In the context of economic security development, attention is focused on solving complex theoretical and applied problems that describe the relationships between various economic objects. In terms of building strategies for managing economic security, a mathematical model of economic security risks has been developed and analyzed. The risks of economic security at the regional and state levels are identified: the risks of employment transformation associated with the aging of the population, the risk of maintaining a significant share of inefficient jobs, the risk of limited access of human capital carriers to productive jobs, the risk of volatility of labor income, the risk of growth in educational and qualification inconsistency of human capital with the needs of the economy. An economic-mathematical model of structural transformations in the sphere of employment of the population depending on the dynamics of the growth of the level of employment of the population in the main sectors of the economy (agriculture, forestry, and fisheries; industry; construction) based on statistical data of the Kyiv region was built and researched. Attention is focused on the selection procedure of factor variables that should be a part of the econometric model, which is one of the key aspects that are studied while constructing a multivariate regression equation. The coefficients of correlation, elasticity, and the average value of the relative error of approximation were calculated and analyzed, and the built model was tested for statistical significance using the Fisher test. Based on the results of the analysis, the model is adequate, statistically significant, and suitable for point and interval forecasting. The article identifies the main threats to the economic security of Ukraine: the mass migration of the population with higher education during the war, and the migration of children and youth, which in the period of post-war reconstruction will be manifested by a shortage of quantitative and qualitative characteristics of the workforce. The priorities for restoring Ukraine's macroeconomic security are indicated. A theoretical analysis of economic security in terms of various spheres of the economy was carried out, in particular, the threats to the macroeconomic security of Ukraine related to employment and the search for ways to overcome them were described in detail.
In the context of the modern development of economic security, special attention is paid to the solution of complex theoretical and applied problems, which quantitatively and qualitatively describe the relationships between various economic objects. This necessitates the development and analysis of mathematical models of economic security risks, which are used to build economic security management strategies. These models usually include elements such as risk identification, risk probability analysis, loss assessment, construction of risk minimization strategies, and development of risk control methods. Different methods can be used to build mathematical models of economic security risks, such as statistical analysis, probability theory, decision-making theory, mathematical modeling and others.
The method of mathematical modeling is one of the most common methods of scientific knowledge. It is used to solve problems in economics, sociology, medicine, and applied sciences. Where the method of scientific observation and the method of the scientific experiment does not provide tangible results (due to the long duration of certain processes or phenomena under investigation, or the impossibility of conducting multi-scale experiments to ensure reliable results), the method of mathematical modeling comes to the rescue.
The use of mathematical modeling in various fields of science allows for deepening quantitative and qualitative analysis, expanding the scope of obtaining information, and speeding up mathematical calculations.
When studying socio-economic phenomena
and processes that characterize one or another
stage of the development of the market economy,
it is necessary to deal with various mass
phenomena, identify existing patterns, and
establish directions for their development. The
task of studying the quantitative aspects of mass
phenomena and processes in an inextricable
connection with their qualitative aspect is
primarily solved by econometric modeling,
which, with the help of its instrumental and
theoretical apparatus, establishes cause-and-effect
relationships in the studied economic systems to
conduct their analysis, synthesis, diagnosing
problems and finding ways to overcome them [
The main task of modeling is the development and analysis of mathematical models, which are represented by certain abstract mathematical relations (equations or systems of equations). The constructed mathematical model must satisfy several requirements: firstly, it must adequately reflect the process or phenomenon under investigation; secondly, to be as simple as possible. Even A. Einstein said: “Models should be as simple as possible, but not simpler.”
It is worth noting that mathematical models can be a useful tool for managing risks and developing effective strategies for managing economic security. However, it is important to remember that models do not always accurately reflect the real world, so it is important to evaluate them and critically evaluate their results.
The state of macroeconomic security during
2010–2019 (with the average value of the state of
macroeconomic security assessment for this
period at the level of 38% of the optimal value)
was characterized as dangerous [
The labor market, in turn, acts as the most specific subsystem of the economy and at the same time, its driving force determines the prospects for ensuring sustainable economic and innovative development, which are primarily related to the quality characteristics of the workforce and decent working conditions.
In recent years, fluctuating dynamics of the
level of macroeconomic security have emerged.
In particular, according to the results of 2019, the
level of macroeconomic security increased by 6
percentage points up to 45% of the optimal value
due to the implementation of the policy aimed at
increasing the level of income of the population
and the implementation of the inflation targeting
policy by the National Bank of Ukraine. However,
according to the results of the first half of 2020,
the level of macroeconomic security decreased by
6 percentage points up to 39% compared to the
corresponding period in 2019, which indicates the
preservation of significant risks of destabilization
of the macro-environment [
Among the theoretical and practical aspects of
the study of the various aspects of economic
security, it is worth noting the works of
O. Tymoshenko (methodical approaches to
assessing the level of economic security of the
state) [
Among the scientists who studied the
interrelationships of structural shifts of economies
at the macro- and meso-levels and employment of
the population, it is worth highlighting;
V. Bliznyuk (study of educational and
qualification disparities in the regional labor
market of Ukraine), [
Modeling the risks of economic security allows you to assess possible risks and prepare for possible negative consequences. Such models help to predict possible risks, analyze their impact on the economy, and develop risk management strategies.
Risk modeling is a tool for managing risks and
ensuring economic security at various levels:
from an individual enterprise to the state level.
Such models can help avoid financial losses, and
reduce the risks of industrial accidents and other
negative events that can harm the economy and
society in general [
In addition, risk models make it possible to ensure a more efficient use of resources, increase the level of competitiveness and reduce the costs of risk management. Considering the complexity of the modern economy and the threats that may appear, risk models are an important tool for ensuring the stability and security of the economy.
The process of modeling the risks of economic security may include various factors that affect economic security. These factors may be:
Economic indicators: such as GDP, inflation, unemployment, the exchange rate, etc.
Political factors: such as the stability of the government, the legal system, international relations, etc.
Social factors: such as the demographic situation, level of education, level of poverty, cultural and religious factors, etc.
Natural factors: such as natural disasters, climate change, environmental problems, etc.
Technological factors: such as innovations, changes in technological approaches, growth in the number of cyber-attacks, etc.
These factors can be taken into account when building a mathematical model of economic security risks to assess the level of risk and develop risk management strategies.
Let’s focus on social factors in more detail. Because a result of modern transformations of the labor market and aggravation of the asynchrony of its situation, there is a contradictory and uneven nature of its development, which is manifested in the imperfection of certain elements of the market mechanism and leads to certain risks at both the regional and state levels, in particular: 1. Risks of employment transformation associated with the aging of the population, deterioration of its age structure, and reduction of the total number. Over the past two centuries, our country has had one of the highest rates of population aging among European countries, which affected the quality of human capital. Now the situation is even more aggravated because of the war and the drain of talent. 2. The risk of maintaining a significant share of inefficient workplaces. The destruction of infrastructure, the slowdown in production rates and the rate of structural restructuring of the economy, limited investment opportunities, and the weak motivation of employers to create new jobs hurt the processes of forming demand for labor, expressed in the number of jobs. Perpetuation of inefficient jobs, which in turn stimulates the supply of low-quality human capital and unproductive employment. 3. The risk of limited access of human capital carriers to productive workplaces, primarily affects young people and the elderly, less qualified workers, and people living in regions with limited employment opportunities. In Ukraine, education, work skills, and personal qualities are less important for employment and maintaining a workplace than personal connections and social status. Since during the economic reform, job creation took place mainly in the informal sector and in sectors with lower labor productivity, such jobs are mainly “survival jobs” and as a result cannot contribute to the long-term development of the economy and the improvement of the quality of human capital in the future. 4. The risk of volatility of labor income is most often caused by endogenous factors that lead to fluctuations in labor demand, changes in workplace and profession preferences, forced transition to part-time employment, permanent or labor migration, etc. Often, in these cases, the so-called poverty of the working people arises. First of all, this is characteristic of situations when employees, due to various reasons, do not receive a decent reward for their work; their wages are lower than the established minimum standard even under full employment conditions. 5. The risk of growing educational and qualification mismatch of human capital with the needs of the economy. In Ukraine, 26.6% of employed people aged 15–70 are characterized by excess education and are mainly concentrated in agriculture, forestry and fisheries, construction, temporary accommodation and catering, wholesale and retail trade, transport and communications, and workplaces, which do not require high qualifications. In this regard, the fact that overeducated workers in these types of economic activity do not fully realize their potential and gradually lose some of the competencies that are not required by their workplaces causes concern. This situation revolves around not only the aging of competencies but also the fact that a more qualified labor force gradually displaces a less qualified one from the economy. There is an erosion of human capital, which further exacerbates the social tension in the labor market. If these trends persist, there will be no incentive for employers to raise wages, since they will be able to hire people with a greater skill set for the same money as a sufficiently skilled workforce.
The problem of the mismatch of qualifications
in Ukraine is deepened by the existence in some
cases of unjustifiably inflated requirements for
job applicants, which encourages them to
constantly improve their educational level, while
in society, meanwhile, there is a growing shortage
of vacancies that do not require higher education.
The shortage of qualified workers in professions
that have a special demand in the labor market
ultimately leads to the impossibility of
highquality staffing of enterprises with the necessary
human capital [
The educational and qualification mismatch of human capital hurts production efficiency, causes staff turnover and talent outflow, increases the cost of finding the right specialist, and prevents the introduction of new technologies. At the macro level, these phenomena are manifested in the spread of unemployment, shadow employment, and economic inactivity, loss of human capital, which in aggregate negatively affects the well-being of the country.
Considering the current situation in Ukraine, the problems of macroeconomic security, the search for methods and ways to protect the economy of Ukraine is more relevant than ever and requires a clear organization of scientific research aimed at identifying challenges and threats in the field of employment and their minimization in the field of economic security. The results of such studies will form the basis for the creation of an effectively functioning system of strategic planning and forecasting, capable of adequately responding to existing and future risks.
The purpose of the article is to identify the risks of transformation of the labor market both at the regional and state levels, to develop an economic-mathematical model of structural transformations in the sphere of employment of the population depending on the dynamics of the growth of the employment level of the population in the main sectors of the economy (agriculture, forestry, and fisheries; industry; construction).
Kyiv region was taken as the object of the study, a region whose economic structure is dominated by construction, real estate operations, and financial services, but the share of industrial production, agro-industrial complex, and food industry is also significant.
The research is based on the use of economicmathematical modeling methods using Excel and Mathcad application packages, including methods of correlation analysis, and tabular and graphic analysis methods. Correlation analysis makes it possible to determine the existence of dependence between two variables, for example, between employment in a certain sector of the economy and the total employment of the population in the region. If the correlation between these variables is strong, then it can be argued that employment in this sector of the economy has an impact on total employment in the region. Regression analysis can be used for a more accurate analysis of dependence. Regression analysis makes it possible to determine how much variable employment in a certain sector of the economy affects the change in total employment in the region. At the same time, it is possible to take into account other factors that can also affect the total employment, for example, demographic and economic indicators of the region.
The purpose of building an
economicmathematical model is to study the dynamics of
the employment level of the population aged 15 to
70 from the dynamics of the number of the
employed population by types of economic
activity in Kyiv and the Kyiv region: agriculture,
forestry, and fishing (Code according to KVED–
2010/Code NACE, Rev .2-A), industry (Code
according to KVED-2010/Code NACE,
Rev.2B+C+D+E), construction (Code according to
KVED-2010/Code NACE, Rev.2-F). The
statistical data were taken from the statistical
information of the State Statistics Service of
Ukraine [
When studying many economic processes, it is necessary to establish and evaluate the dependence of some economic indicator on one or more other indicators. Any economic indicators are usually influenced by random factors, and therefore, from a mathematical point of view, are interpreted as random variables. Strict functional dependence is rarely realized in the economy. The so-called statistical dependence is more often observed when a change in one random variable leads to a change in the law of the probability distribution of another.
Analyzing a statistical series of data, we note that the construction of econometric models requires the presence of stable interrelationships of correlated variables. Periods of economic and political upheavals, and as a result, demographic and social ones, disrupt the stable dynamics of processes and phenomena (which is reflected in the diagram of the dynamics of changes in employment of the population by types of activity by sharp “failures” of certain indicators). This, in turn, although it affects the quality of the built model in the part related to the study of adequacy and calculation of the value of the relative error, does not violate the objectivity of the obtained results regarding the study of the statistical significance of the model as a whole.
The initial stage for the construction of an
econometric model is the identification of
variables [
The diagrams show the dynamics of changes in employment by selected types of activity in comparison to total employment in the region (Error! Reference source not found.–Error! Reference source not found.).
Fig. 1 shows the dynamics of changes in employment by agriculture, forestry, and fisheries in comparison to total employment in the region.
Dymanics of employment changes by the
type of activity 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 0.90 0.40 dynamics of changes in employment of the population by types of activity from 2005 to 2020 employment by industry in comparison to total employment in the region.
Dynamics of employment changes by type of activity
Industry of
Construction changes in and
= =
̅̅̅̅ − ̅ ∙ ̅ √̅̅2̅ − ( ̅)2 ∙ √̅̅̅2̅ − ( ̅)2
̅̅̅̅̅̅ − ̅ ∙ ̅ √̅̅̅̅2̅ − ( ̅ )2 ∙ √̅̅̅2̅ − ( ̅)2 , (1) (2) where , = 1, .
The calculated
values of the correlation coefficients are presented in Fig. 5, where we can note the strength of the correlation: X1 is the rate of growth agriculture, forestry, and fishing with the resulting variable Y as 0.29; X2 is the rate of growth of the employed population in the industry with the effective variable Y as 0.85; X3 is the rate of growth of the employed population in construction with the resulting variable Y as 0.86. It is worth noting that the condition that the factor variables should be weakly correlated with each other is observed. The next step of the research will be to build a model. using the method of least squares. change in factor indicators (X1 is the rate of growth of the employed population in agriculture, forestry, and fishing; X2 is the rate of growth of the employed population in the industry; the rate of growth of the employed population in the industry; X3 is the rate of growth of the employed population in construction) affects 2 = 0.982 ∙ 100% = 80% on the change of the performance indicator, and in the studied model it is the growth rate of population employment. evidenced by the average value of the relative error of the estimated regression values, which are within 10%. For the Kyiv region, the relative error is equal to = 1
∑ | | ∙ 100% = 5%, and it is statistically significant, as evidenced by the comparison of the calculated values using the Fisher test (Ftest = 16.02, Ftable=3.49).
One of the important characteristics for the interpretation of the econometric model is the calculation of the coefficient of elasticity for each of the factors: = ̂ ∙ , ( = 1,3) and general elasticity Е: = ∑3=1 , which shows how the result will change with a simultaneous change of all factors by 1%. So, according to the calculations Е1 = –0.11, Е2 = 1.3, Е3 = 0.51, Е = 1.7. As we can see from the results of the calculations, if all the selected factors increase by 1%, the dynamics of the rate of
general employment of the population will increase by 1.7%.
Analyzing the built model about the found parameter estimates, it is worth noting that the determining factors that affect the dynamics of employment growth in the studied region are industry (a2 = 1.28) and construction (a3 = 0.51). The negative coefficient of the regression model another or other sectors and, as a result, there is a shift in employment. But, of course, before making conclusions about the reasons for the employment shift, it is necessary to carry out a more thorough study in this direction.
Summing up the above, we note that the modern labor market of Ukraine, which is a component of macroeconomic security, functions in conditions of shocks caused not only by the globalization of the economy but also by the complex realities of the Ukrainian-Russian war. The loss of part of Ukrainian territories, the property of legal entities and individuals, and the destruction of critical and social infrastructure led to a drop in production, an increase in inflation, a reduction in the economic activity population, a deepening of poverty problems, etc.
Fleeing from the war, a large part of the
population is forced to seek shelter for themselves
and their loved ones in other regions, and in some
places even abroad, which increases the pressure
on jobs. The Ukrainian-Russian war became a
shock not only for national, but also for global
security. According to estimates of the UN
Refugee Agency, as of the beginning of June
2022, about 7 million people have left Ukraine
since the beginning of the full-scale war.
Twothirds of them have a higher education, and 49%
were employed in occupations that require high
qualifications. From the end of April, Ukrainians
began to return from their countries of temporary
stay and, according to the UN, 2.1 million people
have already done so [
Mass migration of the population with higher
education (more than 60–70% of the total
population of migrants according to the Institute
of Demography and Social Research named after
M. V. Ptukh of the National Academy of Sciences
of Ukraine [
According to the estimates of the World Bank,
60–80 % of the GDP of developed countries is not
provided by physical or financial capital, but
rather by human capital, that is, the population, its
health, education, and qualifications play a
decisive role. One of the important factors in
supporting the population and overcoming threats
to social security in wartime is jobs. They
contribute to the development of the economy,
increase the purchasing power of the population,
and are a reliable tool to overcome poverty [
Information on the employment status of the population is the basis for creating and implementing an effective strategy for the socioeconomic development of a particular region and the state in general. In this regard, the evaluation and analysis of the employment of the population acquire significant importance, which requires the further application of statistical research methods to determine the state and patterns of development of the employment of the population in regional and macroeconomic aspects.
The obtained estimates of the parameters of the built model (a2 = 1.28 and a3 = 0.51) indicate that the determining factors that affect the dynamics of the growth of the level of employment in the studied region are, respectively, industry and construction.
The work analyzes the dynamics of structural
changes in the sphere of population employment
by types of activity. Based on the analysis of the
labor market, a clear positive linear relationship
was established between the dynamics of
population employment and population
employment in agriculture, forestry, fishing,
industry, and construction. The found elasticity
coefficient indicates that a 1% increase in the rate
of population employment in the sectors of the
economy related to agriculture, industry, and
construction will lead to a 1.7% increase in the
overall employment dynamics of the Kyiv region
population. The obtained results are consistent
with the data of the State Employment Service
[
The constructed model is adequate (the relative error does not exceed 5%) and statistically significant in general (according to Fisher’s test), therefore suitable for point and interval forecasts.