The Impact of Migration on Forecasting Budget Expenditures on Education: The Sustainability Context

Abstract

This paper examines the impact of migration and changes in the population’s age structure on government expenditures on education in Ukraine. The cohort method, considering a group of people attending four main types of education, namely, preschool, general secondary, vocational and technical, and higher education, is used to analyze and forecast government expenditures in the medium and long term. The study results show that migration significantly impacts government budget expenditures on education, with the most significant impact being seen on preschool education, followed by higher education, while the impact on general secondary and vocational education is minimal. The number of people receiving education in one of the four main types of institutions funded by state and local budgets was predicted to gradually decrease during the forecast period, except for secondary and vocational education. The overall volume of state expenditures would gradually decrease, both in absolute terms and as a percentage of GDP. Improving educational processes and the quality of budget spending should become an area for state regulation to ensure quality education in all funding conditions. This research’s leading theoretical and practical results show the efficiency of this methodology for analyzing and forecasting budget expenditures on education. They can be helpful in the short and medium terms, considering all potential changes in demographic indicators regarding the population.

1. Introduction

Migration has been a major global factor for centuries, and its importance is undeniable. It involves people, families, or entire populations moving from one place to another, either within a country or across international borders. It has dramatically affected the growth of civilizations, the spread of ideas, the development of countries, and the global economy. Migration is thought to have significantly contributed to developing countries, allowing for the sharing of cultures, goods, services, and knowledge. Migration processes can heavily impact the financial systems of countries and the recipient countries’ attempts to plan for all expenses by creating a budget. However, unexpected events such as environmental disasters and sudden influxes of migrants can disrupt this process. An influx of migrants requires additional resources to support them, which can strain a country’s limited budget.

A prime example is the large number of Ukrainian refugees who migrated to European countries due to Russian aggression in 2022–2023. Migration has enabled the sharing of ideas and resources and the growth of trade and commerce. As migration is a complex process, it is essential to study it to understand the causes of migration and to predict future movements. This research focuses on migration’s impact on forecasting budget expenditures on education.

The research goal is to examine the impact of migration and the resulting changes in the age structure of the population on government expenditures on education in Ukraine using the cohort method, considering several people in four main types of education: preschool, general secondary, and vocational and technical education, as well as higher education. The main tasks are to analyze and forecast government expenditures in the medium and long term.

The central hypothesis is that migration has a different impact on the number of children and adults who receive education at each stage (preschool, general secondary, vocational and technical, and higher education). As a result, there are different dynamics to budget expenditures in the short and long terms.

The paper consists of a detailed description of the methodology for each type of education and the results of the methodology implementation in the example of Ukraine in the conditions of the Russian–Ukrainian war.

2. Literature Review

Budget expenditures are an effective tool for regulating demographic development. Forecasting the expenditure side of the budget while considering demographic factors allows for increased effectiveness when using budget funds for the country’s socio-economic development. It can be argued that budget expenditures improve the country’s demographic situation and economic development [1,2]. One of the main types of budget expenditures that is decisive for economic growth and, as a result, human capital development is budget expenditures on education. Much scientific work is devoted to studying this issue from various perspectives.

Separately, we can single out the most relevant works that examine both budget expenditures and demographic development in general, as well as budget expenditures on education in particular [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. These papers examine the relationship between education spending and economic development. The general conclusion that can be drawn from these works is that investments in education contribute to the development of a qualified workforce, stimulation of innovation, and increase in productivity. Thus, educational investments contribute to the general economic growth and increase the welfare of the society of the country in question.

Among the considered works, those that use modeling for the investigated problem and the construction of forecasts are worth noting. For example, in article [1], the authors examine the labor market returns from investments in education as an essential component of the knowledge economy, considering the quality of management in OECD countries. A strong dependence on these factors is identified using panel data models, especially for higher education. It is shown that the quality of management in educational institutions affects the return on education expenditures in the labor market.

In article [2], budget expenditures are considered as an instrument of the state regulation of the dynamics of the socio-demographic development of a country. The forecasting and planning of budget expenditures while considering demographic factors use the interdependence of the indicators of budget expenditures, population, and age structure.

In article [3], research is conducted on the impact of demographic-related expenditures on the future stability of state finances. An analytical assessment of the impact of changes in education expenditures caused by demographic aging in Ukraine on budget stability was conducted using mathematical modeling and forecasting. As a result of this analysis of demographic trends, the funding volumes for different education levels in Ukraine were determined, the age-related proportions of education financing were identified, and the corresponding expenditures according to the population’s age structure were calculated. Article [4] aims to analyze the impact of state expenditures on education on economic growth in 11 former communist countries of Eastern Europe and current EU members. An ARDL methodology with a structural break was used.

The same approach (ARDL) is used in [5], which is aimed at studying the impact of current expenditures on health care, government expenditures on health care, government expenditures on education, social protection, population growth, and foreign direct investment (FDI) on the formation of human capital in Pakistan.

Article [6] proposes a model for studying the political determination of government spending on education and its distribution among different levels of education. In equilibrium, the government budget for education, private spending, and the distribution of spending among different levels of education depends on country-specific characteristics, such as income inequality and intergenerational persistence in education. A cluster analysis of 32 OECD countries determines the “education regimes” identified in the theoretical analysis.

In [7], a neural network model is proposed, based on socio-economic and investment innovation indicators of Ukraine’s development and the leading countries worldwide in 2000–2021. This model allows forecasting of the main directions of resource allocation and budgeting.

In article [8], to identify the impact of spending on education and education itself on economic growth, data on actual education spending, authentic gross domestic product (real GDP), and the total number of students according to levels of education were analyzed using econometric methods. A long-term positive relationship between increased education spending, an increased number of students at all levels of education, and real GDP growth is identified.

In article [9], a model is constructed to investigate the relationship between economic growth and fiscal policy. The model includes a wide range of fiscal policy tools: budget deficit, the structure of government debt, government spending on education, government consumption, and tax rates. The theoretical results are illustrated by an empirical analysis of Poland based on data regarding the Polish economy after the global financial crisis (2009–2018). The best way to accelerate economic growth is to increase government investment in education.

Government funding of education is one of the most critical fiscal instruments for responding to post-pandemic economic recovery challenges. Article [13] considers a wide range of literature on forecasting the state budget.

Migration issues and increasing migration flows worldwide have become urgent in the 21st century. The impact of migration on the economies of EU countries has significantly intensified because of the beginning of full-scale military operations in Ukraine. Poland has received the most significant number of Ukrainian migrants; therefore, migration has had the most significant impact on the economy of this country. The following works are devoted to the study of migration issues. Refs. [15,16,17,18,19,20] are devoted to studying issues of modeling migration flows related to Ukraine and Poland. It is worth highlighting two studies that use data science tools.

Article [15] studies the Ukrainian people’s internal and external migration flows. Migration flows of different economically active groups in the population of Ukraine, such as students and workers, are analyzed. The main ways and causes of migration processes and their impact on Ukraine’s economic and political situation are considered.

In [16], the factors influencing external labor migration in the economy of recipient countries are identified. In particular, the negative and positive impacts of emigration on the socio-economic situation in Ukraine and the migration attitudes of Ukrainians are assessed. The study’s main result is the further development of an econometric model for predicting the impact of external migration on the economy of recipient countries.

One of the methods used in demographic research, including those works related to migration, is cohort analysis. This method is described in detail in [21,22,23]. The main differences between these papers and our study are that they consider general demography and cohort analysis issues. In addition, these works do not consider forecasting methods in detail. It is also worth noting that these works were written before the Russian–Ukrainian war and do not contain an analysis of their impact on migration processes. Studies related to education financing and using cohort analysis can be found in the following works [24,25,26,27,28]. These works are devoted to various topics that connect the economy with education but do not consider forecasting methods in detail when applied to educational budget expenditures. Also, these works do not consider the impact of war on budgetary processes.

A literature review shows that government spending on education is crucial for responding to migration problems and promoting economic development. These interrelated aspects provide a comprehensive understanding of the role and impact of budget expenditures on education.

Based on an analysis of previous research, it can be concluded that the issue of forecasting budget expenditures using cohort analysis, while considering migration flows, has not yet been studied. In this article, we attempt to address this research gap, highlighting the paper’s main novelty. This work continues our previous research [29,30,31,32,33]. While the previous research focused more on budget expenditures for healthcare, this study will mainly focus on budget expenditures for education, based on Ukrainian data in conditions of high migration after a full-scale Russian invasion.

It is worth noting two works that provide an opportunity to understand better the complex factors that influence migration and education in the context of sustainable development [31,32]. Article [31] discusses the social and demographic implications of the COVID-19 pandemic for education systems. Migration is often driven by social and demographic factors such as poverty, inequality, and conflict. In addition, the COVID-19 pandemic has significantly affected migration processes around the world, as many people have been forced to move to other countries in search of better opportunities. Article [32] discusses the potential of Education 4.0 to promote sustainable student well-being. It is a process of educational transformation characterized by a focus on technology, innovation, and lifelong learning. Education 4.0 can significantly impact the cost of education and the skills and knowledge that students need to succeed in the future. These studies provide opportunities for a more sophisticated analysis of the impact of the social and demographic consequences of COVID-19 and Education 4.0 on migration patterns in the coming years. Migration can also affect the cost of education and the skills and knowledge that students need to succeed in the future. Another area for further research is the use of Education 4.0 by governments to mitigate the negative impact of migration on education systems.

It is also worth citing research on the Ukrainian education system and student mobility for education [33,34,35,36,37]. These works will provide the reader with a complete understanding of the context of the study and the factors that are likely to influence the impact of migration on the forecasting of budget expenditures for education in Ukraine.

3. Methodology

3.1. The Cohort Method for Forecasting Budget Expenditures for Education

According to the research goal related to the prediction of budget expenditures on education in Ukraine, we use the cohort method. Cohort N t comprises a group of permanent residents whose full age at year t is N years, where N = 1, …, 99. Using this method for analyzing and forecasting government expenditures in the medium and long term requires the availability of historical and forecast data on the size of the country’s permanent population according to cohort. The cohort method calculates the number of budget recipients. It estimates the general planned expenditures, based on planned expenditures per 1 recipient at each primary group (in such cases, there is a group for each type of education).

The algorithm for applying the cohort method is as follows:

Step 1. A group of recipients is determined for a particular type of government expenditure, which includes all final recipients of the corresponding government services or payments.

Step 2. The recipient groups determined in the previous step are divided into basic subgroups. This distribution is made according to the following principle: recipients belonging to one cohort, or an adjacent cohort with approximately the same spending per capita, are assigned to another essential subgroup. This type of government spending per member is considered constant within each primary subgroup. The representatives of one cohort may belong to different subgroups.

Step 3. For each primary group identified earlier, we determine the dependence of its size on ’the number of members in the age cohorts of representatives that are included or excluded from its composition according to the definition and formulate it in the form of a mathematical formula.

Step 4. Based on historical data regarding the volume of this type of public expenditure and the corresponding distribution of services (or payments) among the primary groups, the amount of that expenditure per member is identified for each primary group.

Step 5. Based on forecast data regarding the number of age cohorts, the size of each primary group in each year of the forecast period is determined.

Step 6. In each year of the forecast period, the volume of government expenditure of this type is assumed to be equal to the sum of the volumes of corresponding expenditures for all base recipient groups. For each base group, the expenditure volume equals its forecast population multiplied by the forecast expenditure per member. Expected spending per member of each subgroup can be based on the final year of the base period (inertial forecast scenario) or can be determined based on forecasted growth data accuracy and the inflation rate (alternative scenario). In the latter case, the expenditure volume of this type for each primary group in each year of the forecast period is determined by multiplying the corresponding expenditure volume under the inertial forecast scenario by the value of the corresponding index sequence during this time.

Sometimes, splitting a separate type of government expenditure into subtypes makes sense. In this case, it can be seen that the impact on different expenditure subtypes is described using different sets of base groups. There are possible situations when the composition of primary groups may change due to changes in the age population structure and also for other reasons, such as current socioeconomic or political reforms. A useful example involves one of the components of the reform of compulsory secondary education in Ukraine: the transition from an 11-year to a 12-year system of education in general education institutions. In this case, the composition of the primary groups of recipients of this type of public service and their dependence on the size of age cohorts will change over time. Typically, such changes are pre-planned and predictable and must be considered when building a basic forecast scenario. The forecast scenario in such a case can be determined by the orbital changes in expenses per member of the fundamental group by describing the evolution of the primary groups themselves and, if necessary, by making additional assumptions.

Since, in a standard situation, the population size ratio of individual age groups is determined by demographic indicators, which are fairly inert, it makes sense to consider them when performing forecasting tasks for a sufficiently long period. The population’s age structure can be considered as unchanged in short-term expenditure-planning tasks. Even in the case of medium-term planning/forecasting, in most cases, an assumption of the stability of the population’s age structure is quite acceptable. However, there are exceptions to this rule, including those related to significant fluctuations in the population size of adjacent age cohorts, which reflect certain extraordinary events (wars, famines, and “baby booms”). In such cases, the population size of age groups, which significantly impacts various indicators of the state finance system, can vary significantly over a relatively short period, which coincides with or is fully covered by the medium-term forecasting period (3–5 years). The need to consider changes in the population’s age structure when planning/forecasting certain types of government expenditures arises only in cases where such changes are noticeable and significantly affect the required number of corresponding expenditures.

Government expenditures on education can be divided into five components—the first four are determined by the four main types of education provided by state and communal educational institutions, and the fifth component includes other expenditures on education. The rationale for such a distribution is that each of the four main types of education (preschool, general secondary, vocational and technical, and higher education) corresponds to a particular group of recipients that can be linked to specific age groups, which is necessary for applying the cohort method. Other expenditures on education, which mainly include expenditures on postgraduate education, funding for extracurricular educational institutions, research, and development in the field of education, cannot be linked to a specific age group of the population; therefore, a method that is different from the cohort method is proposed for their forecasting.

The basic subgroups of the recipient group are determined for the four main types of education:

• A subgroup of the attendees of preschool education institutions;
• A subgroup of the recipients of general secondary education;
• A subgroup of the recipients of vocational education;
• A subgroup of the recipients of higher education.

Even though most representatives of the specified basic subgroups may be associated with a particular age group, there is no exact coincidence between them. That is, basic subgroups cannot be represented as a simple set of specific age cohorts; accordingly, the relationship between the number of the primary subgroup and the number of individual age cohorts will be represented by a more complex dependence relationship than a simple arithmetic sum.

3.2. The Cohort Method for the Preschool Education Expenditures Forecasting

The subgroup of visitors to preschool education institutions mainly comprises children aged 1 to 6 years. It should be noted that a certain number of children under the age of 1 also attend such institutions or are kept in them. However, the proportion of such children in the corresponding age cohort is small. The number of such pupils of educational institutions is insignificant compared to the number of children aged 1 year and older. Therefore, this corresponding cohort is not considered when determining the number of this primary subgroup. In addition, a certain number of children begin to receive secondary education from the age of 6, thus reducing the number of potential attendees to preschool education institutions. Finally, an argument in favor of relying on the number of members in the age group of 1–6 years, excluding 6-year-old schoolchildren, when determining the number of the essential subgroup is that it is precisely for this group that the State Statistics Committee determines the level of coverage by preschool education institutions, that is, by the ratio of the number of visitors to the population group. Therefore, the general idea of determining the number of this primary subgroup is straightforward: to determine the number of members in the specified population group in each year of the forecast period and multiply it by the forecast coverage level, which is determined by considering historical data, existing trends, and the declared state policy in this area.

However, it should also be noted that the level of coverage in terms of preschool education differs significantly between cities and rural areas. Therefore, when forecasting the overall level of coverage (especially in the long term), it is necessary to take into account, on the one hand, the phenomenon of urbanization and, on the other hand, the difference in birth rates in cities and rural areas, which directly affects the number of age cohorts belonging to the main contingent of preschool educational institutions.

Summing up, the following formula can be written down, which determines the number of members of the essential subgroup of visitors to preschool education institutions:

$$E_1=g\times \left(\sum _{i=1}^5{x}_i+(1-z)\times x_6\right),$$

(1)

where E₁ is the average annual number of visitors to preschool education institutions, x_i (i = 1, …, 6) is the average annual number of the ith age cohort, z is the specific weight of 6-year-old schoolchildren in x₆, and g is the coverage level of children aged 1 to 6 years (excluding 6-year-old schoolchildren) with preschool education.

3.3. The Cohort Method for Secondary Education Expenditures Forecasting

The subgroup of general secondary education recipients includes the students of general educational institutions. The age of majority today is 6–16 years old. However, as in the case of preschool education, some individuals of the corresponding age remain not covered by general secondary education, and some students are over 16 years old. Therefore, it is impossible to define the essential subgroup as a set of age cohorts in this case.

In addition, due to the reform of secondary education, which was initiated in Ukraine in 2001 and provided a transition to a 12-year education system, the essential subgroup’s age composition underwent significant changes in 2013. Namely, starting in 2013, the main contingent of general educational institutions would consist of individuals aged 6–17. Thus, the dependence of the primary subgroup’s size on the size of individual age cohorts would also change. Therefore, to consider the forecast of the impact of the reform of secondary education on the size of the essential subgroup, it is worth considering the period up to and including 2012 separately from the period starting from 2013.

For the period after 2013, the dependency formula will appear thus:

$$E_2=f\times \sum _{i=6}^{17}{x}_i,$$

(2)

where E₂ is the average annual number of students in general education institutions, which can be calculated based on statistical data using the formula:

$$E_2(t)=\frac{4}{12}\times k(t-1)+\frac{8}{12}\times k(t),$$

(3)

where t is the year, k(t) is the number of students in general education institutions as of the end of the academic year ending in the year t, and x_i (i = 6, …, 17) is the average annual population of the ith age cohort.

The coefficient f, which, by definition, is equal to the ratio of E₂ to ${\sum }_{i=6}^{17}{x}_i$, is determined based on statistical data for the historical (base) period, while for the forecast period, it is either fixed at the level of the last year of the base period (inertial forecast scenario) or forecasted while taking into account the existing trend and the officially declared state policy in the field of secondary education (an alternative scenario). Considering the presence of a certain (but insignificant) number of individuals over 17 years old among the students of general educational institutions, this value can be considered as a (reasonably close) lower estimate of the level of coverage of young people aged 6–17 with secondary education.

3.4. The Cohort Method for the Vocational Education Expenditures Forecasting

The subgroup of vocational education students includes students in vocational schools. Most of these students are young people aged 15 to 18. The duration of study in most vocational education institutions is 3–4 years, and most applicants are between 15–16 years old. All previous comments regarding the incomplete coverage of these age cohorts by this type of education and the presence of a particular (but insignificant) number of people who do not belong to these cohorts remain valid in this case. The reform of general secondary education will have little impact on the age composition of this essential subgroup, as the term of study will be extended by extending the term of acquiring general education of the III degrees from two to three years. That is, the age composition of applicants to vocational education institutions, which mainly consists of graduates of secondary schools of the II degree, will not change significantly, even after the final transition to the 12-year education system in secondary school. As an analogy with Formula (2), we can write:

$$E_3=h\times \sum _{i=15}^{18}{x}_i,$$

(4)

where E₃ is the average annual number of vocational and technical educational institutions students, and x_i (i = 15, …, 18) is the average annual population’s ith age cohort. The coefficient h is equal to the ratio of E₃ to ${\sum }_{i=15}^{18}{x}_i$ and is determined for the base period years, based on statistical data. As in the previous case, considering the presence of a small number of individuals over 18 years old among the students of vocational and technical institutions, this value can be considered a sufficiently close lower estimate of the level of coverage of young people aged 15–18 by vocational and technical education.

The following values are also determined:

$$\alpha (t)=\frac{A\left(t\right)}{x_{15}\left(t\right)+x_{16}\left(t\right)}$$

(5)

$$\beta (t)=\frac{B\left(t\right)}{\left(A\right(t-3)+A(t-4\left)\right)/2},$$

(6)

where t is the year, A is the number of students admitted, and B is the number of trained specialists.

These values represent the percentage of young people aged 15–16 who enter vocational and technical education institutions and an approximate estimate of the percentage of students who enter and graduate from such institutions. For the forecast period, the values of a and b are fixed at the level of the last year of the base period (inertial forecast scenario) or are determined as an established trend of the base period (alternative scenario).

For year t of the forecast period, the population of the base subgroup is determined by the following recursive formula:

$$E_3(t)=E_3(t-1)+A(t)-B(t)=E_3(t-1)+A(t)-\frac{\beta \left(t\right)}{2}\times (A(t-3)+A(t-4))$$

(7)

where:

$$A\left(t\right)=\alpha \left(t\right)\ast \left(x_{15}\right(t)+x_{16}(t\left)\right)$$

(8)

Thus, the number of students in vocational and technical institutions is calculated as the previous year’s number of students, plus the number of students admitted and minus the number of trained specialists. The calculation is carried out sequentially, starting from the first year of the forecast period.

3.5. The Cohort Method for Higher Education Expenditures Forecasting

The subgroup of higher-education recipients—university students—predominantly comprises young people aged 17–22. Representatives of this age group make up most of the students in full-time education. Among the students in part-time education, the proportion of individuals over 22 is significantly higher. However, not all representatives of the corresponding age cohorts are university students. Therefore, in this case, we can see a complex relationship between the number of members in the primary subgroup and the number of individual age cohorts. However, despite the fact that as in previous cases, a particular age group (17–22 years old) can be identified, changes in the number of members will have a decisive impact on the number of the primary subgroup.

At the same time, it should be noted that the reform of secondary education in terms of transitioning to a 12-year system of education in secondary schools will directly impact the number of basic subgroups in 2013 and in subsequent years. We assumed that the average term of study at universities is five years (the standard terms necessary to obtain a bachelor’s and master’s degree). Therefore, the “gap” in the number of the basic subgroups that would arise due to the mentioned reduction in the number of admitted students in 2013 would disappear only in 2018 (

Table 1. The value I for the formula E₄.

	Until 2012 Inclusive	2013–2017 (Transition)	2018 and Subsequent Years
I =	{17, 18, 19, 20, 21, 22}	{18, 19, 20, 21, 22}	{18, 19, 20, 21, 22, 23}

).

It should also be added that a particular (quite significant) percentage of students at universities of private ownership are not funded by state or local budgets.

Thus, in general, the dependence of the size of the primary group on the size of age cohorts can be represented by the following formula:

$$E_4=R\times {E_4}^{\prime }=R\times r\times \sum _{i\in I}{x}_i,$$

(9)

where E₄ is the average annual number of university students studying in state and municipal institutions of higher education, $E_4{}^{\prime }$ is the total average annual number of university students, R is the share of students studying at state and municipal universities as part of the total number of university students, and r is the relationship of $E_4{}^{\prime }$ with the number in the base subgroup, which is determined for the years of the base period based on statistical data and can be interpreted as the level of coverage of young people in the corresponding age group in terms of higher education. At the same time, in the right-hand part of the formula, the summation is carried out by the set of indices for I, which varies depending on the period.

The values of the variables E₄ and $E4{}^{\prime }$, as well as the size of the base subgroup for the base period, are determined based on statistical data. The results are then used to calculate the coefficient R and r values. Additionally, based on statistical data for the base period, the values of the following variables are calculated:

$$\gamma (t)=\frac{A\left(t\right)}{x_N\left(t\right)},$$

(10)

$$\eta (t)=\frac{B\left(t\right)}{E_4{}^{\prime }(t-1)},$$

(11)

where t is the year, x_N is the N-th age cohort (N is equal to 17 for the period up to and including 2012, and 18 for 2013 and subsequent years), A is the number of students enrolled, and B is the number of graduates. These values represent the proportion of young people aged N who enter higher education institutions (of all forms of ownership) and the ratio of the number of graduates from higher education institutions to the average annual number of students in the previous year. In the forecast period, the values of γ and η are fixed at the level of the last year of the base period or are determined as a continuation of the trend that emerged in the base period, depending on the assumptions of the forecast.

For the forecast period, the value of $E4{}^{\prime }$ (the total number of students in universities of all forms of ownership) is calculated according to the following recurring formula:

$$E_4{}^{\prime }\left(t\right)=E_4{}^{\prime }(t-1)+A\left(t\right)-B\left(t\right)=(1-\eta (t\left)\right)\times E_4{}^{\prime }(t-1)+\gamma \left(t\right)\times x_N\left(t\right).$$

(12)

The calculation is carried out sequentially, starting from the first year of the forecast period. Finally, for each year of the forecast period, the average annual population of the base group E₄ is determined using the formula:

$$E_4=R\times E_4{}^{\prime },$$

(13)

where the value of the coefficient R is fixed at the level of the last year of the base period or is determined as a continuation of the trend that developed in the base period, depending on the forecast assumptions.

3.6. Education Expenditure Forecasting Using the Cohort Method

In the next step, using the data on the size of the basic subgroups E_i (i = 1, 2, 3, 4) in the base period and the data for the base period on expenditures of the consolidated budget of Ukraine on education according to the functional classification for each of the four main types of education (

Table 2. The summary calculation of E_i (i = 1, 2, 3, 4).

	Preschool Education	Secondary Education	Vocational Education	Higher Education
Ei	$E_1=g\times \left({\displaystyle \sum _{i=1}^5}{x}_i+(1-z)\times x_6\right),$	$E_2=f\times {\displaystyle \sum _{i=6}^{17}}{x}_i,$	$E_3=h\times {\displaystyle \sum _{i=15}^{18}}{x}_i,$	$E_4=R\times E_4{}^{\prime }=R\times r\times {\displaystyle \sum _{i\in I}}{x}_i,$

), expenditures per member of the basic subgroup are calculated:

$$v_i=V_i/E_i,$$

(14)

where V_i is the government spending on a specific type of education. The set of values for v_i in forecasting education expenditures plays the same role as the values for e_j in forecasting healthcare expenditures. Assumptions about their dynamics during the forecasting period completely determine the forecast scenario. In particular, the assumption of the constant value of v_i leads to an inertial forecast scenario, which allows for estimating the “pure” effect of changes in the age structure of the population on government spending on education. A realistic scenario should assume variability in the values of v_i over the forecasting period due to (a) inflation and (b) real growth/a reduction in education spending for each person on whom it is spent.

Inflation assumptions are based on external forecasts of macroeconomic indicators. Assumptions about fundamental changes in per capita spending on education are based on an analysis of the values of this indicator over a fundamental period, considering the medium- to long-term goals of the national education policy. After determining the forecast scenario, i.e., the dynamics of the values of v_i during the forecasting period, it becomes possible to calculate expenditures for the four main types of education for each year of the forecasting period, which is performed using the formula:

$$V{}^{\prime }={\sum }_{i=1}^4{v}_i\times E_i.$$

(15)

Estimating expenditures for other types of education is based on statistical data on the total amount of expenditure on education and expenditures on the four main types of education. The share of expenditures on other types of education in total government expenditures on education is determined for the base period years:

$$\varphi \left(t\right)=V_o\left(t\right)/V\left(t\right).$$

(16)

Depending on the forecast scenario, the value of the quantity φ for the forecast period is fixed at the level of the last year of the base period or its average value for the primary years.

Finally, the total volume of state expenditures on education for the years of the forecast period is determined by the formula:

$$V\left(t\right)=V{}^{\prime }\left(t\right)/(1-\varphi ).$$

(17)

4. Results

The practical application of the described method requires sufficiently detailed projections of demographic development indicators. These should contain information about the number of age cohorts within the forecast period. In addition, forecast data (or well-founded assumptions) on the key indicators of national socio-economic development, such as GDP growth rates, are necessary to correctly formulate forecast scenarios that differ from the inertial scenarios. In addition, to obtain a forecast of budget indicators in nominal terms, it is necessary to have inflation rate forecasts for the entire forecast period as input information. The study used long-term demographic forecast data as input information for demographic forecasts, while official macroeconomic forecast data was used as input information regarding accurate GDP growth rates. The State Statistics Service of Ukraine (providing data on education penetration within all types of primary groups, level of coverage, and number of recipients by each type of education), the National Bank of Ukraine (providing data and forecasts for inflation and GDP), and the Ministry of Finance of Ukraine (providing information on budget expenditures) were the sources of factual data for the base period years.

To determine the dynamics of real growth in expenditures from the long-term perspective, further calculations of indicators that are expressed in monetary units were carried out with constant prices from 2019. For this purpose, data on the nominal volumes of government expenditures were adjusted using a chain index deflator, based on data on the GDP deflator according to the State Statistics Service of Ukraine, to the volumes of corresponding expenditures at fixed prices. At the same time, we calculated the value of the variable v_i, which is equal to the number of annual expenditures per member of the base subgroup.

According to the described methodology, education expenditures are divided into five components:

• Expenditures on preschool education;
• Expenditures on general secondary education;
• Expenditures on vocational education;
• Expenditures on higher education;
• Expenditures on other types of education.

The forecasting was carried out based on the number of basic subgroups covering the four main types of education. In turn, the number of basic subgroups was calculated based on demographic forecast data regarding the number of age cohorts, the levels of coverage of specific age groups of the population in different types of education, or the inclusion of the representatives of specific cohorts in a particular type of education. Expenditures on other types of education were forecasted based on the assumption that they constitute a constant share of the structure of general state expenditures on education. All additional assumptions were based on the results from analyzing historical data.

4.1. Preschool Education

Changes in the number of children attending preschool institutions are determined mainly by the dynamics of the groups of children who comprise the main contingent of such institutions (children aged 1 to 6 years, except for schoolchildren aged six years). However, the level of coverage of children by preschool institutions is also an essential factor. Since 2001, there has been a stable increase in the level of attendance at preschool institutions by children. In recent years, the growth rate has averaged 2% per year, but there has been a slowing down of this growth, and in 2020–2021, the coverage level reached 60–63% (Figure 1). Such dynamics of growth were mainly due to the process of urbanization since a much higher level of attendance at preschool institutions is more typical for urban settlements than in rural areas.

The dynamics of the coefficient g in Formula (1), which is necessary to calculate the size of the primary subgroup, should be determined based on the analysis of this data and considering the gradual increase in the share of the urban population in the population structure of Ukraine (according to the long-term demographic forecast). We assumed that the trend of the coverage level of preschool children with preschool institutions would continue, gradually slowing down. Therefore, the value was assumed to reach 63% by 2025.

The value of another coefficient, which appears in Formula (1), z, equals the share of children in school among all children aged 6 (Figure 2). Since, in this case, there has been unstable behavior by the indicator during the last years of the base period, the value for the forecast period was fixed at the level of the average for 2018–2021, namely, z = 0.624.

Based on the assumptions and results of the long-term demographic forecast, Formula (1) was used to calculate the number of children who would attend preschool institutions during the forecast period. In addition, the forecast for migration levels caused by Russian aggression in Ukraine (~30% of the population, according to UN data) was also considered. The results of these calculations are presented in Table 2 and illustrated in Figure 3. However, regarding the impact of migration, the children of Ukrainian emigrants currently residing in Poland, the Czech Republic, and Germany require additional government spending for organizing their education in preschool institutions.

4.2. General Secondary Education

Considering the consequences of the reform of general secondary education in terms of transitioning to a 12-year education system, the number of students in general education institutions was calculated (depending on the period) using Formulas (2) and (3). This depends mainly on the number of age cohorts that form the group of school-age individuals and this group’s coverage level with general secondary education, which corresponds to the coefficient f in Formula (2).

Analysis of the historical data shows that the level of coverage of school-age children with general secondary education has remained practically unchanged during the last years of the base period, with a minimal tendency to decrease (Figure 4). Therefore, in our forecast, we assumed that in the future, the coefficient f would remain at the level of 77–78%.

It should be noted that some students receive secondary education in private general education institutions. Their share in the total number of schoolchildren is not significant and is less than 3%.

Based on the assumptions made, the number of primary subgroups was calculated using Formulas (2) and (3), based on long-term demographic forecasts regarding the number of age cohorts and considering the impact of migration. Given that the educational process is actively developing using distance learning technologies, students who left the country after the start of the war continue their studies in Ukrainian schools. As a result, the impact of migration on general secondary education will be minimal. The results of these calculations are presented in Table 2 and are illustrated in Figure 5, which indicates a further trend toward an increase in the number of students in general secondary education institutions.

4.3. Vocational Education

The level of coverage of vocational education (coefficient h in Formula (4)) for young people aged 15–18 (the main contingent of vocational institutions) was, on average, 12–14% in the period from 2018 (Figure 6). This level began to gradually decrease due to the increasing demand for workers with higher education and the rapid increase in the number of higher educational institutions, which made higher education more accessible.

We assumed that the demand for workers in technical professions would remain in the labor market in the coming years, so the α indicator would continue the current trends and remain at 12–13%. Further growth is unlikely since, as we will see later, higher education will become increasingly accessible (due to the decrease in the number of age groups of the population that make up the bulk of university applicants, with many universities and available places in them).

We also assumed that the average duration of training in vocational and technical schools would remain unchanged throughout the forecast period and would be equal to the average duration of training in the last years of the base period. From this assumption, the value of β, the ratio of specialists trained in year t to the average number of students enrolled in years t-3 and t-4 would remain unchanged throughout the forecast period. Based on the data analysis presented in Figure 7, we fixed the value of β for the forecast period at 76%.

The assumptions and forecasted data regarding the size of age cohorts in the forecast period allowed us to use Formulas (4), (7), and (8) to calculate the average annual number of students in vocational education institutions during the forecast period. Migration is almost identical to its impact on general education: students are more likely to continue their education in a distance learning mode. The results of these calculations are given in Table 2 and presented in Figure 8.

4.4. Higher Education

Over the past few years, the number of young people attending higher education institutions has been rapidly increasing due to several factors: an increase in the demand for specialists with higher education qualifications in the labor market, an increase in the income of the population, and, accordingly, the possibility of obtaining higher education on a fee-paying basis, as well as an increase in the number of educational institutions while simultaneously increasing the number of places in such institutions. However, over the past two years, there has been a decrease of 47–50%. We assume that in the future, the influence of some of these factors will strengthen while others will weaken. In particular, an increase in the population’s income and a decrease in the number of young age groups (with many places available in higher educational institutions) will make higher education more accessible. However, an increase in the supply of specialists with higher education in the labor market will decrease their comparative “value” and, thus, decrease the interest of young people in obtaining higher education. As a result, the level of young people with higher education will stabilize at around 45–50% (Figure 9).

The conditional coverage level presented in Figure 9 is calculated as the ratio of the number of students to the average number of individuals aged 17–22 years and corresponds to the value r in Formula (9). As mentioned, due to the presence of individuals over the age of 22 among the students of higher education institutions and depending on their relative weight, the actual coverage level of the group of students aged 17–22 by higher education will be slightly lower than the simple ratio of the number of students to the population of this group.

At the same time, it should be noted that over the past decade, the share of students studying in private higher education institutions has been constantly increasing. We assume that this process will continue but will gradually slow down due to a decrease in the number of potential applicants every year and, thus, an increase in the possibility of young people obtaining more accessible higher education in state-funded educational institutions. From 2013, according to our assumption, the distribution of students between state/municipal and private higher education institutions would remain unchanged until the end of the forecast period. At the same time, the share of students studying in state and municipal higher education institutions (corresponding to the coefficient R in Formulas (9) and (13)) was fixed by us at the level of 93%.

The study of the dynamics of the ratio of the number of students enrolled in higher education institutions (HEIs) according to the size of the x18 age cohort (i.e., the γ coefficient in Formulas (10) and (12)) during the forecast period shows that this value gradually increased until 2018 and then decreased from 2019 to 2022 to an average level of 77% (Figure 10). It should be noted that interpreting this fact as meaning that 77% of 17-year-olds enroll in HEIs would be incorrect since although such individuals make up most HEI applicants, there is a specific and significant percentage of applicants who belong to other age cohorts. Instead, the reference to this cohort is explained by the fact that it determines the dynamics of the number of applicants. For the forecast period, we fixed the value of the γ coefficient at 77%.

The value of another critical variable-η from Formulas (11) and (12), which is directly related to the average duration of study in higher education institutions, also demonstrates stable behavior in recent years of the base period (Figure 11). Taking this into account, for the forecast period, we assumed that η is equal to 25%, or equivalently, that the average duration of study in higher education institutions would be four years.

Based on the assumptions described, the average annual number of students who would receive higher education in state higher educational institutions was calculated using Formulas (9), (12), and (13) (Figure 12).

4.5. Budget Expenditures on Education Forecasting

Migration and the more active admission of applicants to European universities, especially of those citizens who left to go abroad after the full-scale invasion of Russia, were considered. The results of these and other calculations mentioned above are presented in

Table 3. The average annual number of individuals receiving education of one of the main types in state or communal educational institutions.

Year	Total by Main Types of Education	Preschool Education	General Secondary Education	Vocational and Technical Education	Higher Education
2018	7,097,080	1,278,237	4,041,652	254,991	1,522,200
2019	7,054,339	1,230,398	4,138,466	245,775	1,439,700
2020	6,750,909	1,150,545	4,211,509	246,855	1,142,000
2021	6,639,052	1,111,358	4,230,358	250,336	1,047,000
2022	6,309,119	825,567	4,202,376	268,176	1,013,000
2023	6,451,566	800,347	4,284,537	275,689	1,090,994
2024	6,407,292	751,314	4,314,493	283,448	1,058,037
2025	6,426,800	705,441	4,403,282	291,463	1,026,614

Source: authors’ calculations, based on data from the State Statistics Service of Ukraine, the United Nations, the National Bank of Ukraine, and the Ministry of Finance.

. The table summarizes the actual data and our forecast estimates of the number of individuals who have received or will receive education of four main types.

According to the methodology described, the next step is a retrospective analysis of data to determine the volume of state expenditures on education per person who received an education. To achieve this, we used historical data regarding the number of people who received education in one of the main types of state-funded institutions from 2018 to 2021 and data on education funding according to its types (budget expenditures on education financing, including loans) at fixed prices in 2019. The planned indicators for 2022–2025 are taken as the average value for 2020–2021 (the period of distance learning). The results of the calculations carried out using Formula (14) are presented in

Table 4. Actual and projected expenses for education per person (in 2019 prices), per thousand UAH.

Year	Total by Main Types of Education	Preschool Education	General Secondary Education	Vocational and Technical Education	Higher Education
2018	28.6	26.9	27.2	42.5	31.5
2019	30.3	29.3	27.9	44.0	35.7
2020	31.3	33.0	26.4	42.3	45.5
2021	30.3	31.7	25.7	41.1	44.9
2022–2025	30.8	32.3	26.0	41.7	45.2

Source: authors’ calculations, based on data from the State Statistics Service of Ukraine, the United Nations, the National Bank of Ukraine, and the Ministry of Finance.

.

The final important step in creating the forecast scenario is to determine assumptions regarding the dynamics of education spending per person by significant types of education and the share of expenditures on other types of education in the structure of total education spending. Historical data analysis shows that the share of expenditures on other types of education averaged 11% over the period from 2018 to 2021. We fixed the value of the coefficient φ from Formula (17) at this level for the forecast period.

The growth rates of government spending on education per person (overall and by significant types) are fairly low, which allowed us to use the average indicators for 2020–2021 for short-term forecasting when distance learning showed the most significant development. Analysis shows that the actual growth rates in education spending for each significant type per person strongly correlate with the actual growth rates in total spending on significant types of education per person. Therefore, in the future, we assume that the rates of real growth in education spending per person for all major types of education will be determined by the trend of real growth in total spending on significant types of education per person, which was determined based on historical data and medium-term forecasts of budget indicators. In this case, we ignore a sharp reduction in education funding and the redirection of budget expenditures to defense.

Thus, we have identified the basis of the forecast scenario for education spending-the actual growth rates of education spending per person by the four major types. Considering historical data, we can now determine the spending volume on major education types per person. Furthermore, using data on the number of people who will receive education in the major types of institutions financed from state and local budgets and considering the share of expenditures on other types of education, we found the forecasted volumes of education spending (overall and by type) using Formulas (15) and (17).

The results of these calculations are presented in

Table 5. Forecast of expenditure of the consolidated budget for education financing using 2019 prices in million UAH.

Year	Expenditure on Education	Preschool Education	General Secondary Education	Vocational and Technical Education	Higher Education	Other Types
2018	227,330	34,407	110,077	10,829	47,893	24,124
2019	241,588	36,045	115,277	10,816	51,358	28,093
2020	236,754	37,920	111,015	10,441	51,919	25,459
2021	226,857	35,190	108,785	10,280	47,010	25,592
2022	218,314	26,675	109,420	11,178	45,769	25,272
2023	224,070	25,860	111,559	11,491	49,293	25,867
2024	221,772	24,276	112,339	11,814	47,804	25,539
2025	221,406	22,793	114,651	12,148	46,384	25,429

Source: authors’ calculations, based on data from the State Statistics Service of Ukraine, the United Nations, the National Bank of Ukraine, and the Ministry of Finance.

(in the constant prices of 2019) and

Table 6. Expenditures of the consolidated budget for financing education, as a percentage of GDP.

Year	Expenditure on Education	Preschool Education	General Secondary Education	Vocational and Technical Education	Higher Education	Other Types
2018	5.9%	0.9%	2.9%	0.3%	1.2%	0.6%
2019	6.1%	0.9%	2.9%	0.3%	1.3%	0.7%
2020	6.2%	1.0%	2.9%	0.3%	1.4%	0.7%
2021	5.7%	0.9%	2.7%	0.3%	1.2%	0.6%
2022	5.1%	0.8%	2.4%	0.2%	1.0%	0.6%
2023	3.9%	0.6%	1.9%	0.2%	0.8%	0.4%
2024	3.3%	0.5%	1.6%	0.2%	0.7%	0.4%
2025	2.8%	0.4%	1.4%	0.1%	0.6%	0.3%

Source: authors’ calculations, based on data from the State Statistics Service of Ukraine, the United Nations, the National Bank of Ukraine, and the Ministry of Finance.

(as a percentage of GDP) without considering the sharp reduction in expenditure of the consolidated budget due to military actions. Considering the change in priorities during a state of war, actual budget expenditures for education were reduced by 23% in 2022, and a reduction of as much as 96% is planned for 2023.

5. Discussion and Conclusions

This paper presents an efficient methodology for analyzing and forecasting the main types of education expenditures. The main conclusions about each type of education level are presented below.

Under the influence of urbanization processes, the coverage of children in preschool educational institutions is increasing, requiring increased maintenance expenses. However, in 2022, some mothers with small children went abroad due to the outbreak of war. Therefore, in the context of the impact of migration, Ukrainian emigrants currently residing in Poland, the Czech Republic, and Germany require additional government spending regarding organizing their children’s education in preschool institutions.

The level of coverage of school-age children regarding general secondary education remained practically unchanged during the last years of the base period, with a minimal tendency to decrease. Given that the educational process is actively developing using distance learning technologies, students who left the country after the start of the war continue their studies in Ukrainian schools. As a result, the impact of migration on general secondary education will be minimal.

The level of coverage of vocational education began to gradually decrease due to the increasing demand for workers with higher education and the rapid increase in the number of higher educational institutions, which made higher education more accessible. However, we assume that the demand for workers in technical professions will increase in the labor market in the coming years. Migration is almost identical to its impact on general education: students are more likely to continue their education in a distance learning mode.

An increase in the population’s income and a decrease in the number of young age groups (with many places available in higher educational institutions) will make higher education more accessible. However, an increase in the supply of specialists with higher education in the labor market will decrease their comparative “value” and, thus, the interest of young people in obtaining higher education. As a result, the level of young people with higher education will stabilize at around 45–50%. Migration will increase the drop in university student numbers due to the relocation of Ukrainian young people to European countries.

The Russian–Ukrainian war strongly influences each area of Ukraine’s socioeconomic development, and education is no exception. Since 2020, after the start of COVID-19, there have been numerous new disruptive factors regarding the level of education penetration [31] and switching to Education 4.0 [32], but after the war started, many Ukrainians have gone abroad, which has a strong negative impact on each level of the education system. There is a necessity to change the budget expenditure forecasting process, taking into account all migration processes.

The above results and analysis allow us to draw the following conclusions, which prove our hypothesis:

• The cohort method is an effective tool for forecasting budget expenditures in the short and medium term, considering all potential changes in the demographic indicators of the population. Such a method is recommended for implementation in governmental structures to plan the necessary volumes of education budgets.
• During the forecast period, the volume of state expenditures on education will be determined by demographic factors, but the impact of war and migration on the population significantly contributes to budget expenditures. Migration has the most significant impact on education expenditures, followed by higher education, and the impact on general secondary and vocational education is minimal. However, it is essential to note that migration, one of the largest seen in 21st-century Europe, leads to Ukrainians immigrating to a wide range of European countries, exerting significant pressure on the budget expenditures of these countries. Research on the impact of migration in European countries is a direction for future research.
• Due to changes in the population’s age structure and the depopulation process, the total number of people receiving education in one of the four main types of institutions funded by state and local budgets will gradually decrease during the forecast period, except for secondary and vocational education.
• Assuming that the existing trend of expenditures on education per person remains unchanged, the overall volume of state expenditures will gradually decrease in absolute terms and as a percentage of GDP. Considering the change in priorities during a state of war, actual budget expenditures for education were reduced by 23% in 2022, and a reduction of as much as 96% is planned for 2023. Improving educational processes and the quality of budget spending should become an area for state regulation, as improving the quality of education in conditions resulting in funding cuts is an urgent problem for the educational community.

Overcoming the limitations of current research, which is related to uncovering the issues about budget expenditures forecasting in conditions of growth regarding internal migration, as well as the increased share of online education, is an area of future research.