CC BY
1DOI: 10.29141/2658-5081-2022-23-1-5
JEL classification: C10, 010, R10
Pavel I. Blus
Perm State University, Perm, Russia
Rustam V. Plotnikov Perm National Research Polytechnic University, Perm, Russia
Abstract. Growing interregional inequality in the Russian economy adversely affects the territorial integrity of the country's socioeconomic system and limits the possibilities for the economic development of territories. The research aims to design a new method for clustering Russia's macroregions with a view to reducing spatial heterogeneity by exploiting the potential of interregional interaction. The new economic geography, regional and spatial economics constitute the methodological basis of the study. The research applies multidimensional statistical methods. Based on the calculation of the Theil index the paper investigates the unevenness of regional development in federal districts and macroregions, which are specified in the Strategy for spatial development of the Russian Federation until 2025. The paper concludes that the suggested territorial organisation of the national economy based on the identification of the 12 macroregions does not quite help reduce the socioeconomic differences between regions keeping them trapped in the current heterogeneity. The paper develops a method for delineating the macroregions that decreases their spatial heterogeneity and favours interregional interaction in order to reduce the differences in the territorial development. The method relies on a gravity model and cluster analysis as tools used by spatial economics.
Keywords: strategic planning; spatial development; identification of functional economic regions; intraregional inequality; macroregions.
For citation: Blus P. I., Plotnikov R.V. (2022). Spatial clustering for reducing intraregional unevenness. Journal of New Economy, vol. 23, no. 1, pp. 88-108. DOI: 10.29141/2658-5081-2022-23-1-5 Received August 5, 2021
Improving the quality of life of a society is inextricably linked with the development of territories. Researchers and practitioners pay special attention to the spatial distribution of economic and social parameters, the formation of social economic communities, mechanisms and results of their interaction, which leads to the emergence
Spatial clustering for reducing intraregional unevenness
Introduction
of many strategies for the territorial organisation and location of production. The spatial approach in the economy fulfills the most important task, specifically, maximises the contribution of a single region to the development of larger systems.
The consequences of interregional inequality include differences in socioeconomic development of subjects, lack and uneven distribution of economic growth points, increased burden on the working-age citizens, migration outflow of the population from a number of strategically important subjects for the state, intensification of agglomeration processes and economic weakening of the periphery, low-productivity low-tech industries and an insignificant level of entrepreneurial activity of the population, and a low level of development of transport infrastructure. They in turn undermine the integrity of the social economic system of the country and decrease the pace of economic development of the territories. Moreover, studies show that interregional inequality in the long term contributes to an increase in the number and intensity of internal conflicts and violence [Ezcurra, 2019; Lee, Rogers, 2019; Tolmachev et al., 2019; Zabelina, 2021].
All these results of the economic reforms of the 1990s, expressed in the disruption of interregional ties and disintegration processes, are not leveled by the Strategy for spatial development of the Russian Federation until 20251 (hereinafter referred to as the Strategy) when determining the key directions of the corresponding development. They keep on existing and even have intensified.
For example, large-scale industrial production still concentrates in a relatively small number of economic centers [Kolomak, 2015]; secondly, transport links between the constituent entities of the Russian Federation remain weak and the some territories remain inaccessible, especially at certain times of the year [Volkova, 2020]; thirdly, the social economic development of the regions is imbalanced [Glazyrina, Zabelina, 2021].
The strategy provides for the territorial organisation of the Russian economy, based on the economic specialisation of its constituent entities. The latter, in turn, will be united into 12 macroregions, which ultimately should intensify the interaction of subjects within these associations and reduce the level of differentiation of their social economic development. However, the Strategy does not substantiate the method for the proposed division into macroregions, which does not allow us to consider this division scientifically justified. At the same time, it is possible that adjustments may be made to the proposed new grid of the spatial organisation of Russia's macroregions.
The purpose of the study is to develop a method for clustering macroregions as a tool to reduce spatial heterogeneity by using the potential of interregional interaction. For
1 On approval of the Strategy for spatial development of the Russian Federation until 2025: Decree of the Government of the Russian Federation of February 13, 2019 no. 207-r (as amended on March 23, 2021). (In Russ.)
this, the following objectives were accomplished: (i) quantitative data indicating the uneven spatial organisation of the Russian Federation was analysed; (ii) a method for clustering the regions of the Russian Federation focused on reducing the spatial differentiation of territorial development was developed; (iii) the efficiency of the method was evaluated by testing it with the statistical data for Russia's constituent entities.
The most significant and effective methods for studying the unevenness of the spatial organisation of the Russian Federation are multidimensional statistical methods, methods and models of spatial econometrics. Therefore, to assess the interregional inequality of the Russian Federation, the Theil index and interregional differentiation are calculated. The method of clustering used in this study is based on the gravity model and cluster analysis.
Prerequisites for Russia's uneven spatial development
The development of society is inextricably bound up with the development of territories and the economy. Currently, managers and researchers focus on the spatial and economic organisation of the state and its regions, consequently, in modern economic theory, there are many strategies for the territorial organisation and location of production.
Today, there is an increase in the role of regional science, leading to the need of strengthening the theoretical basis of identification of functional economic regions. There is a need for an in-depth study of the influence of geographic, climatic, demographic and sociocultural aspects on the possibility of maximising the use of available factors of production.
We emphasise that space should be studied from two positions: economic and social, since this contributes to the development of the regional economics in the interests of not only science and management, but also helps ensure a high quality of life for the country's population.
Within the framework of this study, the issues of the spatial organisation of the economy and the social economic development of space are considered from the standpoint of the cluster approach, which, in the transition to an innovative socially oriented economy, becomes the most principal component of the economic growth of regions.
The distinctive feature of Russia's modern spatial organisation is a polycentric character with uneven settlement across territories. In the political aspect, since the beginning of the 2000s the administrative-territorial division is represented by federal districts, the system of which has formed due to the need to strengthen the vertical of power. These units do not have economic self-sufficiency and are characterised by a high level of social economic differences.
Currently, the network of federal districts that has existed for 20 years as units of strategic planning is overlaid with a network of macroregions that is territorially different from it. It is important to note that among the spatial trends in the context of federal districts, there are sharp interregional differences [Kolomak, 2010]. In order to reduce these differences in the level and quality of life, increase the rates of economic growth and ensure national economic security, a Strategy was approved in February 2019 that brought about 12 macroregions (unlike federal districts, this division is done according to economic principles). With the help of this measure, the federal authorities hope to ensure the sustainable spatial development of the Russian Federation; however, the method for identifying macroregions is not presented in the Strategy [Bukhvald, Kolchugina, 2019].
Thus, there is a need to assess the administrative-territorial division of modern Russia into federal districts and macroregions from the standpoint of the heterogeneity of socio-economic development.
For the purposes of further research, we will choose GRP per capita as an indicator, since it is used by the majority of both Russian [Chitaya, 2007; Feoktistov, Karyukina, 2008; Vasilyeva, 2010; Baranov, 2012; Padisov, Volova, 2013; Ershov, 2016; Ayvazyan, Afanasyev, Kudrov, 2019] and foreign scientists [Ahrend, 2005; Carluer, 2005; Ledy-aeva, Linden, 2008] to assess interregional inequality.
Table 1 presents the results of the analysis of heterogeneity in terms of GRP per capita for 2018. According to data in Table 1, the differentiation is less significant in the context of macroregions: it ranges from 1.58 to 16.24, while in federal districts it ranges from 2.18 to 25.97.
Table 1. Differences between the federal districts of the Russian Federation
in terms of GRP per capita, 2018
Federal district GRP ratio GRP ratio
Federal district (between the poorest and richest subjects in the federal district) Macroregion (between the poorest and richest subjects in the macroregion)
Central 6.61 Central 6.61
Central Black Earth 1.58
Northwestern 25.97 Northwestern 3.18
Northern 15.32
Southern 2.40 Southern 2.40
North Caucasian 2.18 North Caucasian 2.18
Volga 2.36 Volga-Kama 2.36
Volga-Ural 1.58
Ural 16.24 Ural-Siberian 16.24
Northern 3.74 South Siberian 2.15
Angara-Yenisei 3.74
Far Eastern 7.78 Far Eastern 7.78
Note: the data in Tables 1-3 is calculated based on the information from Rosstat (www.rosstat.gov.ru).
A deeper analysis of spatial heterogeneity was carried out by the authors based on the calculation of the Theil index, which makes it possible to identify the contribution to the overall unevenness of various components and their groups [Moroshkina, 2020, p. 2314]. The Theil index is a relative indicator and, unlike the Gini coefficient, is characterised by separability. The components of the index allow us to consider the process of differentiation from the standpoint of various territorial entities. The general Theil index is the sum of the Theil indices characterising the existing differences in the context of federal districts and macroregions.
Mathematically, the Theil index is calculated using the following formula [Kolo-mak, 2013, p. 136]:
where Yr is the value of the variable in a region r; Y is the value of the variable throughout the Russian Federation (Y = £Rr = 1Y); R is the number of regions in the Russian Federation.
The Theil index varies from 0 to lnR. The extreme values correspond to absolute interregional equality (Yr = Y/R) and the concentration of all activity in one area, respectively. The higher the index value, the stronger the spatial differences between regions.
The separability property of the index makes it possible to divide the latter into factors associated with differences between macroregions and territories within each of them. At the same time, the intergroup component characterising the contribution of differences between federal districts (macroregions) is calculated using the formula [Kolomak, 2013, p. 137]:
where Ym is the value ofthe indicator for the fe der al district (macroregion) m Ym = =i Yr, Rm is the number of regions within the federal district (macroregion) m, M is the number of federal districts (macroregions).
The intra-group component that characterises the differences between subjects of the Russian Federation within a federal district (macroregion) is calculated using the formula [Kolomak, 2013, p. 137]:
(1)
(2)
T . . =
unffiin
within
Trn.
(3)
The Theil index for a federal district (macroregion) is calculated using the formula [Kolomak, 2013, p. 137]:
T =
* m
(4)
\RmJ
The calculation of the value of the total Theil index is carried out according to the formula:
T = Tbetween + Twithin. (5)
When analysing GRP per capita, the input data were the indicators of the Federal State Statistics Service of the Russian Federation for 2018 for 85 subjects of the federation. The territorial units are 8 federal districts and 12 macroregions.
The results of the structural analysis of the Theil index for the federal districts and macroregions of the Russian Federation are presented in Table 2.
Table 2. Structural analysis of the Theil index for GRP per capita for federal districts and macroregions of the Russian Federation, 2018
Indicator Federal districts Macroregions according to the Strategy Relative value of the indicator, % pertaining to T
Federal districts Macroregions according to the Strategy
Tbetween 0.1628 0.2411 33.98 50.32
Twithin 0.3163 0.2380 66.02 49.68
T 0.4791 0.4791 100 100
Analysis of the data in Table 2 indicates that the space of the Russian Federation divided into macroregions is more homogeneous, since the shares of Tbetween and Twithin relative to T are 50.32 and 49.68 %, respectively. At the same time, we note that the structure of the country's space divided into federal districts is characterised by the shares of Tbetween and Twithin relative to T , equal to 33.98 and 66.02 %, respectively. When considering the territory in terms of federal districts, the general interregional inequality is mainly determined by the differences in the levels of development of the constituent entities of the Russian Federation within the federal districts (intra-group component). However, the values of GRP per capita chosen as variables do not indicate a higher or lower level of social economic development of the territories.
Regional statistics publish the calculation of GRP per capita in nominal prices, without taking into account the significant difference in the cost of consumer goods and services. This way, their high cost offsets the higher incomes of the population of the northern and eastern regions of Russia [Grigoryev et al., 2018].
Therefore, a significant differentiation is evident in terms of the level of income and well-being of the regional population [Glushchenko, 2010; Sarbitova, Chistik, 2018; Piskun, Khokhlov, 2019]. Accordingly, the definition of the level of well-being based on the nominal income of the population does not reflect the real picture and needs to be adjusted.
In order to improve the objectivity of the assessment of the Theil index, it is necessary to adjust the values of GRP per capita in terms of purchasing power parity. As a variable, we chose GRP per capita modified by the purchasing power of income received, taking into account consumer market prices for 85 constituent entities of the Russian Federation for 2018. The consumer market price level characterises the subsistence minimum. One of the indicators used when adjusting GRP per capita for inter-territorial comparative analysis is the subsistence minimum, which reflects the level of prices in the consumer market in all regions of the Russian Federation. The value of the modified nominal GRP per capita is calculated for each region as follows [Savaley, 2017, p. 40]:
GRP»= S- (6)
where GRP* is the nominal GRP per capita in a specific i region, ISM* is the subsistence minimum index in a specific i region, calculated by normalising a series of data in relation to the national average.
The calculation of ISMi is carried out according to the following formula [Savaley, 2017, p. 39]:
average annual subsistence minimum in the / region , ч
-. (7)
average annual subsistence minimum in the country
If we pay attention to the regions of the 'first echelon' (10 subjects), we can identify a downward trend in GRP per capita, which is associated with a relative decline in the well-being of these regions due to an increase in the level of spending by the population. A completely different situation is observed in the case of the last ten regions of the ranking, where the GRP per capita indicators were adjusted upwards to reflect a decrease in the level of prices in the market. Table 3 presents the results of a structural analysis of the Theil index for GRP per capita for the federal districts and macrore-gions of the Russian Federation.
As follows from Table 3, in accordance with the Strategy the general interregional inequality is mainly due to the differences in the level of development of Russia's constituent entities within the macroregions (the intra-group component). This is also observed in the structure with federal districts.
Table 3. Structural analysis of the Theil index for GRP per capita adjusted for purchasing power parity of the population for federal districts and macroregions of the Russian Federation
Indicator Federal districts Macroregions according to the Strategy Relative value of the indicator, % pertaining to T
Federal districts Macroregions according to the Strategy
Tbetween 0.0753 0.1063 31.18 43.99
Twithin 0.1663 0.1353 68.82 56.01
T 0.2416 0.2416 100 100
The analysis of the Theil index for GRP per capita adjusted for purchasing power parity shows that the structure of the country's space divided into macroregions is heterogeneous. The calculations revealed that the value of the index of intra-group differentiation of the Strategy's macroregions is considerably higher than that of the macroregions obtained on the basis of GRP per capita in nominal prices. This allows us to speak about the inefficiency of the method proposed by the Ministry of Economic Development of the Russian Federation for identifying macroregions.
Method for spatial clustering of Russian regions
Based on the principles laid down in the Strategy for identifying macroregions, we developed own method for their clustering. Its implementation includes 3 stages.
At the first stage, statistical indicators were selected and sub-indices were calculated, characterising the principles of the formation of macroregions in accordance with the method of the Ministry of Economic Development of the Russian Federation:
1) territorial commonality of regions;
2) the potential for interregional interaction;
3) the presence of an administrative-territorial center of economic growth in the macroregion;
4) infrastructural connectivity of the subjects;
5) availability of social services for the population;
6) mechanisms for spatial development of the economy.
To take into account the basic principles (1st and 2nd), the values of the matrix of interaction forces between regions were calculated based on the gravity model. The choice of the model is explained by the fact that it considers both economic and social factors to describe the strength of interaction between territorial units, in our case, between the subjects of the Russian Federation [Lukermann, Porter, 1960]. In addition, the gravity model allows taking into consideration the spatial aspects of the location of industries and their connections, and is distinguished by simplicity and clarity. This tool is popular with scientists and practitioners when developing strategies for the development of territories of both countries and regions and municipalities.
The undoubted advantage of the gravity model with regard to Russia is that it takes into account the distance between territorial units, which is necessary owing to the scale of the country's territory. The use of this model is based on the assumption that the magnitude of the interaction is proportional to the product of the indicators of significance (value, number) of objects and inversely proportional to the distance between them.
We should highlight that the gravity model is not an ideal tool for identifying interregional links, since it is based on the hypothesis that closely spaced regions have stronger interconnections. Thus, researchers criticise this model for the lack of a theoretical basis and the mechanical transfer of the law of universal gravitation from physics to economics [Shumilov, 2017], for a conservative set of parameters, usually limited by the economic 'size' of objects [Smirnov, 2020]. Some scholars also emphasise the mathematical inconsistency of this model [Mele, Baistrocchi, 2012]. However, the model has proved its effectiveness in economic studies, and a conservative set of parameters in the context of our study is offset by a wide range of social economic indicators, on the basis of which composite indices are calculated.
The gravity model is calculated by the formula:
(8)
y
where Fij is an indicator of the strength of interaction between subjects of the Russian Federation i and j, G is an interaction constant; q is some level of significance of subjects of the Russian Federation i and j; d2j is the distance between subjects of the Russian Federation i and j.
We should point to that this model is widely used in describing the processes of urbanization, developing logistics, studying the processes of population migration and optimizing the location of production, because it reflects the interaction between spatial objects.
In order to measure the forces of interaction between the regions of the Russian Federation (Fj), in accordance with the Strategy, three composite indices were calculated: the index of scientific, technical and educational potential (ISTEP), the index of quality of life and infrastructure (IQLI), the production potential index (IPP) (Table 4) [Dubrovskaya, 2018].
To calculate the ISTEP, IQLI and IPP for each region, it is necessary to reflect all indicators on one scale using data normalisation, and then evaluate the asymmetry, showing the deviations of the indicators relative to the mean.
The interaction force matrices were constructed according to the formula Fj = G(qiqj/d2ij) in accordance with the procedure described in the previous section, with the interaction constant taken as unity.
Table 4. Composite indices of the interaction forces between regions
Composite index Statistical indicators that form the composite index Unit of measurement
Index of scientific, technical and educational potential Number of personnel specialising in scientific research and development work people
Number of students enrolled in higher education programs per 10,000 people population people
Volume of internal costs for research and development Monetary units
Number of teaching staff in higher education institutions people
Share of innovative goods, works, services in the total volume of shipped goods, works, services %
Index of quality of life and infrastructure Total area of residential premises per inhabitant m2
Number of people per hospital bed People
Density of paved public roads kilometers of roads per 1,000 km2 of territory
Emissions of pollutants into the atmosphere from stationary sources thousand tonnes
Production potential index Volume of shipped products (works, services) by type of economic activity "Manufacturing" Monetary units
Investments in fixed capital (without budgetary funds) per capita Monetary units
Coefficient of renewal of fixed assets %
Turnover of products (services) produced by small businesses, including microenterprises and individual entrepreneurs Monetary units
Source: own representation based on the information given in the Strategy for spatial development of the Russian Federation until 20251.
As part of the first step to the data were normalised for the indicators presented in Table 4. At the second step, the asymmetry was assessed, which allows demonstrating the asymmetry of the distribution of statistical indicators relative to the mean indicator. If the asymmetry value is greater than 0.5, then the value of the statistical indicator of an individual subject of the Russian Federation changes in accordance with the formula:
(9)
where xij is the transformed value of the j indicator of the i subject of the Russian Federation; Xj0 is the initial value of the j indicator of the i subject of the Russian
1 On approval of the Strategy for spatial development of the Russian Federation until 2025: Decree of the Gov-
ernment of the Russian Federation of February 13, 2019 No. 207-r (as amended on March 23, 2021). (In Russ.)
Federation; к is the degree of asymmetry (takes on values from 2 to 4 depending on the value of the asymmetry coefficient).
Next, the data was normalised using the following formula:
_ _ xiJ - min(x,y)
X'j max(x0) - min(xi:()'
where x is the normalised value of the j quantitative indicator of the i subject of the Russian Federation; Xj is the transformed value of the j indicator of the i subject of the Russian Federation; max (x;j) is the maximum value of the j quantitative indicator of the i subject of the Russian Federation; min (Xj) is the minimum value of the j quantitative indicator of the i subject of the Russian Federation.
For indicators of population per hospital bed and emissions of pollutants into the atmospheric air from stationary sources, the following inverse normalisation formula was used:
_ xtj - min(xi;?)
X,J max(x0) - min(xi:/)' ^ ^ ^
Composite indices are obtained by finding the arithmetic mean of the corresponding groups of indicators. As a result, we have 3 column bit vectors.
As part of the third step, we calculated the intermediate matrices IMISTEP, IMiqli, IMIPP (calculation of the formula numerator) by multiplying the column bit vector by the row bit vector obtained by transposition:
IMistep = ISTEP xISTEP';
IMiqli = IQLI x IQLI'; IMipp = IPP x IPP'. (12)
At the fourth step, the distance matrix was determined based on open Internet sources (the shortest distances between the administrative centers of the constituent entities of the Russian Federation along roads are used)1.
Further, at the fifth step, the matrices of the interaction forces of the regions were constructed (the values of the intermediate matrices are element-wise divided by the square of the value of the distance matrix according to formula (8)).
At the sixth step, the total matrix of interaction forces was calculated by adding the matrices of research, socio-political and economic interaction forces.
At the second stage, macroregions were formed on the basis of cluster analysis. The analysis was carried out on the basis of the calculated sub-indices and the matrix of interaction forces, normalised by row. The latter permits taking into account
1 Distance calculator. https://ru.distance.to.
the relationship between the studied regions [Chen, VanNess, 1996; Flores-Sintas, Cadenas, Martin, 2001]. Clustering is performed by the Ward method.
Let us note that there are many methods for clustering. The advantages of the chosen tool are the use of dispersion analysis methods for measuring distances between cluster centers, the ability to create small clusters, clarity and convenience of calculations [Szekely, Rizzo, 2005; Lee, Willcox, 2014; Murtagh, Legendre, 2014]. The result of clustering by the Ward method are macroregions.
At the third stage, the efficiency of the state strategy for the spatial development of the Russian Federation was assessed from the standpoint of the territorial structure of macroregions. We should note that in the context of our study, by efficiency we mean the effectiveness denominated in relative units of measurement. For this, based on the Theil index, we held a comparative analysis of the heterogeneity of the regional development of the macroregions indicated in the Strategy and the macroregions identified using our method.
The practical significance of the suggested method lies in the formulation of a new approach to the clustering of macroregions, which can be applied to design strategies for both the national spatial development and macroregions' social economic development.
Testing the method for spatial clustering of Russian regions
In accordance with the method, 14 macroregions were identified. The study is based on 7,650 observations in 85 subjects of the Russian Federation. The research was performed in several stages.
Stage 1. Collection of statistical indicators and calculation of sub-indices that characterise the principles of the Strategy (Table 5) [Dubrovskaya, Pestereva, Kozono-gova, 2019] and the principle "mechanisms for spatial development of the economy" (added by the authors).
Let us elaborate on the specifics of the calculation of sub-indices.
Center of economic growth. The region in which there is a large or the largest center of economic growth was assigned a value of 1 (in the absence of such a center - 0). The data for calculating the corresponding sub-index comprised 85 observations. The centers are defined by the Strategy.
Transport. In the presence of the specified object, the region was assigned the value 1, in the absence of it - 0. The overall composite indicator was calculated by finding the arithmetic mean. The data for calculating the sub-index "Transport" consisted of 340 observations.
Information infrastructure. This sub-index is a component of the Digital Russia index and takes into account the development of communication networks and
Table 5. Principles for identifying macroregions according to the Strategy: Systématisation and statistical measurement
Principle Index Statistical indicator
Territorial connectivity Spatial distance matrix Shortest road distances between administrative centers of Russian regions1'
Potential of interregional interaction Composite index of forces of interaction between regions Summary matrix of interaction forces
Presence of a center of economic growth Sub-index "Center of economic growth" Presence of a center of economic growth
Connectivity of subjects Sub-index "Transport" Availability • railway stations; • international airports2'; • access to international markets; • access to the transport corridor "West-East" and (or) "North-South"
Sub-index "Information infrastructure"3' Weighted average score of information infrastructure3'
Availability of social services Sub-index "Education" Availability of rated higher education institutions4'
Sub-index "Health care" Availability of "MRI-Expert" diagnostic centers. Presence of oncology clinics. Number of hospital beds per 10,000 population5'
Mechanisms for spatial development of the economy Sub-index "Mechanisms for spatial development of the economy" Availability • industrial parks in the region; • clusters6'; • special economic zones6'
Source: own compilation based on ^ [Abramov, Gluschenko, 2000]; 2) Federal Air Transport Agency: official website. https://www.favt.ru/dejatelnost-ajeroporty-i-ajerodromy-mezhdunarodnye-ajeroporty/; 3) Moscow School of Management Skolkovo official website. https://finance.skolkovo.ru/ru/sfice/research-reports/1779-2018-10-001-ru/; 4) Methodology for calculating the rating of higher educational institutions. The Vladimir Potanin Charitable Foundation official website. http://www.fondpotanin.ru/ranking; 5) Statistical yearbook 2018. Department of monitoring, analysis and strategic development of health care official website. https://www.rosminzdrav.ru/ministry/61/22/stranitsa-979/statisticheskie-i-informatsionnye-ma-terialy/statisticheskiy-sbornik-2018-god; 6) Geoinformation system. Industrial parks. Technoparks. Clusters. https://www.gisip.ru/#!ru/. (In Russ.).
digital technologies; availability of information infrastructure facilities in the subject; whether the subject has access to electronic computing power. The asymmetry was assessed and the sub-index "Information infrastructure" was normalised (85 observations in total).
Education. The basis for choosing objects from the sphere of education was the rating of higher educational institutions compiled by the Vladimir Potanin Charitable Foundation (85 observations in total), which is one of the most authoritative independent assessments of the quality of education in Russian universities. If there is a university included in the specified rating, the region was assigned a value of 1, in the absence of it - 0.
Health care. When choosing the appropriate objects, the statistical data of the Ministry of Health of the Russian Federation was used, according to which the main causes of death in Russia are diseases of the circulatory system and malignant neoplasms. In the presence of a social infrastructure facility in the health care sector, the region was assigned a value of 1, in the absence of it - a value of 0. Further, the asymmetry was assessed and the number of hospital beds per 10,000 people was normalised. As a result, the composite sub-index "Health care" was calculated by finding the arithmetic mean.
Mechanisms of spatial development of the economy. In the presence of industrial parks, clusters, special economic zones, the region was assigned a value of 1, in the absence of those objects - 0. The general composite indicator "Mechanisms for the spatial development of the economy" was determined in accordance with the following scale: 1 - all objects are present; 0.6 - there are 2 objects; 0.3 - there is 1 object; 0 - no objects.
The arraying of interaction force matrices according to formula (8) was performed in accordance with the steps described in the previous section.
Each index is formed from a number of indicators. These calculations were made for all 85 subjects of the Russian Federation. The database for calculating ISTEP, IQLI and IPP amounted to 1105 observations.
Next, intermediate matrices were calculated.
To obtain the interaction force matrices, it was necessary to element-wise divide the values of the intermediate matrices by the square of the distance matrix value.
In order to measure the complex interaction of a different nature, a total matrix was obtained by adding the matrices of research, socio-political and economic forces of interaction.
Thus, the data compiled for calculations included 7,650 observations in 85 subjects of the Russian Federation.
Stage 2. In accordance with the method described above, macroregions were identified based on cluster analysis. The input parameter was 90 variables for 85 constituent entities of the Russian Federation (Figure).
In the course of the study, the following 14 macroregions were identified, which differ from the macroregions identified in the Strategy in terms of composition:
1} Central (Moscow, Moscow oblast';
2} Surrounding central (Bryansk, Vladimir, Vologda, Ivanovo, Kaluga, Kostroma, Nizhny Novgorod, Oryol, Ryazan, Smolensk, Tver, Tula, Yaroslavl oblasts';
3' South-Central (Belgorod, Voronezh, Kursk, Lipetsk, Tambov oblasts';
4' Northwestern (Saint Petersburg, Leningrad, Novgorod, Pskov, Kaliningrad oblasts';
5' Northern (Arkhangelsk and Murmansk oblasts, Nenets Autonomous district, Republic of Karelia';
6' Southern (Astrakhan, Volgograd, Rostov oblasts, Krasnodar krai, Sevastopol, the Republics of Adygea, Kalmykia, Crimea';
7' Caucasian (Kabardino-Balkarian, Karachay-Cherkess, Chechen Republics, Stavropol krai, Republics of Dagestan, Ingushetia, North Ossetia - Alania';
8' Ural (Kirov, Sverdlovsk oblasts, Republics of Komi, Mari El, Chuvashia, Perm krai';
9' Volga (Penza, Samara, Saratov, Ulyanovsk oblats, Republic of Mordovia';
10' East Ural (Kurgan, Orenburg, Chelyabinsk oblasts, Republics of Bashkortostan, Tatarstan, Udmurtia';
11' Siberian (Tyumen oblast, Khanty-Mansi Autonomous district - Yugra, Yamalo-Nenets Autonomous district, Altai krai';
Macroregions
1 - Central
2 - Surrounding central
3 - South-Central
4 - Northwestern
5 - Northern
6 - Southern
7 - Caucasian 8-Ural
9 - Volga
10 - East Ural
11 - Siberian
12 - Yenisei Siberia
13 - Southern Siberia
14 - Far Eastern
Map of Russia's macroregions according to the developed method
12) Yenisei Siberia (Kemerovo, Tomsk, Omsk, Novosibirsk oblasts, Krasnoyarsk krai, Republics of Altai, Tyva, Khakassia);
13) Southern Siberia (Amur, Irkutsk, Sakhalin oblasts, Jewish Autonomous oblast, Zabaikalsky krai, Primorsky krai, Khabarovsk krai, Republic of Buryatia);
14) Far Eastern (Kamchatka krai, Magadan oblast, Chukotka Autonomous district, Republic of Sakha (Yakutia)).
The derived macroregions also differ significantly in terms of the main social economic characteristics (Table 6)1.
Table 6. Principles for identifying macroregions according to the developed method: Systématisation and statistical measurement
no. Macroregion Territory area as of January1, 2019, thousand km2 Population as of January 1, 2019, thousand people Average annual number of employees, thousand people Average per capita monthly incomes, rubles Average per capita monthly expenditures for the purchase of goods and services, rubles Average monthly nominal wages of employees of organisation, rubles Gross regional product (in current basic prices), billion rubles
1 Central 46.9 20,215 12,180.2 110,374 89,330 134,401 19,527.8
2 Surrounding central 656.7 16,403.1 7,851 341,100 277,763 404,860 5,567.8
3 South-Central 167.8 7,142.3 3 427.8 144,751 119,217 151,046 2,837
4 Northwestern 210.3 9,464 5,024.2 149,554 126,839 193,586 5,670.6
5 Northern 915.3 2,510.2 1,186.8 179,027 109,938 224,524 1,442.1
6 Southern 447.9 16,454.5 7,455.1 204,253 172,714 241,386 5,361.9
7 Caucasian 170.5 9,866.8 3,839.6 150,844 114,794 181,602 1,864.7
8 Ural 933.4 10,932.6 5,049 156,485 127,746 205,700 4,655.4
9 Volga 261.5 8,975.8 4,313.1 112,530 92,611 144,262 2,938.1
10 East Ural 536.5 15,730.5 7,383.7 154,926 127,870 193,257 6,439.4
11 Siberian 1,632.2 6,056.8 3,235.6 181,985 121,835 238,342 7,494.8
12 Enisei Siberia 3,418.9 12,442.8 5,761 186,477 147,615 295,575 5,554.6
13 Southern Siberia 2,995.6 9,113.7 4,351.4 251,338 204,863 363,523 4,228
14 Far East 4,731.8 1,472.6 784.4 230,520 147,071 324,550 1,344.6
In connection with these differences, the heterogeneity of regional development was examined by calculating the Theil index in order to assess the compliance (usefulness, suitability) of the approved spatial development strategy. GRP per capita was analysed modified by the purchasing power of income received, taking into account
1 Russia in numbers. 2019. Brief statistical compendium. Moscow: Federal State Statistics Service. 549 p. https://
rosstat.gov.ru/storage/mediabank/rus19.pdf. (In Russ.)
the price characteristics of consumer markets in different regions for 2018. Geographical units were macroregions according to the Strategy and macroregions identified in this study.
Next, the Theil index was calculated based on the modified GRP per capita for the specified groups of macroregions. Allowing for the separability of this index, it was decomposed into components related to differences between macroregions and between territories within each of them. The results are presented in Table 7.
Table 7. Structural analysis of the Theil index based on modified GRP per capita, calculated for macroregions identified according to the Strategy and according
to the developed method
Indicator Macroregions Relative value of the indicator, % pertaining to T
according to the Strategy according to the developed method macroregions according to the Strategy macroregions according to the developed method
Tbetween 0.1063 0.1197 43.99 49.53
Twithin 0.1353 0.1219 56.01 50.47
T 0.2416 0.2416 100 100
According to the information in Table 7, the structure of the space of the Russian Federation divided into macroregions in line with the developed method is more homogeneous. The unit weight of Tbetween and Twithin relative to T is 49.53 and 50.47 %, respectively. At the same time, the structure of the space of the Russian Federation divided into macroregions in line with the Strategy is characterised by the shares of Tbetween and Twithin relative to T and equals 43.99 and 56.01 %, respectively.
Therefore, the analysis of the heterogeneity of regional development by calculating the Theil index revealed that the value of the index of intra-group differentiation of the territories of macroregions determined by the Strategy is substantially higher than that of the territories of macroregions determined on the basis of our method. This allows us to speak about the usefulness of the proposed method for clustering macroregions.
Conclusion
The spatial organisation of the Russian economy into 12 macroregions does not quite settle the differences in the social economic development of regions, since in this case their heterogeneity persists. In addition, the Strategy lacks substantiated methodological approaches to the spatial division of the territory.
In order to level the spatial heterogeneity of the country, the authors proposed a new method for identifying macroregions, which is based on the tools of spatial economics: a gravity model and cluster analysis. The input parameters were 7,650 variables for 85 regions of Russia. Clustering of macroregions was implemented in
several stages: (i) collection of statistical indicators and calculation of sub-indices characterising the principles of the Strategy; (ii) identification of 14 macroregions on the basis of cluster analysis that are different from the macroregions presented in the Strategy; (iii) analysis of the heterogeneity of regional development by calculating the Theil index. Using the separability property of this index, we decomposed it into elements related to differences between macroregions and territories within them.
Calculations have shown that in the Strategy, the overall interregional inequality is mainly due to the differences in the levels of development of the constituent entities of the Russian Federation within the macroregions (the intra-group component). At the same time, the indices calculated for the macroregions identified according to the proposed method indicate an equal contribution to the overall spatial heterogeneity of both the intergroup and intra-group components. In line with the calculation of the Theil index, the spatial organisation of the country's economy, which involves division into 14 macroregions, helps reduce the level of differentiation in the social economic development of regions.
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Information about the authors
Pavel I. Blus, Cand. Sc. (Geography), Associate Prof., Prof. of Public and Municipal Management Dept., Perm State University, 15 Bukireva St., Perm, 614990, Russia Phone: +7 (342) 2-396-689, e-mail: piblus1962@gmail.com
Rustam V. Plotnikov, Postgraduate of Economics and Finance Dept., Perm National Research Polytechnic University, 24 Komsomolskiy Ave., Perm, 614000, Russia Phone: +7 (342) 2-198-332, e-mail: rusplotnikov120@mail.ru
© Blus P. I., Plotnikov R.V., 2022
