[email protected] Irina Aleksandrovna Elkhina,

postgraduate student of the department economic informatics and management, UDC 338(470) Volgograd State University

STRUCTURAL SHIFT AND STRUCTURAL DIFFERENCES IN ECONOMIC SYSTEMS IN RUSSIA

The article presents the results of calculations of structural changes in the regions of Russia for the period from 2004 to 2011. in terms of gross value added by type economic activity. The calculations are based on the Ryabtsev index, the choice of which is explained by the presence of a scale for assessing the measure of the significance of structural differences and the possibility of obtaining adequate estimates on any set of statistical data. Based on the obtained index values, the author identified six groups of regional economic systems, distinguished by identical structure, very low, low, significant, significant and very significant levels of structural differences. To determine the industries in which structural changes occurred due to changes, the mass, speed, and indices of structural changes for the federal districts of Russia were calculated. The industries are characterized by negative dynamics according to the specified characteristics of structural changes Agriculture and manufacturing industry. Calculated indices of structural differences economic system Russia over a longer period of time (1990 - 2011), covering the ascending and descending phases of the fifth wavelength economic cycles, confirm the presence of structural changes in the economic systems of the Russian economy.

Key words: structural shift, structural differences, economics of Russian regions, industry structure, gross value added.

STRUCTURAL SHIFTS AND STRUCTURAL DIFFERENCES OF ECONOMIC SYSTEMS IN RUSSIA

The paper presents the results of a statistical survey of the structural changes in the Russian regions for the period from 2004 to 2011 in terms of gross value added according to the type of economic activity. The calculations were obtained using the Riabtsev index which was chosen for having a rating scale for measuring the level of structural differences and the ability to obtain adequate estimates of any set of statistical data. Having obtained the values ​​of the relevant indices the author identifies six groups of regional economic systems: with verylow, low, substantial, significant and very significant level of structural differences. In order to determine the sectors that caused the structural shifts, the author calculates mass, velocity, and indices of structural changes in the federal districts of Russia. The author reveals that there is a negative dynamics in these characteristics of structural changes in the agricultural sector and the manufacturing industry. The calculated indicators of the structural differences of the economic system in Russia for a longer time period (1990 - 2011) cover the ascending and descending phases of the fifth long wave of economic cycles and confirm the presence of structural changes in the economy of the Russian Federation.

Keywords: structural shift, structural differences, regional economy in Russia, sectoral structure, gross value added.

The development of convergent technologies and the formation of a new technological structure has a significant impact on the functioning of economic systems and on the level of socio-economic development of regions. New technologies involved in the creation of a regionally produced product determine the structure of the economy and the predominance of certain industries. In order to determine the presence of transformation processes in regional economic systems, it is necessary to assess structural shifts and structural differences. For this purpose, there are a number of indices: the Herfindahl-Hirschman index, the entropy index, the relative concentration index, the dispersion indicator of market shares, the integral coefficient of structural differences by K. Gatev, the index of structural changes by A. Szalai, the V.M. Ryabtseva.

Each of the indicators has advantages and disadvantages. The Herfindahl-Hirschman index is traditionally

is used to measure production concentration, but is not comparable for structures with different numbers of elements. The entropy index is the inverse of the concentration index and is used less frequently. The dispersion of market shares is a rougher analogue of the above-described indices and is used as an auxiliary tool. The relative concentration index does not have clearly defined limits for its interpretation. The Gatev coefficient, the Salai index and the Ryabtsev index are the most accurate and convenient tools to achieve the goals set in the study.

The main problem with using indices from socio-economic statistics is the lack of intuitive understanding and, as a consequence, the difficulty of choosing between them. The Ryabtsev and Gatev indices differ only in the denominator, but the lack of a clear interpretation does not allow us to select the best one.

Gatev Index:

Table 1

Salai Index:

Ryabtsev index:

Scale for assessing the significance of structural differences using the Ryabtsev index

Value range 1„ Characteristics of the measure of structural differences

0.000 - 0.030 Identity of structures

0.031 - 0.070 Very low level of structure difference

0.071 - 0.150 Low level of structure difference

0.151 - 0.300 Significant level of difference in structures

0.301 - 0.500 Significant level of difference in structures

0.501 - 0.700 Very significant level of structural differences

0.701 - 0.900 Opposite type of structures

0.901 and above Complete opposite structures

where bu are the specific weights of features in aggregates; ¡ - number of gradations in structures.

Testing the methodology for calculating structural changes in the sectoral structure of the federal districts of the Russian Federation for the period 2004 - 2011. based on the Ryabtsev, Gatev and Salai indices allows us to conclude that there are structural changes in the regions (Fig. 1).

The reliability of the calculations is confirmed by the fulfillment of the inequality developed by V.M. Ryabtsev:

Ryabtsev index< индекс Гатева < индекс Салаи.

As follows from the results of the dynamics of the indices presented in Fig. 1, the author's calculations are correct.

To further assess the significance of structural changes in gross value added (GVA) by type of economic activity in the regions of Russia, the Ryabtsev index is used due to a number of reasons: 1) the Salai and Gatev indices cannot be calculated if the share of the industry is equal to zero; 2) the Ryabtsev index has a scale for assessing the significance of structural differences (Table 1).

Conducting an assessment study of the structure of GVA of federal districts of the Russian Federation by type of economic activity for the period from 2004 to 2011. allowed us to identify only three levels of structure differences (Table 2).

Table 2

Assessing the significance of structural differences

in gross value added of federal districts for the period 2004 - 2011.

Volga Federal District 0.048 Very low level of differences in structures

Russian Federation 0.060

Central Federal District 0.062

Southern Federal District 0.075 Low level of differences in structures

Ural Federal District 0.077

Northwestern Federal District 0.085

North Caucasus Federal District 0.149

Siberian Federal District 0.168 Significant level of differences in structures

Far Eastern Federal District 0.219

Rice. 1. Graph of the dynamics of structural changes in the Russian economy according to the Salai, Gatev and Ryabtsev indices for the period 2004 - 2011. (compiled by the author based on sources)

The average Russian structure of the economy, the structure of the Central and Volga Federal Districts are characterized by a very low level of difference in structures. A low level of difference in the structures of economic systems distinguishes the Northwestern, Southern, North Caucasus and Ural federal districts. A significant level of difference over a seven-year period is typical for the Siberian and Far Eastern federal districts.

To assess the degree of difference in the structures of the economic systems of the federal districts, the Ryabtsev index was calculated in relation to the structure of the economy of the Southern Federal District (Table 3).

Table 3

Assessment of the significance of structural differences in the gross value added of the Southern Federal District to the federal districts of Russia in 2011.

Region Ryabtsev Index Interpretation

Southern Federal District - Russian Federation 0.218 Significant level of differences in structures

Southern Federal District - Central Federal District 0.298 Significant level of differences in structures

Southern Federal District - Northwestern Federal District 0.224 Significant level of differences in structures

Southern Federal District - North Caucasus Federal District 0.165 Significant level of differences in structures

SFD-VFD 0.246 Significant level of differences in structures

Southern Federal District - Ural Federal District 0.524 Very significant level of structural differences

Southern Federal District-Siberian Federal District 0.264 Significant level of differences in structures

Southern Federal District - Far Eastern Federal District 0.462 Significant level of differences in structures

Based on the obtained data from the Ryabtsev index for federal districts, we can conclude that the sectoral structure of the Southern Federal District of the Russian Federation has a significant level of difference in structure from the sectoral structure on average for Russia. When comparing the structures of the Southern and Ural Federal Districts, the Ryabtsev index has a value of 0.524, which indicates a very significant level of sectoral differences in the compared structures. The Southern Federal District has a significant level of sectoral differences with the Ryabtsev index of 0.462 with the Far Eastern Federal District. When compared with the Central, Northwestern, North Caucasian, Volga and Siberian federal districts, the calculated Ryabtsev index indicates a significant level of difference in structures. The closest to the Southern Federal District in terms of the sectoral structure of the economy is the North Caucasus Federal District, which is explained by territorial-geographical features and the history of the administrative division of Russia into federal districts.

Analysis of the calculated values ​​of indices of structural differences for Russian regions for 2011 in relation to 2004 allows us to identify 6 groups of regions, differing

having identical structure, very low, low, significant, significant and very significant level of structural differences.

Among 92 subjects of the Russian Federation (including federal districts and cities of federal significance), the identical structure of the economy in 2011 in relation to 2004 is noted in the Khanty-Mansiysk Autonomous Okrug.

The group of subjects with a very low level of structural differences includes the structure of the economy on average in the Russian Federation, as well as 5 regions (Nenets Autonomous Okrug, Nizhny Novgorod Region, Tyumen region, Novgorod and Vologda regions) and 2 federal districts (Volga and Central).

The largest group consists of regions with a low level of structural differences - 49 subjects, including the general structure of the economy of the Southern, Ural, Northwestern and North Caucasus federal districts. The structure of cities of federal significance - Moscow and St. Petersburg - is characterized by a low level of structural differences.

A significant level of structural differences distinguishes 30 constituent entities of the Russian Federation, including the Siberian and Far Eastern federal districts with their regions, with the exception of the Altai Territory, Tomsk Region, Novosibirsk Region and the Republic of Sakha (Yakutia). Besides, in this group includes the regions of the Volga Federal District: Kirov (with Ryabtsev index 0.153) and Penza (0.159) regions; regions of the Central Federal District: Kaluga (0.158), Kostroma (0.169) and Lipetsk (0.244) regions; regions of the Southern Federal District: Krasnodar region(0.159) and Astrakhan region(0.187); three regions of the Northwestern Federal District: Arkhangelsk region (0.165), the Komi Republic (0.167) and the Republic of Karelia (0.189); four subjects of the North Caucasus Federal District: Stavropol Territory (0.158), Republic of Dagestan (0.185), Chechen Republic(0.189), Kabardino-Balkarian Republic (0.216).

A significant level of difference in structures over a seven-year period was obtained in two regions: the Republic of Ingushetia - 0.329 and the Jewish Autonomous Region - 0.398.

In general, in the regions of the Russian Federation in 2011, the most significant structural changes were noted in the regions of the Far Eastern Federal District: Sakhalin Region - 0.539 and Chukotka Autonomous District - 0.580. They are part of a group of regions with a very significant level of structural differences throughout the period from 2004 to 2011.

In order to identify industries, due to changes in which transformations are observed in the industrial structure of gross value added, a calculation of mass, speed and indices of structural changes was carried out for the period from 2004 to 2011. by federal districts of the Russian Federation.

Calculated data on the mass of structural shifts in output by economic sectors of federal districts show that for all federal districts and the Russian average, the mass of structural shifts in the agricultural sector is negative, which indicates a decrease in the share of this industry in the overall structure of the gross regional product. The share of manufacturing is also declining. Decrease in the speed and index of structural changes in agricultural sectors

economy and manufacturing confirms the decrease in the share of these industries in the structure of regional economic systems and their stagnation.

The sectors of construction, hotel and restaurant business, operations with real estate, government controlled and ensuring military security and healthcare. In a number of federal districts there is an increase in the share of the mining sector, with the exception of the Central and Ural Federal Districts and the South of Russia.

In general, the calculation of the characteristics of structural changes by industry for the period 2004 - 2011. does not reveal significant structural differences. However, the assessment of the structures of the Russian economic system for the period 1990 -2011. reveals a significant level of structural changes (Fig. 2).

Six groups of regional economic systems in Russia have been identified, distinguished by an identical structure, very low, low, significant, significant and very significant levels of structural differences;

Based on the calculation of mass, speed and index of structural changes, negative dynamics in the agricultural and manufacturing sectors were determined;

For the period 1990 - 2011 the structure of the Russian economy is characterized by significant structural differences determined by the belonging of economic systems to different phases economic cycle, which confirms the influence of new key development factors on the existing system of economic activity.

1. Aralbaeva G.G., Afanasyev V.N. Forecasting structural changes in the sectoral structure of the economy of the Orenburg region

Rice. 2. Histogram of the dynamics of the Ryabtsev index values ​​for GVA by type of economic activity in Russia for the period 1990 - 2011. (compiled by the author based on sources).

The presence of significant structural differences in the economy over the 20-year period under review is explained by a comparison of structures belonging to different phases of the fifth “post-Kondratieff” long wave: the ascending and descending phase. The economy of 2011 is entering a downward phase, the economy of the 1990s. - upward, which determines the presence of a significant level of structural differences in the compared economic systems.

Thus, generalizing the calculations of structural changes and structural differences in the Russian economy, we obtained the following results:

The structure of the economic systems of the federal districts of Russia in 2011 compared to 2004 changed slightly: only two federal districts are distinguished by a significant level of structural differences, the average Russian structure of the economy is characterized by a very low level of structural differences;

region based on a system of econometric equations // OSU Bulletin. 2011. No. 13 (132). pp. 23 - 29.

2. Karpov A.V. Measuring the representativeness of parliament in electoral proportional systems // Modeling in the socio-political sphere. 2008. No. 1 (2). pp. 10 - 21.

3. Polikarpova M.G. Statistical analysis of diversification of integration activity in the Russian economy // Young scientist. 2013. No. 10 (57). pp. 377 - 379.

4. Regions of Russia. Socio-economic indicators. 2007: stat. Sat. / Rosstat. M., 2007.

5. Regions of Russia. Socio-economic indicators. 2010: stat. Sat. / Rosstat. M., 2010.

6. Regions of Russia. Socio-economic indicators. 2013: stat. Sat. / Rosstat. M., 2013.

7. Sadovnichy V.A., Akaev A.A., Korotaev A.V., Malkov S.Yu. Modeling and forecasting of global dynamics. M.: ISPI RAS, 2012.

8. иР1_: https://unstats.un.org/unsd/snaama/Introduction.asp.

The development of a statistical population is manifested not only in the quantitative growth or reduction of elements of the system, but also in changes in its structure. Structure- this is the structure of the aggregate, consisting of individual elements and connections between them. For example, a country's exports (aggregate) consist of various types of goods (elements), the value of which varies by type and by country. In addition, there is a constant change in the dynamics of the export structure. Accordingly, the task of studying the structure of aggregates and their dynamics arises, for which special methods have been developed that will be discussed further.

In topic 2, the structure index was considered, calculated using formula (6), which characterizes the proportion of individual elements in the total absolute attribute of the population. Topic 3 discusses the system of indicators and the methodology for analyzing the distribution of a population according to the values ​​of any individual characteristic (variation series of distribution). Here are the indicators characterizing the change in the structure as a whole, i.e. "structural shift". We will consider the practical application of these indicators using two examples presented in tables 19 and 20 (the first 4 columns in bold are the original data, and the rest are auxiliary calculations).

Table 19. Distribution of the Russian population by average per capita cash income(SDD)

groups (j)	rub./person per month	Population shares		|d 1–d 0|			(d 1–d 0)2	(d 1+d 0)2
		2005 year (d 0)	2006 (d 1)
	up to 1500
	1500-2500
	2500-3500
	3500-4500
	4500-6000
	6000-8000
	8000-12000
	more than 12000
	Total

Table 20. Distribution of the number of unemployed in Russia by level of education in 2006

Group number (j)	Have an education	Men (d 0)	Women (d 1)	|d 1–d 0|			(d 1–d 0)2	(d 1+d 0)2
	Higher professional
	Incomplete higher professional
	Secondary professional
	Initial professional
	Average (full) general
	Basic general
	Initial general, do not have an image
	Total

A generalizing absolute indicator of changes in structure can be sum of absolute change modules of shares, determined by formula (50):

, (50)

Where d 1j– share of the j-th group of elements in reporting period; d 0j– share of the j-th group of elements in the base period.

According to Table 19 in the 5th column, a calculation was made using the formula (50): =0.212, that is, the total change in shares in the distribution of Russians by income amounted to 21.2%. Similarly, according to the same formula according to Table 20: =0.276, that is, the difference in the structure of the unemployed among women and men by level of education is 27.6%.

Calculation of the average absolute change per share (group, element of the population) does not provide any additional information. But you can determine how strong the change in structure that has occurred is in comparison with the maximum possible value of the sum of the modules, which is equal to 2. For this, the indicator is used degree of absolute shift intensity(or Loosemore-Hanby index), which is determined by formula (51): the th object in the overall total of the indicator being studied; k– number of objects.

According to Table 19 in the 6th and 7th columns, the Herfindahl coefficient was calculated using formula (52): H 2005=0.142 and H 2006=0.1687, that is, the level of concentration in the income distribution of Russians increased in 2006 compared to 2005. Similarly, using the same formula according to Table 20: H husband=0.2455 and H women = 0.2177, that is, the level of concentration in the distribution of the unemployed by level of education among men is higher than among women (the impact of education level on the status of the unemployed among men is higher than among women).

The reciprocal of the Herfindahl index is effective number of groups in the structure, which shows the number of groups without taking into account groups with negligible shares, is determined by formula (53):

E= 1/H. (53)

According to Table 19, the effective number of groups according to formula (53): E 2005=1/0.142=7.0 and E 2006=5.9, that is, the effective number of groups in the distribution of Russians by income decreased from 7 in 2005 to 6 in 2005, which indicates the need to revise the intervals of distribution of Russians by income next year. Similarly, using the same formula according to Table 20: E husband=1/0.2455=4.07 and E female = 1/0.2177 = 4.59, then the effective number of groups in the distribution of the unemployed by level of education among men is higher and among women – 4 for men and 5 for women.

Another option for assessing the degree of structuring of the phenomenon as a whole is Grofman index(54), which is the sum of the absolute change modules of the shares per one effective group:

. (54)

According to Table 19 in formula (54): =0.212*0.142=0.030, that is, the change in shares per effective group in the income distribution of Russians is insignificant (3.0%). Similarly, according to the same formula according to Table 20: =0.2455*0.276=0.068, that is, the difference in structure per effective group among unemployed women and men by level of education is weak (6.8%).

To assess changes in the two largest shares (dominant shares) Liphart index (55):

. 55)

Where d 1m And d 0m– share m-th group of elements in the reporting period and base periods; m– maximum share in the aggregate.

According to Table 19 according to formula (55): =0.5*(0.083+0.023)=0.053, that is, the average change in shares in the two dominant groups of the income distribution of Russians was 5.3%. Similarly, according to the same formula according to Table 20: =0.5*(0.060+0.051)=0.056, that is, the difference in structure in the two dominant groups among unemployed women and men by level of education is 5.6%.

The considered indicators are based on the arithmetic mean in various variants, and due to their linearity in deviations, they take into account large and small deviations equally. Quadratic indices allow comparison of different structures that are indistinguishable in terms of the amount of change.

Quadratic index of structural changes Kazintsa (56):

. (56)

According to Table 19 according to formula (56): ==0.035, that is, the average change in shares in the group in the distribution of Russians by income was 3.5% (insignificant). Similarly, according to the same formula according to Table 20: ==0.049, that is, the difference in groups in the structure of the unemployed among women and men by level of education is 4.9% (insignificant).

Similar to the Kazinets index least squares index(or Gallagher index), in the calculation of which, in contrast to formula (51), small differences in shares have a weaker effect on the index than large ones, is determined by formula (57) = =0.117, that is, the difference in the structure of the unemployed among women and men by level of education according to the Monroe formula is 11.7%.

Integral coefficient of structural shifts Gatev(59), which distinguishes structures with equal sums of squared deviations (takes higher values ​​when groups have approximately equal shares):

. (59)

According to Table 19 according to formula (59): ==0.179, that is, the intensity of changes in shares in the distribution of Russians by income according to the Gatev method was 17.9% (insignificant). Similarly, according to the same formula according to Table 20: ==0.192, that is, the difference in the structure of the unemployed among women and men by level of education according to Gatev’s method is 19.2% (insignificant).

Index Ryabtseva, differing from (59) only in the denominator, usually takes lower values, calculated using formula (60):

. (60)

According to Table 19 using formula (60): = =0.127, that is, the intensity of changes in shares in the distribution of Russians by income according to Ryabtsev’s method was 12.7% (insignificant). Similarly, using the same formula according to Table 20: = =0.137, that is, the difference in the structure of the unemployed among women and men by level of education according to Ryabtsev’s method is 13.7% (quite significant).

Structural Difference Index Salai(61), the peculiarity of which is that the larger the fraction j Atkinson index, generalized entropy index, which will be discussed in the course of socio-economic statistics in the topic “Living Standards Statistics”.

Comparison of two structures of the same name in space carried out with the help absolute indicators differences and coefficients absolute shifts. They can be calculated with different numbers of elements in the compared structures.

Changes specific gravity the same structure over time measured relative indicators differences and coefficients relative structural changes. They are counted only if the number of elements in the structures is the same.

Indicators that characterize not a change in a single share, but a change in the structure as a whole - that is, a “structural shift”.

We consider the movement of a system in time, which is of a controlled nature, to be transformation. To measure the strength and depth of transformation, manifested in structural changes, special methods are used in statistics and specific indicators are calculated.

In terms of measuring absolute structural changes, the classical formula for the average linear deviation is transformed into the following:

where is the module of the absolute increase in shares (shares) in the current period compared to the base period; n- number of gradations.

This indicator of L.S. Kazinets called the linear coefficient of absolute structural changes. Statistically, its meaning is that it represents the arithmetic mean of the modules of absolute increases in shares (specific gravities) of all parts of the compared wholes.

This coefficient characterizes the average deviation from the specific weights, that is, it shows how many percentage points on average the specific weights of the parts in the compared populations deviate from each other.

The greater the value of the linear coefficient of absolute structural changes, the more on average the specific weights of individual parts deviate from each other for the two periods being compared, the stronger the absolute structural changes. If the structures for these periods coincide (i.e. d 2 - d 1 = 0), then this coefficient will be equal to zero.

Difference Index

Where d i1 d i0 - specific gravity of individual elements of two compared populations;
n- the number of elements (groups) in total.

The difference index, calculated through specific gravities expressed as percentages, can take values ​​from 0 to 100%; approaching zero means no change; approaching maximum indicates a significant change in the structure.

Structural shift coefficient K. Gateva

The above indicators do not provide an idea of ​​changes in the shares of individual elements of the population. This indicator takes into account the intensity of changes in individual groups in the compared structures.

The number of groups into which the population under study is divided affects the final assessment of structural changes.

Salai Structural Difference Index.

This indicator also takes into account the number of groups or elements in the compared structures. The Salai coefficient (index), like the K. Gatev coefficient, can take values ​​from zero to one. The closer the resulting value is to unity, the more significant the structural changes that have occurred. The Szalai coefficient takes values ​​close to unity when the total a large number of units.

Ryabtsev index

The values ​​of this indicator do not depend on the number of gradations of structures. The assessment is made on the basis of the maximum possible value of discrepancies between the components of the structure; the actual discrepancies of individual components of the structures are compared with the maximum possible values. This coefficient (index) also takes values ​​from zero to one. An advantage of this indicator can be considered the presence of a scale for assessing the obtained indicator values.

The given indicators represent characteristics of structural changes, but do not give an idea of ​​the magnitude of these changes.

To quantify the degree of unevenness, two income concentration coefficients are used - Lorenz and Gini.

Lorentz coefficient

Where y i - share income i groups; x i - population share i th group.

Calculation Gini coefficient is based on determining the fraction of the area of ​​the polygon outlined by the diagonal of the square and the Lorenz curve in half the area of ​​the square:

Where cum y i - accumulated shares of income

Both coefficients range from 0 to 1. The closer the value is to 1, the higher the level of inequality (concentration) in the income distribution. In practice, these coefficients do not reach the maximum values ​​(0 - complete equality, 1 - concentration of income in one group of the population).

When calculating and comparing the values ​​of the Gini coefficient, you should pay attention to which groupings the indicator is calculated for, since the greater the number of groups the analyzed population is divided into, the higher the value of the Gini coefficient will be. For example, the coefficient calculated for 10% groups will always be higher than the coefficient calculated for 20% groups.

The Pareto-Lorenz-Gini theory was proposed to study the uniformity or unevenness (concentration) of the distribution of total income among all population groups. However, these coefficients can be used to study the degree of uniformity of distribution of other social and economic characteristics. For example, the degree of uniformity in the distribution of housing, social transfers, medical and educational services, crime, etc.

When assessing the degree of monopolization of an industry, it is used Herfindahl coefficient

Where d i- specific gravity i-th enterprise;

k- number of enterprises in the industry.

The coefficient is calculated through the sum of the squares of the sales shares of each enterprise in the industry, expressed as a percentage. Therefore, the maximum value of the Herfindahl coefficient can be 10,000, the minimum - 10,000 /k.

An example of solving problem 3.

According to the sample survey, the following distribution of the organization’s employees by salary was obtained:

Define:

1. Average wages.

2.Coefficient of variation.

3.Mode and median

1. The task condition is represented by an interval variation series with equal intervals. Therefore, to calculate indicators, you must first determine the value of the averaged characteristic (X) as the middle of each interval and obtain a discrete distribution series.

2. The coefficient of variation characterizes the measure of fluctuation of individual variants of a characteristic (x) around the average value. It represents the percentage ratio of the standard deviation (σ) and the arithmetic mean () , that is

To calculate the standard deviation, we first calculate the dispersion (σ 2) using the formula:

The calculation can be done using the auxiliary table

x	m	X-	(x- ) 2	(x- ) 2 m
		12500-15095
		13500-15095
		14500-15095
		15500-15095
		16500-15095
Total		-	--

Standard deviation - is the square root of the variance:

σ = ±√ σ 2 = ± ±1100.443 rub.

The coefficient of variation will be:

If the value of the coefficient of variation does not exceed 33.3%, then the population is considered homogeneous, and average value can be considered typical for a given distribution. In our example, the average value is typical.

3. Mode (dominant) is the most common value of the attribute x; in an interval series, the modal interval will be the interval that has the highest frequency (frequency).

In this task, the interval 15,000 - 16,000 rubles has the highest frequency (65), therefore, the mode will be in this interval.

Consequently, the largest number of workers had a salary of 15,280 rubles.

Median is the value of the attribute for that unit of the ranked series that is in its middle. First, let's determine the serial number of this unit. To do this, add one to the sum of all frequencies of the series () and divide the result in half, that is

The median salary value will be the one that is half the sum of the salaries of the 100th and 101st employees. They fall into the fourth interval (10+20+58+65=153) according to the sum of accumulated frequencies, that is, from 15,000 to 16,000 rubles.

Consequently, half of the workers have a salary of no more than 15,184.6 rubles, and the other half - no less than 15,184.6 rubles.

To compare the structure of statistical aggregates, compare actual and normative structures, and to quantify dynamic structural changes (structural shifts), indicators of structural differences can be used. A general quantitative assessment is given integral indicators structural differences:

Salai index:
V. Ryabtsev index:

where d 1i and d 0i are the structural components being compared,

n – number of structural gradations (distinguished groups).

1

Analysis of disparities in employment in municipalities region as a whole, and in the context of large and medium-sized, small and micro-enterprises, was carried out using the Ryabtsev Index, the main advantage of which over other methods for measuring shifts in the number of employed people in the regions of the republic is that its value does not depend on the number of gradations structures, that is, on the number of municipalities, so there is no overestimation of structural changes, and there is also a scale for assessing the significance of differences in structures according to the index. A comparison of the structural indicators of the average number of employees in large and medium-sized enterprises showed that the processes of gradual reduction of workers in large and medium-sized enterprises had similar dynamics in each territorial entity of the Republic of Mari El, while the small business system not only does not cease to exist, but is also constantly expanding, although Of course, the level of small business development in the Republic of Mari El is still extremely low. Its formation is slowed down due to the current concentration of production, unstable economic situation, imperfections of the current tax legislation, weak government support, which makes it necessary to increase the economic efficiency of municipalities.

regional employment structure

employment of the population of municipalities

Ryabtsev index

level of structure difference

1. Bredneva L.B. Study of the structure and structural differences in the economy of the Khabarovsk Territory // Bulletin of the KhSAEP. - 2011. - No. 1 (52). - P. 4-10.

2. Podzorov N.G. Analysis of the influence of factors on the volume and structure of the gross regional product of the Republic of Mordovia [ Electronic resource]. - URL: http://sisupr.mrsu.ru/2010-1/pdf/podzorov3.pdf.

3. Republic of Mari El: statistical yearbook “Republic of Mari El” / Territorial body Federal service state statistics for the Republic of Mari El. - Yoshkar-Ola, 2011. - 464 p.

4. Statva A.L. Geographical analysis of employment of the population of the Omsk region: abstract. dis. ...cand. geogr. Sci. - Barnaul, 2005. - 24 p.

5. Utinova S.S. Employment and labor market in conditions of transformation Russian economy: author's abstract. dis. ... doc. econ. Sci. - M., 2003. - 48 p.

One of the main and most difficult tasks of market transformations is the formation of an effectively functioning, dynamic and civilized labor market. The state has ceased to be the only guarantor of employment, and in the current conditions, each person decides for himself whether to work or not. The idea of ​​the role of employment has changed radically. The results and consequences of the transformation of social and labor relations are reflected in changes in the employed population and its structure, which, under the influence of macroeconomic factors, are subject to further distortions that reduce economic activity and quality of life. First of all, this is due to the restructuring of employment due to changes in structure.

To study employment and the processes of its regulation in the region, it is advisable to carry out a typology of the regions included in it, since the Republic of Mari El does not act as a single monolith, but as a set of regions with specific characteristics of employment, priorities and development prospects.

To analyze employment in 17 administrative units of the republic (3 city districts and 14 municipal districts) we used data for two time periods - 2000 and 2010. - values ​​are the following indicators:

• number of employed population (total), people, calculated according to the ILO methodology based on sample surveys on employment problems at the end of the year;
• average annual number of employees at large and medium-sized enterprises, people, calculated according to data from organizations and enterprises for the year;
• average annual number of employees in small and micro enterprises, people, calculated according to data from organizations and enterprises for the year.

Analysis total number employed showed that the majority of the total employed population in both 2000 and 2010. accounted for urban districts: 63.4 and 60.5%, respectively. In 2000, the share of the employed population in the total number of workers was 53.7% - Yoshkar-Ola; 6.6% - Volzhsk, 3.0% - Kozmodemyansk. A fairly large share of the total employed population at that time belonged to the Gornomarisky (4.5%) and Zvenigovsky districts (3.5%).

In 2010, Yoshkar-Ola continued to account for the largest share of workers - 46.2%. But if during the period under study the number of employees in the capital of the Republic of Mari El decreased by more than 18 thousand people, then the cities of Volzhsk and Kozmodemyansk during the time period under study not only expanded their shares in the distribution of workers to 8.2 and 3.8 %, respectively, but also increased the absolute values ​​of the total number of employees in their territory by 28.2 and 32.0%, respectively. Among the municipal districts in terms of the number of people employed in 2010, the leaders were the Medvedevsky district, which provided jobs for 9.3% of the employed population of the republic, and the Zvenigovsky district, where 5.9% of the employed worked. Such disproportions in employment are primarily associated with the geographical distribution of enterprises on the territory of the republic, which are predominantly located in the cities of the region, which, of course, serves as an additional factor in increasing the role of cities in the development of society - urbanization.

An analysis of the average number of employees at large and medium-sized enterprises showed that the reduction of workers in this group occurred everywhere during the study period. The Paranginsky, Mari-Tureksky, Kuzhenersky and Novotoryalsky districts stand out especially, where the growth rates of the analyzed indicator were 34.8, 39.0, 40.2 and 40.7%, respectively. The Medvedevsky district stands out significantly against the general background, in which the reduction in the average number of employees at enterprises of this group amounted to only 9.0%. In 2000, 54.9% of the average number of employees at large and medium-sized enterprises were in cities (Yoshkar-Ola - 42.4%, Volzhsk - 8.3%, Kozmodemyansk - 4.2%). Among the districts, Zvenigovsky (6.2%) and Medvedevsky (9.6%) stood out in terms of the number of employees in large and medium-sized enterprises. A similar situation was observed in 2010.

As for small businesses, the picture here is somewhat different. If in 2000 in the urban districts of the republic 16,013 people were employed in small enterprises and this accounted for 86.3% of the total number of employees in this group (76.4% worked in the city of Yoshkar-Ola), then by the end of 2010 , despite the impressive growth in the number of workers in this group, only 68.8% of the employed remained in cities (58.6% in Yoshkar-Ola). The Medvedevsky and Morkinsky districts have achieved especially significant success in the development of small businesses. If in 2000 their total contribution to the average number of employees of small and micro enterprises was slightly more than one percent, then by 2010 the Medvedevsky district already provided 6.0% of jobs, and the Morkinsky district - 2.2%.

Figure 1 shows the growth rates of the studied indicators for 2010/2000. The Medvedevsky district had the highest growth rates for all employment indicators. Here, the growth of the total number of employees reached 275.6%, which is primarily caused by the formation and development of small businesses, the average number of employees in which increased by 16.4 times. Yurinsky district, on the contrary, against the backdrop of a reduction in total employment by 51.9%, achieved the most insignificant success in the development of small businesses. The growth rate of the average headcount at enterprises of this group was the smallest in comparison with other administrative units of the republic - only 262.4%.

Rice. 1. Growth rate of the average annual number of employeesin the context of municipalities.

The growth rate of the average number of employees in large and medium-sized enterprises of the republic did not exceed 90.9% (Medvedevsky district). In urban districts alone, the average growth rate of this indicator was only 73.0%.

The negative dynamics of this indicator is due, first of all, to the reduction in the number of large and medium-sized enterprises and organizations on the territory of the Republic of Mari El, which in turn is due to the artificial fragmentation of larger enterprises in order to receive benefits or easier tax regime, as well as redistribution of forms of ownership of enterprises in the region. Number of enterprises state form ownership in the period under study decreased from 861 to 746, of which the republican form of ownership - from 565 to 431.

The problems of small business development both in the country as a whole and in the republic have recently received quite close attention: decrees of the President of the Russian Federation, Government resolutions and decisions of local authorities are issued, various specialized funds and other infrastructure elements are created to support small businesses, since It is small enterprises that occupy a prominent place in the market for goods and services; they are most susceptible to changing conditions, to the introduction of new equipment, and the use of advanced technologies. With the help of individual entrepreneurship, such problems are solved social problems, such as the creation of new jobs and other local problems. Over the past ten years alone, the number of small businesses has grown by 542 units, while the average number of employees here has increased by 2.4 times over the same period.

The transition to market relations led to a transformation of the economy, the objective reflection of which is largely determined by the availability of general information about structural changes. The priority of the study of structure indicators and their dynamics is due to the need to present objective, high-quality, most complete information that adequately reflects the analyzed trends in employment to the heads of government bodies in order to adopt effective management decisions.

At the same time, for adjacent periods of time, discrepancies in the structure of the total working population were interpreted for the most part as “identity of structures” in employment of the population in the context of municipalities, the V.M. index was used. Ryabtseva - integral coefficient of structural differences - criterion , :

(1)

where and are the specific gradations of the two structures; - number of gradations.

The advantage of this index over other methods for measuring changes in the number of employed people in the regions of the republic is that its value does not depend on the number of gradations of structures, that is, on the number of municipalities, therefore there is no overestimation of structural changes, and also in the presence of a scale for assessing the measure the significance of differences in structures by index (Table 1).

Table 1 - Scale for assessing the significance of differences in the number of employees according to the Ryabtsev index

Range of values	Characteristics of the measurestructural differencesin employment	Range of values	Characteristics of the measurestructural differencesin employment
	Identity of structures		Significant level of structural differences
			Very significant level of structural differences
			Opposite type of structures
		0.901 and above	Complete opposite of structures

In order to assess the significance of differences in the structure of employment of municipalities of the Republic of Mari El, calculations were made of the values ​​of Ryabtsev indices by year for the time interval from 2000 to 2010 for each of the previously considered employment indicators: number of employed population (total), people; average annual number of employees at large and medium-sized enterprises, people; average annual number of employees in small and micro enterprises, people.

Table 2 - Assessment of the significance of structural differences in employment in municipalities of the RME

Period	Ryabtsev index(employed population, total)	Interpretation	Ryabtsev index(employment in large and medium-sized enterprises)	Interpretation	Ryabtsev index(employment in small and micro-enterprises)	Interpretation
		Identity of structures		Identity of structures		Identity of structures
		Identity of structures		Identity of structures		Identity of structures
		Identity of structures		Identity of structures		Identity of structures
		Identity of structures		Identity of structures		Significant level of structural differences
		Low level of structure difference		Identity of structures		Identity of structures
		Identity of structures		Very low level of structure difference		Very low level of structure difference
		Identity of structures		Identity of structures		Very low level of structure difference
		Identity of structures		Identity of structures		Very low level of structure difference
		Identity of structures		Identity of structures		Very low level of structure difference
		Identity of structures		Identity of structures		Identity of structures
		Low level of structure difference		Low level of structure difference		Low level of structure difference

As follows from Table 2, the value of the criterion when comparing structural indicators of the number of employed population for the entire observation period (from 2010 and 2000) was 0.098, which indicates a low level of differences in structures in the number of employed population in the municipalities of the republic.

Over adjacent periods of time, discrepancies in the structure of the total working population were interpreted for the most part as “identity of structures,” which indicates that transformations in the distribution of the number of employed within administrative units proceeded at a very slow pace (Fig. 2).

Rice. 2. Dynamics of structural changes in employment in the republic.

The most significant structural transformations during the period under study characterized small businesses in urban districts and municipal areas.

A “significant level of difference in the structures” employed in small businesses was noted in 2003-2004, when the growth rate of the average number of employees in small and large enterprises in the republic was 125.4%. The Gornomariysky district stood out especially strongly against the general background at that time, in which in just one year the average number of workers in this group increased by more than 8 times, while in the urban districts of the republic small businesses were stagnating.

In the last decade, most administrative units of the region have seen an unusually rapid increase in the number of small enterprises. Constantly changing (small businesses appear quickly, but can quickly go bankrupt), the small business system not only does not cease to exist, but is also constantly expanding, although, of course, the level of development of small businesses in the Republic of Mari El is still extremely low. Its formation is hampered by the current concentration of production, unstable economic situation, imperfection of the current tax legislation, and weak government support.

The need to increase the economic efficiency of municipalities poses new challenges for the territories, primarily related to the choice of a competitive model of the regional economy that makes it possible to make maximum use of the existing potential.

Reviewers:

• Katkov Nikolay Semenovich, doctor economic sciences, Professor, Professor of the Department of Economic Cybernetics, Mari State University, Yoshkar-Ola.
• Shvetsov Mikhail Nikolaevich, Doctor of Economics, Professor, Rector of the ANO VPO "Interregional Open social institution", Yoshkar-Ola.

Bibliographic link

Sarycheva T.V. STATISTICAL STUDY OF EMPLOYMENT DISPROPORTIONS AT THE MUNICIPAL LEVEL OF THE REPUBLIC OF MARI EL // Modern problems of science and education. – 2012. – No. 4.;
URL: http://science-education.ru/ru/article/view?id=6865 (access date: 12/20/2019). We bring to your attention magazines published by the publishing house "Academy of Natural Sciences"