The age structure of the scientific and pedagogical staff: data from the regions of Russia

The purpose of our study was to evaluate the indicators characterizing the age structure of the scientific and pedagogical staff of universities and other higher educational institutions in the regions of Russia. In the course of the work, the indicators characterizing the specific weights of teachers belonging to five age groups from 25 to 34 years, from 35 to 44 years, from 45 to 54 years, from 55 to 64 years and over 65 years in the total number of teachers working in higher education institutes were evaluated. The study used official statistical information for 82 regions of Russia. We used the density functions of the normal distribution as models. The results of the research allowed us to draw conclusions: the largest number (more than a quarter) of teachers was observed in the group from 35 to 44 years; 24% of teachers were aged from 45 to 54 years; 20% of teachers were slightly older. The least number of teachers was observed in the age groups over 65 years and from 25 to 34 years. The proposed methodological approach and the results obtained have originality and scientific novelty, since the assessment of regional features of the age structure of scientific and pedagogical personnel in the regions of Russia has not been carried out before.


INTRODUCTION
In the twenty-first century, according to many researchers (for example, Pinheiro et al., 2015) there is an increasing role of higher education institutions in national economies.
In both developed and developing countries, there is an urgent need for the development of human capital based on increasing the level of knowledge and competencies (Pinheiro, Stensaker, 2014). Therefore, a wide range of measures are being implemented to improve higher education (Maassen, 2014). Most States have created conditions that ensure mass access of the population to higher education (Guri-Rosenblit et al., 2007). To solve the problems of higher education, a necessary condition is the availability of scientific and pedagogical personnel for teaching students according to appropriate programs. Taking this into account, one of the urgent scientific problems is the assessment of indicators that characterize the availability of staff, that is, professors, associate professors, as well as other categories of teachers who ensure the availability of higher education (Stiglitz, 2014;Douglas, 2011). One of the most important for governments and regulatory bodies is the assessment of the distribution number of teachers in higher education institutions by their age.
Our research was devoted to this issue on the example of Russian regions. Currently, higher education institutions are present in all 82 regions of Russia without exception. The presence of organizations in the regions that teach students according to the relevant programs, as indicated in the works (Abel and Deitz, 2011;Chiriachi, 2014), increases the attractiveness of regions, positively affects their economic growth and, most importantly, ensures the retention of school graduates in the regional labor market. The total number of teachers working at universities and other higher educational institutions in Russia was 223088 people. Of these, 35039 people are professors, and 129328 people are associate professors (Federal State Statistics Service, 2021).
All this determines the increased interest in studying the age structure of the staff of higher education institutions. Our article responds to the calls made in a number of scientific publications (Blau, Weinberg, 2017;Ghaffarzadegan, Xu, 2018;Larson, Gomez Diaz, 2012), to study the existing features of the age structure of teachers.
The purpose of our study was to evaluate the indicators characterizing the age structure of the scientific and pedagogical staff of universities and other higher educational institutions in the regions of Russia. Our article is aimed at obtaining a certain empirical and methodological contribution to the knowledge about the distribution by age categories of the total number of teachers teaching students in higher education programs. This contribution consists in the fact that the author's method of modeling the age structure of the teaching staff of higher education institutions in the regions of Russia using the density functions of the normal distribution is proposed. The empirical contribution is associated with the determination of the average values and standard deviations by region of such indicators as the share of teachers of different age groups in their total number. In addition, the regions with the maximum and minimum values of these indicators are determined.
The structure of this work is given below. The next section presents an overview of scientific publications of recent years that characterize such aspects of higher education as the age structure of teachers in the regions. Methodology, initial data and design of the study described in our article are presented below. The following sections present the simulation results and their discussion. The last sections contain conclusions and bibliographic references.

LITERATURE REVIEW
A number of scientific publications published in recent years have been devoted to the problem of assessing such an aspect of the development of higher education in Russia, the age structure of the scientific and pedagogical staff of educational institutions. A brief description of these publications is given in table 1.
The study of the dynamics of the age structure of research and teaching staff in Russian universities according to data for 2007-2012. The conclusion is made about the small proportion of teachers under the age of 30 in the total number of teachers of higher education organizations Pugach (2017) The analysis of the distribution of the number of teachers of higher education organizations by age groups for the years 1988 -2014 is given. It is shown that during this period, the proportion of the number of teachers aged 40 to 60 years has decreased and this indicator has increased for teachers older than 65 years Fedosyuk (2020) The results of a sociological survey of university teachers of the Belgorod region aged from 58 to 64 years are presented. The survey results showed that about 80% of respondents plan to continue their activities after retirement Balezina (2017) The features of such a category of personnel of higher education institutions as young teachers, which include people under the age of 35 who carry out scientific and pedagogical activities, are studied. It is concluded that it is necessary to pay great attention to such a problem as the adaptation of young teachers in the team Reznik, Vdovina (2020) The problems of intra-university management and the existing structure of the scientific and teaching staff are considered Bessonova, Paronyants (2020) The assessment of the perception of their profession was carried out according to a survey of teachers Sevastopol State University. The results of the survey showed that young teachers associate their activities with the possibility of improving their social status and self-realization. Middle-aged teachers focus on improving the level of competence and perseverance in teaching students. For older teachers, motivation is associated with freedom of activity and altruism Skvortsova (2016) The changes in the system of value orientations of teachers of higher education institutions were studied on the basis of a questionnaire survey conducted in organizations located in the Penza, Ulyanovsk, Saratov regions and the Republic of Mordovia in 2014. It is shown that such motives as familiarization with new knowledge, self-improvement and the development of creative abilities decrease with increasing age of teachers Lazarev et al. (2015) The article presents measures to reduce the average age of scientific and pedagogical staff from 47 to 42 years at the Vladivostok State University of Economics and Service Ilinykh (2012) The analysis of the influence of the age characteristics of the scientific and pedagogical staff of universities on the quality of education is given. It is shown that in 2010, more than half of the teachers were over 50 years old Source: The table is compiled by the author on the basis of the information provided in the RSCI (Science Electronic Library, 2021).
Based on the information given in Table 1, it can be stated that the problem of studying the age structure of teachers who train students in higher education programs is relevant in Russia. In most of the studies reviewed, various aspects of this problem were analyzed for higher education institutions in Russia. At the same time, a comprehensive assessment of the features of the distribution of the age structure of teachers in all regions of Russia has not been considered in scientific publications. Taking this into account, it seems appropriate to conduct a comparative analysis of the existing relative (specific) indicators characterizing the age characteristics characteristic of scientific and pedagogical personnel in all regions of Russia.

METHODOLOGY
The scientific and pedagogical personnel of higher education organizations, the age structure of which is considered in this article, trained students in 2020 in bachelor's degree programs (four years of study), specialty degree (five years of study), as well as in master's degree programs. The study examined data characterizing the specific weights of the number of teachers who were included in five groups formed in accordance with five age categories: from 25 to 34 years old, from 35 to 44 years old, from 45 to 54 years old, from 55 to 64 years old and over 65 years old. In the course of the work, the following five indicators were evaluated: -the proportion of teachers aged 25 to 34 years, in the total number of teachers working in higher education institutions; -the proportion of teachers aged 35 to 44 years, in the total number of teachers working in higher education institutions; -the proportion of teachers aged 45 to 54 years, in the total number of teachers working in higher education institutions; The age structure of the scientific and pedagogical staff: data from the regions of Russia -the proportion of teachers aged 55 to 64 years, in the total number of teachers working in higher education institutions; -the proportion of teachers aged over 65 years, in the total number of teachers working in higher education institutions.
The research process included five stages. At the first stage, the initial data on the regions were formed, characterizing the number of scientific and pedagogical staff of higher education institutions in five main age categories. At the second stage, indicators were calculated that characterize the specific weights of the number of teachers belonging to each of the age categories in the total number of teachers of higher education institutions in each of the regions. At the third stage, the distribution of indicators by region was evaluated based on the development of mathematical models. At the fourth stage, the average values of indicators for the regions of Russia were determined, as well as the ranges in which the values of these indicators are located for most of them.
The study used official statistical information of the Ministry of Science and Higher Education of the Russian Federation for 2020 on the number and age of teachers who worked in higher education institutions in all 82 regions of Russia (Official statistical information on additional professional and higher education, 2021).
In our study, three hypotheses were tested: hypothesis 1 -among the scientific and pedagogical staff, relatively small proportions belong to the age categories from 25 to 34 years, as well as older than 65 years. The majority of teachers who provide training for students in higher education programs belong to three age categories: from 35 to 44 years old, from 45 to 54 years old and 55 to 64 years old; hypothesis 2 -the values of indicators by region have a small variation, that is, they are homogeneous; hypothesis 3 -the regions characterized by the maximum and minimum values of each of the five indicators are located in different federal districts.
The evaluation of the values of the five considered indicators was carried out on the basis of economic and mathematical modeling of the initial empirical data. As models, we used the density functions of the normal distribution, the method of developing which for estimating the values of relative cost indicators was proposed by the author. Some aspects of the use of the methodology are given in the works (Pinkovetskaya, Slepova, 2018;Pinkovetskaya et al., 2021). During the development of the functions, the initial empirical data were grouped according to the ranges of changes in the values of the indicators. These data groups can be geometrically represented in the form of corresponding histograms. Data approximation using normal distribution functions was carried out using generally accepted statistical methods. It is important to note that the average values of the considered indicators, as well as their standard deviations for the density functions of the normal distribution, were displayed in the formulas of the developed functions themselves. Therefore, by constructing a specific function, we get the specified parameters of the considered indicators without additional calculations.
The obtained functions allowed us to determine the average values of each of the five indicators for the regions under consideration, as well as the ranges of their changes characteristic of most regions. In addition, the study identified regions in which the considered indicators have values above the upper and below the lower limits of the ranges. The boundaries of the indicator ranges for 68% of the regions were determined based on the average values of the indicators and the corresponding standard deviations. The lower bound of the interval is equal to the difference between the mean and the standard deviation, and the upper bound is equal to their sum.

RESULTS
In the course of the computational experiment, economic and mathematical modeling was carried out on the basis of empirical data. The models that describe the distributions (  (1) -the proportion of teachers aged 35 to 44 years, in the total number of teachers working in higher education institutions (2) -the proportion of teachers aged 45 to 54 years, in the total number of teachers working in higher education institutions The quality of functions (1)-(5) we tested using such criteria: by the Kolmogorov-Smirnov, the Pearson and the Shapiro-Wilk. Calculated values of criteria are given in Table 2. Information given in column 2 of Table 2 showed that all calculated values are less than the critical value by the Kolmogorov-Smirnov test (0.174) at significant level equal 0.05. Data in column 3 are less than critical value of Pearson criterion (9.49). Data in column 4 exceed critical value 0.93 Shapiro-Wilk test with significant level of 0.01. Thus, the computational experiment showed that all five developed functions have high quality.
At the next stage of the study, the values of indicators characterizing the number and structure of scientific and pedagogical personnel working at universities and other institutions of higher education in the regions of Russia were determined. The values of the indicators, the average by region, are shown in column 2 of Table 3. The average values were determined on the base of functions (1)-(5). The third column indicates the standard deviation for discussing indicators. The values of the indicators characterizing the upper and lower boundaries of the intervals corresponding to the majority of regions are shown in column 4. We calculate the lower limits as the difference between the average value and the standard deviation, and we calculate the upper limits as the sum of the average value and the standard deviation.

DISCUSSION
The data in Table 3 shows that the regional average value of the proportion of teachers aged 25 to 34 years, in the total number of teachers working in higher education institutions is almost 11.5%. That is, every ninth teacher in such organizations was younger than 35 years old. In most regions, this indicator ranges from 8% to 15%. In 2020, the average proportion of teachers aged 35 to 44 years, in the total number of teachers working in higher education institutions, was 27.5%. That is, a little more than a quarter of all teachers in the Russian regions belonged to this age category. For most regions, the indicator under consideration was in the range from 24% to 31%. The average value of the proportion of teachers aged 45 to 54 years, in the total number of teachers working in higher education institutions, was 23.8%. In most regions, this indicator was in the range from 20% to 27%. The average value and the range of changes in the share of teachers in the age category from 55 to 64 years were slightly less. The corresponding average value was 20.2%, and the range of change was from 18% to 23%. For the category of teachers aged 65 years and older, the average value of their share in the total number of scientific and pedagogical staff by region was 16.7%. At the same time, in most regions, the values of the indicators were more than 12%, but less than 21%.
The analysis showed that among the considered age categories, teachers of higher education institutions were most often aged from 35 to 44 years. In two more age categories of teachers (from 45 to 54 years and from 55 to 64 years) their share in the total number of scientific and pedagogical staff exceeded 20% on average in the regions. The lowest specific weights were typical for the age categories from 25 to 34 years, as well as for older teachers (65 years and older). This situation seems logical, since in order to become a teacher teaching students in higher education programs, it is necessary to complete a bachelor's degree, a master's degree and in most cases get a PhD or a doctor of sciences degree. This training requires a lot of time and a lot of dedication from people. Therefore, most professionals are part of the scientific and pedagogical staff at the age of more than 34 years. A relatively small proportion of older teachers is due to the fact that many people who previously worked as teachers retire at this age. Only a part of the teachers, for whom it is important to maintain their activity, social status, as well as the desire to share their knowledge with students, continue their activities (Tnimova, 2020). It should be noted that some of them continue to work on a reduced schedule. The above analysis confirmed the correctness of the first hypothesis put forward earlier.
The next step was to determine the regions of Russia in which the maximum and minimum values of each indicator were marked. In this case, the maximum values are those that exceed the upper limits of the ranges specified in column 4 of Table 3, and the minimum values are those that are less than the lower limits of the specified ranges. The results of this analysis are shown in Table  4. Along with the lists of regions, this table also shows the values of indicators by region, as well as which of the federal districts the regions belong to. Source: Developed by the author on the basis of data from Table 3. 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.

CONCLUSION
In general, it should be noted that our study makes an important contribution to understanding the age structure of teachers of higher education institutions. The purpose of our study was to evaluate the indicators characterizing the age structure of the scientific and pedagogical staff of universities and other higher educational institutions in the regions of Russia. The conclusions that have scientific novelty and originality are given below. In the course of the study, a method was proposed for evaluating five indicators that characterize the age structure of teachers in higher education organizations, using the density functions of the normal distribution. Based on the proposed methodology, the distribution of indicators corresponding to five age categories in all 82 regions of Russia was estimated. The results of the computational experiment showed that the largest number of teachers was observed in the group from 35 to 44 years old. In this group, in 2020, there were more than a quarter of all teachers who worked in higher education organizations. Almost 24% of the number of all teachers were aged from 45 to 54 years. Thus, more than half of the scientific and pedagogical staff had an age in the range from 35 to 54 years. About 20% of the faculties were slightly older, that is, between the ages of 55 and 64. The least number of teachers was observed in the age groups over 65 years and from 25 to 34 years.
The analysis showed that there was no significant differentiation of the values of all five indicators by region. That is, the distribution of the number of teachers by region for each of the five age groups considered was relatively homogeneous. The regions that were characterized by the maximum and minimum values of the five considered indicators were identified. The study showed that the territorial location of the regions does not significantly affect the maximum and minimum values of the indicators.
The practical significance of the study for the government lies in the possibility of taking into account the age and territorial features of the formation of scientific and pedagogical personnel when developing programs for the development of higher education in Russia and its regions. The results of the work can be used in the activities of regional structures related to the support of educational processes, when justifying their planned activities, improving the quality of higher education by attracting new highly qualified teachers.
The new knowledge gained is of interest and can be used in the educational process at universities. The study had no limitations on empirical data, as it was based on official statistical information for all 82 regions of Russia. Further research may be aimed at establishing gender characteristics describing the number and structure of teachers in higher education institutions in Russia.