Statistical analysis of the differentiation of regions of the Russian Federation by tax revenues of consolidated budgets using the R language

Apal'kova Tamara Gennadievna ORCID: 0000-0001-8094-1588 PhD in Economics Associate Professor, Department of Mathematics, Financial University under the Government of the Russian Federation 49 Leningradsky Prospekt str., Moscow, 125993, Russia apalkova.t.g@yandex.ru

Levchenko Kirill Gennadievich ORCID: 0009-0008-7380-3388 PhD in Physics and Mathematics Associate Professor, Department of Mathematics, Financial University under the Government of the Russian Federation 49 Leningradsky Prospekt str., Moscow, 125167, Russia kglevchenko@fa.ru

Introduction

The study of publications investigating the features, structure and differentiation of tax payments and fees ^[1-5] has shown that mathematical and statistical analysis in these works is rather rare and in most cases reduces to the analysis of dynamics ^{[2, 3]}. However, in combination with modern technical means, methods of mathematical statistics are a powerful tool that allows you to highlight the processes of collecting, calculating, and paying taxes from different sides and thus identify the most problematic and, conversely, positive aspects of these processes. This article aims to demonstrate the capabilities, effectiveness and simplicity of visualization tools, descriptive statistics, aggregation and clustering of the open source programming language R in tax analysis.

Data for modeling.

The initial data was information on the execution of the consolidated budgets of the subjects of the Russian Federation for 2020 (Ministry of Finance of the Russian Federation. Data on the execution of consolidated budgets of the subjects of the Russian Federation), presented by the source in the .xlsx file format. You can import data in this format into the R environment using the readxl::read_excel() function. Here and further in the text, the entry before the double colon indicates the name of the package to which the function specified after the double colon belongs. The mentioned file contains information on income and expenses of the consolidated budget, income is differentiated into tax and non-tax, and the three most "significant" taxes for each region are separately allocated: income, property and personal income. Figure 1 shows a fragment of the source file with a slight change: after the "Region" column, the "District" column was added, the rows with intermediate and final summation (by districts and the country as a whole) were deleted. The data generated in this way is called "rectangular": each row contains information about one object, each column is responsible for a specific feature. In addition to externally obtained data, several synthetic features were added to the data set: the relative contribution of tax revenues (total and for each tax) to the revenue side of budgets.

Figure 1 – A set of source data (fragment)

Data aggregation. If the researcher is interested in the difference in tax revenues to the consolidated budget by federal districts, it is possible to determine the average values for each district. For this purpose, the basic functions are applicable: aggregate() – in the case when you need to calculate averages for several criteria at once, or tapply() ^[6] – if the averages are calculated based on one attribute. Let's consider an example of using the aggregate() function^[7] to calculate the average values of total tax revenues for federal districts (Table 1), as well as the average shares of tax revenues (total and by type) in the budget revenue (Table 2).

In general, the syntax of the aggregate() function looks like this:

aggregate(x =<truncated, or complete data set>,

                         by=list(<one or more grouping features>),

                         FUN = mean)

Table 1- Regional average values of consolidated budget revenues by type of income and federal districts, million rubles

Table 2 - Regional averages of relative contributions of tax revenues to consolidated budgets by type of income and federal districts

Graphs make a more visual comparison of the average values by districts, in this case, bar charts are most appropriate (Figures 1 and 2). Figures 1 and 2 show graphs for the average values of tax revenues for each district, aggregated data from Tables 1 and 2 are used, respectively. The ggplot2::ggplot() function can be used as a visualization tool in combination with one of the quick access functions: geom_bar(), or geom_col() ^[8-10]. At the same time, as arguments for the quick access functions, you should specify the variables responsible for the x and y coordinates – the federal district and the average tax revenues of the budget for the district (for Fig. 1), or the average share of tax revenues in the budget for the district (for Fig. 2) accordingly. In addition, the geom_bar() function in this situation requires additionally specifying the value of the stat='identity' argument, which will allow the y coordinate values to be reflected along the ordinate axis instead of frequencies. The geom_col() function does not require this additional argument.

Figure 1 – Regional average values of tax revenues by federal districts, million rubles

Figure 2 – Regional average values of relative contributions of tax revenues to the consolidated budgets of regions by federal districts

When comparing the diagrams, it becomes obvious that as a result of calculating relative indicators, the scale effect is leveled: for several districts (Far Eastern, Volga, Northwestern, Northern, Central), the average regional shares of tax revenues to budgets differ little, the Central District, the leader in absolute average contribution, is inferior to the Ural District in terms of share contribution (0.64 and 0.75 of all budget revenues, respectively). The regions of the North Caucasus Federal District are characterized on average by both the lowest amounts of taxes collected and the minimum share of tax revenues in the formation of the revenue side of the budget (0.27). The latter conclusion is quite natural, since of the six subsidized regions of the Russian Federation, which at the end of 2019 received subsidies of at least 40% of their own income for two out of three years, three are located in the North Caucasus Federal District (Order of the Ministry of Finance "On approval of the list of Subjects of the Russian Federation in accordance with the provisions of paragraph 5 of Article 130 of the Budget Code Of the Russian Federation").

Clustering. Next, we will consider the possibility of identifying the natural stratification of regions by a set of features characterizing the share of tax payments in the revenue side of budgets. At the same time, payments are taken into account: income taxes, property taxes, personal income and total tax revenues. The most appropriate method in this case is cluster analysis, which provides a classification "without a teacher" - that is, the rule of division into clusters is a priori unknown ^{[11, 12]}.

The procedure of agglomerative cluster analysis in the R language can be implemented using fairly simple code. We will present it in stages with proper comments.

1)                The calculation of distances between objects is carried out by the command

d<-dist(scale(PT)), where PT is the name of the dataset containing the values of classification features (the share of tax payments in the budget). The default metric is a simple Euclidean distance:

,                                      (1)

 where d is the distance, is the coordinate i of the first object (the value of feature i), is the coordinate i of the second object, i=1,...,n, n is the number of classification features.

2)                Clustering in this example is carried out using the Ward method, which implies combining objects at each step, resulting in a minimal increase in the intra-group sum of squares. to do this, run the command:  hcw

3) Next, using the plot command (hcw,cex=0.5) a dendrogram is built and clusters are allocated on it, the number of which is set by the researcher (in the example under consideration there are 4 of them). The rect.hclust(hcw, k = 4) function is used for this. The result of this stage is shown on the graph (Fig. 3):

Figure 3 is the first way to visualize the results of cluster analysis (a fragment of a dendrogram: clusters 2 and 4)

Note that the final number of clusters is determined empirically, there are procedures that evaluate the quality of the partition and allow you to compare different options. Consideration of these procedures is beyond the scope of this work and the example demonstrates one of the possible partitions (4 clusters).

         The functions discussed above, used in the clustering process, belong to the basic category and represent a set of minimally sufficient tools. However, R also provides techniques to facilitate the perception of clustering results. So, the following code:

library("ape") #connecting a special library

colors = c("red", "blue", "green", "black") #allocation of chart colors by number of clusters

groups4

plot(as.phylo(hcw), type = "fan", tip.color = colors[groups4],

     label.offset = 0.5, cex = 0.7,no.margin = TRUE) #plotting

It is an alternative to step 3 and represents a dendrogram in the form of a circle and highlights objects related to each cluster in one color, Fig. 4.

Figure 4 is the second way to visualize the results of cluster analysis using the functionality of the ape library (a fragment of a dendrogram, clusters 1 and 2 are partially represented. Cluster 3 is completely represented)

4) at the last stage, when the composition of the clusters is identified, it is necessary to characterize the resulting clusters and identify the key principles of the resulting partition. In the described case, the composition of the clusters was determined as follows :

The first cluster:  Belgorod Region, Vladimir Region, Voronezh Region, Kaluga Region, Kursk Region, Lipetsk Region, Moscow Region, Ryazan Region, Smolensk Region, Tver Region, Tula Region, Yaroslavl Region, Arkhangelsk Region, Vologda Region, Novgorod Region, Krasnodar Territory, Astrakhan Region, Volgograd Region, Rostov Region, Republic of Bashkortostan, The Republic Tatarstan, Udmurt Republic, Perm Region, Nizhny Novgorod Region, Orenburg Region, Samara Region, Saratov Region, Ulyanovsk Region, Sverdlovsk Region, Chelyabinsk Region, Irkutsk Region, Kemerovo Region, Novosibirsk Region, Omsk Region, Tomsk Region, Primorsky Territory, Khabarovsk Territory, Amur Region, Magadan Region.

The second cluster: Bryansk region, Ivanovo region, Kostroma region, Oryol region, Tambov region, Republic Karelia, Kaliningrad region, Pskov region, Republic Adygea, Republic of Kalmykia, Republic of Crimea, Sevastopol, Republic of Dagestan, Republic of Ingushetia, Kabardino-Balkarian Republic, Karachay-Cherkess Republic, Rep. North Ossetia, Chechen Republic, Stavropol Territory, Republic Mary El, Republic of Mordovia, Chuvash Republic, Kirov region, Penza region, Kurgan region, Republic Altai, Republic Tyva, Republic of Khakassia, Altai Territory, Republic of Buryatia, Republic of Sakha (Yakutia), Trans-Baikal Territory, Kamchatka Territory, Jewish JSC, Chukotka JSC.

The third cluster: Moscow, Leningrad region, Murmansk region, St. Petersburg, Tyumen region, Krasnoyarsk Territory, Sakhalin region.

Fourth cluster: Republic Komi, Nenets Autonomous Okrug, Khanty-Mansiysk Autonomous Okrug, Yamalo-Nenets Autonomous Okrug.

Clusters can be described, for example, by calculating the average values of features for each group. To do this, you can use the aggregate() function with the following set of arguments:

an x – frame consisting of features that need to be used to calculate the average values, in the example under consideration, this is for tax revenues in the revenue part of the budget;

by is a grouping attribute, in this example it is the cluster number;

FUN is a calculated characteristic, in the example under consideration – the average sample value (mean).

In addition to describing the clusters themselves, for the convenience of interpreting the clustering results, it is also useful to calculate the averages for each feature for all objects (regions), this is possible using the basic colMeans() function. As an argument, it is enough to specify a frame consisting of features for which the average values should be calculated.

Thus, you can get the following result:

Table 3 – Regional averages of relative contributions of tax revenues to consolidated budgets by income types and clusters

The clustering results can be commented on as follows.

The characteristics of cluster No. 1 are most closely related to the general regional average.

Cluster No. 2 is characterized by minimum regional average shares of tax payments in the revenue side of the budget – this also applies to total tax revenues and income from each of the three taxes considered separately. On average, for the regions of this cluster, the share of tax revenues is 39% of the budget revenue, conditionally this group can be called "Subsidized regions".

Cluster No. 3 has the highest budget contributions from total tax payments, income tax and personal income tax among all four clusters. These figures exceed the regional average. On average, the budgets of the regions of the third cluster are filled by more than 80% due to tax payments. In addition, the total tax payments of these seven regions account for 37% of all tax payments of the regions of the Russian Federation. Conditionally, this group can be called "Donor Regions".

The regions of cluster No. 4 differ in the maximum share of payments for corporate property tax to regional budgets. It can be concluded that these are the regions where the most expensive assets of organizations in the territory of the Russian Federation are concentrated.

Conclusion

The considered example demonstrates the effectiveness of mathematical and statistical methods in solving problems of describing the characteristics of taxpayer regions. Two methods of classification are considered – aggregation by districts and identification of natural stratification. The federal districts are identified, which are characterized by the minimum and maximum regional average relative contributions of tax revenues to the revenue side of the budget. Cluster analysis made it possible to identify a group of donor regions and a group of subsidized regions. It should be emphasized that all the necessary calculations – visualization, calculation of group averages, clustering - were carried out using a small set of functions of the R language, simple in syntax, the use of which does not require deep programming knowledge. The advantages of using the R language in calculations are its high functionality and financial accessibility, which distinguish it favorably from specialized software and MS Excel, as well as in the command syntax, the simplicity of which, in our opinion, distinguishes this language from Python.