Greenhouse gases, especially carbon dioxide (CO₂) emissions, are viewed as one of the core causes of climate change, and it has become one of the most important environmental problems in the world (Rehman et al. (2021a)). At the press conference on WMO State of the Climate 2019 Report, António Guterres, UN Chief, reported that 2019 was the second hottest year on record during his opening remarks. According to the World Meteorological Organization’s (WMO) flagship State of the Global Climate report, the global average temperature in 2020 was about 1.2°C above preindustrial level.

To mitigate the threat of runaway climate change, the Paris Agreement calls for limiting global warming to well below 2 and preferably to 1.5°C, compared to preindustrial levels. This requires global emissions to peak as soon as possible, with a rapid fall of 45 percent from 2010 levels by 2030, and to continue to drop off steeply to achieve net zero emissions by 2050 (Bertram et al., 2021). The world is way off track in meeting this target at the current level of nationally determined contributions. Global greenhouse gas emissions of developed countries and economies in transition have declined by 6.5 percent over the period 2000–2018. Meanwhile, the emissions of developing countries are up by 43.2 percent from 2000 to 2013. The rise is largely attributable to increased industrialization and enhanced economic output measured in terms of GDP.

Carbon dioxide emissions have been the primary source of extreme environmental pollution (Rehman et al. (2021a)). With the rapidly growing agriculture and farm mechanization, agricultural sector has become a factor in the surge in CO₂ emissions and other greenhouse gases in the globe (Rehman et al. (2021b)).

Economic, social, and environmental suitability are the three core pillars of the UN’s Sustainable Development Goals (SDG) declarations (Rehman et al. (2021a)). In September 2019, Heads of State and Government gathered in the SDG Summit at the United Nations Headquarters in New York to follow up and comprehensively review progress in the implementation of the 2030 Agenda for Sustainable Development and the 17 Sustainable Development Goals (SDGs). The summit resulted in the adoption of the Political Declaration and its core message is to take action to respond to climate emergencies. Relevant research shows that if economic growth and climate and environmental sustainability are achieved at the same time, emission reduction policies need to be incorporated into the economic growth policies of various countries (Murshed et al. (2020), Li et al. (2021), Rehman et al. (2021a)).

As the world’s second largest economy, the Chinese government strives to achieve environmental sustainability through a series of policies and measures. At the General Debate of the 75th session of the United Nations General Assembly on 22nd September 2020, President Xi Jinping of China announced that China will scale up its Intended Nationally Determined Contributions by adopting more vigorous policies and measures. It also aims to have CO₂ emissions peak before 2030 and achieve carbon neutrality before 2060.

Generally speaking, various economic activities will affect carbon emissions, Liu et al. (2021). They include industrial structure (Shen et al., 2021), energy consumption, trade, and urbanization (Kasman and Duman, 2015), consumption structure of fossil fuel and cleaner fuel (Murshed et al., 2020), foreign investment (Elliott and Sun, 2013), and technology advancement (Yu and Du, 2018).

Based on this background, this paper studies the relation between China’s economic growth, industrial structure, urbanization, R&D investment, foreign investment, energy consumption growth, and CO₂ emissions from 2000 to 2018 and predicts it.

Choosing China as an ideal case to study driving factors on CO₂ emissions is because China has accounted for the highest level of CO₂ emissions across the globe in 2017 (Ma et al., 2021). President Xi Jinping addressed the General Assembly of United Nations and declared China’s national goal of turning carbon neutral by 2060. China is an important country to play a key role in achieving the 2030 Sustainable Development Agenda of the United Nations. In order to achieve the 2030 Sustainable Development Agenda of the United Nations and the Paris Agreement at the same time, China must achieve the carbon emissions peak by 2030 and the carbon neutrality by 2060 while sustaining a certain economic growth. To this end, China has formulated a “dual-carbon” strategy. Therefore, it is vital to study the drivers that influence CO₂ emissions. Economic growth and CO₂ emissions go hand in hand as economic activities give rise to CO₂ emissions. Therefore, economic growth is the core factor affecting CO₂ emissions. Industrialization and urbanization are the two main lines of China’s economic and social development that includes the CO₂ emissions of the production side and the consumption side, respectively (Cao et al., 2016; Han et al., 2019). Industrialization and urbanization are compound factors affecting carbon emissions. It is because the process of industrialization and urbanization includes the factors driving CO₂ emissions and limiting CO₂ emissions. Industrialization has brought the change of industrial structure, and the CO₂ emissions of different industries are different. On the one hand, urbanization has an impact on the CO₂ emissions caused by residents’ consumption, which is quite different between urban residents and rural residents. On the other hand, urbanization is the movement of industries and population in different areas. Therefore, urbanization also reflects the different performance of carbon emissions in urban area and rural area. Technological progress, foreign investment, and energy consumption are the specific factors of CO₂ emissions, technological progress reduce CO₂ emissions by exploring and usage of clean energy, foreign investment reflects the pollution haven (tax environmental regulation, good market access to high-income countries, and corruption opportunities) (Candau and Dienesch, 2017), and energy consumption determines the quantity of CO₂ emissions.

This paper contributes to the literature in two ways. 1) This is a comprehensive research; we try to build a framework which includes three levels of six driving factors on CO₂ emissions as shown in Figure 1. The most important factors include economic growth, industrialization, urbanization, technology progress, foreign direct investment, and energy consumption. 2) Most of the existing studies are based on OLS framework to explore the relation between carbon emissions and related factors. It is difficult to avoid the omission of variables or endogeneity issues, Kasman and Duman (2015). An increasing number of recent studies (Li et al., 2021; Liu et al., 2021) have been using cross-sectionally augmented autoregressive distributed lag (CS-ARDL) approach developed by Chudik and Pesaran (2015) for short- and long-term CO₂ emissions forecast. This research applies a suite of machine learning algorithms in predicting CO₂ emissions using the factors discussed. Machine learning avoids omission of variables and endogeneity issues. In addition, the trends and relation between CO₂ emissions and various factors are predicted.

The rest of this paper is organized as follows. Literature Review provides a literature review on CO₂ emissions. Data and the Variables describes the data and variables under study. Methodology describes the machine learning algorithms deployed for predicting the level of CO₂ emissions. Results compares the accuracy of predictions among various machine learning algorithms. Discussions discusses the results using the best performing model, while Conclusion and Policy Implications concludes the paper.

Economic scale, economic structure, and technological level are the three major factors affecting the environment (Grossman and Krueger, 1995). Economic scale is the output of the economy; more economic output means more pollution. It is because that economic growth needs more resources investment and more energy consumption. Economic structure is industry structure. The change of industry structure will reduce the pollution. With economic developing, percentage of secondary industry, especially energy-intensive industry, will reduce percentage of tertiary industry, and energy consumption will increase, so the pollution will be reducing. Technology progress will realize the usage of resource efficiency and reduce the energy consumption. So, technological level is an important factor which influences the energy intensity and pollution. Many research studies are based on these three environment factors and extend them accordingly. The research can be classified into relation between economic growth and CO₂ emissions, industry structure, technology, and CO₂ emissions, and urbanization and CO₂ emissions. But results differ from research focus, theories, and methods. There are three parallel literatures on factors what will influence CO₂ emissions.

The first group of studies has investigated the relation between CO ₂ emission, economic growth, and energy consumption. Environmental Kuznets Curve (EKC) is often used to discuss the relation between environmental pollution and economic growth, which is also the main method to analyze the relation between CO₂ emissions and economic growth (Lin and Jiang, 2009). Grossman and Krueger (1991) found the U-shaped relation between economic growth and CO₂ emissions. But the result is opposite if CO₂ is used as the environmental indicator. Holtz-Eakin and Selden (1995), Sachs et al. (1999), Friedl and Getzner (2003), and Galeotti et al. (2006) found that the relation between CO₂ emission and economic growth is inverted U-shape. It is opposite in the study of Shafik (1994), Martin (2008) and Murshed and Dao (2020) which find that per capita CO₂ emission increased in parallel with per capita income, and there is no turning point. Moomaw and Unruh (1997), Martinez-Zarzoso and Bengochea-Morancho (2004), Friedl and Getzner (2003), and Akpan and Chuku (2011) found that the relation between CO₂ emission and economic growth is N-shape. Saidi and Hammami (2015) examined the effect of energy use and the CO₂ emissions on economic growth for 58 countries, and their empirical results showed that CO₂ emissions negatively affected economic growth. Rahman et al. (2020), Liu et al. (2012), and Lantz and Feng (2006) found that per capita GDP has no relation with CO₂ emission.

Environmental Kuznets Curve describes the economic growth in developed countries and the inverted U-shaped relation between environmental pollution, consciously or unconsciously, as for the developed countries to adjust economic structure and the energy consumption structure and achieve a faster pace of the inverted U-shaped path, the overall environmental quality as economic growth accumulation showed a trend of deterioration before improvement (Lin and Jiang, 2009). Acheampong (2018) found that energy consumption has a negative impact on economic growth in global level, economic growth has a negative impact on CO₂ emission, and CO₂ emission has positive impact on economic growth. In the Asia-Pacific region, economic growth does not cause CO₂ emissions. But in Caribbean-Latin America, there is a feedback causality between economic growth and carbon emissions.

The second group of studies has investigated the relation between CO₂ emissions, industry structure, and technology progress. Bernardini and Galli (1993) found that the decline in energy intensity shows a decline trend with the increase in income. The three reasons behind the relationship descent are the following. First of all, with the development of the economy, the final demand structure changes with changes in the stage of industrialization. In the preindustrial stage, agriculture is the leading industry in economic development, and economic growth is driven by basic needs, which can be met with low energy intensity. In the stage of industrialization, the infrastructure network needs to be built up to facilitate large-scale production and consumption. The primitive accumulation of capital stock related to industrialization can increase energy intensity, but it eventually reached the saturation point. At this time, the consumption of materials tended to replace durables rather than create durables. In the postindustrialized stage, the decline of manufacturing industry in relation between services and energy intensity in service-based economies is smaller than that in manufacturing-oriented economies. Shahbaz et al. (2018) and Khan et al. (2019) found that financial development helps control CO₂ emissions in both France and China. However, Liu et al. (2021) found that with 1% financial development, CO₂ emissions increased 0.17–0.52%.

Technology progress is the dominant factor of long-run economic growth with scarce resources. Technology change has a positive influence on energy efficiency and negative influence on energy intensity (Lin and Du, 2014; Sadorsky, 2013; Yu et al., 2021). Ang (2009) used the framework to combine modern growth theoretically, which can analyze the role of R&D activity and technology progress in reducing pollution. Technology progress is the result of R&D investment, which contributes to energy intensity reduction (Young, 1998). Wei et al. (2010) extended Antweiler’s model (Antweiler et al., 2001) to analyze the influence factors of CO₂ emissions. The study found that GDP, industrialization, and free trade have positive influence on CO₂ emissions, but independent research and development and technology import contribute to reducing CO₂ emissions.

One source of technology progress is independent innovation; another source is FDI and trade. FDI and trade are latecomer advantage of countries, which develops later. Elliott and Sun (2013) found that FDI has negative influence on energy intensity. The last study (Khan et al., 2021) investigates the roles of export diversification and composite country risks in carbon emissions abatement. The researchers found that lowering country risks, undergoing renewable energy transition, and enhancing environmental-related technological innovations assist in reducing CO₂ emissions in the long run.

The third group of studies has investigated the relation between CO₂ emissions and urbanization. At present, there are a large number of literatures on urbanization and its impact on carbon dioxide (CO₂) emissions for reference. A lot of research have directly investigated the positive impact of urbanization on carbon dioxide emissions (Behera and Dash, 2017; York et al., 2003; Zhang and Lin, 2012). Shahbaz et al. (2017) provided evidence showing that the development of urbanization leads to higher demands for food, housing, transportation, land usage, and energy consumption and causes serious environmental degradation problems. For instance, traffic congestion, waste management, and poor sanitation could cause pollution and health problems in most urban areas.

A number of studies have tested the linear impact of urbanization on global carbon dioxide emissions. You can find contributions that support it, such as those by York et al. (2003), Cole and Neumayer (2004), Liddle and Lung (2010), Wang et al. (2012), and Behera and Dash (2017), or those that refute it, such as those by Hossain (2011) and Liu and Bae (2018). Specifically, York et al. (2003) used panel data from 143 countries to record the positive impact of urbanization on CO₂. Cole and Neumayer (2004) and Liddle and Lung (2010) reached similar findings using panel data and Stochastic Impacts by Regression on Population, Affluence, and Technology (STIRPAT). Wang et al. (2012) applied PLS with STIRPAT model in Beijing, China, and concluded that urbanization is the most influential factor that has adverse impact on environmental quality. Subsequently, Wang et al. (2013) found that urbanization, industrial growth, income levels, and population stimulate CO₂ emissions during a provincial study. Behera and Dash (2017) used panel cointegration test to study the positive impact of urbanization on carbon emissions in South and Southeast Asian countries. Conversely, several studies proposed uncertain results and reported the negligible impact of urbanization on CO₂ emissions (Hossain, 2011; Liu and Bae, 2018).

To a large extent, the level of economic development of the country may alleviate the nature of the relation between urbanization and pollution (Fan et al., 2006; Li and Lin, 2015; Poumanyvong and Kaneko, 2010). However, higher urbanization growth rates and development rates can improve the environment by promoting technological innovation in energy usage and efficiency, increasing awareness of environmental issues, and using green technologies, Bekhet and Othman (2017). Urbanization has an inverted U-shaped relation with CO₂ emissions in Asia (Fan et al., 2020). However, Zhu et al. (2012) found there is limited support for inverted U-shaped relation between CO₂ emissions and urbanization in 20 emerging economies. There was a long-run bidirectional positive relation between CO₂ emissions, urbanization, and energy consumption in MENA countries. However, the long-run relation is based on the countries’ income and development (Al-mulalia et al., 2013). Urbanization has a positive influence on CO₂ emissions; in the stage of urbanizing, it needs more energy consumption which will increase CO₂ emissions (Lin and Du, 2013). CO₂ emissions are higher in big cities or urban agglomeration areas, because of the high energy consumption on residential electricity consumption, residential gas consumption, residential heating consumption, and residential transportation energy consumption (Bai et al., 2019). In east and central China, the center and surroundings featured high levels (high-high cluster) of total CO₂ emissions and low levels (low-low-cluster) of per-unit-GDP CO₂ emission in urban agglomerations. The Yangtze-River-Delta, the Beibu-Gulf, and the Guangdong-Hong Kong-Macao UAs were more efficient at emission reduction with the cities’ rising scales, while cities of the Beijing-Tianjin-Hebei UA and the Chengdu-Chongqing UA performed less efficiently (Cui et al., 2020).

Two main methodologies are used by three groups of studies. One of the methodologies is econometrics. Econometric methods include spatial autocorrelation analysis, semiparametric fixed effect (Zhu et al., 2012), panel threshold regression (Zi et al., 2016), panel threshold regression (Du and Xia, 2018), autoregressive distributed lag model and vector-error correction model (Bekhet and Othman, 2017), two-stage least squares (2SLS) and augmented Stochastic Impacts by Regression on Population, Affluence, and Technology (STIRPAT) model (Bai et al., 2019), and autoregressive distributed lag (ARDL) (Ang, 2009). Econometric methods have been used to estimate the long-run relationship and the short-run dynamics for environmental pollution and its determinants. To address the issues of multicollinearity and overfitting, a recent study introduced the least absolute shrinkage and selection operator (LASSO) regression model which can pinpoint the most important determinants to investigate the driving factors influencing household carbon emissions (Shi et al., 2020). Another study on methods called cross-sectionally augmented autoregressive distributed lags (CS-ARDL) can account for cross-sectional dependency, slope heterogeneity, and structural break issues in the data (Li et al., 2021; Ma et al., 2021). The other methodology is calculating the quantity of CO₂ emissions. Many research studies are based on Kaya identity and Logarithmic Mean Divisa Index (LMDI) (Ang and Zhang, 2000). Using these methods, researchers calculate the industrial CO₂ emissions, regional CO₂ emissions, and national CO₂ emissions (Yang and Li, 2017). Based on LMDI, index decomposition analysis (IDA) is developed and becomes one of the most popular methods. However, IDA calculates the technology efficiency of economy system, not the efficiency of energy usage (Lin and Du, 2013). Wang (2011) developed the method based on production-theory decomposition approach (PDA), which is based on output-oriented distance function to decompose the energy production to technology efficiency, technology program, and input alternative. Lin and Du (2014) gave a complex framework (L-D framework) of index decomposition and production theory. Then, Yang et al. (2019) used L-D framework to calculate CO₂ emissions of major industries.

There are two gaps in the above literature. Factor choice is confused by economic methods which do not support all factors (Shi et al., 2020). So, the studies always try to select one or two important factors. Actually, factors framework is a hierarchical structure, and they inevitably influence each other. Methodologies reviewed above are very useful and have been adopted with many successes. However, there are many restrictions such as collinearity and causality issues of variables. On the other hand, it is not necessary to consider these issues in machine learning. Machine learning is a method of data analysis that automates analytical model building. It is a branch of artificial intelligence based on the idea that systems can learn from data, identify patterns, and make decisions with minimal human intervention. Machine learning aims to develop algorithms that can learn and create statistical models for data analysis and prediction. The ML algorithms should be able to learn by themselves, based on data provided, and make accurate predictions, without having been specifically programmed for a given task.

This study uses a number of machine learning algorithms, or function, f, to map the output variable (Y) from input variables (X1, X2, … , X6) so that Y = f(X1, X2, … , X6). Several types of algorithms have been adopted in this study, and they are briefly described here.

To get the best results, it is necessary to understand the data first by inspecting their descriptive statistics and plotting their histograms. The descriptive statistics and histogram of the original data between 2000 and 2015 are shown in Figure 2A; Table 1, respectively.

Looking at the data, it is revealed that better results could be obtained by taking the logarithm of X2, X4, X5, and Y. The descriptive statistics and histograms of the logarithms of X2, X4, X5, and Y are shown in Figure 2B; Table 2, respectively.

Data scaling is important for some machine learning algorithms, e.g., KNN and ANN, and less critical for some others such as linear regression. For consistency and easy comparison, the second step of data preparation is standardization of data with its mean and standard deviation rather than normalization of data with its maximum and minimum vales. It is because the data are Gaussian-like than bounded by a maximum and minimum as shown in the histograms.

Having established that KNN model performs the best in the dataset, we attempt to use KNN model to perform sensitivity analysis of independent variables on CO₂ emissions. We would like to determine how the target variable, CO₂ emissions, is affected based on changes in other input variables. As there are six input variables, we need to select a base case before we conduct sensitivity analysis. The base case consists of the input variables with the most common values. The procedure is described below.

From the histograms, we have divided each variable into 10 bins of equal width that cover the minimum and maximum. For each variable, say X1–Industrial Structure Rationalization, we pick the midpoint value, X_1M, of the bin that contains the highest number of data. With six variables, we have X_1M, X_2M, … and X_6M accordingly. Let us call this the “centroid” of input variables.

Now, we can vary the value of one variable, say X1—Industrial Structure Rationalization, from minimum to maximum while keeping the values of other five variables constant at their midpoint values of the highest bin. In this way, we can inspect the sensitivity of variable, X1—Industrial Structure Rationalization around the centroid. We can repeat this analysis to other input variables and form a more complete picture about the six variables affect the CO2 emission around the centroid. The result is shown in Figure 11.

First, when all the six variables are at centroid, the predicted Ln(CO₂ emissions),Y, is 5.4960 (or equivalent to 543.70 million tonnes CO2 emissions), shown with symbol ○ in Figure 11. Then, when we adjust one of the variables, the change of Ln(CO₂ emissions), Y, is summarized in the following.

Industrial Structure Rationalization, X1: The effect on industrial structure rationalization on CO₂ emissions is shown in Figure 11A. It can be seen that their relationship is nonlinear and nonmonotonic. It exactly demonstrates the strength of machine learning is able to pick up the nonlinearity of the variables and make better predictions. It can be seen that when the industrial structure rationalization increases from 0.7486 to 1.6507, CO₂ emissions increase. Beyond that range, its effect is the opposite. It can be interpreted that industrial structure is not the only target for the policy makers. Industrial rationalization index is the equilibrium in economy; it includes output value, sectors of branch of industry employment, and industrial rationalization. If the industrial structure is rationalized, the industry, especially the output of second and third industry, should be in equilibrium, and the regional disparity should be continuously decreased. But the negative influence of industrialization will lead to the increase of CO₂ emissions. It means that the CO₂ emissions decreasing not only need economic equilibrium but also need the balance between the industrialization and harmful gas emission. Therefore, policy makers should develop economy of each province as rapid as possible. It is because the CO₂ emission will eventually decrease after the saturation point at the postindustrialization stage as explained by Bernardini and Galli (1993). On the other hand, the industrial structure rationalization should stay at 0.7486 for some provinces as their CO₂ emissions would be at minimum.

GDP on a natural log scale, X2: The effect on GDP on CO₂ emissions is shown in Figure 11B. It can be seen that CO₂ emissions are the most sensitive when the range of GDP is from exp(5.0442) to exp(5.6349) (or equivalent to 155.12 billion dollars to 280.03 billion dollars). As mentioned at the beginning of Methodology, X2 is taken logarithmically. Each interval of the x-axis represents 1.8 times of the previous level. Every country would like to develop their economy. Therefore, it would be unlikely that a country would sacrifice economic growth to curb CO₂ emissions. Figure 11B shows that CO₂ emissions will increase when economy grows. It will definitely harm the environment. Furthermore, China cannot simply grow its economy without considering CO₂ emissions. It is because one of the pledges China has committed in Paris Accord is to peak CO₂ emissions by 2030. However, with the advancement of technology, it is possible to reduce emissions without economic sacrifice. One thing that must be noted is that in Figure 11B, there is no inverted U-shaped relation between CO₂ emissions and economic growth as found by Galeotti et al. (2006). However, we can see that when GDP grows beyond exp(8.5883) (or equivalent to 5,368 billion dollars), CO₂ emissions would level off and they could even come down. It means China can fulfill its Paris Accord’s pledges.

Urbanization, X3: The impact of urbanization on CO₂ emissions is very mixed and complicated as shown in literature reviewed in Literature Review. While most of the previous studies indicate a positive relationship between urbanization and CO₂ emissions, in this study, it is found that a flanged U-shape is observed as shown in Figure 11C. Given that the urbanization is 0.4975 at centroid now, policy makers of China can aim to reduce its CO₂ emissions by increasing urbanization to the trough region of 0.571 and 0.6445. This decrease is likely a result of technological innovation in energy usage and efficiency, increasing awareness of environmental issues, and using green technologies (Bekhet and Othman, 2017).

R&D Reinvestment Intensity on a Natural Log Scale, X4: R&D reinvestment intensity stimulates technological advancement, and it also affects economic growth. It can be seen from Figure 11D that CO₂ emissions increase mildly when reinvestment intensity increases from −6.5673 to its centroid position of −4.4802. Afterwards, it decreases mildly. Looking at the figure, the reinvestment intensity is at critical moment now at its centroid position. If it decreases from its current position, CO₂ emissions would decrease too. But it is likely to be accompanied by a decrease of economic growth. The implication is that China should increase its reinvestment intensity so that it could advance technology more rapidly, increase energy usage and efficiency, and make contribution in reducing CO₂ emissions accordingly.

Actual Use of Foreign Capital on a Natural Log Scale, X5: The impact of actual use of foreign capital on CO₂ emissions is shown in Figure 11E. It is observed that CO₂ emissions increase rapidly when actual use of foreign capital increases from 5.1206 to 5.9213. Then, it levels and even decreases gradually, afterwards. According to pollution haven hypothesis, foreign firms in dirty sectors are more likely to relocate pollution activities from developed countries to poorly regulated developing countries to avoid domestic environmental control cost, which directly undermines the environmental interests of recipient countries like China. This implies that the higher the actual use of foreign capital (FDI), the higher the CO₂ emissions, termed “direct” mechanism. However, there is “indirect” mechanism that affect the CO₂ emissions. Foreign capital could act as a channel for environmentally friendly technologies, more stringent environmental regulations can be designed and implemented in low-emissions provinces to attract clean foreign capital. So the two mechanisms have the opposite effect on CO₂ emissions. In China, actual use of foreign capital of most of the provinces has well passed 5.9212 and reached its centroid position of 10.7257 already. The implication is that the impact of actual use of foreign capital is not significant as the CO₂ emissions is quite stable around that position.

Growth Rate of Energy Consumption, X6: When the economy is robust and growing, more energy is consumed. Therefore, it will result in higher CO₂ emissions. Energy consumption is in an interesting situation now. It is because CO₂ emissions are at a local maximum when the growth rate of energy consumption is at 0.0132 as shown in Figure 11F. Interestingly, when the growth rate was higher than 0.0132 during the period under study, CO₂ emissions decreased unless the growth rate was too rapid beyond 0.145 level. It could be explained that China has made good use of foreign capital and R&D investment. Therefore, it is expected that cleaner and greener energy such as hydropower and nuclear power have been used when the growth rate increases from 0.0132 to 0.145. Last, but not least, policy makers should refrain from consuming energy beyond a growth rate of 0.145. It is because it can be seen that CO₂ emissions increases sharply beyond 0.145 level. Also, the results between 0.5403 and 0.9356 can be ignored as there are only one or two (or even zero) pieces of data of that range.

Noting that the above analysis applies to the centroid position, it provides an overall picture for China as a whole. This approach can also be applied to other position that might be more relevant to individual province.

Following the pledges China has committed in Paris Accord is to peak CO2 emissions by 2030 and the declaration of the 2060 carbon-neutrality goal of Chinese government; it requires proactive measures to be undertaken to reduce carbon emissions while maintaining continuous economic growth and improving in living standards. Against this background, this paper analyzed the effects of industrial structure rationalization index, GDP, urbanization, R&D reinvestment, actual use of foreign capital, and growth rate of energy consumption on forecasting CO₂ emissions.

Data across 30 provincial administrative regions of China from 2000 to 2018 are used for the study. Data from 2000 to 2015 are used as training set, and data from 2016 to 2018 are used as testing set. We apply a suite of machine learning algorithms on the testing set and predict the levels of CO₂ emissions for the testing set. Machine learning algorithms include linear and nonlinear models, ensemble methods with boosting and bagging, and artificial neural networks. Employing rmse for model selection, results show that k-nearest neigbors (KNN) model performs the best when the number of neighbors is set to two for the present dataset.

Using KNN model, we conducted a sensitivity analysis of CO₂ emissions around its centroid position on its dependent variables. The overall findings revealed that economic growth measured by GDP, X2, contribute to higher CO₂ emissions. As China needs to maintain its economic growth to continuously improve living standards, it brings several implications for policy makers when setting policies concerning other variables. First, in terms of industrial structure rationalization, X1, not all provinces should develop its industrialization. Some provinces should stay at relatively mild industrialization stage that their CO₂ emissions would be at minimum. For other provinces, they should develop their economy as rapidly as possible. It is because CO₂ emissions will eventually decrease after saturation point. Therefore, the duration of high CO₂ emissions that comes with industrialization would be as short as possible. Second, in terms of urbanization, X3, there is an optimal range for a province. To minimize CO₂ emissions, provinces should try to achieve urbanization around 0.571 and 0.6445. With the range, the CO₂ emissions would be at minimum and the decrease is likely a result of technological innovation in energy usage and efficiency. It also suggests that a province should not be too densely populated. Third, the result of R&D reinvestment intensity, X4, suggests that China should increase its reinvestment intensity further. At present, there is a positive relationship between CO₂ emissions and reinvestment intensity. Therefore, it seems that monies for R&D reinvestment have not been put, or not enough, into green technology yet. Only when there is a further increase of R&D reinvestment intensity into green technology, there will be a decrease of CO₂ emissions. Fourth, it is found that the impact of the actual use of foreign capital, X5, on CO₂ emissions is insignificant, relatively speaking, when compared with other variables. If we assume that R&D reinvestment is associated with actual use of foreign capital, policy makers should prioritize the use of foreign capital for R&D investment on green technology. That would reduce CO₂ emissions while maintaining economic growth. Last, it is possible to increase the growth rate of energy consumption, X6, gradually if R&D reinvestment and use of foreign capital are directed towards cleaner and green energy sources such as hydropower and nuclear power. Policy makers must refrain from consuming energy beyond a growth rate of 0.1450 for economic growth. Otherwise, CO₂ emissions would increase rapidly and may jeopardize the pledges China committed in Paris Accord and the 2060 carbon-neutrality declaration. In summary, the above policy implications provide a blueprint for policy makers for ensuing environmentally sustainability economic development in China.

It is worth noting that the approach applied in this study can easily be replicated for other countries to make better forecasting of CO₂ emissions for the future. The major constraint of this approach is the data limitation. For successful application of machine learning, the number of data required is usually more than traditional econometric models. With more data, more advanced machine learning algorithms can be applied to further check the robustness of the findings.