A Study of GGDP Transition Impact on the Sustainable Development by Mathematical Modelling Investigation

Abstract

GDP is a common and essential indicator for evaluating a country’s overall economy. However, environmental issues may be overlooked in the pursuit of GDP growth for some countries. It may be beneficial to adopt more sustainable criteria for assessing economic health. In this study, green GDP (GGDP) is discussed using mathematical approaches. Multiple dataset indicators were selected for the evaluation of GGDP and its impact on climate mitigation. The k-means clustering algorithm was utilized to classify 16 countries into three distinct categories for specific analysis. The potential impact of transitioning to GGDP was investigated through changes in a quantitative parameter, the climate impact factor. Ridge regression was applied to predict the impact of switching to GGDP for the three country categories. The consequences of transitioning to GGDP on the quantified improvement of climate indicators were graphically demonstrated over time on a global scale. The entropy weight method (EWM) and TOPSIS were used to obtain the value. Countries in category 2, as divided by k-means clustering, were predicted to show a greater improvement in scores as one of the world’s largest carbon emitters, China, which belongs to category 2 countries, plays a significant role in global climate governance. A specific analysis of China was performed after obtaining the EWM-TOPSIS results. Gray relational analysis and Pearson correlation were carried out to analyze the relationships between specific indicators, followed by a prediction of CO₂ emissions based on the analyzed critical indicators.

1. Introduction

Gross domestic product (GDP) is widely recognized as a commonly measured indicator of a nation’s economic situation [1]. However, it fails to reflect a country’s true economic well-being because it does not account for natural resource depletion or environmental degradation [2,3]. For instance, a country with abundant fisheries may boost its immediate economic output by increasing its fish catch. This action could appear to enhance GDP, yet it overlooks the loss of biodiversity and other adverse environmental impacts. If traditional GDP measurements are applied, the country would not face penalties for these environmentally harmful practices. Consequently, GDP can be a misleading measure of national progress [4]. It is imperative for countries to adopt more comprehensive metrics that better capture the true state of their economic health and sustainability [5].

To explore the connections between the environment and the economy, significant focus has been placed on “green” GDP (GGDP). GGDP has emerged as the primary indicator of economic health, shaping policies that promote environmental well-being. This shift is expected to have a significant impact on dealing with the climate crisis by accounting for natural resource factors. Assessing the impact of GGDP may also be essential in various aspects, such as serving as a primary measure of a nation’s economic health [6,7]. Could GGDP, which incorporates environmental and sustainability factors, serve as a more accurate measure than the current conventional GDP? To answer this question, the potential benefits and drawbacks of replacing traditional GDP with GGDP must be carefully evaluated. The primary approach to calculating GGDP involves deducting costs associated with social and environmental factors, like resource depletion and pollution, from the conventional GDP measurement. This adjustment provides a more accurate measure of sustainable economic progress. It accounts for the negative consequences of economic activities on the climate and society. In essence, GGDP offers a holistic view of a nation’s economic health, emphasizing long-term sustainability over short-term gains [8]. Some critics argue that assigning value to certain environmental outputs can be challenging because these assets do not exist in traditional markets and are not tradable [9,10]. This approach raises concerns about the accuracy and reliability of GGDP measures. Other critics contend that the sustainability reflected by GGDP should be further evaluated [11].

An array of research has focused on GGDP as a pivotal measure for sustainable economic growth. Talberth and Bohara pioneered models that highlighted the discrepancies between traditional GDP and GGDP, analyzing data from eight different countries [12]. Following this, Boyd [13] explored how non-market environmental benefits should be incorporated into GGDP calculations, enhancing their accuracy and relevance. Subsequently, Xu et al. [14] developed a new methodology for GGDP accounting that emphasizes ecosystem services, exemplified through a case study in Wuyishan, China. This approach was further explored by assessing the challenges and progress of GGDP implementation in China, particularly within the context of ecological modernization [15]. Further contributions have studied the interplay between China’s energy use, environmental health, and economic growth [16]. This research underscored the importance of integrating industrial ecology into GGDP frameworks to foster sustainable development. Continuing this trajectory, Li and Fang [17] developed techniques to correlate ecosystem service values with GDP measurements on multiple scales—from local to global. More recent studies have expanded the application of GGDP. Kunanuntakij et al. [18] tailored a GGDP model for Thailand using environmentally adjusted input–output models, which helped understand the environmental impacts of various economic activities. Gao et al. [19] examined how higher education could contribute to a green economy, proposing innovative methods to estimate GGDP indirectly. More recently, Sheikh et al. [20] and Sun et al. [21] broadened the scope of GGDP analysis. Sheikh analyzed how India’s trade openness influences sustainable development, whereas Sun provided a detailed assessment of the resource and environmental costs of China’s rapid growth through an integrated environment and economic accounting framework. These studies collectively enhance our understanding of GGDP and underscore its critical role in tracking and fostering sustainable economic development.

Several studies have determined the GGDP for both developed and developing countries, analyzing different stages of development [6]. They have also compared the GGDP of countries at various development levels to provide insights for sustainable development [22,23]. The transition from GDP to GGDP is worth more thorough and quantitative studies. Hence, we developed a comprehensive model to calculate GGDP and estimate the impacts by introducing GGDP calculations using historical data. Our research aimed to establish a robust model based on GGDP calculations, categorizing countries into various developmental stages. By analyzing data from different historical periods, we explored the potential of GGDP metrics and predictive analyses for climate issues. This study underscores the importance of GGDP in promoting sustainable development and presents an approach for future studies on economic sustainability.

Consider the adoption of GGDP as the major indicator of a nation’s development goals. What changes should we anticipate? What would be the environmental impacts of such a shift? The evaluation method should be objective. Some data-driven expert-neutral weighting could be adopted in comprehensive evaluation problems [24]. In our modeling process for analyzing the impact of transitioning to GGDP, an objective weighting method and the technique for order preference by similarity to ideal solution (EWM-TOPSIS) methods were combined [25] to assess the impacts. This combined method has been effectively used in various fields for quantitative evaluation and decision-making, including the assessment of power data assets and enterprise sustainable development [26,27,28,29]. The method has demonstrated precision in capturing the real dynamics of business operations, and it has also been used to evaluate the societal benefits of investments through an integrated EWM-TOPSIS model [30]. The EWM-TOPSIS method has proven to be a feasible tool for systematic and effective decision-making across various sectors. This approach allowed us to quantify and compare environmental impacts, ensuring a thorough evaluation of the potential consequences of transitioning to GGDP in different scenarios.

In this study, we first developed an evaluation approach of GGDP. Since countries’ economic statuses vary and can be differentiated through effective clustering methods [31], we divided countries into three categories by k-means clustering based on GGDP indicators. A mathematical model was established to predict the potential consequences of climate mitigation using ridge regression [32] for the three categories. Then, the potential advantages of pursuing GGDP were analyzed across different time periods for countries worldwide. The economic development of China has distinctive characteristics [33]. As China experiences rapid economic growth, environmental pollution becomes a significant issue. Consequently, sustainable development has gained greater importance [34,35]. As one of the world’s largest carbon emitters, China plays a pivotal role in global climate governance. The country’s ability to balance economic growth with environmental protection influences not only its own environmental quality and ecological security but also sets a precedent for global environmental governance strategies. This balance is crucial in shaping how nations worldwide address the dual challenges of economic development and environmental sustainability. Hence, from the countries divided by k-means clustering, we selected China for specific analysis. It was necessary to establish a theoretical framework to analyze the economic indicators and environmental accounts for sustainable development. Alfsen and Greaker favored the comprehensive national wealth mathematical approach [36]. In our study, the indicators related to natural resource utilization and GDP changes were analyzed using Gray relational analysis and Pearson correlation analysis.

The rest of this paper is structured as follows: Section 2 describes the data source and methodology used for the analysis. Section 3 presents the regression results for different types of countries. Section 4 shows the results of the global analysis, followed by a specific analysis of China. Section 5 concludes this study and demonstrates our limitations.

2. Analysis of GGDP and Impact of Climate Mitigation

2.1. GGDP

First, the mathematical calculation of GGDP was established. Based on its definition, four aspects of indicators were selected: economy, resources, environment, and people’s livelihood. Simultaneously, we categorized the countries into three groups to assess the impact of transitioning to GGDP on different countries. The GGDP calculation method aims to meet the following requirements: it must be applicable to countries at various stages of development, accurately represent impacts on climate mitigation, and be both stable and comprehensive.

Currently, there are two mainstream definitions of GGDP. The first defines GGDP as GDP plus the valuation of ecosystem services, which is still in the conceptualization stage. The second definition considers GGDP as GDP, excluding the costs of environmental depletion and natural resources. The second definition was adopted in this study. The abbreviated notations is listed in

Table 1. Abbreviated notations are used in this work.

Symbol	Description
NRC	Natural resource cost
EDC	Environmental degradation cost
CIF	Climate impact factor
NRCe	Cost of energy sources (non-renewable)
NRCw	Cost of water resources
NRCs	Cost of soil resources
FCA	Forest coverage area
REC	Renewable energy source consumption
Pa	Exhaust emissions environmental degradation costs
CE	CO2 emissions
FP	Fishery production
FW	Renewable freshwater resources
GI	Deviation between the GGDP growth rate and the GDP growth rate index

.

Definition 1.

The economic growth indicator GGDP is as follows:

$$\mathrm{GGDP}=\mathrm{GDP}-\mathrm{NRC}-\mathrm{EDC},$$

(1)

where NRC indicates the natural resource cost and EDC indicates the environmental degradation cost. The NRC is composed of several components, including the cost of non-renewable energy sources (indicated as NRCe), the cost of water resources (indicated as NRCw), and the cost of soil resources (indicated as NRCs). Due to the limited available data sources, EDC only takes into account the cost of air pollution. To demonstrate the potential impact of transitioning to GGDP on climate mitigation, a global impact factor considering climate factors was defined and evaluated using a potential impact of GGDP on climate mitigation prediction (PIGCMP) model indicator system in the following sections.

The percentage difference between the GGDP and GDP growth rate index GI was adopted as the deviation of GDP to measure the degree of importance of the country’s environmental impact during the pursuit of economic development. The formula for the deviation is as follows:

$${GI}_i=k_i-w_i,$$

(2)

where $w_i$ denotes the growth rate of GDP in year $i$ and $k_i$ denotes the growth rate of GGDP in year i.

2.2. k-Means Clustering for Country Classification and Data Preprocessing

This mathematical modeling study aimed to investigate the impacts of transitioning to GGDP for countries with different levels of development. Different countries adopt different policies and receive corresponding feedback. This study aimed to evaluate whether GGDP can better reflect the impact on countries with different development statuses. GGDP transition in this paper represents using GGDP as the goal for development. By transiting into the pursuit of GGDP development at different times for different countries, we may have different potential impacts evaluated from a perspective of sustainable development. Sixteen countries were selected for this preliminary study, representing both developed and developing countries according to UN standards. The data were accessed from public databases of the National Bureau of Statistics of China, Our World in Data, Eurostat, and the World Bank and spanned from 2012 to 2020. Most data were comprehensive, including population, renewable freshwater resources, CO₂ emissions, and forest area. However, the coal, oil, and natural gas consumption data for some countries are not comprehensive. The mean values of the variables were imputed for the missing data in the modeling process. These mean values were calculated by averaging data from neighboring years.

K-means clustering, an unsupervised machine learning method, was used to classify countries with different levels of development. The datasets, including indicators for the determination of GGDP in different countries, were supplied for the k-means clustering algorithm [37].

$$\sum _{i=1}^{\mathrm{n}}\sum _{k=1}^{\mathrm{m}}{r}_{ik}‖{p_i-c_k‖}^2$$

(3)

For the n data points, $r_{ik}$ was 1 when point $p_i$ was located in a cluster with centroid $c_k$. The m clusters were generated based on the distance to the centroids formed. Principal component analysis was conducted to downscale these datasets, and a 2D clustering figure was generated. The countries were iteratively divided into several clusters (Figure 1).

The countries were divided into three categories (

Table 2. Division of 16 countries using the k-means clustering algorithm.

Category	Country
1	France, UK, Israel, Japan, Finland, Sweden, Netherlands, Australia, USA
2	Mexico, Chile, China, Bulgaria
3	Croatia, Turkey, Poland

). The developed countries were categorized into cluster 1, while the developing countries were divided into two clusters based on their industrial structure, resource consumption, and services. GGDP and the predicted impact of transitioning to GGDP were determined for the three country categories.

2.3. The Potential Impact of GGDP on the Climate Mitigation Prediction (PIGCMP) Model

To understand the impact of GGDP on climate mitigation, we established a PIGCMP model to identify changes in national development goals and the potential climate impact. The adoption of GGDP may benefit the goal of sustainable development and climate issues. After establishing an indicator system of the model, we defined the combined global impact caused by using the GGDP evaluation method. Then, the entropy weight method was used to determine the weight of the global impact caused by adopting GGDP, and ridge regression was used to perform the prediction and analysis. Finally, we make predictions for the three categories of countries adopting GGDP as the primary development goal. The PIGCMP model metrics considered three major factors in conducting the analysis. When the primary indicators were analyzed, their secondary indicators were selected. The indicators included (1) GDP, representing the economic situation and development level, which could be further divided into values related to the primary, secondary, and tertiary sectors for later analysis; (2) natural resource consumption costs, referring to the reduction in the number of natural resource entities that occur as a result of the exploitation of natural resources, including fossil energy consumption, water, and soil cost; (3) environmental degradation costs, representing the actual cost of environmental damage, including the cost of exhaust air emissions associated with economic development (

Table 3. The primary and secondary indicators to determine the impact of transitioning to GGDP.

Level 1	Level 2	Description
Economy	GDP	Gross domestic product
Natural Resources Cost	NRCe	Cost of energy sources (non-renewable)
	NRCw	Cost of water resources
	NRCs	Cost of soil resources
Environment Degradation Cost	Pa	Exhaust emissions Environmental degradation costs

).

To assess the global impact, four indicators directly related to climate mitigation (

Table 4. CIF dependent variable indicators.

Property Category	Level 1	Level 2 Indicators	Description
Cost attributes	Air	CE	CO2 emissions
Benefit attributes	Forest	FCA	Forest coverage area
	Energy	REC	Renewable energy source consumption
	Fishery	FP	Total fishery production
	Freshwater	FW	Renewable freshwater resources

) were selected from the datasets. We adopted the CIF as the impact on climate change based on these indicators [38].

Definition 2.

The CIF that measures the extent of climate mitigation is as follows:

CIF = W1 * CE + W2 * FCA + W3 * REC + W4 * FP + W5 * FW.

(4)

2.4. Prediction Using the PIGCMP Model

Countries at different levels of development have different economic structures. Many developed countries have shifted their high-emission industries and thus have low levels of environmental pollution. Some developing countries actively expand their secondary industries, leading to high levels of environmental pollution. In contrast, other developing countries may rely on the tertiary industry sector. These three categories of countries have distinct economic and environmental goals when pursuing GGDP as a replacement for GDP, according to the GGDP evaluation index. Therefore, the PIGCMP model was established and used for prediction.

To identify the different development goals for the three categories of countries, the entropy weight method (EWM) was adopted to calculate the weights of the global impact indicators (Table 4). Then, we used the obtained GGDP values and related indicators to predict the CIF.

2.4.1. Calculation of Indicator Weights: EWM

EWM, an objective weighting analysis method, was used to quantify the weights of the PIGCMP model and measure the uncertainty. A smaller entropy represents a larger amount of information, indicating less uncertainty. The determined value of an indicator can quantify its dispersion degree. A smaller value corresponds to a higher dispersion degree and, thus, a greater impact of this indicator. The weight calculation steps were as follows:

Step 1: Each indicator was normalized according to the number of each option.

For positive indicators,

$$x_{ij}^{\mathrm{’}}={\displaystyle \frac{X_{ij}-\mathrm{m}\mathrm{i}\mathrm{n}\left(X_{1j},X_{2j},...,X_{nj}\right)}{\mathrm{m}\mathrm{a}\mathrm{x}\left(X_{1j},X_{2j},...,X_{nj}\right)-\mathrm{m}\mathrm{i}\mathrm{n}\left(X_{1j},X_{2j},...,X_{nj}\right)}}.$$

(5)

For negative indicators,

$$x_{ij}^{\mathrm{’}}={\displaystyle \frac{\mathrm{m}\mathrm{a}\mathrm{x}\left(X_{1j},X_{2j},...,X_{nj}\right)-X_{ij}}{\mathrm{m}\mathrm{a}\mathrm{x}\left(X_{1j},X_{2j},...,X_{nj}\right)-\mathrm{m}\mathrm{i}\mathrm{n}\left(X_{1j},X_{2j},...,X_{nj}\right)}}.$$

(6)

Step 2: $j$ indicator’s entropy value was found;

$$e_j=-k{\sum }_{i=1}^n{p}_{ij}ln\left(p_{ij}\right),j=1,...,m.$$

(7)

Step 3: The information entropy redundancy (variance) was determined;

$$w_j={\displaystyle \frac{d_j}{\sum _{j=1}^m{d}_j}},j=1,\cdots ,m.$$

(8)

Step 4: The information entropy redundancy (variance) was obtained;

$$w_j={\displaystyle \frac{d_j}{\sum _{j=1}^m{d}_j}},j=1,\cdots ,m.$$

(9)

Step 5: A composite score of each country was achieved;

$$s_i={\sum }_{j=1}^m{w}_j{x}_{ij},i=1,\cdots n.$$

(10)

Based on the score of each impact indicator, we obtained the importance ranking of all indicators.

2.4.2. PIGCMP Prediction Results: Ridge Regression

Ridge regression [39] was used to predict the impact of the GGDP transition. The procedure for ridge regression was as follows:

Step 1: We set up the regression analysis in the following form:

$$y=\sum _{j=1}^p{\beta }_j{x}_j+{\beta }_0$$

(11)

Step 2: The least squares method was used to obtain the solution;

$$\widehat{\beta }=arg\mathrm{m}\mathrm{i}{\mathrm{n}}_{\beta }{\left(y_i-{\beta }_0-{\sum }_{j=1}^p{\beta }_i{x}_i\right)}^2,.$$

(12)

Step 3: We added a penalty term to the minimization objective;

$${\widehat{\beta }}^{bridge}=arg\mathrm{m}\mathrm{i}{\mathrm{n}}_{\beta }\left\{\sum _{i=1}^N{\left(y_i-{\beta }_0-{\sum }_{j=1}^p{\beta }_i{x}_i\right)}^2+\lambda \sum _{j=1}^p{\beta }_j^2\right\},$$

(13)

where λ is a parameter to be determined by regression.

Step 4: A ridge plot was conducted to determine the K-value. This ridge plot determines the minimum value when the regression coefficients of the independent variables tend to stabilize. Normally, a smaller bias is associated with a smaller K-value.

By analyzing the F-value, we determined whether the model was significant (p < 0.05). A regression relationship exists between the transition to GGDP and the CIF for the analyzed countries if it is significant.

Step 5: The formula of the predicted CIF with the transition to GGDP was fitted by regression.

3. CIF Analysis

In order to more accurately reflect the global impact of adopting GGDP, the PIGCMP model was used for the three categories of countries determined by the k-means clustering method. First, the GGDP values were obtained from the GGDP formula. Then, for each category of countries, we analyzed the forecast results using the PIGCMP model with GGDP.

3.1. The Impact of GGDP Transition on the CIF

Forecasts for category 1 countries. All countries in category 1 were developed countries. The model fits well, and the CIF formula for this category of countries was determined based on ridge regression. The predicted CIF obtained by transitioning to GGDP increased by 9.2% for category 1 countries.

CIF = 0.038 + 0.272 × GDP + 0.194 × NRCe + 0.302 × NRCw + 0.235 × NRCs − 0.639 × EDC.

(14)

The results show that with the introduction of K = 0.094, the model fit the dependent variable CIF (which may represent a particular economic or environmental indicator) extremely well, with both R² and adjusted R² close to 1 (0.975 and 0.974, respectively), suggesting that the model can explain the majority of the variability in the dependent variable. The F-statistic was significant (593.495, p < 0.001), strongly supporting the model’s overall validity. The effect of GDP on the CIF (t = 14.264, p < 0.001) suggests that as GDP grows, the level of the CIF also increases significantly, in line with the expected positive drive of economic growth on environmental or economic indicators. NRCw likewise had a significantly positive effect (t = 17.585, p < 0.001), and its coefficient value indicates that ECW is one of the important drivers of changes in the CIF. NRCs had a relatively non-significant effect (t = 1.335, p = 0.186), suggesting that changes in controlling for the others have a weaker direct effect on the CIF. NRCe had a significant positive effect on the CIF (t = 6.428, p < 0.001), indicating that improvements in NRCe contribute positively to the CIF. EDC had a significant positive effect on the CIF (t = 13.846, p < 0.001) with a large coefficient value, indicating that EDC is one of the key factors influencing changes in the CIF.

For category 2 countries (developing countries with a good secondary sector, e.g., China), the CIF was obtained from the forecast and increased by 32.5%. The ridge regression model outlines the formula as follows:

CIF = 0.064 + 0.221 × GDP + 0.226 × NRCe + 0.269 × NRCw + 0.078 × NRCs − 0.178 × EDC.

(15)

For category 3 countries, the CIF was obtained from the forecast and increased by 20.1%. The ridge regression model outlines the formula as follows:

CIF = 0.064 + 0.221 × GDP + 0.226 × NRCe + 0.269 × NRCw + 0.078 × NRCs − 0.178 × EDC.

(16)

3.2. Weightings of the CIF

We can obtain the CIF indicator weights for each country using EWM (

Table 5. CIF indicator weights by country categories are determined using EWM.

Indicator	Cluster 1 Countries (Developed Countries)	Cluster 2 Countries (Developing Countries)	Cluster 3 Countries (Developing Countries)
CE	2.7	5.5	13.5
FCA	26	17.8	19.4
REC	23.8	32.2	16.7
FP	21.7	29.2	18.9
FW	25.8	15.2	31.5

). The weights allow us to account for the relative importance of each country category in the generation of changes in air, water, forests, and human activities. The leading impact of the indicator on the CIF in category 2 countries (developing countries with a large secondary sector, including China) was energy consumption. Air pollution was found in developing countries with a large share of the tertiary sector. The largest decline in air pollution was found in developed countries (category 1 countries).

3.3. Error Analysis

We performed an error analysis on the global impact forecasting using the model for category 2 countries with a relatively large secondary sector. Fifteen data points were randomly selected for the predicted data, and they were dropped into the model to obtain the predicted values. The real values and the simulated forecasting were compared to demonstrate the model’s fitness. As shown in Figure 2, the red line represents the true values, and the blue line represents the predicted values, and the two lines basically overlap. Therefore, the model we built fits well with less error and meets the requirements for the analysis.

4. GGDP Transition Analysis

To determine whether it is worth it for countries to adopt the GGDP transition at the proper stage, we defined a value of deviation. The smaller the value of deviation, the more worthwhile it is for this country to adopt GGDP when aiming for sustainable development. This study divided time into three stages: 2012, 2016, and 2020. EWM-TOPSIS was further adopted to evaluate GI and study the potential advantages of transitioning to GGDP.

4.1. Entropy Weight Method and Technique for Order Preference by Similarity to Ideal Solution (EWM-TOPSIS)

The TOPSIS method [40], a comprehensive evaluation method, utilizes the information within an entire group of data. The results demonstrate the differences between the schemes to be evaluated. The fundamental procedure is to construct a normalization matrix following the same trend as the original data, followed by determining the difference between the object and the best and worst vectors so as to measure the difference between the evaluation objects. Assuming that there are n objects to be assessed and m indicators, the procedure can be described as follows:

Step 1: Raw data with trending were determined.

We determined the indicators in the indicator system (high or low superiority). We followed different formulas for the forwarding process based on the different types of indicators. A matrix $X$ was established in which $X_{ij}$ indicates the value of indicator j for the object i.

Step 2: The matrix $X$ was normalized;

$$Z_{ij}={\displaystyle \frac{X_{ij}}{\sqrt{{\sum }_{k=1}^n}{\left(X_{ij}\right)}^2}}.$$

(17)

Step 3: The difference between each evaluation index and the optimal and inferior vectors was determined;

$$D_i^{+}=\sqrt{\sum _{j=1}^m{w}_j{\left(Z_j^{+}-z_{ij}\right)}^2},D_i^{-}=\sqrt{\sum _{j=1}^m{w}_j{\left(Z_j^{-}-z_{ij}\right)}^2.}$$

(18)

where $w_j$ is the weight of indicator j.

Step 4: The distance between the object and the ideal solution was measured;

$$C_i={\displaystyle \frac{D_i^{-}}{D_i^{+}+D_i^{-}}}.$$

(19)

The EWM-TOPSIS outcome $C_i$ value corresponds to the evaluated GI of a specific country at a certain time.

4.2. GI Value Evaluation for Different Country Categories

Based on the EWM-TOPSIS results, we plotted the GI value of the major countries in 2012, 2016, and 2020 at four-year intervals, representing stage 1, stage 2, and stage 3, respectively (Figure 3). The lighter the color, the more urgent it is to transition to GGDP when aiming for sustainable development. Among the 16 countries classified by the k-means clustering method, the average deviation scores for developed countries (category 1) and developing countries (categories 2 and 3) were 2.8 and 1.3 in 2012, respectively. In 2016 (stage 2), the average deviation values for the three categories of countries were 3.2, 1.58, and 2.0, respectively. In 2020, the average deviation values for the three categories of countries were 3.6, 1.73, and 2.2, respectively. The category 1 countries, all developed countries, demonstrated better development, balancing economy and environment. For the category 2 countries, they demonstrated development toward more sustainable development with gradually increasing average deviation values. There is still some gap due to the structure of the economy industries.

It is worth noting that the results are limited by data constraints. To accurately map and account for GGDP, spatial information data collection should be important. In calculating global economic indicators, nighttime imagery datasets were used to map GGDP globally for the year 2009 [17]. For the regression work we conducted, the data changes over the year are needed. The modeling work can further incorporate satellite imagery information into the data source under the circumstance that a reliable relation is established between the collected image information and the economic indicators.

Figure 4 shows the transition weights of indicators for different country categories and their impact on climate mitigation (CIF). On the whole, developed countries have advantages in terms of good economic development and low energy and environmental losses. Category 1 countries achieved higher scores alongside development. Many countries in category 1 demonstrated the advantages of good secondary sector development and the disadvantages of high energy and environmental losses.

We increased the weight of the advantage indicators and decreased the weight of the disadvantage indicators for each of the three country categories by 10% and substituted the improved GGDP values into the PIGCMP model. The predicted deviation values are demonstrated in Figure 5. According to the simulation, category 1 (developed) countries demonstrated greater sustainable development. However, all countries should pay attention to their energy consumption. Change in developing countries, particularly category 2 countries, will bring a greater increase in GI scores.

4.3. Analysis of the Changes in China’s Transition to GGDP

Among the category 2 countries, China was selected for further analysis. GRA and Pearson correlation [41] were used to determine the major indicators during the transition to GGDP in China based on the previous two models. After conducting Gray relational analysis in the secondary sector of China, CO₂ emissions and natural resource consumption were shown to have a more significant impact on the GGDP transition outcome (

Table 6. The Gray relational analysis value for each indicator.

Indicator	CO2 Emissions	Natural Resource Consumption	Percentage of First Sector	Percentage of Secondary Sector	Percentage of Tertiary Sector
GRA Value	0.996	0.995	0.61	0.837	0.581

). Pearson correlation was carried out for these indicators(Figure 6).

Chinese provincial data were used for the Pearson correlation analysis. During the economic development of China, the correlation between the first, secondary, and tertiary sectors and the CO₂ emissions demonstrated a downward trend. In particular, the secondary sector and CE correlation decreased from 0.57 to 0.29. The results illustrate a transition toward more sustainable development, though there is still some gap with developed countries as per the GI values obtained in the last section. China’s policy of promoting cleaner energy industries, such as developing photovoltaic power and electric vehicles, may be beneficial for balancing economic development and environmental protection [42]. As China enters a new phase of its economy, the high-tech industrial and tertiary sectors are attracting more attention, making net-zero emissions more achievable [43]. To achieve greater sustainable development and higher GGDP, the CO₂ emissions corresponding to different energy source structures are provided in Figure 7. When adopting the GGDP development goal as simulated, the increase in the rate of emissions due to energy utilization gradually slowed down, and the peak in CO₂ emissions will be achieved around 2030, as proposed by the national goal. However, the possible spillover effects of adopting policies related to electric vehicles or other clean energy industries should be investigated, which is one of the limitations of this study.

5. Conclusions

This study evaluated the potential benefit of transitioning to GGDP on sustainable development using mathematical modeling integrated with ridge regression analysis. Considering the limited data obtained, this study used EWM-TOPSIS, which combines the objective assignment method, minimizing the bias caused by human factors, and the TOPSIS method, avoiding the subjectivity of the data. The countries were divided into three categories for analysis. Developing countries with a relatively higher proportion of their economy in the secondary sector demonstrated greater potential for climate mitigation when adopting GGDP. Some countries in category 2, such as China, also achieved higher scores during development, though there is still a gap compared to developed countries. As for the specific analysis, the Gray relational analysis and Pearson correlation methods were used. The analysis revealed a trend in China’s sustainable development, particularly concerning the secondary sector and CO₂ emissions. The improvement in scores may be attributed to the cleaner energy policy that has been advocated.

Given China’s large population, limited resources per capita, and significant environmental pressure, it is crucial to focus on the efficient utilization of scarce resources and environmentally friendly sustainable development. Introducing the concept of GGDP into China’s national economic accounting system is, therefore, of great practical significance. Furthermore, developing a GGDP framework will help address these challenges by incorporating environmental considerations into economic measurements, ensuring a more sustainable approach to national progress. The integration of GGDP into policy frameworks offers a crucial tool for governments, particularly in developing countries with a substantial secondary sector, to harmonize economic growth with environmental sustainability. Mathematical modeling approaches, such as ridge regression and EWM-TOPSIS used in this study, provide a clear, quantifiable method to assess and strategize economic activities that align with sustainable development goals. This is particularly useful for policymakers who need to mitigate the inherent subjectivity in environmental impact assessments and ensure that economic policies incorporate and address the real environmental costs. For stakeholders, including government agencies, environmental groups, and international development organizations, this approach should inform more effective policies, investment decisions, and international aid allocations. Specifically, it may guide the optimization of industrial practices, energy production, and resource management in countries like China, where there is a critical need to manage environmental pressures alongside economic development. This GGDP-focused approach thus serves not only to evaluate current impacts but also to shape future economic and environmental policies in a way that promotes long-term sustainability.

The analysis in this work suffers from some limitations. These are common problems when assessing environmental damage. Some monetary value allocation methods exhibit a degree of arbitrariness. Many data are missing for developing countries, which may be supplemented using data from different approaches, such as estimations from satellite imagery. Environmental protection expenditure should also be taken into consideration after obtaining more data. When analyzing the impact of China’s GGDP transition, the optimal values and predicted impact of some indicators, such as wind and hydroelectric power generation, may be further refined. Furthermore, our method only considered some countries from 2012 to 2020. The robustness of the methodology should be assessed by testing different countries at different time periods, which will be carried out in our future work, together with a comparison with other modeling methods.