The Influencing Factors of Carbon Emissions in the Industrial Sector: Empirical Analysis Based on a Spatial Econometric Model

Abstract

To promote the low-carbon, high-quality development of China’s industrial sector and achieve the national carbon peak goal as soon as possible, this study explores the influencing factors of carbon emissions among industrial sectors. Based on the panel data of 36 industrial sectors in China from 2009 to 2021, the spatial effects and characteristics of industrial sectors are examined by the spatial Durbin model (SDM) based on analyzing the spatial correlation among industrial sectors. The results show the following: (1) Moran’s I statistical results show that China’s industrial carbon emissions have a strong positive spatial correlation, and with time, the spatial correlation between industrial sectors gradually increases. (2) The empirical results of the whole industrial sector show that the property rights structure, capital intensity, and energy structure are the main driving forces promoting carbon emission reduction; the grouping analysis results show that the impact of FDI and property rights structure on the carbon emissions of the industrial sector in different sample groups is different. Among them, the energy structure and research and development play a role in reducing carbon emissions in each sample group. (3) Therefore, in the future, to reduce carbon emissions in the industrial sector, it is necessary to inhibit growth factors and promote the role of reduction factors; optimizing the energy structure and improving the rationality of the property rights structure are effective ways to achieve energy conservation and emission reduction.

1. Introduction

In recent years, the peak of carbon emissions has become a hot topic in the fields of international energy conservation and emission reduction [1]. Since its reform and opening up, China has undergone swift economic expansion and consequently encounters significant global pressure to effectively tackle climate change issues. This research examines the factors influencing carbon emission variations across different industries, aiming to offer insights for developing policies to reduce industrial carbon emissions. China’s economy has developed rapidly, with its GDP increasing by 310.9 times since the reform and opening up, largely fueled by the extensive consumption of primary energy and fossil fuels. This economic model, while successful, has led to increased CO₂ emissions, contributing significantly to global climate deterioration [2,3]. Therefore, an in-depth study of industrial carbon dioxide emissions can provide effective help for the government’s macro-control and industry’s spontaneous adjustment. The industrial sector, accounting for 37.8% of China’s GDP, plays a pivotal role in national economic development. However, it also contributes to 70% of total carbon dioxide emissions [4], as shown in Figure 1. The spatial spillover effect of industrial carbon emissions among provinces presents additional complexities. Addressing the challenges of unbalanced industrial structure and unreasonable energy structure is crucial in achieving emission reduction targets [5]. This necessitates not only a clear understanding of the spatial effects between different regions but also a heightened focus on the interactions between different industries [6]. CO₂ emissions from various industries not only differ significantly but also exhibit increasingly close spillovers [7]. In this context, exploring ways to reduce industrial carbon emissions becomes a key step in lowering China’s total carbon footprint [8]. This article aims to clarify the spatial spillover effect of carbon emissions in different industries and deeply explore the factors that affect the differences in carbon emissions among different industries so as to understand the overall development of carbon emission levels in various industries and the impact of different factors on their differences. This is of great significance for developing appropriate carbon reduction plans for various industries and providing a basis for informed decision making in the field of industry emission reduction.

With the pressing issues of the environment and energy, an increasing number of scholars, both domestically and internationally, have begun to examine carbon emissions-related topics in recent years. However, research specifically addressing the influencing factors of carbon emissions among industrial sectors requires further exploration. Currently, the primary research methods on the drivers of carbon emissions can be categorized into two groups: The first is the factor decomposition method [9,10], including the commonly used LMDI method. Moutinho et al. [11] conducted a study on the factors that affect carbon emissions in EU nations, employing the LMDI technique for their analysis. Similarly, Yang [12] and Ma et al. [13] constructed an optimized carbon emission decomposition model with the LMDI method. Subsequently, Liu et al. [14] employed the GDIM technique to investigate the determinants influencing CO₂ emissions utilizing an exponential decomposition approach.

The second category comprises econometric model analysis methods, including STIRPAT, GMM, and ARDL. In their research, Poum et al. [15] utilized the STIRPAT model to examine the determinants influencing carbon emissions during different phases across a range of countries. Hussain et al. [16] applied the same model to study the carbon emissions of countries along the Belt and Road Initiative. Furthermore, Zhang et al. [17], Wang et al. [18], Zhang et al. [19], and Guan et al. [20] evaluated the primary driving factors of CO₂ emissions in China at the provincial and county levels using the STIRPAT model. Additionally, Kais et al. [21] employed the GMM model for an empirical analysis of carbon emissions’ influencing factors in 58 countries. Employing panel data and the GMM model, Chen et al. [22] conducted an analysis of the diverse factors that drive carbon emissions in China’s Yangtze River Delta region. This body of literature undoubtedly provides valuable insights for China’s carbon emission reduction efforts. The “high emissions and high energy consumption” characteristic of the industrial sector underscores its crucial role in achieving China’s carbon emission reduction goals, drawing extensive scholarly attention. For instance, Dong [4] and Ma [23] highlighted that carbon emissions predominantly originate from the industrial sector. Concurrently, the analysis of industrial carbon emissions has garnered significant interest. Zhao [24], Cui [25], Lin [26], and Shen et al. [27] scrutinized the determinants impacting carbon emissions within China’s industrial domain. Conversely, Wang [28] and Ouyang et al. [29] utilized the LMDI technique to explore the primary elements influencing CO₂ emissions in the industrial sector. Their findings suggested that China’s industrial carbon emissions primarily result from a coal-dominated energy structure, and R&D has led to a notable decline in these emissions. Wang [30] and Yu et al. [31] utilized the STIRPAT model for a quantitative evaluation of the effect of factors such as per capita income, energy structure and R&D intensity on industrial carbon emissions. Lin [32] and Liu et al. [33] utilized a spatial econometric framework for examining the spatial–temporal evolution of increasing CO₂ emissions in industries and their influencing elements at both municipal and county tiers. The results indicated varying degrees of influence of economic level, capital investment, and technological progress on industrial carbon emissions. Zhang [34] and Ren [35] explored the impact of environmental regulation, R&D, and FDI inflow on China’s carbon emissions from a provincial perspective, finding that FDI is a primary driver of industrial carbon emissions, while environmental regulation and R&D can reduce the growth rate of these emissions.

Subsequently, the scope of scholarly research has broadened to encompass various sectors, including transportation [36], logistics [37], manufacturing [38], mining [39], and additional fields.

In summary, existing research on carbon emissions provides diverse perspectives and improved methodologies. However, there are still shortcomings: The exponential decomposition method is limited in its ability to analyze the impact of a single absolute factor on carbon emissions, as it fails to consider the influence of other absolute factors or potential implicit factors during the decomposition process, thus compromising the reliability of its results. Moreover, it may not be suitable when there is a high correlation between variables. On the other hand, the STIRPAT method has inherent limitations that lead to inadequate factor selection. Both methods are constrained by their reliance on time series data and a limited number of influencing factors, which can pose challenges in obtaining and applying them to practical problems. In contrast, spatial regression models offer greater flexibility in data usage as they can incorporate both time series and panel data that are readily available and applicable to real-world issues. In fact, the carbon emissions of one industry are interdependent with those of closely related industries. Analogously, just as there is a spatial spillover effect between provinces, a similar relationship exists between industries [19,40]. Then, spatial econometric models primarily encompass the spatial Durbin model (SDM), spatial lag models (SARs), and spatial error models (SEMs). The SDM not only enables an analysis of variable relationships within a defined region but also investigates the impact of lagged variables on both the region itself and its neighboring areas. Furthermore, it can be decomposed into an SAR and an SEM, offering comprehensive and flexible advantages compared to the other two spatial models. Therefore, this study employs the spatial Durbin model (SDM) to examine whether there are spatial effects in the influencing factors of CO₂ emissions among industrial sectors, aiming to elucidate their underlying laws and mechanisms. It is essential to first identify and understand the key factors that drive the fluctuations in China’s industrial carbon emissions. Once these elements are comprehended, it becomes possible to pinpoint the specific stages where an effective reduction in these emissions can be achieved. This paper is inspired by the existing literature on industrial CO₂ emissions. The potential marginal contributions of this study include, firstly, an analysis of the action path and heterogeneity of CO₂ emission influencing factors among 36 industrial sectors.

The structure of the paper is outlined as follows: In the subsequent section, we construct a spatial weight matrix for gauging inter-industrial distances utilizing an input–output table, process data for relevant variables, and formulate the spatial Durbin model applied here. The third section is dedicated to the exposition of the empirical results. The paper is concluded in Section 4 with a comprehensive discussion of the findings and policy recommendations. For ease of reference, the research framework is illustrated in Figure 2.

2. Research Design

2.1. Moran Index Method

The First Law of Geography posits that all things are interrelated, but closer objects are more strongly related than those further apart. Prior to constructing a spatial econometric model, it is customary to select Moran’s I [41], as proposed by Anselin, to test for spatial autocorrelation among variables. The Moran’s index can be divided into global Moran’s I and local Moran’s I. The former indicates the presence and strength of a spatial correlation, while the latter reveals the aggregation and dispersion of elements in specific areas. Numerous scholars have utilized the Moran’s index to examine the spatial correlation of carbon emissions. For instance, Jun et al. [42] employed the global Moran’s I statistic to analyze the clustering characteristics of industrial carbon emission efficiency in Chinese cities using equilibrium panel data from 2005 to 2020. LONG et al. [43] used the Moran’s I index to analyze the spatiotemporal characteristics of industrial carbon productivity in 30 provinces and cities across China. Zhang et al. [43] applied the Moran’s I index to investigate the spatiotemporal distribution patterns of carbon emissions in the Yellow River Delta between 2000 and 2019, providing a comprehensive understanding of land use as a carbon source/sink within this region.

Therefore, in order to explore whether there is a spatial autocorrelation in the carbon emissions of the industrial sector and whether there is a significant spatial spillover effect within this space, this paper uses the global Moran’s I value to analyze whether the carbon emissions of the industrial sector in China from 2009 to 2021 have spatial autocorrelation, and its formula is as follows:

$$I=\frac{{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{W}_{ij}(x_i-\overline{x})}}(x_j-\overline{x})}{S^2{\displaystyle \sum _{i=1}^n{(x_i-\overline{x})}^2}}$$

(1)

where $S^2=\frac{1}{n}{\displaystyle \sum _{i=1}^n}{(x_i-\overline{x})}^2$, $\overline{x}=\frac{1}{n}{\displaystyle \sum _{i=1}^n{x}_i}$, n represents the total number of industries studied, and w_ij represents the elements of the spatial weight matrix. x_i and x_j represent the carbon emissions of industry i and industry j, and $\overline{x}$ represents the average carbon emissions of China’s industrial sector.

The spatial weight matrix can be normalized, and the Moran index can be written as follows:

$$I=\frac{{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{W}_{ij}(x_i-\overline{x})}}(x_j-\overline{x})}{{\displaystyle \sum _{i=1}^n{(x_i-\overline{x})}^2}}$$

(2)

where the value range of I is [−1, 1]. If the test result is 0 < I ≤ 1, it means that carbon emissions in the industrial sector show a positive spatial correlation, and the larger the value is, the more obvious the spatial correlation is, indicating the existence of spatial convergence characteristics; if I = 0, it means that the spatial distribution of carbon emissions in the industry is independent of each other; and if the test result is −1 ≤ I < 0, it means that carbon emissions in the industrial sector show a negative spatial correlation, and the larger the absolute value is, the more obvious the spatial difference is, indicating the existence of spatial heterogeneity characteristics.

The local Moran’s index (I_i) is used to investigate the spatial agglomeration of an industry, and its calculation formula is as follows:

$$I_i=\frac{(x_i-\overline{x}){\displaystyle \sum _{j=1}^n{w}_{ij}(x_j-\overline{x})}}{S^2}$$

(3)

where $i=1,2,\cdots ,n$. If the test result I_i > 0, it means that the high (low) value of industry i is surrounded by the high (low) value of the surrounding adjacent industries, namely HH agglomeration and LL agglomeration; if the test result I_i < 0, it means that the high (low) value of industry i is surrounded by the low (high) value of the surrounding adjacent industries, namely LH agglomeration and HL agglomeration.

2.2. Configuration of the Spatial Weighting Matrix

Before analyzing the spatial distribution characteristics of industrial carbon emissions, it is necessary to determine the spatial weight matrix, which is the key and basis of the spatial analysis in this paper. The inclusion of spatial effects into the econometrics model is realized by introducing a spatial weight matrix, which should be used to express the proximity relationship of spatial individuals before establishing the spatial measurement model.

The spatial weight matrix, W, needs to be determined in advance during the calculation of the Moran’s index:

$$W=\left(\begin{array}{ccc}{w}_{11}& \cdots & w_{1m}\\ ⋮& \ddots & ⋮\\ w_{m1}& \cdots & w_{mm}\end{array}\right)$$

(4)

where $w_{ij}$ represents the proximity between industry i and industry j, and n = 36.

Typical spatial matrices encompass the spatial adjacency matrix, the economic distance matrix, and the geographic distance matrix [44]. Based on the consideration of physical geography and social economic factors, this paper adopts the widely used geographical distance matrix and introduces the “space” weight matrix, W. In this paper, the “distance” between industrial industry i and industrial industry j is set as $d_{ij}$, and its spatial weight can be defined as follows:

$$w_{ij}=\{\begin{array}{l}1,if{d}_{ij}<d\\ 0,if{d}_{ij}\ge d\end{array}$$

(5)

where $d_{ij}$ is the “distance” critical value given in advance, which is set in this paper as the average of the direct consumption coefficient of all industries (0.018). Obviously, the spatial weight matrix obtained under the above definition is not necessarily symmetric. For example, 1 unit of output in the petroleum processing, coking, and nuclear fuel processing industries requires 0.618 units of output from the mining industry as an intermediate input (that is, a direct consumption coefficient of 0.618), but 1 unit of output from the mining industry only requires 0.0009 units of output from the petroleum processing, coking, and nuclear fuel processing industries as an intermediate input. In Formula (5), conditions for $w_{ij},w_{ji}$ are given, where i represents the oil processing, coking, and nuclear fuel processing industries; j is for mining. In the case that the elements in this symmetric position are not equal, in order to obtain a symmetric spatial weight matrix, the two elements can be defined as one.

$$w_{ji}=w_{ij}=\{\begin{array}{l}0,if{w}_{ij}=0\mathrm{and}{w}_{ji}=0\\ 1,if{w}_{ij}=1\mathrm{or}{w}_{ji}=1\end{array}$$

(6)

Finally, to exclude the self-neighborhood effect, we also need to set the elements on the main diagonal to 0, resulting in the following spatial weight matrix (where m = 36), within which the main diagonal element $w_{11}=\cdots =w_{mm}$.

$$W=\left(\begin{array}{ccc}{w}_{11}& \cdots & w_{1n}\\ ⋮& \ddots & ⋮\\ w_{n1}& \cdots & w_{nn}\end{array}\right)$$

(7)

2.3. Empirical Model

2.3.1. Variable Selection and Data Description

In this research, the variables are defined as follows: Carbon emission (E) serves as the response variable. Utilizing the China Carbon Accounting Database, this research compiles the carbon dioxide emissions data of 36 industrial sectors (See

Table 1. Sample industries.

Code	Industry	Code	Industry
H01	Coal mining and mining	H19	Manufacturing of chemical raw materials and chemical products
H02	Oil and gas extraction industry	H20	Pharmaceutical manufacturing industry
H03	Ferrous metal mining and beneficiation	H21	Chemical fiber manufacturing industry
H04	Non-ferrous metal mining and beneficiation	H22	Rubber and plastic products industry
H05	Non-metallic mining	H23	Non-metallic mineral products industry
H06	Agricultural and sideline food processing industry	H24	Ferrous metal smelting and rolling industry
H07	Food manufacturing industry	H25	Nonferrous metal smelting and rolling industry
H08	Wine, beverage, and refined tea manufacturing	H26	Metal products industry
H09	The tobacco product industry	H27	General equipment manufacturing
H10	Textile industry	H28	Special equipment manufacturing industry
H11	Textile and garment industry	H29	Railway, Marine, aerospace and other transportation equipment manufacturing
H12	Leather, fur, feathers, and their products and footwear	H30	Electrical machinery and equipment manufacturing
H13	Wood processing and wood, bamboo, rattan, brown, and grass product industries	H31	Computer, communications and other electronic equipment manufacturing
H14	Furniture manufacturing industry	H32	Instrumentation manufacturing industry
H15	Paper and paper product industry	H33	Other manufacturing
H16	Printing and recording media reproduction industry	H34	Production and supply of electricity and heat
H17	Cultural, educational, industrial, sports, and entertainment product manufacturing	H35	Gas generation and supply industry
H18	Oil, coal, and other fuel processing industries	H36	Water production and supply industry

) in China from 2009 to 2021, expressed in million tons.

In consideration of China’s industrial sector’s current economic model and energy CO₂ emissions status, the following factors influencing carbon emissions have been selected:

(1)

Foreign direct investment (FDI): FDI can enhance the industrial scale, structure, and technological advancement in China [45]. This measure is defined as the aggregate value of assets held by foreign-invested enterprises, translated into RMB based on the annual average exchange rate, and expressed in units of ten thousand CNY.

(2)

Property right structure (G): Because state-owned and non-state-owned enterprises differ in terms of production mode, operation efficiency, innovation cost, incentive mechanism, energy conservation, emission reduction system, and many other aspects, they will have differentiated impacts on industrial carbon emissions. At the same time, state-owned enterprises are subject to more government and social constraints and have to assume more social responsibilities, so they will also reduce pollution emissions [46,47]. Therefore, the property right structure can affect industrial carbon emissions to a certain extent. This paper selects the proportion of state-owned and state-controlled output in the total output value of each industry above the scale as the property right structure [48], denoted as G. The unit is %.

(3)

Energy structure (ES): The ES represents a crucial strategy for diminishing the intensity of energy usage [49]. Elevating the utilization of non-fossil fuels is a key focus for the Chinese government to achieve its strategic objectives of ‘carbon peak’ and ‘carbon neutrality.’ The composition of the energy mix is denoted by the ratio of total electricity usage to overall energy consumption, expressed as a percentage (%).

(4)

Industry enterprise scale (SZ): The number of enterprises and their size are significantly correlated with carbon emissions [50]. The industry scale is measured by the ratio of the industry’s average employee count to the number of enterprises, as a percent (%).

(5)

Total labor productivity(Y): The growth in energy consumption has led to both wealth accumulation and significant greenhouse gas emissions [51]. Y is determined by expressing the annual industrial output value as a percentage of the industry’s average workforce size, as a percent (%).

(6)

Capital intensity (K): Capital-intensive industries, which require substantial fixed asset investment, impact CO₂ emissions [52]. K is characterized as the quotient of net industrial capital assets relative to the mean count of workers, quantified in ten thousand CNY per individual.

(7)

Research and development (RD): The impact of R&D expenditure on industrial carbon emissions is uncertain [53]. On the one hand, R&D expenditure reduces energy consumption per unit of GDP, thereby reducing CO₂ emissions, by promoting the advancement of low-carbon technologies. On the other hand, R&D expenditure may promote economic growth and expand the scale of production, which increases the new demand for energy, that is, the “rebound effect” of energy [54,55]. In this paper, the proportion of technological innovation cost selected by the government and the total industrial output value represent R&D expenditure, reflecting the financial support of industry for scientific research [55], which is recorded as RD. The unit is %.

(8)

Environmental regulation (ER): “Porter’s hypothesis” [56] believes that reasonably set environmental regulation policies can stimulate enterprises to carry out technological innovation, improve product capabilities, generate innovation compensation, make up for or even exceed the cost of environmental regulation, and thus achieve a “win–win” state in which both environmental and economic performance are improved. Therefore, the impact of environmental regulation on industrial carbon emissions should be paid attention to. There are many methods to measure the intensity of environmental regulation in the existing literature. In this paper, the ratio of energy consumed by the industrial industry to the total output value of the industrial industry is used to measure the environmental regulation intensity of the industrial industry [57], that is, the energy consumption of various industries/total output value of the industry, recorded as ER, and the unit is TCE/ten thousand CNY. The larger the ER value, the less stringent the environmental regulations, and the smaller the ER value, the more stringent the environmental regulations.

Based on the principles of data authenticity and availability, this study collected and collated the panel data of 36 industries in China from 2009 to 2021 to explore the influencing factors of carbon emissions in industrial sectors. The data for the variables FDI, G, ES, SZ, Y, K, and RD are derived from the China Industrial Statistical Yearbook (2009–2022), the China Environmental Statistical Yearbook (2009–2022), the China Energy Statistical Yearbook (2009–2022), and the website of the National Bureau of Statistics (https://www.stats.goV.n/ (accessed on 1 July 2023)). Chinese profession carbon dioxide emissions data in 2009–2021 were collected from CEADS (https://www.ceads.net/user/login.php?lang=en (accessed on 1 July 2023)). Among them, there are some problems with industry segmentation data, such as missing data, different industry classification standards, and inconsistent statistical caliber of indicators. The missing data from several years in some industries are processed by a linear interpolation method. Through statistical calculation, all the index variables are positive. In order to maintain stationarity, mitigate multicollinearity, and reduce heteroscedasticity and autocorrelation, all the variables in this study were logarithmically transformed. A statistical summary of each variable is displayed in Figure 3, with the mean values represented by black dots within the box plots.

2.3.2. Construction of Empirical Model

This paper takes industrial carbon emissions as the explained variable, assumes that there are n explanatory variables, respectively, recorded as $X_i$, and studies foreign direct investment, property rights structure, energy structure, capital intensity, industry enterprise scale, research and development, environmental regulation, etc., as explanatory variables. To address heteroscedasticity issues, this study applies a logarithmic transformation to each variable and constructs an economic framework for analyzing industrial carbon emissions, excluding spatial influence factors.

$$\begin{array}{l}\ln E_{it}={\beta }_0+{\displaystyle \sum _{j=1}^{m_0}{\beta }_j\ln X_j}+{\mu }_i+{\chi }_t+{\epsilon }_{it}\end{array}$$

(8)

where the subscript i represents various industrial sectors, with $i=1,2,\cdots ,36$; $t$ represents the year, with $t=2009,2010,\cdots ,2021$; and ${\beta }_i(i=1,2,\cdots ,7)$, respectively, represents the coefficients of each explanatory variable. ${\mu }_i$ represents the individual effect of industry i, ${\chi }_t$ is the time effect at a specific time, and ${\epsilon }_{it}$ is the random disturbance term in period $t$ of industry $i$.

When there is a spatial dependence between variables, the traditional model estimation method is very limited. This study employs spatial panel measurement models to characterize the input–output relationships among industries, accounting for industry-specific effects that vary across industries but remain constant over time. This paper uses a set of spatial panel measurement models: a spatial error model (SEM), a spatial lag model (SAR), and the spatial Durbin model (SDM). Spatial error models (SEMs) and spatial lag models (SARs) are special cases of the spatial Durbin model, and in practice, spatial lag and spatial error may exist simultaneously. Meanwhile, the spatial Durbin model (SDM) has more advantages in analyzing indirect and direct effects than other models. The spatial Durbin model (SDM) can analyze the influence of explained variables on the explanatory variables of an industry and identify the influence of the explanatory variables and explained variables of other industries. Given the relative advantages of the spatial Durbin model (SDM) [55], based on Equation (9), it is further developed into a spatial metrology model, considering spatial factors. The model’s equation is established as follows:

$$\ln E_{it}=\rho {\displaystyle \sum _{j=1}^n{W}_{ij}\ln E_{it}+}{x}_{it}\beta +{\displaystyle \sum _{j=1}^n{W}_{ij}{x}_{it}\theta +{\mu }_i+{\lambda }_t+{\epsilon }_{it}}$$

(9)

where $W_{ij}$ represents the spatial weight matrix, while $x_{it}$ represents explanatory variables, $\beta$ represents the regression coefficient vector, $\theta$ represents a parameter vector, ${\mu }_i$ is the individual fixed effect of industry $i$, ${\lambda }_t$ is the time fixed effect, and ${\epsilon }_{it}$ is the random disturbance term of industry $i$ during the period $t$.

Within the spatial Durbin model (SDM), a spatial lag term for the variables is included. While the coefficient estimated for this lag term remains significant for the study, the lag term’s influence on the dependent variables is no longer represented solely by its coefficient value. Instead, the spatial impact is assessed through the total, direct, and indirect effects. The direct effect is calculated as the mean sum of the changes in the industry’s dependent variables due to all its independent variables. This includes both the average impact of the industry’s independent variables on its dependent variables and the feedback effect of the industry’s independent variables on the dependent variables of neighboring industries. The indirect effect is derived from the average of the sum of the changes in the dependent variables of adjacent industries, triggered by changes in all the independent variables of the industry. The total effect signifies the average sum of the changes in the dependent variables of both the industry in question and its adjacent industries, caused by all the industries’ independent variables, encompassing both direct and indirect effects.

As outlined by LeSage and Pace [58], a partial differential equation model is utilized to decompose these direct, indirect, and total effects. First, the partial derivative of the rth explanatory variable (or control variable) is calculated from industry 1 to industry n with respect to the explained variable LnE:

$$\begin{array}{l}\left[\frac{\partial \ln E}{\partial x_{1r}}\cdots \frac{\partial \ln E}{\partial x_{nr}}\right]=S_r{(W)}_{ij}\\ ={(I-\rho w)}^{-1}\left[\begin{array}{cccc}{\beta }_r& w_{12}{\lambda }_r& \cdots & w_{1n}{\lambda }_r\\ w_{21}{\lambda }_r& {\beta }_r& \cdots & w_{2n}{\lambda }_r\\ ⋮& ⋮& \ddots & ⋮\\ w_{n1}{\lambda }_r& w_{n2}{\lambda }_r& \cdots & {\beta }_r\end{array}\right]\end{array}$$

(10)

where I is the identity matrix, with the number of rows and columns being N, and $S_r{(W)}_{ij}$ denotes the (i, j) elements that depend on ${\beta }_r$ and the spatial weight matrix, W. When i = j, $S_r{(W)}_{ij}$ represents the effect of the ith variable on the explanatory variable, E, of the industry x_ii, which is ${\beta }_r$ of the dominant diagonal.

In a mathematical sense, the average value of the main diagonal elements of the partial derivative matrix obtained by the model is a direct effect, and the average value of the non-diagonal elements of the partial derivative matrix is an indirect effect. Therefore, the direct effect (DE) and indirect effect (IE) of the industry can be calculated by the following formula:

$$\mathrm{DE}=\frac{1}{n}{[S_r{(W)}_{ij}]}^{\overline{d}}$$

(11)

$$\mathrm{IE}=\frac{1}{n}{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{S}_r}}{(W)}_{ij}-\frac{1}{n}{[S_r{(W)}_{ij}]}^{\overline{d}}$$

(12)

where $\overline{d}$ is the sum of the main diagonal elements of the solution matrix.

The total effect (TE) is the sum of the direct and indirect effects, which can be explained as the average effect of a change in a certain explanatory variable of a certain industry on the explanatory variable of all industries; the formula is as follows:

$$\begin{array}{l}\mathrm{TE}=DE+IE\\ =\frac{1}{n}{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{S}_r}}{(W)}_{ij}\end{array}$$

(13)

In a practical sense, the direct effect and indirect effect reflect the impact of explanatory variables on the carbon emissions of an industry and the impact on the carbon emissions of other industries, respectively, and the total spatial effect reflects the average impact of the explanatory variables on the carbon emissions of all industries.

3. Analysis of Empirical Results

3.1. Spatial Correlation Analysis of Influencing Factors of Industrial Carbon Emissions

Prior to developing a model, it is essential to evaluate the presence of a spatial autocorrelation between industrial carbon emissions and the explanatory variables. Moran’s I test employed in this analysis reveals a statistically significant positive spatial autocorrelation of carbon emissions across 36 industries. This finding underscores the necessity of constructing a spatial measurement model that accounts for the input–output relationships between industries.

In order to assess the spatial autocorrelation in the data, this paper utilizes Moran’s I value, based on the economic distance weight matrix. The null hypothesis of the Moran index test posits an absence of spatial correlation between the variables. The I statistic, which is crucial for this test, is defined as follows:

$$M\mathrm{o}ran’sI=\frac{{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{W}_{ij}(x_i-\overline{x})}}(x_j-\overline{x})}{S^2{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{W}_{ij}}}}$$

(14)

where $S^2=\frac{1}{n}{\displaystyle \sum _{i=1}^n{(x_i-\overline{x})}^2}$ represents the sample variance, and $\overline{x}=\frac{1}{n}{\displaystyle \sum _{i=1}^n{x}_i}$ represents the arithmetic mean value of the spatial weight matrix elements. The value of Moran’s I, ranging from −1 to 1, assesses global correlation through a combined analysis of the p-value and Z-value. A Moran’s I significantly below 0 suggests a spatial correlation among similar industries. As evident in

Table 2. Moran’s I index of China’s industrial carbon emissions from 2009 to 2021.

Year	Moran’s I	E(I)	SD(I)	Z	p
2009	0.382	−0.029	0.120	3.424	0.001
2010	0.398	−0.029	0.120	3.559	0.000
2011	0.395	−0.029	0.120	3.533	0.000
2012	0.393	−0.029	0.120	3.520	0.000
2013	0.397	−0.029	0.120	3.556	0.000
2014	0.394	−0.029	0.120	3.537	0.000
2015	0.385	−0.029	0.120	3.461	0.001
2016	0.382	−0.029	0.119	3.436	0.001
2017	0.383	−0.029	0.119	3.446	0.001
2018	0.401	−0.029	0.120	3.587	0.000
2019	0.407	−0.029	0.120	3.642	0.000
2020	0.416	−0.029	0.120	3.708	0.000
2021	0.426	−0.029	0.120	3.796	0.000

, the Moran’s I values for the carbon emissions of the 36 industrial sectors are all above 0 and pass the significance tests at both the 5% and 1% levels. This implies a robust spatial positive correlation in the carbon emissions of China’s industrial sectors. For example, industries with high carbon emissions tend to be close to others with high carbon emissions (such as the ferrous metal smelting and rolling processing industry (H24), the non-ferrous metal smelting and rolling processing industry (H25), and the non-metallic mineral products industry (H23)). These industries have a large amount of energy consumption, mainly fossil energy consumption. Industries with low carbon emissions tend to be close to others with low carbon emissions (such as the printing and recording media reproduction industry (H16), the textile and clothing industry (H11), and the leather, fur, feather, and its products and shoemaking industry (H12)). These industries have strong technological innovation abilities and low energy consumption, so their carbon emissions are low. From the perspective of the time dimension, Moran’s I index gradually increases with the passage of time, and the spatial correlation of carbon emissions among the industrial industries is gradually enhanced.

After the calculation, the global Moran index of carbon emissions in 36 industries in China from 2009 to 2021 is obtained (See Table 2). The specific results are shown in Table 2. And it can be observed from Table 2 that during this period, the global Moran indexes all meet the significance level requirements of p < 0.01 and Z > 2.58, and all indexes are positive, with a value in the range [0.382, 0.426]. This indicates that there is a strong positive spatial correlation between the carbon emissions of various industries. In terms of the change trend, although the global Moran index fluctuates slightly, it generally presents a gradually increasing trend, which means that the correlation is gradually improving. Therefore, it can be inferred that the spatial correlation of the carbon emissions of industrial industries is constantly strengthening.

To further investigate local correlations, this study presents the local Moran’s I index scatter plots for carbon emissions from 36 industrial sectors in China for the years 2009 and 2021, with their local characteristics illustrated in Figure 4.

Examining the dynamic evolution over recent years, the location and quantity of ‘high-high’ and ‘low-low’ carbon emission clusters in China’s industrial sectors have shown relative stability. This trend indicates that industries with high carbon emissions tend to be surrounded by similarly high-emitting industries, while those with low emissions are typically adjacent to industries with lower emissions. There is a clear positive correlation between industrial carbon emissions and time. Notably, sectors H01, H02, H06, H07, H08, H23, H24, H25, H27, and H34 consistently appear in the first quadrant. This placement suggests that these industries not only maintain high levels of carbon emissions but also significantly influence an increase in emissions in their neighboring industries. Conversely, sectors H09, H11, H12, H13, H14, H16, H17, H20, H22, H32, and H36 consistently appear in the third quadrant, indicating lower levels of industrial carbon emissions, which, due to the unique nature of these industries, is mirrored in their similar industrial counterparts.

3.2. Selection of Spatial Metrology Model

This study further establishes an appropriate form of the spatial econometric model by conducting a correlation test, with the results presented in

Table 3. Results of spatial measurement test.

Test Method	Statistical Value	p
Moran’s I	20.139	0.000
Lagrange multiplier error test	199.364	0.000
Robust Lagrange multiplier error test	63.764	0.000
Lagrange multiplier lag test	182.754	0.000
Robust LM-Lag	47.154	0.000
Hausman	127.220	0.000

. Initially, the Lagrange multiplier (LM) test, guided by Anselin’s criteria, is applied. Over the years, the Moran index has consistently met the 1% significance level threshold, rejecting the null hypothesis of independent residuals. This finding reaffirms the presence of a spatial autocorrelation. Additionally, both the Robust LM and the LM tests exceed the 1% significance threshold, suggesting a preference for the spatial Durbin model in analyzing the sample data of this study.

As indicated in

Table 4. Estimation results of spatial panel data.

Variable	SAR	SEM	SDM
LnFDI	0.2792 *** (0.050)	0.0908 ** (0.035)	0.8855 *** (0.106)
LnG	−0.2524 ** (0.051)	−0.2563 *** (0.063)	−0.1030 (0.129)
LnES	−0.5319 *** (0.149)	−0.7796 *** (0.158)	0.2351 (0.215)
LnSZ	0.2773 ** (0.084)	0.3184 * (0.125)	−0.0632 (0.158)
LnK	0.3525 (0.053)	0.0356 (0.068)	1.1249 *** (0.275)
LnRD	0.0414 (0.033)	0.0291 (0.139)	−0.1440 (0.097)
LnY	0.4084 ** (0.120)	0.4359 ** (0.139)	0.2915 (0.273)
LnER	0.9977 *** (0.078)	1.0218 ** (0.086)	0.9275 *** (0.159)
Wx-lnFDI			−1.0052 *** (0.176)
Wx-LnG			−0.1758 (0.179)
Wx-LnES			−3.2906 *** (0.425)
Wx-LnSZ			1.0320 ** (0.393)
Wx-LnK			−1.6264 *** (0.377)
Wx-LnRD			0.9321 *** (0.163)
Wx-LnY			0.7498 * (0.419)
Wx-LnER			0.3765 (0.276)
Sigma2	1.1954 *** (0.000)	1.2691 *** (0.000)	1.0396 *** (0.000)
R-squared	0.7301	0.7227	0.8296
Log-L	−744.708	−749.274	−671.502

***, ** and * represent p < 0.01, p < 0.05 and p < 0.1, respectively.

, the regressions of the three models—SAR, SEM, and SDM—demonstrate favorable goodness of fit. Notably, the R², Sigma², and log-likelihood statistics reveal that the SDM exhibits superior fitting performance and overall regression credibility, rendering it the more accurate choice for the analysis. In

Table 5. Results of Wald test and LR test.

	Statistical Value	p
Wald spatial lag	27.360	0.000
LR spatial lag	32.900	0.000
Wald spatial error	28.960	0.000
LR spatial error	34.180	0.000

, the p-values from the Wald and likelihood ratio (LR) tests for whether the SDM is simplified into an SAR model and an SEM model are below 1%. This statistically justifies choosing the SDM in this particular context. Additionally, both the Wald and LR tests yield significant results at the 1% level, further affirming the appropriateness of selecting the spatial Durbin model to scrutinize the determinants of carbon emissions in the industrial sector.

Furthermore, the regression outcomes for all three models—SAR, SEM, and SDM—reveal that foreign direct investment, property rights structure, technological innovation, per capita total labor productivity, and environmental regulation all pass the 5% significance threshold, underscoring their substantial impact on carbon emissions within the industrial sector. The spatial econometric model incorporates the lag factor into the regression analysis, and the estimated coefficient of explanatory variables cannot directly reflect the impact of explanatory variables on the explained variables [59], but we can still see some information about the influencing factors of carbon emissions in the industrial sector from the results of the above table. After adding spatial factors, except for some variables, FDI, energy structure, capital intensity, and research and development are all significant at the 1% level, and the scale of industrial enterprises is significant at the 5% level. Among them, FDI, energy structure, and capital intensity are significantly negative, indicating that the carbon emissions of an industry are not only affected by these factors of this industry but also affect the carbon emissions of similar industries. There is a significant spatial dependence between the two, and this dependence is related to technology spillover and personnel flow between industries. Compared with the estimated results of the non-spatial panel model, the spatial panel model weakens the impact of explanatory variables on the carbon emissions of the industrial sector and classifies the impact of explanatory variables on the carbon emissions of the industrial sector into the spatial lag variables caused by the spillover effect of similar industries, proving that there is a spillover effect of similar industries on the carbon emissions of the industrial sector in many aspects.

3.3. Spatial Spillover Effect Decomposition

In the regression analysis, an industry’s explanatory variables not only exert a direct influence on this industry’s explained variables but also affect other industries’ explained variables. To accurately assess the determinants of industrial carbon emissions, the spatial effects were categorized into direct and indirect effects using Stata Statistical Software 16 (StataCorp, College Station, TX, USA). Calculations were performed using the time-fixed space Durbin model, leading to the findings presented in

Table 6. Spatial spillover effect decomposition of the SDM in the whole sample.

Variable	Direct Effect	Indirect Effect	Total Effect
LnFDI	0.4572 *** (0.061)	−0.5742 *** (0.106)	−0.1170 (0.108)
LnG	−0.1807 ** (0.0692)	−0.0978 (0.097)	−0.2785 ** (0.085)
LnES	−1.1618 *** (0.156)	−1.8906 *** (0.227)	−3.0524 *** (0.258)
LnSZ	0.3892 *** (0.105)	0.5959 ** (0.210)	1.9851 *** (0.186)
LnK	0.4137 ** (0.157)	−0.9274 *** (0.192)	−0.5137 ** (0.186)
LnRD	0.2568 *** (0.056)	0.5288 *** (0.085)	0.7856 *** (0.089)
LnY	0.6251 ** (0.197)	0.4239 * (0.214)	1.0490 *** (0.278)
LnER	1.0963 *** (0.109)	0.2167 * (0.118)	1.3130 *** (0.143)
spat.aut			0.0082 * (0.118)
Sigma2			1.0396 *** (0.125)
R-squared			0.7525
Log-L			−671.502

***, ** and * represent p < 0.01, p < 0.05 and p < 0.1, respectively.

.

In this study, an in-depth examination is conducted on the direct, indirect, and aggregate effects of industrial carbon emissions. The findings are as follows:

(1) Foreign direct investment (FDI): The direct effect of foreign direct investment (FDI) is significantly positive, the regression coefficient of the indirect effect is significantly negative, and the total effect presents a weak negative effect. That is, FDI in an industry will lead to an increase in carbon emissions in the industry and has a certain effect on reducing carbon emissions in other industries, but the total effect presents a trend of carbon emission reduction. The reason for this is that foreign direct investment may affect carbon emissions outside the region through technology spillover such as labor flow, technology share, and product diffusion [60]. In other words, although foreign direct investment can only weakly reduce carbon emissions in the industrial sector, it still maintains a downward trend.

(2) Property right structure (G): The property right structure shows significant negative effects in both direct and total effects, while its indirect effect is not markedly significant. This indicates that compared to private companies, state-owned enterprises, which are subject to stricter energy-saving regulations and greater responsibilities, tend to respond more effectively to policies aimed at reducing emissions. Overall, a higher degree of nationalization in enterprises correlates with stronger emission reduction capabilities.

(3) Energy structure (ES): The impact of ES on industrial carbon emissions is significantly negative across direct, indirect, and total effects. An increased proportion of electricity in total energy consumption not only curbs the rise in carbon emissions within an industry but also contributes to a significant spatial spillover effect. This is due to the inherently low emissions of clean energy sources.

(4) Enterprise size (SZ): The direct, indirect, and total effects of enterprise size on carbon emissions are all positive and significant. This indicates that as enterprises expand, their carbon emissions increase, along with a positive spillover effect on the industry’s emissions. This trend is often due to enterprises prioritizing profits over energy conservation and emission reduction efforts.

(5) Total labor productivity (Y): Total labor productivity’s influence on carbon emissions consistently presents as both positive and noteworthy. The growth in carbon emissions is linked to economic development characterized by industrialization and urbanization, leading to increased energy use and carbon dioxide emissions.

(6) Capital intensity (K): The indirect and overall impacts on carbon emissions are notably inverse, whereas direct influences exhibit positivity. However, overall, a 1% increase in capital intensity reduces carbon emissions by 0.5137 percentage points. This is because investments in fixed assets, under energy conservation policies, tend to include considerations for low-carbon development.

(7) Research and development (RD): The effects, whether direct, indirect, or total, are all positively significant. The possible reason for this is that spending on R&D investments increases the use of fossil fuels to replace labor and capital inputs, leading to an increase in carbon emissions at the expense of investments in low-carbon technologies and energy efficiency [61], i.e., the “rebound effect” of energy. Although the progress of low-carbon technology plays an important role in the reduction of carbon emissions, at present, China’s low-carbon research and development technology is in the initial stage of development, there is a certain gap with developed countries, and the transformation ability of low-carbon technology achievements is weak [62].

(8) Environmental regulation (ER): Environmental regulation (ER) is expressed by the ratio of total energy consumption to the total industrial output value, and the direct, indirect, and total effects of ER are significantly positive. When the total effect value of ER increases by 1 percentage point, that is, when the environmental regulatory capacity decreases by 1 percentage point, carbon emissions increase by 1.313 percentage points. That is, with an increase in the total effect value of ER, the ability for environmental regulation becomes weaker, and carbon emissions increase. This indicates that environmental regulation has a significant impact on the development of industrial carbon emissions; that is, the stricter environmental regulation is, the more enterprises will be motivated to take initiative in technological innovation, and enterprises will reduce production costs or pollutant emissions through technological innovation, thus reducing the carbon emissions of China’s industrial sectors [63,64].

3.4. Heterogeneity Test

In estimating the relationship between carbon emissions and explanatory variables across the 36 industrial sectors, the initial assumption was that each sector operates with identical production technologies, resulting in consistent coefficient values across the industries. However, this assumption overlooks the variability in the relationships among these variables within different industries. Factors such as varying levels of energy consumption, ownership structures, and capital intensity also impact the interaction between carbon emissions and explanatory variables in the industrial sector. To accurately identify the specific influence of these three factors, the 36 industrial sectors were categorized based on their respective energy consumption, ownership structures, and capital intensity. This categorization facilitates an in-depth exploration of the relationships between carbon emissions and explanatory variables under various constraints in each industrial sector.

3.4.1. Sample Estimation Results and Analysis of High- and Low-Energy-Consumption Groups

Referencing the work of Wang et al. [65], industries with significant energy use are marked by notable carbon dioxide output, including sectors like coal, oil, and natural gas. This study categorizes the 36 industrial sectors into a pair of categories based on energy usage: those with lower energy consumption and those with higher energy consumption, as elaborated in

Table 7. SDM regression results of high- and low-energy industry group.

	Variable	High-Energy-Consumption Group	Low-Energy-Consumption Group
Direct effect	LnFDI	0.7233 *** (0.084)	0.3348 *** (0.043)
	LnG	0.5039 *** (0.143)	−0.1892 *** (0.039)
	LnES	−1.1532 *** (0.212)	−3.3132 *** (0.181)
	LnSZ	0.0425 (0.139)	0.1081 (0.076)
	LnK	0.6400 ** (0.239)	−0.3953 *** (0.096)
	LnRD	0.5371 *** (0.080)	0.3010 *** (0.047)
	LnY	0.4166 (0.249)	0.7640 *** (0.116)
	LnER	0.2972 (0.189)	1.0660 *** (0.080)
Indirect effect	LnFDI	−0.4882 *** (0.122)	−0.0407 (0.105)
	LnG	−0.5477 * (0.215)	0.1099 * (0.064)
	LnES	−2.1666 *** (0.226)	2.6797 *** (0.283)
	LnSZ	0.3749 ** (0.199)	0.6315 *** (0.176)
	LnK	0.0041 (0.404)	−0.1050 (0.115)
	LnRD	0.6364 *** (0.113)	−0.1579 * (0.085)
	LnY	−0.3024 (0.392)	0.9163 *** (0.233)
	LnER	0.6656 * (0.285)	−0.7088 *** (0.129)

***, ** and * represent p < 0.01, p < 0.05 and p < 0.1, respectively.

.

The estimated direct effects for the high-energy-consuming industry group align closely with the broader industry model results. Specifically, the direct effect of the property right structure (G) in this group is significantly negative. This may be attributed to the fact that investments in these industries predominantly follow an extensive growth model. Furthermore, the high costs of new environmental technologies and materials, coupled with insufficient government and market mechanisms to encourage emission reduction and environmental protection, contribute to increased carbon emissions.

Conversely, the estimated indirect effects for the low-energy industry group diverge from the overall industry findings. Notably, the spillover effect of the energy structure (ES) on adjacent industries is significantly positive, likely due to China’s shift from high-pollution to green, clean energy sources. However, the impacts of research and development (RD) and environmental regulation (ER) are significantly negative, indicating a tendency to attract talent and technology into neighboring industries, thereby reducing their carbon emissions and creating a negative spillover effect.

3.4.2. Estimate Results by Ownership Sample

Considering the diversity in property rights structures, the 36 industrial sectors were categorized into two groups, those with a high ownership structure and those with a low ownership structure, based on the average value of the industrial property rights structure. The regression outcomes are detailed in

Table 8. SDM regression results of high- and low-ownership-structure group.

	Variable	High-Ownership-Structure Group	Low-Ownership-Structure Group
Direct effect	LnFDI	0.5672 ** (0.076)	0.9056 *** (0.087)
	LnG	0.3667 *** (0.154)	0.1463 * (0.079)
	LnES	−1.2429 (0.204)	−2.8032 *** (0.180)
	LnSZ	−0.4100 (0.132)	−1.7233 *** (0.142)
	LnK	0.3407 (0.204)	−1.3013 *** (0.246)
	LnRD	0.2951 *** (0.077)	−0.1688 * (0.071)
	LnY	−0.8584 (0.267)	−0.0526 (0.302)
	LnER	0.8476 *** (0.121)	1.0494 *** (0.112)
Indirect effect	LnFDI	−0.4816 *** (0.105)	0.6459 *** (0.165)
	LnG	−0.3808 *** (0.216)	−0.0462 (0.139)
	LnES	−1.2603 *** (0.234)	0.4759 * (0.268)
	LnSZ	0.5482 * (0.152)	−0.2583 (0.439)
	LnK	−0.2983 ** (0.213)	0.0095 (0.346)
	LnRD	0.6247 *** (0.081)	−0.2527 * (0.115)
	LnY	−0.2126 (0.272)	−0.6851 (0.507)
	LnER	0.2074 *** (0.132)	0.3408 ** (0.131)

***, ** and * represent p < 0.01, p < 0.05 and p < 0.1, respectively.

.

The direct effect estimation in the low-ownership-structure group, compared to the entire industry, shows significant variations. Notably, factors such as the industry enterprise scale (SZ), capital intensity (K), and research and development (RD) are markedly negative. This suggests that capital investments in industries with lower ownership structures have shifted away from traditional models, favoring new emission reduction technologies to enhance resource utilization and effectively control carbon emissions. Concerning the indirect impacts, it is noted that foreign direct investment (FDI) markedly augments carbon emissions in groups with lower ownership concentrations, notably at a significance threshold of 1%. A plausible rationale is the diminished inclination of non-state firms to adopt cutting-edge technologies for reducing emissions in the absence of robust incentives and regulatory measures from the government. This leads to a reduced competitive drive within these companies.

3.4.3. The Results of Capital Intensity Estimation

Reflecting on the heterogeneity of capital intensity, the 36 industrial sectors were divided into two groups, capital-intensive and labor-intensive groups, using the overall average of the industrial sector’s capital intensity as the classification criterion [66].

Table 9. SDM regression results of capital-intensive group and labor-intensive group.

	Variable	Labor-Intensive Group	Capital-Intensive Group
Direct effect	LnFDI	0.4211 ** (0.135)	0.1270 * (0.057)
	LnG	0.8115 *** (0.156)	0.1489 ** (0.046)
	LnES	−0.4012 (0.282)	−2.9500 *** (0.197)
	LnSZ	−0.2496 (0.183)	−0.2722 * (0.158)
	LnK	0.4518 (0.311)	−0.4578 *** (0.116)
	LnRD	0.6037 *** (0.101)	−0.295 *** (0.055)
	LnY	−0.3735 (0.294)	−1.0722 *** (0.168)
	LnER	0.7388 *** (0.253)	0.7453 *** (0.085)
Indirect effect	LnFDI	0.9972 *** (0.140)	−0.6833 *** (0.182)
	LnG	1.1206 *** (0.280)	0.1771 * (0.093)
	LnES	−0.8000 *** (0.227)	0.6382 * (0.319)
	LnSZ	−0.6497 * (0.258)	1.6311 *** (0.438)
	LnK	−1.2579 ** (0.436)	0.5306 ** (0.167)
	LnRD	0.4227 *** (0.095)	−0.4993 *** (0.112)
	LnY	0.1247 (0.560)	1.2265 ** (0.399)
	LnER	1.2583 *** (0.317)	−1.0360 *** (0.196)

***, ** and * represent p < 0.01, p < 0.05 and p < 0.1, respectively.

displays the outcomes of the regression analysis.

Analyzing the direct effects, it is apparent that the property right structure (G) significantly escalates carbon emissions in both labor-intensive and capital-intensive industries. However, this effect is more pronounced in capital-intensive industries. Research and development (RD) notably curbs carbon emissions within the capital-intensive group. This difference may stem from the distinct objectives of each group, where the capital-intensive group, with more substantial investments, achieves a higher emission reduction efficiency, thereby impacting carbon emissions both positively and negatively. The estimated indirect effects in the capital-intensive group diverge from those of the overall industry, with property right structure (G), energy structure (ES), enterprise size (SZ), and capital intensity (K) demonstrating significant positive spillover effects, while research and development (RD) and environmental regulation (ER) exhibit significant negative spillover effects.

According to this study, Figure 5 shows the classification diagram of 36 industries in China under three conditions. Among them, the numbers represent the corresponding industries in Table 1.

4. Conclusions and Suggestions

Estimations of carbon emissions were conducted for 36 industrial sectors in China over the period from 2009 to 2021 in this research. And then, a spatial weight matrix was developed to delineate the inter-industry ‘distance’ based on the input–output table. Subsequently, the spatial autocorrelation in these emissions was investigated using Moran’s I test. To conduct a comprehensive regression analysis on the factors influencing these emissions, a spatial Durbin model was utilized with the available data. The key findings are as follows:

(1)

Our analysis reveals a substantial positive spatial autocorrelation in the carbon emissions of the 36 industrial sectors throughout the study period. The local spatial autocorrelation assessment indicates that industries such as coal mining and mineral processing, petroleum and other fuel processing, and non-metallic mineral production, ferrous and non-ferrous metal smelting and rolling exhibit a pronounced ‘high–high’ cluster effect. Conversely, sectors like tobacco products, textiles and apparel, leather goods, wood products, and several others, including cultural and educational goods manufacturing, demonstrate a ‘low–low’ clustering pattern.

(2)

From the perspective of the whole industrial sector, an increase in G, ES, and K reduces the carbon emissions of the industrial sector. However, an increase in SZ, RD, Y, and ER increases the carbon emissions of the industrial sector. The impact of FDI on carbon emissions is not significant, and an increase in FDI presents a weak trend of carbon emission reduction for the industrial sector.

(3)

① The direct effects of the high- and low-energy-consuming industries are basically consistent with the estimated results for the whole industry, but the indirect effects of the low-energy-consuming industries are slightly different, among which the spillover effect of ES on other adjacent industries is significantly positive. ② The SZ, K, and RD of the low-ownership-structure group have significant negative effects on carbon emissions, while FDI has a negative spillover effect on it. ③ G significantly increases the carbon emissions of the labor-intensive and capital-intensive industries, while RD can inhibit the carbon emissions of the capital-intensive group. The estimated results of the indirect effects of the capital-intensive group and the whole industry are different, among which G, ES, SZ, and K have significant positive spillover effects, while RD and ER have significant negative spillover effects.

In light of this research’s conclusions, the paper offers several policy suggestions aimed at curbing carbon emissions within China’s industrial sectors:

(1)

Optimize the energy structure, support the development of a new energy industry, and establish a sound energy price adjustment mechanism to guide the adjustment of the energy structure of industrial industries.

(2)

Deepen the reform and transformation of state-owned enterprises, develop a diversified ownership economy, effectively promote the industrial sector to achieve a low-carbon economic transformation, constantly promote industry to adapt to the sustainable development of the economy and society, and minimize the carbon emissions of industry.

(3)

Introduce the concept of low carbon into the research and development process, increase investment in low carbon technology infrastructure, and pay attention to the training and introduction of technological innovation talents.

(4)

Improve the level of foreign investment introduction by improving the threshold of foreign investment introduction, further strengthen the screening and management intensity of foreign technology introduction, give priority to foreign-funded enterprises with low energy consumption and advanced technology, and focus on learning their advanced industrial low carbon emission standards and technologies.

(5)

To reduce carbon dioxide emissions from the industrial sector, corresponding strategies should be formulated according to different industries. For a high-emission industry, it is necessary to reduce backward production capacity, increase advanced production capacity, and increase the proportion of clean energy; for a low-emission industry, it is necessary to adjust the number of personnel and improve the quality.

In addition, considering the spatial effect, a more reasonable combination of more complex models, fully extracting the data of other subdivision industries, or using more micro-level data will be the focus of future research work.