CC BY
1DOI: 10.29141/2658-5081-2021-22-4-5 JEL classification: F14, F17, F41
Leonid A. Serkov Institute of Economics (Ural branch of RAS), Ekaterinburg, Russia
Mikhail B. Petrov Institute of Economics (Ural branch of RAS), Ekaterinburg, Russia
Konstantin B. Kozhov Institute of Economics (Ural branch of RAS), Ekaterinburg, Russia
Cluster-based econometric analysis to study the heterogeneity of Russian regions
Abstract. Differences in economic development between regions remain one of the most acute and debatable problems. The paper focuses on developing the tools for clustering the subjects of the Russian Federation according to their transport economic indicators in the railway industry, determining the transport economic potential of regions, and assessing the impact of specific regional factors behind this potential. Methodologically, the research relies on regional and spatial economics, and the theory of industrial markets. At the first stage, the authors cluster regions on the basis of the established comprehensive characteristics, and at the second stage, build explanatory multinomial logistic regressions for the objective function (transport economic potential) for each cluster. The objective function is the integral level of development of regions in a cluster, represented by a set of transport economic indicators. The most significant factors explaining the transport economic potential of a cluster are a level of urbanisation, market potential, and territory's saturation with capital. The factors of average wages in a region, number of the employed in the processing industry, and the level of urbanisation reduce the probability of regions' appearing in the clusters with low and medium transport economic potential. Of special interest is the fact that investment per person in the fixed assets decrease the probability of regions' joining the cluster with low potential and are insignificant for the cluster with medium transport economic potential. The research findings favour a more complete account of the territorial specifics and socioeconomic situation in the regions while improving their systems of rail transport.
Keywords: region; regional development; territorial heterogeneity; cluster analysis; regression analysis; transport and economic potential; railway industry.
Acknowledgements: The paper is prepared in accordance with the approved R&D Plan for the Institute of Economics (Ural Branch of RAS).
For citation: Serkov L. A., Petrov M. B., Kozhov K. B. (2021). Cluster-based econometric analysis to study the heterogeneity of Russian regions. Journal of New Economy, vol. 22, no. 4, pp. 78-96. DOI: 10.29141/2658-5081-2021-22-4-5
Received July 21, 2021.
Introduction
Freight and passenger rail transport is an important part of the national economy and has a significant impact on the life of society as a whole. They contribute to the fullest involvement of production factors in the creation of a social product, ensuring its physical network distribution. The activities of railway transport have an impact on economic growth by serving the processes of cooperation and integration of production, and increasing the efficiency of its concentration. Investment attractiveness and transport accessibility of territories depend on the quality of transport services. In addition, rail transport stimulates other sectors of the economy through direct, indirect and induced effects; contributes to the formation of employment and income growth; gives rise to positive economies of scale, helping to improve competitiveness; and, finally, it is an important factor in the dissemination of technical knowledge [Petrov, Serkov, Kozhov, 2021]. The infrastructural development of the regions of the Russian Federation, an important part of which is the improvement of the railway industry, corresponds to the priorities set forth in the Strategy of Scientific and Technological Development of the Russian Federation1.
The creation of a railway transport infrastructure, taking into account regional characteristics, contributes to socioeconomic stability. At the same time, the transport infrastructure affects such an important property of the socioeconomic space of a subject of the Russian Federation as its heterogeneity [Tarasova, 2020]. In this regard, it is required to develop a methodological approach that allows clustering territories taking into account their transport economic indicators.
Currently, there are no railways in six Russian regions, and in ten regions they are underdeveloped. In remaining constituent entities of the Russian Federation, the provision of railway transport is significantly less than in other countries. For example, in the United States, the length of all railways is three times longer than in Russia. However, in the Russian Federation, their construction does not stand still: the constructed Crimean bridge, which connects the Kuban with the Crimea and Sevastopol, made it possible to establish a railway connection with these subjects of the Russian Federation; the construction of a railway line to the Republic of Tuva is underway; a number of major railway lines in the Siberian and Far Eastern regions of the country are either at the design stage or at the beginning of construction.
Nevertheless, the existing shortage of railways in the constituent entities of the Russian Federation interferes with the normal development of the country's economy: natural resources are not involved in its economic turnover, part of the population does not have sufficient access to transport communications. The situation in
1 The Strategy of Scientific and Technological Development of the Russian Federation: Decree of the President of the Russian Federation of December 1, 2016 no. 642. https://sochisirius.ru/sntr. (in Russ.)
the railway sector is negatively affected by the high level of wear of rolling stock as well as of many structures of the freight car fleet and locomotive fleet, and ineffective activities in the field of commuter traffic. To eliminate the problems, a mechanism is being developed to support unprofitable passenger traffic, specialised carriers are being created - transit, intermodal and refrigerated, but without a clear cluster picture of the potential state of the railway network in each region of the country, the measures taken are not always targeted and the order of investment of measures may be violated.
The aim of the study is to create a regional typology according to the level of transport economic potential and to explore the factors affecting it.
Theoretical approaches to the use of cluster-based econometric analysis in the spatial development research
The problem of uneven development of territories is relevant for many countries, and therefore the spatial aspect of economic development is a subject of scientific interest. There are a number of alternative theories explaining the factors and mechanisms underlying the formation of the spatial proportions of the economic and spatial development of the country's territories [Kolomak, 2020]. Analysing the problems of strategic planning, Minakir [2015] draws attention to the conflict between the national strategy of spatial development of Russia and its regional strategies. On the basis of the theory of regional integration, the processes of synchronisation of economic dynamics and their relationship with the assessment of the real level of inter-territorial integration in the territories of the regions of the Ural Federal District was investigated [Petrov, Kurushina, 2018]. The conclusion about the expediency of the formation of large macro-regions and their territorial-industrial hubs as objects of integrated management of the development of productive forces was confirmed. Macro-regional structures can become levels of manifestation of synergistic effects in accordance with the Spatial Development Strategy of the Russian Federation1. Researchers proved that the success of integration projects significantly depends on the degree of implementation of national priorities in programs [Tatarkin, 2012; Lavriko-va, Andreeva, Ratner, 2020]. Considering this, it becomes possible to more efficiently select complex investment projects of interregional importance with high economic potential for the implementation at the macroregional level. In turn, their implementation will expand the possibilities of scientific and technological development of the regions with allow for the priorities of spatial development. One of the works in detail studied the indicators of investment activity in the subjects of the Russian Federation.
1 Spatial Development Strategy of the Russian Federation for the period up to 2025: Order of the Government of the Russian Federation of February 13, 2019 no. 207^. https://www.economy.gov.ru. (in Russ.)
The research showed that an increase in investments in fixed assets necessary to accelerate the growth rates of their spatial development and the country's economy as a whole, requires an increase in financial resources. In addition, the authors considered the possibility of increasing the financial resources of leading companies in various regions of the country by attracting additional debt financing and proposed a methodology for determining the potential demand for appropriate financing taking into account the fulfillment of regulatory requirements for financial stability indicators [Turygin, 2020].
The work of Demidova and Ivanov [2016] is devoted to the development of a methodological approach to the spatial development of the regions of the Russian Federation and their territorial systems and the modeling of spatial processes. Based on the theory of competitive development of territories, which is currently being implemented, Dubrovskaya [2017] investigated the intensification of interregional interaction of various systems. In her opinion, a promising model for the spatial development of the economy at this stage is interregional interaction within the framework of the format of interregional clusters, when there is a "dominant cluster" and "satellite clusters". The author emphasises the importance of analysing interregional interactions both from the standpoint of globalisation and from the point of view of uneven spatial regional development.
The publications also analyse the factors in the interaction between regions [Con-ley, Ligon, 2002; Le Gallo, 2004; Nizhegorodtsev, Arkhipova, 2009; Ayvazov, 2012]. Most scholars identify the next factors contributing to this process, accompanying it, and affecting, among other things, the level of heterogeneity of the subjects of the Russian Federation: the need to exchange goods or services, knowledge and information; strengthening social integration based on cooperation between business structures, mobility in the labour market, etc., and economic ties based on integration processes. Scientists have analysed in detail the role of geographical factors and the results obtained based on the theory of spatial development in socioeconomic geography [Krugman, 1993; Fujita, Krugman, 2004].
Nizhegorodtsev and Arkhipova [2009] investigated the dynamics of uneven development of regions and, using the example of changes in the indicator of the volume of industrial production per capita in the constituent entities of the Russian Federation in 2000-2005 demonstrated that regional differentiation is increasing every year. Bazueva and Radionova [2020] provide an econometric assessment of the impact of social indicators on the dynamics of regional economic growth considering the case of the subjects of the Volga Federal District. The scientific novelty of their work is determined by the next conclusions: 1) the effect on the GRP of the levels of fertility, mortality and morbidity of the population corresponds to the nature of the
dependencies identified for countries that have experienced the second demographic transition; 2) the nature of the influence on the GRP of the indicators "life expectancy", "the number of students enrolled in bachelor's, specialty, master's programs" and "the number of people employed with higher education in the regional economy" does not correspond to the tendencies of developed countries; 3) the inconsistency of the results obtained is a consequence of the underestimation of human capital as the main factor in the development of the Russian economy at the present stage. In addition, the authors determined the scale and consequences of the constraining effect of the examined social indicators on the dynamics of regional economic growth.
Based on the analysis of socioeconomic performance and the development dynamics of the Russian regions, Lapin, Vuyko [2019] investigated the impact of regional factors on the regional typology taking into account the strengths and weaknesses of the studied territories, geographical location and available resources. Infrastructure factors have a great influence on the development of the regions of the Russian Federation, which is confirmed by the results of econometric analysis and regional typology performed using the k-means method [Ignatyeva, Mariev, Serkova, 2019]. Experts note the importance of improving the efficiency of regional structures from the standpoint of rational use of resources to reduce the deficit of regional budgets in a number of constituent entities of the Russian Federation in order to overcome the uneven development of the country's territories [Aivazian, Afanasiev, Kudrov, 2016].
The works of Naumov [2019] and Ayvazov [2012] are devoted to the issues of clustering territories. Naumov investigated interregional relationships in the formation of investment potential in priority areas of economic activity using the method of spatial autocorrelation (Moran's method [1950]), and various types of distance matrices. The application of this approach made it possible to divide the entire set of subjects of the Russian Federation into four clusters. The results obtained were confirmed when compared with the investment territorial-production clusters already created in the country and complying with the cluster theory of economic development [Naumov, 2019]. The research of Ayvazov [2012] on the development of the world diamond market directs particular attention to the multidimensional grouping of countries participating in the international diamond trade. This problem is resolved by the method of cluster analysis, which allowed constructing a typology of countries with similar parameters.
In Russia, with its vast territory and federal form of state structure, great importance is attached to the problems of spatial development, since ignoring the factors of socioeconomic inequality of territories is fraught with regional separatism. Currently, decisions on the location of enterprises, the volume of investments and production are determined by market mechanisms that support the processes of concentration
and stimulate the growth of spatial differences in the subjects of the Russian Federation, as well as active migration of the population from rural areas to cities, from small towns to capital cities [Gurbanova, Kleshch, 2018].
Makarova [2021] considered the issues of modeling socio-demographic asymmetry using the methods of spatial econometrics and applying the graph theory. The economist studied the factors behind the growing disproportion of demographic dynamics in the regional space, proposed a typology of municipalities according to their contribution to the formation of socio-demographic asymmetry, which enables determining the points of agglomeration attraction and the presence of direct and reverse spatial relationships between key areas.
Turgel and Pobedin [2007] note that the inclusion of a regional-spatial aspect in the sphere of traditional economic analysis and the integration of the methodology and theory of regional studies, development economics, and economic dynamics gave a powerful impetus to the research of issues of regional development and inequality of territories of the Russian Federation.
Other works, on the basis of extensive empirical material, confirmed the fact that urbanisation is a valuable spatial resource of development at the present time. Cities and urban agglomerations act as points of growth, generators of innovation and the knowledge economy, and thus contribute to an increase in the economic and transport potential of the region [Fujita, Krugman, Venables, 1999; Anas, 2004; Duranton, Puga, 2004].
The problem of spatial connectivity of territories is considered from the perspective of transport and communications infrastructure, its ramification and coverage. At the same time, the presence of a developed network of railways in the region is an important technical element and a condition for the interaction of economic agents dispersed in space to benefit from the division of labour due to climatic, natural and geographical conditions. Spatial connectivity, which has an economic content, is determined by the intensity of interregional interaction, which depends on the infra-structural component and the depth of specialisation, the development of cooperation institutions, and the level of economic activity of various territories. The system of these factors transforms over time under the influence of changes in production technologies, institutional barriers to cooperation, internal and external conditions for the development of the country. At the same time, significant external isolation of the state increases internal integration, forges ties between domestic producers, and contributes to the formation of large infrastructure projects [Granberg, Suslov, Sus-pitsyn, 2007].
Thus, the study of the spatial features of territories and the analysis of factors affecting spatial development and enhancing the infrastructure connectivity of territories
is an important task. According to the research hypothesis, there is a possibility of typifying the regions of the Russian Federation in terms of transport economic potential using cluster analysis and econometric tools to understand the impact of specific characteristics of regions on this potential.
Research methods
The typology of the Russian regions according to the level of transport economic potential was performed by the method of cluster analysis. The advantages of this method include the ability to split objects not by one parameter, but by a whole set of features. In addition, unlike most mathematical and statistical methods, it does not impose any restrictions on the type of objects under study and allows interpreting a lot of initial data of almost arbitrary nature, as well as sharply reducing, compressing large arrays of socioeconomic information, making them compact and visual. This is significant, for example, for forecasting the market situation, when indicators have a varied form, which makes it difficult to apply traditional econometric approaches.
The task of cluster analysis is to divide the set of objects G into m (m is an integer number) clusters (subsets) Q1, ... Qm based on the data from the set X so that each object belongs to only one subset of the partition, and objects belonging to the same cluster, were similar, while objects belonging to different clusters were heterogeneous.
The solution to the problem of cluster analysis is partitions that satisfy a certain criterion of optimality. This criterion can be a functional expressing the levels of desirability of various partitions and groupings, which is called an objective function. For example, the within-group sum of the squares of the deviation can be taken as the objective function.
The study relied on two-step cluster analysis using the intergroup linkage algorithm. Within the framework of this approach, unlike other approaches, the optimal number of clusters is determined on the basis of information criteria. At the first step, a hierarchical tree for combining cases (regions) into groups is built according to the likelihood distance measure criterion, and then, based on the Schwarz's Bayesian Criterion (BIC) criterion, the optimal number of clusters is selected1. The average values of the transport economic indicators of the regions included in a particular cluster (the centre of the cluster) determine its transport economic potential.
The influence of specific characteristics of regions on the transport economic potential (type) was analysed using multinomial logistic regression2. This regression
1 Cluster analysis was conducted using the SPSS package (IBM).
2 The analysis was conducted using the Stata package.
belongs to the class of discrete choice models with more than two alternatives [Cameron, Trivedi, 2005; Kleinbaum, Klein, 2010; Hosmer, Lemeshow, Sturdivant, 2013]. Different multinomial models arise from the use of different functional forms to determine the probability of an event with a multinomial distribution. In the multinomial logistic regression model, a binary logistic regression equation is constructed for each category of the dependent variable (alternative). In this case, one of the categories of the dependent variable becomes the reference (base) and all other categories are compared with it. The multinomial logistic regression equation predicts the probability of belonging to each category of the dependent variable based on the values of the independent variables. The estimation of the parameters of this model is most often performed using the maximum likelihood method. For this model, the probability of the i region choosing the j alternative is determined as follows:
lexp (xtpy)
where fy are the parameters of the multinomial logit model for the j alternative; y is a dependent variable.
The log-likelihood function is described by the expression:
N m
L=1 Shinty,
1=1 7=1
where m is the number of alternatives, pj = Fj (xh fy) is a function of the parameter 0 and the independent variable (regressor) xt.
The estimate of the parameter 0 will be a solution to the conditions of the first order of maximisation of the likelihood function [Xu, Long, 2005; Hole, 2007]:
dL="™ yij_dPij_ _ Q dP ¿iyti PtJ ^ .
Research results and discussion
For the clustering of territories in order to identify their spatial heterogeneity, economic indicators and most important indicators characterising the activity of railway transport in the Russian Federation in 2018 were used:
• gross regional product per capita (GRP, thousand rubles per person);
• dispatch of goods by public railway transport (Freighttraffic, thousand tonnes);
• transit of passengers by public railway transport (Passtraffic, thousand people);
• density of railway tracks by the end of the year (RWarea, km of tracks per 10,000 km2 of territory);
• share of employed in railway transport (Shareempi, %);
• investments in fixed assets in the railway industry per capita (INV, thousand rubles per person);
• cost of fixed assets, taking into account depreciation1 in the region (Costfa, million rubles).
Note that the indicators Freighttraffic, Passtraffic, RWarea characterise transport accessibility and security of the railway network. At the initial stage of the analysis, the regions of the Russian Federation without railways were excluded from the clustering calculations: Chukotka Autonomous District, Kamchatka krai, Magadan region, Altai and Tyva Republics, and the city of Sevastopol.
In order to form a more homogeneous sample of observations, the following were also excluded:
• the largest export-oriented oil and gas regions of the Russian Federation with a highly specialised fuel focus, such as the Khanty-Mansi Autonomous District, the Yamalo-Nenets Autonomous District, the Sakhalin region;
• Kemerovo oblast is the largest coal mining region, supplying fuel mainly by rail to the countries of the Asia-Pacific region;
• Moscow, Saint Petersburg and Moscow oblast, which stand out in terms of the studied indicators due to the federal structure of the Russian Federation.
Taking into consideration the listed exceptions, calculations to identify clusters were carried out on observations in 71 subjects of the Russian Federation. Initially, the relevant statistical data was brought to a standardised form in order to exclude possible distortions in cluster analysis. Research based on a two-step cluster analysis made it possible to divide the entire set of considered constituent entities of the Russian Federation into three groups allowing for the value of transport economic indicators of the railway industry (Table 1). Cluster 1 (industrial) includes 26 industrially developed regions of the country with high indicators in terms of freight traffic and railroad density, which is apparently due to the need for interregional technological transportation of raw product, materials and components along existing production chains in the process of manufacturing final products. Cluster 2 (a cluster of moderately developed regions) consists of 25 constituent entities with moderate transport economic potential, characterised by average indicators for both cargo and passenger traffic. Cluster 3 (a cluster of underdeveloped regions) unites 20 subjects of the Russian Federation, mainly the Caucasian regions of the country and regions with an agricultural focus, which have an underdeveloped railway network.
1 For the determination of the degree of depreciation of fixed assets, see below.
Table 1. Distribution of the subjects of the Russian Federation by clusters based on transport economic indicators of the railway industry
Cluster Regions of the Russian Federation
Industrial cluster (26 industrial regions with high transport economic potential) Orenburg, Samara, Arkhangelsk, Vologda, Leningrad, Murmansk, Irkutsk, Novosibirsk, Sverdlovsk, Tyumen, Chelyabinsk, Belgorod, Kursk, Lipetsk, Astrakhan, and Rostov oblasts, Krasnodar, Perm, Krasnoyarsk, and Khabarovsk krais, republics of Bashkortostan, Tatarstan, Karelia, Komi, Khakassia, Sakha
Cluster of moderately developed regions (25 regions with medium transport economic potential) Kirov, Nizhny Novgorod, Saratov, Kaliningrad, Novgorod, Omsk, Tomsk, Kurgan, Bryansk, Vladimir, Voronezh, Kaluga, Ryazan, Smolensk, Tver, Tula, Yaroslavl, Volgograd, and Amur oblasts, Stavropol, Altai, Trans-Baikal, and Primorsky krais, republics of Udmurtia, Buryatia
Cluster of underdeveloped regions (20 regions with low transport economic potential) Penza, Ulyanovsk, Pskov, Ivanovo, Kostroma, Oryol, and Tambov oblasts, republics of Mari El, Mordovia, Dagestan, Ingushetia, North Ossetia - Alania, Adygea, Kalmykia, Crimea, Jewish Autonomous oblast, Chuvash, Kabardino-Balkar, Karachay-Cherkess, Chechen republics
Clustering of the regions of the Russian Federation by transport economic indicators is shown in Figure.
Industrial cluster
Cluster of moderately developed regions
■ Cluster of underdeveloped regions
■ Regions not included in the sample
Distribution of the subjects of the Russian Federation by clusters characterising the transport economic indicators, 2018
Table 2 presents the mean values of indicators in the original (non-standardised) form for each cluster. These data shows that the influence of the transport economic potential is greater in regions with large GRP per capita, as well as in areas where there is a significant amount of fixed assets, substantial large-scale industrial cargo transportation and passenger traffic. At the same time, the grouping of regions by clusters is neutral (approximate equality of mean values) to the density of the railway network and the number of employees in the industry. There is also a considerable
excess of investment per person in fixed assets of the railway industry in the industrial cluster compared to other clusters.
Table 2. Initial mean values of transport economic indicators for each cluster
Cluster name GRP, thousand rubles per person FreighttraffiC) thousand tonnes Passtraffic> thousand people RWarea, km of tracks per 10,000 km2 of territory Shareempi, % Costfa, million rubles INV, thousand rubles per person
Industrial cluster 565.7 30 431.2 6 809.9 136.5 7.9 2 783 392 600.1
A cluster of moderately developed regions 359.4 10 601.8 4 755.0 169.3 7.3 1 387 216 450.1
A cluster of underdeveloped regions 239.1 1 699.7 863.0 156.8 6.0 650 546 402.1
As already noted, the mean values of the transport economic indicators of the regions included in a cluster (the center of the cluster) determine the transport economic potential of these regions.
To identify specific regional factors affecting the division of subjects into clusters, we tested a multinomial logit model with a dependent variable - the type of transport economic potential (type of cluster (see Table 1)). The preference for choosing this model, rather than a similar probit model, is confirmed by comparing the information criteria of the models, the higher value of the likelihood function for the logistic model and the better quality of the model. The number of alternatives is three in accordance with the results of cluster analysis. The basic category of the model was the potential of the industrial cluster. The explanatory variables were chosen based on model considerations. As a model, the approach of the extended production function was chosen, according to which, along with the fundamental factors (labour, capital), disaggregated factors of the spatial development of regions are introduced.
The description of the explanatory variables and the results of the estimation of the parameters of the multinomial logit model are given in Table 3. The choice of the analysed factors of spatial development is due to the fact that, according to the authors, these are factors that have the greatest impact on the transport economic indicators of the regions and determine their transport potential. Note that the market potential of the region MPr is defined as the sum of regional outputs of neighboring subjects, weighted by the value inverse to the linear distance to the region under study [Kolo-mak, 2020]:
MPr = £ -7^-.
s±r &lStrs
This indicator takes into account the availability and capacity of regional markets.
Table 3. Evaluation results of the multinomial logit model
Factor Transport economic potential
Average Low
Coefficient Odds ratio1 Coefficient Odds ratio
Average wage, rubles -0.009*** (0.001) 0.991*** -0.155*** (0.016) 0.856***
Distance from the region's centre to Moscow, km 0.077*** (0.007) 1.080** 0.123** (0.054) 1.131**
Expenditures on innovations. thousand rubles for 10,000 people 0.005 (0.009) 1.005 0.004 (0.013) 1.004
Number of people employed in the manufacturing industry, thousand people -0.049*** (0.009) 0.952*** -0.171*** (0.034) 0.843***
Number of employed with higher education, people for 10,000 people population 0.141 (0.111) 1.151 0.094 (0.087) 1.099
Urbanisation rate, % -0.023** (0.012) 0.977** -0.036* (0.021) 0.965*
Investments in fixed capital by the number of employees, thousand rubles per person 0.003 (0.012) 1.003 -0.013** (0.006) 0.985**
Market potential of the region, million rubles / km -0.143*** (0.021) 0.867*** -0.134*** (0.017) 0.875***
Capital saturation of the territory, million rubles / km2 -0.092** (0.047) 0.912** -0.129** (0.014) 0.879**
Likelihood logarithm -23.77
Likelihood ratio 108.55
Pseudo-Ä2 0.699
Notes: *, ** and *** denote the statistical significance at the 10 %, 5 % and 1 % levels, respectively. The basic category is an industrial cluster with high transport economic potential. Standard errors are indicated in parentheses.
The capital saturation of the territory Fs is equal to the ratio of the value of the region's fixed assets at the end of the year Fp (million rubles) to the area of the territory S (thousand km2), taking into account the depreciation rate of the assets Kda:
1 Odds ratio is a statistic that quantifies the strength of the association between two events.
„ _ (1 ~Kda)Fp Fs----.
The depreciation rate of fixed assets reflects the share of worn-out fixed assets.
A specific feature of the multinomial logit model (as well as binary choice models) is that the coefficients of this model are interpreted using the odds ratio [Davidson, MacKinnon, 1993]. For example, for the basic category (normalised alternative) "industrial cluster" (j = 1):
pr (y. = i)
where, expfy is the ratio of the probability of choosing the j alternative to the probability of choosing the base alternative when the value of the regressor x¡ changes by one (the probability of choosing the latter is equal to one). The considered model belongs to the class of multiple-choice models. The task of its assessment is to determine what factors and to what extent affect the location of a region in a cluster with a certain transport economic potential.
The results of the corresponding assessment indicate that the factors associated with the innovative activity of the regions (expenditures on innovation, the number of employees with higher education) are insignificant. This rather unexpected conclusion requires further research. We only note that these factors characterise the economy of the region as a whole, but not innovative activity in the railway industry, which is determined by internal and external factors. The former include competently motivated management and personnel of the industry, effective relationships with personnel, an effective marketing system, etc., the latter embrace competent relationships with consumers, business partners, competitors; changes in the prices of raising capital to finance all phases of the innovation process, etc. The variables characterising these factors are unobservable and difficult to evaluate in terms of the appropriate choice of proxy variables.
The factors of the average wage in the region, the number of people employed in the manufacturing industry and the level of urbanisation reduce the likelihood of finding regions in clusters with low and medium transport economic potential. At the same time, the factor of average wages is more significant for regions with low transport economic potential. The results obtained are expected, based on the analysis of the spatial imbalances given in Tables 1, 2. In particular, to ensure the profitability of the railway industry, it requires average population density to be at least 8.4 m2 in the Russian Federation [Petrov, Serkov, Kozhov, 2021]. The average wage factor reflects the level of well-being in the regions. According to research data, an increase in this indicator leads to a decrease in interregional
differentiation in the economic development of subjects and, as a consequence, in the development of the transport railway industry [Kolomak, 2020]. This explains the influence of the factor of average wages in the region on its transport economic potential. The number of people employed in the manufacturing industry is directly related to transportation and the development of the transport infrastructure of the railways. It is interesting that specific investments in fixed assets reduce the likelihood of regions being in a cluster with low potential and are insignificant for a cluster with an average transport economic potential. This is most likely due to the increased depreciation of fixed assets and lower efficiency of their management in clusters with low potential. In particular, according to Russia's Federal State Statistics Service (Rosstat), the average value of the degree of depreciation of fixed assets in the regions included in clusters 1 and 2 (industrial and moderately developed regions) is approximately 50 %, and in cluster 3 (a cluster of underdeveloped regions) - 59 %.
A particularly significant decrease in this probability is observed for the factors "market potential of the region" and "capital saturation of the territory". These results indicate the importance of the influence of the availability of regional markets and the state of fixed assets on the development of the railway industry. At the same time, neighboring regions and regions with a lesser degree of depreciation of fixed assets contribute the most to the indicator of market potential. On the contrary, an increase in the distance from region's centre to Moscow increases the likelihood of regions to be found in clusters with low (by 0.08) and medium (by 0.13) transport economic potential. This explains the less developed infrastructure of the railways of the subjects of the Russian Federation that are more distant from Moscow, which is associated with the cost of freight and passenger transportation and special climatic conditions.
Conclusion
The observed interregional differentiation in economic development in general and in the transport sector in particular is currently a pressing problem. To rectify it, within our study, we developed methods that make it possible to group the constituent entities of the Russian Federation according to the most informative statistical indicators of the railway industry, determine the transport economic potential of regions, and assess the impact of specific regional factors on this potential.
We propose a research toolkit that employs cluster analysis and allows distributing regions of the Russian Federation with significantly different parameters in the transport economic sphere into groups (clusters), as well as performing a wide range of model studies using a multinomial logit model to more accurately determine
the type of transport economic potential based on the known parameters of cluster centres across the entire set of considered regions.
The application of this toolkit, as shown by its testing, increases the efficiency of the process of typifying regions of the Russian Federation and the accuracy of assessing the impact of specific regional factors on the transport economic potential due to the following features:
• preliminary diagnostics of the clustered regional space according to the indicators of the railway industry for its subsequent research based on the multinomial logit model;
• identification of factors affecting the uneven development of regions in terms of transport and infrastructure parameters;
• use of cluster analysis for dividing a large initial set of regions into a relatively small number of groups (from three to four) and finding cluster centres that determine the corresponding type of transport economic potential;
• assessment of the influence of specific characteristics of regions on the type of potential through a multinomial logit model in order to reasonably confirm the following:
- factors of the average wages in the region, the number of people employed in the manufacturing industry and the level of urbanisation reduce the likelihood of regions to be found in clusters with low and medium transport economic potential;
- of all the factors studied, the most significant ones are urbanisation, market potential and capital saturation of the territories;
- specific investments in fixed assets reduce the likelihood of regions being in a cluster with low potential and are insignificant for a cluster with an average transport economic potential.
Implementing the proposed approach will allow analysing the differentiation of regions based on a wide range of indicators, not only transport economic indicators, but also indicators of energy and communications, sector of non-tradable goods, etc.
The research findings can be used to formulate recommendations for creating a strategy for the long-term railway industry development and will help assess the demand for freight and passenger transportation, which ultimately will lead to a decrease in industry costs, qualitative improvements in business processes, and increase their transparency and contribution to the economy.
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Information about the authors
Leonid A. Serkov, Cand. Sc. (Physics & Mathematics), Associate Prof., Sr. Researcher of the Center for Development and Location of Productive Forces, Institute of Economics (Ural branch of RAS), 29 Moskovskaya St., Ekaterinburg, 620014, Russia Phone: +7 (343) 371-04-11, e-mail: dsge2012@mail.ru
Mikhail B. Petrov, Dr. Sc. (Engineering), Cand. Sc. (Econ.), Associate Prof., Head of the Center for Development and Location of Productive Forces, Institute of Economics (Ural branch of RAS), 29 Moskovskaya St., Ekaterinburg, 620014, Russia Phone: +7 (343) 371-04-11, e-mail: petrov.mb@uiec.ru
Konstantin B. Kozhov, Cand. Sc. (Engineering), Sr. Researcher of the Center for Development and Location of Productive Forces, Institute of Economics (Ural branch of RAS), 29 Moskovskaya St., Ekaterinburg, 620014, Russia Phone: +7 (343) 371-04-11, e-mail: jefytt11@mail.ru
© Serkov L. A., Petrov M. B., Kozhov K. B., 2021
