How the pandemic affected interregional inequality in Russia

ABSTRACT Analysis of trends in interregional inequality in Russia in 2015–21 and of the actual outcome during the 2020 pandemic and the subsequent recovery in 2021 reveals short-term regional convergence in seven indicators, albeit of different depth and duration. Sub-federal budget revenue experienced the most significant and persistent reduction in interregional disparities, the main sources of which were a reduction of unevenness in a number of taxes, a significant increase in federal transfers and a change in their nature. After a strong short-term convergence, industry, trade, transport and investment all tended to return to long-term divergence paths. Personal income and wage inequality responded weakly to the shock in the short term and entered the new long-term path. Multidirectional spatial trends resulted from the interaction of sectorial and fiscal policy effects during the pandemic.


INTRODUCTION
Economic crises usually affect the economic situation in regions in different ways, thereby changing the spatial imbalance in a number of indicators. It is difficult to predict with certainty how a particular crisis will affect interregional inequality, whether it will reduce or exacerbate regional disparities. Much depends on which sectors the crisis will hit hardest and how the regional authorities will respond to new challenges. In addition, the crisis can have different short-and long-term implications for inequality due to the multiple regional recovery paths.
The economic crisis caused by the 2020-21 COVID-19 pandemic is somewhat similar to ordinary financial crises, since, in its acute phase, it was associated with a fall in oil prices. However, it differs from conventional financial crises in reasons and industries affected, as well as contagion mechanisms, which reduces the applicability of past experience to overcome it. Due to the connection of the pandemic with limited population mobility, the pandemictriggered crisis primarily affected transport, services and hospitality, as well as fuel production. At the same time, healthcare and digital spheres received an impetus for development. The sectorial structure of the regional economy, the severity of the restrictions imposed and the strength of regional support measures turned out to be the most important factors of regional development amid the pandemic.
This prompts an analysis of the spatial effects of the 2020-21 pandemic and its impact on interregional inequality. In the case of Russia such an analysis is of particular interest due to its vast territories, which differ in levels of development and economic structure. Understanding the spatial effects of the pandemic in Russia could support the development of a balanced interregional policy in the new conditions.

THEORETICAL FRAMEWORK
A number of researchers have examined differences in the resilience of regional economies to crises of various types, including the current pandemic crisis. Since regional economies exhibit different degrees of sensitivity to shocks, they can lead to changes in the level of interregional inequality. For example, in a study on the northern Chinese provinces, Hu et al. (2021) demonstrated a greater vulnerability of megacities and urban areas to the COVID-19 infection. It also highlighted the difference between the economic impact of the current pandemic shock and the financial crisis of 2008-09 on the Chinese provinces (Hu et al., 2021). Another paper, based on data from 130 countries and Bayesian model averaging (Glocker & Piribauer, 2021), provided evidence that the largest drop in production was in countries with large contact-intensive service industries and increased voluntary spatial distancing regarding containment measures.
Research on the Russian economy showed that the oil industry suffered the most during the pandemic, because of a sharp drop in oil prices and limited sales in the first months of the crisis (Malkina, 2021). The largest decline in revenues in 2020 was in the oil-producing regions, automotive centres and megalopolises with a developed service sector (Zubarevich, 2021b). On the contrary, regions with metallurgical industries received an impetus for development due to the soaring prices for metals and a threefold increase in the profit tax (Zubarevich, 2021a).
According to Malkina (2021), tax revenues, considered as a proxy for output volumes in the absence of other operational statistics, fell largely in the more developed Russian regions, which are characterized by a higher gross regional product (GRP) per capita and a concentration of capital-intensive industries. At the same time, tax revenues increased in regions where trade and the public sector accounted for a large share of the economy, and small and medium-sized businesses accounted for a higher share of turnover. More diversified economies showed greater resilience to the pandemic crisis than specialized economies (Malkina, 2021). This result is consistent with the findings of another study on the Russian economy (Kolomak, 2020), according to which more urbanized territories with diversified economic structures, as well as regions with a larger share of small and medium-sized businesses, showed greater flexibility during the pandemic, making them more resilient to the crisis.
Scientists identify different response and adaptation paths of Russian regions to external shocks. For example, Mikheeva (2021) distinguished four types of region: stable regions not subject to external shock (R1); stable regions in which the pre-crisis peak level was restored during the established crisis period (R2); unstable regions in which growth was recorded, but, until the end of the crisis period, it was not possible to restore the pre-crisis peak level (NR1); and unstable regions in which the pre-crisis peak levels of the indicator had not recovered and the indicators continued to decline (NR2). Based on the calculation of the resilience index, Turgel et al. (2021) identified four development paths for highly urbanized regions of Russia in the first wave of the pandemic: adaptively stable, vulnerable labile-adaptive, remissionadaptive and low-adaptive.
Despite detailed studies of the spatial effects of the pandemic, modern scientists have not paid sufficient attention to its impact on processes of regional convergence or divergence. Previous researchers who have focused on pre-pandemic crises have examined their short-and long-term effects on interregional inequality. However, their conclusions turned out to be ambiguous, depending on the specific crisis, country or group of countries and the indicator under consideration (Cuadrado-Roura et al., 2016;Iammarino et al., 2019).
Some scholars argue that crises have a greater negative impact on the economies of lagging regions than on the economies of developed ones; therefore, during an economic downturn, differences in the main indicators of regional production and income increase. For example, in a study of Greece, Petrakos and Psycharis (2016) concluded that the economic crisis had exacerbated regional inequality by strengthening the position of the Athens capital region. Developed regions with a higher specialization in tradable and export-oriented sectors adapted better to the economic crisis. However, in another study of Greece, Salvati (2016) showed that while the 2008-12 recession widened the gap between Athens and the rest of Greece, the differences in per capita income between the rich and poor regions narrowed. Omstedt (2016), considering the impact of the 2007-08 financial crisis on the economic gap between the North and South of England, concluded that, contrary to expectations, the gap had widened. The author attributed growing interregional inequality to policies supporting the banking sector while imposing austerity in the public sector. This policy contributed to the redistribution of the consequences of the crisis from the centre of financial capitalism in England to its periphery. A study of 199 regions of Central and Eastern Europe (CEE) (Brada et al., 2021) provided evidence that the 2008 crisis exacerbated regional income disparities due to strong positive spillovers across regions and the formation of clusters of high-and lowperformance areas. The authors extended their findings to the 2020 crisis. Mikheeva (2020), when examining the consequences of the crises of 1998, 2009 and 2015 for the Russian economy, indicated that they all began with regions most dependent on the conjuncture of world markets, with megalopolises and oil-and gas-producing regions. However, a deeper decline in production and a slow economic recovery were observed in regions focused on domestic demand. This contributed to the growth of interregional differences in the Russian economy. Malkina (2017) also confirmed that the 2008-09 crisis led to a short-term surge in interregional income inequality and almost all its components.
Other researchers argue that a crisis is more likely to lead to a decrease in interregional inequality if it affects more developed industries and regions, or if the government's anti-crisis policy is more conducive for lagging regions. For example, using a sample of 25 Organisation for Economic Co-operation and Development (OECD) countries over the period 1990-2014, Furceri et al. (2021) showed that economic downturns are associated with large and long-term reductions in regional inequality. They explain this phenomenon by the fact that expansionary fiscal policies and European Development (Cohesion) Funds help lagging regions better respond to national shocks. At the same time, Alexandre et al. (2018) explained the decline in interregional inequality in Portugal after the international financial crisis by non-equal response to the crisis in regions with different ratios of debt and exports to gross domestic product (GDP). Heavily indebted regions experienced a more severe recession and slower recovery; while the regions that were more open to trade saw a more moderate recession and stronger recovery.
The dynamics of interregional inequality during crises is sometimes associated with the dynamics of interpersonal inequality. For example, UK research (Hacıoğlu-Hoke et al., 2021) provided evidence that during the 2020 pandemic high-income quintiles of population experienced a stronger spending cut than lower income quintiles, and therefore rich regions moved closer to poor regions. Based on data for 143 countries in 2010-18, Shchepeleva et al. (2022) did not confirm a significant impact of the Global Financial Crisis (GFC) on wealth inequality. However, they concluded that the GFC exacerbated wealth inequality in countries with higher levels of economic and financial development and lower baseline wealth inequalities. Das et al. (2021) explored the impact of the five previous pandemics on interpersonal income inequality as measured by the Gini coefficient. The authors revealed a positive influence in a group of high-income countries and in the entire sample of 70 countries. However, pandemics negatively affected interpersonal inequality in the upper middleincome group of countries. This study also highlighted the impact of economic policies on inequality during a pandemic.
As for the Russian economy, according to Glazyrina et al. (2010), the 2008-09 crisis caused a short-term regional convergence of nominal and real GDP per capita. At the same time, Alexeev and Chernyavskiy (2018) revealed opposite consequences of the crises of 2009 and 2014-15. During the first crisis, inequality in Russian regional budget expenditure declined; in the second crisis, on the contrary, it increased. The authors attributed this difference to large federal transfers to lagging regions in 2009 and much smaller nontargeted transfers in 2014-15. Thus, the state's inter-budgetary policy can have a strong impact on interregional inequality, along with the changing sectorial effects of the crisis. In addition, specific indicators used to measure inequality (related to production in the main industries, income in the private and public spheres, etc.) may respond differently to the same crisis and lead to opposite conclusions about the dynamics of regional inequality.
Some researchers focused directly on the impact of the 2020 pandemic crisis on interregional inequality. Cerqua and Letta (2022) identified significant spatial effects of the coronavirus crisis in Italy. Using causal machine-learning models, they identified the factors that made regional labour markets vulnerable to the crisis: industrial specialization; exposure of economic activities to high risks of social aggregation; and pre-pandemic labour market vulnerability. The authors found no significant spatial correlation between the economic and epidemiological foci of the pandemic, or between the COVID-19 crisis hotspots and the Great Recession hotspots. Gbohoui et al. (2019) showed the importance of labour mobility in reducing inequality, which can also be an argument in favour of increasing interregional inequality in the pandemic. Fedajev et al. (2021) claimed that tighter restrictions on the movement of goods, services, capital, labour, technology, data and information following the pandemic will also contribute to divergence in Europe. This claim rests on the view that mobility of factors of production reduces inequality. This argument is contentious: although most authors accept that labour mobility may reduce wage inequality it may have adverse effects if high-quality human capital moves from less to more developed areas, while neoclassical and new economic geography models arrive at different conclusions concerning the mobility of capital which in conditions of increasing returns to scale and strong agglomeration economies may reinforce the growth of more developed areas (Dunford & Greco, 2008). Kuznetsova (2021) argued that the crisis caused by the COVID-19 pandemic did not lead to the emergence of fundamentally new patterns of the spatial development in Russia. However, the pandemic did bolster the advantages of large cities associated with higher levels of human capital. At the same time, Zemtsov (2021) pointed out the importance of accelerated digitalization during the pandemic and its greater potential in more developed regions, which may lead to an increase in interregional differences. Klimanov and Mikhaylova (2021) emphasized that the shortfall in regional tax revenues and growing regional spending during the pandemic were offset by a significant increase in intergovernmental transfers, which were extremely unevenly distributed between Russian regions. The share of lagging regions, primarily the republics of the North Caucasus, in inter-budgetary aid increased, contributing to a decrease in interregional differences (Zubarevich, 2021a). However, a decline in transparency and formalities in transfers (Yushkov & Alexeev, 2021) negatively affected regional development incentives. All these factors determined the short-and long-term impacts of the pandemic crisis on interregional inequality in Russia.
The following study focuses on the short-and long-term impacts of the 2020-21 pandemic on interregional differences in the Russian economy. The differences are assessed using data on personal and budgetary incomes, production volumes and turnover in the main industries, trade and transport, and the level of fixed capital investment. These data provide a complete picture of the dynamics of interregional inequality during and after the pandemic. Two measures of interregional inequality were used: the Gini coefficient (GC) and the coefficient of variation (CV). They meet the basic requirements for spatial inequality indicators: insensitivity to the number of regions and to changes in the average level of the indicator examined; and implementation of the Pigou-Dalton transfer principle (Lessmann, 2009). When using scale-invariant regional per capita variables, applying population/employment weights to the inequality measures returns the national average. Given the debate about the validity of weighting in cross-regional studies (Gluschenko, 2018), scholars, meanwhile, favour a weighted approach when dealing with political economy issues where the size of the groups subject to interregional inequality matters (Achten & Lessmann, 2020;Hrzic et al., 2021;Van Rompuy, 2021).
This study tests two alternative hypotheses regarding the impact of the 2020-21 pandemic on the change in interregional inequality in Russia (convergence versus divergence) and explains the results obtained by specific sectorial effects and economic policy during the pandemic.

METHODOLOGY AND DATA
The study employed annual data for 2015-21 for the 85 constituent entities of the Russian Federation (hereinafter referred to as regions) provided by the Federal State Statistics Service (Rosstat) and the Federal Treasury of the Russian Federation.
Interregional inequality was assessed for the following indicators of Russian regions: • per capita revenue of the consolidated budgets of the Russian regions (roubles), BR pc , 1 which were also broken down into own (tax and non-tax) sub-federal budget revenues (BRown pc ) and transfers to sub-federal budgets from budgets of other levels of government and non-governmental organizations, TRANS pc , most of which are federal budget transfers to the regions; • average per capita monetary income of the population (roubles), inc pc ; 2 • average monthly nominal accrued wages (roubles), w pc ; • per capita industrial production (roubles), Ind p pc ; industrial production is the sum of the value of shipped goods an entity itself produces as well as works and services performed on their own in four types of economic activity: mining and quarrying; manufacturing; electricity, gas, steam and air-conditioning supply; and water supply, sewerage, waste management and remediation activities; • per capita volume of wholesale and retail trade per capita (roubles), trade pc ; • per capita road transport freight turnover (ton-km), transp pc ; and • per capita fixed capital investment (roubles), Invest pc ; As already indicated, the level of interregional inequality for each indicator in each period was measured using two weighted coefficients. The first is the coefficient of variation (CV): where x i is the value of the corresponding indicator in the i-th region (i = 1, . . ., N); ρ i is the population share of the i-th region or (for the wage and investment indicators) is the share of the number of the employed persons aged 15-72 years; μ is the weighted average of the indicator in the country; and σ is its interregional standard deviation. The second was the Gini coefficient (GC): is the total share of regions from first to i-th in the value of the corresponding indicator, determined on an accrual basis. In this case, all regions should be arranged in ascending x i order.
After measuring actual regional inequality, it was necessary to determine what the level of inequality would have been were it not for the pandemic. First, linear or exponential timeseries regressions were estimated for all studied indicators (income, production, investment per capita, etc.) in all regions based on 2015-19 pre-pandemic data: linear: exponential: its linearization: where γ 0 and γ 1 are estimated linear regression coefficients; ε t denotes linear regression residuals; α 0 and α 1 are estimated exponential regression coefficients; and υ t ¼ lnðe t Þ are the corresponding residuals. Note that in linear regressions, the parameter γ 1 is the average annual marginal value of the indicator under study; while in exponential regression, α 1 is the average annual growth rate of the indicator. The choice between the two types of regression for each of the nine indicators for 85 regions (765 regional variables) was made in the light of estimates of the coefficient of determination, R 2 , Student's t-test scores and their significance. Sometimes, when forecasting, it is advisable to identify the cyclical component in addition to the trend. However, in this case, due to shortness of the time series, there was not enough data for this. Moreover, individual spikes of indicators (e.g., a sharp decline in tax revenues or a surge in transfers) may be sporadic and caused by irregular political decisions. Therefore, in this study, forecasts ignored various irregularities and took into account only trends.
The constructed regressions were then used to predict the non-pandemic values of the analysed variables in the pandemic period. Further, on their basis, the prognostic values of the inequality coefficients were calculated according to formulae in equations (1) and (2). Comparing actual and projected inequality coefficients suggested whether inequality decreased or increased during the pandemic.
Next, the application of the method of additive decomposition of variance (Shorrocks, 1982) makes it possible to determine the drivers of the dynamics of inequality in budget revenue per capita (BR pc ) and the magnitude of their effects: where BR pc_k denotes budget revenue from the k-th source (tax revenues, non-tax revenues, transfers and their types); K is the number of these sources; and BR pc ¼ P K k¼1 BR pc k . The calculation of the interregional variance (Var i ) and covariances (Covar i ) again used population/employment weights. It should be noted that the Shorrocks technique, having much in common with the portfolio approach, captures the contribution to inequality of three factors: the inequality of each income source, the share of each source in total income and the correlation of income from different sources. Finally, the proportional method of factor analysis helped evaluate the contribution of various income sources to the change in budget inequality during the pandemic compared with its nonpandemic forecast.
Applying the methods described above permitted identification of the impact of the 2020 pandemic and subsequent recovery in 2021 on spatial inequality as measured by the selected variables and the factors influenced it. Table 1 presents summary statistics for all linear and exponential regressions that could be used for non-pandemic forecasts of the indicators under consideration. The results do not indicate a great advantage of exponential over linear regressions. Both types of regression successfully explain the dynamics of variables in circa 76% of cases. They are ideal for describing the dynamics of per capita wages in the regions. At the same time, they are not well suited for tracking changes in transfers, road transport freight turnover, and investments. Despite this, the choice of linear regressions is justified by the fact that at the country level, linear regressions are of high significance (for six variables at p < 0.01 and for three variables at p < 0.05). Since regional fluctuations offset rather than reinforce each other nationwide, the unstable dynamics of some regional indicators can be ignored in the future.

RESULTS AND DISCUSSION
The following figures report the actual evolution of the interregional coefficients of variation and Gini for the seven indicators for 2015-21 (represented by solid lines) and the forecasts based on the forecasting models for 2020-21 (represented by dashed lines). The forecasts indicate the path of inequality were there no pandemic. A comparison of the actual and projected inequalities reveals the impact of the 2020 pandemic crisis and subsequent recovery in 2021 on regional convergence/divergence as measured by the respective variables.
First, the pandemic was accompanied by a significant decrease in spatial inequality in per capita consolidated sub-federal budget revenue (Figure 1). In 2020 alone, the interregional CV for per capita budget revenue decreased by 9.5% compared with 2019, and the GC declined by 8.3%. Moreover, in 2021, interregional inequality in per capita budget revenue did not experience a pronounced reversal. In 2020, the reduction in per capita budget revenue inequality relative to its forecast was 9% in terms of the GC and 8.4% in terms of the CV. In 2021, convergence was 7.5% and 10.4%, according to the two measures, respectively.
The trend towards convergence in the budget sector can be explained by at least three factors. First, due to the specific sectorial effects of the pandemic, which primarily affected the  more profitable sectors such as mining, automotive industries, etc. (Malkina, 2021;Zubarevich, 2021a), there was a stronger reduction in own (tax and non-tax) revenues in some more prosperous regions. Second, during the pandemic there was an unprecedented growth of federal transfers to the regions. In 2020 alone, they increased by 54%. Extra transfers often assumed the form of per capita subsidies for social needs and health care, which had a levelling effect. In addition, a greater increase in transfers to some regions that previously received less (Figure 2) reduced the unevenness of transfer incomes of sub-federal budgets.
Third, in the context of the pandemic, a negative relationship between the level of own regional budget revenue and the share of allocated federal transfers remained. However,  according to Figure 3, the negative elasticity of the share of transfers with respect to own budget revenue per capita in the regions decreased from 11.84 in 2019 to 9.56 in 2020, which means a decline in the levelling effect of this factor. Meanwhile, as early as in 2021, the prepandemic elasticity of the exponential function had almost recovered.
In the first approximation, these three factors together contributed to the convergence of Russian regions in terms of budget revenue per capita. The decomposition of the coefficients of variation using the Shorrocks technique (equation 7) provides a more detailed analysis of the factors that led to a significant reduction in interregional fiscal disparities. The results of this decomposition for all years are presented in Table A1 in Appendix A in the online supplemental data. Table 2 reports the contributions of various budget revenue sources to reducing fiscal inequality in 2020 and 2021 compared with the forecasts, computed using proportional factor analysis. First of all, the reduction in interregional budget inequality in 2020 and 2021 was due to both the response of tax revenues and transfers to the pandemic.
Tax revenues were the largest contributor to fiscal convergence, accounting for 6.7% of the 8.5% decline in budget inequality in 2020 and 4.6% of the 10.5% decline in 2021. The main drivers were the reduction in the share of taxes in sub-federal budget revenue (from 74.4% in 2019 to 67.2% in 2020, and 72% in 2021) and the decrease in their unevenness in 2021  (Table 3). Profit tax and property taxes had the greatest impact on reducing inequality, with the decline in their share in total tax revenues being the most significant factor. Federal transfers accounted for a smaller but growing share of the decrease in fiscal inequality (29.9% in 2020 and 41.6% in 2021) compared with tax revenues (78.9% and 43.5%, respectively). Among the transfers, subventions were the most equal (Table 4) because they are allocated on a per capita basis for the implementation of decrees and resolutions of higher authorities and are often associated with social spending. However, in two years they  grew by only 31%, while all federal transfers increased by 49.9%, and the share of subventions in total federal transfers fell from 16.2% in 2019 to 14.1% in 2021. This reduced their levelling effect. Grants are characterized by average inequality among all transfers, with the most uniform being grants to equalize the budgetary provision of the regions, and the least uniform are grants to balance regional budgets. During the pandemic, equalization grants grew at the slowest pace (in 2020 they increased by 6.3%, and in 2021 by only 0.1%). As a result, their share in federal transfers dropped from 27.5% to 19.5% in two years. At the same time, grants for balancing increased at a significant pace. This increase also reduced the potential for fiscal equalization during the pandemic.
At the same time, the so-called other inter-budgetary transfers had the greatest convergence effect among all transfers. Along with subsidies, the equalizing effect of which turned out to be the second largest, they were distributed outside uniform rules and were often allocated to regions for investment purposes and in connection with the implementation of national projects. The downward trend in the regional share of co-financing of such transfers allowed the federal centre to more abundantly finance projects in regions with lower investment capacity. A significant increase in the uniformity of the distribution of subsidies and other federal transfers (Table 4), along with an increase in their share in federal transfers (by 9.7% and 2.2% over two years of the pandemic), became meaningful factors in fiscal equalization. However, the effectiveness of raising these funds in terms of cost feasibility and longterm impact on regional development is still questionable and requires a separate analysis.
As far as the impact of the pandemic on inequality as measured by other regional indicators, it turned out to be similar and at the same time different.
Population incomes ( Figure 4) and their main component, wages ( Figure 5), saw only a slight decrease in spatial differences during the 2020-21 pandemic. According to the GC, interregional income inequality in 2020 remained almost at the level of the previous year, while spatial wage inequality decreased by only 1.4%. According to the CV, income inequality increased slightly (+1.2%), and wage inequality fell by only 0.7%. However, in 2021, the growth of inequality resumed: in the case of income, it increased at +2.9% (according to the CV) and +3.3% (according to the GC); in the case of wages, increased at +0.5% and +1.2%, respectively. Meanwhile, both graphs clearly show that the inequality curve is below the nonpandemic forecast, suggesting a continuing, albeit weak, convergent effect.
Trends in spatial inequality in industry, trade, and transport appear to be somewhat similar both before and during the pandemic (Figures 6-8). According to the two measures of inequality, regional disparities in industrial production and trade fell sharply in 2020. The dynamics of the two coefficients of inequality in road transport freight turnover differ markedly. The CV in 2020 was 15.4% below its non-pandemic forecast for per capita industrial production, 14.5% below for road transport freight turnover and 5.1% lower for wholesale and retail trade. The GC confirms the convergence in these sectors, but the estimated declines were more moderate. The reduction in spatial inequality in aggregate industries during the pandemic may be due to the greater vulnerability to the crisis of economic sectors located in more prosperous regions. Indeed, economic growth rates in the leading industries declined at a faster pace (Malkina, 2021).
The volume of industrial production per capita in nominal terms is the only indicator under study for which the reduction in interregional inequality in 2020 was accompanied by a decrease in the absolute value compared with 2019. However, during the economic recovery, interregional inequality in industrial production took revenge, and by 2021 exceeded the 2019 pre-crisis level by 1.9-3.3%, approaching the predicted non-pandemic trend ( Figure 6). This result may be due to the peculiarities of regional resilience with the regions that declined most during the crisis showing the highest post-crisis growth rates. The rebound allowed them to climb even higher, which could lead to further widening of interregional disparities and is suggestive of long-term effects of the crisis on inequality.
Interregional differences in wholesale and retail trade volume (Figure 7) behaved similarly to industrial production, showing a significant decline in 2020 and a return to the prepandemic trajectory in 2021. A similar convergence trend was observed for transport in 2020 (Figure 8), giving way to a moderate increase in interregional inequality in 2021, albeit not reaching the predicted level. COVID-19 pandemic and Russian regional inequality Finally, the pandemic crisis affected interregional inequality in fixed investment (Figure 9). First, in the period under review, the unevenness indicators changed asynchronously, possibly due to the peculiarities of their calculation. Second, both indicators of spatial investment inequality showed little change during the 2020 shock. For example, the 2020 CV was 1.8% lower than the  2019 CV, while the GC was slightly higher. Third, similar to sectorial inequality, investment inequality was approaching the pre-pandemic path in 2021. However, unlike sectorial production, investment responded to the pandemic shock more weakly and recovered more slowly.
Thus, the results confirm a short-term convergence across the majority of indicators in the acute phase of the pandemic, albeit varying in strength and persistence, and a reverse trend during  COVID-19 pandemic and Russian regional inequality the recovery phase. However, only in the case of sub-federal budget revenue did the convergence effect almost completely extend to the recovery period. This outcome was mainly due to a change in revenue structure in favour of transfers, as well as a decrease in the share of profit and property taxes and an increase in the share and uniformity of transfers intended for investment purposes and national projects. The major sectors of the economy provide empirical support for the concept of path dependency or lock-in effect in the long run. In the cases of population incomes and wages, there was evidence of a slight decrease in spatial inequality, entering into a new stable trend.

CONCLUSIONS
This paper examined the impact of the 2020-21 pandemic on interregional economic inequality in Russia. Inequality was measured using seven indicators relating to sub-federal budget revenues, personal incomes, production volumes in industry, transport, and trade, as well as investments in fixed assets, calculated per capita or per person employed. Inequality in these indicators was measured using the coefficient of variation and the Gini coefficient, weighted by the region's share in total population or total employment. Assessment of the impact of the pandemic on interregional inequality was conducted in three stages. First, using pre-pandemic data, time series regressions were estimated for all regional per capita indicators. Second, based on these regressions, non-pandemic regional indicator values were projected for the pandemic period. Third, these forecasts were used to predict the values of inequality coefficients that would have prevailed in the absence of the pandemic. Comparisons of actual and forecast values of inequality made it possible to determine the influence of the pandemic on short-and long-term Russian regional convergence or divergence as measured by the chosen indicators. The contribution of various budget revenue sources to the per capita regional convergence was estimated using Shorrocks' variance decomposition method.
The research provides evidence that the pandemic affected Russian interregional inequalities in similar but somewhat different ways. Per capita sub-federal budget revenue showed the most significant reduction in inequality. This reduction persisted into the recovery period, partly because of the predominant fall in tax revenues in more prosperous regions during the acute phase of the pandemic, and a decrease in the share of the most uneven taxes (e.g., profit tax) in budget revenues. Federal aid also played an important role in the convergence of per capita regional budget revenues, mainly due to the strengthening of the regional uniformity of transfers allocated for financing investment and implementing national projects. The share of subsidies and other intergovernmental transfers in federal aid rose sharply during the pandemic, and their degree of inequality narrowed. However, their impact on the development of regional potential and long-term economic efficiency remain in question and require independent study. Generally, the current tendencies in the distribution of transfers fits into both the dirigisme policy of the Russian state and the new paradigm of fighting poverty.
Interregional differences in industrial production and trade declined significantly during the pandemic crisis and returned to previous growth trends in the recovery period. In contrast, personal income and wage inequality responded slightly to the shock in the short term and continued to increase after it, albeit below the non-pandemic trend. Transport turnover and investment showed a weaker response to the shock than production in the main sectors, but also a slower recovery. In general, the results support the concept of the path dependence in economic development.
A limitation of the study stems from the inability to fully assess the inequality implications of the pandemic shock because it is still ongoing. Further development of the study assumes a more accurate distinction between the short-and long-term consequences of the pandemic in Russia, and the relationships between interregional inequality dynamics in various sectors of the economy, budget revenues and income requires a separate, more delicate analysis. In addition, the peculiarities of the pandemic crisis in the Russian regions and the way the