A Study on the Heterogeneity of China’s Provincial Economic Growth Contribution to Carbon Emissions

Abstract

Achieving “dual carbon” targets by containing carbon emissions while sustaining economic growth is challenging. This study examines the varying carbon dependency levels among China’s 30 provincial-level administrative units, considering spatial correlations in emissions. Using a semi-parametric varying coefficient spatial autoregressive panel model on 2004–2019 panel data, this study shows the following: (i) The relationship between economic growth and carbon emissions forms an “S”-shaped curve, with the contribution decreasing as tertiary industry grows, defining three stages of carbon dependency. (ii) There is significant heterogeneity in carbon dependency across provinces, with some advancing to “weak dependency” or an “economic carbon peak” due to advantages and policies. (iii) Dependency levels shift over time, with “weak dependency” being the predominant stage, though transitions occur. (iv) A positive spatial spillover effect in emissions was noted. This study recommends tailored policies for each provincial-level administrative unit based on their carbon dependency and development stage.

1. Introduction

In the 21st century, the rapid increase in global carbon emissions has led to frequent extreme weather events, gradually posing a survival challenge that all mankind must face. On 22 September 2020, China announced at the 75th United Nations General Assembly that it aimed to reach a peak in carbon dioxide emissions by 2030 and to achieve carbon neutrality by 2060, namely the “dual carbon” strategy. China has taken a comprehensive and long-term approach, setting a timeline for achieving carbon neutrality, even during the carbon peak phase, indicating that this is a protracted battle spanning the medium to long term. As China is currently in the initial stage, it is essential to coordinate national resources to refine the “dual carbon” strategic goals; decompose them into annual, regional, and staged targets; implement these tasks in accordance with actual conditions; and firmly adhere to the carbon neutrality road map of “carbon control–carbon reduction–low carbon–neutrality” for steady development. Currently, energy conservation and emission reduction are the focus of the carbon peak phase. Balancing economic growth with reduced carbon emissions remains a significant challenge on the path to peak carbon, with two primary solutions. Firstly, optimizing the energy structure and controlling or even reducing the utilization rate of fossil fuels. To achieve the carbon peak, it is necessary to address the energy structure issue squarely, actively develop clean energy, and gradually shift towards a development model dominated by clean and renewable energy, to achieve true energy sustainability. Secondly, optimizing the industrial structure and reducing energy dependency. This involves optimizing and adjusting the internal structure of secondary industry; eliminating traditional industries with high input, high emissions, and low output; and increasing support for high-tech industries. This relies on high-tech, high value-added, knowledge-intensive, and technology-intensive industrial sectors to guide economic development.

Due to the varying levels of development and the unique characteristics of the industrial structure, economic growth, energy utilization, and carbon emission contributions among the different provinces in China, the carbon emission reduction strategic plans for the various provinces need to be customized to local conditions. For instance, in provinces like Shanxi and Shandong, where long-term reliance on secondary industry for economic growth has led to a heavy industrial structure and insufficient incentives for emission reduction, the “dual carbon” policy has been slow to take effect. Therefore, these regions need to prioritize the internal transformation and upgrading of secondary industry, reduce heavy dependence on fossil fuels, and supplement this with the development of tertiary industry to build new low-carbon economic growth points. In contrast, some developed regions such as Beijing, Shanghai, and Tianjin have a highly optimized industrial structure, with tertiary industry predominantly contributing to the economy. Their economic growth has been decoupled from carbon emissions, and a few regions have already reached their carbon emission peaks. In these areas, the focus should be on optimizing the energy structure, actively developing new energy sources, improving energy utilization efficiency, and researching and developing emission reduction technologies. Therefore, it is both meaningful and necessary to capture the heterogeneity in the economic growth–carbon emission relationship across provinces and over different periods within each province. Province-specific policies will benefit from this heterogeneity in analysis.

In practical analysis, it has been found that a key aspect of breaking down emission reduction targets is to divide them by region and allocate them reasonably among the provinces. By the end of 2022, 16 provincial-level administrative units had issued “carbon peak” programs, and 7 others had issued “carbon peak” recommendations. The “dual carbon” “1 + N” policy system has begun to show results. In practice, there are differences among provinces in terms of population size, economic strength, industrial structure, ecological environment, and resource endowment. Consequently, there are variations in the number of emission reduction tasks and the timeline for achieving a “carbon peak”. Thus, a spatial spillover effect from carbon emission reduction is inevitable. The spatial spillover effect is essentially an externality affecting neighboring regions. Therefore, the spatial spillover effect from carbon emission reduction may manifest as either a trickle-down effect or a polarization effect. If it manifests as a trickle-down effect, it is easier to establish a virtuous cycle in which provinces that have taken the lead in emission reduction can drive those that are lagging behind, with all provinces collaborating in emission reduction efforts. If it is a polarization effect, then the provinces leading in emission reduction may achieve their “dual carbon” goals more quickly.

Upon reviewing the existing literature, we found that most research employs linear models, the environmental Kuznets curve, and the Tapio decoupling model to investigate carbon emissions. Applying linear models to analyze heterogeneity is inappropriate; if linear models are fitted separately for each province, this comes at the cost of a significant loss in degrees of freedom, leading to an inadequate estimation accuracy. While the EKC and Tapio decoupling models can reveal certain dynamic changes between economic growth and carbon emissions, their primary drawback lies in their inability to incorporate other factors for consideration. This paper adopts a novel perspective by utilizing a spatial semi-parametric model to analyze the heterogeneity in carbon emissions. This approach not only avoids a loss of degrees of freedom, but also allows for the consideration of other social factors influencing carbon emissions. Furthermore, it enables the examination of spatial spillover effects. Consequently, to consider the spatial spillover effect of carbon emissions and explore the variations in carbon emissions among China’s 30 provincial-level administrative units, we employed a semi-parametric varying-coefficient spatial autoregressive panel model to characterize the heterogeneity in the contribution of economic growth to carbon emissions across different provinces. Furthermore, we proposed a theoretical framework to explain the underlying mechanisms through which economic growth contributes to carbon emissions.

The primary contents of this study can be summarized into three main parts. Firstly, we aimed to precisely identify the spatial and temporal heterogeneities in carbon dependency. By quantitatively analyzing the mechanisms through which economic growth contributes to carbon emissions at the provincial level, we categorized the stages of carbon dependency associated with economic growth. Based on this heterogeneity across provinces, we offer tailored suggestions for carbon emission reduction pathways. Secondly, we investigated the spillover effects of carbon emissions among provinces, analyzing the potential for provinces leading in emission reduction to drive other provinces and to foster a coordinated effort in emission reduction across provinces. This analysis took into account geographical locations to understand the potential impact of geographical proximity on these efforts. Thirdly, this study examined the potential influence of various factors, including population, finance, transportation, and technology, on carbon emissions. By employing variable selection methods to screen for factors with a substantial impact, we reinforced the theoretical analysis and conclusions.

2. Literature Review

In the 21st century, the research and analysis of carbon emissions have gradually begun to attract the attention of statistics and economics. Carbon dioxide, as an unavoidable by-product of human socio-economic development since the first industrial revolution, is closely related to the growth rate and economic growth rate; thus, many scholars began to quantitatively study the relationship between carbon emissions and economic growth, in the hope of identifying the mechanism of economic growth on carbon emissions, and thus to determine the “win–win” path of carbon emission reduction and economic growth at the same time. The environmental Kuznets curve (EKC) has been used to characterize the relationship between carbon dioxide emissions and economic growth (Jalil and Mahmud [1]), argues that an “inverted U-shaped” curve between carbon dioxide emissions and economic growth exists, and that the contribution of economic growth to carbon dioxide emissions first increases and then decreases. However, Liu et al. [2] empirically estimated the EKC of China’s ${\mathrm{CO}}_2$ emissions, and found that the EKC of total ${\mathrm{CO}}_2$, per capita ${\mathrm{CO}}_2$ emissions, and per capita GDP was an increasing curve. In their research, they only considered the relationship between economic growth and carbon emissions, ignoring the impact of other possible factors on carbon emissions. The differences in their conclusions also indicated that an “inverted U-shaped” EKC does not always exist, and that the EKC of different research objects varies greatly and is heterogeneous.

To avoid these discrepancies in EKC conclusions, decoupling theory was introduced to dynamically identify and classify the synchronous state of carbon emissions and economic development. In 2005, Tapio [3] developed an economic growth and transportation volume decoupling model based on the OECD model, classifying decoupling into eight states. Scholars now apply the Tapio decoupling theory to study how to achieve economic development without increasing carbon emissions. Zhang et al. [4] used the decoupling model to study China’s counties and found that, while weak decoupling was prevalent from 2002 to 2007, 37.39% of counties achieved strong decoupling from 2012 to 2017, indicating sustainable development. Hu et al. [5] studied the decoupling relationship in the Yangtze River Economic Belt and found that the decoupling status improved from 2004–2008 to 2008–2014 but fluctuated from 2014 to 2018, without achieving strong decoupling, indicating a heavy reliance on carbon emissions by transportation and energy. However, when studying the synchronized state, the Tapio decoupling model encounters the same issue as the EKC, which is the neglect of other influencing factors, which may lead to biased conclusions.

When studying the factors affecting carbon emissions, some scholars have focused on the regression relationship between carbon emissions and various factors such as economic development, population, and science and technology. The commonly used model for this purpose is the stochastic impacts by regression on population, affluence, and technology (STIRPAT, Dietz and Rosa [6], York et al. [7]) model. When analyzing carbon emission data across multiple regions, this model is extended to the STIRPAT panel model, and its basic logarithmic form is as follows:

$$\begin{array}{c}\hfill \ln I_{it}=a\ln P_{it}+b\ln A_{it}+c\ln T_{it}+{\epsilon }_{it},\end{array}$$

(1)

where $i=1,\dots ,N;t=1,\dots ,T$ represent the regions and the periods, respectively; $\ln I_{it}$ is a log dependent variable that represents environmental impact; $a,b,c$ are the coefficients (elastic coefficients) for the log population variable $\ln P_{it}$, log wealth variable $\ln A_{it}$, and the log technology variable $\ln T_{it}$; and ${\epsilon }_{it}$ is the random disturbances. The STIRPAT model or its panel form have already been used for carbon emission factor analysis in many studies and discussions. Dietz and Rosa [6], Shi [8], and York et al. [7] analyzed the relationship between population and ${\mathrm{CO}}_2$ emissions by applying the STIRPAT model. All of their conclusions pointed towards the elasticity coefficient of the population being either close to or exceeding 1. Cole and Neumayer [9] conducted an empirical analysis of the relationship between population size, other demographic factors, and pollution, utilizing a panel of 86 countries. Their research revealed a positive correlation between urbanization and the increase in ${\mathrm{CO}}_2$ emissions. Fan et al. [10] analyzed all the countries in the world and all countries at high, upper-middle, lower-middle, and low income levels, and analyzed the historical characteristics of the relations between total ${\mathrm{CO}}_2$ emissions and the impact factors between the years 1975 and 2000. Their main results showed that, at the global level, economic growth had the greatest impact on ${\mathrm{CO}}_2$ emissions. Haseeb et al. [11] empirically investigated how urbanization, energy consumption, and per capita GDP influence ${\mathrm{CO}}_2$ emissions across all BRICS member countries. They showed that GDP per capita in Brazil, Russia, and South Africa contributes to mitigating ${\mathrm{CO}}_2$ emissions, while the results were the opposite in the cases of India and China. Khan and Su [12] considered a panel threshold regression model to analyze the heterogeneity in urbanization’s contribution to carbon emissions in newly industrialized countries. Their results showed a negative effect of urbanization on carbon emissions when it exceeds a threshold value, concluding that higher economic development enables these countries to invest in renewable energy and the development of tertiary industry, thereby reducing carbon emissions. These studies explored carbon emission factors from a national-level perspective using linear regression models, revealing heterogeneity in the relationship between economic growth and carbon emissions across countries. However, they lacked a more microscopic view. Substantial heterogeneity among nations is expected, but the conclusions may differ when focusing on a single country.

Focusing their research scope on China, a major carbon emitter, Li et al. [13] analyzed the driving forces influencing China’s ${\mathrm{CO}}_2$ emissions using the Path-STIRPAT model. Their analysis indicated that per capita GDP, industrial structure, population, urbanization level, and technology level are the primary factors that interactively and collaboratively influence China’s ${\mathrm{CO}}_2$ emissions. Zhu and Peng [14] examined 1978–2008 data in China using the STIRPAT model and found that consumption level and carbon emissions were highly correlated. Li et al. [15] discussed the regional differences in impact factors on ${\mathrm{CO}}_2$ emissions in 30 provincial-level administrative units in China. Their findings revealed that, despite varying degrees of influence across distinct emission zones, factors such as per capita GDP, industrial structure, population, urbanization rate, and technology level consistently emerged as the primary drivers of ${\mathrm{CO}}_2$ emissions across all emission regions. Liu et al. [16] employed the STIRPAT model to decompose and assess eight factors influencing the carbon emissions of 30 provinces, discovering the existence of provincial heterogeneity and providing targeted suggestions for differentiated government policies. Liu and Deng [17] constructed a STIRPAT panel model with fixed effects for the panel data of China’s 30 provincial-level administrative units from 2000 to 2017, which assigned distinct intercept terms for each province. They found that the level of carbon emissions in these provinces was closely related to per capita GDP, fixed asset investment, energy intensity, as well as policies. In the Chinese context, per capita GDP often contributes significantly to carbon emissions, as indicated by various studies. A possible reason for this is that China’s industrial structure has been heavily biased towards secondary industry over the past 20 years, leading to both high economic growth and high emissions. However, those studies still considered the relationship between economic growth and carbon emissions to be fixed in China, which may become inappropriate as the industrial structure improves.

More microscopic research was conducted on the carbon emissions of prefecture-level cities in the Yangtze River Delta, China, using spatial panel data models. These studies examined the existence of spatial spillover effects on the carbon emissions of those cities [18,19]. Wang et al. [20] examined the impact factors of energy-related ${\mathrm{CO}}_2$ emissions in Guangdong Province, China, from 1980 to 2010. Their STIRPAT model suggested that population was the most important impact factor for ${\mathrm{CO}}_2$ emissions. Industrialization level, urbanization level, energy consumption structure, service level, and GDP per capita were also found to be significant impact factors in their model. Shi et al. [21] attempted to quantify and compare impact factors for ${\mathrm{CO}}_2$ emissions between prefectures and provinces levels using spatial models. Their results showed that the proportion of secondary industry was a major factor influencing ${\mathrm{CO}}_2$ emissions at both levels. Qi et al. [22] studied the carbon emission data of 62 counties in Zhejiang Province, China, considering the geographical correlation among counties, and established a spatial STIRPAT model. They found a significant positive correlation between county-level carbon emissions, suggesting that adjacent counties’ carbon emissions reinforce each other. Chen and Zhang [23] attempted to analyze the impact of financial development on carbon emissions from a dynamic spatial perspective. Their study, which examined panel data on carbon emissions from China’s 30 provincial-level administrative units between 1996 and 2012, revealed that an expansion in financial scale significantly increased carbon emissions, while improvements in financial efficiency did not have a pronounced effect on carbon emissions.

The literature studies mentioned above analyzed the impact factors of carbon emissions within the framework of the STIRPAT model. They commonly pointed out that GDP per capita is an important factor affecting carbon emissions, but due to differences in the research subjects, the elasticity coefficients of GDP per capita varied in their conclusions. Therefore, it is quite reasonable to consider provincial heterogeneity in the impact of GDP per capita on carbon emissions when studying the 30 provinces of China. Indeed, the research of Liu et al. [16] incorporated this aspect, but they established models independently for each province, which may have resulted in a considerable loss of degrees of freedom, and failed to take into account the correlation of carbon emissions among provinces. Furthermore, the term “spatial correlation” frequently appears in studies focusing on China, indicating the existence of a correlation in carbon emissions among Chinese provinces. Additionally, in order to mitigate the impact of multicollinearity, a significant number of studies have used ridge regression to estimate model parameters, which is widely known to introduce a degree of subjective judgment.

In summary, based on the STIRPAT panel model, per capita GDP or total GDP, which are commonly used as economic growth variables, were positively correlated with carbon emissions in various studies. This is due to the high economic growth in China over the past decade, which has been accompanied by high emissions. However, the contribution of economic growth to carbon emissions in different regions and at different times exhibits regional and temporal heterogeneity. Therefore, the traditional panel STIRPAT model is unable to explore these heterogeneous characteristics. Additionally, referring to the conclusions of the carbon emission EKC curve, nonlinear models are highly suitable for describing the relationship between economic growth and carbon emissions. Regrettably, few scholars have applied nonlinear models to study this issue. Du et al. [24] proposed a partially linear additive spatial autoregressive model that incorporated both linear and nonlinear components, making the model more flexible and interpretable. Zhang and Shen [25] theoretically examined the parameter estimation in spatial autoregressive models with varying coefficients under panel data settings. Tian et al. [26] proposed a semiparametric varying-coefficient spatial autoregressive panel models with fixed effects. We found that these models are highly suitable for analyzing the heterogeneity in economic growth’s contribution to carbon emissions. Placing the analysis of heterogeneity among 30 provinces under a unified model framework could offer a novel perspective, integrating the advantages of the EKC, the Tapio decoupling model, and the traditional STIRPAT model.

Therefore, this study employed a semi-parametric varying-coefficient spatial autoregressive panel model to overcome the limitations of the EKC, Tapio decoupling model, and traditional STIRPAT model. By considering the spatial spillover effect of carbon emissions, this model can quantitatively investigate the spatial and temporal heterogeneity in the contribution of economic growth to carbon emissions. We estimated and screened highly correlated influencing factors using the penalized likelihood method. Based on this research, the heterogeneity in carbon emissions was visualized, and multiple stages were identified according to the degree of carbon dependency. This study examined the changing trends in carbon dependency stages among China’s 30 provincial-level administrative units over the past 16 years and provides specific staged policy recommendations.

3. Research Data and Methodology

3.1. Variables and Interpretation

This section selected panel data on carbon emissions from China’s 30 provincial-level administrative units (excluding Tibet Autonomous Region, Taiwan Province, Hong Kong Special Administrative Region, and Macao Special Administrative Region) over a 16-year period from 2004 to 2019, along with other relevant data, amounting to a total sample size of 480. The dependent variable was the total ${\mathrm{CO}}_2$ emissions, while the covariates included eight primary indicators and 13 secondary indicators. The specific variable measures and data sources are presented as follows:

(i)

Dependent variable: We evaluated carbon emissions using China’s provincial ${\mathrm{CO}}_2$ data, which were sourced from the China Emission Accounts and Datasets (CEADs) ([27,28,29,30]).

(ii)

Independent variables: Per capita GDP (denoted as GDP) and the proportion of GDP contributed by tertiary industry (denoted as TR). In the context of China, many studies have verified that GDP contributes to carbon emissions [14,15,16,17,18]. However, we believe that this contribution is not constant over time and varies among provinces, and is likely closely related to TR. Therefore, we chose GDP as an indicator of economic growth, while TR served as a direct descriptive variable capturing the heterogeneity in the contribution of economic growth to carbon emissions. In Section 3.2, we elaborate on this process in detail. These data were obtained from the China Statistical Yearbook.

(iii)

Control variables: Per capita disposable income (denoted as DI), financial interrelation ratio (denoted as FIR), financial efficiency (denoted as FE), mileage of highways (denoted as MH), afforestation area (denoted as AFF), per capita fixed asset investment (denoted FI), per capita fixed asset investment in the state-owned energy industry (denoted as EFI), per capita technology market transaction volume (denoted TM), patents for inventions authorized per 10k persons (denoted PA), size of population(PO), and urbanization rate (denoted UR). The data of FIR and FE were obtained from the China Financial Yearbook and the remaining data were retrieved from the national data website (https://data.stats.gov.cn/, accessed on 22 August 2024), as well as the China Statistical Yearbook.

According to the STRIPAT theory [6], carbon emissions can be assessed by population, affluence, and technology. Specifically, population and affluence growth tend to contribute to increased carbon emissions, while technological advancements can help mitigate them. In this context, it was natural for us to represent population with PO and UR; affluence with DI, FI; and technology with EFI, TM, and PA. Some studies have pointed out that China’s financial development can promote carbon emissions [23,31]. Therefore, we followed their settings and took FIR and FE as indicators of finance. A significant source of carbon emissions is the use of gasoline-powered vehicles, hence it was reasonable to consider the impact of transportation development on carbon emissions. For this reason, we adopted MH as a representative indicator of transportation. Photosynthesis in trees is a crucial component of the carbon cycle, and it is therefore reasonable to consider the impact of greening levels on carbon emissions. For this purpose, we adopted afforestation area as a representative indicator of greening levels.

To sum up,

Table 1. Explanation of variables.

Primary Indicators	Sub Indicators	Unit	Symbol
Carbon emission	-	million tons	CE
Economic growth	Per capita GDP	10k Yuan	GDP
Industrial structure	The proportion of the GDP contributed by the tertiary industry	-	TR
Wealth	Per capita disposable income	10k Yuan	DI
	Per capita fixed asset investment	10k Yuan	FI
Finance	Financial interrelation ratio	-	FIR
	Financial efficiency	-	FE
Transportation	Mileage of highways	10k km	MH
Greening level	Afforestation area	1000 acres	AFF
Technology	Per capita fixed asset investment in the state-owned energy industry	10k Yuan	EFI
	Per capita technology market transaction volume	10k Yuan	TM
	Patents for inventions authorized per 10k persons	items per 10k persons	PA
Population	Size of population	10k persons	PO
	Urbanization rate	-	UR

presents the actual meanings of the variables, and

Table 2. Descriptive statistical analysis.

Indicators	Unit	Mean	Standard Deviation	Maximum	Minimum
CE	million tons	312.442	263.806	1700.040	7.550
GDP	10k Yuan	3.012	1.895	11.524	0.424
TR	-	0.439	0.093	0.840	0.300
DI	10k Yuan	1.703	0.741	5.261	0.722
FI	10k Yuan	2.101	1.261	6.500	0.222
FIR	-	3.026	1.067	7.552	1.445
FE	-	0.763	0.124	1.244	0.455
MH	10k km	13.008	7.561	33.710	0.780
AFF	1000 acres	192.216	168.761	861.900	0.710
EFI	10k Yuan	0.074	0.067	0.406	0.013
TM	10k Yuan	0.061	0.193	1.852	0.000
PA	items per 10k persons	1.176	2.507	24.259	0.024
PO	10k persons	4469.157	2684.577	11,521.000	539.000
UR	-	0.539	0.143	0.900	0.263

presents a descriptive analysis of the variables, revealing that the maximum carbon emission value was 1700.04, while the minimum was only 7.550, indicating significant variations and a high degree of differentiation among provinces.

3.2. Analysis of Carbon Dependence Heterogeneity and Spatial Spillover Effects of Carbon Emissions

Carbon emissions primarily stem from the consumption of fossil fuels, which in turn serve as a significant driving force for economic growth. The chain of relationships between economic growth, energy consumption, and carbon emissions is crucial in understanding the mechanism of how economic growth contributes to carbon emissions. The achievement of the “dual carbon” goals essentially aims to sever this relationship chain. There are two primary directions to pursue in this effort:

First, weakening the economic growth–energy consumption sub-chain essentially means weakening economic growth’s dependence on energy. To achieve this, we need to start by adjusting the industrial structure. From the perspective of the nature of industry, although secondary industry has a strong economic driving capacity, its dependence on energy is also the most significant. On the other hand, tertiary industry has a strong pulling effect on economic development, covers a wide range of areas, has a large employment capacity, and is less dependent on energy. From the perspective of the actual national situation, the proportion of China’s tertiary industry in 2019 was 53.9%, far below the world average of 65.4%, and its development was relatively immature. This fact also reflects that China’s tertiary industry still has a large space for development. Therefore, appropriately compressing the scale of secondary industry and relying on tertiary industry to drive economic development is of great practical significance in interrupting the sub-chain of economic growth–energy consumption. According to Table 2, the industrial structure of provinces varies greatly, and adjusting the industrial structure of each province can reduce the dependence of economic growth on carbon emissions. In addition, the internal transformation and upgrading of secondary industry is also important. At present, manufacturing industry, as the pillar industry of most provinces, mostly relies on the introduction of core technologies from abroad, and the utilization rate of equipment, raw materials, and energy is low, resulting in a situation of high consumption, high emissions, and low output.

Therefore, secondary industry is in urgent need of reform and development towards high-end manufacturing industries with production digitization, production automation, independent research and development, and green manufacturing, so as to maximize the utilization rate of resources and energy, which is also an important part of the transformation and upgrading of the industrial structure.

Second is weakening the energy consumption–carbon emissions subchain. Fossil energy consumption is the main source of carbon emissions, so the core approach to interrupting this subchain is to optimize the structure of energy consumption, develop renewable and clean energy technologies, vigorously promote clean energy, and reduce or even phase out fossil energy consumption, which is a sure way to achieve “dual carbon” targets. Regrettably, according to China’s current national situation, fossil energy is still the absolute mainstay of consumption in all provinces, and the gap in the energy consumption structure is relatively small, with less than 10 per cent of energy consumption accounted for by cleaner energy sources, even in the most developed provincial-level administrative units such as Beijing and Shanghai.

In summary, there are significant differences in economic development, industrial structure, and carbon emissions among provinces. Figure 1 demonstrates the relationship between industrial structure, economic development, and carbon emissions. The dots in the lower right corner of Figure 2 represent provinces that possess a significant proportion of tertiary industry, a high economic level, and low carbon emissions. The industrial structure of these provinces is highly optimized. Consequently, a structural breakdown of the three major industries in each province can reveal the heterogeneity their contributions to carbon emissions in terms of economic growth.

With the development of the transportation industry, frequent industrial transfers, market flows, and population relocations have occurred between neighboring provinces, resulting in increasingly close links between them in various aspects. Many studies have confirmed the existence of spatial spillover effects in regional economic development. Since economic development is closely related to carbon emissions, it is plausible that carbon emissions might also exhibit spatial spillover effects. Figure 2 depicts the distribution of provincial carbon emissions in China over the years. It illustrates that high carbon emissions are primarily concentrated in North China and parts of East China and Northwest China, whereas low carbon emissions are clustered in Southwest China and West China. Therefore, carbon emissions display a pattern of high-value aggregation, indicating the potential for a positive spatial spillover effect, or in other words, a trickle-down effect.

4. Model Construction and Empirical Analysis

4.1. Model Building

This paper established a varying-coefficient spatial autoregressive panel model for carbon emission data and related covariate data from China’s 30 provincial-level administrative units, spanning from 2004 to 2019. Prior to analyzing the data, several tests were required. To avoid pseudo-regression, a panel data cointegration test was first conducted on the variable data from 30 provinces, covering 16 years and 14 dimensions. Before conducting the unit root test on panel data, it was necessary to confirm cross-sectional dependence to select an appropriate testing method. We adopted the Pesaran cross-section dependence (CD) test [32], which revealed a statistic of 10.329 with a p-value less than 0.01, indicating significant cross-sectional dependence consistent with the anticipated spatial dependence, thereby justifying spatial modeling. Given the presence of cross-sectional dependencies in the panel data, the first-generation conventional panel unit root tests, such as the Levin–LinChu (LLC), Im, Pesaran, Shin (IPS), and augmented Dickey Fuller (ADF) tests, were no longer suitable. Accordingly, the Pesaran cross-sectionally augmented IPS (CIPS) test proposed by Pesaran [33], which allows for cross-sectional dependence, was more appropriate in this study. Following the CIPS test, the data for each variable became stationary after taking the first-order difference, thus indicating that all variables were integrated in the same order at 0.1 level. The CIPS test results are presented in

Table 3. CIPS tests results.

Variables	Level		First-Order Difference
	p-Value	Stationarity	p-Value	Stationarity
ln CE	>0.1	not stationary	<0.01	stationary
ln GDP	>0.1	not stationary	0.011	stationary
ln TR	>0.1	not stationary	0.048	stationary
ln DI	>0.1	not stationary	<0.01	stationary
ln FI	>0.1	not stationary	0.073	stationary
ln FIR	>0.1	not stationary	<0.01	stationary
ln FE	>0.1	not stationary	<0.01	stationary
ln MH	<0.01	stationary	<0.01	stationary
ln AFF	>0.1	not stationary	<0.01	stationary
ln EFI	>0.1	not stationary	<0.01	stationary
ln TM	>0.1	not stationary	<0.01	stationary
ln PA	>0.1	not stationary	<0.01	stationary
ln PO	>0.1	not stationary	0.097	stationary
ln UR	>0.1	not stationary	<0.01	stationary

. Subsequently, a Johansen cointegration test was performed on the variables. The test rejected the null hypothesis that there was no cointegration relationship between the variables at a 0.01 level, indicating that the variables could be regressed for modeling.

Furthermore, the establishment of a spatial autoregressive panel model necessitates the testing of spatial correlation. However, in this paper, variable selection was carried out during the estimation of model parameters. Insignificant coefficients were eliminated, and the spatial autoregressive coefficients $\rho$ were no exception. If $\rho =0$, this indicates that there is no spatial spillover effect; if $\rho >0$, this suggests the presence of a trickle-down effect; and if $\rho <0$, this implies the existence of a polarization effect. Therefore, spatial correlation was not explicitly tested here.

For the particular form of the panel model, the model was first tested for the presence of individual and time effects. The time effect F-test statistic was 1.032 with a p-value of 0.404; therefore, a time effect did not exist. The individual effect F-test statistic was 8.091 with a p-value smaller than 0.01; therefore, the null hypothesis that there is no individual effect term in the model was rejected at a 0.01 significance level and an individual effect existed. In addition, the chi-square statistic of the traditional Hausman test was 369.68 with a p-value of less than 0.01, and the chi-square statistic of the robust Hausman test was 97.7 with a p-value of less than 0.01, both of which rejected the null hypothesis of an individual random effect, thus the individual effect was not from a random perturbation and there was a substantial difference.

Therefore, we utilized the STIRPAT modeling framework to establish a semi-parametric varying-coefficient spatial autoregressive panel model with fixed effects. In this model, carbon emissions were set as the dependent variable. The coefficients of the economic growth variables were set in a functional form to capture the heterogeneity in the relationship between economic growth and carbon emissions. Additionally, a spatial autoregressive term was included to reflect the spatial spillover effect of carbon emissions, and individual fixed effects were incorporated to account for the inherent endowment of provinces and municipalities that remained unvarying over time. A semi-parametric varying-coefficient spatial autoregressive panel model with fixed effects was constructed:

$$\begin{array}{cc}\hfill \ln {\mathrm{CE}}_{it}=& \rho \sum _{j=1}^{30}{w}_{ij}\ln {\mathrm{CE}}_{jt}+g\left({\mathrm{TR}}_{it}\right)\ln {\mathrm{GDP}}_{it}+\hfill \\ \hfill & {\beta }_1\ln {\mathrm{DI}}_{it}+{\beta }_2\ln {\mathrm{FI}}_{it}+{\beta }_3\ln {\mathrm{FIR}}_{it}+{\beta }_4\ln {\mathrm{FE}}_{it}+\hfill \\ \hfill & {\beta }_5\ln {\mathrm{MH}}_{it}+{\beta }_6\ln {\mathrm{AFF}}_{it}+\hfill \\ \hfill & {\beta }_7\ln {\mathrm{EFI}}_{it}+{\beta }_8\ln {\mathrm{TM}}_{it}+{\beta }_9\ln {\mathrm{PA}}_{it}+\hfill \\ \hfill & {\beta }_{10}\ln {\mathrm{PO}}_{it}+{\beta }_{11}\ln {\mathrm{UR}}_{it}+{\alpha }_i+{\epsilon }_{it},\hfill \end{array}$$

(2)

where $i(=1,2,\dots ,30)$ denotes province, $t(=1,2,\dots ,16)$ denotes year, and $w_{ij}$ is the element of the spatial weight matrix $\mathit{W}$; $\mathit{W}$ is a given N dimensional square matrix that satisfies ${\sum }_{j=1}^N{w}_{ij}=1$ and $w_{ii}=0$, and therefore ${\sum }_{j=1}^{30}{w}_{ij}\ln {\mathrm{CE}}_{jt}$ can be regarded as the weighted average of all other regions’s $\ln CE$ in year t; $\rho$ is the unknown spatial autoregressive coefficient, valued in $(-1,1)$, which is used to indicate the degree of spatial correlation between individuals. Obviously, $\rho >0$ indicates a positive carbon interaction among different regions, and a larger value of $\rho$ indicates a stronger interaction; $g(·)$ is the coefficient of $\ln GDP$, which appears as an unknown smooth function; ${\beta }_1,\dots ,{\beta }_{11}$ are the unknown constant coefficients corresponding to their respective variables; ${\alpha }_i$ denotes the individual fixed effect term, which can be considered as the intercept term for each region; ${\epsilon }_{it}$ is random disturbance; and the rest of the variables are shown in Table 1.

The spatial weight matrix $\mathit{W}=\left\{w_{ij}\right\}$ in model (2) is the key to studying the spatial spillover effect of carbon emissions, and its construction represents the spatial structure of carbon emissions, which was particularly important in the subsequent analysis. Analysis based on Figure 2 demonstrated that provincial carbon emissions in our country are characterized by high-value aggregation, indicating that the carbon emissions in various regions are likely to be related to adjacent provinces or regions. Consequently, this article employed two methods to construct the spatial weight matrix $\mathit{W}$. (i) Contiguity rule. Using the classical contiguity relationship, which determines whether two regions are adjacent based on whether they have a common boundary. When region i and region j have a common boundary $w_{ij}=1$, otherwise $w_{ij}=0$. Finally, transformation is used to ensure that the row sum is 1 and the diagonal is 0. To avoid the island effect, Guangdong, Guangxi, and Hainan had a common boundary. (ii) Group rule. A matrix was constructed using the seven major geographic divisions in China. Assign $w_{ij}=1$ when regions i and j are within the same geographical division; otherwise, assign $w_{ij}=0$. Similarly, through transformation, the matrix is also satisfied when the row sum is 1 and the diagonal is 0. The final spatial weight matrix $\mathit{W}$ obtained is a $30\times 30$ dimensional matrix and does not vary with time.

4.2. Methods of Estimation

The general form of model (2) was abbreviated as a semi-parametric varying-coefficient spatial autoregressive panel model:

$$\begin{array}{c}\hfill y_{it}=\rho \sum _{j=1}^N{w}_{ij}{y}_{jt}+z_{it}g\left(u_{it}\right)+{\mathit{X}}_{it}^{\prime }\mathit{\beta }+{\alpha }_i+{\epsilon }_{it},\end{array}$$

(3)

where $i=1,2,\dots ,N; t=1,2,\dots ,T$. $y_{it}\in \mathbb{R}$ and ${(z_{it},u_{it},{\mathit{X}}_{it}^{\prime })}^{\prime }\in {\mathbb{R}}^{p+2}$ represent the response variable and covariates for the observation of individual i at period t, respectively; $g(·)$ is the unknown smooth function, ${\alpha }_i$ is the fixed individual effect term, which only depends on the individual i and implies that ${\alpha }_i$ can capture unobservable inter-individual heterogeneity; $\mathit{\beta }={({\beta }_1,\dots ,{\beta }_p)}^{\prime }$ is a vector of unknown regression coefficients; $\epsilon$ is a random disturbance term with mean 0 and unknown variance ${\sigma }^2$, which satisfies $E\left({\epsilon }_{it}{\epsilon }_{js}\right)=0$ for all $i\ne j$ or $t\ne s$. $w_{ij}$ is the element of the spatial weight matrix $\mathit{W}$, and $\mathit{W}$ is a given N dimensional square matrix, for $i=1,2,\dots ,N$ satisfies ${\sum }_{j=1}^N{w}_{ij}=1$ and $w_{ii}=0$. $\rho$ is the unknown spatial autoregressive coefficient, valued in $(-1,1)$, which is used to indicate the degree of spatial correlation between individuals. Obviously, $\rho >0$ indicates a positive carbon interaction among different regions, and a larger value of $\rho$ indicates a stronger interaction. When $\rho =0$, the model degenerates into a general varying-coefficient panel model, i.e., there is no interaction between different individuals. There are 11 explanatory variables in model (2), and too many explanatory variables may not only lead to the problem of multicollinearity, but may also include irrelevant variables in the model and produce an overfitted model. Therefore, we considered the variable selection for the general model (3). The function coefficients $g\left(u\right)$ were first approximated using a linear combination of B-spline basis functions:

$$\begin{array}{c}\hfill g\left(u\right)\approx {\mathit{B}}^{\prime }\left(u\right)\mathit{\gamma },\end{array}$$

(4)

where $\mathit{B}\left(u\right)={\left(B_1\left(u\right),B_2\left(u\right),\dots ,B_{K+g+1}\left(u\right)\right)}^{\prime }$ is a series of known B-spline basis functions of order g with K knots, and $\mathit{\gamma }={({\gamma }_1,{\gamma }_2,\dots ,{\gamma }_{K+g+1})}^{\prime }$ are the unknown coefficients to be estimated, and $\widehat{g}\left(u\right)$ can be obtained from the estimator $\widehat{\mathit{\gamma }}$ by $\widehat{g}\left(u\right)=\mathit{B}\left(u\right)\widehat{\mathit{\gamma }}$. Denote $n=N\times T$, substituting (4) into model (3) and organizing it into matrix form yields

$$\begin{array}{c}\hfill {\mathit{Y}}_n\approx \rho {\mathit{W}}_n{\mathit{Y}}_n+{\mathit{X}}_n\mathit{\beta }+{\mathit{S}}_n\mathit{\gamma }+{\mathit{D}}_n\mathit{\alpha }+{\mathit{V}}_n,\end{array}$$

(5)

where ${\mathit{Y}}_n={({\mathit{Y}}_1^{\prime },\dots ,{\mathit{Y}}_t^{\prime },\dots ,{\mathit{Y}}_T^{\prime })}^{\prime }$, and ${\mathit{Y}}_t={(y_{1t},\dots ,y_{Nt})}^{\prime }; {\mathit{W}}_n={\mathit{I}}_T\otimes \mathit{W}$, ⊗ represents the Kronecker product notation and ${\mathit{I}}_T$ represents T dimensional identity matrix; the covariates ${\mathit{X}}_n={({\mathit{X}}_1^{\prime },\dots ,{\mathit{X}}_t^{\prime },\dots ,{\mathit{X}}_T^{\prime })}^{\prime }$, and ${\mathit{X}}_t={({\mathit{X}}_{1t},\dots ,{\mathit{X}}_{Nt})}^{\prime }$; ${\mathit{S}}_n={({\mathit{S}}_1^{\prime },\dots ,{\mathit{S}}_t^{\prime },\dots ,{\mathit{S}}_T^{\prime })}^{\prime }$, and ${\mathit{S}}_t={(\mathit{B}\left(u_{1t}\right)z_{1t},\dots ,\mathit{B}\left(u_{Nt}\right)z_{Nt})}^{\prime }$; ${\mathit{D}}_n={\mathit{\iota }}_T\otimes {\mathit{I}}_N$, ${\mathit{\iota }}_T$ is a T dimensional column vector with element 1; $\mathit{\alpha }={({\alpha }_1,\dots ,{\alpha }_N)}^{\prime }$ is the individual effect vector. Therefore, the parameters to be estimated in model (5) are ${\sigma }^2,\rho ,\mathit{\beta },\mathit{\gamma },\mathit{\alpha }$. Let ${\mathit{M}}_n\left(\rho \right)={\mathit{I}}_n-\rho {\mathit{W}}_n$, then the log Gaussian likelihood function (also known as the quasi-likelihood function) of model (5) is

$$\begin{array}{cc}\hfill L_1({\sigma }^2,\rho ,\mathit{\beta },\mathit{\gamma },\mathit{\alpha })=& -{\displaystyle \frac{n}{2}}\ln 2\pi +\ln \left|{\mathit{M}}_n\left(\rho \right)\right|-\hfill \\ \hfill & {\displaystyle \frac{n}{2}}\ln {\sigma }^2-{\displaystyle \frac{1}{2{\sigma }^2}}{\mathit{U}}_1^{\prime }\left(\mathit{\delta }\right){\mathit{U}}_1\left(\mathit{\delta }\right),\hfill \end{array}$$

(6)

where $\mathit{\delta }=(\rho ,\mathit{\beta },\mathit{\gamma },\mathit{\alpha })$, and ${\mathit{U}}_1\left(\mathit{\delta }\right)={\mathit{M}}_n\left(\rho \right){\mathit{Y}}_n-{\mathit{X}}_n\mathit{\beta }-{\mathit{S}}_n\mathit{\gamma }-{\mathit{D}}_n\mathit{\alpha }$. To avoid the “curse of dimensionality” caused by the N dimensional parameter $\mathit{\alpha }$, $\mathit{\alpha }$ need to be concentrated out from function (6). That is, for a given ${\sigma }^2,\rho ,\mathit{\beta },\mathit{\gamma }$, one can obtain the solution $\widehat{\mathit{\alpha }}({\sigma }^2,\rho ,\mathit{\beta },\mathit{\gamma })={\left({\mathit{D}}_n^{\prime }{\mathit{D}}_n\right)}^{-1}{\mathit{D}}_n^{\prime }({\mathit{M}}_n\left(\rho \right){\mathit{Y}}_n-{\mathit{X}}_n\mathit{\beta }-{\mathit{S}}_n\mathit{\gamma })$ from Equation (6). Then, substitute this solution into Equation (6):

$$\begin{array}{cc}\hfill L_2({\sigma }^2,\rho ,\mathit{\beta },\mathit{\gamma })=& -{\displaystyle \frac{n}{2}}\ln 2\pi +\ln \left|{\mathit{M}}_n\left(\rho \right)\right|-{\displaystyle \frac{n}{2}}\ln {\sigma }^2-\hfill \\ \hfill & {\displaystyle \frac{1}{2{\sigma }^2}}{\mathit{U}}_2^{\prime }(\rho ,\mathit{\beta },\mathit{\gamma }){\mathit{J}}_n{\mathit{U}}_2(\rho ,\mathit{\beta },\gamma \mathit{)},\hfill \end{array}$$

(7)

where ${\mathit{J}}_n={({\mathit{I}}_n-{\mathit{Q}}_n)}^{\prime }({\mathit{I}}_n-{\mathit{Q}}_n)$ is a projection matrix and ${\mathit{Q}}_n={\mathit{D}}_n{\left({\mathit{D}}_n^{\prime }{\mathit{D}}_n\right)}^{-1}{\mathit{D}}_n^{\prime }$; ${\mathit{U}}_2(\rho ,\mathit{\beta },\mathit{\gamma })={\mathit{M}}_n\left(\rho \right){\mathit{Y}}_n-{\mathit{X}}_n\mathit{\beta }-{\mathit{S}}_n\mathit{\gamma }$. Likewise, given ${\sigma }^2,\rho ,\mathit{\beta }$, the solution of Equation (7) is derived as $\widehat{\mathit{\gamma }}({\sigma }^2,\rho ,\mathit{\beta })={\left[{\mathit{S}}_n^{\prime }{\mathit{J}}_n{\mathit{S}}_n\right]}^{-1}{\mathit{S}}_n^{\prime }{\mathit{J}}_n({\mathit{M}}_n\left(\rho \right){\mathit{Y}}_n-{\mathit{X}}_n\mathit{\beta })$, substituting into (7) yields the profile quasi-likelihood function:

$$\begin{array}{cc}\hfill L({\sigma }^2,\rho ,\mathit{\beta })=& -{\displaystyle \frac{n}{2}}\ln 2\pi +\ln \left|{\mathit{M}}_n\left(\rho \right)\right|-{\displaystyle \frac{n}{2}}\ln {\sigma }^2-\hfill \\ \hfill & {\displaystyle \frac{1}{2{\sigma }^2}}{\mathit{U}}^{\prime }(\rho ,\mathit{\beta }){\mathit{P}}_n\mathit{U}(\rho ,\mathit{\beta }),\hfill \end{array}$$

(8)

where ${\mathit{P}}_n={({\mathit{I}}_n-{\mathit{Q}}_n)}^{\prime }{\mathsf{\Omega }}_n({\mathit{I}}_n-{\mathit{Q}}_n)$, ${\mathsf{\Omega }}_n={\mathit{I}}_n-({\mathit{I}}_n-{\mathit{Q}}_n){\mathit{S}}_n{\left[{\mathit{S}}_n^{\prime }{\mathit{J}}_n{\mathit{S}}_n\right]}^{-1}{\mathit{S}}_n^{\prime }{({\mathit{I}}_n-{\mathit{Q}}_n)}^{\prime }$ and $\mathit{U}(\rho ,\mathit{\beta })={\mathit{M}}_n\left(\rho \right){\mathit{Y}}_n-{\mathit{X}}_n\mathit{\beta }$. To achieve variable selection, a penalty is imposed on $\rho ,\mathit{\beta }$ in Equation (8), resulting in the penalized profile quasi-likelihood function:

$$\begin{array}{c}\hfill Q({\sigma }^2,\rho ,\mathit{\beta })=L({\sigma }^2,\rho ,\mathit{\beta })-n{p}_{\lambda }\left(\right|\rho \left|\right)-n\sum _{j=1}^p{p}_{\lambda }\left(\right|{\beta }_j\left|\right),\end{array}$$

(9)

where $p_{\lambda }(·)$ represents the penalty function, it is typically selected as the lasso penalty function (Tibshirani [34]), the SCAD penalty function (Fan and Li [35]), or the adaptive lasso penalty function (Zou [36]) and $\lambda$ is a tuning parameter. Then, the penalized estimators ${\widehat{\sigma }}^2,\widehat{\rho },\widehat{\mathit{\beta }}$ can be obtained by maximizing $Q({\sigma }^2,\rho ,\mathit{\beta })$, that is

$$\begin{array}{c}\hfill {\widehat{\sigma }}^2,\widehat{\rho },\widehat{\mathit{\beta }}=\underset{{\sigma }^2,\rho ,\mathit{\beta }}{arg\; max}Q({\sigma }^2,\rho ,\mathit{\beta }).\end{array}$$

(10)

The varying-coefficient part can then be derived from the following equations

$$\left\{\begin{array}{c}\widehat{\mathit{\gamma }}={\left[{\mathit{S}}_n^{\prime }{\mathit{J}}_n{\mathit{S}}_n\right]}^{-1}{\mathit{S}}_n^{\prime }{\mathit{J}}_n({\mathit{M}}_n\left(\rho \right){\mathit{Y}}_n-{\mathit{X}}_n\mathit{\beta }),\hfill \\ \widehat{g}\left(u\right)={\mathit{B}}^{\prime }\left(u\right)\widehat{\mathit{\gamma }}.\hfill \end{array}\right.$$

(11)

The estimator derived from (10) can shrink the coefficients with smaller estimation values to zero, thus achieving the purpose of variable selection.

4.3. Empirical Result Analysis

Referring to the algorithms of penalized quasi-maximum likelihood estimation of Liu et al. [37] and Xia et al. [38], variable selection for model (2) was conducted based on the objective function (9), incorporating both SCAD and adaptive LASSO penalties, and the tuning parameter $\lambda$ was selected using the BIC criterion. Within this framework, the varying-coefficient functions were approximated using B-splines. The estimation results obtained under two distinct spatial weight matrix configurations are summarized in

Table 4. Parameter estimation results.

Estimator	Indicator	Contiguity Rule		Group Rule
		Adaptive LASSO	SCAD	Adaptive LASSO	SCAD
${\sigma }^2$	-	0.0260	0.0263	0.0257	0.0258
		(0.0018)	(0.0018)	(0.0017)	(0.0017)
$\rho$	-	0.2892	0.2660	0.2513	0.2644
		(0.0225)	(0.0346)	(0.0294)	(0.0578)
${\beta }_1$	ln DI	0.0336	0	0.1157	0.1301
		(0.0033)	(-)	(0.0019)	(0.0273)
${\beta }_2$	ln FI	0	0	0	0
		(-)	(-)	(-)	(-)
${\beta }_3$	ln FIR	0.3586	0.3837	0.3410	0.3600
		(0.0215)	(0.0834)	(0.0302)	(0.0845)
${\beta }_4$	ln FE	−0.1781	−0.2082	−0.142	−0.0015
		(0.0118)	(0.0195)	(0.0129)	(−0.0004)
${\beta }_5$	ln MH	−0.0710	0	−0.1029	−0.1142
		(−0.0062)	(-)	(0.0125)	(0.0213)
${\beta }_6$	ln AFF	−0.0657	−0.0559	−0.0713	−0.0746
		(0.0043)	(0.0018)	(0.0068)	(0.0104)
${\beta }_7$	ln EFI	0	0	0	0
		(-)	(-)	(-)	(-)
${\beta }_8$	ln TM	0	−0.0045	−0.0155	−0.0143
		(-)	(0.0005)	(0.0019)	(0.0012)
${\beta }_9$	ln PA	0	0	0	0
		(-)	(-)	(-)	(-)
${\beta }_{10}$	ln PO	1.1827	1.2072	0.8170	0.8472
		(0.0728)	(0.2266)	(0.0690)	(0.2300)
${\beta }_{11}$	ln UR	0	0	0	0
		(-)	(-)	(-)	(-)
R-squred	-	0.9618	0.9614	0.9623	0.9621

and Figure 3.

Based on Table 4, the following observations can be drawn: (i) The positive spatial correlation coefficient $\rho$ revealed the existence of spatial dependency in the carbon emission data, indicating that neighboring provinces exhibit mutual reinforcement in their carbon emissions. (ii) Carbon emissions displayed a strong positive correlation with the financial interrelation ratio and population. (iii) However, the correlation between carbon emissions and various factors such as per capita fixed asset investment, investment in state-owned energy industries, patents for inventions authorized per 10k persons, and urbanization rate remained insignificant. (iv) It is noteworthy that all four models exhibited R-squared values exceeding 0.96, indicating a strong fit of the models to the data. Furthermore, Figure 3 presents the estimated varying coefficient functions for per capita GDP, revealing similar dynamic trends across different functions despite significant variations, thus validating the reasonableness of the varying-coefficient function setting for per capita GDP.

4.3.1. Empirical Analysis of Spatial Spillover Effects

Based on Table 4, the estimators of the spatial autoregressive coefficient $\rho$ remained relatively consistent across the different spatial weight structures, all exceeding 0.2. This coefficient directly reflected the elasticity of carbon emissions in one province to its neighboring regions. Specifically, an increase (or decrease) of 1% in carbon emissions in province j would lead to an increase (or decrease) of over $(0.2\ast w_{ij})\%$ in carbon emissions in provinces i, where $w_{ij}$ is the element of the spatial weight matrix $\mathit{W}$. As a result, the spatial spillover effect of carbon emissions manifested primarily as a trickle-down effect. According to the theory of industrial relocation, during the process of regional industrial optimization, industries with relatively high consumption, high emissions, and low output tend to be transferred to surrounding less developed regions. For these less developed regions, these industries are considered relatively low-consumption, low-emission, and high-output quality industries. Therefore, the trickle-down effect of reducing carbon emissions in leading provinces on their neighboring regions was particularly evident. For instance, the trickle-down effect of carbon emissions was particularly prominent in the Beijing–Tianjin–Hebei region, where Hebei primarily experiences industrial relocations from Beijing and Tianjin, leading to increasingly significant emission reduction effects in recent years.

4.3.2. Analysis of Heterogeneity in Provincial Economic Growth Contributions to Carbon Emissions

Figure 3 illustrates the functional relationship between the coefficient of log per capita GDP (i.e., ln GDP) and the proportion of GDP contributed by the tertiary sector (i.e., TR). This graph provides a visual representation of the degree of carbon dependency. As TR increases, the coefficient of ln GDP decreases. When TR reaches 0.3, the coefficient of ln GDP is within the range of 0.9 to 1. This implies that a 1% increase in per capita GDP would result in a corresponding increase of 0.9% to 1% in carbon emissions, indicating that per capita GDP and carbon emissions are growing at a similar rate. However, when TR exceeds 0.7, the coefficient of ln GDP approaches zero, suggesting that economic growth no longer significantly contributes to an increase in carbon emissions. Furthermore, Figure 4 presented coefficients of ln GDP across various provinces in key years. Over the span of 16 years, as society progressed, the overall trend of coefficients across provinces has been downward. Additionally, a comparison among 30 provinces revealed a gradual narrowing of the differences in their coefficients of ln GDP.

Upon further examination, it was discovered that there are two inflection points in Figure 3. Based on these inflection points, this paper divided the relationship between economic growth and carbon emissions in China’s 30 provincial-level administrative units into three stages:

(i)

“Strong dependency” stage: When TR $\in [0,0.4)$, and the coefficient of per capita GDP is greater than 0.4.

(ii)

“Weak dependency” stage: When TR $\in [0.4,0.6)$, with the coefficient of per capita GDP is approximately between 0.2 and 0.4.

(iii)

“Economic carbon peak” stage: When TR $\in [0.6,1)$, indicating a per capita GDP coefficient of less than 0.2.

According to a report released by the World Resources Institute in 2017, 49 countries worldwide have achieved carbon peak, with the majority of these countries having a proportion of tertiary industry exceeding 60%, and many exceeding 75%. This adds credibility to the three-stage classification standard.

The “strong dependency” stage is characterized by a high level of contribution from economic growth to carbon emissions and a relatively low proportion of growth in the tertiary industry. Most provinces in this stage rely on secondary industry as their pillar industry, driving economic growth through its size, often at the cost of the environment. High consumption, high emissions, and extensive development are the dominant patterns in this stage. Furthermore, within secondary industry, which dominates the “strong dependency” stage, there is a considerable proportion of industries with high consumption, high emissions, and low output. As the industrial structure adjusts during this stage, the weak players within secondary industry are eliminated, and most extensive industries are jointly rectified by the government and the market, leading to a gradual slowdown in carbon emissions and a transition to the “weak dependency” stage.

The “weak dependency” stage is characterized by a moderate correlation between economic growth and carbon emissions. As the proportion of tertiary industry increases, the coefficient of per capita GDP continues to decline, but at a slower rate. Emission reduction efforts in this stage are protracted, as secondary industry remains rigid, and significant structural adjustments cannot be achieved quickly. Focusing solely on expanding tertiary industry and reducing secondary industry’s share will yield limited results. Therefore, it is crucial to actively shift carbon emission reduction strategies and adjust specific strategic deployments to achieve carbon neutrality and peak carbon emissions. The “carbon peak” stage is marked by the decoupling of economic growth and carbon emissions, with the latter reaching its peak. In this stage, the industrial structure is highly optimized, with tertiary industry driving economic growth. The focus should be on the second phase of the “dual carbon” goal, namely, achieving carbon neutrality.

We categorized China’s 30 provincial-level administrative units into three stages: “strong dependency”, “weak dependency”, and “economic carbon peak”, as shown in Figure 5. This figure illustrates the heterogeneity in the contribution of economic growth to carbon emissions among provinces, as well as the heterogeneity across different time points. In 2004, the number of provinces in the “strong dependency” stage was comparable to those in the “weak dependency” stage. Coastal provinces were mostly in the strong dependency stage, with Beijing being the only provincial administrative region at the “economic carbon peak” stage. During the early 2000s, China’s economy was undergoing rapid development, with industrialization booming. Coastal provinces, leveraging their geographical advantages and China’s recent accession to the World Trade Organization, witnessed a rapid growth in primary manufacturing and processing trade industries. Typical examples included the emergence of the Yangtze River Delta and Pearl River Delta as manufacturing hubs, marking the beginning of the “Made in China” era. However, this primary manufacturing-driven economic growth had a significant downside: it locked the relationship between economic development and environmental burden, leading to a surge in carbon emissions alongside economic growth. Given China’s national conditions, sacrificing economic growth to reduce carbon emissions was not feasible, and low-carbon technologies, carbon recycling techniques, and corporate environmental awareness were still at a low level. Therefore, coastal areas, which were in the mid-stage of industrialization, were mostly in the “strong dependency” stage.

In 2009, the number of provinces in the “strong dependency” and “weak dependency” stages remained similar, but there were changes in their distribution. Zhejiang, Fujian, Sichuan, Yunnan, and Guizhou moved from “strong dependency” to “weak dependency”, while Liaoning, Inner Mongolia, Qinghai, Anhui, and Hubei shifted from “weak dependency” to “strong dependency”, indicating that the transition from “strong dependency” to “weak dependency” is a reversible process.

Zhejiang and Fujian, as coastal provinces, started industrialization early and have mature industrial chains. By 2009, they were transitioning from the mid to late stages of industrialization, with their manufacturing industries moving in higher-end, technology-intensive, knowledge-intensive, low-carbon, and high value-added directions. Simultaneously, low-output industries and primary manufacturing, due to their lack of competitiveness, were gradually phased out by the local market, triggering a trend in industrial relocation. In this process, high-carbon industries also migrated out, contributing to the transition from “strong dependency” to “weak dependency”.

Sichuan, Yunnan, and Guizhou, due to their geographical conditions, have difficulty forming complete industrial chains, resulting in weak industrial foundations and inability to support high-quality development. However, they have leveraged their unique geographical advantages to vigorously develop tourism as a pillar industry for economic development, entering the “weak dependency” stage without relying on industrial structure optimization.

Inner Mongolia, Anhui, and Hubei showed a “reverse trend” from 2004 to 2009, following in the footsteps of coastal areas and undertaking industrial relocations. Their industrialization processes lagged behind those of coastal areas. It can be seen that the contribution of economic growth to carbon emissions should follow an inverted “U”-shaped pattern with social development. Between 2004 and 2009, some provinces were in the “climbing” stage, thus possibly exhibiting a “reverse trend”.

By 2014, the number of provinces in the “weak dependency” stage had significantly increased, with only one-third remaining in the “strong dependency” stage. Shanghai emerged from the “weak dependency” stage and joined Beijing as one of the two provincial administrative regions at the “economic carbon peak” stage. Most provinces followed the coastal developed areas into the “weak dependency” stage, driven by industrial relocations. Their industrial chains gradually improved, industrial structures optimized, secondary industries became more refined, and tertiary industry flourished, marking significant progress in the transformation of economic development patterns.

By 2019, all 30 provinces had moved out of the “strong dependency” stage, with Tianjin officially entering the “economic carbon peak” stage alongside Beijing and Shanghai as the leading provincial-level administrative units for emission reduction. The three provincial-level administrative units at the “economic carbon peak” stage are all municipalities, which is undoubtedly supported by policy, but the role of industrial relocations should also be acknowledged. In 2014, the government proposed “deconcentrating Beijing’s economic center status”. Tianjin, which is adjacent to Beijing, directly received complete industrial chains, high-tech enterprises, and production factors from Beijing, enabling it to rapidly complete the transformation and upgrading of its industrial structure in the following five years and enter the “economic carbon peak” stage.

In the most relevant work by Liu et al. [16], where the STRIPAT model was independently fitted for 30 provinces and cities, their conclusion that the coefficients of lnGDP vary significantly across provinces, with notably lower values for Beijing and Shanghai compared to other provinces, aligned well with ours. However, aside from the loss in degrees of freedom mentioned in Section 2, their study assumed a constant coefficient for economic growth in each province, implying an unchanging contribution of economic growth to carbon emissions. While they considered cross-sectional heterogeneity, they overlooked heterogeneity across time dimensions, which our study aimed to address.

4.3.3. Analysis of Other Factors

Table 4 comprehensively reveals the variables that may influence carbon emissions. Most of these variables, potentially affected by population size, have been normalized on a per capita basis, eliminating the influence of population base. Consequently, population size, as a fundamental factor for carbon emissions, should have a growth rate aligned with carbon emissions. Our model corroborates this fact, with the coefficient for population size approaching 1 in the fitting results, indicating a nearly 1:1 correlation between carbon emissions and population size, with both increasing and decreasing together. This conclusion aligns closely with numerous academic studies, greatly enhancing the credibility of our model.

To a certain extent, the financial interrelation ratio represents the scale of the financial industry. Our results suggest that financial scale positively impacts carbon emissions, consistent with the findings of Chen and Zhang [23]. The rapid development of the financial sector has significantly stimulated China’s real economy, particularly secondary industry. Currently, China’s scientific and educational stock, industrial structure specialization, and national environmental awareness are all at relatively low levels, leading to unavoidable increases in fossil energy utilization and carbon emissions during the development process. Financial efficiency signifies the contribution rate of the financial sector to the economy, while the financial sector itself does not directly emit carbon. A negative coefficient associated with financial efficiency indicates that China’s financial sector, through effective allocation of funds, is indirectly promoting the development of a low-carbon economy. This underscores the role of the financial industry in facilitating the transition towards more environmentally sustainable economic growth. Both the afforestation area and the per capita technology market transaction volume have inhibitory effects on carbon emissions, albeit with relatively small coefficients that may even be omitted in certain models. This is due to the fact that, given China’s significant carbon emission volume, these factors have limited capacity to curb emissions. This precisely underscores the paramount importance of optimizing industrial and energy structures as the top priorities for China’s carbon reduction.

Interestingly, the increase in highway mileage has an inhibitory effect on carbon emissions. This could be attributed to the vast territory of China, where the addition of highway mileage does not significantly boost transportation volume. Vehicles with high emissions and low efficiency, such as tractors, which were originally relied upon due to poor road conditions, were phased out after the construction of highways, indirectly optimizing the transportation vehicle structure and thereby suppressing carbon emissions.

5. Conclusions and Policy Suggestions

5.1. Main Conclusions

This paper delved into the disparities in how economic growth contributes to carbon emissions at the provincial level in China. Notably, there are marked variations in this contribution across different provinces and time points. Our findings revealed that the root of this heterogeneity primarily lies in the distinct industrial structures prevalent at the current stage.

To illustrate the industrial structure and accordingly demonstrate the extent of economic growth’s impact on carbon emissions, this paper employed the proportion of GDP contributed by the tertiary sector. Based on this metric, we categorized the pursuit of the “dual carbon” goals into three stages: “strong dependency”, “weak dependency”, and “economic carbon peak”. Each stage displays unique characteristics, necessitating customized carbon emission reduction strategies and focal points for “dual carbon” efforts.

Our research underscores that this three-stage categorization comprehensively outlines the heterogeneity in economic growth’s contribution to carbon emissions across China’s 30 provincial-level administrative units, as well as the phased transitions of each province over the past 16 years. Coastal provinces, benefiting from their strategic locations, have progressed to the “weak dependency” stage, gradually decoupling economic growth from carbon emissions. Notably, Beijing, Shanghai, and Tianjin, buoyed by both locational advantages and policy incentives, have taken the lead in decoupling economic growth from carbon emissions.

5.2. Policy Suggestions

Based on the preceding analysis, tailored policy implications are proposed to facilitate the achievement of the “dual carbon” targets across various provinces. Recognizing the heterogeneity in carbon emissions contributions from economic development, emission reduction strategies must be adapted to different stages. Most provinces currently find themselves in the “weak dependency” stage, where economic growth still leads to increased carbon emissions, albeit with a weakened positive relationship compared to the early 20th century. This suggests that sacrificing economic growth is not necessary to achieve the “dual carbon” targets. Instead, provinces should focus on steadily improving the internal industrial structure of the secondary sector, enhancing industrial quality and production efficiency, and upgrading infrastructure. Additionally, efforts should be directed towards vigorously developing the tertiary sector, including tourism, trade, and finance, to identify new economic growth points and achieve high-quality, rapid, and comprehensive development.

For Beijing, Shanghai, and Tianjin, which have essentially decoupled their economies from carbon emissions, the focus should shift to optimizing their energy structures. This involves developing clean energy utilization technologies and enhancing energy efficiency through technological advancements. These measures will further stabilize their decoupling status and serve as models for other regions.

Given China’s positive spatial spillover effect in provincial carbon emissions, where early emission reductions drive subsequent reductions, and early peak attainment leads to later peaks, establishing “carbon peak” pilot provinces is crucial. These pilot regions can leverage their first-mover advantages to provide valuable emission reduction experience to surrounding areas, thereby accelerating the overall emission reduction process and contributing to the “dual carbon” goals.