R-ECONOMY, 2022, 8(1), 5–20 doi: 10.15826/recon.2022.8.1.001 5 r-economy.com Online ISSN 2412-0731 Original Paper © Naumov, I.V., Krasnykh, S.S., Otmakhova, Yu.S., 2022 doi 10.15826/recon.2022.8.1.001 UDC 330.43 JEL C33, C53, R11 Scenario forecasting of the socio-economic consequences of the COVID-19 pandemic in Russian regions I.V. Naumov1, 2 , S.S. Krasnykh1, Yu.S. Otmakhova3 1 Institute of Economics of the Ural Branch of Russian Academy of Sciences, Ekaterinburg, Russia; naumov.iv@uiec.ru 2 Ural Federal University named after the first President of Russia B. N. Yeltsin, Ekaterinburg, Russia 3 Central Economic and Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia ABSTRACT Relevance. There is a perceived lack of methods that can accurately, reliably and comprehensively reflect the epidemiological situation in regions and its impact on their socio-economic development. The approaches that are currently described in research literature do not take into account the mul- tivariance of scenarios of the COVID-19 pandemic, both in time and space. Research objective. The article aims to present a methodological frame- work that could be used to predict the socio-economic consequences of the COVID-19 pandemic in regions and to detect the most vulnerable regions. Data and methods. The study relies on a set of methods, including the methods of regression modeling, ARIMA forecasting and spatial correla- tion analysis. Results. The panel regression analysis has confirmed the negative im- pact of the pandemic on socio-economic development, in particular, the growth of overdue wage arrears, unemployment, arrears, the number of liquidated organizations, and the industrial production index. We have also identified the most vulnerable regions that need to be prioritized for government support. Conclusions. The resulting models and scenarios can be used by poli- cy-makers to set the priorities of state policy for the economic support of the regions and stabilization of the epidemiological situation in the country. KEYWORDS scenario forecasting, COVID-19, regression analysis, ARIMA forecasting, spatial correlation analysis ACKNOWLEDGMENTS The research was supported by the Russian Foundation for Basic Research (grant No. 20-04-60188 “Methods for forecasting and scenario modeling of socio-economic consequences of viral epidemics, taking into account spatial and communicative interactions”). FOR CITATION Naumov, I.V., Krasnykh, S.S., & Otmakhova, Yu.S. (2022). Scenario forecasting of the socio-economic consequences of the COVID-19 pandemic in Russian regions. R-economy, 8(1), 5–20. doi: 10.15826/recon.2022.8.1.001 Сценарное прогнозирование социально-экономических последствий пандемии COVID-19 в регионах России И.В. Наумов1, 2 , С.С. Красных1, Ю.С. Отмахова3 1 Институт экономики Уральского отделения Российской академии наук, Екатеринбург, Россия; naumov.iv@uiec.ru 2 Уральский федеральный университет, Екатеринбург, Россия 3 Центральный экономико-математический институт Российской академии наук, Москва, Россия АННОТАЦИЯ Актуальность. Ощущается недостаток методов, способных точно, достоверно и всесторонне отражать эпидемиологическую ситуацию в  регионах и ее влияние на их социально-экономическое развитие. Подходы, описанные в настоящее время в научной литературе, не учитывают многовариантность сценариев пандемии COVID-19 как во времени, так и в пространстве. Цель исследования. В статье ставится задача представить методоло- гическую базу, которая может быть использована для прогнозиро- вания социально-экономических последствий пандемии COVID-19 в регионах и выявления наиболее уязвимых регионов. Данные и методы. Исследование опирается на методы регрессион- ного моделирования, ARIMA-прогнозирования и пространственного корреляционного анализа. КЛЮЧЕВЫЕ СЛОВА сценарное прогнозирование, COVID-19, регрессионный анализ, ARIMA-прогнозирование, пространственный корреляционный анализ БЛАГОДАРНОСТИ Исследование выполнено при финансовой поддержке РФФИ в рамках научного проекта № 20-04-60188 «Методы прогнозирования и сценарного моделирования социально- экономических последствий https://doi.org/10.15826/recon.2022.8.1.001 http://r-economy.com https://doi.org/10.15826/recon.2022.8.1.001 6 r-economy.com R-ECONOMY, 2022, 8(1), 5–20 doi: 10.15826/recon.2022.8.1.001 Online ISSN 2412-0731 Introduction The deterioration of the epidemiological situ- ation in Russia caused by the spread of the novel coronavirus infection (Naumov et al., 2021) has spatial heterogeneity. There are poles of growth in the incidence of the COVID-19 (regions with a high concentration of cases), spatial clusters (re- gions with similar characteristics), and zones of their influence (directions in which the infection is spreading). In other words, the pandemic has affected the socio-economic development of Rus- sian regions differently. In the light of the above, the research and fore- casting of the pandemic’s spatial patterns, mode- ling their impact on socio-economic development have now become urgent tasks. Such research could provide evidence for policy-makers in set- ting spatial priorities for the stabilization of the epidemiological situation and in identifying the most vulnerable regions in need of state support. The purpose of this work is to model and predict the socio-economic consequences of the COVID-19 pandemic in the regions of Russia and to search for spatial priorities of their state sup- port. To achieve them, we set the following tasks: first, to analyze the main methodological ap- proaches to scenario forecasting of the socio-eco- nomic consequences of the pandemic; second, to create an approach for scenario forecasting of the pandemic in Russian regions; third, to model Результаты. Панельный регрессионный анализ подтвердил негатив- ное влияние пандемии на социально-экономическое развитие, в част- ности, на динамику индекса промышленного производства, уровня безработицы, просроченной задолженности по выплате заработной платы и числа ликвидированных организаций в регионах России. Мы также определили наиболее уязвимые регионы, которые нуждаются в приоритетной государственной поддержке. Выводы. Полученные модели и сценарии могут быть использованы политиками для определения приоритетов государственной полити- ки по экономической поддержке регионов и стабилизации эпидемио- логической ситуации в стране. от вирусных эпидемий с учетом пространственных и коммуникативных взаимодействий» ДЛЯ ЦИТИРОВАНИЯ Naumov, I.V., Krasnykh, S.S., & Otmakhova, Yu.S. (2022). Scenario forecasting of the socio-economic consequences of the COVID-19 pandemic in Russian regions. R-economy, 8(1), 5–20. doi: 10.15826/recon.2022.8.1.001 动态预测新冠疫情（COVID-19）对俄罗斯地区社会经济的冲击 诺莫夫1, 2 ，克拉斯尼赫1，奥特玛哈娃3 1 俄罗斯科学院乌拉尔分院经济研究所；naumov.iv@uiec.ru 2 俄罗斯乌拉尔联邦大学 3 俄罗斯科学院中央经济数学研究所 摘要 现实性：现在缺乏能够准确、可靠、全面地反映地区疫情状况及其 对社会经济发展影响的研究方法。 目前在科学文献中没有考虑到新 冠疫情在时间和空间上的多变量动态情景。 研究目标：本文旨在提出一个研究框架，可用于预测新冠疫情对地 区社会经济的冲击。并从而确定受影响最大的地区。 数据和方法：该研究基于回归建模、ARIMA预测和空间相关分析的 方法。 研究结果：面板数据回归分析证实了新冠疫情对社会经济发展的负 面影响。特别是对俄罗斯地区工业生产指数、失业率、拖欠工资和 清算组织数量的动态影响。 该研究还确定了需要国家优先支持的最 脆弱地区。 结论：政治活动家可以使用该模型来确定国内的一些地区。这些地 区可优先获得国家财政支持，从而稳定流行病期间的社会状况。 关键词 动态预测，COVID-19，回归分 析，ARIMA预测，空间相关分析 致謝 該研究得到了俄羅斯基礎研究基金 會的支持（第 20-04-60188 號贈 款“考慮到空間和交流互動的病毒 流行的社會經濟後果的預測和情景 建模方法”）。 供引用 Naumov, I.V., Krasnykh, S.S., & Otmakhova, Yu.S. (2022). Scenario forecasting of the socio-economic consequences of the COVID-19 pandemic in Russian regions. R-economy, 8(1), 5–20. doi: 10.15826/recon.2022.8.1.001 http://r-economy.com https://doi.org/10.15826/recon.2022.8.1.001 R-ECONOMY, 2022, 8(1), 5–20 doi: 10.15826/recon.2022.8.1.001 7 r-economy.com Online ISSN 2412-0731 the impact of the pandemic on the indicators of socio-economic development in Russian regions; fourth, to design the most probable basic scenar- ios of the pandemic in Russian regions and the corresponding forecast scenarios for changing the socio-economic indicators of their development; and, finally, to conduct a spatial analysis of the impact of the pandemic on the socio-economic development of regions and identify the most vul- nerable territories. Thus, our findings could help substantiate the spatial priorities of the state policy to stabilize the epidemiological situation in Russia until 2022. Literature review In the research literature, there are several methodological approaches to predicting the socio-economic consequences of the COVID-19 pandemic in territorial systems of various levels, ranging from municipal to macroeconomic. The most widely used methods include multiple re- gression on panel data, Box-Jenkins autoregres- sive moving average models (ARIMA), agent- based modeling, artificial neural networks, SEIR, SIRD and so on. The SEIR and SIRD methods as well as their modified versions were mainly used by Russian researchers to study the localization of the COVID-19 pandemic in Rus- sia (Osipov et al., 2021); to model the impact of the pandemic on household finances (Lebedev & Lebedev, 2021); and to model the spread of the COVID-19 in the Republic of Khakassia (Kozlitin & Shiganov, 2021). We found that these methods are well suited for predicting the dynamics of the pandemic, but at the same time, they are not sufficient to conduct a full assessment of its impact on the socio-eco- nomic development of various territorial systems. Similarly, these methods are not enough to realize the full potential of the scenario approach to fore- casting, which implies creating a system of various scenarios to take into account multiple factors. Agent-based modeling can be used to design various predictive scenarios of the pandemic in different territorial systems and to estimate its so- cio-economic consequences. This method is sui- table for developing a model of a real epidemiolo- gical situation in a certain area, taking into account many factors. For example, a team from the Cen- tral Economic Mathematical Institute of the Rus- sian Academy of Sciences designed such a model for the municipality of Moscow (Makarov et al., 2020). In this model, human agents pass through various stages of the disease from infection to re- covery or death, and these transitions are mode- led not on the group level but on the individual level. This way it is possible to take into account the heterogeneity of the population in terms of the vulnerability to catching coronavirus and the part each individual takes in spreading the disease (Makarov et al., 2020). This model is suitable for creating various predictive scenarios concerning the number of cases and deaths, the date when the peak of the wave is reached, the number of hospi- tal beds needed, including intensive care units in Moscow, taking into account various quarantine measures. However, the model cannot be used to assess the socio-economic consequences of the pandemic in this municipality. Another study that used agent-based mo- delling was conducted by Kerr et al. (2021). Their open-source model included the demographic in- formation about age and population size, realistic modes of transmission among the populations in- cluding households, schools, workplaces, age-spe- cific incidence rates, dynamics of the spread of the virus, etc. Agent-based modeling is a power- ful tool for multivariate scenario modeling and forecasting of the socio-economic consequences of the deteriorating epidemiological situation in territorial systems. However, its main limitation is the need to create a large number of agents that reflect actual socio-economic processes, to con- struct a complex system of equations describing the influence of various factors on the pandemic in various groups of agents, and its impact on the indicators of the socio-economic development of the given territory. Moreover, such models are not very good at capturing the spatial aspects of the pandemic. The most popular method of scenario-based forecasting of the impact of the pandemic on the socio-economic development of territories is currently the method of regression analysis. This method was used to form a predictive model for assessing the impact of the COVID-19 pandemic on the economies of some countries in Eastern Eu- rope (Vasileva et al., 2021). The study investigated the impact of the pandemic on the labor produc- tivity index, the growth rate of production and services, the world oil price index, the trade cost index, the growth rate of exports and imports, and other indicators of economic development. As a result, it was predicted that the pandemic would lead to a 6.1% decline in GDP in Eastern Europe by the end of 2020 (Vasileva et al., 2021). https://doi.org/10.15826/recon.2022.8.1.001 http://r-economy.com 8 r-economy.com R-ECONOMY, 2022, 8(1), 5–20 doi: 10.15826/recon.2022.8.1.001 Online ISSN 2412-0731 Yiting et al., (2021), using a multiple stepwise linear regression, investigated the impact of the de- teriorating epidemiological situation on the indi- cators of socio-economic development of 39 large cities in China (population size, population densi- ty, regional gross domestic product, GDP per cap- ita, number of migrants from rural areas, share of migrants from rural areas, level of urbanization, disposable incomes of the population, number of hospitals and doctors). The authors found that the level of urbanization, socio-economic develop- ment, infrastructure, including the urban density, directly affects the number of cases of the corona- virus infection. Multiple regression analysis was used by Uttra- ni et al., (2021) to model the impact of the pande- mic on global population mobility and mental health. The authors found a significant negative correlation between the reported cases of domestic violence and mobility in the workplace. This indi- cates an increased level of stress and anxiety in peo- ple due to forced isolation during the pandemic. Regression analysis has also been used to study the impact of the COVID-19 on financial markets in developing countries. The authors confirmed the negative impact of the COVID-19 on the daily market profitability of various sectors of economy, the resilience of the healthcare and banking sector (Rao et al., 2021). Shimizutani & Yamada (2021), using regres- sion analysis, assessed the impact of the pandemic on food security, financing of basic needs, health care costs, employment, economic and financial well-being of households in Tajikistan. This tool was also used to assess the impact of the COVID-19 on GDP of developed countries. Yan (2021) studied the impact of the coronavirus on the US economy based on a simple linear re- gression model. Shanshan et al. (2022) used bina- ry logistic regression to investigate the impact of the COVID-19 on the purchasing power and be- havior of consumers and food security in China. This method was also used in (Chan et al., 2021; Ogundokun et al., 2021; Raji, Lakshmi, 2020; Khan et al., 2021). The main advantage of regression analysis is the ability to establish cause-and-effect rela- tionships between the processes of the pandemic in territorial systems and indicators of their so- cio-economic development, and to study the fac- tors that are detrimental to the epidemiological situation. Geographically weighted regression modeling can also be applied to take into account spatial effects when generating data for forecast scenarios. Regression analysis fully realizes the possibi- lities of the scenario approach. Moreover, by using regressing analysis, we can give due regard to the so-called “controlled variables” in designing pre- dictive scenarios. However, the models built with the help of regression analysis do not always ade- quately describe the relationship between the pro- cesses in question. The relationships between the variables may turn out to be false or change over time, and this requires constant updating and in some cases rebuilding of the regression models. To assess the impact of the pandemic on the socio-economic development of territories, we also used integrated autoregressive modeling with a moving average according to the Box-Jenkins methodology (ARMA, ARIMA). This method was applied by Davidescu et al. (2021), to pre- dict the unemployment rate, taking into account the dynamics of the incidence of COVID-19. As a result, the authors showed an increase in unem- ployment in 2020 and predicted its slight decrease until the end of 2023. Altig et al. (2020) built a regression model to show the uncertainty of the socio-economic development of territories during the pandemic. This method was used to predict the spread of the coronavirus infection in (Ahmar & del Val, 2020; Benvenuto et al., 2020; Bertschinger, 2020; Ding et al., 2020; Kumar et al., 2020; Singh et al., 2020). The main advantage of this forecasting method is that it is easy to use and the resulting data are easy to interpret. The forecasts are sufficiently ac- curate for the short term if the trends are stable. This method, however, cannot be used to design a system of various scenarios, it is suitable only for building the most probable scenarios (inertial, that is, scenarios assuming that the current trends will continue in the future, extremely pessimis- tic and optimistic scenarios). The Box-Jenkins models, in contrast to multiple regression, are not suitable for establishing causal relationships be- tween the spread of the infection and indicators of socio-economic development or for studying the spatial characteristics of the epidemiological situation. The method for predicting the socio-econo- mic consequences of the pandemic that has re- cently gained popularity is neural network mode- ling based on a multilayer artificial neural network (MLANN). This method was used by Jena et al. (2021) to study the impact of the COVID-19 on http://r-economy.com https://doi.org/10.15826/recon.2022.8.1.001 R-ECONOMY, 2022, 8(1), 5–20 doi: 10.15826/recon.2022.8.1.001 9 r-economy.com Online ISSN 2412-0731 GDP in developed countries. The authors pre- dicted a decrease in the economic growth rates of eight countries from April to June 2020. Thus, the neural network has proven effective for cap- turing nonlinearities present in quarterly time series data and for making accurate predictions. The machine learning methods were used in other studies (Gambhir et al., 2020; Majumder et al., 2021; Zoabi et al., 2021; Gavrilov et al., 2021; Kushwaha et al., 2020; Mahdavi et al., 2021). The methods such as ARIMA modeling, however, are capable of predicting with high accuracy the so- cio-economic consequences of pandemic only in a particular region. These methods cannot identi- fy the spatial patterns of the pandemic but, unlike ARIMA modelling, they can help detect cause- and-effect relationships. To develop mechanisms for stabilizing the socio-economic situation in regions, a more com- prehensive approach is needed that integrates var- ious methods of modeling and forecasting. Such an approach is more suitable for considering the spatial characteristics of the pandemic and for identifying the most vulnerable territories. Thus, not only the most probable basic scenarios can be designed, but a whole system of these scenarios. Methodology As was shown in the previous section, re- gression analysis is an effective method for pre- dicting the socio-economic consequences of the pandemic. Using the established functional de- pendencies, this method can be applied to de- sign a system of predictive scenarios, which is why we have chosen it to build the methodolo- gical framework of our study. At the initial stage, we used panel data to as- sess and build models of the impact of the pan- demic on the following socio-economic indica- tors: the industrial production index, the volume of shipped products, the unemployment rate, overdue wage arrears, the number of liquidated organizations, and the volume of exports of pro- ducts (see Figure 1 below). The choice of indica- tors was limited due to the lack of monthly data required for panel regression analysis for 2020 and 2021 in the statistical database of the Federal State Statistics Service. The regression models using panel data will be used to test the hypothesis about the negative impact of the pandemic on the socio-economic development of the regions. In the process of modeling, we are going to build regressions with fixed and random effects, assess their adequacy using the Hausman test, Schwarz, Akaike and Hennan-Quinn information tests, analyze the statistical significance of the regression param- eters, check the autocorrelation between model errors using the Darbin-Watson test, the nor- mality of  the distribution of residuals using the Jarque-Bera test, etc. The panel data regression models were built with the following variables: the number of cases of coronavirus infection, the industrial produc- tion index, the unemployment rate, the volume of overdue wage arrears, the number of liquidated organizations in the regions, and the volume of products shipped. The data were obtained by us- ing the Yandex DataLens service1 and official sta- tistics from Rosstat2 for 85 regions of the Russian Federation between March 2020 and August 2021 (1530 observations). Panel models were built us- ing the Gretl software. The use of panel data in modeling is necessary to take into account space and time as the two key criteria in scenario forecasting to form a signi- ficant sample of observations. The models built this way, however, can be used to assess the im- pact of the pandemic on the economic develop- ment of regions in general but they do not reflect the strength of the pandemic’s impact on certain regions. Therefore, in order to assess the spatial characteristics of the impact of the pandemic and identify the most vulnerable regions, at the next stage, it is planned to conduct a correlation ana- lysis. The value of the correlation coefficient ex- ceeding 0.7 will indicate a strong negative impact of the pandemic on the socio-economic deve- lopment of the regions. In addition, it is planned to identify the regions with less significant con- sequences of the pandemic (with the correlation coefficient ranging from 0.3 to 0.7) and regions that were slightly affected by the pandemic (with the correlation coefficient of less than 0.3). Thus, we will be able to assess and predict the spatial characteristics of the impact of the pandemic and make recommendations concerning the spatial priorities of the state policy. At the third stage of the study, we will con- struct regression models of the pandemic’s impact on the index of industrial production, the volume of shipped products, the unemployment rate, the 1 Coronavirus. Dashboard and data / YandexCloud. Re- trieved from: https://cloud.yandex.ru/marketplace/products/ yandex/coronavirus-dashboard-and-data 2 Operational statistics / Rosstat. Retrieved from: http:// bi.gks.ru/biportal/contourbi.jsp?solution=Dashboard&allsol=1 https://doi.org/10.15826/recon.2022.8.1.001 http://r-economy.com https://cloud.yandex.ru/marketplace/products/yandex/coronavirus-dashboard-and-data https://cloud.yandex.ru/marketplace/products/yandex/coronavirus-dashboard-and-data http://bi.gks.ru/biportal/contourbi.jsp?solution=Dashboard&allsol=1 http://bi.gks.ru/biportal/contourbi.jsp?solution=Dashboard&allsol=1 10 r-economy.com R-ECONOMY, 2022, 8(1), 5–20 doi: 10.15826/recon.2022.8.1.001 Online ISSN 2412-0731 amount of arrears on wages, the number of liqui- dated organizations and the volume of exports in regions with a high correlation. This will help us clarify the models obtained at the first stage and improve their accuracy. This stage is necessary for the construction of scenario and multivariate forecasts of the socio-economic consequences of the pandemic, because panel regression models complicate this process and lead to errors and in- accuracies. The regression models formed at this stage will allow us in the future to design “active” forecast scenarios of changes in the indicators of the socio-economic development of regions, de- pending on the changes in the dynamics of the COVID-19 morbidity. To form the basic predictive scenarios of the pandemic in Russia regions, we are going to use integrated autoregressive moving average mode- ling (ARIMA). This toolkit is suitable for building an accurate inertial forecast, assuming that the trends observed for March 2020-October 2021 will remain stable. We are also going to build two extreme scenarios (optimistic and pessimistic). The assessment of the adequacy of the ARIMA models will be made according to the statistical significance of their parameters, the size of the de- termination coefficient and information criteria of Akaike, Schwartz, Hennan-Quinn. The forecasts of the pandemic will be used in the future to design the corresponding fore- cast scenarios for changes in the socio-econo- mic consequences in the regions according to the models developed at the third stage. For each indicator, we intend to create the most probable inertial scenario, which assumes that the rates of the pandemic will remain stable in the future. We also going to build extreme scenarios (opti- mistic and pessimistic). The methods of regres- sion analysis and autoregressive modeling by time series (ARIMA) will be applied to design not only basic, but the whole system of different predictive scenarios. At the final stage, the models will be used to determine the target values of the incidence of coronavirus infection in the regions. After these values are reached, it will be possible to reduce the negative socio-economic consequences. The proposed approach, in contrast to those currently used, can be applied to systematically assess and predict the socio-economic consequen- ces of pandemic, taking into account the most probable scenarios. The novelty of this approach 1. Regression modeling using panel data A study of the in�uence of the pandemic on: • industrial production index; • volume of products shipped, • unemployment rate; • amount of overdue wage arrears; • number of liquidated organizations; • exports • • • 6. Development of state policy measures for stabilization of the epidemiological situation in Russian regions and their economic support 5. Designing the basic, most likely predictive scenarios of the pandemic and its in�uence on regional socio-economic development 5. Construction of the most probable forecasts of changes in the dynamics of the pandemic in the regions according to ARIMA models 4. ARIMA modeling the dynamics of COVID-19 cases in regions heavily a�ected by the pandemic 3. Construction of regression models of the in�uence of pandemic on the socio-economic development of vulnerable regions Search for regions experiencing a strong negative impact of the pandemic (R > 0.7); Search for regions experiencing the average negative impact of the pandemic (0.3 < R < 0.7); Search for regions experiencing a weak negative impact of the pandemic (R < 0.3) 2. Correlation analysis of the in�uence of the pandemic on the socio-economic development of Russian regions: Figure 1. Research methodology Source: developed by the authors http://r-economy.com https://doi.org/10.15826/recon.2022.8.1.001 R-ECONOMY, 2022, 8(1), 5–20 doi: 10.15826/recon.2022.8.1.001 11 r-economy.com Online ISSN 2412-0731 lies in the possibility to assess the spatial charac- teristics of the influence of the pandemic on the socio-economic development of regions by using correlation analysis. By applying this approach, the most vulnerable regions can be identified. Results In accordance with the procedure described above, we built panel regression models of the im- pact of the number of COVID-19 cases on such indicators as the industrial production index, un- employment rate, overdue wage arrears, the num- ber of liquidated organizations in the regions and the volume of shipped products. We used panel data for 85 Russian regions from March 2020 to August 2021 (1,530 observations). For each indi- cator, we built three types of models by applying the combined least squares method, with random and fixed effects and assessed their reliability by using the Hausman test and information criteria. As a result, we found the negative impact of the pandemic on the amount of overdue wage arrears (Table 1). As the regression model shows, an increase in the number of cases in Russian regions leads to an increase in arrears in wage payments. The re- gression parameters confirming this relationship are statistically significant (regression coefficients have low p-values, less than 5%). The model's re- liability is also confirmed by the low values of the information criteria. There is no autocorrelation of residuals and a normal distribution of errors in the model. The model only shows the negative impact of the pandemics on the dynamics of this indicator. For a more detailed study of the spatial characteristics of this impact, we conducted a cor- relation analysis (see Fig.2). We found a close correlation exceeding 0.7 that confirms the strong influence of the pan- demic on the growth of overdue wage arrears in Kursk, Tambov, Novgorod, Tyumen, Mos- cow, Rostov, Lipetsk, Kaliningrad, Krasnodar, Khabarovsk and Stavropol regions, and the Ud- murt Republic. The dynamics of overdue debt in these regions may be due to other factors, how- ever. The pandemic had a less significant impact on the growth of arrears in the Republic of Mor- dovia (R = 0.68), Crimea (0.61), Nenets Autono- mous District (0.54), in Smolensk region (0.35), and in the Republic of Altai (0.32). The dynamics of the incidence of COVID-19 had a weak effect on the indicator under consideration in Oryol (0.27), Amur (0.26), Irkutsk (0.22), Sakhalin (0.1), and Sverdlovsk (0.1) regions. In these re- gions, other factors contributed to the growth of overdue wage arrears. To form predictive scenarios concerning the dynamics of overdue wage arrears in regions heavily influenced by COVID-19, we built re- gression mo-dels (see Table 2 below). While ac- cording to the results of panel regression analysis, the increase in the incidence of COVID-19 in the regions on average contributed to an increase in overdue debt by 59 rubles, the temporary mod- els built separately for each region showed a more significant increase in this indicator. For example, in Kursk region, an increase in the incidence of coronavirus infection contributed to the growth of the prophesied wage arrears by 1600 rubles; in Khabarovsk region, 1080  rubles; in Tambov Table 1 Regression model of the dependence of the volume of overdue wages on the number of cases of COVID-19 with fixed effects Coefficient Standard error t-statistic P-value const 20596.7 1209.7 17.03 1.05e-194*** X1 0.059 0.012 4.87 7.10e-06*** LSDV R-squared 0.749 Within R-squared 0.015 LSDV F (85, 1359) 47.8 P-value (F) 0.000 Schwarz criterion 33620.3 Akaike Criterion 33166.6 Rho parameter 0.86 Hennan-Quinn Criterion 33335.9 Breusch-Pagan test statistic: LM = 5147,5 0.000 Hausman test statistic: H = 9,56 0.0019 Wald test for heteroscedasticity (null hypothesis – observations have total error variance): Chi-square (85) = 6,5e+013 0.000 Source: the authors’ calculations based on statistical data (Rosstat), indices: Overdue wages, 2021. URL: https://rosstat.gov. ru/compendium/document/13267; Yandex Cloud, Coronavirus. Dashboard and data, 2021. URL: https://cloud.yandex.ru/market- place/products/yandex/coronavirus-dashboard-and-data/ (Accessed: 13.01.2022) https://doi.org/10.15826/recon.2022.8.1.001 http://r-economy.com https://rosstat.gov.ru/compendium/document/13267 https://rosstat.gov.ru/compendium/document/13267 https://cloud.yandex.ru/marketplace/products/yandex/coronavirus-dashboard-and-data/ https://cloud.yandex.ru/marketplace/products/yandex/coronavirus-dashboard-and-data/ 12 r-economy.com R-ECONOMY, 2022, 8(1), 5–20 doi: 10.15826/recon.2022.8.1.001 Online ISSN 2412-0731 Strong negative impact of COVID-19 on the Industrial Production Index (R2 > 0.7) Average negative impact of COVID-19 on the Industrial Production Index (0.3 < R2 < 0.7) Weak negative impact of COVID-19 on the Industrial Production Index (R2 < 0.3) Figure 2. Diagram of the correlation dependence of overdue wage arrears on the number of COVID-19 cases Source: Developed by the authors based on the model Table 2 Models of the dependence of the volume of overdue wage arrears on the number of COVID-19 cases and forecast scenarios for this indicator by May 2022, thousand rubles Correlation Model Current value Forecast scenarios Inertial Pessimistic Optimistic Kursk region 0.94 Y = –17113 + 1.6x 85569 109099 135989 82208 Tambov Region 0.93 Y = 39291 + 0.97x 85087 102198 113957 90441 Novgorod region 0.89 Y = 820 + 0.31x 15968 19396 24976 13816 Tyumen region 0.87 Y = –2139 + 0.31x 19182 26123 31813 20433 Moscow region 0.86 Y = 7456 + 0.24x 128004 144392 161427 127356 Krasnodar region 0.85 Y = –6250 + 0.67x 47286 65197 79616 50779 Kaliningrad region 0.85 Y = 8326 + 0.14x 17045 18480 21573 15388 Stavropol region 0.85 Y = 5740 + 0.4x 43818 85643 116253 55034 Khabarovsk region 0.74 Y = 3938 + 1.08x 103030 141826 175554 108098 Rostov region 0.73 Y = 5888 + 0.45x 74460 98276 119390 77163 Udmurtia 0.70 Y = –243.5 + 0.2x 10800 18492 23239 13860 Lipetsk region 0.70 Y = –933.6 + 0.2x 12941 16549 21276 11822 Source: Developed and predicted by the authors based on calculations Region, 970 rubles; in Krasnodar region, 670 ru- bles. The forecast scenarios built on the basis of the regression models and the results of ARIMA modeling indicate a further deterioration in the socio-economic situation of the regions. The level of overdue debt, according to op- timistic forecasts, will be lower than the current value for October 2021, only in a few regions: Kursk, Novgorod, Moscow, Kaliningrad and Li- petsk. In the rest of the regions, by May 2022, we forecast a significant increase in overdue wage ar- rears, which will exacerbate the already high level of social tension in the regions. As a result, we found the negative impact of the pandemic on the unemployment rate in the regions (Table 3). http://r-economy.com https://doi.org/10.15826/recon.2022.8.1.001 R-ECONOMY, 2022, 8(1), 5–20 doi: 10.15826/recon.2022.8.1.001 13 r-economy.com Online ISSN 2412-0731 Thus, according to the panel regression mod- el with fixed effects, an increase in morbidity per 100 people leads to an increase in the number of unemployed people by an average of 6 people. The correlation analysis showed that the pandemic had the strongest impact on the unemployment rate in Lipetsk region, the Republic of Ingushetia and Dagestan, and the Altai Republic (Figure 3). The pandemic had a less significant impact on the unemployment rate in Magadan (R = 0.68), Astrakhan (0.65), Smolensk (0.64), Novosibirsk (0.57), Moscow (0.48), Nizhny Novgorod (0.43), Tyumen (0.41), Novgorod (0.32), Saratov (0.31) regions, the Altai Republic (0.66), North Ossetia (0.57), Tyva (0.47), Moscow (0.63), the Yama- lo-Nenets Autonomous District (0.58), Khan- Table 3 Regression model of the dependence of the unemployment rate on the number of COVID-19 cases with fixed effects Coefficient Standard error t-statistic P-value const 49196.1 295.7 166.3 0,000*** X1 0.06 0.005 11.5 2.3e-029*** LSDV R-squared 0.95 Within R-squared 0.101 LSDV F (865, 1189) 300.5 P-value (F) 0.000 Schwarz criterion 27456.1 Akaike Criterion 27013.1 Rho parameter 0.84 Hennan-Quinn Criterion 27179.5 Breusch-Pagan test statistic: LM = 7020.2 0.000 Hausman test statistic: H = 20.3 6.49e-6 Wald test на гетероскедастичность (null hypothesis – observations have total error variance): Chi-square (85) = 1.13e+9 0.000 Source: the authors’ calculations based on statistical data (Rosstat), indices: Total number of unemployed, 2021. URL: https:// fedstat.ru/indicator/33414с; Yandex Cloud, Coronavirus. Dashboard and data, 2021. URL: https://cloud.yandex.ru/marketplace/ products/yandex/coronavirus-dashboard-and-data/ (Accessed: 13.01.2022) Strong negative impact of COVID-19 on the Industrial Production Index (R2 > 0.7) Average negative impact of COVID-19 on the Industrial Production Index (0.3 < R2 < 0.7) Weak negative impact of COVID-19 on the Industrial Production Index (R2 < 0.3) Figure 3. Diagram of the correlation dependence of the unemployment rate on the number of COVID-19 cases in Russian regions Source: Developed by the authors based on the model https://doi.org/10.15826/recon.2022.8.1.001 http://r-economy.com https://fedstat.ru/indicator/33414с https://fedstat.ru/indicator/33414с https://cloud.yandex.ru/marketplace/products/yandex/coronavirus-dashboard-and-data/ https://cloud.yandex.ru/marketplace/products/yandex/coronavirus-dashboard-and-data/ 14 r-economy.com R-ECONOMY, 2022, 8(1), 5–20 doi: 10.15826/recon.2022.8.1.001 Online ISSN 2412-0731 ty-Mansi Autonomous District (0.52) and in Stav- ropol region (0.38). In other regions, the increase in the unemployment rate is largely caused by oth- er factors that are unrelated to the deterioration of the epidemiological situation. The regression models of the dependence of the indicators on the time series confirmed the significant influence of the pandemic on unemployment in regions with high correlation values (Table 4). An increase in the number of COVID-19 cases in Dagestan per 100 people provides an in- crease in the number of unemployed people by 85  people; in Ingushetia, by 79 people; the Al- tai Republic and Lipetsk region, 15 people. If the growth in morbidity continues by May 2022, the number of unemployed people in Dagestan may increase by 6.6%. In the pessimistic scenario, the number of unemployed people may increase by 9.8%. According to the optimistic scenario, the unemployment rate is expected to exceed the current value in almost all the regions, which signifies serious socio-economic consequences of the pandemic. We used a regression model with random effects to show the relationship (1) between the industrial production index and the number of cases of COVID-19: IPP = 102,347 + 0.000015 · C# (1) where IPP is the industrial production index, %; C is the number of cases of COVID-19 in Russian regions Although we found a direct relationship be- tween these indicators, the correlation analysis and subsequent regression modeling showed the negative impact of the pandemic in some regions (Figure 4). According to the correlation diagram, the pandemic has a strong impact on the decline in the industrial production index in Tambov, Sakhalin, Tyumen, Tula, Irkutsk, Voronezh, Sverdlovsk, Volgograd and Amur regions, in the Kabardino-Balkarian Republic, the Republic of Dagestan, Ingushetia, Karelia, Jewish Autono- mous Region, and Chukotka Autonomous Dis- trict. The correlation coefficient in all of the above regions significantly exceeds the value of 0.7, indicating a close relationship of the indicators (Table 5). These regions faced serious socio-eco- nomic consequences of pandemic. For example, an increase in the number of COVID-19 cases per 1,000 people leads to a decrease in the indus- trial production index by 9.4% in the Chukotka Autonomous District; by 3% in the Jewish Au- tonomous Region; by 2.1% in the Republic of In- gushetia; and by 1.8 % in the Kabardino-Balkari- an Republic. In more resource-rich regions, such as Sverdlovsk and Tyumen regions, the level of decline in the industrial production index is lo- wer. However, there is still evidence of the strong impact of the pandemic on these regions. The regions shown in Table 5 thus should be priori- tized for state economic support. The projected forecast scenarios showed that even a significant reduction in the number of COVID-19 cases will not help these regions recover their current level of the industrial production index (as of October 2021) by May 2022. According to the results of the correlation analysis shown in Figure 4, the pandemic also had a negative impact on industrial production in Arkhangelsk (R = –0.62), Vladimir (–0.46), Magadan (–0.43), Belgorod (–0.36), Penza (–0.35), Astrakhan and Lipetsk (–0.3) regions, Khabarovsk (–0.61), Transbaikal (–0.39) territo- ries, the Republic of Adygea (–0.58), Mordovia (–0.56), Chechnya (–0.49), Komi (–0.4), Altai (–0.31), and the Khanty-Mansi Autonomous Dis- trict (–0.38). However, this influence is less sig- nificant in comparison with the above considered territories. As a result, we showed the negative impact of the pandemic on the number of liquidated orga- nizations (Table 6). Table 4 Models of the dependence of the number of unemployed on the number of COVID-19 cases and forecast scenarios for this indicator by May 2022, thousand people Correlation Model Current value Forecast scenarios Inertial Pessimistic Optimistic Republic of Ingushetia 0.90 Y = 73750.8 + 0.789x 89.1 94.5 98.6 90.3 Lipetsk region 0.87 Y = 24965.6 + 0.146x 33.8 36.1 39.1 33.1 Republic of Dagestan 0.84 Y = 192682 + 0.853x 236.0 251.6 259.3 243.9 Altai region 0.77 Y = 63123.5 + 0.154x 76.9 80.7 84.4 77.0 Source: Developed and predicted by the authors based on calculations http://r-economy.com https://doi.org/10.15826/recon.2022.8.1.001 R-ECONOMY, 2022, 8(1), 5–20 doi: 10.15826/recon.2022.8.1.001 15 r-economy.com Online ISSN 2412-0731 Strong negative impact of COVID-19 on the Industrial Production Index (R2 > 0.7) Average negative impact of COVID-19 on the Industrial Production Index (0.3 < R2 < 0.7) Weak negative impact of COVID-19 on the Industrial Production Index (R2 < 0.3) Figure 4. Diagram of the correlation dependence of the industrial production index on the dynamics of COVID-19 cases in Russian regions Source: Developed by the authors based on the model Table 5 Models of the dependence of the industrial production index on the number of COVID-19 cases and scenarios for this indicator by May 2022, % Correlation Model Current value Forecast scenarios Inertial Pessimistic Optimistic Tambov Region –0.92 Y = 111.8 – 0.0003x 98.2 93.0 89.5 96.6 Sakhalin Region –0.96 Y = 100.8 – 0.0005x 83.9 78.4 74.2 82.6 Kabardino-Balkar Republic –0.96 Y = 133.8 – 0.0018x 71.9 48.8 37.1 60.5 Republic of Dagestan –0.93 Y = 123.1 – 0.00056x 92.3 81.4 76.0 86.8 Tyumen region –0.91 Y = 136.9 – 0.00069x 89.5 74.1 61.4 86.7 Jewish Autonomous Region –0.90 Y = 136.9 – 0.003x 81.0 73.6 54.2 93.1 Republic of Ingushetia –0.89 Y = 121.41 – 0.0021x 72.7 59.3 46.9 71.7 Tula region –0.87 Y = 124.7 – 0.0005x 94.8 87.0 78.1 95.9 Chukotka Autono- mous District –0.84 Y = 103.3 – 0.0094x 82.0 85.4 82.5 88.3 Irkutsk region –0.83 Y = 105.1 – 0.00009x 94.4 91.5 88.8 94.2 Republic of Karelia –0.80 Y = 105.8 – 0.00014x 95.6 93.2 88.3 98.0 Voronezh region –0.79 Y = 113.2 – 0.00013x 93.8 82.8 76.5 89.1 Sverdlovsk region –0.75 Y = 104.1 – 0.00007x 93.3 91.1 89.5 92.7 Volgograd region –0.68 Y = 101.2 – 0.00001x 91.0 86.4 83.4 89.4 Amur region –0.66 Y = 102.3 – 0.00024x 93.0 89.6 85.5 93.8 Source: Developed and predicted by the authors based on their calculations https://doi.org/10.15826/recon.2022.8.1.001 http://r-economy.com 16 r-economy.com R-ECONOMY, 2022, 8(1), 5–20 doi: 10.15826/recon.2022.8.1.001 Online ISSN 2412-0731 Table 6 Regression model of the dependence of the number of liquidated organizations on the number of COVID-19 cases and predictive scenarios for this indicator by May 2022, units Coefficient Standard error z-score P-value const 300.86 40.37 7.45 <0.0001 X1 0.006 0.0004 15.97 <0.0001 Schwarz criterion 24654.9 Akaike Criterion 24644.3 Rho parameter 0.05 Hennan-Quinn Criterion 24648.3 Breusch-Pagan test statistic: LM = 669.45 1,3e-147 Hausman test statistic: H = 1895.98 0.000 Wooldridge test for assessing autocorrelation: Statistic: F (1, 84) = 6.57 0.012 Null hypothesis – normal distribution: Chi-square (2) = 43509.4 0.000 Source: the authors’ calculations based on statistical data (Rosstat), indices: Number of registered and liquidated organizations, 2021. URL: http://bi.gks.ru/biportal/contourbi.jsp?solution=Dashboard&allsol=1&project=%2FDashboard%2Fcompany_statis- tics/; Yandex Cloud, Coronavirus. Dashboard and data, 2021. URL: https://cloud.yandex.ru/marketplace/products/yandex/corona- virus-dashboard-and-data/ (Accessed: 13.01.2022) Table 7 Scenarios of changes in the incidence of COVID-19 in regions with serious economic consequences of the pandemic by May 2022, cases Regions Current value Inertial scenario Pessimistic scenario Optimistic scenario Moscow region 502,283 570,563 641,542 499,583 Sverdlovsk region 153,237 185,394 207,974 162,813 Rostov region 152,382 205,307 252,226 158,389 Voronezh region 149,620 234,070 282,385 185,756 Irkutsk region 119,001 151,229 181,089 121,369 Volgograd region 101,459 147,260 177,127 117,393 Stavropol region 110,850 199,758 276,282 123,234 Khabarovsk region 91,752 127,674 158,904 96,444 Altai region 85,889 110,134 133,229 87,040 Krasnodar region 79,905 106,638 128,158 85,117 Republic of Karelia 72,745 90,390 125,076 55,703 Tyumen region 68,778 91,168 109,522 72,814 Kursk region 64,176 78,883 95,689 62,076 Kaliningrad region 62,275 72,532 94,622 50,442 Udmurtia 61,354 104,085 130,461 78,355 Lipetsk region 60,324 76,011 96,562 55,459 Tula region 58,695 74,061 91,478 56,645 Republic of Dagestan 55,059 74,453 84,083 64,823 Novgorod region 48,863 59,922 77,921 41,923 Tambov Region 47,212 64,853 76,975 52,732 Amur region 38,800 52,979 70,240 35,717 Sakhalin Region 34,415 45,715 54,247 37,184 Kabardino-Balkar Republic 34,360 47,190 53,686 40,694 Republic of Ingushetia 23,193 29,577 35,484 23,668 Jewish Autonomous Region 8,983 11,442 17,929 4,955 Chukotka Autonomous District 1,847 1,903 2,207 1,598 Source: Developed and predicted by the authors based on calculations According to the regression model with ran- dom effects, an increase in the number of cases per 1,000 people on average leads to the liquida- tion of 6 enterprises. Unfortunately, the correla- tion analysis has failed to identify the regions where the business bankruptcy rate was seriously affected by the pandemic. As a result, we identi- fied he territories that are experiencing a medium influence of the pandemic (Stavropol and Kaluga regions and the Nenets Autonomous District) and a weak influence of the pandemic (other regions). Thus, we can conclude that socio-economic fac- tors have a greater impact on the number of liqui- dated organizations in the regions. The impact of http://r-economy.com https://doi.org/10.15826/recon.2022.8.1.001 http://bi.gks.ru/biportal/contourbi.jsp?solution=Dashboard&allsol=1&project=%2FDashboard%2Fcompany_s http://bi.gks.ru/biportal/contourbi.jsp?solution=Dashboard&allsol=1&project=%2FDashboard%2Fcompany_s https://cloud.yandex.ru/marketplace/products/yandex/coronavirus-dashboard-and-data/ https://cloud.yandex.ru/marketplace/products/yandex/coronavirus-dashboard-and-data/ R-ECONOMY, 2022, 8(1), 5–20 doi: 10.15826/recon.2022.8.1.001 17 r-economy.com Online ISSN 2412-0731 the epidemiological situation in the regions is less significant. Scenario modeling and forecasting of the socio-economic consequences of the pandem- ic showed that the most vulnerable regions are Moscow, Sverdlovsk, Rostov, Voronezh, Irkutsk, Volgograd, Khabarovsk, Stavropol, Altai, and Krasnodar (see Table 7). Despite the lower num- ber of COVID-19 cases compared to Moscow, Sverdlovsk and other regions, certain regions are strongly affected by the pandemic. These regions include the Republic of Ingushetia, Dagestan, Ka- bardino-Balkaria, Sakhalin, Amur, Novgorod and Tambov regions, the Jewish Autonomous Region, and the Chukotka Autonomous District. Correlation analysis confirmed a close rela- tionship between the increase in the incidence of COVID-19 in the regions presented in Table 7 and the decrease in the industrial production index, increase in the number of unemployed people, the volume of overdue wage arrears, and the number of liquidated enterprises. Other regions not pre- sented in Table 7 are less affected by the pandem- ic. The decline in the indicators of socio-economic development of these regions depends to a greater extent on other factors. The above findings can be used by poli- cy-makers in developing measures for stabilizing the epidemiological situation and providing sup- port for the most vulnerable regions. Conclusion The proposed methodological approach in- volves studying the influence of the pandemic on specific indicators of socio-economic development of regions by using panel regression analysis and correlation analysis. The latter is used to assess the tightness of the relationship between these indica- tors for each region. We have also built regression models to create active predictive scenarios of the pandemic and applied ARIMA forecasting meth- ods to design the most probable (inertial) and ex- treme scenarios (pessimistic and optimistic). The panel regression analysis has confirmed the negative impact of the pandemic on socio-eco- nomic development, in particular, the growth of overdue wage arrears, unemployment, arrears, the number of liquidated organizations, and the indus- trial production index. We have also identified the most vulnerable regions with the help of correla- tion analysis. Scenario modeling and forecasting of the socio-economic consequences of the pandemic showed that the regions that were hit the hardest were Moscow, Sverdlovsk, Rostov, Voronezh, Ir- kutsk, Volgograd, Khabarovsk, Stavropol, Altai, and Krasnodar. These regions should, in our opin- ion, be targeted by the state policy for containing the coronavirus pandemic and providing econom- ic support. Our findings can thus be used to deve- lop regulatory tools to minimize the adverse effects of the pandemic on regional development. References Ahmar, A.S., & del Val, E.B. (2020). SutteARIMA: short-term forecasting method, a case: Covid-19 and stock market in Spain. 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Digital Medicine, 4(3), 1–5. doi: 10.1038/s41746-020- 00372-6 Information about the authors Ilya V. Naumov – PhD in Economics, Head of the Laboratory for Modeling the Spatial Devel- opment of Territories, Institute of Economics of the Ural Branch of Russian Academy of Sciences (620014, Russia, Ekaterinburg, Moskovskaya St. 29), Ural Federal University named after the first President of Russia B. N. Yeltsin (620002, RF, Ekaterinburg, st. Mira, 19); e-mail: naumov.iv@uiec.ru Sergey S. Krasnykh – Junior Researcher, Laboratory for Modeling the Spatial Development of Territories, Institute of Economics of the Ural Branch of Russian Academy of Sciences (620014, Rus- sia, Ekaterinburg, Moskovskaya St. 29); e-mail: krasnykh.ss@uiec.ru Yulia S. Otmakhova – PhD in Economics, Leading Researcher of the Laboratory of Computer Modeling of Socio-Economic Processes, Central Economic and Mathematical Institute of the Rus- sian Academy of Sciences (117418, Russia, Moscow, Nakhimovsky prospect, 47); e-mail: otmakho- vajs@yandex.ru ARTICLE INFO: received December 16, 2021; accepted March 01, 2022 Информация об авторах Наумов Илья Викторович – кандидат экономических наук, руководитель Лаборатории моделирования пространственного развития территорий, Институт экономики Уральского отделения Российской академии наук (620014, Россия, г. Екатеринбург, ул.  Московская,  29), Уральский федеральный университет имени первого Президента России Б.Н. Ельцина» (620002, Россия, г. Екатеринбург, ул. Мира, 19); e-mail: naumov.iv@uiec.ru Красных Сергей Сергеевич – младший научный сотрудник Лаборатории моделиро- вания пространственного развития территорий, Институт экономики Уральского отделе- ния Российской академии наук (620014, Россия, г. Екатеринбург, ул. Московская, 29); e-mail: krasnykh.ss@uiec.ru https://doi.org/10.15826/recon.2022.8.1.001 http://r-economy.com https://doi.org/10.1016/j.foodcont.2021.108352 https://doi.org/10.1371/journal.pone.0257469 https://doi.org/10.1371/journal.pone.0257469 https://doi.org/10.1016/j.chaos.2020.109866 https://doi.org/10.3390/joitmc6030092 https://doi.org/10.1145/3465631.3465778 https://doi.org/10.3389/fpubh.2020.546637 https://doi.org/10.1038/s41746-020-00372-6 https://doi.org/10.1038/s41746-020-00372-6 20 r-economy.com R-ECONOMY, 2022, 8(1), 5–20 doi: 10.15826/recon.2022.8.1.001 Online ISSN 2412-0731 Отмахова Юлия Сергеевна – кандидат экономических наук, ведущий научный сотрудник Лаборатории компьютерного моделирования социально-экономических процессов, Центральный экономико-математический институт Российской академии наук (117418, Рос- сия, г. Москва, Нахимовский пр., д. 47); e-mail: otmakhovajs@yandex.ru ИНФОРМАЦИЯ О СТАТЬЕ: дата поступления 16 декабря 2021 г.; дата принятия к печати 1 марта 2022 г. 作者信息 诺莫夫·伊利亚·维克托罗维奇 – 经济学博士，地区空间发展建模实验室主任，俄罗斯 科学院乌拉尔分院经济研究所（邮编：620014，俄罗斯叶卡捷琳堡市，莫斯科路29号） ，乌拉尔联邦大学（邮编：620002，俄罗斯叶卡捷琳堡市，米拉路19号），邮箱：nau- mov.iv@uiec.ru 克拉斯尼赫·谢尔盖·谢尔盖耶维奇 – 地区空间发展建模实验室初级研究员，俄罗斯科 学院乌拉尔分院经济研究所（邮编：620014，俄罗斯叶卡捷琳堡市，莫斯科路29号）， 邮箱：krasnykh.ss@uiec.ru 奥特玛哈娃·尤利娅·谢尔盖耶娃 – 经济学博士，社会经济计算机建模实验室高级研究 员，俄罗斯科学院中央经济数学研究所（邮编：117418，俄罗斯莫斯科市，纳希莫夫街 47号），邮箱：otmakhovajs@yandex.ru http://r-economy.com https://doi.org/10.15826/recon.2022.8.1.001