The Optimization of Industrial Structure Under the ‘Dual Carbon’ Goal via Multi-Objective Programming Model: Evidence from Guangdong Province, China

Abstract

With the increasing frequency of extreme weather events, global concerns regarding climate change have intensified, with carbon dioxide widely recognized as the primary driver of global warming and climate disruption. It is necessary to investigate how to develop industries to meet the constant GDP growth and minimum carbon emissions. This study investigates the optimization of industrial structure under China’s ‘Dual Carbon’ Goal in Guangdong Province from 2012 to 2017, employing a multi-objective programming model. Using the input–output table, carbon emissions across 42 industries are calculated based on the Intergovernmental Panel on Climate Change (IPCC) carbon emission factor method. According to Hirschman’s theory of industrial interdependence, the economic and carbon emission linkage coefficients between these industries are obtained by calculating the Ghosh inverse matrix and the Leontief inverse matrix to analyze the economic forward and backward linkage of the industries, as well as the carbon emission forward and backward linkage. The impact of industry input and output on the urban economy and the resulting carbon emission problems are discussed, and industries are divided into encouraged and restricted industries. Using a multi-objective programming model, the expected final demand, changes in final demand, and expected carbon emissions of these industries under the ‘Dual Carbon’ Goal, with the target of maintaining the same economic growth rate and promoting carbon reduction, are analyzed. The results show that most industries in Guangdong Province need to reduce final demand, including the highest carbon-emitting industries and industries that are relatively restricted by scale in development. The policy implications of optimizing the industrial structure to reduce carbon emissions are provided.

1. Introduction

Since the start of the 21st century, the escalating frequency of extreme weather events has significantly heightened global concerns over climate change, which has progressively emerged as a central focus of the international community. Carbon dioxide is widely recognized as the primary greenhouse gas contributing to global warming and associated climatic shifts.

As the world’s largest emitter of carbon dioxide and energy consumer, as well as the second-largest economy, China’s rapid economic growth has been accompanied by surging energy consumption and mounting environmental pressure. To achieve sustainable development, it is imperative to restructure the economy, reduce the reliance on traditional high-carbon energy, enhance resource utilization efficiency, and mitigate environmental pollution and ecological damage. Moreover, as a signatory to the Paris Agreement, the Chinese government announced at the United Nations General Assembly on 22 September 2020 that China will strive to reach its carbon peak before 2030 and achieve carbon neutrality before 2060. The proposal of the ‘Dual Carbon’ Goal demonstrates the government’s commitment to adopting more proactive measures, such as promoting clean energy and low-carbon technologies and addressing air pollution and water scarcity, to improve domestic environmental quality. Amid the global shift toward green and sustainable economic development, China aims to seize new economic opportunities and enhance its competitiveness through a low-carbon development paradigm.

Industrial structure refers to the proportion and interrelationships of various industries in the entire economy of a country or region. It is an important component of economic structure, which can directly reflect the level of economic development of a country or region. Optimizing industrial structure can adjust the proportion and structure of various industries to make the entire economy more rational, efficient, and sustainable [1,2]. It is conducive to achieving a high degree of industrial structure, thereby improving the competitiveness of the industrial economy and urban sustainable development [3]. The optimization of industrial structure is closely related to reducing carbon emissions [1,2]. In the past decade, according to the Chinese Statistical Yearbook, China’s GDP growth rate has increased from 2.3% to 8.1%, and per capita GDP has surged from 36,300 CYN to 80,000 CYN. The economy has developed rapidly, but due to the initial vigorous development of heavy industry, carbon emissions have also increased. In 2021, China’s total carbon emissions reached 11.9 billion tons, accounting for about 33% of global carbon emissions. The total energy consumption was 5.24 billion tons of standard coal, for a year-on-year increase of 5.25%. Therefore, it is necessary to start from the industrial structure and explore the development path of carbon reduction in order to change the current situation of high economic growth but high carbon emissions in China.

Studying the optimization of industrial structure under the ‘Dual Carbon’ Goal carries profound significance. Traditional high-energy-consuming and high-emission industries have long served as the primary drivers of economic growth, yet they have simultaneously imposed enormous carbon emission pressures. Therefore, through industrial structure optimization and the promotion of economic transformation toward low-carbon and high-value-added industries, it is feasible to significantly reduce carbon emission intensity while sustaining economic growth, thereby achieving the decoupling of economic expansion from carbon emissions. Industrial structure optimization can enhance resource utilization efficiency and mitigate the environmental costs of economic development [1,2,3]. By fostering a diversified low-carbon industrial system, it not only strengthens economic resilience and reduces reliance on traditional high-carbon industries but also ensures long-term and stable economic growth.

Guangdong Province plays an indispensable role in the national economic development. According to the Statistical Yearbook of Guangdong Province, in 2012, its GDP was approximately 6.66 trillion CYN, accounting for about 12.85% of the national GDP. In 2017, its GDP was approximately 8.99 trillion CYN, accounting for about 10.95% of the national GDP. This shows that Guangdong Province’s economy has played a major role in the national economy in the past decade. From an economic perspective, studying Guangdong Province can provide effective experience for other countries or cities with similar economic levels. As one of the first provinces in China to carry out low-carbon economy pilot projects, Guangdong Province is also a major manufacturing province in the country. Since entering the 21st century, its heavy industry has developed rapidly. Primary energy consumption has grown rapidly in the past 30 years, from 36.9025 million tons of standard coal in 1990 to 256.3629 million tons of standard coal in 2014, an increase of 5.95 times in 24 years, accounting for a large proportion of the primary energy consumption in China. From the perspective of energy consumption, Guangdong Province is a good epitome of the characteristics of developing heavy industry to drive economic growth. Therefore, investigating Guangdong Province can effectively analyze the relationship between industrial structure and carbon emissions and provide effective experience for other countries or cities with similar industrial structures.

Based on the above-mentioned background, some research questions are proposed. Firstly, how do we distinguish between encouraged and restricted industries? Secondly, will industries with strong economic interdependence have higher carbon emissions? Thirdly, in order to minimize carbon emissions while maintaining the same economic growth rate, will restricted industries need to reduce final demand?

This study investigates the optimization of industrial structure under China’s ‘Dual Carbon’ Goal in Guangdong Province from 2012 to 2017, employing a multi-objective programming model. Using the input–output table, carbon emissions across 42 industries are calculated based on the Intergovernmental Panel on Climate Change’s (IPCC) carbon emission factor method. The economic linkage coefficient and carbon emission linkage coefficient between these industries are obtained by calculating the Ghosh inverse matrix and the Leontief inverse matrix. The economic forward and backward linkage of the industries, as well as the carbon emission forward and backward linkage, are analyzed. The impact of industry input and output on the urban economy and the resulting carbon emission problems are discussed, and industries are divided into encouraged industries and restricted industries. Using a multi-objective programming model, the expected final demand, changes in final demand, and expected carbon emissions of these industries under the ‘Dual Carbon’ Goal, with the target of maintaining the same economic growth rate and promoting carbon reduction, are analyzed. The results show that most industries in Guangdong Province need to reduce final demand, including the highest carbon-emitting industries and industries that are relatively restricted by scale in development. The policy implications of optimizing the industrial structure to reduce carbon emissions are provided.

The contribution of this study is that (1) the framework combining economic and carbon emission linkages and the multi-objective programming model is proposed to analyze the optimization of industrial structure under the ‘Dual Carbon’ Goal; (2) the whole industry, including primary, secondary, and tertiary industries, is considered as the research object; and (3) quantitative decision-making tools are provided for Guangdong Province to achieve the ‘Dual Carbon’ Goal.

2. Literature Review

The literature is reviewed from the perspectives of carbon emissions of industries, the interaction between industrial structure and carbon emissions, and industrial structure under the ‘Dual Carbon’ Goal.

2.1. Carbon Emissions of Industries

The adjustment and optimization of industrial structure have a positive effect on reducing carbon emissions [1,2,3], and the development of highly energy-intensive and highly carbon-intensive industries needs to be strictly controlled. From a spatial perspective, the carbon intensity of various provinces in China exhibits a clear spatial positive correlation and regional heterogeneity [4,5], and this correlation shows a gradually increasing trend over time [5]. The formation of this spatial distribution pattern is closely related to regional industrial structure differences. There are significant regional differences in the industrial structure of the eastern, central, and western regions [6]. The differences in carbon emissions between regions are increasing, mainly due to significant regional differences in industrial structure, economic growth, population, and urbanization [7]. Specifically, upgrading and optimizing industrial structure can effectively reduce regional carbon intensity levels [4,8], among which industrial agglomeration effects and industrial structure transformation play important roles in reducing carbon dioxide emissions [9]. In addition, economic growth increases carbon dioxide emissions [9], which shows that significant differences exist in carbon emission characteristics among different industrial sectors. The main reason for that is dependent on the proportion of sectors in the economic structure [8]. The proportion of added value in agriculture, manufacturing, and transportation industries is negatively correlated with carbon emissions, while the added value in construction, retail, accommodation, and other industries is positively correlated with carbon emissions [10]. The secondary industry, especially traditionally carbon-intensive industries such as manufacturing and mining, remains the main source of carbon emissions [9]; the construction industry is one of the fastest-growing emission sectors [11,12], while the carbon emissions from the service industry also show a continuous upward trend [11]. In contrast, while maintaining rapid growth, mechanical manufacturing and the light industry have achieved significant reductions in carbon emissions related to changes in carbon dioxide intensity and production structure [12]. However, the improvement of the existing industrial structure is far from sufficient [12].

2.2. Relationship Between Industrial Structure and Carbon Emissions

The impact of industrial restructuring on carbon emission reductions has multidimensional mechanisms. On the one hand, the rationalization and upgrading of industrial structure can significantly suppress carbon emissions, with the emission reduction effect of industrial upgrading being more prominent than rationalization [6,13,14,15]. On the other hand, the optimization and transformation of industrial structure can effectively eliminate the carbon lock-in effect [16,17], which is more pronounced in cities with better economic foundations [16]. From the perspective of specific pathways, industrial structure upgrading can not only directly suppress carbon emissions but can also have a significant indirect inhibitory effect on carbon emissions by promoting energy structure optimization [18]. In addition, the development of industrial clusters has also demonstrated significant advantages in carbon reduction, manifested by a significant negative correlation between the intensity of industrial clusters and carbon intensity [19]. However, there is still a significant dynamic imbalance between carbon emissions and industrial upgrading in China, and nearly half of the provinces are in a mild to moderate state of disharmony [20], which reflects that there is still a lot of room for improvement in the current production structure [12]. The energy efficiency of the industrial sector is relatively low, with heavy industry having higher energy efficiency than light industry [21]. The concentration of industrial structure is closely related to the improvement of economic and social benefits of carbon emissions and is in a state of extremely coordinated coupling and highly coordinated running, respectively [22].

At the policy implementation level, the proposal of the ‘Dual Carbon’ strategic goal has had a profound impact on industrial upgrading and transformation, urban sustainability [23], and enterprise cost [24]. Research has shown that setting a target for peak carbon dioxide emissions will have a significant inhibitory effect on high-carbon-emitting industries, while having a strong promoting effect on low-carbon-emitting industries [25]. In the context of the strategic interaction between governments, low-carbon policies have not only significantly improved the rationalization and upgrading level of local industrial structure but also had a significant impact on the industrial structure of spatially related regions [26]. The low-carbon city pilot policy has significantly promoted the optimization and upgrading of industrial structure, but its promotion effect on the rationalization of industrial structure is relatively limited, and this policy effect is more pronounced in cities with higher levels of economic development [27]. To comprehensively promote the goal of carbon neutrality, Feng et al. constructed a multi-objective optimization model for the industrial structure of the socio-economic environment system with the objectives of minimizing carbon emissions, maximizing economic benefits, and promoting social employment [28].

2.3. Multi-Objective Planning Model of Industrial Structure Optimization

Regarding the multi-objective planning model of industrial structure optimization, Zhou et al. adopted a multi-objective input–output optimization model to investigate the trade-off between maximizing GDP growth, minimizing carbon emissions, and minimizing energy consumption during China’s 2017–2035 planning period [29]. The results indicated that industries with high output and low energy consumption are growing, while industries with high pollution and high energy consumption are declining, mainly driven by technological level, followed by policies and development preferences. Zhang et al. explored how to maintain economic growth while protecting the environment and achieving sustainable development goals based on a multi-objective optimization model. Through research on the Chinese power sector, they analyzed the synergistic effects and trade-offs between economic, energy, environmental, and social goals [30]. It is shown that during the period of industrial restructuring (2020–2030), China’s GDP, employment, carbon emissions, and energy consumption increased by 96.1%, 7.2%, 16.8%, and 16.8%, respectively, while pollutant emissions decreased. This emphasizes that priority should be given to the conservation and utilization of energy and water resources in industrial restructuring [30]. Jiang et al. proposed a network-based multi-objective optimization model that considers the comprehensive impact of supply chain structure on carbon emissions and analyzed how to reduce global carbon emissions by adjusting industrial structure [31]. The results showed that with the increase in gross domestic product, carbon emissions decreased by 4.31%, 6.26%, and 8.07% in different scenarios, respectively. Liu et al. used a combination of multi-regional input–output model and linear programming models to explore economic structural adjustment strategies for reducing carbon dioxide emissions [32]. It was shown that a reduction in final demand leads to a simultaneous decrease in GDP and carbon emissions, but relevant measures can be taken to achieve the maximum reduction in carbon emissions with minimal economic losses. Zhu et al. used the Yangtze River Delta region as a case study, applied a cross-regional multi-objective programming model, and combined data envelopment analysis to explore the impact of cross-regional industrial structure optimization on economic development, carbon emissions, and energy consumption [33]. The conclusion points out that through cross-regional industrial structure optimization and industrial transfer, each province can achieve a reasonable industrial distribution and achieve the phased goals during the 13th Five-Year Plan period. At the same time, the ecological efficiency of each province has been improved, and the economic gap has also been narrowed.

At present, the existing research on industrial structure related to carbon emissions mainly focuses on the mutual influence and coupling mechanism between industrial structure changes and carbon emissions. Most studies focus on the optimization of industrial structure in the secondary industry, and there are relatively few studies on the whole industry. Therefore, this study will take the whole industry as the research object and study the industrial structure optimization in Guangdong Province to meet the constant GDP growth and minimum carbon emissions under the ‘Dual Carbon’ Goal.

3. Materials and Methodology

3.1. Methodology

This paper investigates the optimization of industrial structure under the ‘Dual Carbon’ Goal in Guangdong Province of China via a multi-objective programming model. Firstly, based on the input–output table, the carbon emission factor method by the IPCC is used to calculate the carbon emissions of 42 industries. The economic linkage coefficient and carbon emission linkage coefficient between these industries are obtained by calculating the Ghosh inverse matrix and the Leontief inverse matrix, and the industries are divided into encouraged and restricted industries. Then, using a multi-objective programming model, the expected final demand, changes in final demand, and expected carbon emissions of these industries under the ‘Dual Carbon’ Goal, with the target of maintaining the same economic growth rate and promoting carbon reduction, are analyzed.

Based on the research questions, several hypotheses are proposed. Firstly, encouraged industries include industries with high added value, low energy consumption, and low emissions, such as services, high-end manufacturing, agriculture, etc. Restricted industries include low value added, high emissions, and low value-added industries, such as coal and coal-fired power industries, petrochemical and coal chemical industries, etc. Secondly, industries with strong economic interdependence have higher carbon emissions. Thirdly, in order to minimize carbon emissions while maintaining the same economic growth rate, restricted industries need to reduce final demand.

3.1.1. Economic and Carbon Emission Forward and Backward Linkages of Industries

According to the Statistical Yearbook of Guangdong Province, industrial emission sources are identified. The IPCC method is used to determine carbon emission factors, the carbon emissions of 42 industries are calculated, and the impact of carbon emissions on these industries is analyzed. An input–output model-based linkage analysis method is applied to investigate the economic forward and backward linkages of each industry, as well as carbon emission forward and backward linkages, to analyze the impact of industry inputs and outputs on the urban economy and the resulting carbon emission issues. The formulas for calculating the economic forward and backward linkages of industries are

$$F{L}_i={\displaystyle \frac{{\displaystyle {\sum }_{j=1}^n{g}_{ij}^d}}{\frac{1}{n}{\displaystyle {\sum }_{i=1}^n({\displaystyle {\sum }_{j=1}^n{g}_{ij}^d})}}}$$

(1)

$$B{L}_j={\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n{l}_{ij}^d}}{\frac{1}{n}{\displaystyle {\sum }_{j=1}^n({\displaystyle {\sum }_{i=1}^n{l}_{ij}^d})}}}$$

(2)

where $F{L}_i$ and $B{L}_j$ represent the economic forward and backward linkages of industry $i$ and $j$, $n$ is the number of industries, $g_{ij}^d$ is the element in the adjusted Ghosh inverse matrix, indicating the total output of industry $j$ driven by an increase of 1 unit in the initial input of industry $i$, and $l_{ij}^d$ is the element in the adjusted Leontief inverse matrix, indicating the total output of industry $j$ required by an increase of 1 unit in the final use of industry $i$.

$F{L}_i>1$ indicates that when the initial input of industry $i$ increases by 1 unit, its driving effect on the economy of Guangdong Province is greater than when the initial inputs of all industries increase by one unit. $B{L}_j>1$ indicates that when the final use of industry $j$ increases by one unit, its stimulating effect on the economy of Guangdong Province is higher than when the final uses of all industries increase by one unit.

The formulas for calculating the carbon emission forward and backward linkages of industries are

$$F{L}_i^c={\displaystyle \frac{{\displaystyle {\sum }_{j=1}^n{g}_{ij}^d{c}_j}}{\frac{1}{n}{\displaystyle {\sum }_{i=1}^n({\displaystyle {\sum }_{j=1}^n{g}_{ij}^d}{c}_j)}}}$$

(3)

$$B{L}_j^c={\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n{c}_i{l}_{ij}^d}}{\frac{1}{n}{\displaystyle {\sum }_{j=1}^n({\displaystyle {\sum }_{i=1}^n{c}_i{l}_{ij}^d})}}}$$

(4)

where $F{L}_i^c$ and $B{L}_i^c$ represent the carbon emission forward linkage and backward linkage of industry $i$ and $j$, and $c_i$ and $c_j$ are the direct carbon emissions generated per unit of output from industry $i$ and $j$.

$F{L}_i^c>1$ indicates that when the initial input of industry $i$ increases by one unit, the carbon emissions resulting from its contribution to the growth of Guangdong Province’s output are greater than the average carbon emissions resulting from an equal increase in the initial input of all industries. $B{L}_i^c>1$ indicates that when the final use of industry $j$ increases by one unit, the carbon emissions resulting from its contribution to the growth of Guangdong Province’s output are higher than the average carbon emissions resulting from an equal increase in the final use of all industries.

Industries are classified into restricted industries and encouraged industries based on their economic and carbon emission forward and backward linkage values. Restricted industries include those with the highest carbon emission forward and backward linkages but without significant economic linkages ($F{L}_i<1$, $B{L}_j<1$, and $F{L}_i^c>1$, $B{L}_i^c>1$). These industries have greater potential for emission reductions so their production proportion should be limited. Encouraged industries have significant economic linkages and insignificant carbon emission linkages ($F{L}_i>1$, $B{L}_j>1$, and $F{L}_i^c<1$, $B{L}_i^c<1$), thus the production proportion of these industries needs to be further increased.

3.1.2. Multi-Objective Programming Model

Based on the forward and backward linkages of the economic and carbon emissions of industries, corresponding objective functions and constraints are set, and a multi-objective programming model is used to analyze the expected final demand, changes in final demand, and expected carbon emissions of the industries in Guangdong Province. The multi-objective programming model uses multi-objective decision analysis methods to establish objective functions and constraint equations, considering the development trajectory of each industry and the impact of structural adjustments on economic growth, balancing economic growth and carbon reduction targets, and evaluating the impact of reducing carbon emissions on economic development.

In the multi-objective programming model, the objective function is set as the economic development goal of maintaining a constant GDP growth rate and the emission reduction goal of minimizing carbon emissions, with constraints including industrial structure. The constraints of industrial structure include restricting industries and encouraging industries and their final demand as a percentage of GDP. The formula of the multi-objective programming model is

$$\left\{\begin{array}{c}\min {\displaystyle \sum _{t=1}^T{E}_t}\\ \mathrm{s}.\mathrm{t}. Y_{t+1}\ge (1+g)Y_t\\ E_t={\theta }_t{Y}_t\\ {\theta }_{t+1}\le (1-\delta ){\theta }_t\end{array}\right.$$

(5)

where $Y_t$ is the GDP for the t-th period, $E_t$ is carbon emissions for the t-th period, ${\theta }_t$ is the carbon intensity, g is the target GDP growth rate, and $\delta$ is the attenuation rate of the carbon intensity.

The algorithm process of Equation (5) is presented as follows:

(1)

Initialization:

• Set the initial time period $t$.
• Input the initial GDP $Y_0$, initial carbon intensity ${\theta }_0$, target GDP growth rate g, and attenuation rate of carbon intensity $\delta$.
• Initialize the total carbon emissions TotalEmissions = 0.

(2)

Loop through each time period:

For each time period $t$ from l to $T$, perform the following steps:

• Use the formula $E_t={\theta }_{t}Y$ to calculate the current carbon emissions $E_t$.
• Update the total carbon emissions TotalEmissions = $E_t$.
• According to the GDP growth constraint $Y_{t+1}\ge (1+g)Y_t$, choose a value for $Y_{t+1}$ (typically taking equality, i.e., $Y_{t+1}=(1+g)Y_t$) to ensure the GDP grows at least by the rate $g$.
• According to the decay constraint ${\theta }_{t+1}\le (1-\delta ){\theta }_t$, choose a value for ${\theta }_{t+1}$ (typically taking equality, i.e., ${\theta }_{t+1}=(1-\delta ){\theta }_t$) to ensure the carbon intensity decays at the rate $\delta$.
• Check the termination condition. If $t<T$, set $t=t+1$ and continue the loop. If $t=T$, end the loop and output the result of carbon emissions TotalEmissions.

3.2. Data Collection

The data of the input–output table, energy consumption data, and carbon emission factors are collected to analyze the optimization of industrial structure under the ‘Dual Carbon’ Goal.

According to the Statistics Yearbook of Guangdong Province, the 42 industries include sub-industries of primary, secondary, and tertiary industries. The detailed industries and their descriptions are shown in

Table A1. The 42 industries and their descriptions.

Industry	Name	Descriptions
1	Agriculture, forestry, animal husbandry, and fishery products and services	Production of primary agricultural products such as planting, forestry, animal husbandry, aquaculture, and aquaculture.
2	Coal mining and selection products	Coal mining, washing and supporting services.
3	Oil and gas extraction products	Extraction of crude oil and natural gas, development of shale gas and coalbed methane, etc.
4	Metal ore mining and selection products	Mining and beneficiation of metal ores.
5	Non-metallic minerals and other mineral mining products	Mining and processing of non-metallic minerals.
6	Food and tobacco	Manufacturing of deep processed foods and production of tobacco products.
7	Textile	Cotton, synthetic fiber, wool textile and printing and dyeing precision processing.
8	Textile, clothing, shoes, hats, leather, down and its products	Manufacturing of ready to wear and clothing. Leather tanning, luggage, leather shoe manufacturing, etc.
9	Wood processing products and furniture	Manufacturing of sawn timber, artificial boards, wooden furniture, bamboo and rattan furniture.
10	Paper printing and cultural, educational, and sports equipment	Production of pulp, paper, cardboard, and paper containers. Manufacturing of stationery, toys, arts and crafts, and sports equipment.
11	Petroleum, coking products, and nuclear fuel processing products	Crude oil refining, coal to oil, biofuel processing, etc.
12	Chemical products	Manufacturing of basic chemical raw materials, fertilizers, pesticides, and synthetic materials.
13	Non-metallic mineral products	Production of cement, flat glass, ceramic products, and refractory materials.
14	Metal smelting and rolling processed products	Steel smelting and rolling.
15	Metalware	Manufacturing of metal tools, containers, steel structural components, and hardware products.
16	General equipment	Manufacturing of boilers, machine tools, bearings, and mechanical components.
17	Special equipment	Manufacturing of medical equipment, agricultural machinery, mining machinery, and environmental protection equipment.
18	Transportation equipment	Manufacturing of passenger cars, commercial vehicles, new energy vehicles, and their components.
19	Electrical machinery and equipment	Manufacturing of generators, transformers, wires and cables, and household appliances.
20	Communication equipment, computers, and other electronic devices	Manufacturing of computer systems, communication equipment, semiconductors, and electronic components.
21	Instruments and apparatuses	Manufacturing of industrial automation instruments, environmental monitoring instruments, and optical instruments.
22	Other manufactured products	Comprehensive utilization of waste resources, handicrafts, and other unspecified manufacturing industries.
23	Waste and scrap materials	Recycling and processing of scrap metal and non-metallic waste materials.
24	Repair services for metal products, machinery, and equipment	Repair of metal products, repair of general/specialized equipment, repair of electrical equipment, repair of transportation equipment, etc.
25	Production and supply of electricity and heat	Thermal, hydro, nuclear, wind power and other power generation and grid operation, and regional heating.
26	Gas production and supply	Natural gas liquefaction and transportation, gas supply, etc.
27	Production and supply of water	Tap water production, sewage treatment, seawater desalination, etc.
28	Architecture	Housing construction, civil engineering, building installation and decoration.
29	Wholesale and retail	Wholesale of goods and retail.
30	Transportation, warehousing, and postal services	Railway/road freight, air passenger transport, warehousing, and postal express delivery services.
31	Accommodation and catering	Hotels, homestays, restaurants, and fast food services.
32	Information transmission, software, and information technology services	Telecommunications, Internet access, software development, data processing, and information technology consulting.
33	Finance	Banking, securities, insurance, trust, financial leasing, etc., providing services such as fund financing, risk management, payment settlement, etc.
34	Real estate	Land and building development, sales, leasing, and management.
35	Leasing and business services	Provide asset leasing and specialized commercial services.
36	Scientific research and technical services	Natural science/engineering technology research and development, technology testing, and technology intermediary services.
37	Management of water resources, environment, and public facilities	Operation and maintenance of public facilities such as water supply, sewage treatment, environmental governance, parks, and urban greening.
38	Resident services, repairs, and other services	Convenient services and non productive activities for families and individuals.
39	Education	All forms of education (preschool education, primary education, secondary education, higher education, vocational skills training, etc.)
40	Health and social work	Medical and health services and social welfare services.
41	Culture, sports, and entertainment	Cultural and artistic activities, sports events, leisure and entertainment, etc.
42	Public administration, social security and social organizations	Administrative agency operations, social insurance management, and non-profit organization activities.

.

The study period is from 2012 to 2017. The input–output table is obtained from the China Statistical Yearbook. Energy consumption data for 42 industries is sourced from the China Energy Statistical Yearbook. Carbon emission factors are collected from documents issued by the IPCC. The carbon emission calculation method is used to calculate the fossil energy consumption of all major industries multiplied by the carbon emission coefficient and then calculate the carbon emissions of each segmented industry through the proportion of added value of segmented industries. The input–output table of Guangdong Province is compiled every five years, and no input–output survey was conducted in 2022. Therefore, the latest input–output table was compiled in 2017. In addition, the period from 2012 to 2017, spanning the middle and late stages of China’s 12th Five-Year Plan and the early stages of the 13th Five-Year Plan, was a critical stage for the adjustment of industrial structure in Guangdong Province. In 2012, China explicitly proposed the construction of ‘ecological civilization’, and Guangdong Province launched low-carbon pilot projects, gradually strengthening policies for optimizing industrial structure. After the signing of the Paris Agreement in 2015, China accelerated its low-carbon transformation, and Guangdong Province, as a major economic province, took the lead in responding. The 13th Five-Year Plan for 2016–2017 specifies the goal of reducing carbon emission intensity, and Guangdong Province has intensively introduced industrial upgrading policies.

The limitations of the data are that the input–output table has a static nature, and it assumes that the technical coefficient remains constant in the short term, but in reality, industry technological progress may be underestimated. Secondly, industry classification may mask differences in segmented industries.

4. Results and Discussion

The results are discussed from the perspectives of economic and carbon emission forward and backward linkages and the optimization of industrial structure based on the multi-objective programming model.

4.1. Economic and Carbon Emission Forward and Backward Linkages

From Equations (1)–(4), the results of the economic and carbon emission forward and backward linkages of 42 industries are shown in Figure 1 and Figure 2. A detailed summary of the results is shown in

Table 1. Detailed summary of the results.

Industry	Economic Forward	Economic Backward	Carbon Emission Forward	Carbon Emission Backward
1	1.3702	1.011	0.4179	0.3167
2	0.4938	0.5785	0.1483	0.1784
3	0.4938	0.5785	0.1483	0.1784
4	0.7973	0.7854	0.5952	0.6021
5	0.7307	0.7382	0.5078	0.5268
6	0.4358	0.6168	0.4367	0.6348
7	1.3266	1.1568	1.4223	1.2736
8	0.9877	1.0074	0.9266	0.9706
9	0.677	0.7411	0.7224	0.8121
10	0.5381	0.5985	0.6856	0.7831
11	1.1098	0.8478	1.3352	1.0474
12	1.5146	1.22	1.6701	1.3814
13	3.818	2.8265	3.9201	2.9802
14	0.8801	1.3108	1.3045	1.9953
15	3.0033	3.1616	3.3735	3.6468
16	1.2163	1.5055	1.5242	1.9374
17	0.7436	0.9304	0.713	0.9161
18	0.5979	0.6876	0.6493	0.7666
19	1.1654	0.9151	1.4357	1.1575
20	1.1236	1.1022	1.3853	1.3955
21	3.4048	3.0002	3.1588	2.8583
22	0.3271	0.7164	0.3609	0.8117
23	0.1474	0.3897	0.179	0.4858
24	1.3521	1.011	1.7247	1.3242
25	0.0648	0.3674	0.0624	0.3635
26	2.4258	1.8613	3.3247	2.6196
27	1.0412	1.5356	0.9092	1.377
28	0.4226	0.6902	0.0879	0.1475
29	0.2022	0.4037	0.0431	0.0884
30	1.3979	1.2674	6.3089	5.8735
31	1.8474	1.4658	0.5583	0.4549
32	0.8198	0.7324	0.1601	0.1469
33	0.4649	0.555	0.0877	0.1075
34	1.5381	1.1436	0.2204	0.1683
35	0.5973	0.6276	0.1306	0.1409
36	1.5812	1.17195	0.3716	0.2829
37	0.1209	0.4044	0.0225	0.0772
38	0.0184	0.3317	0.0035	0.0648
39	0.5049	0.5317	0.0767	0.083
40	0.1023	0.3623	0.0209	0.0761
41	0.0007	0.3238	0.0001	0.0662
42	0.0887	0.3659	0.014	0.0594

.

From Table 1, we can determine that the industries with high economic forward and backward linkages ($F{L}_i>1$, $B{L}_j>1$) are industry 1, industry 7, industry 12, industry 13, industry 15, industry 16, industry 20, industry 21, industry 24, industry 26, industry 27, industry 30, industry 31, industry 34, and industry 36, which have significant effects on economic development. Some industries are fundamental industries that serve as the basis for social and industrial security, such as industries 1, 7, 12, and 15. The manufacturing industry of industry 20 in Guangdong Province occupies an important position nationwide. In 2017, the proportion of added value in high-tech manufacturing continued to increase, promoting the transformation of the industry towards intelligence and low-carbon. The general equipment, instruments, and equipment manufacturing industry provides various mechanical equipment and tools that improve production efficiency and reduce production costs. The maintenance services for metal products, machinery, and equipment are an important component of the service industry, ensuring the stable operation of production equipment and reducing the risk of production interruptions. The production and supply of natural gas and water are key industries in energy and resource supply, providing necessary energy and resources for industrial production and residential life. Industry 30 ensures the rapid circulation of goods and information, improving the efficiency of economic activities. Industry 31, industry 34, and other industries have driven consumer demand and promoted economic growth by providing services and goods. Industry 36 is a key force driving technological innovation and industrial upgrading. They promote the optimization of economic structure and industrial upgrading through the research and development of new technologies and products.

The industries with high carbon emission forward and backward linkages ($F{L}_i>1$, $B{L}_j>1$) are industry 7, industry 11, industry 12, industry 13, industry 14, industry 15, industry 16, industry 19, industry 20, industry 21, industry 24, industry 26, and industry 30, which have large impacts on the environment. These industries mainly include heavy metal design industries. Industry 7 has a high dependence on direct energy resources such as coal, electricity, oil, and natural gas in the production process, including water consumption, energy consumption, wastewater discharge, and waste disposal. Industry 11 requires a large amount of energy consumption in the production process, especially the amount of coking clean coal and ingredients, coke production, coke oven gas production, etc., in the coking process, which will generate a large amount of carbon emissions. The carbon emission intensity per unit of GDP in industry 12 is relatively high, especially in the coal chemical industry, where processes such as coal-to-methanol conversion generate a large amount of carbon emissions. Industry 13, especially cement products, is one of the main sources of energy consumption and carbon emissions during processing. Industry 14 is an energy-intensive and greenhouse gas-emitting industry, especially the fossil fuel and energy consumption in the metal smelting process, which generates a large amount of carbon emissions.

Industry 1, industry 31, industry 34, and industry 36 represent the encouraged industries. The economic forward and backward linkages are greater than 1, and the carbon emission forward and backward linkages are lower than 1. These industries positively impact economic development, and their pollution to the environment is also relatively small, and so they are encouraged to develop in the future. Industry 1 serves as a carbon source and sink, absorbing carbon dioxide from the atmosphere. At present, the agricultural industry is beginning to develop in a green direction, and the carbon emissions from agriculture are decreasing [34]. Guangdong has launched the first mangrove carbon-inclusive methodology in China, promoting ocean carbon trading and transforming ecological resources into economic benefits. Agricultural modernization and ecological breeding can not only improve production efficiency but also reduce the environmental load, which is in line with the development direction of green and beautiful Guangdong. Regarding industry 31, Guangdong Province promotes low-carbon industries through strict emission standards, such as the Emission Standards for Oil Fume Pollutants in the catering industry, and online monitoring systems. At the same time, this industry has strong employment absorption capacity and has a significant driving effect on industries such as tourism and logistics, making it a low-emission, high-employment service industry. Industry 34 has a strong driving force for industries such as building materials, home appliances, and finance, and promoting green buildings can significantly reduce carbon emissions. Guangdong is promoting the ‘integrated light storage and charging’ building model. Industry 36 is crucial for economic transformation, as the research and development of low-carbon technologies such as new energy technologies and carbon capture and storage (CCS) can promote emission reductions in high-carbon industries.

The industries with forward and backward linkages of carbon emissions greater than 1 and economic forward or backward linkages less than 1 are identified for relative restrictions by scale, which are industry 11, industry 14, and industry 19. These industries belong to the manufacturing sector. Industry 11 is a highly polluting and energy-consuming resource-based industry that often relies on the massive consumption of fossil fuels, resulting in significant carbon emissions [35]. The technological progress of these industries is slow, and their energy efficiency is low, so their role in promoting the economy may be relatively small, while their carbon emissions are relatively high. The supply chain and electricity demand of industry 19 indirectly led to significant environmental impacts, and it was listed as a key control measure in Guangdong Province in 2017.

As shown in Figure 1, the economic forward and backward linkages of the industries, i.e., industry 13, industry 15, and industry 21, have values higher than 2. These industries make greater contributions to economic development because they are the driving force of secondary industries. In Guangdong Province, industrial added value and industrial investment growth are leading in China. Thus, as traditional industries, these industries have a growth effect on the economy. At the same time, these industries also impact the environment negatively due to the larger value of carbon emission forward and backward linkages.

From Figure 2, the carbon emission forward and backward linkages of industry 13, industry 15, industry 21, industry 26, and industry 30 are higher than 2, meaning more carbon dioxide is released. The value of industry 30 is more than 5. Industry 13 and industry 21 can be considered restricted industries, despite having positive effects on the economy. Industry 26 and industry 30 are fundamental industries related to the basic guarantee of people’s livelihood and society; thus, they are excluded from the group of industries that restrict development. These industries can improve carbon emissions through methods such as increasing industry concentration, transforming energy consumption to become clean, low-carbon, and efficient, and innovating low-carbon technologies.

To further analyze the correlation between economic and carbon indicators and validate the results, the Pearson correlation analysis was applied. The results are shown in

Table 2. Results of Pearson correlation analysis.

Indicator	Economic Forward	Economic Backward	Carbon Emission Forward	Carbon Emission Backward
Economic forward	1	0.9533	0.7298	0.6662
Economic backward	0.9533	1	0.7273	0.7209
Carbon emission forward	0.7298	0.7273	1	0.9771
Carbon emission backward	0.6662	0.7209	0.9771	1

. From Table 2, we can determine that there is a moderate correlation (ranging from 0.66 to 0.73) between economic and carbon indicators, which suggests that industries with strong economic interdependencies also tend to be significant carbon emitters. This supports the central policy discussed in the paper and reinforces the importance of a multi-objective framework. A very high correlation (0.977) between carbon emission forward and backward linkages indicates that high-emission sectors have consistent impacts on both supply-driven and demand-driven processes, validating the classification of restricted industries. There is a strong correlation (0.953) between economic forward and backward linkages. As a global manufacturing base, Guangdong Province has formed a highly coordinated industrial chain network. Some industries, such as electronic manufacturing and electrical machinery, both have strong demand- and supply-driven effects, leading to the convergence of two related indicators. The strong interdependence among variables suggests that future work should explore dimensionality reduction to synthesize linkage indicators into interpretable composite measures.

4.2. Optimization of Industrial Structure

Using Equation (5), the results of the changes in final demand, expected final demand, and expected carbon emissions of the industries are shown in Figure 3 and Figure 4. The detailed results of the multi-objective programming model are presented in

Table 3. Detailed results of multi-objective programming model.

Industry	Expected Final Demand (10,000 CNY)	Change in Final Demand (%)	Expected Carbon Emissions (10,000 tons)
1	48,643,840	30.57	7,944,626.7
2	7,516,568.6	42.19	1,208,668.36
3	7,516,568.6	42.19	1,208,668.36
4	2,953,923.9	−16.97	1,180,730.72
5	4,109,981.7	−18.23	1,529,370.47
6	55,459,659	−12.64	29,758,771.35
7	22,755,744	−11.82	13,062,811.09
8	56,312,865	−13.5	28,289,313.39
9	20,905,496	−11.87	11,944,624.04
10	64,339,905	−9.94	43,894,349.23
11	33,522,124	−0.53	21,594,735.58
12	106,280,370	−11.49	62,748,395.59
13	35,612,630	−12.34	19,578,415.59
14	47,537,440	−8.55	37,729,472.41
15	48,877,853	−11.28	29,396,740.93
16	33,606,476	−10.11	22,549,568.38
17	19,921,788	−13.21	10,228,116.93
18	53,127,462	−11.67	30,887,221.29
19	96,379,988	−10.29	63,571,494.09
20	220,933,440	−10.28	145,859,453.8
21	7,512,812.1	−13.66	3,732,062.45
22	2,898,799.4	−11.48	1,712,744.76
23	7,655,328.2	−10.44	4,976,823.24
24	1,081,520.9	−9.93	738,647.37
25	54,966,560	−13.15	28,359,567.81
26	5,350,535.9	−9.24	3,926,489.88
27	3,322,467.5	−14.51	1,553,478.25
28	77,596,720	−10.8	8,644,395.3
29	83,001,910	29.51	9,477,804.38
30	58,303,218	−19.39	140,888,805.2
31	30,360,800	−20.83	4,912,402.23
32	30,534,600	−26.9	3,193,432.65
33	58,239,693	27.85	5,882,053.89
34	54,331,800	36.66	4,168,977.41
35	44,021,280	−24.03	5,152,851.69
36	13,086,400	−22.35	1,646,859.13
37	4,498,440	28.25	448,028.43
38	16,560,600	27.61	1,687,343.12
39	21,529,000	34.57	1,752,114.83
40	16,617,480	25.7	1,819,104.12
41	6,323,880	26.37	674,515.41
42	26,319,560	33.22	2,228,663.1

. Under the economic development goal of maintaining a constant GDP growth rate and the emission reduction goal of minimizing carbon emissions, the expected final demand of industries, changes in the final demand of industries, and expected carbon emissions are shown.

From Table 3, we can determine that Guangdong Province, as a major economic province, has relatively high total carbon emissions. Most industries (73%) need to reduce their final demand, including most industries with high carbon emissions. In terms of increasing final demand, the final demand of two encouraged industries, including industries 1 and 34, has increased, reaching 30.57% and 36.66%, respectively.

Industries 11, 14, and 19 are considered to be relatively restricted by scale, which should decrease their final demand. These industries have high carbon emissions and relatively low economic growth, which is needed to transform their industries. Industries 32 and 35 require a maximum reduction in their final demand, reaching 26.9% and 24.03%, respectively. These two industries have low economic linkage and low carbon emissions. Two encouraged industries need to reduce their final demand, namely, industries 36 and 31. Reducing the final demand of these industries can minimize carbon emissions. Industries with carbon emissions greater than 1 and economic forward or backward linkages smaller than 1 all need to reduce their final demand, as they have a relatively small impact on economic growth but generate more carbon emissions. Therefore, it is necessary to reduce the proportion of these industries. Reducing their final demand can directly lower overall carbon emissions with minimal impact on the economic system. Most industries that require a reduction in final demand are those with high economic interdependence and carbon emissions. It is necessary for these industries to reduce emissions through structural adjustment, technological progress, or clean energy substitution, rather than relying solely on demand growth.

The two encouraged industries can drive the coordinated development of upstream and downstream industries. Agriculture and forestry support multiple industries such as food processing, textiles, and bioenergy, and the real estate industry is deeply tied to industries such as building materials, home appliances, and finance. Increasing their final demand can stimulate broader economic growth while not significantly exacerbating environmental burdens due to their low carbon emission intensity. Meanwhile, these industries play a crucial role in the low-carbon transformation. Modern agriculture and forestry can reduce net carbon emissions through ecological planting, carbon sequestration afforestation, and other methods, becoming important carriers of carbon absorption [36]. The development of green buildings and energy-efficient real estate can significantly reduce energy consumption in the construction industry.

Other industries that increase final demand have the characteristic of very small linkages with carbon emissions. The industries with significant growth rates include industries 2 and 3, industry 39, and industry 42, all of which exceed 30%. The economic forward or backward linkages of these industries, or both, are greater than 0.5. Although oil and gas extraction products belong to the traditional energy industry, the relatively small linkage between their carbon emissions may be due to the industry’s own low-carbon transformation, such as reducing carbon emissions per unit output through CCS technology. The education industry drives long-term economic growth through the accumulation of human capital, and its demand growth can drive related industries such as publishing, information technology, and construction. Public management and social security indirectly promote economic vitality by enhancing the effectiveness of social governance. The expansion of these industries will not only not increase carbon emissions pressure but can also enhance social resilience and sustainable growth potential.

To further analyze the relationship between the expected final demand and expected carbon emissions and validate the results, the Pearson correlation coefficient is calculated. The results show that the correlation coefficient between these two variables is 0.768, indicating a strong positive relationship, which quantitatively supports the main conclusions that industries with higher economic importance (in terms of demand) are also typically associated with higher carbon emissions.

The optimization of industrial structure in Guangdong Province under the ‘Dual Carbon’ Goal is consistent with the Porter hypothesis. The encouraged industries in this paper have high environmental compatibility, which is in line with Porter’s hypothesis of promoting economic transformation to become green through environmental regulations [35]. The scientific research and technical service industries can support the green upgrading of other industries through technological innovation, while the sustainable development of agriculture and fisheries can help reduce the excessive exploitation of natural resources and environmental damage. The restricted industries in this paper are also a reflection of Porter’s hypothesis that environmental regulations promote corporate innovation and economic transformation. These industries come with high environmental costs under traditional development models, and by limiting their scale of development, companies can seek cleaner and more efficient production methods, thereby driving the entire economic system towards sustainable development [24]. In addition, most industries in Guangdong Province need to reduce their final demand, especially those with the highest carbon emissions, which further reflects the Porter hypothesis of guiding economic structural adjustment through environmental policies.

The conclusions are consistent with the relevant research results. There are significant differences in the relationship between different industries and carbon emissions. The secondary industry, especially traditional carbon-intensive industries such as manufacturing and mining, remains the main source of carbon emissions, while industries such as agriculture and services are low-carbon emission and low-pollution industries [10,35]. Policy formulation should implement differentiated measures based on industry characteristics. Firstly, the expansion of highly polluting industries such as coking and metal smelting is restricted through regulatory measures such as carbon pricing and technical standards [34]. Secondly, innovative resources to tilt towards clean industries such as renewable energy, green agriculture, and machinery manufacturing can be actively guided [35]. In addition, innovation in environmentally friendly industries such as agriculture can be encouraged [34].

5. Conclusions

This paper investigates the optimization of industrial structure under the ‘Dual Carbon’ Goal in Guangdong Province of China via a multi-objective programming model.

The conclusions are as follows: industries 1, 31, 34, and 36 are classified as encouraged industries, demonstrating positive contributions to economic development and relatively low environmental pollution, thus warranting future promotion. Industries 11, 14, and 19 are identified as scale-restricted industries, predominantly high-pollution, high-energy-consuming manufacturing and resource-based industries. Most industries in Guangdong Province require a reduction in final demand, including the highest carbon-emitting industries and those restricted by scale. In terms of final demand growth, two encouraged industries have witnessed growth, along with industries exhibiting strong forward or backward economic linkages or both linkages exceeding 0.5.

Some policy implications are provided. For encouraged industries, the government can provide incentives such as tax reductions and green loans to guide capital to flow toward low-carbon and high-value-added industries. Additionally, a special industry fund can be established to support technological research and development. For restricted industries, strict capacity control and exit mechanisms are essential. The government may develop phased production reduction plans and implement mandatory elimination of outdated production capacity. Furthermore, the government can support carbon reduction technologies, such as those applied in clean energy or energy-efficient processes through financial subsidies, thereby promoting technological and low-carbon transformation. For industries requiring a reduction in final demand, green procurement policies can be enforced to restrict high-carbon products, while circular economy models can be developed to facilitate industrial restructuring and upgrading. For industries with strong economic linkages, e.g., electronic manufacturing, that need adjustment, moderate growth may be permitted, but it must be coupled with the adoption of emission reduction technologies. The policy implications are helpful for optimizing and adjusting the industrial structure to reduce carbon emissions to achieve the ‘Dual Carbon’ Goal.

The limitations of this paper are as follows: the input–output table exhibits static characteristics, assuming that technical coefficients remain constant in the short term, which may lead to an underestimation of industrial technological progress. Additionally, the industry classification might obscure differences among segmented industries. The constraints of multi-objective programming models could inadvertently amplify other factors, such as energy and water consumption. For future research, integrating dynamic input–output models and introducing time-varying variables, such as the technological progress rate and energy structure changes, would be beneficial. Furthermore, the multi-objective programming framework could be enhanced by incorporating diverse scenario settings.