Index Method of Evaluating the Performance of Economic Activities

The subject of the research is the economies of the constituent entities of the Russian Federation and the branches of economic activity functioning in their territories. The aim of the study is to develop methods for assessing the efficiency of economic sectors and types of economic activity within the boundaries of 85 constituent entities of the Russian Federation and to create a rating of the efficiency of the constituent entities by the type of economic activity “Production and distribution of electricity, gas and water”. Economic and statistical methods, system analysis, as well as general scientific methods of comparison were used. The main calculations are based on the tax revenue efficiency index developed by the authors by types of economic activity. It is based on 13 indicators, where each corresponds to the type of economic activity and assesses the level of economic development of a constituent entity of the Russian Federation. The authors analyzed the reports on tax revenues and the number of employed population in the context of economic activities. Data analysis and parameter estimation were carried out by means of the statistical information processing program IBM SPSS Statistics 20, the analytical module of the Russian Taxes regional tax revenue information analysis system and the MS Excel 365 tabular processor. Based on the proposed method, the distribution of the constituent entities of the Russian Federation was obtained according to the values index of tax revenues for all types of economic activity in 2016. The effectiveness of tax revenues for individual indicators included in the index was considered. The distribution of the constituent entities of the Russian Federation by the type of economic activity “Production and distribution of electricity, gas and water” was obtained. The distribution indicators for each constituent entity of the Russian Federation were calculated. Graphs showing the structure of the tax revenues efficiency index in the Moscow region and in the Altai Republic in 2016 were built. The proposed method allows to obtain a comprehensive indicator of the system’s activities and development, to assess its potential, to define goals, to identify infrastructural problems and the shortcomings in economic diversification, as well as to evaluate investment risks and threats.


INTRODUCTION
The economy of the Russian Federation is in a difficult situation. The economic development of the country is influenced by both external and internal factors. The external factors hampering the development of the economy include the aggravation of the geopolitical situation, the continuously extension of the sanctions lists against the activities of Russian companies, the instability of world markets, the fall in energy prices, etc. The list of internal factors slowing down the economic development is even more extensive. These include: prolonged financial and economic crisis, technological backwardness of domestic companies and industries, inefficient use of human and natural resources, unfavorable conditions for lending to companies in the domestic market, aging and low rates of input of fixed assets, etc.
In work [1, p. 118-127], the functioning of the Russian economy as a diffuse system is considered, and a model of a macroeconomic production function is developed, an analogue to Cobb-Douglas function [2, p. 139-165]. Work [3, p. 120-127] presents a conceptual model of the financial and economic functioning of a constituent entity of the Russian Federation, where the efficiency of economic activities in the region is estimated through the tax revenues produced in its territory. This type of aspect will be applied in the studies described below.
In article [4, p. 63-70], the first attempt was made to use the index method to analyze the performance of the constituent entities of the Russian Federation. It also presents a rating of the performance of the constituent entities of the federation. As a result, all the constituent entities of the Russian Federation were divided into three clusters: the constituent entities of advanced development, the constituent entities aspiring to the average value, and the constituent entities lagging behind in economic development.
In work [5, p. 139-145], by the example of the Ivanovo region, the technological backwardness of the manufacturing industries located on its territory, aging and low rates of introduction of fixed assets and the inefficient use of the active and busy population are shown. Similar studies are devoted to the following works of domestic and foreign authors [6; 7, p. 113-116; 8, p. 7-10].
The authors attempted to investigate the financial and economic state of the constituent entities of the Russian Federation based on the index method in the context of economic activities. The index method refers to the methods of statistical analysis and its applied aspect of research is used in many branches of science and technology. This method has received particular application in economic research. At the same time various aspects of economic and management activities are touched upon.
This method has won the greatest popularity in the field of macroeconomic research. For example, at the World Economic Forum in Davos in 2018, it was proposed to use the Inclusive Development Index; IDI. This index assesses the economic situation in 107 countries according to the criteria of economic growth, sustainability and equity. The IDI is based on twelve indicators combined into three groups. Forum experts believe that the IDI reflects the level of a country's economic development better than an indicator of GDP growth 1.
According to the IDI, Norway ranks the first place, and the Republic of Mozambique is the last. The Russian Federation is in the 19th place, losing four points to the Republic of Kazakhstan.
A number of works by foreign authors are devoted to the application of the index method in economic research. Special attention is paid to the development of methods for calculating the index of stable economic well-being, known as the Genuine Progress Indicator (GPI). The GPI was developed by Herman Daly and John Cobb in 1989. This index was proposed by the scientists as "a way of measuring the economy that will give better guidance to those interested in promoting economic welfare" [9]. GPI is the value of GDP per capita of a country, adjusted for the amount of expenditure invested in socioeconomic and environmental development. Creating a GPI is one of the successful attempts to synthesize an aggregated monetary index. Today in the field of GPI research the following works are known: [10, p. 13-28], [11, p. 162-172], [12, p. 330-341].
The index method is also used to assess the development of the territories of the Russian Federation. The Consortium Leontief Centre -AV Group has developed a document entitled "Regional Competitiveness Index -Growth Poles of Russia (AV RCI-2015)" 2. This paper describes the methodology for creating and applying the "Regional Competitiveness Index" where it determines the ability of a region to compete for markets and resources. Similar studies are carried out in the works "Analysis of the factors of improving Russia's competitiveness in the international market" [13] and "Estimating the economic development of countries based on the global competitiveness index" [14, p. 128-138].
Ecological economics often uses the Environmental Sustainability Index (ISE), developed by Columbia and Yale Universities for the World Economic Forum in Davos. The applied aspect of using the ISE at the present stage is reflected in works [15, p. 13-28] and [16, p. 285-300.].
The subject of this research is the economics of the constituent entities of the Russian Federation and the branches of economic activity functioning in their territories. 85 territories of the Russian Federation were considered as constituent entities. 13 types of economic activity were analyzed.
The aim of the study is to develop methods to assess the performance of the industries in 85 constituent entities of the Russian Federation in the context of economic activities. It will include a performance rating of the constituent entities of the Russian Federation by type of economic activity, in particular, the distribution of electricity, gas and water.
The studies were based on economic-statistical methods, system analysis, as well as general scientific methods of comparison. The main calculations were made by means of the index method developed by the authors to analyze the types of economic activity of the constituent entities of the Russian Federation.

RESEARCH RESULTS
To give an objective account of the economic activity of the constituent entities of the Russian Federation, the authors propose a method based on an integral indicator of tax revenues for all types of economic activity -an efficiency index of tax revenues. To assess the efficiency of tax revenues in the constituent entities of the Russian Federation, it is proposed to use the index method.
When calculating the index values, the statistical data for 2015-2016 were used, presented by the Federal Tax Service of the Russian Federation and the statistical data on the main socioeconomic indexes provided by the Federal State Statistics Service of the Russian Federation. To simplify the subsequent analysis, the collected data was consolidated in the database of the information-analytical system of regional tax receipts "Taxes of the Russian Federation" [21, p. 56-57].
Let us introduce the next relative performance index. It is equal to the ratio of the value of tax income to the average annual number of the employed population of a constituent entity of the Russian Federation for a certain type of economic activity. Let us call this index a relative performance index of tax revenues (OPEN) by type of economic activity. For each constituent entity, thirteen indexes can be determined (by the number of types of economic activity, m = 13) -OPEN ij , where the index i takes values from 1 to 85 (by the number of constituent entities in the Russian Federation, n = 85), and the index j corresponds to the type of economic activity and, therefore, varies from 1 to 13.
This index characterizes the tax income on average for a constituent entity that is brought to the country budget by one employee engaged in the relevant type of economic activity. In the future, this index will be denoted as X i j for simplicity. Now, we will calculate the average value of the relative performance index of tax revenues for all constituent entities for each type of economic activity. As a result, we will obtain thirteen values determined by the formula of a simple average Then, for each tax, we will determine the variance j D and the standard deviatio j σ of the relative performance index of tax revenues for constituent entities. These variation indexes were calculated by means of the following formulas: Using the calculated average values, we will center all relative indexes ij X by the following formula .
If we now apply the valuation operation using the standard deviations ij X  to the centered relative indexes , j σ we will obtain standardized relative performance indexes of tax revenues (indexes) for each type of economic activity in all constituent entities Since the value of tax income for various types of economic activity is influenced by numerous diverse factors, it can be assumed that standardized values ij U are subject to different laws of distribution, but with the same averages and variances. Thus, each constituent entity of the Russian Federation can be characterized by a system of dimensionless indexes with the same average values equal to zero and variances equal to one.
If the obtained indexes for all types of economic activity are summed up for each constituent entity, we will eventually have the values of a certain aggregate index reflecting the efficiency of tax collection in the constituent entity for all types of economic activity: resulting index of tax collection efficiency is based on 13 indicators, each of them corresponding to the type of economic activity and assessing the level of economic development of the constituent entity (the index value in the i-th constituent entity is equal to i I ). Let us estimate the share of each type of economic activity in the total tax revenue and in the number of the employed population ( Table 1).  Table 1 shows that the share of foreign economic activity "Mining" is almost a third of all tax revenues.

TAXES AND FEES
Comparing the structure of tax revenues and the employed population, we see that the ratios of the shares of tax revenues d tr to the shares of the employed population d ep by types of economic activity differ significantly among themselves (for example, in 2016 the highest value of 19.01 was observed for the foreign economic activity "Mining", and the smallest -0.11 for the foreign economic activity "Agriculture, hunting and forestry; fishing, fish farming"). They differ from the even distribution of tax revenues (in this case, the ratio of the shares of d tr to d ep is equal to 1). Figure 1 shows a graph of the distribution of tax revenues by type of economic activity (analogous to the Lorenz curve), which clearly demonstrates the inequality of such a distribution (a significant deviation from the uniform distribution).
The degree of uneven tax revenues by type of economic activity can be quantified. For such an

TAXES AND FEES
that can be used to measure the level of economic development in the regions, their intersubjective comparison and to assess the effectiveness of tax revenues in various types of economic activity. The method of building up the index makes it possible to analyze its (and its individual indicators) dynamics, which allows to assess changes in the economic activities of the constituent entities in the role redistribution of economic activities in terms of the effectiveness of tax revenues.
The proposed method of calculating the index makes it possible to use a variety of measurements in any socio-economic system (evaluating the resource, economic, social, etc. system potentials), which allows to obtain a comprehensive indicator of the economic development of the system, to assess its potential, to define goals, to identify infrastructure problems, gaps in the diversification of the economy, and to assess investment risks and threats.
Here are some examples demonstrating the possible use of the index of efficiency of tax revenues in analyzing the economic activities of the constituent entities of the Russian Federation. Figure 2 shows the distribution of the constituent entities of the Russian Federation according to the values of the index of efficiency of tax revenues I.
It can be seen that there is a fairly strong stratification of the constituent entities of the Russian Federation on the effectiveness of tax revenues. For example, the number of the constituent entities whose index value is positive (above the average level) is 28, and in 57 constituent entities the value of this index is below zero.
The effectiveness of tax revenues can be considered by certain types of economic activity, i. e. by individual indicators included in the index. Table 2 presents the distribution of the constituent entities of the Russian Federation by the indicator in the foreign economic activity "Production and distribution of electricity, gas and water". It follows from the table that the most developed constituent entities in this foreign economic activity are: Moscow, the Krasnoyarsk Territory and the Khanty-Mansiisk autonomous district. A total of 26 constituent entities are above the average level (zero), and 59 of them are below. The Republic of Ingushetia, the Chechen Republic, the Republic of Kalmykia, the Pskov and Kirov Regions are the weakest. It can be concluded that the development of foreign economic activity "Production and distribution of electricity, gas and water" among the constituent entities of the Russian Federation is very uneven.
Based on table 2 we will make figures 3 and 4. Figure 3 shows the distribution curve of the constituent entities according to the index reflecting the efficiency of tax revenues from the foreign economic activity "Production and distribution of electricity, gas and water". Figure 4 shows a histogram of positive index values of efficiency of tax revenues for the foreign economic activity "Production and distribution of electricity, gas and water" (index I 4 ) in descending order.
Let us consider the effectiveness of tax revenues by type of economic activity. For this, it is necessary to evaluate all summands (indicators) included in the index. For example, figure  5 shows a histogram reflecting the structure of the index of efficiency of tax revenues for the Moscow region (the index value is 8.72; it is the 10th among the constituent entities of the Russian Federation on this indicator). It can be seen that the highest efficiency of tax revenues in this constituent entities is observed in such foreign economic activity as "Production and distribution of electricity, gas and water".
Let us consider the efficiency of tax revenues in a constituent entity in the middle of the ranked list (the index value is -2.44; it is 43rd among the constituent entities of the Russian Federation on this indicator).
The structure of the index for this constituent entity, presented in figure 6, indicates that for all FEA, the efficiency of tax revenues is close to the average values, practically the values of all indicators are within the intervals (-σ; + σ). Table 2 Indicator of distribution of the constituent entities of the Russian Federation by type of economic activity "Production and distribution of electricity, gas and water" in 2016  Production and distribution of electricity, gas and water

CONCLUSIONS
The article reviews the scientific works of domestic and foreign authors in the field of application of the index method and its indicators. It is revealed that this method is widely used in various fields of economics and management. The index of efficiency of tax revenues is proposed, based on 13 indicators, each of them corresponding to the type of economic activity and assessing the level of economic development of a constituent entity of the Russian Federation.
Based on the proposed method, the distribution of the constituent entities of the Russian It should be noted that the presented index method allows to evaluate the efficiency (effectiveness) of tax revenues in the constituent entities of the Russian Federation simultaneously for all types of economic activity, to compare the constituent entities among themselves accord-ing to the values and structure of this index, to classify the constituent entities of the Russian Federation in terms of tax revenues, to analyze the change in dynamics and to predict its values in the future. The proposed method of calculating the index makes it possible to use a variety of diverse factors that affect the socio-economic system (economic, socio-demographic, technological, etc.), which allows to obtain a complex index of the system activities and development, to assess its potential, to define goals, to identify infrastructure problems, gaps in the diversification of the economy, and to evaluate investment risks and threats.   A. Sh. Kamaletdinov, A. A. Ksenofontov