**4. Discussion**

This study focused on the socio-economic assessment of the attractiveness of Arctic territories to potential migrants. We should note that the regions under consideration are significantly heterogeneous in terms of most indicators. The Murmansk region is characterized by the highest population, which is largely due to its milder climatic conditions, proximity to European countries, and developed infrastructure. The lowest population for the 9 studied years was in the Nenets Autonomous district, whose indicator values are 17–19 times lower than those in the Murmansk region. The rest of the indicators are also scattered for different Arctic regions. However, the territories under consideration have a common problem: the outflow of the working population to more favorable climatic zones.

The main limitations of the study are discussed below.

It is evident that the migration attractiveness of the Arctic region to the working population is determined by a range of indicators. However, not all indicators can be quantified. This is due to the fact that people rarely base their choices only on quantitative indicators in the decision-making process. In particular, it seems doubtful that a potential immigrant would analyze regional statistics on indicators such as GRP per capita, investment in fixed assets, or infant mortality rates before moving to a region. The decision to move is made on the basis of the individual's principles, life attitudes, beliefs, and other personal characteristics that cannot be quantified, as mentioned in [71].

Thus, the migration attractiveness of a region also depends on a range of non-measurable personal characteristics, such as tolerance to difficult weather conditions. Our research does not separate the influence of quantitative and qualitative parameters on migration processes, as the qualitative characteristics of the research object are difficult to formalize. This fact also prevents their use for assessing the attractiveness of the region together with socio-economic indicators. In addition, only measurable parameters can be analyzed with the proposed research methods. For these reasons, we limited our research to the investigation of quantitative characteristics of the object. Additional research covering qualitative characteristics in order to analyze their influence on migration processes in the Russian Arctic and assess the attractiveness of regions would provide further insight into the problem of migration outflows. Nevertheless, we consider it possible to identify key economic and social indicators that can be used to objectively assess the attractiveness of the Russian Arctic regions based on statistical data, which was performed in the framework of this study.

The second limitation is that this study focuses only on simple linear regression relationships between migration indicators and the indicators that cause their variation. In this regard, as dependent variables of the models, we studied only those indicators that have a close linear correlation with migration. The presented models do not account for other factors. In the future, we plan to apply complex-valued non-linear econometric models and include a wider range of indicators. In addition, it is possible to apply an individual approach to each region separately, adjusting the list of indicators for building regression models depending on their individual characteristics.

Finally, the research was limited by the relatively small amount of retrospective data for the following key reasons: (1) the investigated time series data must be stationary, and (2) statistical data are not publicly available for all analyzed regions. Since migration processes are very sensitive to changes such as legislative and legal regulations, social benefits, and economic incentives, we considered time series that were formed in relatively stable conditions, which limits the study timeframe. Moreover, we faced a data acquisition problem when trying to separate the statistical data for areas located beyond the Arctic Circle from the whole administrative region's dataset. For this reason, we had to analyze only those regions that are fully located beyond the Arctic Circle. In addition, some Arctic regions do not have any publicly available unified statistical information within the 2010–2019 timeframe, which also limited our research.

There is also one disputable point that should be mentioned. The choice of specific indicators for assessing the social and economic attractiveness of regions and building regression models may seem controversial. However, in the course of the study, the authors conducted a thorough analysis and selected attractiveness indicators based on the works of Russian and foreign researchers, specifics of the studied regions, and possibilities of accessing quantitative information for their assessment. According to our assessment, the list of selected indicators best characterizes the attractiveness of the Arctic region to migrants from other territories, especially Russian ones. Choosing equal weight coefficients for all indicators is debatable, although it prevents the excessive influence of any indicator on the result.

The objectivity of the research in selecting indicators for estimating the attractiveness of regions was achieved by using a number of independent experts and conducting correlation analyses to determine indicators that have a significant linear relationship with migration processes. The use of complex-valued econometric methods makes this study unique, since this is the first time that the tools of a complex-valued economy are used to simulate migration processes in the Arctic regions. The procedure for evaluating regional attractiveness is also new, as it involves a unique list of indicators identified during the research, which are specific to Arctic regions.

Thus, the results of this study are the six economic and six social indicators identified on the basis of a thorough literature review and expert surveys; the assessments of the linear relationship between each indicator and migration processes in the Arctic regions; four complex linear regression models that can be used to predict the number of arrivals and departures in the region; and evaluation of the attractiveness of four Arctic regions in terms of their social and economic development.

The key findings of the research are as follows: (i) all Russian Arctic regions are characterized by a stable outflow of the population throughout the 10 studied years; (ii) migration processes are more linearly dependent on social indicators than on economic ones, which confirms the importance of the former; (iii) the four presented complex linear models produced better forecasting results than the simple extrapolation of the trends, so linear complex-valued models are suitable for predicting migration processes in the Arctic regions of Russia; (iv) the Chukotka Autonomous district has the highest social attractiveness, while economic incentives for migration are the highest for the Yamalo-Nenets Autonomous district.

The unexpected result of the study was that among all Arctic regions, the Chukotka Autonomous district took the lead in terms of social attractiveness. It should be emphasized that Chukotka is the most sparsely populated region of Russia and the most distant from the center. According to the Russian Statistical Agency, the area of the region is 4% of the total area of Russia, the population in 2021 is 49,527 people (0.03% of the population of Russia), and the population density is only 0.07 people/km2. The region is very rich in mineral resources, so all socio-economic indicators are at a high level. The finding that the Yamalo-Nenets Autonomous district emerges at the top in terms of economic indicators is more predictable since oil and gas resources, the basis of the national budget, are concentrated in this region. The region is in 7th place for GRP among all regions of the country. However, due to the larger population (547.01 million people) and the population density (0.71 people/km2) compared to Chukotka, the Yamalo-Nenets Autonomous district has a lower score in terms of social attractiveness.

The scientific contribution of this article to the study of migration processes in Arctic regions is the use of complex-valued econometric models to predict future migration flow. These studies were conducted for the first time, and the calculations proved to be effective and have potential practical applications.

We sugges<sup>t</sup> that this method be tested on a larger dataset on migration.
