Revista
de la
Universidad
del Zulia
Fundada en 1947
por el Dr. Jesús Enrique Lossada
NÚMERO ESPECIAL
DEPÓSITO LEGAL ZU2020000153
Esta publicación científica en formato digital
es continuidad de la revista impresa
ISSN 0041-8811
E-ISSN 2665-0428
Ciencias
de la
Educación
Año 12 N° 35
Noviembre - 2021
Tercera Época
Maracaibo-Venezuela
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Regional differentiation of higher education in Russian regions in
2020
Iuliia Pinkovetskaia*
Magomedsaid Yakhyaev**
Elena Sverdlikova***
Daniela S. Veas Iniesta****
ABSTRACT
The aim of this study was to evaluate the specific values of the indices that describe the
spread of higher education institutions in all regions of Russia and the number of their
students in the total working-age population living in these regions. The initial empirical
data were the results of official statistical surveys conducted on information on the
development of higher education, as well as the number of working-age population in
eighty-two regions of the Russian Federation for 2020. In the course of the research, four
mathematical models were developed. The study showed that on average, there are almost
14.8 higher education organizations per million working-age residents in the regions. It is
proved that every twenty-fourth person of working age in 2020 studied under higher
education programs. The conducted analysis showed the presence of a significant
differentiation of the values of the considered indicators by region. The regions with the
maximum and minimum values of the considered indicators were identified. It is shown
that higher education has received significant development in Russia.
KEYWORDS: Higher education; university students; Russia; higher education institutions;
working population.
*Department of Economic Analysis and State Management, Ulyanovsk State University,
Ulyanovsk, Russia. ORCID: http://orcid.org/0000-0002-8224-9031. E-mail:
pinkovetskaia@gmail.com
**
Department of Economics and Management, Institute of Social Sciences, Moscow, Russia.
ORCID: https://orcid.org/0000-0002-2938-7689 .
***
Department of Economic Sociology and Management, Lomonosov Moscow State
University, Moscow, Russia. ORCID: https://orcid.org/0000-0003-3518-4455 .
****
Institute of Engineering Economics and Humanities, Moscow Aviation Institute,
National Research University, Moscow, Russia. ORCID: https://orcid.org/0000-0002-8473-
0670 .
Recibido: 04/08/2021 Aceptado: 30/09/2021
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Diferenciación regional de la educación superior en las regiones de
Rusia en 2020
RESUMEN
El objetivo de nuestro estudio fue evaluar los valores específicos de los indicadores que
caracterizan la dispersión de las instituciones de educación superior en todas las regiones
de Rusia, y el número de sus estudiantes en el número total de la población activa que vive
en estas regiones. Los datos empíricos iniciales fueron los resultados de las encuestas y
estadísticas oficiales realizadas sobre el desarrollo de la educación superior, así como el
número de personas en edad de trabajar en ochenta y dos regiones de la Federación de Rusia
para el año 2020. Durante el estudio, se desarrollaron cuatro modelos matemáticos. El
estudio reveló que, en promedio, hay casi 14,8 organizaciones de educación superior por
millón de habitantes en edad de trabajar en las regiones. Se ha demostrado que una de cada
24 personas en edad de trabajar en 2020 se inscribió en programas de educación superior. El
análisis mostró una diferencia significativa entre los valores de los indicadores examinados
por región. Se identificaron las regiones con valores máximos y mínimos de los indicadores
considerados. Se muestra que la educación superior ha recibido un desarrollo significativo
en Rusia.
PALABRAS CLAVE: Educación superior; estudiantes universitarios; Rusia; instituciones de
educación superior; población activa.
Introduction
The role of the higher education system has significantly increased in recent years in
developed and developing countries. According to many authors (for example, Pinheiro et
al., 2015; Avdeeva et al., 2017) this is due to the fact that organizations specializing in
teaching students in higher education programs provide significant economic growth and
have a positive impact on the social climate in modern countries. Without specialists with
higher education, both enterprises that produce various goods and specialized in providing
various services cannot work in the twenty-first century. The introduction of technological
and managerial innovations also requires highly qualified employees (Tamayo & Huergo,
2017; Schaarschmidt & Kilian, 2014). Therefore, conditions have been created in most states
that provide access to higher education for the population (Guri-Rosenblit et al., 2007). As
shown in the study (La mobilité internationale, 2019), in 2016, the number of students of
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higher education institutions in all countries increased by one and a half times compared to
2006 and reached 218 million people.
As indicated in scientific publications (Stiglitz, 2014; Douglas, 2011), one of the most
urgent problems for modern national economies is the study of the achieved level of
accessibility of education in higher education organizations. Our research is devoted to
assessing the level of accessibility of higher education in the regions of Russia. Previous
studies (for example, Abel & Deitz, 2011; Ciriaci, 2014) have proved the importance of
developing the higher education system in the regions. This is especially true for countries
with a large number of regions, where there is a need to consolidate young people in
regional labor markets. The possibility of obtaining higher education in your region
significantly improves the social climate and promotes higher education without moving to
a new place of residence. In addition, the social status of the regions is increasing, and the
prerequisites for their further economic growth are being created.
All this determines the increased interest in the study of regional aspects of the
development of higher education. Calls for an in-depth study of the regional features of
such education and the identification of differences between regions were expressed in the
works (Cervantes, 2017; Unger & Polt, 2017).
In 2020, there were 1,259 institutes of higher education in Russia (Official statistical
information on additional professional and higher education, 2021). Of these, 710 were
independent organizations, in which 3550137 students studied. In addition, there were 549
separately located branches, which enrolled 499,196 students. Of the total number of
students, 60% studied during the day with a break from work, 35% of students studied in
the evening after finishing work. The remaining 5% of students received education by
correspondence.
The purpose of our study was to evaluate the indicators describing the distribution
of higher education organizations by regions of Russia, the share of students in the total
population of working age in each of the regions, as well as the share of students admitted
to study and graduated in 2020.
Our article makes a certain contribution to the knowledge about the regional
features of the higher education system in Russia. The theoretical contribution is related to
the methodology proposed by the authors, which allows us to estimate the distribution of
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the values of the indicators of the level of higher education by regions based on the
development of mathematical models that represent the density functions of the normal
distribution. Based on empirical data, in the course of the study, new knowledge was
obtained about the number of higher education organizations per million working-age
residents, the share of students receiving higher education in the working-age population
by region, as well as the share of students admitted to higher education organizations in the
working-age population and the share of students who received higher education. In
addition, the regions with the maximum and minimum values of indicators characterizing
the regional features of the higher education system are determined.
The structure of this work is as follows. The first section of the article presents a
literary review devoted to scientific research on the problems of higher education in Russia.
The second section demonstrates the methodological approach to the study of the problem
under consideration, as well as the sources of empirical information used in the research
process. The results of a computational experiment related to the development of normal
distribution density functions are given in the third section. The fourth section contains a
discussion of the results obtained, as well as a description of the regions with maximum
and minimum values of indicators. The penultimate section is devoted to conclusions. The
following is a list of the bibliography used.
1. Literature review
A brief analysis of scientific papers devoted to general issues of higher education in
Russia and some of its regions is given in Table 1. The first column of the table shows the
authors of scientific publications, the second column shows the main issues described in
the publications and related to the assessment of the number of higher education
institutions and the number of students studying in these organizations. The articles have
been published in recent years.
As the data in Table 1 show, the problem of studying the indicators of the higher
education system, and in particular the number of higher education institutions and the
number of students studying in them, is relevant in Russia. Most of the scientific
publications listed in Table 1 analyzed such indicators for Russia as a whole and its
individual federal districts.
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Table 1. Scientific publications on the volume of higher education development in Russia
Authors
Problems under study
Type of
indicators
1
2
4
Bekmurzaev &
Shamilev (2015)
Dynamics of the number of
students in 2010-2014
studying at higher education
institutions
Comparative
Kashepov (2019)
The number of higher
education organizations and
students studying in them
for the period from 2000 to
2018. Average duration of
training
Factual
Krivich (2019)
The share of students who
studied at state and non-
state institutions of higher
education in the total
number of students for the
period from 2013 to 2018
Factual
Sudakova (2018)
Change in the number of
universities and their
students for the period from
2011 to 2016
Factual
Ushakova (2017)
Distribution by year from
2000 to 2016 of the number
of students who studied
under the master's,
specialist's and bachelor's
degree programs
Factual
Yudina (2019)
Analysis of the number of
new students admitted to
universities. The dynamics
of changes in the indicator
for 2001-2019 shows its
decline for demographic
reasons
Factual
Zborovsky ( 2018)
From 2013 to 2017, the
number of independent
higher education
Factual
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organizations decreased by
25% (from 71 to 53)
Cherednichenko
(2018)
Forms of study and the
number of students enrolled
in higher education
organizations in 2000-2017
Factual
Bezhanova,
Shkhagoshev, Shetov
(2019)
Forecast of the dynamics of
changes in the number of
students at universities
Factual
Dorofeeva (2020)
Provision of educational
services for the period 2007-
2019
Factual
Belyaev (2021)
Comparative analysis of the
change in the number of
students in 2019 compared
to 2015
Factual
Kurbatova, Donova,
Kranzeeva (2021)
Accessibility of higher
education in mineral-rich
regions
Comparative
Source: The table is compiled by the author on the basis of the information provided in the
RSCI.
The issues of a comprehensive analysis of regional features of accessibility of higher
education have been studied to a small extent in published works. Accordingly, there was
no comparative analysis of the number of educational organizations in the regions of
Russia, as well as the number of students in these organizations. Data in table 1 show that
in the majority (83%) discussing publications we analyze factual values of indicators, that
does not allow to make comparative analyze, since the regions differ from each other in the
number of population, territorial features and economic development. Taking into account
this conclusion, it is advisable to conduct a comparative analysis on the basis of
comparative values of indicators, for example, taking into account the number of able-
bodied population in the regions.
2. Methodology and design
Our paper examines information on all universities and other institutions of the
higher education system that are located in each of the regions of Russia in 2020. As you
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know, in Russia, students receiving higher education study for a different number of years.
Thus, students study for four years in bachelor's degree programs, students belonging to
the specialty degree study for five years, and students who additionally receive a master's
degree study for two years. The number of students belonging to these three groups was
considered in our study.
Our study consisted of four main stages. The first stage was associated with the
definition of the initial empirical data, which for each of the 82 regions of Russia described
such indicators as the number of public and private institutions of higher education, as well
as the number of students who studied in them. At the same stage, data on the working-age
population living in the regions in 2020 were determined. The second stage was devoted to
the calculation of indicators that describe the number of higher education institutions per
million residents of working age, as well as the share of the number of students in the total
number of people of working age. The third stage was associated with the development of
density functions for the normal distribution of indicators across the regions of Russia. The
fourth stage was devoted to the discussion of the results obtained and the identification of
regions with maximum and minimum values of indicators.
The study was based on data included in the official statistical report (Official
statistical information on additional vocational and higher education, 2021). Data on the
number of working-age population by region were taken on the basis of information from
Rosstat (Official statistical information on the population of the Russian Federation by
municipalities, 2021).
In our study, three hypotheses were tested:
- the first hypothesis is that higher education institutions operated in each of the
regions of Russia in 2020;
- the second hypothesis is that there are significant differences in regional indicators
that characterize the development of higher education;
- the third hypothesis is that the minimum and maximum values of the indicators
were in the regions of Russia, which belong to different federal districts.
Mathematical modeling of the distribution of indicator values across the regions of
Russia was based on the development of density functions of the normal distribution. The
corresponding technique was demonstrated in the articles (Pinkovetskaya & Slepova, 2018;
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Pinkovetskaya et al., 2021). Both the average values of the indicators and the average square
deviations of the indicators for the totality of all regions are indicated directly in the
functions.
The development of mathematical models describing the distribution of indicators
using the density functions of the normal distribution is based on the construction of
histograms. With a large amount of empirical input data (35 or more), we can group this
information into intervals to make working with the data more comfortable. To do this, the
source data is divided into a certain number of intervals.
The general form of the density function of the normal distribution is as follows:
2
2
)(
2
)(
mx
e
A
xy
,
where:
x - the indicator whose distribution we are studying;
m - the average value of the indicator for all observed objects;
- the mean square (standard) deviation.
The obtained functions allow us to estimate the average values of each of the five
indicators in the regions under consideration, as well as their variations typical for most
regions. In addition, the study identifies regions where the indicators considered are above
the maximum and below the minimum ranges. The limits of the indicator ranges for the
majority (68%) of the regions are calculated based on the average values and the
corresponding standard deviations. The lower bound of the range is equal to the difference
between the mean and the standard deviation, and their sum corresponds to the upper
bound of the range.
3. Modeling and results
The assessment of the distribution of indicators characterizing the activity of the
higher education system in the regions of Russia was based on the development of
mathematical models. Results of the development of models representing the density
functions of the normal distribution (
1
y
;
2
y
;
3
y
;
4
y
) on such indicators (
1
x
, %;
2
x
, %;
3
x
;
4
x
) across all regions of Russia are specified further:
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- the quantity of higher education institutions in calculation on million working-age
people in the region
36.536.52
2
)79.14
1
(
11
236.5
29.398
)(
x
exy
; (1)
- the proportion of university students in the whole quantity working-age people in
the region, %
72.172.12
2
)20.4
2
(
22
272.1
57.140
)(
x
exy
; (2)
- the proportion of students admitted in 2020 in universities in the whole quantity
working-age people in the region, %
47.047.02
2
)07.1
3
(
33
247.0
51.44
)(
x
exy
; (3)
- the proportion of students finished universities in 2020 in the whole quantity
working-age people in the region, %
38.038.02
2
)85.0
4
(
44
238.0
80.32
)(
x
exy
. (4)
The quality of functions (1)-(4) we tested using such criteria: by the Kolmogorov-
Smirnov, the Pearson and the Shapiro-Wilk. Calculated values of criteria are given in Table
2.
The data shown in the second table shows that all four models well approximate the
original empirical information. This conclusion is confirmed by comparing the calculated
statistics and critical values. So, the calculated statistics on the Kolmogorov-Smirnov test in
the second column of the table are in the range from 0.05 to 0.06, that is, less than the
critical value equal to 0.174. Similarly, the calculated statistics on the Pearson test (the third
column of table 2) are in the range from 2.35 to 4.49, that is, less than the critical value
equal to 9.49. It is known that the critical value of the Shapiro-Fork test is 0.93, and the
calculated statistics for this test are in the range from 0.95 to 0.98. Thus, the test showed
that the requirements of all three criteria are met and the developed functions are of high
quality.
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Table 2. Calculated values of criteria
Indicators
Criteria
The Kolmogorov-
Smirnov test
The
Pearson
test
The
Shapiro-
Wilk test
The quantity of higher education
institutions in calculation on million
working-age people in the region
0.06
4.48
0.95
The proportion of university students in
the whole quantity working-age people in
the region
0.06
4.13
0.96
The proportion of students admitted in
2020 in universities in the whole quantity
working-age people in the region
0.06
4.49
0.95
The proportion of students finished
universities in 2020 in the whole quantity
working-age people in the region
0.05
2.35
0.98
Source: The data in the table are based on the results of calculated functions.
Based on the developed functions (1)-(4), an assessment of the average values of
indicators, average square deviations and intervals in which the values of indicators
characteristic of most regions of Russia are located, which are demonstrated in Table 3, was
carried out.
4. Discussion
The analysis showed that in 2020 there were institutes of higher education in all 82
Russian regions. Therefore, the first hypothesis was confirmed. It should be noted that this
fact seems to be fundamental, since it indicates the availability of higher education directly
in the regions where adults live.
The information given in column 2 of Table 3 shows that for every million of the
working-age population, on average, there are 14.8 institutes of higher education in Russia.
The number of universities and their branches in most regions is in the range from 9.4 to
20.1 per million people of working age.
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Table 3. The values of indicators describing the level of development of higher education in
the regions of Russia in 2020
Indicator numbers
Average values
Standard
deviation
Values for most
regions
1
2
3
4
The quantity of higher education
institutions in calculation on
million working-age people in the
region
14.79
5.36
9.43-20.15
The proportion of university
students in the whole quantity
working-age people in the region,
%
4.2
1.72
2.48-5.92
The proportion of students
admitted in 2020 in universities in
the whole quantity working-age
people in the region, %
1.07
0.47
0.6-1.54
The proportion of students
finished universities in 2020 in the
whole quantity working-age
people in the region, %
0.85
0.38
0.47-1.23
Source: The calculations are carried out by the authors on the basis of functions (1)-(4).
The average share of university students is almost 4.2% of the total population of
working age. Accordingly, out of twenty-four people of working age, one in 2020 was a
student who studied at the institute of higher education. In most regions, the share of
students in the working-age population was in the range from 2.5% to 5.9%.
In 2020, about 1.1% of all people of working age entered higher education
institutions. For most regions, this indicator was in the range from 0.6% to 1.5%.
About 0.8% of the working-age population of Russia in 2020 successfully graduated
from higher education institutions and became qualified specialists. For most regions, the
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values of this indicator were in the range from 0.5% to 1.2%. It should be noted that the
number of students who successfully graduated from higher education institutions was less
compared to those who entered the training. This seems logical, since not all those who
have started their studies fully master the programs and become certified specialists.
Using the data in Table 3, the coefficients of variation for all four indicators were
calculated. The coefficient of variation is the ratio between the mean square deviation and
the average value of the indicator. The calculated coefficients of variation are given below:
- the first indicator is 36%;
- the second indicator is 41%;
- the third indicator is 44%;
- the fourth indicator is 45%.
The obtained coefficients of variation indicate that there was a significant (more
than 33%) differentiation of the regional values of the considered indicators. Thus, the
second hypothesis was confirmed.
The minimum and maximum values of the indicators were noted in the regions of
Russia, the lists of which are shown in the fourth table. In the regions with the maximum
values, the indicators exceeded the upper limits of the intervals indicated in the fourth
column of the third table. Accordingly, in regions with minimal values, the indicators were
less than the lower limit of these intervals. The fourth table for each of the regions shows
not only the value of the indicator, but also the location of the region.
Table 4 provides information on the values of indicators for each of the regions
(column 3), as well as their territorial location (column 4). The analysis of this information
showed that there is no connection between the maximum and minimum values of the
indicators and the territorial location of the regions. That is, the regions with high and low
values of indicators are located in different federal districts. Thus, we can state the
confirmation of hypothesis 3.
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Table 4. Characteristics of Russian regions with maximum and minimum indicator values
Indicators
Region
Value
Federal district
1
2
3
4
The quantity of higher
education institutions
in calculation on
million working-age
people in the region
With maximum values of indicators
Moscow city
20.54
Central
Saint Petersburg city
21.87
North-West
Yaroslavl region
21.89
Central
Orel region
22.45
Central
Astrakhan region
23.26
South
Pskov region
23.60
North-West
Sevastopol city
23.64
South
Kamchatka territory
26.18
Far Eastern
Sakha republic
26.34
Far Eastern
Smolensk region
30.35
Central
Chukotka autonomous
district
31.53
Far Eastern
With minimum values of indicators
Chechen republic
4.81
North
Caucasian
Tyumen region
4.90
Ural
Kostroma region
5.87
Central
Kabardino-Balkar republic
5.93
North
Caucasian
Novgorod region
6.31
Privolzhsky
Ingushetia republic
6.68
North
Caucasian
Sakhalin region
7.13
Far Eastern
Mari El republic
8.04
Privolzhsky
Altai republic
8.41
Siberian
Leningrad region
9.24
North-West
The proportion of
university students in
the whole quantity
working-age people in
the region
With maximum values of indicators
Kursk region
6.12%
Central
Novosibirsk region
6.17%
Siberian
Tatarstan republic
6.50%
Privolzhsky
Voronezh region
6.55%
Central
Orel region
6.85%
Central
Omsk region
6.85%
Siberian
Tomsk region
9.15%
Siberian
Moscow city
9.89%
Central
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Saint Petersburg city
9.99%
North-West
With minimum values of indicators
Chukotka autonomous
district
0.44%
Far Eastern
Leningrad region
0.58%
North-West
Murmansk region
1.49%
North-West
Moscow region
1.76%
Central
Sakhalin region
1.96%
Far Eastern
Jewish autonomous region
2.17%
Far Eastern
Altai republic
2.23%
Siberian
Tyumen region
2.24%
Ural
The proportion of
students admitted in
2020 in universities in
the whole quantity
working-age people in
the region
With maximum values of indicators
Sevastopol city
1.59%
South
Oryol region
1.67%
Central
Novosibirsk region
1.73%
Siberian
Voronezh region
1.75%
Central
Tatarstan republic
1.75%
Privolzhsky
Omsk region
2.04%
Siberian
Tomsk region
2.63%
Siberian
Saint Petersburg city
2.98%
North-West
Moscow city
3.01%
Central
With minimum values of indicators
Chukotka autonomous
district
0.08%
Far Eastern
Leningrad region
0.09%
North-West
Murmansk region
0.36%
North-West
Jewish autonomous region
0.43%
Far Eastern
Sakhalin region
0.43%
Far Eastern
Moscow region
0.45%
Central
Tyumen region
0.55%
Ural
Magadan region
0.56%
Far Eastern
Kamchatka territory
0.56%
Far Eastern
The proportion of
students finished
universities in 2020 in
the whole quantity
working-age people in
the region
With maximum values of indicators
Kursk region
1.28%
Central
Omsk region
1.38%
Siberian
Tatarstan republic
1.41%
Privolzhsky
Voronezh region
1.42%
Central
Adygea republic
1.45%
North
Caucasian
Oryol region
1.50%
Central
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Iuliia Pinkovetskaia et al. /// Regional differentiation of higher education in Russian regions … 428-445
DOI: http://dx.doi.org/10.46925//rdluz.35.25
442
Tomsk region
1.69%
Siberian
Saint Petersburg city
2.04%
North-West
Moscow city
2.26%
Central
With minimum values of indicators
Chukotka autonomous
district
0.05%
Far Eastern
Leningrad region
0.09%
North-West
Sakhalin region
0.31%
Far Eastern
Murmansk region
0.31%
North-West
Moscow region
0.35%
Central
Magadan region
0.43%
Far Eastern
Altai Republic
0.45%
Siberian
Tyumen region
0.46%
Ural
Source: Developed by the authors on the basis of data from Table 3.
Conclusion
The research described in this article allowed us to gain new knowledge about the
regional features of the development of the higher education system in Russia. The study
contributed to the assessment of the accessibility of students' education in higher
education institutions in regions where young people who want to study according to the
relevant programs permanently live. In addition, a certain contribution was made to the
study of the share of students in the working-age population of each of the 82 regions of
Russia. The methodology proposed by the authors was based on the development of
mathematical models describing the distribution of indicators by region. The purpose of
our study was to evaluate the indicators describing the distribution of higher education
organizations by regions of Russia, the share of students in the total population of working
age in each of the regions, as well as the share of students admitted to study and graduated
in 2020. The results of the study have a certain novelty and originality. Thus, based on
empirical data, it was found that there are higher education organizations in each of the
Russian regions. Consequently, people could receive higher education in the territory of the
region in which they live. The study was based on the calculation of relative indicators that
describe the relationship between the number of institutions of higher education and the
number of university students and such a generalizing indicator as the number of able-
bodied people. The study proved that the saturation of higher education institutions in
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443
2020 was almost 14.8 institutes for every million people of working age on average in
Russian regions. Calculations showed that out of twenty-four people of working age, one
person studied at the Institute of higher education. In 2020, about 1.1% of people of
working age started studying at higher educational institutions, and more than 0.8% of
people of this age successfully completed their studies and became qualified specialists.
The results of the mathematical modeling of empirical data allowed us to conclude
that there are significant differences in the values of each of the four indicators under
consideration for different regions. A list of regions was compiled, which included regions
in which the values of each of the four considered indicators were maximum and minimum.
The proposed author's methodology and the results of calculations are of interest to
researchers, and can also be used in monitoring regional features of higher education in
Russia and other countries. Especially those that have a significant number of territorial
elements. In addition, the research results can be used in the practical activities of
governments and public organizations directly related to the regulation and support of
higher education institutions and the development of educational systems and
technologies. The data directly related to the Russian regions can be used by applicants
when choosing the direction and place of study.
The study used official statistical information on the quantity of institutions of
higher education and the number of university students in all 82 regions of Russia, that is,
there were no restrictions on empirical data in the study. Future research may be related to
the assessment of the gender structure of university students in Russia.
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