**3. Research Design**

#### *3.1. Hypotheses*

Our paper proposes a new approach to indirectly estimate green GDP, and based on this indicator, it is designed to address two main questions: (1) How does higher education affect green economic development? (2) Is there any difference of the role higher education plays in green GDP and in the traditional GDP? According to the prior literature, the traditional GDP is inextricably linked with higher education, and it is quite meaningful to evaluate the effect of higher education on green economic growth. Furthermore, to compare the different impacts on green GDP and the traditional GDP will offer us an in-depth understanding of the role of higher education. It is very convincing that countries with higher levels of education on average may have higher quality of human capital and more optimized industrial structures, which allow them to utilize resources in a more efficient and environmentally friendly way. Thus, this paper puts forward two main hypotheses to verify.

**Hypothesis H1:** *Higher education has positive influence on building green economies.*

**Hypothesis H2:** *Green GDP is more responsive to changes in higher education than the traditional GDP.*

#### *3.2. Green GDP Calculation*

Though the concept of green GDP has been proposed long ago, prior research had not made satisfactory achievements, given that there was no sufficient data to support the theoretical models by deducting costs of natural resources and environmental pollution from the traditional GDP. Our paper tries to measure green GDP from the perspective of the efficiency of energy resources utilization, which is regarded as one of the fundamental differences between the traditional and green economic development. In practice, we adopt two variables accordingly, one of which is the rate of energy use, calculating how much monetary output can be produced by one unit of energy resources. The other refers to the ratio of renewable energy of the total, which is more about assessing the damages caused by production. Therefore, we create a new indicator "green GDP" here to assess the development of green economy to some extent:

$$\text{GreenGDP} = \text{GDP} \ast \text{energy} \ast \text{memory}.\tag{4}$$

The variable *energy* is measured by the GDP produced through consuming per unit of energy resources, while *renew* represents the proportion of renewable energy of the total, an indicator of environmental damages. It can reflect the environmental pollutions caused by excessive consumption of fossil fuels and their irreparable dangers and damage to human society. Usually, the higher the share of renewable energy is, the more clean energy can be used and the less waste will be produced. Here, the term "green GDP" stands for both the domestic productivity and energy efficiency as well as environmental preservation of a country or region.

In this way, the rates of energy utilization and the proportion of renewable resources are much more accessible. However, this method has obvious weaknesses. It cannot be considered as the real green output of a country, but merely an indicator logically related to green GDP, so the absolute value generated from this equation has little practical significance. In spite of this, the indicator still reveals the costs in resources and environment to a certain extent. When studying the economic growth of countries, usually we are more concerned about the relative changes than the absolute values of economic output. Therefore, it is still meaningful to focus on the diachronic changes and cross-country comparison by applying this approach in economic analysis.

#### *3.3. Modified Solow–Swan Model with Higher Education*

In order to identify the influence of higher education on green GDP, this paper first incorporates variables of higher education into the Solow model. Based on the human capital theory, economic development depends not only on the quantity of labor, but also on their quality. In this way, it is not enough to just include the number of human capitals, namely the variable *L* in the Solow model. The quality of labor should also be taken into account, which can be reflected by the overall educational level of a country.

The newly proposed form can be written as follows:

$$
\Upsilon = \mathcal{A} \mathcal{K}^{\alpha} L^{\beta} E^{\gamma}.\tag{5}
$$

Y here refers to either the traditional GDP, or the green GDP, and the independent variables *K*, *L*, and A respectively stand for capital, labor, and other factors in production. The variable *E* represents the quality of labor and its proxy variable in our research is the gross enrollment rate of higher education.

#### *3.4. Modelling the Impact of Higher Education on Green GDP*

The empirical analysis of our paper mainly consists of two parts. The goal of the first stage is to verify the first hypothesis mentioned above, i.e., whether higher education has positive influence on building green economies. We standardize the traditional and green GDP of countries and regions in our sample using the following equations.

$$\text{standardized GDP} = \frac{\log(GDP) - \log(GDP)}{SD(\log(GDP))},\tag{6}$$

$$\text{standardized green GDP} = \frac{\log(\text{green GDP}) - \overline{\log(\text{green GDP})}}{SD(\log(\text{green GDP}))} \tag{7}$$

The standardized GDP and green GDP are both lognormal distributed with a mean of 0 and variance of 1. The values of normalized GDP and green GDP represent the position of the original values in the overall distribution. In this way, the differences between the standardized green and traditional GDP can be a signal to determine whether the national economy is greener.

$$GAP = \text{standardized green GDP} - \text{standardized GDP} \tag{8}$$

If the difference, or the variable *GAP*, is positive, then the country's green GDP ranks higher in the overall distribution than the conventional GDP, indicating its national economy is green; otherwise, if *GAP* is negative, the nation's GDP outranks its green GDP, which means the corresponding economic growth is not so sustainable and environmentally friendly. Here, we build a general linear regression of *GAP* on higher education.

$$GAP = \pi\_0 + \pi\_1 \ast K + \pi\_2 \ast L + \pi\_3 \ast E \tag{9}$$

In the above equation, *GAP* serves as the dependent variable. The independent variables *K* and *L* represents capital and labor separately; while *E* stands for the gross enrollment rate of higher education, whose coefficient reveals the effect of higher education in the national green economic development.

The second part compares the contribution rates of higher education to the traditional and green GDP growth. By taking the logarithm on both sides of Equation (5), we build log–log models of green GDP as well as the traditional GDP.

$$
\ln(\text{GDP}) = \ln(\text{A}) + \alpha\_1 \ln(\text{K}) + \beta\_1 \ln(\text{L}) + \gamma\_1 \ln(E) \tag{10}
$$

$$
\ln(\text{Green GDP}) = \ln(\text{A}) + \alpha\_2 \ln(\text{K}) + \beta\_2 \ln(\text{L}) + \gamma\_2 \ln(E) \tag{11}
$$

After regressing the traditional GDP and green GDP separately on capital, labor and higher education, we plan to compare the parameters of these two models in order to explore differential impacts of factors pertaining to production on the green and traditional GDP. It should be noted that the output of these two models are both elasticity coefficients, measuring the percentage change in the traditional GDP and in the green GDP as a result of a percentage change in capital per capita, labor per capita, and enrollment rate of higher education, respectively. Given that elasticity is a dimensionless measure of the sensitivity or responsiveness of one variable to changes in another, the coefficients in the two models are easily interpreted and compared across categories.

### **4. Data and Empirical Results**
