Human Capital Dynamics Are the Key to Economic Growth: Source of Value of the Future

Abstract

Sustainable economic growth is possible not only with physical investments but also with strong human capital that enables the training of qualified, productive, and innovative individuals. The relationship between the number of university students (doctorate, master’s, and undergraduate) in higher education was selected as a proxy for human capital, and economic growth was estimated using vector autoregressive analysis with four models for the periods 1982Q1–2021Q4. In addition, the effect of gender was examined for all levels of education. While economic growth has a stable effect at the doctoral level, it positively affects master’s and undergraduate students. A one-unit shock in economic growth does not affect gender at doctoral, master’s, and undergraduate education levels. It was determined that the master’s degree explained the economic growth variable more than other education levels. It is seen that female students explain more at the doctoral level of education, and male students at the master’s and undergraduate levels of education. In sustainable economic growth and development, it is much more important and valuable to strengthen graduate education qualitatively and increase knowledge production capacity rather than simply increasing it. Education policies should focus on strengthening education, which is the building block of human capital that contributes to economic growth and social welfare.

1. Introduction

Human capital is one of the most critical elements that form the basis of economic and social structures. The construction of this capital is possible only through education. In the formation of human capital, education not only increases the knowledge and skills of individuals but also stands out as a fundamental element that improves the quality of human resources and fosters productivity, economic growth, and social welfare. It is indisputable that the return on education has strategic importance in terms of micro (such as profit, wages, and entrepreneurship) and macro (such as economic growth, development, increase in productivity, technological development, and international competitiveness). Besides the individual benefit of education, its social benefit is also much more remarkable.

Although human capital is important on a global scale, the Turkish economy’s ability to achieve sustainable growth targets depends on the development of qualified human capital. While a young and dynamic population structure offers significant potential for the country, this potential can only be transformed into economic value through an effective education system. Investments, especially at the graduate level, support Türkiye’s transition to a knowledge-based economic model and increase innovation, productivity, and competitiveness. Therefore, policies aimed at improving the quality of human capital affect not only individual welfare but also sustainable economic growth and development.

Education enables companies to increase their profitability and strengthen their competitiveness by increasing the quality of the workforce, contributing to technological progress and added value creation capacity, and increasing productivity. These effects play an essential role in increasing countries’ sustainable economic growth and development potential. For these reasons, expenditure on education is a substantial investment for long-run economic success and social welfare. Education contributes to the progress of society by encouraging the development of knowledge and technology and spreading it more widely, thus ensuring the development and democratization of society, ensuring equitable income distribution, reducing poverty, and increasing the quality of life.

Education investments have different effects on people, the economy, and society. Educational investments have important characteristics. Education investments are permanent investments. Education that helps people acquire knowledge and develop their skills, and therefore educational investments, is a continuous investment for the long-run development of individuals and society. These investments positively affect many areas, such as sustainable economic growth and development.

Education investments are indivisible. Education investments should be sustained throughout life and constantly renewed because, with the changing and developing world and technology, the learning process is essential to ensure that knowledge and skills remain current and competitive.

Education is both a consumption good and a factor of production. Education can be considered a consumer good because it is a tool that helps individuals improve their knowledge and skills. Education is a factor of production because it helps people develop their abilities, acquire knowledge and skills, and increase the workforce’s productivity by encouraging innovation and technological progress, supporting economic growth and development. However, expenditures on education have both consumption and investment features. Since all expenditures made during the education process do not yield any returns in the short-run, consumption expenditure is an important investment tool because it positively affects individual earnings and national income in the long run (Savaş, 1986). In addition to individual and social benefits, education investments will also positively affect other investments. Education investments are a complement, not a substitute, for other human capital investments such as health and nutrition.

To produce a certain amount of output to increase the amount of production and, therefore, the national income, inputs such as physical capital, labor force, natural resources, human capital, different production factors, and different technological methods are used by entrepreneurs (Kibritçioğlu, 1998). The input used in the production process and the importance given to each input, as well as the usage rates of inputs, vary from country to country. These differences determine the economic growth and development of countries.

Education is an important tool for increasing the quality of human resources, but it is not the main driving force of economic growth. The development of qualified, productive, and innovative individuals supports not only individual development but also social welfare. The quality, content, and accessibility of education are of great importance in the development of human capital. Postgraduate education, in particular, contributes to structural transformation in the economy by increasing individuals’ capacity to produce information, use technology, and make decisions. Educational policies should also be developed and implemented in this direction.

The main purpose of the study is to examine the impact of human capital on economic growth. In this respect, it is aimed to estimate the relationship between economic growth and human capital by taking the number of university students (postgraduate students (PhD), master’s, and undergraduate) in human capital size. In addition, another objective of the study is to examine the effect of gender in this relationship for all education levels.

Although there are many studies in the literature on human capital, this study details three different levels of graduate education and gender-based distinctions. In addition, Vector Autoregression (VAR) analysis was applied to reveal the causal relationships and dynamic interactions over time, and the study aimed to contribute to the literature.

This study is comprised of six sections. Following the introduction, the concept of human capital, its importance, and its basic characteristics are discussed in the Section 2. The Section 3 includes a literature review of the subject, and the Section 4 presents the methodological framework used in the study. The Section 5 evaluates the econometric estimation results, and the sixth and final sections include the conclusions.

2. The Concept of Human Capital, Its Importance and Features

Capital is one of the factors of production; It covers the total of machines, tools and equipment, raw materials, facilities, and other durable production factors. Additions to the physical capital stock within a certain period are defined as investments. Human capital is the whole of the knowledge, skills, and experiences contained by the workforce (Kibritçioğlu, 1998).

According to the OECD, human capital is an individual’s knowledge, skills, and other features regarding economic activities. Human capital is all the qualities that shape an individual’s ability and productivity to contribute economically, socially, and culturally. According to Frank and Bernanke, human capital, education, training, intelligence, energy, experience, work habits, and reliability are a whole of factors that affect the marginal product value. If a broader definition is given, the concept of human capital refers to all concepts such as individuals’ knowledge, skills, education level, health status, abilities, and place in society (Kar & Ağır, 2006). In a sense, human capital is the whole of the characteristics that an individual has.

Positive qualities such as knowledge, skills, experience, and dynamism possessed by the individual participating in production, characteristics that generally reflect the quality of the human being and create economic value, constitute human capital. Human capital is formed through processes such as education, health, skill development, and gaining experience so that individuals can develop these characteristics and contribute to the workforce. It is a process that increases individuals’ ability to realize their potential and economic value. Human capital contributes greatly to the economic success of both individuals and societies.

Considering that individuals are constantly changing in terms of quality and quantity, there is a risk of wasting this resource whenever human capital, like physical capital, is not a fixed and storable resource and is not used continuously. In addition, human capital is an active player that decides on its working conditions and where and how to work. It differs from physical capital in these aspects. Despite these differences, these two types of capital complement each other in the production process. It is clear that it is almost impossible to produce using only physical capital or only human capital. Depending on the production technology, human capital and physical capital come together at different rates (Eser & Gökmen, 2009). When qualified human capital is insufficient, other policies aimed at increasing technological innovation activities (increasing R&D expenditures, university-industry cooperation, etc.) will not be effective; however, physical investments and therefore physical capital will not be used efficiently and effectively.

It is clear that knowledge and skills can also be provided through education. These attributes are of great importance for economic productivity and innovation. The quality of human capital and the qualifications of the individuals who make up this capital are critical factors determining a country’s or organization’s sustainable growth. In this context, elements such as education, professional development, health services, and labor market efficiency are fundamental components that shape the quality and capabilities of human capital. It is necessary for human capital to be sufficient, qualified, and diverse to support economic growth, increase competitiveness, and promote social development.

Human capital indicators generally focus on education data because the most common way for individuals to increase their knowledge and skills is through education. Human capital basically consists of education and health indicators. Human capital can be divided into two main categories: stock and investment indicators (

Table A1. Summary of literature studies.

Author(s)	Years	Countries	Human Capital Indicators	Methods Used	Obtained Results
Barro (1991)	1960–1985	98 countries	School records	Regression analysis	The increase in KGDP increases human capital.
Barro (1996)	1965–1995	100 countries	Higher education schooling rate	Horizontal section analysis	He found that growth rate showed a strong connection with education and life expectancies. Countries with a high concentration of individuals participating in long-run education have great potential for accelerating economic growth. At the same time, it is concluded that physical capital positively affects economic growth and birth rate negatively affects human capital accumulation. The increase in the real value of KGDP has a positive relationship with initial human capital. However, a negative relationship is observed between the initial value of KGDP and human capital.
Romer (1990)	1960–1985	112 countries	Education, KGDP	Least squares method	It has been stated that regardless of technological development, the return on physical capital accumulation decreases. Considering the entire sample, it can be seen that investments are determined by human capital and openness in 90 countries, and by the number of scientists and engineers in 22 countries, among the factors affecting technological development.
Denison (1962)	1929–1957	US	Education, economic growth	Regression analysis	It was concluded that while 0.92% of the total growth rate of 2.93% resulted from labor and capital, most of the remaining 2% was achieved through education.
Denison (1962)	1910–1960	US	Education, physical capital, economic growth	Regression analysis	Emphasizing that the increases in GNP are not only due to increases in physical capital and labor force, Barro stated that the reason behind this increase is the residual factor. Factors affecting this surplus factor include technological development and economies of scale, and a significant part of the developments in the workforce stem from the increase in education. According to Barro, 23% of the increase in GNP is due to the increase in the education level of the workforce.
Mankiw et al. (1992)	1960–1985	98 countries	Physical capital investments, number of students enrolled in secondary school and national income per capita	Regression analysis	They concluded that the results obtained by country groups were statistically significant and that the Neoclassical economic model was valid in this context.
Kar and Ağır (2006)	1926–1994	Türkiye	Health and education expenditures	Causality test	The causal relationship between economic growth and human capital is sensitive to the chosen human capital measure and may vary.

).

3. Literature Review

Economists’ views on human capital are included in this section. In addition, empirical studies on human capital, especially studies using time series methods, are summarized in the appendix in tabular form so as not to take up too much space.

Although classical growth theories argue that physical capital accumulation and population growth are effective on economic growth, Smith, Mill, and Marshal are considered the first economists to mention the concept of human capital. However, they are different from the recently mentioned human theories. Classical economists argued that physical capital is more important for economic growth. Although Alfred Marshall considered the human capital conceptually in his economic thought, he did not include human capital as a production factor in his analysis. Marshall emphasized that the concept of capital is not suitable for humans and cannot be applied to humans, but that the quality of people should be increased through factors such as education, and that such investments are more valuable than other capital investments (Schultz, 1961). Mill argues that welfare is for people; He stated that people should not be seen as a source of welfare.

Three basic growth models have gained importance since the second half of the 20th century in terms of economic growth theories, Harrod-Domar, Solow (Harrod, 1939; Domar, 1946) (Neoclassical model, Becker, Schultz, Denison, and Mankiw-Romer-Weil) (Solow, 1956; Becker, 1993; Schultz, 1968; Denison, 1962; Mankiw et al., 1992) and endogenous growth models (Lucas and Barro). These plans offer different theories and policy recommendations for the development of economic growth (Lucas, 1988, 1990; Barro, 1991).

Many economists (such as Schultz, Becker, Mincer, Lucas, Barro, and Romer) define the concept of human capital, develop it, and prove its validity through practice. Theodore Schultz, one of the first to define the concept of human capital, explained how investments in human resources such as education, health, and skills contribute to economic growth and development (Schultz, 1971). Schultz’s theory of human capital explained the difference between traditional capital (machinery, equipment, etc.) and human resources. Schultz thought of schools as an education service industry and stated that expenditures on education could only be considered investments if they increased the future benefit and productivity of the individual (Schultz, 1968). Education: It is the most effective tool that, in addition to supporting economic growth, improves the quality of life of individuals, increases human capital, and contributes to a better standard of living.

Economist Gary Becker, winner of the Economics Prize, stated that people can increase their future productivity by investing in areas such as education, health, and skills. These investments allow individuals to earn higher incomes in the labor market and contribute to economic growth (Becker, 1993).

Jacob Mincer, known for his studies on education, labor market, wage theories, and human capital, examined the relationship between lifetime earnings and education. This model explains how individuals’ level of education (school education) and work experience (on-the-job training and after-school learning) affect their future earnings (Mincer, 1981).

Frederick P. Harbison is known for his research on issues such as human capital development, education, and labor productivity, especially in developing countries. Frederick Harbison argues that human capital investments are critical to economic growth and development sustainability. He noted that education, skills development, and productivity improvement are central to developing countries’ economic and social transformation (Mincer, 1981).

Charles A. Myers emphasized that investments in human resources, such as education and skill development, positively affect economic growth and development and argued that investments in these areas could increase economic productivity and increase the competitiveness of countries in the long run. According to Harbison and Myers, there are different ways of increasing human capital accumulation. First, it is formal education, which includes officially recognized education. It includes various levels of education, from primary school to university. The second is informal or on-the-job training. This type of training can be achieved by gaining experience in a person’s workplace or by participating in adult education programs. It involves employees seeking opportunities to improve their professions or acquire new skills (Frederick & Myers, 1964).

Singer (1964) emphasized two important features of educational investments. First, it is not the law of diminishing returns on education investments; On the contrary, the law of increasing returns is valid. Traditional production factors (such as labor, capital, and land) have diminishing returns and will decrease over time as they are used (Singer, 1964). While production factors may wear out as they are used, information becomes more valuable as it is used and shared. Instead of these traditional factors, endogenous growth models emphasize that knowledge is a resource with increasing returns and is the key to sustainable growth.

Additionally, when traditional factors of production are used in one activity, it is often difficult or impossible to use them in another activity simultaneously. However, information is not subject to such limitations. Information can be used and shared simultaneously across different activities, increasing value. While these features sometimes make knowledge an independent production factor, they sometimes function to prevent the diminishing returns of traditional production factors. In the endogenous growth model, increasing returns to scale are not enough; the main thing is to ensure a condition in which the marginal productivity of the factors of production that can be accumulated does not decrease.

Information may be a public good, partially or wholly. There is no competition among consumers in the use of information, and no one can be excluded from the use of information. How much the information emerging from technological developments can be used by other economic units (the degree of technological externalities or spillovers) is extremely important (Kibritçioğlu, 1998).

The endogenous growth model differs from the Neoclassical growth model in several ways. In the endogenous growth model, technological development occurs within the economic system and is affected by economic decisions, meaning technology is an endogenous variable. At another point, instead of the Neoclassical production function based on decreasing returns, the production function based on increasing returns is valid.

In the 1950s, the Solow growth model dominated; by the 1980s, it was seen that the determinants of economic growth were human capital, information, education, research and development, and technology rather than physical capital. Romer’s (1990) and Lucas’s (1988) studies are considered the beginning of research on this subject.

Prominent economists like Romer and Lucas are known for their important work on endogenous growth models. In particular, Robert Lucas focused on three essential elements of endogenous growth in his work titled “On the Mechanics of Economic Development,” published in 1988. These elements are physical capital accumulation, technological development, human capital accumulation through school, and the accumulation of specialized human capital through learning by doing (Lucas, 1990).

Lucas contributed to Solow’s growth model, emphasizing human capital as the driving force of long-run economic growth. According to the Lucas growth model, countries with substantial human capital factors will exhibit faster economic growth than countries with weak human capital factors (Lucas, 1990). This model explains that while capital and labor have decreasing marginal productivity, human capital does not have this feature. Education is considered a fundamental component of human capital and creates the phenomenon of externalities, which is one of the primary sources of increasing returns based on economies of scale.

In Lucas’s growth model, human capital affects growth and productivity in two different ways. First, internal effects relate to the skill levels of individuals and only increase the productivity of the individuals concerned. Therefore, skills acquired through education and other learning tools make individuals more productive. The second effect is known as the exogenous effect and includes externalities that arise from information sharing between individuals (Lucas, 1988). Externalities arise from the increased possibility of learning or sharing knowledge with other people as human capital develops. This increased information sharing both increases the stock of information and encourages the use of other production factors, such as capital and labor, more effectively, which leads to increased productivity and growth.

Mankiw et al.’s model addresses the contribution of human capital to economic growth, especially through education investments, and shows that changes in resource allocation in this economic growth model can significantly affect the results (Mankiw et al., 1992).

Although human capital theory was first brought to the agenda by S. R. Kuznets and M. Friedman, its theoretical foundations were firmly established thanks to the work of T. W. Schultz. Schultz’s research outlined this theory and emphasized the critical role of human capital in economic growth. Therefore, with the contributions of Schultz, human capital theory was presented with a clearer theoretical structure and introduced to economic literature (Berkman, 2008).

Barro and Lee’s (2015) global education data show that the average years of schooling increased from approximately 4.5 years to 8.3 years worldwide during the period 1950 to 2010. This increase reveals not only that the quality of the workforce has increased at the individual level, but also that the potential for economic growth through education has expanded (Barro & Lee, 2015).

Schultz gave great importance to education for human capital investments and gave importance to formal education organized by companies, including on-the-job training (informal education), including old-style apprenticeship (Schultz, 1961). Education expenditures qualify as investments. Emphasizing that education, which is accepted as an essential component of human capital, has two primary dimensions, Schultz defines the consumption dimension as the expenditures made by individuals for educational services (individuals’ acquisition of knowledge and skills, providing personal development) In the other dimension, the fact that people who receive education become more productive and their productivity increases constitute the production dimension of education that contributes to economic growth. Education: It not only provides individuals with personal development opportunities but also increases productivity, which supports economic growth. Seeing education as an investment, Schultz stated that individuals’ spending on education represents a consumption element that enhances their development and a production factor that encourages economic growth (Schultz, 1961). Education is considered a durable investment because it can increase future incomes. According to Schultz’s studies, human capital investments significantly contribute to the economy by improving the qualifications of individuals and increasing their productivity.

Education is a major determinant of economic well-being. Hanushek and Woessmann highlight at least three mechanisms by which education can affect economic growth. First, education is a factor of production that is combined with physical capital to produce GDP as a component of the workforce. The added human capital for the workforce increases total inputs and output (as in the neoclassical growth theories of Mankiw, Romer, and Weil). Second, education can increase the innovative capacity of the economy, and the development of new technologies stimulates economic growth (as in Lucas’s endogenous growth theories). Third, education can facilitate the diffusion of the knowledge needed to understand new knowledge and successfully apply new technologies, which can lead to increased economic growth (Hanushek & Kimko, 2000).

4. Econometric Analysis

4.1. Dataset and Methods

Since higher education is accepted as a level of education where the highest level of specialization of human capital is achieved, this study used the number of students graduating from higher education as a human capital indicator. Higher education was chosen among the educational levels because the duties of higher education institutions to train the workforce, conduct research, and serve society play a critical role in achieving the long-run development goals of countries. To carry out a detailed analysis, VAR analysis was estimated according to doctoral, master’s, and undergraduate degree education levels and gender. Gross domestic product per capita is compiled from the IMF, and graduate student numbers are compiled from the TÜİK database.

While the Gross Domestic Product per capita series representing economic growth is presented at a quarterly frequency, the student number data used to represent human capital are presented at an annual frequency. To avoid the loss of observations in the analyses and to obtain results compatible with high-frequency series, annual data were converted to a quarterly frequency using the interpolation method. The interpolation method is a technique widely used in the literature to eliminate similar frequency incompatibilities. In this study, pioneering studies (Chow & Lin, 1971; Denton, 1971) on the subject were used as the basis for the application of the method in question. While the Chow-Lin method offers a regression-based approach to generate high-frequency estimates of low-frequency series, the Denton method aims to provide a smooth distribution by preserving the original trend of the series. Annual data from 1982 to 2021 were converted into quarterly data using the EViews 12 program.

However, it should be noted that converting the data to a different frequency may lead to misleading results if not appropriately performed. Therefore, the necessity and importance of diagnostic tests applied after the analysis are increasing more than ever.

Additionally, a linear interpolation method was applied to eliminate the frequency mismatch of the datasets used in the study. Although this method aims to preserve analytical integrity, particularly in the conversion of annual data to quarterly intervals, it may introduce some statistical bias risks through the production of artificial data. Therefore, a cautious approach was adopted in the interpretation of the model results, considering the potential deviations that may arise from this method. The findings were evaluated within the framework of methodological limitations.

Four models estimate the VAR analysis. Model 1 consists of the variables of gross domestic product per capita (DKGDP), the total number of students with a doctoral degree (DDT), the total number of students with a master’s degree (DYT), and the total number of students with an undergraduate degree (DLT). Model 2 variables show the gross domestic product per capita (DKGDP) and the number of female (DDK) and male students (DDE) who graduated from doctoral education. Model 3 shows the gross domestic product per capita (DKGDP) and the number of female (DYK) and male students (DYE) who have a master’s degree. Model 4 consists of variables showing the gross domestic product per capita (DKGDP) and the number of undergraduate degree female (DLK) and male students (DLE). The letter D in the abbreviation of all variables indicates that they are first-order stationary.

Before estimating the VAR analysis, stationarity analyses of the study’s series were carried out to reach accurate and consistent results. Although the R² value is actually low, it may be high and give misleading results. Granger and Newbold (1974) stated that if the Durbin-Watson statistical value is very low compared to the R² value, this regression may exhibit a spurious relationship. Therefore, such a time series will not reflect reality. In the analysis, stationary series are used, which do not have a strong trend and have a constant mean and variance, and whose period-to-period differences are used in the calculation of covariance.

In this study, Stationarity analyses were carried out using Augmented Dickey Fuller (ADF), Phillips-Perron (PP), Kwiatkowski, Phillips, Schmidt, and Shin (KPSS), ADF considering structural breaks, and Fourier KPSS (FKPSS) unit root tests (Dickey & Fuller, 1979; Phillips & Perron, 1988; Kwiatkowski et al., 1992). According to the joint stationarity degrees of the tests, it is seen that all series used in the study are stationary at the first difference and, therefore, do not contain unit roots, and these results are presented in

Table A2. Results of unit root tests.

	ADF	PP	KPSS	KADF	FKPSS
DK	2	1 *	1	1 2019Q2
DE	2	1	1	1 *** 1985Q2
DT	2	1 **	1	2 1983Q2	(1, 7) Fist 1.70
YK	2	1 **	1	1 1985Q4
YE	2	1	1	1 ** 2020Q1
YT	1 *	1 **		1 ** 1985Q4	(3, 7) Fist 2.18
LK	2	1 *	1	0 2010Q1 **
LE	2	1 *	1	0 ** 2010Q1
LT	2	1 *	1	0 ** 2010Q1	(1, 9) Fist 4.03
KGDP	1 **	1 **	1	2 1985Q2	(1, 19) Fist 0.86

* 10% ** 5% *** 1%. T = 100 6.35 7.58 10.35 T = 200 6.25 7.41 10.02.

.

4.2. Estimation of Johansen Co-Integration Test

VAR-based cointegration tests using the methodology developed in Johansen (1991, 1995) are performed using a group object or an estimated VAR object. Consider a VAR of order p: (Johansen, 1991, 1995).

$${\mathrm{y}}_{\mathrm{t}}={\mathrm{A}}_1{\mathrm{y}}_{\mathrm{t}-1}+\dots +{\mathrm{A}}_{\mathrm{p}}{\mathrm{y}}_{\mathrm{t}-\mathrm{p}}+\mathrm{B}{\mathrm{\aleph }}_{\mathrm{t}}+{\mathsf{\epsilon }}_{\mathrm{t}}$$

where y_t is a k-vector of non-stationary I (1) variables, is a d-vector of deterministic variables, and is a vector of innovations. This can be rewritten as VAR,

$${∆{\mathrm{y}}_{\mathrm{t}}=\mathsf{\Pi }}_{{\mathrm{y}}_{\mathrm{t}-1}}+\sum _{\mathrm{i}=1}^{\mathrm{p}-1}{\mathsf{\Gamma }}_{\mathrm{i}}{△}_{\mathrm{y}-\mathrm{i}}+\mathrm{B}{\mathrm{\aleph }}_{\mathrm{t}}+{\mathsf{\epsilon }}_{\mathrm{t}}$$

where

$$\mathsf{\Pi }=\sum _{\mathrm{i}=1}^{\mathrm{p}}{\mathrm{A}}_{\mathrm{i}}-\mathrm{I}$$

$${\mathsf{\Gamma }}_{\mathrm{i}}=-\sum _{\mathrm{j}=1+1}^{\mathrm{p}}{\mathrm{A}}_{\mathrm{j}}$$

Granger argues that if the coefficient matrix Π has reduced rank r < k, then there exist kxr matrices α and B, each of rank r. r is the number of cointegration relations (cointegration order), and each column B is the cointegration vector. The α elements are known as tuning parameters in the VEC model. Johansen’s method is to estimate the matrix Π from an unconstrained VAR and test whether the reduced order of Π can reject the constraints (Johansen & Juselius, 1990).

4.3. Estimation of the VAR Model

In economic life, the interactions among macroeconomic variables can be complex. The complexity of economic events can be solved by estimating simultaneous equations rather than single-equation models (Darnell & Evans, 1990). However, in some equation systems, it is not easy to clearly separate endogenous and exogenous variables. In simultaneous equation systems, to solve such difficulties, Vector Autoregressive Models (VAR) are used as a powerful tool to study the interrelationships and interactions of a large number of economic variables. These models help us better understand the connections between economic events and variables and play an essential role in economic analysis (Darnell & Evans, 1990). VAR models offer the opportunity to explain dynamic relationships without imposing special restrictions on a structural model. Since the VAR model does not require predetermined restrictions or assumptions on the relationships between variables, it facilitates the model-building phase and provides the opportunity to estimate flexibly, provided that it does not violate the definition of the model.

Sims, who considers all variables selected in an econometric model as a part of the system without making internal or external distinctions between variables, developed the VAR model, in which each variable is affected not only by its own past values but also by the past values of other variables in the system (Sims, 1972).

VAR (p) process as

$${\mathrm{y}}_{\mathrm{t}}={\mathrm{A}}_1{\mathrm{y}}_{\mathrm{t}-1}+\dots +{\mathrm{A}}_{\mathrm{P}}{\mathrm{y}}_{\mathrm{t}-\mathrm{p}}+\mathrm{C}\mathrm{x}\mathrm{t}+{\mathsf{\epsilon }}_{\mathrm{t}}$$

where

$${\mathrm{y}}_{\mathrm{t}}=({\mathrm{y}}_{1\mathrm{t}}{,\mathrm{y}}_{2\mathrm{t}},\dots ,{\mathrm{y}}_{\mathrm{k}\mathrm{t}}{)}^{\prime } \mathrm{i}\mathrm{s} \mathrm{a} \mathrm{k}\times 1 \mathrm{v}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{r} \mathrm{o}\mathrm{f} \mathrm{e}\mathrm{n}\mathrm{d}\mathrm{o}\mathrm{g}\mathrm{e}\mathrm{n}\mathrm{o}\mathrm{u}\mathrm{s} \mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}\mathrm{s},$$

• ${\mathrm{x}}_{\mathrm{t}}=({\mathrm{x}}_{1\mathrm{t}},{\mathrm{x}}_{2\mathrm{t}},\dots ,{\mathrm{x}}_{\mathrm{d}\mathrm{t}})\prime$ is a d × 1 vector of exogenous variables,
• ${\mathrm{A}}_1,\dots ,{\mathrm{A}}_{\mathrm{p}}$ are k × k matrices of lag coefficients to be estimated,
• C is a k × d matrix of exogenous variable coefficients to be estimated,
• ${\mathsf{\epsilon }}_{\mathrm{t}}={\left({\mathsf{\epsilon }}_{1\mathrm{t}},{\mathsf{\epsilon }}_{2\mathrm{t}},\dots ,{\mathsf{\epsilon }}_{\mathrm{k}\mathrm{t}}\right)}^{\prime }$ is a k × 1 white noise innovation process, with

$$\mathrm{E}\left({\mathsf{\epsilon }}_{\mathrm{t}}\right)=0,\mathrm{E}\left({\mathsf{\epsilon }}_{\mathrm{t}}{\mathsf{\epsilon }}_{\mathrm{t}}^{\prime }\right)={\sum }_{\mathsf{\epsilon }} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{E}\left({\mathsf{\epsilon }}_{\mathrm{t}}{\mathsf{\epsilon }}_{\mathrm{t}}^{\prime }\right)=0 \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{t}\ne \mathrm{s}$$

The last statement implies that the vector of innovations is contemporaneously correlated with full rank matrix $\sum {\mathsf{\epsilon }}_{\mathrm{t}}$, but are uncorrelated with their leads and lags of the innovations and (assuming the usual ${\mathrm{X}}_{\mathrm{t}}$ orthogonality) uncorrelated with all of the right-hand side variables.

Let the (pk + d) × 1 vector

$${\mathrm{Z}}_{\mathrm{t}}=({\mathrm{y}}_{\mathrm{t}-1}^{\prime },\dots ,{\mathrm{y}}_{\mathrm{t}-\mathrm{p}}^{\prime },{\mathrm{x}}_{\mathrm{t}}^{\prime }{)}^{\prime }$$

represent all of the period t regressors in the VAR. Then for observations, this model can be written in compact system form as follows:

Y = BZ + E

where

$\mathrm{Y}=\left({\mathrm{y}}_1,{\mathrm{y}}_2,\dots ,{\mathrm{y}}_{\mathrm{t}}\right) \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{E}=\left({\mathsf{\epsilon }}_1,{\mathsf{\epsilon }}_2,\dots ,{\mathsf{\epsilon }}_{\mathrm{T}}\right) \mathrm{a}\mathrm{r}\mathrm{e} \mathrm{k}\times \mathrm{T}$ matrices of endogenous variables and innovations

$$\mathrm{B}=({\mathrm{A}}_1,{\mathrm{A}}_2,\dots ,{\mathrm{A}}_{\mathrm{p}},\mathrm{C})$$

$$\mathrm{Z}=\left({\mathrm{Z}}_1,{\mathrm{Z}}_2,\dots ,{\mathrm{Z}}_{\mathrm{T}}\right)$$

Are the k(pk + d) matrix of system coefficients and the matrix of regressor data, respectively. In stacked form,

$$\mathrm{y}=\left({\mathrm{Z}}^{\prime }⨂{\mathrm{I}}_{\mathrm{k}}\right)\mathsf{\beta }+\mathsf{\epsilon }$$

Since only lagged values of the endogenous variables appear on the right-hand side of the VAR equations Equation (1) and the innovations are assumed to be uncorrelated with lagged innovations and the exogenous regressors, standard orthogonality conditions hold, and OLS yields consistent estimates (Sims, 1972).

4.4. Estimation Results of the Johansen Co-Integration Test

According to the Johansen cointegration results, the null hypotheses that there is no relationship between the trace statistics and the largest eigenvalue statistics and that there is at most one relationship are rejected at the 5% significance level. According to all models, it was determined that there was a long-run relationship between the variables (

Table 1. Johansen co-integration test.

	H0	Trace			Max-Eigen
		Eigenvalue	Statistic	0.05 Critical Value	Eigenvalue	Statistic	0.05 Critical Value
Model 1	r = 0	0.18	65.16 * 0.0005	47.86	0.18 *	30.10	27.58
	r ≤ 1	0.11	35.05 * 0.01	29.80	0.11	17.75	21.13
	r ≤ 2	0.10	17.30 * 0.03	15.50	0.11 *	17.01	14.26
	r ≤ 3	0.001	0.29 0.59	3.84	0.001	0.29	3.84
Model 2	r = 0	0.16	45.55 * 0.0004	29.79	0.16 0.0059	27.32 *	21.13
	r ≤ 1	0.07	18.23 * 0.0189	15.49	0.07 0.1512	11.06	14.26
	r ≤ 2	0.04	7.16 * 0.0074	3.84	0.04 0.0074	7.16 *	3.84
Model 3	r = 0	0.18 0.0013	41.96	29.79	0.18	30.24 0.0020	21.13
	r ≤ 1	0.07 0.1709	11.71	15.49	0.07	11.71 0.1217	14.26
	r ≤ 2	1.83 × 10−5 0.9555	0.002	3.84	1.83 × 10−5	0.002 0.95	3.84
Model 4	r = 0	0.17	42.03 * 0.0012	29.79	0.17	28.14 * 0.004	21.13
	r ≤ 1	0.08	0.0859	15.49	0.08	13.11 0.0752	14.26
	r ≤ 2	0.005	0.77 0.3790	3.84	0.005	0.77 0.37	3.84

* A cointegration relationship exists.

).

$$\mathrm{D}\mathrm{K}\mathrm{G}\mathrm{D}\mathrm{P}=0.0029\mathrm{D}\mathrm{T}-0.00033\mathrm{Y}\mathrm{T}-0.000005\mathrm{L}\mathrm{T}$$

(0.00148) (0.00013) (1.6 × 10⁻⁵)

$$\mathrm{D}\mathrm{K}\mathrm{G}\mathrm{D}\mathrm{P}=-0.0033\mathrm{D}\mathrm{K}+0.0027\mathrm{D}\mathrm{E}$$

(0.00304) (0.00287)

$$\mathrm{D}\mathrm{K}\mathrm{G}\mathrm{D}\mathrm{P}=-0.00056\mathrm{Y}\mathrm{K}+0.00048\mathrm{Y}\mathrm{E}$$

(0.00032) (0.00031)

$$\mathrm{D}\mathrm{K}\mathrm{G}\mathrm{D}\mathrm{P}=-0.5\mathrm{L}\mathrm{K}-0.5\mathrm{L}\mathrm{E}$$

(4.7 × 10⁻⁵) (5.6 × 10⁻⁵)

In all models, it is seen that the probability values of all long-run coefficients obtained are statistically significant at the 5% significance level. Since the long-run model obtained is logarithmic, the coefficients also give elasticity values. However, it is seen that the values of the coefficients are pretty low.

Many studies have shown that human capital has a positive and significant effect on economic growth (Barro, 1991; Mankiw et al., 1992; Barro & Lee, 2013, 2015; Jin & Kim, 2024; Barro & Sala-i-Martin, 1995). On the other hand, studies have emphasized that the determinant of economic growth is not only the quantitative increase in the level of education, but also the quality of education (Hanushek & Kimko, 2000; Hanushek & Woessmann, 2015, 2020). The findings of the study support the first view by showing that human capital has a positive effect on growth, and the fact that this effect remains limited supports the second view because of the emphasis on quality.

The results show that the increase in the number of higher education institutions has a positive effect on economic growth, but the effect is limited. The limited impact of the increase in postgraduate education on economic growth shows that simply increasing the number of students is not enough and that the quality of education and its compatibility with the labor market are decisive. Sustainable growth is achieved through an education system that is supported by qualified employment areas and that can meet market needs.

Another important finding that can be derived from these results is that, in addition to the limited effect of postgraduate education on economic growth, this limited effect does not differ by gender.

4.5. Estimation Results of VAR Model

Instead of focusing on the estimation results of the VAR model, analysis is performed with error terms obtained by the estimation of the model. In this context, impulse response functions are used to measure the effect of shocks occurring in the error terms of the variables in the model on other variables. Variance Decomposition, another technique used in error term analysis, determines the effects of shocks on variables. It gives the rate at which a shock occurring in the error term of a variable is explained by other variables and, therefore, allows us to better understand the economic relationships between variables (Enders, 1995).

Determining the appropriate lag length in the VAR model is extremely important for accurately estimating the model. Suppose many variables are in a model, and many lagged values for these variables are included in the model. In that case, the number of parameters that the model needs to be estimated will increase, and it will inevitably encounter a degree of freedom problem. Optimal lag lengths in the VAR model; Likelihood Ratio Test (LR), Akaike Information Criterion (AIC), Schwarz Information Criterion (SIC), Hannan-Quinn Information Criterion (HQ), Final Prediction Error (FPE), etc. determined using information criteria. The lag lengths to be used in the models are presented in

Table A3. Delay length criteria.

	Optimal Delay Length Criteria	Optimal Delay Length
DKGDP DDT DYT DLT	LR, AIC and FPE	5
DKGDP DDK DDE	LR, AIC and FPE	5
DKGDP DYK DYE	LR, AIC and FPE	5
DKGDP DLK DLE	LR, AIC and FPE	5

. According to the common lag length of the information criteria (LR, AIC, and FPE), the VAR (5) model is considered appropriate.

Education policies do not directly affect economic growth in the short run. A certain amount of time is required for the emergence of the effects of human capital investments. Since the training of the workforce, its integration into the employment market, and its contribution to productivity are processes that take time, the contribution of education policies to economic growth emerges only in the long run.

The polynomial created in the data analysis is an important indicator to evaluate the stationarity of the model. In addition, the fact that the inverse roots of the AR characteristic polynomial of the estimated model are located within the unit circle shows that there is no problem in terms of stationarity of the model. As seen in Figure A1, the fact that the inverse roots of the AR characteristic polynomial are not located outside the unit circle confirms that the established VAR system has a stable structure.

A one-unit shock in gross domestic product per capita (DKGDP);

While a one-unit shock in the gross domestic product per capita (DKGDP) has a stable effect on the total number of students with a doctorate degree (DDT), it has a positive effect on the total number of students with a master’s degree (DYT) and the total number of students with an undergraduate degree (DLT) shows effect (Figure 1).

The stable effect at the doctoral level indicates that economic growth does not significantly increase the number of students at this level, but rather has a stable impact. It can be stated that doctoral education is shaped by the needs of academic structures rather than the economic conjuncture (Figure 1).

The positive effect at the master’s and undergraduate levels and economic growth increases the demand for master’s and undergraduate education. With the increase in income levels, more individuals turn to higher education, especially in the labor market, where competition is intense, and the tendency to increase the level of education comes to the fore. Thus, growth triggers a social demand for education and the formation of human capital (Figure 1).

These results draw attention to the fact that the increase in economic growth mostly directs broad-based education levels (undergraduate and graduate), whereas development at the doctoral level is more specific and dependent on structural factors. In educational planning, it is important to consider these different trends.

Effect of shock on the number of doctoral graduates (DDT)

The effect of a shock on the number of doctoral graduates (DDT) has a stable effect on the gross domestic product per capita (DKGDP). An increase in qualified human capital can contribute to sustainable growth potential by supporting innovation capacity, research efficiency, and long-run productivity.

The effect of a shock on the number of doctoral graduates (DDT) had a negative effect on the total number of students with a master’s degree (DLT). The fact that the increasing number of students at the doctoral level reduces the demand for a master’s degree may indicate the possibility of level substitution or demand saturation in the higher education system. Individuals aiming for an academic career directly moving towards the doctoral level may trigger a short-run decline in the master’s level. This may indicate the risk of vertical imbalance in the education system.

The effect of a shock on the number of doctoral graduates (DDT); There is a positive effect on the total number of students with an undergraduate degree (DLT), but it converges to the average after approximately the sixth period. The positive reflection of the increase in the doctoral level on the undergraduate level may have created an educational chain motivation, which, in turn, may have encouraged expansion at the undergraduate level (

Table 2. Summary of the effects of a one-unit shock to DKGDP on other variables.

Model 1	Gross Domestic Product per Capita (DKGDP)	Doctorate Degree (DDT)	Master’s Degree (DYT)	Undergraduate Degree (DLT)
A one-unit shock in gross domestic product per capita (DKGDP)		Stable effect	Positive effect	Positive effect
Effect of shock on the number of doctoral graduates (DDT)	Stable effect		Negative effect	Positive effect
Effect of shock on the total number of students with a master’s degree (DYT)	Stable effect	Stable effect		Positive effect
Shock in the total number of students with an undergraduate degree (DLT)	Stable effect	Stable effect	Stable effect

).

Effect of shock on the total number of students with a master’s degree (DYT);

A shock in the total number of students with a master’s degree (DYT) has a stable effect on the gross domestic product per capita (DKGDP) and the number of students with a doctoral degree (DDT), whereas a positive effect is observed in the total number of students with an undergraduate degree (DLT).

The effect of changes in the number of students at the master’s and doctoral levels on economic growth remains fixed; these effects are limited in the short and medium terms. This indicates that it has a positive effect on the number of undergraduate students. The increase in master’s degrees stimulates the demand for undergraduate education and has a spillover effect from top to bottom in the academic education chain. This situation shows that there is a dynamic interaction between master’s and undergraduate education levels (Table 2).

Shock in the total number of students with an undergraduate degree (DLT);

A shock occurring in the total number of students with an undergraduate degree (DLT) has a stable effect on the gross domestic product per capita (DKGDP), total number of students with a doctoral degree (DDT), and total number of students with a master’s degree (DYT). These results show that changes in the number of undergraduate students do not make a significant change in the short- and medium-run economic growth, the demand for doctoral and master’s education, and that the undergraduate level remains limited in shaping other levels of education. Therefore, it is extremely important for policymakers to integrate all levels of education in a way that supports each other and adopt a balanced and holistic approach when developing educational strategies (Table 2).

Figures show the shares in the forecast error variance, that is, the share of other variables in the variance in future forecasts. It is seen that the gross domestic product per capita (DKGDP) variable has a high explanatory power of its share, while the share of other variables is small (total number of graduate students at master’s, doctoral, and undergraduate education levels, respectively). The number of students graduating from doctoral education (DDT) is largely explained by its values, and to a lesser extent, it is explained by the total number of students with master’s degrees (DYT) and the gross domestic product per capita (DKGDP) variable. The variable of the total number of students with a master’s degree (DYT) is largely explained by its values. While the variable of the total number of students graduating from doctoral education (DDT) is effective, it affects the gross domestic product per capita (DKGDP) to a lesser extent. The total number of students graduating from undergraduate education (DLT) is again explained with its values. The variable number of students with doctoral education (DDT) is more effective than the variable of the total number of students with master’s degrees (DYT). It seems that the gross domestic product per capita (DKGDP) variable has a more significant impact on the total number of students graduating from undergraduate education (DLT) than other variables (Figure 2).

A one-unit shock occurring in the DKGDP is similar to each other in the DDK and DDE variables; a slightly positive effect is observed in the fourth period, and a negative effect is observed in the fifth period. A one-unit shock occurring in the DDK has a positive effect on the DKGDP until approximately the fifth period and converges to the average after the ninth period, and has a negative effect on the DDK until the seventh period. A one-unit shock occurring in DDE has a stable effect on DKGDP and DDK (Figure 3).

Their values largely explain the variables DKGDP, DDK, and DDE. While the DKGDP variable affects the DDK variable slightly, it has a very low effect on the DDE variable. DKGDP explains the DDK variable, and the DDK variable explains the DDE variable (Figure 4).

A one-unit shock occurring in DKGDP has the same effect on DYK and DYE variables; It is positive until the fifth period, constant until the eighth period, and a negative effect is observed until the ninth period. A one-unit shock occurring in DYK has a stable effect on DKGDP, and a negative effect is observed in DYE until the fifth period. A one-unit shock occurring in DYE has a stable effect on DKGDP, a positive effect until the fifth period, and a negative effect until the ninth period (Figure 5).

Their values largely explain the variables DKGDP and DYK. The DYE variable affects the DKGDP variable, albeit to a lesser extent than the DYK variable; the DYK variable is affected by the DKGDP and DYE variables. The DYK variable explains the DYE variable in proportion to its values. It is seen that the DKGDP variable has little effect on the DYK and DYE variables (Figure 6).

It is seen that a one-unit shock occurring in DKGDP has the same effect on DLK and DLE variables and has a positive effect until approximately the eighth period. Although a one-unit shock occurring in DLK is constant until the fourth period in DKGDP, it has a negative effect until the fifth period and a positive effect in later periods, while a negative effect is observed in DLE. While a one-unit shock occurring in DLE has a stable effect in DKGDP, a negative effect is observed in DLK until the eighth period (Figure 7).

Their values largely explain the variables DKGDP, DLK, and DLE. The DDE variable affects the DKGDP variable to a small extent; The DLE variable affects DKGDP compared to the DLK variable. Notably, the DKGDP variable has an explanatory effect at the undergraduate level (Figure 8).

5. Conclusions

In traditional growth theories, the increase in savings, physical capital investments, population growth, and capital stock is accepted as the driving forces of economic growth. In neoclassical growth models, technological development is included as an exogenous variable that determines growth. When it comes to endogenous growth theories, technology, which is considered external in Neoclassical growth theory, has become internalized in endogenous growth theory. However, the fact that physical capital alone is insufficient to explain economic growth in the long run has drawn attention to the labor force factor and has been effective in the formation of the concept of human capital. Mankiw, Romer, and Weil created the Extended Solow Model by adding the human capital term (H) to the production function proposed by Solow. According to this model, education, which is the human capital component, was added to the Cobb-Douglas production function as a separate variable.

Strengthening human capital, which generally occurs through education, contributes to a country’s achievement of long-run sustainable economic growth and development goals. Education: Its difference from other factors in the production function is that it can direct processes not only in economic but also in social dimensions. Another difference is that it does not have depreciation like physical capital; on the contrary, its value increases as you use it. In the Lucas model, it is emphasized that physical capital and labor force have decreasing marginal productivity, while human capital does not have decreasing marginal productivity. However, education plays a vital role not only in preparing individuals for business life but also in the intergenerational transfer of knowledge and experience.

One of the most critical resources supporting long-run and stable growth in developed countries is the increase in the volume of human capital. The main reason for this is that human capital leads to a greater increase in the total production level compared to the accumulation of natural resources and physical capital. People’s education, health, and capabilities are critical to economic growth. It explains the basic logic behind developed countries’ support for sustainable growth. Critical dimensions explaining development: It includes many factors such as education, income, health, environmental sustainability, social equality, and human rights. The realization of development becomes more meaningful not only through economic growth but also through efforts to raise universal living standards and make these benefits equally accessible to everyone, adhering to the principles of sustainable development.

Goals such as economic growth, development, and being able to compete in international markets cannot be achieved with physical investments alone. No matter how high the accumulation of physical capital is, it is not possible to achieve sustainable economic growth and development without human capital investments. Human capital is the most important factor explaining income differences and convergence between countries. People are at the center of human capital, and any investment made in people enables the development of physical capital and the process to be more efficient.

This study estimated VAR analysis using four models for the period 1982: Q1–2021: Q4. The number of graduate students and the level of higher education (doctoral, master’s, and undergraduate education levels) were chosen as the human capital representation variable, as it was thought that it would be better represented by human capital. Additionally, the effect of gender was examined for all education levels. In addition, gross domestic product per capita was taken as the representative economic growth variable.

According to the Johansen cointegration results, the null hypotheses that there is no relationship between the trace statistics and the largest eigenvalue statistics and that there is at most one relationship are rejected at the 5% significance level. According to all models, it was determined that there was a long-run relationship between the variables. Another important finding that can be derived from these results is that, in addition to the limited effect of postgraduate education on economic growth, this limited effect does not differ by gender.

The limited impact of the increase in postgraduate education on economic growth shows that an increase in the number of students alone is insufficient for economic growth. This situation shows that education should be developed not only quantitatively but also qualitatively. At the same time, the education system should not only equip individuals with knowledge but also provide them with the skills in demand in the employment market. However, education of this quality ensures the creation of employment that can contribute to economic growth. Therefore, an education system that cannot provide employment can become a factor that limits growth potential rather than supporting economic growth. Therefore, it is essential that education policies focus not only on providing diplomas but also on raising productive, innovative, and adaptable individuals.

In this context, education policies should focus on strategies that not only provide knowledge-based diplomas but also take into account the equivalent of graduates in the labor market. Especially at the postgraduate level, it is extremely important that program content is updated by academic and sectoral needs, and includes skills required by the age, such as entrepreneurship, digital competence, critical thinking, and research ability. In addition, university-industry collaborations should increase the applicability of the curriculum and provide students with access to employment opportunities. Education policies should be addressed not only from the supply side (number of graduates) but also from the demand side (employment capacity) perspective, and education policies should be strengthened. Thus, human capital investments do not remain only in the dimension of education expenditures but also become structural policy tools that encourage a sustainable economy and even contribute directly to economic development goals.

Although the effect of postgraduate education on economic growth is limited, the fact that this effect does not show a significant difference on the basis of gender indicates equality, at least for male and female students. Although this situation has a negative aspect of low contribution to growth, the fact that there is no injustice in the gender dimension is evaluated as positive.

To increase the number of postgraduate students to make a meaningful contribution to economic growth, it will be possible for these individuals to be employed in qualified and productive positions in the labor market. Otherwise, an increase in education level does not have a potential impact on growth and cannot be transformed into concrete economic outputs.

On the other hand, these results reveal the necessity of examining the education-employment-growth cycle not only in this flow but also in the opposite direction. The creation of effective employment areas that will support economic growth and the sustainable and productive structure of this employment depends on the education system providing education that can meet this demand. Sustainable economic growth is only possible when education policies and employment strategies are considered in a way that complements each other.

While the effect of a shock occurring in the total number of doctoral, master’s, and undergraduate students has a stable effect on the gross domestic product per capita (DKGDP), there is a difference at the gender level. It is seen that a one-unit shock occurring in female doctoral graduate students has a positive effect until approximately the fifth period and converges to the average after the ninth period, while a one-unit shock occurring in male doctoral graduate students has a constant effect on DKGDP. A one-unit shock occurring on female master’s graduate students has a stable effect on the DKGDP, while a one-unit shock occurring on male master’s graduate students has a stable effect on the DKGDP until the fourth period, a positive effect until the fifth period, and a stable effect after that. While a one-unit shock for undergraduate female students has a constant effect on the DKGDP until the fourth period, a negative effect until the fifth period, and a positive effect in the following periods, a one-unit shock for undergraduate male students has a fixed effect on the DKGDP.

A one-unit shock in the gross domestic product per capita (DKGDP); While it has a stable effect on the number of students with a doctoral degree (DDT), it has a positive effect on the total number of students with a master’s degree (DYT) and the total number of students with an undergraduate degree (DLT) (Model 1). The effect of a one-unit shock in DKGDP on male and female doctoral graduates is similar; a positive effect is observed until approximately the fourth period, and a negative effect is observed until the fifth period. The effect on male and female master’s degree students is similar; it has a positive effect until the fifth period, a constant effect until the eighth period, and a negative effect until the ninth period. The positive effect is observed until approximately the eighth period, when the effect on male and female graduate students is similar. In conclusion, while DKGDP has a stable effect at the doctoral level, it positively affects master’s and undergraduate students. It is seen that the gender effect of a one-unit shock in DKGDP is not different at the doctoral, master’s, and undergraduate education levels.

Variance decomposition, which shows their share within the forecast error variance, determines how many of the changes occurring in a variable are due to its own internal dynamics and how much of it is due to other variables. This variance decomposition is important in determining which variable explains more within a model and the relationships between variables.

According to the result of variance decomposition, it can be seen that the gross domestic product per capita (DKGDP) variable is under the influence of its own lagged values, and the share of other variables is small. The total number of graduate students at the master’s, doctoral, and undergraduate education levels, respectively, explains the DKGDP variable, albeit to a small extent. The number of students with a doctorate degree (DDT) is largely explained by its values, and the total number of students with a master’s degree (DYT) and the gross domestic product per capita (DKGDP) affect the variable, albeit to a lesser extent. The variable of the total number of students with a master’s degree (DYT) is largely explained by its values, while the variable number of students with a doctorate degree (DDT) is seen to be effective and explains the gross domestic product per capita (DKGDP) to a lesser extent. It is noteworthy that the variable of the total number of students with a undergraduate degree (DLT) is under the influence of its own lagged values, and the number of students with a doctorate degree (DDT) has a greater impact than the variable of the total number of students with a master’s degree (DYT). It seems that the gross domestic product per capita (DKGDP) variable is more effective on the total number of undergraduate students (DLT) variable than other variables (Model 1).

Their lagged values largely explain DKGDP, DDK, and DDE variables. While the DKGDP variable affects the DDK variable slightly, it has a very small effect on the DDE variable. DDK variable DKGDP; The DDK variable explains the DDE variable (Model 2). DKGDP and DYK variables are largely explained by their lagged values. The DYE variable affects the DKGDP variable, albeit to a lesser extent, than the DYK variable; the DYK variable is affected by DKGDP and DYE variables. The DYK variable explains the EDC variable in proportion to its explanatory power. It is seen that the DKGDP variable has little effect on the DYK and EDC variables (Model 3).

Their values largely explain the variables DKGDP, DLK, and DLE. The DLE variable affects the DKGDP variable to a lesser extent; the DLE variable affects DKGDP more than the DLK variable (Model 4). In conclusion, it is noteworthy that the DKGDP variable has a slightly greater explanatory effect on the undergraduate education level compared to other education levels. However, while all variables except the DYE variable are largely explained by their own lagged values, the DYK variable also explains the DYE variable in proportion to its explanatory power.

It has been determined that there is a long-run relationship between economic growth and variables indicating the number of students graduating from higher education levels. According to the results of the VAR analysis, education levels at different levels do not affect GDP much because entering the labor market and earning income after graduation takes a certain period. It has a limited effect due to such factors. According to the study results, although a fixed and limited effect is observed in some periods, doctoral, master’s, and undergraduate education levels positively affect economic growth. Another important result is that female students positively impact economic growth. It is seen that female students at the doctoral level and male students at the master’s and undergraduate levels have a positive impact on economic growth. In this context, when making policy, it is important to integrate gender equality measures into economic growth strategies, especially to promote higher education levels. These findings highlight the positive effects of gender-based education policies on sustainable economic development and offer a new perspective for future research.

Higher education is a fundamental platform where human capital is shaped and has indispensable importance. Developing and supporting higher education institutions will be important to achieving economic and social development goals. Therefore, improving the quality and accessibility of higher education shapes future success. Human capital development in higher education is an area that requires investment. In addition to providing quality education, higher education institutions should also focus on diversity, accessibility, and equity. In the future, supporting and strengthening higher education will be a fundamental step towards more equitable and sustainable development worldwide. In the future, increasing investments in this area will be an important step for sustainable development.

Higher education not only contributes to the personal development of individuals and their realization of their potential but also triggers economic growth, encourages innovation, increases the workforce’s productivity, and has a significant potential to increase the welfare of societies. It is clear that higher education is a critical factor in building human capital and that investments in this field provide a great return in economics and development.

Higher education is a strategic element for economic growth and development. Policymakers must implement various measures to support and develop higher education to achieve long-run development goals. This study highlights the central role of higher education in this context and highlights the importance of future research and policymaking. Higher education is more than just a means of knowledge transfer; it is also the source of innovation, progress, and transformation. In the future, fully understanding and appreciating the influential role of higher education will be fundamental to global development.

Higher education has the potential to develop in terms of innovation, research, and human resource development, and will only gain total value with the right policy and resource direction. Investments in education and higher education systems in the future will create a vision of more fair, accessible, and sustainable development worldwide. From this perspective, higher education is actually the development compass of the world and the gathering of a bright future for humanity. In the future, a more general examination of these magical powers worldwide is critical to fairer and more sustainable monitoring. One of the most important accumulations of economic growth is human capital, and education is the primary variable aimed at human capital.