Configuration paths of carbon emission efficiency in manufacturing industry

From the perspective of configuration, this paper takes the region of manufacturing efficiency as the explanatory variable, selects eight antecedent conditions, and applies fuzzy set qualitative comparative analysis (fsQCA) to study the paths and methods of improving manufacturing emission efficiency. The results of the study show that there are two configuration paths of carbon emission efficiency in manufacturing industry, namely, research frontier and technological innovation level and labour force structure, R&D investment, science and technology innovation level, manufacturing output value, and environmental regulation synergistic path.

The manufacturing industry, as the engine of economic growth and the pillar of the national economy, directly reflects the level of productivity in China, and, as an important foundation for the transformation of China’s economy and the leading industry of economic development, has been maintaining an upward trend of development., the optimisation, upgrading and rapid development of the manufacturing industry means that China has initially established its status as a “manufacturing power”, laying a solid foundation for its transformation into a “manufacturing power”. However, due to the rapid development of the manufacturing industry and the increasing use of fossil energy, global carbon dioxide emissions have increased sharply, and the original natural balance has been upset, triggering a series of environmental problems and natural disasters and posing a serious threat to the survival and development of mankind. Therefore, improving the carbon emission efficiency of the manufacturing industry will become an important issue for economic development.

In order to be able to better understand the carbon emission efficiency of China’s manufacturing industry and to find out the best way to improve the carbon emission efficiency, the study starts from the perspective of configuration, takes the region of the manufacturing industry’s efficiency as the explanatory variable, selects eight antecedent conditions, such as the labour structure, the structure of energy consumption, the degree of opening up to the outside world, the investment in research and development, the level of scientific and technological innovation, the manufacturing industry’s output value, the environmental regulations, and the size of the enterprise, and applies the method of comparative analysis of the fuzzy qualitative set The fuzzy qualitative set comparison analysis is used to explore the improvement paths and methods of manufacturing emissions, and specific countermeasures and suggestions are given according to the results of the analysis.

Overview of Carbon Emission Efficiency and Allocation pathways Theory

Carbon emission efficiency

Carbon emission efficiency refers to the economic benefits derived from a unit of carbon emission, specifically the input-output benefits of carbon dioxide (Ge et al. 2024a, b; He et al. 2023; Xu et al. 2023; Zhang et al. 2023a, b, 2024; Panagiotopoulou et al. 2023; Tang et al. 2023). It can also be defined as the carbon emissions generated by each unit of industrial added value (Zhang and Wang 2023; Tan et al. 2024; Ge et al. 2024a, b; Liu et al. 2024; Wang et al. 2023; Li and Tian 2023). Additionally, it represents the ratio between the minimum achievable carbon emissions through production and the actual emissions under the conditions of given expected output and input factors (Wu et al. 2023; Chen and Jin 2023; Li et al. 2023; Peng et al. 2023a, b; Mu and Zhao 2023; Lu et al. 2023; Wang and He 2023). The higher actual carbon emissions indicate lower carbon emission efficiency (Li et al. 2023). In light of this analysis, this paper defines the carbon emission efficiency of the manufacturing industry as achieving minimal carbon emissions while maximizing profits, taking into account various input factors such as capital, energy consumption, and labor.

Configuration path

The core concept of configuration is the configuration path and antecedent configuration formed by the combination of configuration patterns and relationships between variables, producing performance and positive configuration effects on the outcome variables. Configuration emphasizes that the factors are interrelated, the combination produces a certain result, and the result is not a single factor. Configuration emphasizes the influence of the relationship between antecedent conditions and their interactions with the outcome variables and is not limited to the effect of the antecedent condition itself. The characteristics of configuration include equivalence and concurrency (Verma et al. 2023).

Calculation of carbon emission efficiency of the manufacturing industry

Measurement index system of carbon emission efficiency of the manufacturing industry

The selection of carbon emission efficiency measure indicators can be categorized into two groups. The first group consists of single-factor indicators, which analyze the influence of a single factor on outcome variables. The second group consists of multi-factor indicators, which analyze the influence of multiple factors and their interactions with outcome variables. In this study, multi-factor analysis and data envelopment analysis (DEA) were utilized to calculate the carbon emission efficiency of the manufacturing industry. The DEA method selected input and output indicators as the chosen indicators. Due to the lack of data for Inner Mongolia Autonomous Region, Heilongjiang Province, and Tibet Autonomous Region in the statistical yearbook, this study focused on manufacturing data from 28 provinces, autonomous regions, and municipalities in 2019 and 2020 excluding these three regions.

Screening and determination of input indicators

The input indicators commonly used in the study of carbon emission efficiency typically encompass labor, energy consumption, and capital. The specific input indicators chosen for this study are as follows.

1) Energy consumption Upon reviewing the Statistical yearbooks of each region in 2020 and 2021, it was found that Tianjin, Liaoning, Jilin, Anhui, Jiangxi, Hubei, Hunan, Chongqing and Shaanxi did not provide the total energy consumption of the manufacturing industry directly in their statistical yearbooks. As a result, this information had to be calculated. Furthermore, due to differences in energy consumption units across regions, it was necessary to convert them into a uniform unit for calculation and summarization. The calculation formula for the total energy consumption of the manufacturing industry is as follows Eq. (1):

where \(\:{\text{E}}_{\text{j}}\) represents the total energy consumption of the manufacturing industry in region j, \(\:{\text{e}}_{\text{i,j}}\) denotes the consumption of the ith energy in region i, and \(\:{\text{k}}_{\text{i}}\) signifies the conversion coefficient of the ith energy. The conversion coefficients for various energy sources can be found in Table 1, while Table 2 displays the total energy consumption after converting energy into standard coal.

2) Labor force In this study, the average number of manufacturing workers in 28 regions in 2019 and 2020 the labor force index was chosen for representation, with the data sourced from the China Industrial Statistical Yearbook 2020–2021.

3) Capital investment This index is denoted by the capital stock. However, since statistics related to the capital stock cannot be found in existing statistical yearbooks, based on the research results and practical achievements (Verma et al. 2023; Kaur et al. 2024; Yi et al. 2023; Peng et al. 2023a, b; Shi 2023; Bin et al. 2023; Zou et al. 2023), the net value of fixed assets in the manufacturing industry was chosen to represent the capital input for each region, with the data sourced from the China Industrial Statistical Yearbook 2020–2021.

Screening and determination of output indicators

In the analysis of carbon emission efficiency, the output index typically utilizes the GDP of each region as the expected output and carbon emissions as the non-expected output. However, due to a lack of regional statistics on gross manufacturing product in existing statistical yearbooks, this study has opted to use total profit of the manufacturing industry as the expected output. The specific output indicators selected for this paper are as follows.

1) Carbon emissions This paper draws on conclusions drawn by the relevant research literatures (Zhang et al. 2023a, b; Graevenitz and Rottner 2023; Wang et al. 2024a, b; Guo et al. 2024; Yang et al. 2023; Martinsson et al. 2024). The carbon emission value of standard coal is 0.69TC/TCE; 0.69 tons of carbon emission will be generated for each ton of standard coal (Yi et al. 2023). The calculation formula for carbon emissions in the manufacturing industry of each province is as follows Eq. (2):

\(\:{\text{C}}_{\text{j}}\) represents carbon emissions in region j. \(\:{\text{E}}_{\text{j}}\) represents the energy consumption in region j, and the specific data for \(\:{\text{E}}_{\text{j}}\) is shown in Table 2. The carbon emissions of manufacturing industries in each region are shown in Table 3.

2) Total profit The average total profits of the manufacturing industry in each region for 2019 and 2020 were selected. The data is sourced from the China Industrial Statistical Yearbook 2020–2021.

Measurement index system of carbon emission efficiency of the manufacturing industry

Upon analysis of the characteristics and indicators of carbon emission efficiency in the manufacturing industry, the measurement index system for carbon emission efficiency in the manufacturing industry is presented in Table 4.

Measurement method of carbon emission efficiency of the manufacturing industry

This study employs data envelopment analysis (DEA) to assess the carbon emission efficiency of the manufacturing industry. The DEA model is a scientific method used to evaluate the relative efficiency of multiple factor inputs and outputs among decision-making units. By maintaining constant input or output levels for each decision-making unit, statistical and mathematical methods are used to project the corresponding input and output points onto the production frontier. The efficiency value of each type of decision-making unit is determined by measuring the deviation between that unit and the production frontier. The mathematical form of the DEA model is as follows Eqs. (3)-(4): insert mathematical form here:

\({{\lambda}}_{\text{j}}\) is the decision variable, n is the number of decision variables. \(\theta^*\) denotes the optimal solution of the linear programming model. \(\:{\text{x}}_{\text{ij}}\) represents the ith input factor of the jth decision-making unit, and there are m input indexes. \(\:{\text{y}}_{\text{ij}}\) represents the ith output factor of the jth decision making unit. There are S output indicators, which require a minimum input when output is fixed.

There are two fundamental types of DEA methods: the input-oriented CCR model (CRS model with fixed return to scale) assumes constant output and minimal input factors. This method is utilized to analyze the comprehensive efficiency of decision-making units, encompassing pure technical efficiency and scale efficiency. The other approach is the output-oriented BCC model (VRS model with variable return to scale), which is employed to assess the pure technical efficiency, technical efficiency, and scale efficiency of decision-making units while assuming constant input factors and maximum output.

Measurement process and results of the carbon emission efficiency of the manufacturing industry

(1) Data sources and processing

This study utilized the DEA method and SPSSPOR software to determine the carbon emission efficiency of manufacturing industries in various regions. The specific data sources can be found in Table 5.

Given that carbon emissions in the output index serve as a negative indicator, it is essential to conduct data standardization processing in order to accurately measure and analyze the carbon emission efficiency of the manufacturing industry in each province. The results before and after processing with SPSSPOR software are presented Table 6.

(2) Measurement of carbon emission efficiency

Based on the data in Tables 5 and 6, the DEA-BCC model and SPSSPOR software can be utilized to calculate the carbon emission efficiency of the manufacturing industry in each region, along with its decomposition terms - scale efficiency and technical efficiency, as presented in Table 7.

It is evident from Table 7 that the carbon emission efficiency of Beijing, Fujian, Hainan, and Guizhou is 0.99999, indicating that the carbon emission efficiency of the manufacturing industry in these regions is approaching optimal levels. In Shanghai and Guangdong, the carbon emission efficiency value falls between 0.8 and 0.99999, suggesting that the manufacturing industry in these regions operates with effective and high levels of carbon emission efficiency. Conversely, Tianjin, Hebei, Shanxi, Liaoning, Shandong, Guangxi, Ningxia, and Xinjiang exhibit a carbon emission efficiency below 0.5. Theoretically speaking, the manufacturing industry in these eight regions could potentially reduce their carbon emissions by an additional 50%, highlighting significant potential for further reduction efforts in these areas. In addition to the 14 regions, the carbon emission efficiency of the remaining 14 provinces and cities is between 0.5 and 0.8, which also suggests significant potential for carbon emission reductions.

It is not difficult to see from Table 7 that regions with a carbon emission efficiency lower than 0.5 in manufacturing industry are affected by technical efficiency. All of these regions have a high level of scale efficiency, whereas the average technical efficiency is only 0.44284, it can be observed from the analysis that enhancing technological innovation plays a crucial role in improving carbon emission efficiency. Despite the inefficiency in scale and comprehensive efficiency of Jiangsu Province and Zhejiang Province, their technical efficiency remains consistently high. This suggests that the technological input in the manufacturing industry of these two provinces is effective, while carbon emissions are inefficient due to mismatched scale and input-output. In conclusion, besides improving technical efficiency, attention should also be paid to optimizing the matching degree between scale and input-output in order to enhance carbon emission efficiency.

Theoretical model construction of configuration path of carbon emission efficiency in manufacturing industry

Identification of antecedent conditions

Based on a thorough review and analysis of multiple studies, eight antecedents have been identified for investigating the pathway to enhancing the carbon emission efficiency of the manufacturing industry. The number of antecedent conditions falls within the optimal range.

According to relevant literature, the composition of the labor force in the manufacturing industry is expected to impact carbon emissions. However, further research is needed to understand its specific influence on carbon emission efficiency. This study aims to examine how the structure of the labor force affects the carbon emission efficiency of the manufacturing industry. In this study, we measured the structure of the labor force using the ratio of average workers in the manufacturing industry to industrial enterprises above a designated size; a higher index value indicates a greater share of manufacturing labor.

In a review of relevant literature, it was discovered that enterprises with higher coal consumption tend to exhibit elevated carbon emissions. The utilization of coal is not conducive to the enhancement of carbon emission efficiency in the manufacturing sector. To investigate the impact of energy consumption structure on carbon emission efficiency, this study expressed the energy consumption structure as the ratio of coal consumption to total energy consumption in the manufacturing industry; a higher index value indicates a greater proportion of coal in the energy consumption structure.

Regarding openness to foreign investment, on one hand, the influx of foreign capital will heighten market competition. Additionally, developed nations may shift pollution to developing countries, thereby negatively impacting carbon emission efficiency. On the other hand, foreign investment has potential for knowledge spillovers. The Chinese government’s prohibition against high-polluting enterprises operating within its borders will contribute to improving carbon emission efficiency. To examine how openness influences manufacturing’s carbon efficiency, this study utilized foreign direct investment in the manufacturing industry as an indicator of external openness; a higher index signifies greater openness to international markets.

R&D and innovation are the driving forces of enterprises’ sustainable development. Increasing R&D investment and enhancing the scientific and technological strength of enterprises are conducive to improving their competitiveness and industrial status, which will lay the foundation for long-term, high-quality development. In this study, R&D investment was measured as the internal expenditure of R&D expenditure of manufacturing industry in each region in order to study the impact of R&D investment on the carbon emission efficiency of the manufacturing industry. A higher value of this index indicates a larger investment in R&D.

The level of scientific and technological innovation plays a pivotal role in the development of the manufacturing industry. Technological innovation can enhance production efficiency, while scientific and technological advancements can drive the development of energy-saving, emission-reduction, and environmental pollution treatment technologies within enterprises. This study aims to investigate the impact of technological innovation on carbon emission efficiency in the manufacturing industry by measuring the number of manufacturing patent applications in each region as an indicator of scientific and technological innovation level; a higher value indicates greater innovation.

Enterprise output value refers to the total production of an enterprise. Holding carbon emissions constant, higher enterprise output values result in greater unit carbon emission generation. To examine the impact of manufacturing output value on carbon emission efficiency, this study measures manufacturing output value using regional manufactured goods’ monetary value as an index; a higher index signifies increased manufacturing output.

Environmental regulations will impose a financial burden on manufacturing enterprises, thereby reducing their competitiveness and hindering the improvement of carbon emission efficiency. However, these regulations can also incentivize enterprises to engage in technological innovations aimed at developing and utilizing more efficient technologies and equipment, ultimately promoting the enhancement of carbon emission efficiency. To analyze the impact of environmental regulations on the carbon emission efficiency of the manufacturing industry, we represent environmental regulation by the ratio of manufacturing business revenue to total energy consumption. A higher index value indicates stronger environmental regulation.

The size of an enterprise directly correlates with its economic strength, risk resistance, and sustained R&D investment, all of which contribute to improved carbon emission efficiency. However, larger enterprises often have more management layers and require higher costs for internal coordination, which may be detrimental to improving carbon emission efficiency. To study the impact of enterprise scale on the carbon emission efficiency within the manufacturing industry, we represent enterprise scale as the ratio of main business income for industrial enterprises above a certain scale to the number of enterprise units; a higher index value signifies a larger-scale enterprise. The data pertaining to these eight indicators are based on average figures from 2019 to 2020 within each region’s manufacturing industry.

Theoretical hypothesis

The correlation degree between the labor force scale and carbon emissions in all agricultural industries in central China and provinces was greater than 0.5 (Guo et al. 2024). The degree of correlation was relatively high, and the impact of the scale of labor force on carbon emissions in various industries varied. It may be inferred that the scale of the labor force in manufacturing also has an impact on carbon emissions. The structure of the labor force may also affect the carbon emission efficiency of the industry (Yang et al. 2023; Martinsson et al. 2024; Hudaifah et al. 2024; Li et al. 2024). Therefore, this study proposes the following hypothesis:

H₁.

In the manufacturing industry, the composition of the labor force is a crucial factor in enhancing the carbon emission efficiency of enterprises.

There is obvious positive spatial correlation between the structure energy consumption and carbon emission levels (Chen et al. 2023; Liu et al. 2023; Zębala and Gaweł 2024; Zhou et al. 2023; Wang et al. 2024a, b). The spatial representation of energy consumption structure shows the characteristics of regional aggregation consistent with carbon emissions. Therefore, it can be inferred that in the energy consumption structure of the manufacturing industry, a higher proportion of coal consumption will result in increased carbon emissions, ultimately leading to a reduction of carbon emission efficiency (Peng et al. 2023a, b). Therefore, this study proposes the following hypothesis:

H₂.

In the manufacturing industry, analyzing the structure of energy consumption is a crucial step towards enhancing the carbon emission efficiency of enterprises.

Foreign direct investment is found to have an inverse relationship with carbon emissions. The technology spillover effect of foreign direct investment is expected to enhance production technology, expand production scale, increase energy consumption, and consequently lead to a rise in carbon dioxide emissions. According to this study, it can be inferred that the higher the level of openness of the manufacturing industry in each province, the greater the absorption of foreign direct investment will be. In this case, the production scale of the manufacturing industry may be expanded, resulting in a reduction in carbon emission efficiency (Lu et al. 2023). Therefore, this study puts forward the following hypothesis:

H₃.

In the manufacturing industry, reducing exposure to external factors is a necessary prerequisite for improving the carbon emission efficiency of enterprises.

In the research on R&D investment, energy efficiency, and the reduction of industrial carbon emissions, a 1% increase in R&D intensity results in a 0.0501% reduction in industrial carbon emissions at the industrial level. Throughout various stages of development, R&D investment plays a positive role in decreasing industrial carbon emissions. This research suggests that higher R&D investment within the manufacturing industry in each province may lead to a certain extent of reduction in carbon emissions, and the carbon emission efficiency will also be affected to a certain extent (Kaur et al. 2024). Therefore, this study proposes the following hypothesis:

H₄.

In the manufacturing industry, R&D investment is a necessary condition to improving the carbon emission efficiency of enterprises.

The efficiency of scientific and technological innovation, industrial structure, foreign trade, economic development level, and other factors will have a significant positive impact on carbon emission efficiency at different levels of significance. Furthermore, considering heterogeneity, it is found that scientific and technological innovation efficiency has the most significant influence on regional carbon emission efficiency among all variables. Based on this research, it can be inferred that the higher the technological innovation level of the manufacturing industry in each province, the higher the carbon emission efficiency will be (Martinsson et al. 2024). Therefore, this study proposes the following hypothesis:

H₅.

In the manufacturing industry, achieving a high level of scientific and technological innovation is essential for improving the carbon emission efficiency of enterprises.

Per-capita GDP serves as an indicator of the economic development level in each province, which in turn has a significant impact on the carbon emission efficiency of tourism within each region. Based on this research, as the manufacturing output value is an important component of the total manufacturing output value, it is predicted that the manufacturing output value will have an impact on the carbon emission efficiency (Hudaifah et al. 2024; Li et al. 2024; Chen et al. 2023; Liu et al. 2023). Therefore, this study proposes the following hypothesis:

H₆.

In the manufacturing industry, increasing manufacturing output value is a crucial factor in enhancing carbon emission efficiency.

The lower the intensity of environmental regulation, the greater the technological level and scale efficiency of environmental regulation inhibition. The impact of environmental regulation on carbon emission efficiency is negative. However, as the intensity of environmental regulation increases, its inhibitory effect on technological level and scale efficiency decreases. Therefore, the overall impact of environmental regulation on total factor carbon emission efficiency is positive. Based on this research, it can be inferred that after the environmental regulation of manufacturing industry in each province exceeds a certain intensity, the stronger the environmental regulation, the higher the carbon emission efficiency (Verma et al. 2023). Therefore, this study proposes the following hypothesis:

H₇.

In the manufacturing industry, environmental regulations are essential for improving the carbon emission efficiency of enterprises.

The size of the enterprise may determine its financial strength and ability to increase R&D investment and improve technological innovation. This, in turn, can enhance the energy conservation, emission reduction, and pollution control capabilities of the enterprise, ultimately improving carbon emission efficiency. Based on this research, it may be inferred that the scale of manufacturing enterprises in each province is proportional to carbon emission efficiency (Zębala and Gaweł 2024; Zhou et al. 2023; Wang et al. 2024a, b). Therefore, this study presents the following hypothesis:

H₈.

In the manufacturing industry, the scale of an enterprise is a crucial factor in improving the carbon emission efficiency of enterprises.

Through the analysis of multiple documents, in conjunction with the above\(\:\:{\text{H}}_{\text{1}}\text{~}{\text{H}}_{\text{8}}\), the following theoretical hypotheses have been formulated. It is suggested that there may exist various configuration paths for the labor force structure, energy consumption structure, degree of openness to international trade, investment in research and development, level of scientific and technological innovation, manufacturing output value, environmental regulations, and enterprise scale within each province’s manufacturing industry. Furthermore, it is noted that these different paths have differing impacts on carbon emission efficiency.

Theoretical model of configuration path of carbon emission efficiency in the manufacturing industry

In conclusion, numerous studies have been conducted on the carbon emission efficiency of the manufacturing industry. However, there is a noticeable dearth of research focused on analyzing the carbon emission efficiency of the manufacturing industry from a comprehensive perspective. Therefore, this paper takes the manufacturing industry as the object and applied the NCA-fsQCA analysis method. The study integrated the eight antecedents of labor force structure, energy consumption structure, openness to the outside world, R&D investment, scientific and technological innovation level, output value of manufacturing, environmental regulation, and enterprise scale. The configuration of these factors was analyzed to determine the synergistic mechanism that may improve the carbon emission efficiency of the manufacturing industry. It was found that the combination matching relationships among these eight antecedents can positively promote the carbon emission efficiency of the manufacturing industry. This includes labor force structure, energy consumption structure, openness to the outside world, R&D investment, scientific and technological innovation level, manufacturing output value, environmental regulation, and enterprise scale.

Empirical analysis of configuration path of carbon emission efficiency in the manufacturing industry

Data sources and variable measurement

(1) Source of variables

In this study, the chosen variable for empirical analysis of the configuration path of manufacturing carbon emission efficiency is the carbon emission efficiency of the manufacturing industry in 28 regions. The antecedent conditions include labor force structure, energy consumption structure, openness to international trade, R&D investment, level of scientific and technological innovation, manufacturing output value, environmental regulation, and enterprise scale. Specific sources for variables are presented in Table 8. The data were obtained from China Statistical Yearbook 2020–2021 and China Industrial Statistical Yearbook 2020–2021. Owing to the absence of data in the statistical yearbook for Inner Mongolia Autonomous Region, Heilongjiang Province, and Tibet Autonomous Region, this study focuses on 28 provinces, autonomous regions, and municipalities across China excluding these three regions.

(2) Variable measurement

Based on the variable meanings in Table 8, the index data required by NCA-fsQCA software operation could be obtained through calculation. The relevant calculation results for carbon emission efficiency are presented in Tables 9 and 10.

(3) Variable calibration

Because fsQCA is based on set theory, it was essential to transform the original data into a set membership between 0 and 1 before conducting empirical analysis. The original data needed to be converted into data with characteristics suitable for collection. This study adopted the direct calibration method by referring to previous research (Zębala and Gaweł 2024), and the direct calibration method was used to calibrate the variables into fuzzy sets. The three calibration points for eight antecedent conditions and one outcome variable (carbon emission efficiency) were determined based on full membership, crossing point, and no membership at all. These points were set as the upper quartile (75%), median (50%), and lower quartile (25%) of descriptive statistics from the case sample. The calibration anchors for each variable can be found in Table 9, while the calibrated results for each variable are presented in Table 10.

Selection of empirical analysis method (NCA-fsQCA)

(1) Principle

Necessary condition analysis (NCA) is a research method proposed by Professor Jan Dul (2016) based on identifying and detecting necessary and insufficient conditions in data. In addition to being able to figure out whether X was necessary for Y, it was possible to determine what level of Y was necessary for X to be Y. The principle is based on the scatter diagram composed of the potential necessary condition X and the corresponding multiple results Y. When drawing an upper bound envelope between the area of lower right with the observed value and upper left blank area, in the upper left area of the scatter plot, there was a blank ceiling area. The size of the necessary conditional effect could be measured by the size of the ceiling area compared to the size of the entire area that could be observed. The larger the ceiling area, the greater the constraint of X on the result Y, that is, X is a necessary condition for Y. The effect value ranged from 0 to 1, when 0 < d < 0.1, it was “low effect”. When 0.1 ≤ D < 0., it was “medium effect”; when 0.3 ≤ D < 0.5, it was “high effect”.

The principle of the Fuzzy Set Qualitative Comparative Analysis (fsQCA) is as follows: Firstly, a single factor necessary condition analysis was conducted on the calibrated data to determine whether the condition set was a superset of the result set. It is generally believed that, if the consistency exceeds 0.9, the antecedent conditions are considered necessary for the outcome variables. The truth table was then built, and the condition configuration that met certain standards through the reference case threshold and consistency threshold screen was selected to reduce the number of truth table rows. The truth table data were then standardized and analyzed using the algorithmic logic of Boolean algebra to study the causal relationship between antecedent conditions and outcome variables. Upon conducting this analysis, three distinct results were derived: a complex solution, an intermediate solution, and a parsimonious solution. Finally, according to the occurrence of antecedent conditions in the parsimonious and intermediate solution, the configuration results with high carbon emission efficiency were constructed. The core condition refers to that the current cause condition occurs simultaneously in the parsimony and intermediate solution. When the current factor condition only appeared in the middle solution, it was the edge condition.

(2) Advantages

In theory, necessary insufficient conditions (NCA) are common in scientific studies, but most of the traditional research methods have focused on the study of sufficient conditions and ignored the study of necessary conditions. In practical research, sufficient conditions and necessary conditions for research are just as important. If the necessary conditions do not exist, the desired outcome will not occur, and the “one-vote veto” effect of the necessary condition takes precedence over the sufficient condition. Therefore, the necessary condition analysis method can achieve more accurate results because it can comprehensively test and deduce the influencing mechanism of various factors on the results.

The fsQCA method was used in this study because of the following considerations. In order to investigate the relevant factors influencing the carbon emission efficiency of the manufacturing industry, it was imperative to systematically analyze the manufacturing industry across 28 regions. Selecting a single region would result in unreliable findings. As a qualitative and quantitative analysis method, fsQCA allows for the cross-case comparative analysis of small and medium-sized samples. There are some asymmetric relationship combinations among the factors affecting carbon emission efficiency, and fsQCA is appropriate in addressing this problem and calibrates the data before operation, which could make the factors affecting the carbon emission efficiency of manufacturing industry more effective and the conclusion more reasonable. The factors influencing the carbon emission efficiency of the manufacturing industry are intricate and multifaceted. Carbon emission efficiency is influenced by a combination of various factors, resulting in multiple concurrent impacts. Compared with other methods, fsQCA is more suitable for this kind of research. In summary, the fuzzy qualitative set comparison method was selected to investigate the configuration path of carbon emission efficiency in the manufacturing industry. This approach enabled the research to closely approximate reality and have a more practical impact.

(3) Analysis of applicability and rationality

This study combined NCA and fsQCA. fsQCA is able to identify necessary relationships but cannot quantify how necessary it is; it can only provide a qualitative reflection of whether a condition is essential or nonessential for a particular outcome. The combination of NCA and fsQCA could reflect the extent to which a condition is necessary for a result, particularly for fuzzy sets because the variation not only is “yes” or “no”, but also includes detailed membership scores, which make the combination of NCA and fsQCA more valuable.

This study used NCA to test whether each antecedent condition was necessary to produce high carbon emission efficiency; if the answer was yes, it was necessary to identify the level. fsQCA was used to test the robustness of the necessary conditions, and fsQCA was used to study the causal and complex mechanisms of each antecedent condition affecting carbon emission efficiency. fsQCA can make comparative analysis across cases from a holistic perspective and is devoted to the complex question of which configurations of conditions cause expected results and result in the lack or failure to achieve the expected outcomes. Therefore, the NCA-fsQCA method is particularly appropriate for this study.

Process of NCA empirical analysis

This study analyzed nine causal variables of the manufacturing industry in 28 regions after calibration using R software, obtaining the results as depicted in Table 11.

The effect size obtained using two different methods, CR and CE, was the software processing result of the NCA method, as shown in Table 11. The necessary conditions had to satisfy two criteria in the NCA method: specifically, the effect size (d) was required to be not less than 0.1, and Monte Carlo Simulations of Permutation tests showed that the effect size was significant. In conclusion, while the structure of labor force and environmental regulation were found to be significant, the effect size was deemed too small to be considered necessary conditions for carbon emission efficiency (Bin et al. 2023). However, test results indicated that the structure of energy consumption (P = 1.0), openness to the outside world (P = 0.464), R&D investment (P = 1.0), level of scientific and technological innovation (P = 1.0), output value of manufacturing (P = 1.0), and enterprise scale (P = 1.0) were not found to be significant or necessary for carbon efficiency.

The results of the bottleneck analysis are presented in Table 12. The term “bottleneck level (%)” refers to a specific threshold within the maximum range of observations, representing the minimum level (%) that must be achieved within the maximum range of antecedent conditions. For instance, achieving approximately 60% carbon emission efficiency necessitates a 0.6% composition of labor force, while the remaining seven conditions do not exhibit any bottleneck levels, as indicated in Table 12.

The process of fsQCA empirical analysis

Necessity analysis

Before using fsQCA for configuration analysis, it was essential to analyze the necessary and sufficient conditions of each individual antecedent factor in order to determine whether there were the requisite conditions for improving the carbon emission efficiency of the manufacturing industry. Generally, when the necessity test value (consistency) exceeds 0.9, the individual antecedent factor can be deemed as a necessary condition.

The consistency of the necessity of a single condition was generally low, measuring less than 0.9. This finding aligns with the results of NCA, which indicate that there is no necessary condition for high carbon emission efficiency as presented in Table 13. This finding indicates that these single factor antecedents have weak explanatory power for the carbon emission efficiency of high manufacturing or non-high manufacturing. Therefore, these variables could be included in fsQCA for configuration analysis to study which combination of conditions is a sufficient explanation for the high or non-high carbon emission efficiency of manufacturing.

Analysis of configuration

None of the antecedent conditions were able to satisfy the necessity criteria after a configuration analysis, it was necessary to study the influence of different configurations of multiple antecedent conditions on results through configuration analysis. In the analysis of condition combinations, the truth table should be established to convert the original fuzzy value into clear value. Referring to the relevant practice (Chen et al. 2023), this study deleted cases with a continuity of less than 0.8 and threshold of 1 when constructing the truth table. Finally, 15 cases were retained, and 0.7 was taken as the consistency threshold; combination code less than this value was set as “0”, and the rest as “1”. The final truth table is shown in Table 14.

After the truth table was constructed, standard analysis was employed to derive three solutions: a complex solution, a simple solution, and an intermediate solution, as presented in Table 15. These three solutions reflect which logical residuals were included and which combinations of counterfactual conditions could be formed respectively. The complex solution removed all combinations of counterfactual conditions. The simple solution consisted of multiple counterfactual combinations. The intermediate solution contained several counterfactual combinations consistent with the intermediate solution number. As a matter of fact, researchers of qualitative comparative analysis have tended to adopt intermediate solutions that are both close to theoretical practice and not overly complex.

According to the results presented in Table 15, the eight antecedent conditions form four causal combination paths eventually made five combinations, which could explain approximately 36.37% of the cases because of the comprehensive coverage was 0.363701. The overall consistency of the four solutions reached 0.897213, which indicates that the analysis results are convincing to a certain extent.

Combination of core elements and auxiliary elements

Qualitative comparative analysis is an analytical method grounded in causal theory. In order to more accurately explore the causal process, this study drew on the relevant practice and divided the causal conditions into core elements and auxiliary elements (Yi et al. 2023). The core element refers to the factors that simultaneously appear in both the simple solution and intermediate solution, holding fundamental significance. By combining and analyzing the solutions presented in Table 5.8, core conditions and auxiliary conditions were identified to establish the antecedent condition configuration of carbon emission efficiency within the manufacturing industry, as outlined in Table 16.

Empirical analysis results of configuration path of carbon emission efficiency in manufacturing industry

In this study, through the analysis of these four configurations, the combinations with the same core conditions were merged, and the following two configuration paths were formed:

(1) Configuration path 1: S1 and S2 configuration

The fundamental conditions encompass the lack of openness to the outside world and the level of scientific and technological innovation. S1 suggests that regions with high levels of scientific and technological innovation may exhibit strong carbon emission efficiency even in the absence of sufficient openness to the outside world. For instance, Guizhou Province boasts the highest level of scientific and technological innovation among the 28 regions, despite having lower openness to the outside world compared to other regions; nevertheless, its carbon efficiency ranks highest. In contrast to S1, S2 imposes greater demands on R&D investment, environmental regulation, and enterprise scale. For example, Hunan Province demonstrates a high level of openness to the outside world, as well as substantial R&D investment and a high level of scientific and technological innovation. Consequently, its manufacturing carbon emission efficiency is also at a high level among all 28 regions.

(2) Configuration path 2: S3 and S4 configuration

The core conditions encompass the structure of the labor force, non-structure of energy consumption, R&D investment, level of scientific and technological innovation, output value of manufacturing, and environmental regulation. S3 suggests that even when the structure of the labor force, R&D investment, level of scientific and technological innovation, output value of manufacturing and environmental regulation are relatively high, carbon emission efficiency remains high despite a low level energy consumption structure. For instance, Shanghai’s energy consumption structure is at a low level compared to regions with high coal consumption; however, its carbon emission efficiency remains high. In addition to highlighting these core conditions, S4 embodies the core condition of non-openness to the outside world. For example, although Fujian Province has a low level openness to the outside world its carbon emission efficiency ranks fourth in the region.

As the cornerstone of the national economy and a driving force for economic growth, enhancing the carbon emission efficiency of the manufacturing industry is crucial for achieving high-quality development in this sector. This study utilized data from 28 regions in China from 2019 to 2020 to select the carbon emission efficiency of the manufacturing industry as the outcome variable, along with eight antecedent conditions that may impact it.

Fuzzy set qualitative comparison analysis was employed to investigate the path towards improving carbon emission efficiency in the manufacturing industry. The structure of this paper consists of six chapters detailing this study.

The study used DEA model, Necessary Condition Analysis (NCA), Fuzzy Set Qualitative Comparative Analysis (fsQCA), Theoretical Analysis, and Literature Research to investigate the allocation pathway of carbon emission efficiency in the manufacturing industry. By constructing the carbon emission efficiency measurement index system of China’s manufacturing industry, the measurement method is proposed, and the measurement process and results are finally determined. Using the DEA model, the following conclusions are drawn. The carbon emission efficiency of Beijing, Fujian, Hainan and Guizhou is 0.99, indicating that the carbon emission efficiency of the manufacturing industry in these regions is close to optimal. The carbon emission efficiency values of Shanghai and Guangdong are between 0.8 and 0.99, indicating that the carbon emission efficiency of manufacturing industries in these regions is high. Tianjin, Hebei, Shanxi, Liaoning, Shandong, Guangxi, Ningxia, and Xinjiang all have carbon efficiencies below 0.5. Overall, the results of the study provide valuable insights into the regional differences in the carbon efficiency of China’s manufacturing sector. The carbon emissions of the manufacturing industry in these eight regions theoretically have the potential to be reduced by an additional 50%. These regions show significant potential for carbon emission reduction. Additionally, the carbon emission efficiency of the remaining 14 provinces and cities ranges between 0.5 and 0.8, indicating significant potential for carbon emission reduction as well. It can also be concluded from the calculation results that some regions have a lower carbon emission efficiency due to technical inefficiency, with an average technical efficiency of only 0.44284 despite high scale efficiency. This highlights the importance of strengthening technological innovation in enhancing carbon emission efficiency. Furthermore, while Jiangsu Province and Zhejiang Province exhibit ineffective scale and comprehensive efficiencies, their technical efficiencies remain consistently high, suggesting effective technological input in their manufacturing industries. The low carbon emission efficiency observed is attributed to a mismatch between scale and input-output. In summary, improving carbon emission efficiency requires not only strengthening technical efficiency but also paying attention to the link between scale and input-output.

The study identifies the antecedent conditions, theoretical assumptions, and establishes a theoretical model of the allocation path of carbon emission efficiency in the manufacturing industry by combing through a variety of literature.

By outlining the data sources, measuring variables and determining the empirical analysis methods, the empirical analysis of the allocation path of carbon emission efficiency in the manufacturing industry is carried out, and the results of the empirical analysis of the allocation path of carbon emission efficiency in the manufacturing industry are summarised. The results of the empirical analyses mainly include the following two aspects:

(1) The structure of the labor force, energy consumption, openness to the outside world, R&D investment, level of scientific and technological innovation, manufacturing output value, environmental regulation, and enterprise scale are all non-essential factors affecting the carbon emission efficiency of the manufacturing industry.

(2) Through the analysis of eight non-essential antecedents, four antecedent configurations affecting the carbon emission efficiency of the manufacturing industry were identified. Additionally, two explanatory paths of carbon emission efficiency in the manufacturing industry were summarized. The primary path, scientific and technological innovation level, pertains to enhancing carbon emission efficiency by improving scientific and technological innovation and reducing external openness. The synergy path involving labor force structure, R&D investment, scientific and technological innovation level, manufacturing output value, and environmental regulation aims to enhance carbon emission efficiency by optimizing labor force structure, increasing R&D investment, improving scientific and technological innovation level, boosting manufacturing output value, and strengthening environmental regulation.

According to the results of the empirical analysis can be put forward from the government and business aspects of the relevant countermeasures and recommendations, specifically:

Government level

Strengthening of environmental regulation

To improve the carbon emission efficiency of the manufacturing industry, the Government and enterprises must co-operate fully to strengthen environmental protection regulation within the industry. The environmental protection system of manufacturing enterprises should be strengthened by increasing the operating income of the manufacturing industry, optimising the energy consumption structure of the entire industry. In regions where environmental regulations are not strict, government departments can take administrative measures to limit the proportion of coal in the energy consumption of the manufacturing industry, thereby optimising the energy consumption structure. In addition, enterprises can improve their operating income by controlling costs, increasing sales, and adjusting prices. For example, seven regions, including Ningxia, Qinghai, Xinjiang, Shanxi, Liaoning, Shaanxi and Gansu, have weak environmental regulation, so they need to focus on increasing operating revenues and optimising the energy consumption structure in these regions in order to strengthen the environmental regulation of manufacturing enterprises.

Improving regulatory standards

The Government should strengthen the monitoring and assessment of the current situation of carbon emissions in the manufacturing industry, and make use of advanced technical means, such as the super-efficiency DEA model and the LMDI method, to conduct detailed analyses of the carbon emission efficiency of different industries and regions, and to clarify the main sources of carbon emissions and the factors affecting them. This not only helps identify industries and areas with high emission reduction potential, but also provides a scientific basis for subsequent policy formulation.The government needs to improve and refine the regulatory standards for carbon emissions. At present, although China has established a certain environmental regulatory system, there are still problems such as unclear standards and insufficient enforcement in the specific implementation process. Therefore, the government should make reference to international advanced experience and combine it with China’s actual situation to formulate stricter and more specific regulatory standards for carbon emissions, as well as clarify the requirements and timetable for various industries to meet the standards.

Increased financial support

The Government should increase its support for the research, development and application of energy-saving and emission-reduction technologies in the manufacturing sector. Through the provision of R&D subsidies, tax incentives and other measures, enterprises should be encouraged to adopt advanced low-carbon technologies and equipment, thereby reducing carbon emissions per unit of product. For example, special funds can be set up to support energy-saving renovation and technological upgrading in energy-consuming industries.

The government should optimise the structure of fiscal expenditure and increase investment in environmental protection projects. This includes, but is not limited to, supporting the construction of green infrastructure, promoting the use of clean energy and strengthening environmental regulatory efforts. At the same time, preference should be given to low-carbon products and services through government procurement and other means, thereby driving the green transformation of the entire industrial chain.

Enterprise level

The combination of necessary and sufficient conditions

Based on the results of the analysis, it can be concluded that the improvement of China’s carbon emission efficiency should focus on the combination of necessary and sufficient conditions, specifically: All regions should adjust relevant policies and efforts, paying attention to the effective coordination of the necessary integrated conditions. Policy adjustments and efforts should be focused on increasing investment in research and development, raising the level of science, technology and innovation, optimizing environmental regulation, increasing the output value of enterprises and optimizing the structure of the labour force.

Improvement of technological innovation

Improving the carbon efficiency of the manufacturing sector should be achieved by increasing investment in research and development and enhancing the capacity of manufacturing enterprises to support scientific and technological innovation. For regions with a low level of scientific and technological innovation, favourable policies can be formulated to attract talents, promote the transfer of high-tech talents to the manufacturing industry, and promote scientific research investment within the manufacturing industry. By attracting and cultivating scientific research talents and establishing a strong scientific research team, the ability of scientific and technological innovation can be effectively improved. Increasing investment in scientific research funding and implementing specialised talent training programmes are necessary steps to achieve this goal. For example, compared with other regions, R&D investment in Qinghai, Hainan, Ningxia, Gansu, Jilin, Guizhou and Guangxi is relatively low. Therefore, it is important to increase R&D investment in these regions to improve their technological innovation capacity. In addition, the number of patent applications in Hainan, Qinghai, Ningxia, Xinjiang, Gansu, Jilin and Guangxi is relatively low compared to other regions, and further attention should therefore be given to increasing the number of patent applications in these regions.

Increasing output value of enterprise

To improve the carbon efficiency of manufacturing firms, the output value of the firm should be increased. To increase output value, it is necessary to start with both price and production. The price of the product can be increased by optimising the product, improving product quality and reliability and branding the product so as to expand its reach. On the other hand, increasing product output can be achieved by improving production processes, providing staff training to enhance labour skills, introducing advanced production equipment, and refining management and operational methods. All of these strategies have the potential to increase the output value of enterprises and effectively enhance the carbon emission efficiency of the manufacturing sector. For example, the output value of the manufacturing sector in regions such as Hainan, Qinghai, Ningxia, Gansu, Guizhou and Xinjiang is below RMB 50 billion, which is relatively low compared to other regions. Therefore, it is necessary to focus on increasing the manufacturing output value in these six regions.

Optimization of the structure of the labor force

The proportion of labour employed in the manufacturing sector in industrial enterprises above designated size in Shanxi, Xinjiang, Guizhou, Gansu, Qinghai and Ningxia is below 70 per cent, which is relatively low compared with other regions. Therefore, these six regions should be taken as key areas for optimising the labour force structure. By strengthening the tracking and analysis of the manufacturing labour market and regularly releasing information on changes in the manufacturing labour force; expanding the space for the development of the manufacturing labour force, in particular the construction of infrastructure in the central, western and northeastern regions; and focusing on optimizing the environment of the manufacturing labour market, providing employment policies for the manufacturing industry and improving the attractiveness of the manufacturing industry to the labour force, in order to enhance the efficiency of carbon emissions.

No datasets were generated or analysed during the current study.

This research is funded by 2021 scientific research project of department of education of Liaoning Province (LJKR0225, LJKR0224), Research Base of Science and Technology Innovation Think Tank of Liaoning Province (Research Base of High Quality Development of Equipment Manufacturing Industry, NO. 09).

Authors and Affiliations

1. School of Economics and Management, Liaoning University of Technology, Jinzhou, 121001, China

   Yafeng Li & Jingting Sun

2. School of Business Administration, University of Science and Technology Liaoning, Anshan, 114051, China

   Jing Bai

Contributions

Y.L. contributed to Writing - Original Draft; J.S. contributed to Investigation; J.B. contributed to Writing - Review & Editing.

Corresponding author

Correspondence to Jing Bai.

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Competing interests

The authors declare no competing interests.

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