and [8].

We will say that a country belongs to the MI-SuperGiant military level if the country's Military Index exceeds India’s Military Index (MI_IND=44.13). The electronic appendix to paper [1] (https://bit.ly/3SviXZL) provides a list of countries with known Military Indices 2021. This list is sorted by descending MI index. In addition to the index MI, for each country in this list, the economic indices PI, DI, EPI 2021, as well as the MI/PI and MI/DI ratios are indicated.

In 2021, there were three countries at the MI-SuperGiant level: USA (MI=100), Russia (MI=89.64), China (MI=87.75). Two of the three countries, USA and China, belong to the SuperGiant level in terms of both economic potential and demographic potential. Russia, in accordance with its PI and DI index values, belongs to the Giant level [6]. The military potential exceeds its economic and demographic potential. In such a situation, one can speak of an excessive militarization of the country.

We will say that a country belongs to the military level MI-Giant (or “a country is a military giant”) if its Military Index MI is in the interval 10<MIMI_IND=44.13.

In 2021 21 countries belonged to this level. Thirteen countries of them belong to the Giant level according to the value of the Product Index PI: for these thirteen countries there is a correspondence between military potential and economic potential. One country belonging to the MI-Giant level belongs to the SuperGiant level (India) in terms of demographic potential. Accordingly, we can talk about the insufficient of militarization of India (by demographic criteria).

The eight countries with MI-Giant military capability belong to the Giant level of the demographic index. For these countries, there is a correspondence between military and demographic potential. For some countries that have MI-Giant military potential, one can speak of excessive militarization either by economic criteria or by demographic criteria. The five MI-Giant military-level countries are excessively militarized by both of these criteria, economic and demographic criteria. These are Israel (PI=2.09, DI=0.66, MI=16.08), Saudi Arabia (PI=3.62, DI=2.51, MI=14.19), Taiwan (PI=3.43, DI=1.66, MI=13.07), Ukraine (PI =0.86, DI=2.91, MI=12.87), Poland (PI=2.93, DI=2.68, MI=10.03).

We will say that a country belongs to the military level MI-Big (or “a country has a military potential of the MI-Big level”) if its military index MI is in the interval 5<MI10. In 2021, there were 28 countries at the military level of MI-Big.

We will say that a country belongs to the MI-Medium military level (or “a country has MI-Medium level military potential”) if its military index is in the interval 2<MI5. In 2021, 33 countries had MI-Medium level military potential. Most of these countries (21 countries) have an economic potential of Medium level. For these countries, military potential and economic potential correspond to each other. Five MI-Medium military-level countries can be considered insufficiently militarized by economic criteria (they belong to the Big economic level according to the PI index values). These include Denmark, Austria, Finland, Belgium and New Zealand. All these are highly developed countries. They create the military potential they desire without straining their economic possibilities. The seven MI-Big military-level countries can be considered excessively militarized by economic criteria. They belong to the Small level according to their PI values. These are Libya, Sudan, Jordan, Yemen, Bolivia, Chad and Georgia.

We will say that a country belongs to the military level MI-Small (or “a country has a military potential of the MI-Small level”) if its military index MI is in the interval 1<MI2. In 2021, there were 33 countries at the military level of MI-Small. Twenty-three of them have Small economic potential in terms of their PI values. For these countries, the military potential and economic potential are in accordance.

We will say that a country belongs to the MI-VerySmall military level (or “a country has a military potential of the MI-VerySmall level”) if its military index does not exceed 1% (MI1). In 2021, there were 19 countries at the military level of MI-VerySmall.

It is appropriate to recall that in 2021, 56 countries with known values of economic indices PI and DI were absent from The Global Firepower ranking [10], on the basis of which the value of the Military Index MI was calculated in the paper [1]. Nearly all of these fifty-six countries have small PI and DI economic indices, and most likely could have very small MI Military Index values.

Table 1 provides a summary of information about the six-level interval classification for the three economic indices PI, DI and MI. The interval classification according to the Product Index PI and the Demographic Index DI was introduced in the paper [7]. The interval classification of countries by levels of the MI Military Index is described above.

Table 1 - Interval levels of economic potential (according to the index PI), demographic potential (according to the index DI) and

military potential (according to the index MI)

Economic index

Level’s

number and name PI DI MI

1

SuperGiant 21.47=PI_JPN<PI100 19.27=DI_IND<DI100 44.13=MI_IND<MI100

2

Giant 5<PIPI_JPN 5<DIDI_IND 10<MIMI_IND

3

Big 1<PI5 1<DI5 5<MI10

4

Medium 0.2<PI1 0.2<DI1 2<MI5

5

Small 0.04<PI0.2 0.04<DI0.2 1<MI2

6

VerySmall PI0.04 DI0.04 MI1

Global Matrix of connection of military potential with economic potential. The relationship between military level and product level can be shown in a compact form by constructing the matrix 〖МР〗_αβ (16, 16). Each country with known indices PI and MI is characterized by two integers: its military level number in accordance with the military level scale described above, and its economic level number in accordance with table 1. The military level number is some condensed assessment of the country’s military capabilities. The economic level number is a concise assessment of a country’s economic capabilities. With the help of these two integer indices, it is possible to form the Global Matrix of the relationship between military potential and economic potential. We will denote this matrix as 〖МР〗_αβ. This matrix can be treated as a numeric object. An element of such a numerical matrix is the number of countries that have a military level number  and a product level number . Such a numerical matrix is presented in table 2.

Table 2 - Global MR-matrix as a numerical object (2021)

Economic potential’s levels

and names

Military potential’s

levels and names 1

SuperGiant 2

Giant 3

Big 4

Medium 5

Small 6

VerySmall

1

SuperGiant 2 1 0 0 0 0

2

Giant 0 13 7 1 0 0

3

Big 0 1 19 8 0 0

4

Medium 0 0 5 21 7 0

5

Small 0 0 1 6 23 3

6

VerySmall 0 0 0 2 7 10

For those countries that belong to the 〖МР〗_66 element, the position of the country in this element does not unambiguously indicate the ratio of the Military Index MI and the Product Index PI: at the VerySmall level, both indices are small, and the ratio of two small numbers can be both very small or sufficiently big. If we temporarily exclude 10 countries of the element 〖МР〗_66 from our analysis, then the remaining 127 countries obey the law of dominance of the main diagonal of the matrix: on the main diagonal (excluding the element 〖МР〗_66 there are 78 countries (more than 60%). For these countries, the military potential corresponds to the economic potential.

Nineteen countries belonging to the diagonal 〖МР〗_(α,α-1) (36) can be interpreted as “insufficiently militarized”. The military index of these countries is less than the range of values that their economic potential allows them to have.

Three countries belonging to the diagonal 〖МР〗_(α,α-2) (=5 и =6) can even be called “military careless”. The Military Indices of these military careless countries are much lower than the possible values that the economic potential of these countries generates. These are Ireland, Luxembourg and Panama.

Twenty-six countries belonging to the diagonal 〖МР〗_(α,α+1) (15) can be called excessively militarized. These countries maintain a level of military potential higher than their economic potential allows.

In the Global Matrix 〖МР〗_αβ there is only one country belonging to the element 〖МР〗_2,4. Its military potential in 2021 is two levels higher than its economic potential. This country (Ukraine) can be called the “super-militarized” country of 2021.

Countries belonging to the element 〖МР〗_66require special attention. Of these ten countries, six have an MI/PI ratio greater than twenty. Outside the 〖МР〗_66 element, countries with such a large MI/PI ratio also occur, but almost five times less frequently (17 countries out of 127). The country with the highest MI/PI ratio (Eritrea, MI/PI=101.37) belongs to the element 〖МР〗_66. Countries with a high MI/PI ratio maintain their desired military potential by significantly straining their economic capabilities.

According to the data provided in the electronic supplement to the paper [1] (https://bit.ly/3SviXZL), in 2021 there were only two countries with an MI/PI ratio less than one: Ireland (MI/PI=0.829) and Iceland (MI/PI=0.477). Iceland is the most peaceful country in the world: it has the lowest Military Index (MI=0.0528) and the lowest MI/PI ratio.

United States have an MI/PI ratio of one (MI=100, PI=100). Germany has an MI/PI ratio almost equal to one (MI/PI=0.990). It can be assumed that the MI/PI ratio equal to one sets the lower boundary of military security on the {PI, MI} plane.

The matrix 〖МР〗_αβ can be interpreted not only as given in table 2 a numeric object. This matrix is also a “list of lists”. Each element of such a “list of lists” contains a list of countries belonging to this element of the matrix. In the electronic appendix 1 (https://rb.gy/d0snyc) to this paper, the matrix 〖МР〗_αβ is presented as a “list of lists”. The countries within each element are arranged in descending order of military index MI.

Global Matrix of Relations between military potential and demographic potential. Let's build a matrix 〖МD〗_αβ (16, 16), which will display the relationship between the country's military potential and its demographic potential in the same way as the above matrix 〖МР〗_αβ displays the relationship between military and economic potentials.

In the matrix 〖МD〗_αβ, as in the 〖МР〗_αβ matrix, the rows correspond to military levels, arranged from top to bottom in descending order of level from SuperGiant to VerySmall. The columns in the 〖МD〗_αβ matrix correspond to demographic levels, from left to right in descending order from SuperGiant to VerySmall. In the electronic appendix 2 (https://rb.gy/hnelx5) to this paper, the matrix 〖МD〗_αβ is presented as a “list of lists”. An element of such a list matrix is a list of countries belonging to this element by a combination of military and demographic levels.

Table 3 presents the matrix 〖МD〗_αβ as a numeric object. Each element of such a matrix is equal to the number of countries belonging to this element.

Table 3. Global MD-matrix as a numeric object

Levels and names of

demographic potential

Levels and names of

military potential 1

SuperGiant 2

Giant 3

Big 4

Medium 5

Small 6

VerySmall

1

SuperGiant 2 1 0 0 0 0

2

Giant 1 8 12 0 0 0

3

Big 0 5 14 9 0 0

4

Medium 0 2 9 19 3 0

5

Small 0 0 14 14 5 0

6

VerySmall 0 0 3 7 8 1

The matrix 〖МD〗_αβ can be called diagonally dominant to a certain extent. Most of the countries are located on the main diagonal 〖МD〗_(α,α) (49 countries) and on the two adjacent diagonals 〖МD〗_(α,α-1) (37 countries) and 〖МD〗_(α,α+1) (25 countries). In total, 111 countries out of 137 are located on these three diagonals. This diagonal dominance means that the country's military potential is in some balance with its demographic potential. But this balance is not strict. This balance is diffuse. Countries with similar military indices can differ significantly in their demographic DI. The economic potential of the country affects its military potential more strongly and more severely than its demographic potential.

If we rebuild the list of countries with a known military index MI from the electronic supplement to paper [1] in descending order of MI/DI ratios, then it is easy to see that the first 20 countries from this list with MI/DI>10 all have a small demographic index DI (DI<1), and four of them have DI<0.1. It can be assumed that these countries with not very large populations form the military potential they desire, focusing mainly on their economic capabilities, without taking into account the limitations that are born of a low demographic potential. This approach can lead to high MI/DI values. Israel had the highest MI/DI value in 2021 (MI/DI=24.25). This country with a not very large population (DI=0.663) is in constant readiness for a possible attack by its densely populated neighbors and therefore maintains a very high value of the military index (MI=16.08), which makes Israel a military giant, although neither in terms of economic potential, nor in terms of demographic potential this country is not included in the Giant class. The second highest MI/DI in 2021 was Luxembourg (MI/DI=20.79), which does not appear to be in danger of being attacked from outside. But Luxembourg, being a champion in economic productivity (EPI=100), can afford to have the military potential it wants (MI=0.935), despite its small population (DI=0.045).

Ten of these twenty countries with a high MI/DI ratio belong to the world's most productive economies, which we call “hot economies” (EPI≥EPI_JPN=28.78, see eg [11]). Eight countries out of these twenty countries belong to the class of “warm economies” (11.9EPI<EPI_JPN). And only two countries from this list of 20 countries belong to the low-productive “cold economies”: Montenegro (EPI=6.84, MI/PI=34.26, MI/DI=19.66) and Suriname (EPI=3.42, MI/PI=45.12, MI/DI=12.97). Only these two countries of all countries with a high MI/DI value can be called “excessively militarized”. They have built their military capabilities as independent entities based on real or imagined military threats, regardless of the constraints imposed by the low economic productivity, weak economy and low demographic potential of these two countries.

Conclusions

The paper provides a detailed description of the military levels. Military levels are a six-level classification of countries with a known military index MI according to some discrete levels of military potential. This discrete scale of levels is based on the details of the one-dimensional distribution of countries according to the military index MI. This distribution is presented in the paper [1] in the form of a Pareto diagram and a histogram.

The paper describes the Global Matrix of Relations between military potential and economic potential 〖МР〗_αβ and the Global Matrix of Relations between military potential and demographic potential 〖МD〗_αβ. The fulfillment of the law of dominance of the main diagonal in the matrix 〖МР〗_αβ is revealed. This law means that most countries build their military potential in accordance with their economic capabilities. For the 〖МD〗_αβ matrix, a similar but less categorical law of diagonal dominance is formulated: the demographic potential of a country affects the formation of its military potential, but in a less rigid and binding form than its economic potential. Highly developed countries build the military potential they want, without attaching much importance to the restrictions that a not very large population can impose.

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