Dynamic Effects of Education Investment on Sustainable Development Based on Comparative Empirical Research Between China and the United States

Abstract

Sustainable development is a complex dynamic process covering economic, social, and ecological dimensions. Theoretically, education investment can enhance educational capacity and offer high-quality education services, thus improving human resource quality, promoting social justice, and strengthening ecological awareness, which significantly and positively impacts sustainable development across these three dimensions. An empirical study using four-variable vector autoregressive models, with data from 2003 to 2020 on education investment and sustainable development in China and the United States as a contrast, reveals the following: (a) The impact of educational investment on sustainable development is dynamic, with the direction and strength of the effect varying over time and depending on different countries’ development conditions. In the U.S., previous-year educational investment can boost its own growth, social equality, and ecological development but may reduce per capita schooling years and human capital growth due to diminishing marginal effects. (b) In China, the previous year’s educational investment promotes current social equality but slightly hampers talent capital accumulation, ecological development, and its own growth. The investment from the year before last still promotes social equality, increases per capita schooling years for talent capital accumulation, has a less negative impact on ecological development, and inhibits its own growth more weakly than the previous year, showing declining effect strength. (c) Policy-wise, countries should diversify education investment sources, target areas with high positive marginal effects on sustainable development, and establish a dynamic adjustment mechanism for education investment to better promote sustainable development.

1. Introduction

Sustainable development, defined by the 1987 United Nations Brundtland Commission, is development that meets present needs without harming future generations’ ability to meet theirs. The pursuit of sustainable development is a global imperative, uniting nations in the face of complex environmental, social, and economic challenges. Education, as a cornerstone of human progress, has emerged as a pivotal factor in driving sustainable development. Its influence permeates all aspects of the sustainable development agenda, from fostering economic growth to promoting social equity and environmental stewardship.

The role of education in sustainable development has deep roots in economic theory. In the 1960s, Schultz [1] introduced the human capital theory, positing that education is a primary means of augmenting human capital. This investment in people, through formal education and training, enhances productivity and innovation, thereby fueling economic growth. Fitzgerald [2] further elaborated on the significance of education in shaping the labor force structure, emphasizing its role in promoting sustainable economic development.

Since the turn of the 21st century, sustainable development has ascended to the forefront of the global policy agenda. Mounting challenges, including climate change, demographic shifts, resource scarcities, and uneven development, have underscored the urgency of adopting sustainable practices. The United Nations’ “2030 Agenda for Sustainable Development” encapsulates this global commitment, with Goal 4 dedicated to ensuring inclusive and quality education for all [3]. This goal not only highlights the intrinsic value of education but also its instrumental role in achieving broader sustainable development outcomes.

As the world’s most populous nation and largest developing economy, China faces unique and formidable challenges in its pursuit of sustainable development. In recent years, China has made significant strides in implementing a comprehensive sustainable development strategy, with the ambitious targets of peaking CO₂ emissions by 2030 and achieving carbon neutrality by 2060 (the “dual-carbon” goal) [4]. However, this path is fraught with obstacles, including a rapidly aging population (with an aging rate of 18.7% [5]), the lingering impacts of the COVID-19 pandemic, and economic headwinds [6]. Against this backdrop, educational investment has emerged as a critical driver of sustainable development, capable of fostering innovation, enhancing human capital, and promoting resilience.

Despite the growing recognition of the importance of education investment for sustainable development in China, the existing literature is characterized by several limitations. Most Chinese research has concentrated on qualitative analyses of the static relationship between education investment and sustainable development, predominantly from an economic perspective. This narrow focus overlooks the multi-dimensional and dynamic nature of sustainable development, which encompasses social and ecological dimensions in addition to economic growth [3,7]. Moreover, empirical-based quantitative studies on the dynamic effects of education investment on China’s sustainable development are scarce. Additionally, research in this area has primarily focused on domestic regional comparisons, with few cross-national studies, particularly those comparing China with major economies such as the United States, which share similar scale and global influence.

This paper aims to bridge these research gaps by adopting a comparative approach, focusing on the United States and China. Through empirical analysis, we seek to understand the impact of education investment on sustainable development in both countries. Our objectives are three-fold: first, to fill the void in existing quantitative research on the relationship between education investment and sustainable development in China; second, to enrich the cross-national case study literature in this field; and third, to provide evidence-based policy recommendations for enhancing the effectiveness of education investment in promoting sustainable development in both countries.

The remainder of this paper is structured as follows. Section 2 provides a comprehensive review of the relevant literature on the relationship between education investment and sustainable development. Section 3 elucidates the theoretical mechanisms through which education investment impacts sustainable development, within a three-dimensional framework. Section 4 outlines the methodology, including the construction of a quaternary vector autoregression model that incorporates education investment and variables representing the three dimensions of sustainable development. Section 5 presents the empirical results of the comparative analysis, using annual data from 2003 to 2020 for both China and the United States. Finally, Section 6 concludes with policy implications and recommendations for future research.

2. Literature Review

The literature relevant to this study mainly encompasses the understanding of the connotations of sustainable development and research on the impact of education investment on sustainable development.

2.1. On Connotations of Sustainable Development

Sustainable development, as defined by the United Nations Brundtland Commission in 1987, is development that meets the needs of the present without compromising the ability of future generations to meet their own needs [8]. This concept has evolved over time, with scholars exploring its economic, social, and environmental dimensions. Duran et al. [9] posited that the core of sustainable development encompasses three interdependent dimensions—economic, ecological, and humanistic—that necessitate synergistic interaction. Chen et al. [10], during their research on the relationship between natural resources consumption and social development levels in 136 countries from 1996 to 2005, placed greater emphasis on understanding sustainable development as ecological sustainability based on the harmonious coexistence between humanity and nature. The “Sustainable Cleveland 2019-Action and Resources Guide” offers a comprehensive local perspective covering economic, ecological, and social aspects to facilitate sustainable development in Cleveland [7]. Schebesta et al. [11], from an economic–environmental perspective, evaluated the European Commission’s Farm to Fork Strategy and advocated for defining sustainable development as the integration of sustainable economic development and environmental protection processes.

The United Nations’ “2030 Agenda for Sustainable Development” [3], on the other hand, sets 17 goals for global sustainable development, integrating economic, social, and ecological perspectives. For example, Goal 1 aims to end all forms of poverty globally, highlighting the need for inclusive economic growth. Goal 7 focuses on ensuring accessible, reliable, and sustainable energy, promoting clean energy use. Ecologically, Goal 13 calls for urgent action against climate change. Socially, Goal 4 emphasizes inclusive and equitable education. This agenda offers a holistic framework for countries to align their development strategies. It spurs international cooperation, as the goals’ challenges are global.

Overall, these literatures explore sustainable development from various economic, social, and ecological perspectives, demonstrating a process of deepening understanding of sustainable development. Based on previous research, this study argues that sustainable development is not a single-dimension development process but a multi-dimensional dynamic process integrating economic, social, and ecological aspects.

2.2. On the Impact of Education Investment on Sustainable Development

In terms of education investment’s impact on sustainable development, numerous studies have been conducted, which can be classified into the following three categories.

Firstly, sustainable development is taken as an economic process, in which human capital investment, technological innovation, and market organization are involved. Psacharopoulos and Patrinos [12] demonstrated that advanced education investment yields marginally lower human capital accumulation efficiency compared to general education, yet higher allocations to advanced education enhance the overall technical efficiency of human capital formation. Li et al. [13] augmented the differential effects of general and advanced education investments on human capital accumulation and economic growth under endogenous growth theory using Chinese provincial panel data. Findings revealed general education significantly boosted per capita economic output, while advanced education had no measurable impact. These results underscore the education system structure’s role in optimizing human capital returns for sustainable growth. Acemoglu and Restrepo [14] pointed out that education investment in the era of artificial intelligence needs to focus on skill reshaping and enhance the adaptability of the workforce through vocational education and lifelong learning, so as to achieve sustainable economic growth. Li et al. [15] analyzed the moderating effect of financial development on education investment’s impact on economic growth using Chinese provincial panel data (2005–2019). It found financial intermediation significantly enhanced education’s growth effects only in underdeveloped regions, even when education/finance proxies showed negative individual impacts, and advocated for targeted financial strategies for lagging provinces to maximize education investment returns for inclusive growth. Chen and Wang [16] applied panel data analysis and concluded that higher education-based human capital led to increased productivity of sustainable economic growth. Zhang [17] conducted a meta-analysis on education investment and human capital, showing that education investment significantly enhanced human capital quality. Bhattarai and Shrestha [18] conducted an ordinary least square (OLS) analysis on Nepal’s agricultural sector and found that education investment positively influenced agricultural talent capital accumulation, which in turn contributed to agricultural sustainable development. Yang et al. [19] studied the spillover effect of higher education investment and human capital structure on regional economic growth, revealing that these factors had a positive impact on regional economic sustainable growth. Iqbal et al. [20] adopted a case-study approach and found that specific companies’ employee education and training investments improved the market organization’s learning mode and sustainability.

The literature shows that education investment improves human capital quality. Workers with better education are more productive, adaptable to technological changes, and can drive technological innovation. This, in turn, optimizes the national economic structure, for example, by promoting the shift from low-value-added to high-value-added industries, thus promoting sustainable economic development.

Secondly, sustainable development is understood more inclusively, which is regarded as a social process concerning social networking and the balance of regional development and social equity. Arsani et al. [21] examined the nexus of education, health, and poverty in developing countries, identifying tertiary education as a critical determinant of household wealth and health alongside demographic variables, and recommended targeted interventions such as Indonesia’s PIP and Bidikmisi programs to address poverty and public health through education. Yu et al. [22] used social network analysis to study the influence of education-related activities on social networking. They found that higher education levels were linked to more extensive social networks. Yang and Yu [23] compared regional development differences in areas with different education investment levels. Their results indicated that higher investment was associated with more balanced development. Chen et al. [24] analyzed case studies of regions with education-driven social change. They concluded that education investment could promote social justice through knowledge dissemination and behavior guidance. Yuen-Tsang et al. [25] used a case-study method on a Master of Social Work program in China, showing that social work education can act as a catalyst for sustainable social development. Hien [26] used a longitudinal study to track the social development of certain regions with changes in education investment. The results showed that increased investment gradually reformed the regional development layout. Iqbal and Piwowar-Sulej [27] used a mixed-method approach, combining surveys and interviews, to explore education’s role in promoting social equity. They found that education investment could mediate regional development.

These studies reveal that education investment promotes social networking, facilitating information sharing and resource allocation. It also mediates regional development by providing educational resources to less-developed areas, reducing disparities. Through knowledge and behavior guidance, it enhances social justice, which is fundamental for sustainable development.

Thirdly, the implication of sustainable development extends beyond economic and social bounds, incorporating into the relationship between humankind and the natural environment, which leads to the ongoing green growth wave. Li and Gan [28], along with Ouyang and Wang [29], used literature-review-based qualitative analysis to explore green growth. They emphasized integrating ecological concerns into sustainable development. Al-Zayyat et al. [30] and Usman [31] used environmental impact assessment methods to study the relationship between economic development and environmental protection in the context of sustainable development. Mo et al. [32] conducted environmental education programs in schools and communities. By measuring participants’ ecological awareness changes, they found that education investment could shape ecological awareness. Stanger [33] proposed a theoretical and policy-oriented reorientation of ecological literacy in human developmental models and school systems, concluding that integrating ecological literacy into education can promote sustainable development by enhancing ecological awareness and leading to more sustainable behaviors and policies. Akesson et al. [34] used a conceptual and empirical approach to re-examine the person-in-environment model in social work, suggesting that rethinking this model in education can contribute to sustainable social development by improving social work effectiveness. Zhao and Zou [35] as well as Zhu et al. [36] used surveys and field observations to study the long-term impact of environmental education on people’s behavior.

The impact mechanism is that education investment, through environmental education, cultivates people’s ecological awareness. Those with higher ecological awareness are more likely to engage in environmentally friendly behaviors, which promotes sustainable development ecologically.

2.3. Summary

Most existing research has delved relatively deeply into the impact of education investment on sustainable development in one or two aspects, such as the economic, social, and ecological aspects. However, based on the three-perspective framework of the United Nations’ 2030 Agenda for Sustainable Development, discussions on the dynamic impact of education investment on the dynamic process of sustainable development are still insufficient. Furthermore, the impact of educational investment on sustainable development is often discussed qualitatively. Although quantitative empirical research methods, such as OLS analysis or panel data analysis, are occasionally employed in a few studies, they mainly concentrate on analyzing the influence of the scale of educational investment on economic sustainable development. Mturi and Fuseini [37], based on the comprehensive analysis framework of economic–social–ecological sustainable development in the United Nations’ 2030 Agenda, conducted a comprehensive analysis of the impact of education investment on sustainable development in South Africa. Their study revealed the three-dimensional relationship between education investment and sustainable development, initially demonstrating that this three-dimensional comprehensive analysis is more comprehensive than single- or two-dimensional analyses in revealing the relationship between education investment and sustainable development.

Regrettably, the analysis by Mturi and Fuseini only qualitatively discussed the relationship between education investment and the sustainable development of industries based on typical industrial cases. It has not yet measured the dynamic impact of education investment on a country’s macro-level sustainable development from the perspective of the dynamic change process of sustainable development. As a result, its reference value for the dynamic adjustment and optimization of education investment and sustainable development policies is limited.

Therefore, this study will utilize a vector autoregression (VAR) model to focus on the multi-dimensional dynamic effects of educational investment on sustainable development. This approach will enable us to capture the dynamic characteristics of the effects of educational investment on the economic, social, and ecological dimensions of sustainable development over multiple periods, which will be further clarified in Section 4.

3. Theoretical Analysis

3.1. General Discussion on the Impact Mechanism of Education Investment on Sustainable Development

Education investment plays a pivotal role in the sustainable development process. The United Nations’ 2030 Agenda for Sustainable Development emphasizes the interconnectedness of economic, social, and ecological aspects [3]. In this context, education investment impacts sustainable development through a complex, dynamic, and systematic process. It is not merely a one-time input but an ongoing interaction between the education system and the sustainable development system. This interaction occurs across different time scales and involves multiple factors. The three social functions of education investment, including knowledge dissemination, skill training, and social tradition transformation [38], are the cornerstones of this impact mechanism. They work in tandem, constantly reshaping the elements within the economic, social, and ecological spheres, thus promoting sustainable development in a holistic and dynamic way.

3.2. Impact Mechanism of Education Investment on Economic Sustainable Development

In the economic perspective, education investment has a profound and dynamic impact on sustainable development. Through knowledge dissemination, which includes both human capital accumulation and the cultivation of innovative talents, a more educated workforce emerges. These individuals bring new ideas and technologies, leading to enhanced economic productivity. For example, in high-tech industries, employees with advanced education can drive innovation, which in turn improves production efficiency and product quality. Skill training, involving social skills acquisition and better work collaboration, also contributes. A skilled workforce can adapt to new production models and work more effectively in teams, further boosting economic growth [39]. Over time, as the economic structure evolves due to technological advancements and market changes, education investment continuously adjusts the labor quality structure. This dynamic adjustment ensures that the economy remains competitive and sustainable, adapting to various external shocks, such as economic recessions or changes in global trade policies.

3.3. Impact Mechanism of Education Investment on Social Sustainable Development

From a social perspective, education investment is crucial for promoting social justice and stability. Education as a social institution has a great social importance, especially in modern, complex societies [21,40]. Well-educated individuals have better access to higher-paying jobs, which reduces income inequality. Skill training, enabling better social skills and work collaboration, also promotes social integration [34]. People with diverse educational backgrounds can communicate and cooperate more effectively, building a more inclusive society. Moreover, the transformation of social traditions gradually changes social values. As the public becomes more environmentally conscious, social norms shift towards sustainable practices. This dynamic process is not static; it evolves with social changes, such as demographic shifts and cultural exchanges. Education investment continuously adapts to these changes, strengthening the foundation of social justice and promoting social sustainable development.

3.4. Impact Mechanism of Education Investment on Ecological Sustainable Development

In the ecological sphere, education investment exerts its influence through a dynamic and systematic process. Knowledge dissemination about environmental protection and sustainable development concepts raises public awareness [41]. For instance, educational programs on climate change can make people more conscious of their environmental impact. Skill training related to sustainable practices equips individuals with the ability to implement green technologies and participate in environmental protection activities. The transformation of social traditions towards green development consciousness further encourages sustainable behaviors at the community and individual levels. As society progresses, new environmental challenges emerge, such as the need to address plastic pollution or promote renewable energy use. Education investment responds to these challenges by updating curricula and training programs. This continuous adaptation ensures that the public’s ecological awareness and ability to act sustainably keep pace with the changing ecological landscape, thereby promoting ecological sustainable development. Figure 1 shows the impact mechanism of education investment on sustainable development.

Since the impact of education investment on the multi-dimensional dynamic system of sustainable development is a dynamic process [11], the influence of education investment on sustainable development is also time-varying. The development structures of the economy, society, and ecology determine their sensitivity to education investment, and the effects of education investment on sustainable development will also exhibit different inter-temporal dynamic characteristics. Generally speaking, the impact of external shocks on the system will gradually weaken over time until the shock is fully absorbed and digested by the system, and the system itself returns to a new dynamic equilibrium state. Therefore, the short-term effects of current education investment on sustainable development will be more significant than the long-term effects, and the impact of education investment on sustainable development will present a dynamic process of decay over time.

Thus, the hypotheses about the dynamic effects of educational investment on sustainable development can be proposed as follows:

H1: 

The effects of educational investment on sustainable development are generally positive and can promote sustainable development.

H2: 

The impact of educational investment on sustainable development is generally a dynamic process of decay over time.

H3: 

The effects of educational investment on sustainable development are time-varying, and the dynamic features of the effects of educational investment on specific aspects of sustainable development depend on the specific structures of economic, social, and ecological development.

4. Research Design

4.1. General Design

Existing studies generally adopt ordinary least square (OLS) regression or panel data analysis methods when analyzing the impact of education investment on sustainable development [16,18]. The OLS model is typically used to analyze the linear impact of independent variables on the dependent variable in a single equation. It assumes that the relationships between variables are static and fixed [42]. When studying the impact of education investment on sustainable development, due to the close connection and continuous dynamic changes among the economic, social, and ecological dimensions of sustainable development, the OLS model cannot effectively capture the complex dynamic interactions among variables [43]. For example, while education investment enhances labor quality and promotes economic growth, it also affects social equity and ecological awareness. The OLS model struggles to comprehensively depict these linkage effects.

The panel data analysis model, although it takes into account the differences in individual and time dimensions and can, to some extent, analyze the relationship between education investment and sustainable development in different regions or individuals at different times, still has limitations in handling the dynamic relationships among multiple variables. It cannot fully reflect the immediate feedback and long-term dynamic adjustments among the economic, social, and ecological dimensions [44].

The vector autoregressive model (VAR) is different. The vector autoregressive model (VAR) is an autoregressive dynamic model proposed by Christopher Sims in 1980 [45]. The model treats each endogenous variable in a system as a hysteresis function of all endogenous variables in the system, establishing a dynamic system composed of multivariate time-series variables [46]. It can simultaneously consider the lagged terms of multiple variables and incorporate variables such as education investment, economic development, social progress, and ecological protection into the same system. Through the impulse response function, the VAR model can clearly show how the shock of education investment affects the three dimensions of sustainable development in different periods. For instance, when education investment is increased, the VAR model can intuitively present the dynamic response processes of economic growth, social equity improvement, and ecological awareness enhancement in the short term and also reveal the continuous evolution of these effects in the long term. Meanwhile, variance decomposition can determine the contribution degree of each variable to the fluctuations of other variables, accurately quantifying the relative importance of the impact of education investment on each dimension of sustainable development. Therefore, in analyzing the three-dimensional dynamic impact of education investment on sustainable development, the VAR model provides a more comprehensive, in-depth, and dynamic perspective, offering a more powerful tool for research.

Additionally, the VAR model is chosen in this study because it can effectively handle multi-variable time-series data. In the context of this study, there are complex dynamic interactions among education investment and the economic, social, and ecological dimension variables of sustainable development. The VAR model regards each endogenous variable in the system as a function of the lagged values of all endogenous variables, which can comprehensively capture these dynamic relationships. For example, changes in education investment not only directly affect current economic development but also indirectly affect each dimension of sustainable development in subsequent periods by influencing talent capital accumulation, social equity, and ecological awareness. The VAR model can accurately describe this multi-period dynamic impact process. As for empirical studies, the VAR model is one of the commonly used empirical research methods in the field of econometrics to analyze the dynamic relationships among variables, which is in line with the requirements of our study to explore the dynamic effects of education investment on sustainable development.

In terms of variables, the average number of years of schooling per capita is selected to represent talent capital in the economic dimension because it directly reflects labor quality. The Gini coefficient of per capita disposable income is used to measure social equity, and per capita carbon emissions are used as an indicator of ecological development level. These variables can effectively represent different dimensions of sustainable development based on the references [24,42,47,48,49,50].

As for assumptions, according to theoretical analysis and hypothesis made in Section 3, we assume that the impact of education investment on sustainable development is affected by various factors within the economic, social, and ecological systems, and these factors interact with each other. This design and the choice of variables and assumptions are crucial for accurately exploring the dynamic effects of education investment on sustainable development in the context of a comparative study between China and the United States.

4.2. Model Construction

Specifically, for the VAR model to be effectively applied, each variable series must be stationary, and the overall model system should be robust. Once the prerequisite of variable stationarity is satisfied and the number of lag periods is determined, the binary structure of the model can generally be expressed as follows:

$$\left({\displaystyle \genfrac{}{}{0pt}{}{y_{1t}}{y_{2t}}}\right)=\left({\displaystyle \genfrac{}{}{0pt}{}{a_1}{a_2}}\right)+\left(\begin{array}{cc}{\eta }_{11}^1& {\eta }_{12}^1\\ {\eta }_{21}^1& {\eta }_{22}^1\end{array}\right)\left({\displaystyle \genfrac{}{}{0pt}{}{y_{1 t-1}}{y_{2 t-1}}}\right)+\dots +\left(\begin{array}{cc}{\eta }_{11}^n& {\eta }_{12}^n\\ {\eta }_{21}^n& {\eta }_{22}^n\end{array}\right)\left({\displaystyle \genfrac{}{}{0pt}{}{y_{1 t-n}}{y_{2 t-n}}}\right)+\left({\displaystyle \genfrac{}{}{0pt}{}{{\mu }_1}{{\mu }_2}}\right)$$

(1)

Equation (1) represents the basic form of the VAR model. We set the left-hand side as the vector of endogenous variables. The right-hand side consists of the lagged values of these endogenous variables. Among these variables in Equation (1), $\left({\displaystyle \genfrac{}{}{0pt}{}{y_{1t}}{y_{2t}}}\right)$ denotes the explained endogenous variable vector, subscripts 1 and 2 represent the variable serial number in the vector, t stands for the current period, n represents the number of lag periods, $y_{1 t-1}$ means variable $y_1$ at period t − 1 (for example), η represents the coefficient matrix, and μ represents the random disturbance term. Equation (1) demonstrates that in the vector autoregressive (VAR) model, the two dependent variables are explained by their respective time-series variables lagged by n periods. Consequently, this model can capture the impact effects of the variables lagged by n periods on the variables in the current period.

The model can leverage the impulse response function to analyze the dynamic effect on the system when the error term or the model is subjected to a certain shock. A VAR model can be transformed into an infinite-order vector moving average model:

$$y_t=\delta +{\chi }_1{\lambda }_1+{\chi }_2{\lambda }_2+\dots +\mathrm{\infty }$$

(2)

χ represents the coefficient matrix of the lag disturbance term $\lambda$ in the infinite-order vector moving average model. Equation (2) implies the following relationship:

$${\chi }_{ij}^P={\displaystyle \frac{\partial y_{i,t+p}}{\partial {\lambda }_{j,t}}}$$

(3)

Equation (3) reflects an impulse response function that measures a shock response of y_i,t + p to y_i,t when other variables in period t and variables in early periods remain unchanged.

This study posits that education activities and sustainable development endeavors are intricately linked within the human social system. Education investment, which turns into human capital, financial resources, and facilities for educational activities, is the ongoing force that drives educational development. When the investment in teaching staff and teaching venues remains relatively stable, the total education investment mainly takes the form of educational capital investment. Moreover, through market mechanisms, educational capital investment can be converted into other elements such as educational human resources and facilities. For the sake of research convenience and data availability, the term “education investment” in this paper refers specifically to educational capital investment in a narrow sense.

Educational capital investment acts upon and is transformed into diverse elements of educational activities. Subsequently, through educational activities, it influences the quality of human capital in economic development, the equity foundation of social development, and the environmental awareness in ecological development, thereby indirectly affecting sustainable development comprehensively. Thus, it can be inferred that education investment and the specific dimensions of sustainable development are organically interconnected, both being integral parts of a unified social education and development system.

To simplify the analysis, let us assume a social system made up of proxy variables including education investment, economic sustainable development, social sustainable development, and ecological sustainable development. This social system exhibits the dynamic characteristics inherent in both the education investment and sustainable development systems. Given the striking similarity of these variation characteristics to the multivariate system of the VAR model, a quaternary VAR model (see Equation (4)) can be constructed using the education investment variable and the connotative variables of sustainable development, which in our case includes education investment, talent capital (represented by the average years of schooling per capita), social equity (measured by the Gini coefficient of per capita disposable income), and ecological development level (represented by per capita carbon emissions). This model enables an in-depth analysis of the impact of the education investment variable on each connotative variable of sustainable development in a multi-period process. Simultaneously, based on the impulse response analysis function of the VAR model, a random disturbance shock generated by a one-unit standard deviation of the education investment variable can be introduced to explore the dynamic responses of each connotative variable within the sustainable development system over multiple periods.

$$\left(\begin{array}{c}{y}_{1t}\\ \dots \\ y_{4t}\end{array}\right)=\left(\begin{array}{c}{a}_1\\ \dots \\ a_4\end{array}\right)+\left(\begin{array}{ccc}{\eta }_{11}^1& \dots & {\eta }_{14}^1\\ \dots & \dots & \dots \\ {\eta }_{41}^1& \dots & {\eta }_{44}^1\end{array}\right)\left(\begin{array}{c}{y}_{1 t-1}\\ \dots \\ y_{4 t-2}\end{array}\right)+\dots +\left(\begin{array}{ccc}{\eta }_{11}^n& \dots & {\eta }_{14}^n\\ \dots & \dots & \dots \\ {\eta }_{41}^n& \dots & {\eta }_{44}^n\end{array}\right)\left(\begin{array}{c}{y}_{1 t-n}\\ \dots \\ y_{4 t-n}\end{array}\right)+\left(\begin{array}{c}{\mu }_1\\ \dots \\ \mu \end{array}\right)$$

(4)

4.3. Indicator Selection and Data Sources

In this study, drawing on relevant research and considering data availability, the ratio of education expenditure to Gross Domestic Product (GDP) is selected to represent the education investment variable [24,47]. The average years of schooling per capita is used to represent the talent capital variable in the economic dimension [48,49]. The Gini coefficient of per capita disposable income is adopted to measure the degree of social justice [42], and per capita carbon emissions are employed to indicate the level of ecological development [50].

Furthermore, a comparative analysis will be carried out, with the United States serving as a parallel reference for China. The United States is selected as the country for comparison because it is comparable to China in terms of national economic scale, social scale, and natural resources. The United States stands as one of the exemplary developed countries globally, boasting large-scale education investment and a high level of educational development. In contrast, China, as the world’s largest developing country, has a relatively lower scale and level of educational development. Comparing these two countries helps to reveal the differential impacts of education investment on sustainable development in countries at different stages of development.

This approach aims to more objectively and clearly reveal the dynamic effects of education investment on sustainable development. The relevant annual data of these specific indicators in China and the United States from 2003 to 2020 will be utilized to analyze the dynamic impacts of education investment on sustainable development.

The specific indicators and their data sources are as follows in

Table 1. Variable indicators’ data sources and statistical characteristics.

Indicator	Code	Data Sources	Average	Standard Deviation
China
The ratio of education funding to GDP	ei	Official website database of National Bureau of Statistics of China	0.0488	0.0032
Schooling years per capita	lc	UNDP Human Development Report database	7.6326	0.7034
Gini coefficient of disposable income per capita	se	Official website database of National Bureau of Statistics of China	0.4754	0.0092
Carbon emission per capita	ce	The World Bank Databank	6.2564	1.3643
The United States
The ratio of education funding to GDP	uei	The World Bank Databank	0.0591	0.0067
Schooling years per capita	ulc	UNDP Human Development Report database	13.5151	0.2232
Gini coefficient of disposable income per capita	use	The World Bank Databank	0.4088	0.0050
Carbon emission per capita	uce	The World Bank Databank	16.7827	1.9700

.

5. Empirical Analysis and Results Discussion

5.1. Empirical Analysis

It is necessary to take the logarithm of the indicator value and perform a first-order difference in order to make the time series of indicator value stationary at first. Through the processing step above, the ratio of education expenditure to GDP (ei), per capita schooling years (lc), Gini coefficient of per capita disposable income (se), and per capita carbon emissions (ce) are turned into dei, dlc, dse, and dce; similarly, duei, dulc, duse, and duce are attained.

By the Phillips–Perron (PP) tests, both groups of four series display as stationary. The groups of four series are put into a quaternary VAR model system and regressions are conducted with the use of a software tool dedicated to econometrical computation—Eviews 9.0. First, according to the information criteria of the Akaike Information Criterion (AIC), Schwarz Criterion (SC), Likelihood Ratio (LR), Log-Likelihood (LogL), and Final Prediction Error (FPE), the number of lag periods in the Chinese VAR model and the United States are both designated as 2 based on the “majority principle”.

The unit root tests of two models show that the unit root points are all in the unit circle, except for two unit-root points of the United States model that fall slightly outside, manifesting that the overall model was robust. The regression results are shown in

Table 2. VAR regression results based on Chinese data vs. the United States.

	Explained Variable	Results Based on Chinese Data				Results Based on the United States’ Data
Explanatory Variable		dei	dlc	dse	dce	duei	dulc	duse	duce
DEI (−1)		−0.45377	−0.01684	−0.03571	0.52884	0.271611	−0.008	−0.13939	−0.05493
		[−1.55383]	[−0.20094]	[−0.27943]	[2.07067]	[0.66893]	[−0.91270]	[−2.77315]	[−0.29241]
DEI (−2)		−0.33036	0.10166	−0.0368	0.283974	−0.31066	0.002568	0.004702	−0.03079
		[−1.26468]	[1.35597]	[−0.32185]	[1.24303]	[−0.94986]	[0.36365]	[0.11614]	[−0.20347]
DLC (−1)		0.224503	0.678307	−0.50467	−0.92245	16.82513	0.369055	−2.52884	−4.26985
		[0.19113]	[2.01211]	[−0.98171]	[−0.89799]	[0.97355]	[0.98898]	[−1.18207]	[−0.53404]
DLC (−2)		−3.48881	−0.41236	0.317742	−1.57815	−7.1577	0.249097	2.907098	4.491658
		[−1.88664]	[−0.77697]	[0.39260]	[−0.97584]	[−0.49426]	[0.79662]	[1.62168]	[0.67043]
DSE (−1)		−1.33274	−0.26719	0.039017	1.408128	−6.33655	−0.0039	0.746142	3.451227
		[−1.86240]	[−1.30097]	[0.12458]	[2.25002]	[−1.92707]	[−0.05495]	[1.83312]	[2.26872]
DSE (−2)		−1.061994	−0.151582	−0.321017	0.730957	0.260544	−0.08727	−0.87572	0.765893
		[−1.46003]	[−0.72611]	[−1.00839]	[1.14907]	[0.11646]	[−1.80662]	[−3.16224]	[0.74001]
DCE (−1)		−0.23986	−0.06274	−0.04171	0.388943	−0.16326	−0.00504	0.091278	−0.56308
		[−0.63904]	[−0.58245]	[−0.25390]	[1.18489]	[−0.22544]	[−0.32216]	[1.01819]	[−1.68062]
DCE (−2)		0.145416	0.037773	0.043463	−0.25508	1.193776	−0.01193	−0.51792	−1.59133
		[0.53903]	[0.48786]	[0.36812]	[−1.08117]	[1.10301]	[−0.51032]	[−3.86581]	[−3.17818]
C		0.070539	0.011068	8.90 × 10−5	0.070201	−0.00752	0.000246	−0.01439	−0.07596
		[1.79070]	[0.97899]	[0.00516]	[2.03776]	[−0.16044]	[0.24306]	[−2.48134]	[−3.50407]
R-squared		0.665892	0.713399	0.27278	0.838056	0.499583	0.750175	0.855958	0.706677

. The R-squared values of the Chinese model regression are all above 0.65, except for the dse equation with a 0.27278 R-squared value. The R-squared values of the United States’ model regression are all above 0.70 except for duei equation with a slightly low value of R-squared value of 0.499583, showing that both groups of regression fit generally well.

The intertemporal dynamic effects of a one-unit standard deviation impulse shock of each variable on other variables in the Chinese and the United States’ models are as shown in Figure 2.

(1)

Table 2 reveals the following findings:

(a)

Impact of Lagged Chinese Educational Investment

Firstly, the one-period lagged educational investment variable (dei − 1) has negative impacts on the current values of dei, dlc, and dse but a positive effect on dec. This implies that China’s educational investment in the previous year can stimulate an increase in per capita carbon emissions in the subsequent period, while reducing the growth of per capita schooling years, the Gini coefficient of per capita disposable income, and the ratio of education funding to GDP. It indicates that the previous year’s educational investment can indeed promote current social equality. However, it slightly hinders talent capital accumulation, ecological development, and its own growth. This might be because it takes a relatively long time for adjustments in educational investment to have a positive impact on ecological development. Additionally, China has implemented nine-year compulsory education for an extended period. Given that the per capita schooling years reached 8.67 in 2020, the short-term effect of educational investment on further increasing the already relatively high per capita schooling years is not significant.

Secondly, the two-period lagged educational investment variable (dei − 2) has positive impacts on dlc and dce but negative effects on dei and dse. This suggests that the educational investment from two years ago can still promote social equality. Moreover, it can increase per capita schooling years, thereby facilitating talent capital accumulation. In terms of the coefficients, it has a less negative impact on ecological development compared to the previous year, and it inhibits the current growth of educational investment more weakly than the previous year, showing a declining trend in the strength of its effects. This provides support for Hypothesis 2.

   (b)

Impact of Lagged American Educational Investment

It is also evident from Table 2 that, firstly, the one-period lagged American educational investment variable (duei − 1) has a positive impact on duei itself but negative effects on dulc, duse, and duce. This indicates that the previous year’s American educational investment can promote its own growth in the current year, improve social equality, and promote ecological development, which partially supports Hypothesis 1. However, it reduces per capita schooling years and curbs the growth of human capital accumulation in the United States. This may be attributed to the diminishing marginal effect of educational investment on human capital growth in the advanced American education system.

Secondly, the two-period lagged American educational investment variable (duei − 2) has positive impacts on dulc and duse but negatively influences duei and duce. This suggests that the educational investment two years ago can promote talent capital accumulation and carbon emission reduction, which also supports Hypothesis 1. Nevertheless, it curbs its own growth in the current year and increases the Gini coefficient. This could be because long-term investment in the rich elite education in the United States may widen the gap between the rich and the poor.

(2)

Figure 2a,b illustrate the following:

Firstly, the time-varying effects of educational investment on sustainable development in China and the United States are similar. The impulse response curves triggered by a one-standard-deviation shock fluctuate over a 10-year period, which supports Hypothesis 3.

Secondly, the impulse response curves of other variables to educational investment shocks in the previous two periods generally align with the regression results in terms of the direction and strength of the effects in both China and the United States. However, the responses of economic, social, and ecological development to educational investment differ between the two countries, which is likely due to their different national conditions. For example, in the 3rd–7th periods of the response curves, the positive effect of educational investment on per capita schooling years in China is significantly stronger and more long-lasting than in the United States. This is mainly because, according to the law of diminishing marginal effects, the marginal effect of educational investment in China, with its large population, relatively underdeveloped education system, and need for advanced talent reserves, is stronger than that in the United States.

5.2. Discussion Between Findings in This Study and Previous Studies

(1)

Impact on Economic Sustainable Development

Previous research has firmly established the positive influence of education investment on economic sustainable development. Lewis [12] demonstrated that education serves as a catalyst for enhancing human capital and productivity, which are fundamental drivers of economic sustainability. Jorgenson and Fraumeni [13] conducted an in-depth analysis on the relationship between education investment, human capital, and U.S. economic growth, concluding that educational investment is a significant contributor to the nation’s long-term economic development. Zhang [17] further emphasized the role of education investment in improving human capital quality. A well-educated workforce is more productive, adaptable to technological changes, and capable of driving technological innovation, which in turn optimizes the national economic structure by promoting the shift from low-value-added to high-value-added industries.

In the current study, the findings present a more complex picture. The one-period lagged Chinese educational investment variable (dei − 1) has a negative impact on the ratio of education funding to GDP (dei) and per capita schooling years (dlc). This seems to deviate from the consistent positive relationship reported in previous studies. One possible reason for this discrepancy could be the short-term adjustment mechanisms within the education system. In the short run, an increase in education investment might face challenges such as inefficiencies in resource allocation. For example, new educational facilities might not be fully utilized immediately, or there could be a time lag in training and deploying qualified teachers.

However, the two-period lagged variable (dei − 2) can increase per capita schooling years, facilitating talent capital accumulation. This is in line with the general conclusion of previous studies that education investment is beneficial for economic development in the long run. The time lag allows for the proper implementation and adjustment of educational policies and resource allocation, enabling the positive effects of education investment to materialize.

In the case of the United States, the one-period lagged American educational investment variable (duei − 1) promotes its own growth in the current year. This is consistent with the idea in previous studies that education investment can drive economic-related growth. The well-developed education system in the United States may have more efficient mechanisms for translating investment into growth in the short term, such as a more flexible labor market and a higher degree of innovation-driven economic development.

(2)

Influence on Social Sustainable Development

A significant body of previous research has highlighted the positive impact of education investment on social sustainable development. Adams and Adams [21] found that education has a far-reaching positive impact on social development, which is a cornerstone of sustainable development from a social perspective. Chen et al. [24] concluded that education investment can promote social justice through knowledge dissemination and behavior guidance. By providing equal educational opportunities, education can empower individuals from different social backgrounds, reducing social inequality. Yang and Yu [23] showed that higher education investment is associated with more balanced regional development. Education can attract talent and resources to less-developed regions, promoting economic and social development in those areas.

In the Chinese context of this study, one-period lagged educational investment (dei − 1) reduces the Gini coefficient of per capita disposable income, indicating that it can promote social equality. This is in perfect alignment with the previous conclusion that education investment promotes social justice. The education system in China may be effective in quickly spreading knowledge and skills, which in turn helps to narrow the income gap.

The two-period lagged variable (dei − 2) also promotes social equality. This further validates the long-term positive impact of education investment on social justice. In the United States, the one-period lagged variable (duei − 1) improves social equality, and the two-period lagged variable (duei − 2) promotes social equality-related indicators. These results are consistent with the previous research findings on the positive social impact of education investment. The education system in the United States, although facing some challenges such as educational inequality, still has the ability to contribute to social equality through various educational programs and policies.

(3)

Effect on Ecological Sustainable Development

Previous studies have emphasized the role of education investment in promoting ecological sustainable development. Mo et al. [32] found that education investment can shape ecological awareness through environmental education programs. By educating the public about environmental protection, individuals are more likely to adopt environmentally friendly behaviors. Stanger [33] proposed that integrating ecological literacy into education can promote sustainable development by enhancing ecological awareness and leading to more sustainable behaviors and policies.

In the current study, the results regarding ecological sustainable development are somewhat mixed. The one-period lagged Chinese educational investment variable (dei − 1) has a positive effect on per capita carbon emissions (dec), which seems contrary to the previous view that education investment should promote ecological sustainability. One possible reason for this could be the short-term nature of economic development associated with education investment. In the short run, an increase in education investment may lead to an expansion of economic activities, such as the construction of new educational institutions and the development of related industries. These activities may initially result in higher carbon emissions.

However, the two-period lagged variable (dei − 2) has a less negative impact on ecological development compared to the previous year, showing a trend towards a positive impact on the ecological aspect as time passes. This indicates that as the education system matures and the public’s ecological awareness improves, the positive effects of education investment on ecological sustainability start to emerge.

For the United States, the one-period lagged variable (duei − 1) promotes ecological development, and the two-period lagged variable (duei − 2) promotes carbon emission reduction, which is consistent with the previous studies highlighting the positive role of education investment in ecological sustainability. The more advanced environmental education and policies in the United States may enable the education investment to have a more immediate and positive impact on ecological development.

In conclusion, while there are some discrepancies between the current results and previous studies, especially in the short-term economic and ecological aspects, the long-term trends generally support previous research findings. The differences can be attributed to various factors such as the short-term adjustment mechanisms, the specific characteristics of different education systems, and the complex interactions between education investment, economic development, social progress, and ecological protection. Future research should further explore these factors to better understand the dynamic impact of education investment on sustainable development.

5.3. Limitations

Although the dynamic effects of educational investment on sustainable development have been comprehensively investigated in a multi-dimensional framework based on the comparative studies with VAR model, this research is far from perfect. Constrained by the availability of data, this study has not been conducted on data of recent years like 2021 up to now; renewing the data will be highly valuable for the improvement of this study if possible and available in the future.

Additionally, it is also a pity not to analyze the impacts of economic, social, and ecological development on educational investment, which needs a far and broad research scope and daunting efforts. That is yet for authors to further study in the future.

6. Conclusions and Recommendations

6.1. Research Conclusions

This paper engages with the impact of education investment on sustainable development. With China as a sample and United States as a parallel reference, based on VAR regressions and impulse response analysis, the following conclusions have been reached:

(a)

Theoretically, sustainable development is a sophisticated and dynamic process characterized by a three-dimensional connotation structure encompassing economic, social, and ecological dimensions. Education investment, by enhancing educational capacity and delivering high-quality education services, can positively influence human capital accumulation. This, in turn, drives economic sustainable development. It also promotes social justice, which is the cornerstone of social sustainable development, and contributes to carbon emission reduction, facilitating ecological sustainable development.

(b)

Empirical studies provide partial support for the theoretical hypothesis. Specifically, the VAR regression results and impulse response curves of China and the United States corroborate the theoretical perspective that the impact of educational investment on sustainable development is a dynamic process. The direction and strength of the effect of educational investment on sustainable development vary over time and depend on the development conditions of different countries. This is consistent with the need for a more comprehensive and dynamic analysis of the relationship between education investment and sustainable development, as previous studies have mainly focused on single- or two-dimensional aspects, and discussions on the dynamic impact are still insufficient.

(c)

In the context of China, the previous year’s educational investment can indeed promote current social equality. However, it slightly impedes talent capital accumulation, ecological development, and its own growth. This short-term deviation from the general theoretical expectation may be due to inefficiencies in resource allocation in the short run, as discussed in the comparison with previous studies. For example, new educational facilities may not be fully utilized immediately, or there could be a time lag in training and deploying qualified teachers. The educational investment from the year before last still promotes social equality. Additionally, it can increase per capita schooling years, thereby promoting talent capital accumulation. In terms of coefficients, its negative impact on ecological development is less severe compared to the previous year, and it inhibits the current growth of educational investment to a lesser extent. This shows a declining trend in the strength of its effects, indicating that over time, the positive impacts of education investment on economic and ecological aspects start to emerge, which is in line with the long-term positive relationship between education investment and sustainable development found in previous studies.

6.2. Recommendations

Based on the theoretical analysis and empirical research findings of this paper, the following conclusions are provided as follows:

(1)

Broaden and Diversify Education Investment Sources

The research findings indicate that education investment is crucial for sustainable development across economic, social, and ecological dimensions. However, in many cases, limited funding sources can restrict the scale and effectiveness of education investment. To address this, China should strive to broaden and diversify their education investment channels.

Governments should continue to be the mainstay of education investment. They can increase the proportion of financial funds allocated to education in their budgets, ensuring a stable and growing source of investment, for example, by formulating long-term education investment plans and gradually increasing the percentage of GDP spent on education.

In addition to government funds, social capital should be actively attracted. Governments can introduce a series of preferential policies to encourage enterprises and individuals to invest in education. For enterprises, tax incentives can be provided for those that sponsor educational projects, especially in areas related to sustainable development such as environmental education and vocational training for emerging industries. For individuals, donation-based education funds can be established, and donors can receive certain tax deductions or social recognition.

Public–private partnerships (PPPs) can also be an effective way to mobilize resources. The Chinese government and private enterprises can jointly invest in the construction of education infrastructure, such as schools, training centers, and educational research facilities. This not only shares the financial burden but also combines the advantages of the government’s policy-making and the private sector’s efficiency and innovation.

(2)

Targeted Allocation of Education Investment

The results show that the impact of education investment on sustainable development varies in different regions and for different groups. Therefore, education investment should be targeted to areas where it can have the greatest positive marginal effect on sustainable development.

In underdeveloped regions, such as rural areas, remote areas, and regions with a high proportion of ethnic minorities, more education investment should be directed. This can include building new schools, improving teaching facilities, and providing more teacher training opportunities. By enhancing the education level in these regions, it can promote talent retention and attraction, narrow the development gap between regions, and contribute to social justice and balanced regional development.

For socially disadvantaged groups, such as migrant workers, low-income families, and the elderly, customized education services should be provided. For migrant workers, vocational training programs can be developed to improve their employment skills and income levels. For low-income families, scholarships and subsidies can be provided to ensure that their children have equal access to quality education. For the elderly, continuing education courses can be offered to improve their quality of life and social participation.

In the field of ecological and environmental protection, more education investment is needed. This can involve integrating environmental education into the formal education curriculum at all levels, from primary schools to universities. Specialized training programs can also be established for environmental protection professionals, and research projects on sustainable development-related topics such as carbon emission reduction and ecological restoration can be funded.

(3)

Implement Dynamic Adjustment of Education Investment

The dynamic nature of the impact of education investment on sustainable development is clearly demonstrated in the research. To make the most of education investment, a dynamic adjustment mechanism should be established.

A comprehensive monitoring and evaluation system should be set up to track the impact of education investment on various aspects of sustainable development, including economic growth, social equality, and ecological protection. This system can collect and analyze relevant data regularly, such as student performance, employment rates, and environmental indicators. Based on the evaluation results, the direction and intensity of education investment can be adjusted in a timely manner.

If the data show that a certain area or field of education investment is not achieving the expected results, the investment can be redirected to more effective areas. For example, if an education project in a particular region is not effectively promoting talent capital accumulation, the funds can be reallocated to other regions or projects with higher potential.

In terms of the term structure of education investment, a balance should be struck between long-term and short-term goals. Long-term investment should be committed to building a solid foundation for education and sustainable development, such as improving the overall quality of the education system. At the same time, short-term flexible adjustment mechanisms should be in place to respond to immediate needs and emerging challenges. This way, the periodic inefficiencies of education investment can be minimized, and the potential of education investment in promoting sustainable development can be fully realized.