Measurement and influencing factors of industrial carbon unlocking efficiency under the background of “double carbon”

Based on the panel data of 11 provinces and cities in the Yangtze River Economic Belt of China from 2011 to 2018, the DEA model and Malmquist index were used to calculate the industrial carbon unlocking efficiency of the Yangtze River Economic Belt in a static and dynamic way, and the Tobit model was used to empirically test its influencing factors. The results show that (1) the overall efficiency of industrial carbon unlocking in the Yangtze River Economic Belt is on the rise, but there are regional differences. The efficiency of industrial carbon unlocking in the lower reaches of the Yangtze River is higher than that in the upper and middle reaches. (2) The total factor productivity of industrial carbon unlocking in the Yangtze River Economic Belt has increased steadily on the whole, and technological progress is the main source of growth. (3) Industrial carbon unlocking efficiency is affected by many factors. Environmental regulation and degree of openness have a promoting effect on industrial carbon unlocking efficiency, while government investment and innovation level have a restraining effect on industrial carbon unlocking efficiency.


Introduction and literature review
Extensive consumption of fossil fuel in production system is one of the reasons of greenhouse gas emissions which is the main cause of climate change (Elahi et al. 2022a;Abbas et al. 2022).Not only did the extreme weather impact human health, but it also had an effect on the production systems (Elahi et al. 2022b;Waseem et al. 2021).In 2020, China proposed the "Dual carbon" goal, aiming to peak carbon dioxide emissions by 2030 and achieve carbon neutrality by 2060.Realizing "Double carbon" goal has become the strategic goal and direction of the transformation and development of each industry in the current and the following long period of time.
At present, China is in the stage of deepening industrialization and urbanization development.Industry is still the main source of energy consumption and carbon emissions, and its energy consumption and carbon emissions have accounted for more than 70% of the total national energy consumption and carbon emissions.Therefore, the lowcarbon development of the industrial sector is crucial for achieving China's "Dual carbon" goals.As a high carbon economy with a fossil energy consumption ratio of up to 80%, China's industrial development is facing the dilemma and challenge of carbon locking.Carbon unlocking in the industrial sector is a complex system process, and the effective measurement and supervision of carbon unlocking efficiency in the industrial sector is an important prerequisite for the effective implementation of this process.Therefore, it is of great practical significance to establish a scientific evaluation model to measure industrial carbon unlocking efficiency and explore the influencing factors of industrial carbon unlocking efficiency.
Literature search shows that most of the existing studies on carbon unlocking focus on two aspects: (1) the connotation of carbon locking, including concept, type, and evaluation.The concept of carbon unlocking was first proposed by Spanish scholar Unruh (2000).Unruh defined carbon locking as "The phenomenon that the current economic development is locked in the carbon-intensive energy system based on fossil fuels due to the increasing returns to scale driving technology and institutions."Subsequently, scholars redefined carbon lock-in based on this definition and combined with specific research objects.For example, Liang (2017) defined carbon locking as "A special lock-in mechanism with the context characteristics of underdeveloped regions" from the industrial level.Under this mechanism, economic development would be path-dependent on high-carbon industries.On the basis of concept definition, some scholars have studied the types, sources, and effect evaluation of carbon unlocking.For example, Seto et al. (2016) summarized carbon locking into three main types: infrastructure and technology, system, and behavior.Janipour et al. (2020), based on the case study of Dutch chemical production, found that the sources of carbon locking in the Dutch chemical industry include five aspects: technology incompatibility, system integration, sunk costs, policy inconsistency, and safety practices.Niu and Liu (2021a, b) constructed a measurement index system of carbon locking from four dimensions: fixed investment, technology, system, and social behavior, and calculated and analyzed China's carbon locking level based on relevant data from 2003 to 2016.Some scholars explored the causes of carbon locking.For example, Haley (2011) took the European power sector as the research object and proposed that the influencing factors of carbon locking in the power sector were changes in climate policies and fluctuations in energy prices.Driscoll (2014) studied the transportation industry and found that the main reason for carbon lock-in in the large-scale road transportation industry was path dependence and increasing returns to scale.Janipour et al. (2020) studied the potential carbon locking effect in the Dutch chemical industry and believe that the intensification of carbon locking is caused by the incompatibility between relevant policies promulgated by the government and low-carbon technologies.(2) In paths and impact factors of carbon unlocking, the existing researches mainly focus on technology, policy, infrastructure, industrial structure, and other factors.Scholars generally believe that technology innovation and technology investment are important factors to alleviate the dilemmas of carbon locking.For example, Xu et al. (2021) found via researches that technology progress has direct or indirect effect on carbon unlocking.Niu and Liu (2021a, b) also believed that measures, such as the improvement of low-carbon technology and its application and promotion, and more efforts of the government in energy saving and emission reduction, as well as innovation, are the primary path of carbon unlocking.The impacts of policies on carbon unlocking have also been widely concerned by scholars.For example, Kalkuhl et al. (2012) and some other scholars explored the possible path of carbon unlocking from the perspective of cost and benefit and believed that policy subsidies and taxes could be used to encourage the popularization of low-carbon technologies and the elimination of backward energy utilization technologies.Mattauch et al. (2015) also showed that carbon tax policies and increased subsidies for clean technologies played a significant role in carbon unlocking.Sun et al. (2020) research results show that carbon emission trading can effectively reduce the degree of industrial carbon locking in the region.Wang-Helmreich and Kreibich (2019) found that the implementation of carbon tax offsets may have both positive and negative impacts on national emission reduction.Other scholars have studied the relationships between infrastructure supply, market structure, and carbon unlocking.For example, Carley (2011) thought that the improvement of market structure would help to alleviate the carbon lock-in dilemmas of the USA electricity market.Mattaucha et al. (2015) thought that the provision of infrastructure was the necessity to promote low-carbon transformation.A few scholars have explored the paths of carbon unlocking from the micro level.For example, Liang et al. (2020) studied the micro-driving mechanism of "regional carbon unlocking" and put forward the policy suggestions referring to perfecting the "governance-driven" mechanism, establishing carbon unlocking mechanism coordinated by region, and attaching importance to the "regulation-driven" power of the public.
In summary, scholars have conducted a large number of studies on carbon locking and carbon unlocking, mainly focusing on the connotation, measurement, cause of carbon locking and path of carbon unlocking, etc.There are relatively few articles specializing in carbon unlocking efficiency, especially since the research on the measurement and influencing factors of industrial carbon unlocking efficiency is still in its infancy.As a pilot demonstration belt of ecological civilization construction in China, the Yangtze River Economic Belt shoulders the important mission of taking the lead in achieving "Carbon peak" and "Carbon neutrality," and its industry plays a pivotal role in the whole country.Based on this, this paper constructed an evaluation system of industrial carbon unlocking efficiency.Based on the panel data of 11 provinces and cities in the Yangtze River Economic Belt, the DEA-Malmquist model was used to calculate the industrial carbon unlocking efficiency, and the Tobit model was used to explore the influencing factors of industrial carbon unlocking efficiency.This paper mainly addresses the following questions: (1) How about the industrial carbon unlocking efficiency in China's Yangtze River Economic Belt?By establishing an industrial carbon unlocking efficiency evaluation system, the industrial carbon unlocking efficiency of 11 provinces and cities in the Yangtze River Economic Belt of China was evaluated.(2) What factors affect industrial carbon unlocking efficiency?
Through the empirical test of the influencing factors of industrial carbon unlocking efficiency, it provides a reference for the introduction of government policies.
There are three possible contributions and innovation of this paper: Firstly, based on the theoretical framework of environmental economics and sustainable development, this paper constructs an evaluation model of industrial carbon unlocking efficiency, which can provide a theoretical model for subsequent researches on industrial carbon unlocking efficiency.Secondly, the Yangtze River Economic Belt, as the leading demonstration belt of China's ecological civilization construction, shoulders the major mission of taking the lead in achieving "Carbon peak" and "Carbon neutrality," and its industry occupies a pivotal position in China.However, there are few papers on the measurement and analysis of carbon unlocking efficiency in the Yangtze River Economic Belt.This paper measures and compares the carbon unlocking efficiency of 11 provinces and cities in the upper, middle, and lower reaches of the Yangtze River Economic Belt, which can provide provides useful guidance for policymakers to optimize their efforts towards "double carbon" goals.Thirdly, although most scholars and industry believe that technological level, government policies, and other factors affect the efficiency of industrial carbon unlocking, relevant studies are mainly limited to the theoretical level, and systematic empirical studies are lacking.This paper focuses on the three dimensions of DEA (technical efficiency, pure technical efficiency, and scale efficiency), systematically exploring the influencing factors of industrial carbon unlocking efficiency of the Yangtze River Economic Belt, which can provide a useful reference for policy formulation and optimization of the "double carbon" goal.

Research methods
Based on the input-output theory, this paper constructs an evaluation index system of industrial carbon unlocking efficiency by referring to the methods of Zhang et al. (2021), Lin and Liu (2015), and other scholars.The industrial carbon unlocking efficiency is calculated by taking capital investment, manpower investment, R&D investment, and environmental governance investment as input elements, economic benefits output as expected output, and environmental pollution output as unexpected output.As a nonparametric method, the characteristics of DEA model, such as "multi-inputs and multi-outputs," no need to artificially set the functional relationship between input and output and index weight and avoid the interference of subjective factors, meeting the research needs of this paper.Therefore, this paper chooses the DEA model to calculate the industrial carbon unlocking efficiency and analyzes statically the industrial carbon unlocking efficiency.On this basis, in order to understand the dynamic changes, this paper constructs the Malmquist index to find out the dynamic changes of industrial carbon unlocking efficiency from all aspects.

DEA model
DEA model was first proposed by Charnes et al. (1978), which measures the efficiency of each DMU based on the assumption of constant returns to scale (CCR model), and then, Banker et al. (1984) extended it and decomposed the technical efficiency (TE) in the CCR model into pure technical efficiency (PTE) and scale efficiency (SE), thus obtaining the BBC model with variable returns to scale.At present, the BBC model has been widely used, and its concrete construction is as follows (Formula 1): According to Formula 1, ∈ [0, 1] is the efficiency value of the decision-making unit; j represents the input-output index weight of the decision-making unit; X j is the input amount; Y j is the output amount; slack variables S − and S + indicate insufficient output and redundant input, respectively.And when = 1 and S − = S + = 0 , the decision-making unit k is strong, and then, DEA is effective; when = 1 and S + ≠ 0 , the decision-making unit k is weak, and DEA is effective; when  < 1 , the decision-making unit k is respec- tively effectiveness, then DEA effectiveness.

Malmquist index
The Malmquist index was first proposed by Swedish economist Malmquist in 1953 to analyze changes in consumption over time.Later, Caves et al. (1982) extended this model to measure productivity changes.After the continuous improvement of a large number of scholars, today's Malmquist productivity index model was gradually formed.Based on the distance function, this model is used to calculate the inefficiency of production efficiency, so as to explore the causes of inefficiency as well as the direction of improvement.According to Fare et al. (1994), total factor productivity (tfpch) can be divided into two indicators: technical efficiency (effch) and technical progress (techch), among which the former can be divided into pure technical efficiency (pech) and scale efficiency (sech), and its calculation formula is as follows (Formula 2): According to Formula 2, M 0 (X t+1 , Y t+1 , X t , Y t ) is Malmquist index, and M 0 mainly reflects the change of pro- ductivity from t to t + 1 M 0 > 1 shows that the total factor productivity is on the rise; M 0 = 1 indicates that the effi- ciency has not changed compared with before; M 0 < 1 sug- gests that the overall efficiency shows a downward trend.However, when the change of technical efficiency (effch) > 1, the decision-making unit approaches the frontier, indicating that the efficiency rises, vice versa; when technological progress (techch) > 1, the production possibility frontier moves out, indicating that the efficiency is higher than before, which has positive significance for improving the dynamic change of industrial carbon unlocking efficiency.

Index selection
Input indicators.Based on the principles of data availability and scientific validity.In this paper, the input indicators of industrial carbon unlocking calculated include capital investment, human resource investment, R&D investment, and environmental governance investment, which are measured by "newly in fixed Assests," "equivalent full-time R&D personnel of industrial enterprises above designated size," "internal expenditure of R&D funds of industrial enterprises above designated size," and "completed investment in industrial environmental pollution control." Output indicators.In this paper, the output indicators of industrial carbon unlocking include economic benefit output and environmental pollution output, and "New product sales revenue of industrial enterprises above designated size" and "industrial carbon emissions of industrial enterprises above (2) designated size" are selected as the measurement indicators.
Referring to 2006 IPCC Guidelines for National Greenhouse Gas Inventories, the carbon emission factor is adopted, and the calculation formula of carbon emissions is as follows (Formula 3): According to Formula 3, i represents all provinces and cities; C i is the sum of carbon emissions of industrial enter- prises above designated size in i province; N ij is the car- bon emission factor of the j energy in i province; u j is the j energy consumption of industrial enterprises above des- ignated size in i province.For the sake of data availability, this paper selects coal, petroleum, and fuel oil as the energy consumption.The evaluation index system of unlocking carbon efficiency is shown in Table 1.

Empirical results of calculation of industrial carbon unlocking efficiency
Based on the input-oriented DEA model with variable returns to scale (VRS), this paper uses Deap2.1 to calculate the technological efficiency (effch), pure technical efficiency (pech), and scale efficiency (sech) of industrial

The analysis of technological efficiency
As can be seen from Fig. 1 and Table 2, the technological efficiency (effch) of industrial carbon unlocking in the Yangtze River Economic Belt shows a spiral upward trend from 2011 to 2018, which indicates that the carbon unlocking ability gradually increased, but it still does not reach the DEA effective state.From the spatial structure perspective, there are obvious differences between the upper, middle, and lower reaches of the Yangtze River, representing that the efficiency value of the lower reaches is obviously higher than that of the middle and upper reaches, and the carbon unlocking ability of the middle reaches is steadily increasing.The possible reason is that the lower reaches are the frontier area of China's opening to the outside world, and the local actively introduces advanced technology; high-tech industry development is very good, promotes economic development, and also promotes environmental protection.
In addition, the downstream areas continue to increase green technology innovation and advanced technology, and ecological environment investment increased; the efficiency of enterprises has been significantly improved, with less energy consumption and pollution to create a greater output value, industrial economic benefits, and resource utilization that reached a high degree of coordination.The overall economic development level of the upper reaches is respectively low, but the carbon unlocking efficiency is high.The carbon unlocking efficiency of Sichuan is lower than that of other provinces and cities, possibly due to the high carbon emissions of industrial production and life and terrain.In the middle reaches, since 2010, Hunan and other provinces have actively responded to the call of national industrial low-carbon transformation, promoted new industrialization, effectively reduced industrial carbon dioxide emissions, and steadily enhanced carbon unlocking efficiency.Nevertheless, the reason why the carbon unlocking efficiency of Hubei is relatively low without DEA efficiency in all years is mainly that the energy consumption structure is unreasonable with  the high proportion of coal in primary energy consumption, resulting in high energy consumption per unit of industrial added values.From the regional perspective, Shanghai, Zhejiang, and Chongqing have been the DEA effectiveness of carbon unlocking technology during the sample study period, among which Chongqing may benefit from the support of national policies, as well as its focus on ecological environment development Platforms such as the Green Intelligence Institute of the Chinese Academy of Sciences in Chongqing provide a good ecological environment for industrial development.On the contrary, although Jiangsu is located in the lower reaches of the Yangtze River and its industrial investment is large, it consumes a lot of energy in industrial production, uses resources with a low repetition rate, and faces high carbon emissions, resulting in low carbon unlocking efficiency.

The analysis of the change trend of efficiency
From the average efficiency change trend in Fig. 2, we can see that the change trends of technological efficiency (effch), pure technical efficiency (pech), and scale efficiency (sech) are generally consistent, a slight decrease in 2011 and 2015, and then a gradual rise, which indicates that pure technical efficiency (pech) and scale efficiency (sech) both play an important role in improving carbon unlocking efficiency, and scale efficiency (sech) has a more significant role, while pure technical efficiency (pech) has further potential to be adjusted and improved.

The analysis of pure technological efficiency
As can be seen from Fig. 3, except Sichuan Province, the pure technological efficiency of industrial carbon unlocking in the Yangtze River Economic Belt is generally on the rise, and five provinces (Shanghai, Jiangsu, Zhejiang, Chongqing, and Guizhou) have achieved DEA efficiency in all years.Among them, the pure technological efficiency value of the lower reaches is close to 1 (DEA is effective), while the efficiency value of the middle reaches, except Hubei, has a small difference with that of the upper reaches.The lower reaches has the most advanced technology, strong economic strength, more reasonable industrial structure, strong resource management ability, and can make full use of its input factors, so it can achieve a higher pure technical efficiency of carbon unlocking.
Chongqing and Guizhou in the upper reaches are DEA effective during the sample study period, which is mainly due to the inclination of national policies.The state continuously increases support for the construction of Chongqing and Guizhou and promotes the steady growth of economic development in the upper reaches of the Yangtze River Economic Belt with points to lay the foundation for improving the efficiency of carbon unlocking in the upper reaches.The middle reaches have undertaken part of the industrial transfer from eastern China and are more dependent on traditional industries, which has a certain hindering effect on the improvement of regional carbon unlocking efficiency.

The analysis of scale efficiency
Table 3 shows that the overall scale efficiency of the Yangtze River Economic Belt is high, reaching 0.964.As can be seen from Table 4, the scale efficiency of industrial carbon unlocking is obviously higher than its pure technological efficiency, which suggests that pure technological efficiency is the key constraint factor to improve the carbon unlocking efficiency of the Yangtze River Economic Belt.According to the three regions, the lower reaches have the highest scale efficiency, and the difference between the upper and the middle reaches is minimal.There are also obvious differences in the lower reaches.Shanghai and Zhejiang are DEA effectiveness in scale efficiency and a stable return on scale, which is the result of their long-term emphasis on sustainable economic development, while Jiangsu and Anhui have an increasing return on scale, indicating that they still have the potential to improve the carbon unlocking efficiency.The increasing return on scale in the middle reaches indicates that the industrial carbon unlocking efficiency is improved by expanding the scale of input elements.The industrial carbon unlocking efficiency in the upper reaches shows a decreasing return on scale, which may be due to the fact that China attaches great importance to the protection of the ecological environment, which makes the enterprises with high investment and high pollution in the middle and lower reaches transfer to the upper reaches.The economic development of the upper reaches is already relatively backward, so in recent years, the protection of the ecological environment has been sacrificed to a certain extent for the sake of economic development.

The analysis of dynamic efficiency
In order to further understand the dynamic change trend of carbon unlocking efficiency in the Yangtze River Economic Belt, the Malmquist index was used to make a dynamic  4 and 5. Table 4 shows, overall, that the total factor productivity of industrial carbon unlocking in the Yangtze River Economic Belt is a 5.8% increase of the annual average from 2012 to 2018 where the technological efficiency decreased by 1.3% and the technological progress increased by 7.2%, respectively.It can be concluded that technological progress is the main source of carbon unlocking efficiency growth in the Yangtze River Economic Belt, while the growth of technological efficiency has a significant hindrance to it.In terms of years, the industrial carbon unlocking efficiency in the Yangtze River Economic Belt is on the rise year by year, and the efficiency values are greater than 1 in all other years except 2015 and 2016.Specifically, in 2014 and 2015, pure technological efficiency shows an upward trend, while technological progress shows a decline, which indicates that technological progress was the main factor hindering the improvement of carbon unlocking efficiency in that year.
Table 5 shows that the total factor productivity of industrial carbon unlocking efficiency in the Yangtze River Economic Belt from 2012 to 2018 was greater than 1 except for Hubei Province, which indicates that except Hubei Province, the industrial carbon unlocking efficiency of other provinces is on the rise.Further analysis shows that the technical efficiency and scale efficiency values of Hubei Province are both lower than 1, which leads to the decline of total factor productivity, indicating that there is still room for progress in environmental resource utilization and other aspects.Other provinces and cities showed an upward trend during 2012-2018, and the reasons for the efficiency increase can be classified into two types: The first is the improvement of technological progress, which promotes the improvement of industrial carbon unlocking efficiency in Jiangsu, Anhui, Jiangxi, Hunan, and Guizhou provinces, and the growth of technological progress also narrows the gap caused by low technological efficiency to a certain extent.However, the technical efficiency of these provinces tends to decline, indicating that the main reason for the low technological efficiency is the decreasing returns to scale.The other is that technical efficiency and technological progress jointly promote the improvement of carbon unlocking efficiency.Shanghai, Zhejiang, Chongqing, Sichuan, and Yunnan provinces belong to this category of reasons, and the influence of technological progress on carbon unlocking efficiency is higher than that of technical efficiency.Meanwhile, both pure technical efficiency and scale efficiency in this category show a positive growth trend.

The analysis of impact factors
Based on the carbon locking theory, this paper selects five variables including government investment, environmental regulation, degree of openness, level of technological innovation, and regional human capital as explanatory variables to study the key influencing factors of industrial carbon unlocking efficiency by referring to the existing research results on influencing factors of industrial carbon unlocking efficiency and general carbon unlocking efficiency and considering the availability of data.
(1) Government investment.The impact of government investment on industrial carbon unlocking efficiency has two aspects: Firstly, government investment affects regional economic construction and energy consumption and then affects carbon emission; secondly, government investment affects the efficiency of carbon unlocking by affecting scientific and technological innovation, energy saving, and emission reduction technologies.In this paper, the government investment (× 1) is measured by the proportion of government investment to the internal R&D expenditure of industrial enterprises above designated size.(2) Environmental regulation.The impact of environmental regulation on industrial carbon unlocking efficiency has two aspects: Firstly, at the macro level, environmental regulation promotes regional industrial transformation and industrial structure adjustment through strategic layout, thus promoting the process of carbon unlocking; at the micro level, environmental regulation promotes technological innovation, energy saving, and emission reduction by restricting or encouraging the behavior of enterprises, so as to improve carbon unlocking efficiency.Secondly, environmental regulation will increase the cost of pollution discharge and control, crowding out the investment in technological R&D and innovation of enterprises, which may have a certain negative impact on carbon unlocking efficiency (Lin and Liu 2015).This paper uses the proportion of energy conservation and environmental protection expenditure in total financial expenditure to measure environmental regulation (× 2).( 3) Degree of openness.The impact of openness on industrial carbon unlocking efficiency has two aspects: Firstly, opening to the outside world affects the scale of investment and then affects the carbon emission.Secondly, opening to the outside world affects carbon emissions by influencing the introduction of advanced technology and advanced management.In this paper, the proportion of import and export trade volume to regional GDP is used to measure the degree of openness (× 3).Since the data of import and export trade volume in the statistical yearbook is the dollar, this paper will convert it into RMB according to the dollar exchange rate of that year and then calculate it.(4) Technological innovation level.Technological innovation is an important way to improve total factor productivity.Studies by scholars such as Jing and Chen ( 2018) have confirmed that technological innovation has remarkable results in improving energy and environmental efficiency and promoting green development.This paper measures technological innovation (× 4) by the logarithmic form of the number of domestic patents granted.The patent right helps to encourage technological innovators to continue technological innovation, advance the technological progress of the whole society, and promote the industrial carbon unlocking efficiency.(5) Human capital level.Human capital is a major factor to boost total factor productivity.The impacts of human capital on industrial carbon unlocking efficiency include two aspects.One is the direct effect.As an important production factor, human capital can directly affect the industrial carbon unlocking efficiency.The other is the indirect effect.Human capital can indirectly affect the industrial carbon unlocking efficiency by impacting technological innovation, foreign capital utilization efficiency, and other factors.According to "primary school, 6 years; junior high school, 9 years; high school, 12 years; junior college or above, 16 years," this paper adopts the education year approach to calculate human capital (× 5).

Data sources
The data used in this part are from the panel data of 11 provinces and cities in the Yangtze River Economic Belt from 2011 to 2018.The data were obtained from China Statistical Yearbook and Provincial Statistical Yearbook from 2012 to 2019, and some values were supplemented by interpolation method.

Model construction
The industrial carbon unlocking efficiency is influenced by many factors, and the explained variables are all between 0 and 1.In this paper, the Tobit model is selected to test the relationship between the aforementioned impact factors and industrial carbon unlocking, and the model is set as follows (Formula 4): According to Formula 3, Y is the explained variable, k are different decision-making units, Y k is truncated dependent variable, X is explanatory variable, is regression parameter variable, u is random interference term, and k=1,2,⋯,n is the explained variable, and k = 1, 2, 3, which respectively represents technological efficiency, pure technological efficiency, and scale efficiency in the industrial unlocking.The reason why the latter two are chosen as the explained variables at the same time is mainly to consider the influencing mechanism of various factors on industrial unlocking technical efficiency.X are explanatory variables, including government investment (× 1), environmental regulation (× 2), degree of openness (× 3), technological innovation (× 4), and human capital (× 5).The definition and description of each variable are shown in Table 6.The Pearson correlation analysis found that there was a significant correlation between the three variables of industrial unlocking technology efficiency, pure technology efficiency, and scale efficiency.Therefore, the above variables were separately put into the model for estimation.There are significant correlations between the five explanatory variables and the three explained variables, which indicates that the selection of variables is reasonable.At the same time, except for the coefficient between individual explanatory variables slightly greater than 0.4, the correlation coefficient between other explanatory variables is below 0.4, which is lower than the collinearity threshold value of 0.7.Therefore, the empirical analysis here does not need to worry about collinearity.

The analysis of empirical results
In this paper, Stata14.0 software and cluster robust standard error are used to perform panel Tobit regression of mixed effects.The estimated results of the regression model are shown in Table 7, and columns (1), (2), and (3) are regression results with explained variables as technical efficiency, pure technical efficiency, and scale efficiency respectively.
(1) The influences of government investment on industrial carbon unlocking efficiency.The results in Table 7 show that government investment (× 1) has a signifi-cant negative correlation with technological efficiency and pure technological efficiency of industrial carbon unlocking, and both of them are significant at the level of 1%, while the impact on scale efficiency is negative, but it fails the significance test.When the ratio of government investment to the internal expenditure of industrial R&D funds above designated size increases by 1%, the efficiency of industrial carbon unlocking technology will decrease by 0.5806.The empirical results show that government policy support and subsidies have not reached the expected goal, because the government will limit the carbon emissions of industrial enterprises when formulating corresponding policy subsidies.If the carbon emissions of enterprises exceed the government limit, there will be a certain impact on the carbon unlocking efficiency of industrial enterprises, that is to say, the influence of government support will be weakened when exceeding the limit.It is also possible for enterprises to generate rent-seeking behavior in order to account for more emission allowances in the industry, which violate the original intention of policy makers in formulating policies.
(2) The influences of environmental regulation on industrial carbon unlocking efficiency.The results in Table 7 show that the impact of environmental regulation (× 2) on industrial carbon unlocking technological efficiency and pure technological efficiency is significantly positive at the level of 1% and 10% respectively, while its impact on scale efficiency has not passed the significance testing.Provided the proportion of energy saving and environmental protection expenditure to total fiscal expenditure increase by 1%, technological efficiency of the industrial carbon unlocking will increase by 5.4889.
The empirical results show that environmental regulation has remarkable effects in leading to the green, low-carbon, and high-efficiency development of industries, as well as guiding enterprises in technological innovation, energy saving and emission reduction, and so on.In recent years, the Yangtze River Economic Belt has been significantly affected by haze weather, which has promoted various provinces and cities to accelerate environmental governance, which has significantly reduced pollutant emissions and, to a certain extent, curdled the trend of urban haze pollution.Therefore, strengthening and improving the construction of environmental regulations are effective ways to improve the efficiency of industrial carbon unlocking.
(3) The influences of the degree of openness on the industrial carbon unlocking efficiency.The results in Table 7 show that the degree of openness (× 3) is significantly positive for the technological efficiency and pure technological efficiency of industrial carbon unlocking at the level of 1%, but its influence on scale efficiency has not passed the significance testing.When the ratio of import and export trade volume to regional GDP increases by 1%, the efficiency of industrial carbon unlocking technology will increase by 0.2197.The empirical results show that openness improves the production efficiency mainly by improving the management and technological levels of enterprises and then promotes the pure technological efficiency of industrial carbon unlocking.However, it does not play a significant role in improving the outputs by optimizing and allocating the industrial structure, which leads to an unremarkable impact on the scale efficiency of industrial technology.(4) The influences of technological innovation on industrial carbon unlocking efficiency.The results in Table 7 show that the impacts of technological innovation level (× 4) on industrial carbon unlocking technological efficiency and pure technological efficiency are significantly negative at the level of 10% or 1%, but its impact on scale efficiency has not passed the significance testing.The empirical results of this paper are quite different from the existing research conclusions.The possible reason is that there are time differences in the impact of the number of patents on industrial carbon unlocking efficiency.In the early stage of patent right, it helps to motivate technological innovators to continue technological innovation, promote technological progress of the whole society, and promote the improvement of industrial carbon unlocking efficiency.However, the continuous expansion of the scope of intellectual property protection and the level of protection may inhibit social innovation and increase the cost of using new technologies, thus inhibiting the diffusion and promotion of new technologies (Zhang et al. 2015).(5) The influences of human capital on industrial carbon unlocking efficiency.The empirical results show that the influence coefficients of human capital (× 5) on industrial carbon unlocking technical efficiency, pure technical efficiency, and scale efficiency are negative, but none of them have passed the significance testing.This shows that the improvement of human capital level measured by education years fails to promote the industrial carbon unlocking efficiency in which the possible reason is that the economic development of various regions has long depended on the inputs of material capital, which has formed the path locking effect of development (Zhao et al. 2016).Although the level of human capital in the provinces and cities of the Yangtze River Economic Belt has improved to a certain extent during the study period, except Shanghai, the level of human capital in the other 10 provinces is still low on the whole, and the proportion of college education or above is only 16%, resulting in an insignificant role of human capital in the improvement of industrial carbon unlocking efficiency.

Conclusion
The industry is the pillar industry of the Yangtze River Economic Belt, as well as the main industry of carbon emission and energy consumption.How to develop the industry under the new development goal is a question worth pondering and discussing.Accelerating the process of industrial carbon unlocking plays a vital role in realizing the carbon neutrality of the industry.Based on the panel data of all provinces and cities in the Yangtze River Economic Belt from 2011 to 2018, this paper uses the DEA model and Malmquist index to make static and dynamic research on industrial carbon unlocking efficiency of the Yangtze River Economic Belt and uses the Tobit model to empirically test its impact factors.The empirical analyses show that (1) the results calculated by the DEA model show that the overall efficiency of industrial carbon unlocking in the Yangtze River Economic Belt is on the rise, and the carbon unlocking capacity is constantly enhanced.However, there are regional differences.The efficiency of industrial carbon unlocking in the lower reaches of the Yangtze River is higher than that in the upper and middle reaches.
(2) The Malmquist index model results show that the total factor productivity of industrial carbon unlocking in the Yangtze River Economic Belt has increased steadily on the whole, and technological progress is the main source of growth, but currently, technological efficiency growth still has a significantly hindering effect on carbon unlocking efficiency.
(3) The empirical results show that government investment and innovation level have significantly negative impacts on industrial carbon unlocking efficiency, and environmental regulation and the degree of opening to the world have positive impacts, while human capital level has no significant impact.

Policy implications
The research of this paper has the following inspirations for the practice and policy formulation of energy saving and emission reduction: (1) Narrow the gap of the carbon unlocking development differences in different regions and consolidate the overall industrial development of the Yangtze River Economic Belt.Firstly, industrial enterprises in various provinces and cities should appropriately adjust the layout of industrial structure, actively respond to the national green development strategy, clearly formulate measures of energy saving and emission reduction for some firms in the dirties industries, and integrate and reorganize regional pillar industries, so as to make overall plans for the development of economic benefits and environmental protection, promote the maximum utilization of resources, and finally promote the whole society to form a new situation of the circular economy.Secondly, it is necessary to consider the misunderstandings and contradictions caused by different industrial development policies among provinces and cities and establish a cooperation and exchange mechanism for environmental protection among regions.The provincial and municipal governments will give policy support to encourage better cooperation among industrial enterprises and jointly promote industrial development of the Yangtze River Economic Belt.
(2) Rationally allocate green resources along the belt, build an innovative model of high-quality green development, and actively introduce advanced technologies and models to control local environmental pollution.In addition, we should strengthen the cooperation of carbon emission reduction among regions in the Yangtze River Economic Belt, rely on technological innovation and policy measures to promote the improvement of carbon unlocking efficiency, and incorporate the green innovation performance into the assessment standards of urban development to mobilize the enthusiasm of enterprises to participate in energy saving and emission reduction.(3) Efforts should be made to improve the efficiency of carbon unlocking in the Yangtze River Economic Belt from three aspects.Firstly, we should improve the policy system of environmental regulation; rely on the joint efforts of the government, enterprises, and society; and form a mechanism of company-led, government supervision, and public participation.At the same time, we should further open up to the outside world and guide foreign enterprises to invest and develop in low-pollution industries and build a green economic development model.Secondly, according to the characteristics of industrial structure development and the relationship between the supply and demand of talents, the government should adjust the human capital training plan in time and support the cultivation of talents that promote green development in policies, funds, platforms, and other aspects.By encouraging school-enterprise cooperation, it can improve the pertinence of human capital cultivation and reduce the structural imbalance between the supply and demand of human capital.Thirdly, the government should continue to encourage enterprises to carry out technological research and innovation, so as to promote the technological progress of the whole society and improve the industrial carbon unlocking efficiency.At the same time, it is necessary to accelerate the transformation and application of new technologies, reduce the use cost of new technologies, and reduce the inhibition of technological innovation on industrial carbon unlocking efficiency.
China's Yangtze River Economic Belt as an example to measure industrial carbon unlocking efficiency.The data used are from the panel data of 11 provinces and cities in the Yangtze River Economic Belt from 2011 to 2018.The research data are from China Statistical Yearbook, China Statistical Yearbook on Science and Technology, China Statistical Yearbook on Environment, and all provincial statistical yearbooks from 2012 to 2019, and some values are supplemented by interpolation.Because of the change of main business income of industrial enterprises above designated size in 2011 and the time lag of research data, the research time lag is set to 1 year, and the data is within 2011-2018.

Fig. 1
Fig. 1 Average efficiency of industrial carbon unlocking technology in the Yangtze River Economic Belt from 2011 to 2018

Fig. 2 Fig. 3
Fig. 2 Change trend of the overall average efficiency of the Yangtze River Economic Belt from 2011 to 2018

Table 1
Selections of evaluation index of industrial carbon unlocking efficiency

Table 2
Technological efficiency values of industrial carbon unlocking in the Yangtze River Economic Belt from 2011 to 2018

Table 3
Scale efficiency values of industrial carbon unlocking in the Yangtze River Economic Belt from 2011 to 2018