*2.1. Economic Growth Model*

Solow–Swan growth model is one of the classical models of economic development, which is also known as neoclassical economic growth model or exogenous economic growth model. It was developed by Solow to theoretically analyze the relationship between savings, capital accumulation, and economic growth within the framework of neoclassical economics [6]. The basic form of Solow–Swan model is as follows:

$$\mathbf{Y} = \mathbf{A} \mathbf{A}^{\alpha} L^{1-\alpha}. \tag{1}$$

Y refers to the economic growth measured by GDP, while the three independent variables *K*, *L*, and A, respectively, represent capital, labor, and other factors in production such as technological development. This fundamental model has been developed in later research, mostly by separating other influencing factors from the variable A. For example, Barro and Sala-i-Martin [7] modified this model by taking knowledge and technology (variable T) into account:

$$\mathbf{Y}(\mathbf{t}) = \mathbf{F}[\mathbf{K}(\mathbf{t}), \ \mathbf{L}(\mathbf{t}), \ \mathbf{T}(\mathbf{t})]. \tag{2}$$

Mankiw, Romerm and Weil [3] developed a Mankiw–Romer–Weil version of the model considering human capital (variable H) in their analysis:

$$\mathbf{Y}(\mathbf{t}) = \mathbf{F}[\mathbf{K}(\mathbf{t}), \ \mathbf{L}(\mathbf{t}), \ \mathbf{H}(\mathbf{t})]. \tag{3}$$

Furthermore, the "new growth theory" developed by Romer and Lucas highlighted the role of knowledge and technology and suggested technological progress was the determining factor to ensure sustainable economic development.

These modifications of Solow–Swan model may be used in various contexts based on their applicability. The Mankiw version, for instance, can be used to explain why capital always flows from labor-intensive poor countries to the developed countries. In general, the Solow model has been recognized as the most fundamental and commonly used version in pertinent studies of economic growth, which will also be employed in our study.

#### *2.2. Impact of Higher Education on Economic Growth*

Prior research about the impact of education on GDP were often based on human capital theory, according to which human capital is tightly related to education and makes great contribution to economic growth. Lucas proposed that human capital is accumulated by both education in school and learning in practice. School education forms general human capital, which determines, to a large extent, the accumulation of specialized human capital generated via work experience. In workplaces, it is difficult to acquire human capital for people with a low educational level [8]. Therefore, education, serving as a prerequisite for human capital accumulation, is commonly employed as a proxy variable when analyzing the significance of human capital on economic development.

Most of the empirical research consistently concluded the positive effects of education at all levels on economic growth. Kyriacou proved that the stock of human capital was positively related to a nation's economic growth by using the data on average years of schooling as a proxy for human capital and regressing the Lucas endogenous economic growth model [9]. Barro and Lee explored how a set of quantifiable explanatory variables gave rise to differences in growth rates across countries, identifying the significant role of secondary-school attainment in the growth regression [2]. Apart from the general consideration, there were some research looking into the role of education in different contexts. For example, Yang, Gong, and Zhang used the panel data of 29 provinces in China during the period 1985–2000 and analyzed how education influenced economic development with the Solow model, measuring education by the proportion of people at least graduating from junior high school among the population aged 15 and over. It turned out that education had a significant positive impact on economic growth and the coefficient was much higher compared to other similar international empirical studies [10]. Interestingly, Wang, Fan, and Liu measured the educational level with an index calculated from average education years of the working population, and the coefficient in the Solow model indicated much less of an effect of education on economy in China in comparison with other countries like the United States [11]. Notwithstanding the disaccord in different degrees of the importance of education by using different measures, they did agree on the key role of education in promoting economic growth. In addition, there were also some studies comparing the heterogenous effects of different educational levels on economic growth, highlighting that globally, countries with higher enrollment rates in secondary and higher education have grown faster economically [12].

Particularly for the impact from higher education, Yue made an international comparison of the status of higher education and economic development from 1978 to 2017, and the results indicated that there was heterogeneity among different countries, with a more pronounced influence in developed countries [13]. Gyimah-Brempong, Paddison, and Mitiku found a significant relationship between higher education capital and the growth rate of per capita income in African countries [14]. Tin-Chun Lin focused on the role of higher education on economy using data from 1965 to 2000 in Taiwan, and found that higher education, particularly the fields of engineering and natural sciences, contributed greatly to economic growth [15]. Song and Wang showed that the labor productivity of higher education graduates was 2.17 times higher than that of primary education graduates; yet the contribution to economy was limited to the small scale of higher education in China [16]. Despite different empirical conclusions of relevant studies with various databases and methodologies, a general consensus has been reached that higher education promotes the sustainable economic growth and human capital may be the core driving force for sustainability.

#### *2.3. Research Gaps*

#### 2.3.1. Limitations of Traditional GDP as a Measure of Economic Growth

In the existing literature, the traditional national economic accounting system has long been used to estimate the contribution of education to economic growth. Dating back to the 1940s, many Western countries pursued Keynesianism, which inspired government intervention in the national economy. In light of the government involvement, it was essential to analyze economic

development macroscopically. To achieve this goal, Kuznets, Epstein, and Jenks [17] then proposed the concept of gross national product (GNP), from which the gross domestic product (GDP) derived. Later, the United Nations adopted GDP as an important indicator of economic growth worldwide. At that time, the theory of property rights still needed to be further developed and improved, while natural resources and the ecological environment were regarded as free public goods, so they were excluded from the accounting system.

Nevertheless, in recent years, environmental deterioration with the shortage of resources globally has posed an unprecedented and grave threat to human development. This has raised people's awareness of the need for environmental preservation. Under this circumstance, the limitations of traditional GDP became evident. On the one hand, human economic activities have positively influenced society by creating wealth; on the other hand, the same activities have brought in negative effects by hindering the development of social productivity in many forms. For instance, relentless overexploitation has resulted in the diminishing supply of natural resources. Moreover, the discharge of sewage and waste, as well as deforestation, have been major contributors to environmental degradation. These downsides, however, have not received adequate attention. The current national economic accounting system only looks at the bright side of economic activities, which does not reflect practices of sustainable development.

Taking the trajectory of the Chinese economy as an example, in the year 1980, China was the most populous yet one of the poorest countries. Within approximately three decades, however, it has taken a significant leap, becoming the world's second largest economy only after the United States, which was exclaimed by many international media as the "Chinese miracle" [18]. Unexpectedly, in recent decades, the Chinese economic boom has started to tail off, with some social conflicts—previously concealed by the economic prosperity—standing out. One of the major problems was the imbalance in national industrial structure. The central government was forced to cut capacity in sectors such as coal and steel and to facilitate the deleveraging process, which, inevitably led to mass unemployment [19]. Furthermore, China's development has overlooked the destruction of environment and immoderate consumption of non-renewable resources; this, in turn, brought about environmental deterioration, such as more serious water pollution and an increase in carbon dioxide emission. Fortunately, this issue has been receiving more attention than before, given the improved living standards of Chinese people and increased public awareness in environmental protection. With this particular case of China, it is apparent that the traditional measurement of economic development merely by GDP may be misleading, and we are in urgent need to embrace new approaches to gauge economic growth, thereby guaranteeing the long-term benefits for human beings.

#### 2.3.2. Difficulties in Measuring Green GDP in Empirical Analysis

"Green GDP" was conceptualized to consider environment on an equal footing with economy. It refers to the results of economic activities while also considering their impacts on natural resources (mainly including land, forests, minerals, water, and oceans) and the environment as a whole (such as ecological, natural, and human environments) [20]. In other words, green GDP takes into account the costs of resource depletion and environmental degradation incurred in economic activities. Green GDP is regarded as the indicator for sustainable economic development for several reasons. First, it measures the actual achievements in productivity in order to avoid pure pursuit of economic growth rate that neglects the externalities of economic activities. Second, it mirrors the scenarios of social welfare and progress, highlighting the importance of coordinating harmonious development of man and nature. Meanwhile, green GDP helps enhance public awareness in environmental protection and promote the transformation of development patterns. Nevertheless, this does not mean that the traditional GDP should be replaced by green GDP as a better solution. The traditional GDP is still the most important and direct indicator reflecting the levels of national economic development, while green GDP serves as a supplement in an ecological manner.

As early as 1971, the concept of "Eco-Requirement Indication (ERI)" was proposed by the Massachusetts Institute of Technology to reflect the relationship between economic growth and environmental resource pressure [21]. In the 1980s and 1990s, the World Bank tried to spread "green accounting" [22] and established the system of environmental economic account (SEEA) in some countries. However, this approach has not been applied extensively and most countries and regions barely take into account their natural resources and environmental conditions nationwide when assessing the economic growth. For example, China, in 2006, first published the research report of green national economic accounting of 2004, but there were no subsequent reports due to the accounting difficulties and data unavailability.

Generally, most of the previous research on green GDP were still at the exploratory stage, trying to discuss and develop green GDP theoretically considering its calculation difficulties. Boyd discussed the possibility to measure non-market value of natural resources in his article and proposed that national culture and social stability should be included when evaluating green GDP [23]. Li and Fang employed the ecological and geological methods to measure the consumption of global natural resources, with the purpose of calculating the green GDP of different countries [24]. There were also some other scholars who made intensified efforts to calculate green GDP using the input–output model. This model assessed the national inputs and outputs in industry, energy, transportation, and agriculture based on the environmental and economic account of World Bank. On this basis, the scholars adjusted GDP values by considering the actual consumption in various sectors. So far, they have calculated green GDP for different countries and regions, including Australia [25], Austria [26], Brazil [27], and Italy [28,29], the Netherlands [30], Sweden [31], the United Kingdom [32], and the United States [33], etc. Even so, it was still not easy to measure the resources and environmental inputs required in various industries, so this input–output model posed similar challenges in complexity and precision during calculation compared to the previous models. Furthermore, other studies focused on the determinants of green GDP. Talberth and Bohara found that the openness of countries was significantly negatively correlated to national green GDP, while there was a positive correlation between the countries' openness and the difference between their green GDP and traditional GDP [34].

Overall, higher education has positive effects on economic growth. Nevertheless, when measuring economic growth, traditional GDP may neglect some negative effects of production, such as resource depletion and environmental damage; while green GDP, though considering environmental influence simultaneously with the economy, is only theoretically feasible due to the complexity in calculating environmental pollution and the unavailability of data about resource consumption. Our paper aims to fill these gaps by proposing a new approach to indirectly estimate green GDP, and identifying how higher education exerts differential effects on green GDP and on the traditional GDP.
