Research on carbon productivity and its spatial convergence of steel industry in China

The Global-Malmquist-Luenberger (GML) index was applied to analyze the carbon productivity in steel industry (SICP) of 29 provinces in China from 2006 to 2019, and then, the SICP was decomposed into technical efficiency change index (TC) and technical progress index (EC). On this basis, the spatial effect is introduced into the traditional convergence model to investigate the spatial convergence of SICP. The empirical results show that: (1) the overall carbon productivity of China’s steel industry is at a relatively low level, showing a slow growth trend. (2) The average value of the GML index of SICP is higher than 1, showing obvious inter-provincial and regional heterogeneity. Compared with TC, EC is the leading factor that promotes the increase of SICP. (3) The spatial absolute and condition β convergence of SICP exist in the whole country and the three major regions, but the σ convergence feature is not significant. The addition of spatial factors speeds up the convergence trend, and the speed of spatial absolute β convergence is about 3 times that of the classical convergence model. At the same time, the conditional convergence rate is significantly faster than the absolute convergence, which is closely related to the differences in influencing factors such as the industrial structure, economic development level, human capital, energy consumption intensity, and R&D investment among regions. There is still much room for improvement in carbon productivity in China’s steel industry, and investment in scientific research must be increased in order to achieve the upgrading of the industrial structure and technological innovation. The existence of spatial convergence requires strengthening the joint reorganization of steel enterprises between provinces and regions, making full use of the spatial spillover effects of production technology, and realizing regional green and coordinated development.


Introduction
As the frequency of mankind activities continues increasing, environmental issues such as global warming have attracted the attention of all countries, human environmental awareness has increased, and traditional economic development methods have gradually been replaced by low-carbon economies. In order to cope with the deteriorating human living environment and achieve sustainable economic and social development, it is imperative to make low-carbon economy one of the focuses of future research. The essence and core of a low-carbon economy is to achieve a win-win situation between economic growth and carbon dioxide emission reduction, and carbon productivity (CP) refers to the "GDP output per unit of CO 2 emission" for a period (Kaya and Yokobori 1997), which is an important bridge connecting these two goals. China is one of the world's major carbon emitters; in September 2020, it is announced that China will strive to peak carbon dioxide emissions by 2030 and to achieve carbon neutrality by 2060. Under the dual carbon goal, China's various industries are facing tremendous pressure to reduce carbon emissions. As an important pillar industry of social and economic development, the steel industry is one of the industries with high emission and high energy consumption, and it is also a key field for the country to achieve carbon peak and carbon neutrality. The IEA proposed that direct carbon emissions from the steel industry must fall in 2050 by at least 50% from 2019 to achieve its global climate target, meaning that China's steel industry will face great pressure to transition to a low-carbon industry in the coming decades. At present, China is one of the largest steel producers in the world (Han et al. 2019). In 2020, China's crude steel production exceeded the 1 billion tons for the first time, accounting for 56.75% of global production (Sun and Tao 2020), and total CO 2 emissions from the steel industry increased from 278 million tons in 1991 to 1.756 billion tons in 2020, accounting for 15% of China's carbon emissions (ShangGuan et al. 2021). Therefore, the environmental problems brought about by the growth of China's steel industry are very prominent. In the background of low-carbon economy, reducing CO 2 emissions is a hard constraint facing the steel industry, and improving the carbon productivity of the steel industry (SICP) is the key to realize the low-carbon transformation of China's steel industry. At the same time, with the acceleration of China's urbanization process and the expansion of regional openness, steel demand has also continued to increase. The spatial linkages of steel production in various provinces have become closer and the spatial liquidity of steel production factors has become more frequent. Due to the heterogeneity of the economy, geography, resources, policies and regulations across regions, the SICP is spatially unbalanced, so what are the trend characteristics of the provincial SICP in China? Is there a spatial correlation for the SICP in each region? Does the SICP gap between regions show a spatial convergence over time? If so, then what kind of spatial convergence features will it appear? The exploration of the above problems helps us to have a deep understanding of the characteristics of spatial and temporal evolution, spatial differences and convergence of SICP, and is of great theoretical and practical significance for exploring the low-carbon transformation path, promoting the high-quality and sustainable development of China's steel industry.
Academically, the research on energy conservation in iron and steel industry of China has attracted more and more attention in recent years, mainly including the following aspects. First, in terms of energy efficiency and relative impact factors. Yi et al. (2018) proposed a comprehensive decomposition model to determine the main factors affecting carbon dioxide emissions in China's steel industry.  analyzed the energy efficiency of China iron and steel industry by considering the heterogeneity of the regional techniques. Second, the steel industry CO 2 emission reduction potential is another topic of general concern in the previous literature. For example, many scholars have investigated the production process and technological innovation to calculate the energysaving potential of the Chinese steel industry (Kuramochi 2016;Wang and Lin 2017). Zhang et al. (2017) compared the impact of the energy-saving potential of various waste energy recovery technologies. Moreover, a flood of literature pays close attention to the key factors affecting carbon emissions in China's steel industry under different approaches. He et al.(2021) studied the factors influencing carbon emissions in China's steel industry. Zhang et al. (2012) found that different emission reduction measures can produce significant differences in emission reduction effects. Lastly, many scholars have also adopted various frameworks and methods to study the carbon emission reduction measures in China's steel industry Dai 2015;Ma et al. 2014;Zhang et al. 2018). As seen from the existing literature, it is important to research the carbon emission of the China's steel industry. However, the above papers either predict emission reduction potential or explore factors and technologies, and lack the research on the carbon productivity of China's steel industry, so there is a research gap in the spatial convergence of carbon productivity in the steel industry.
Increasing carbon productivity can effectively improve energy efficiency, stabilize greenhouse gas emissions and maintain economic stable economic growth, which is one of the important indicators to evaluate the economic development of developing countries. In recent years, scholars at home and abroad have gradually carried out relevant research on carbon productivity. The existing literature can be roughly divided into the following categories: (1) in terms of research methods, the research results in carbon productivity measurement methods at home and abroad have been relatively rich, mainly including the measurement of single factor carbon productivity and total factor carbon productivity. The measurement of single factor carbon productivity is relatively simple and unified, and it is often expressed by the ratio of economic output and carbon emissions (Sun and Deng 2018;Westerlund and Basher 2008). The measurement methods of total factor carbon productivity are more widely used, including methods such as growth accounting, production function, stochastic frontier analysis, and data envelopment analysis. Among them, data envelopment analysis and stochastic frontier analysis are more commonly used methods. Kortelainen (2008) and Martin et al. (2000) earlier adopted the DEA model to measure the carbon productivity of a country or region. Ping et al. (2020) used Stochastic Frontier Analysis (SFA) to evaluate the carbon productivity of the Yangtze River Economic Belt from 2003 to 2016. Wang et al. (2019) measured the carbon productivity in different cities based on the ultra-efficiency SBM model. (2) On the research scale, more attention is paid to the difference of national Haini 2021;Song et al. 2013) or regional Li et al. 2019aLi et al. , 2019bWu et al. 2014) carbon productivity. Most of these papers point out that the level of carbon productivity is closely related to economic development and plays a vital role in improving the low-carbon economy. (3) In terms of the factors affecting carbon productivity, Ahmed et al. (2020) found that the industrial transformation, along with the speed of both globalization and urbanization, has significant consequences to the carbon productivity. Jahanger et al. (2021) pointed out that as the human capital continues to cross the threshold, the influence of globalization on carbon productivity has been progressively transformed from negative to positive. Meng and Niu (2012) found that technological innovation has a more significant positive role in promoting carbon productivity in China than industrial structure adjustment. Tang et al. (2018) used the spatial autocorrelation to analyze the factors restricting the carbon productivity improvement in the service industry. Most domestic and foreign studies believe that the main factors affecting carbon productivity are economic development level (Ahmed et al. 2020;Bekun et al. 2019), industrial structure (Aslam et al. 2021), technological level (Zhang et al. 2014;Du and Li 2019), energy structure (Long et al. 2016;Meng and Niu 2012;Zhou et al. 2010), etc. In addition, some papers also included urbanization rate (Destek and Ozsoy 2015), education level (Li et al.2016a(Li et al. , 2016b, environmental regulation, degree of openness to the outside world (Wen et al. 2021;Xie 2018), and industrial agglomeration (Lin et al. 2013;Liu et al. 2017) as a way to improve carbon productivity. (4) In terms of research on carbon productivity in specific industries or sectors. Yang et al. (2015) used the GML index and discovered that the carbon productivity of the manufacturing industry has obvious σ convergence and β convergence. Li et al. (2020) found the difference in carbon productivity of various industries is significant.
The first research on productivity convergence appeared in the Solow-Swan model proposed during the period of New-Classical Economic Growth Theory. This model believes that under the influence of the law of diminishing marginal returns, the differences in per capita income and resource endowments of countries may decrease over time, and the level of economic development will gradually approach, eventually showing a steady state. The endogenous growth theory takes human capital and knowledge capital as the endogenous driving forces for sustained economic growth. Low-productivity countries can take advantage of late-mover advantage in international trade and rely on knowledge spillovers from high-productivity countries to narrow the economic gap (Riasanovsky and Gerschenkron 1963). At the same time, the theory also points out that, due to externalities, learning effects and other factors, the economic development levels of various countries will not converge, and there may even be a tendency for differences to expand. The debate about whether there is convergence of productivity in various countries led to the rapid development of relevant empirical research in the 1980s. Early domestic and foreign scholars' research on convergence issues focused on per capita income, gross national product (Barro 1991;Baumol 1986;Song 1996), and total factor productivity. Miller (2002) discovered that total factor productivity is more convergent than real GDP per capita through data research on developed and developing countries. Strazicich and List (2003) were the first to study the convergence of carbon dioxide emissions, and found that the per capita carbon dioxide emissions of 21 industrial countries are spatially convergent. Westerlund and Basher (2008) revealed the convergence of per capita carbon dioxide emissions in developed and developing countries. Zhang et al. (2013) found that the national carbon productivity and per capita GDP have conditional β convergence.
The abovementioned papers provide theoretical references for revealing the differences in economic growth between countries and regions, but there are few papers on productivity convergence analysis for a specific industry, and some scholars in the later period began to fill the gaps in this area. Gouyette and Perelman (1997) calculated the convergence of total factor productivity (TFP) in the manufacturing and service industries in 13 OECD economies. Miketa and Mulder (2005) conducted an empirical study on the energy productivity of 10 manufacturing sub-sectors in 56 economies from 1971 to 1995. The research results of Xu and Zhao (2019) provide strong evidence for the absolute and conditional convergence characteristics of the information service industry's TFP. Liu and Zhang (2010) pointed out that the growth and decomposition of service industry TFP in each province manifested as a long-term convergence trend. The study of  prove that service industry energy productivity has absolute and conditional β convergence but no σ convergence. The above literature provides important reference value for studying the productivity of the industry, but unfortunately most of the literature only studies its convergence in terms of time changes, ignoring the spatial correlation between regions. In fact, the production and operation activities between regions are not independent of each other. The cross-regional flow of production factors will impact the economic convergence between regions, and ignoring the spatial interaction will bias the convergence results. Therefore, it is necessary to add the spatial effect into the convergence model for analysis (Xiao et al. 2018).
The spatial convergence of carbon productivity is also one of the important topics of carbon productivity research. At present, the research on spatial convergence of carbon productivity is relatively limited, and most of the research mainly focuses on verifying the absolute convergence and conditional convergence of carbon productivity. Jobert et al. (2010) took 22 European countries as the subjects to verify that the absolute convergence effect of carbon emissions. Huang and Meng (2013) found that the convergence rate shows an increasing trend when spatial effects are taken into account. Spatial panel data models were used by Li et al. (2017) to investigate the β convergence of carbon intensity, accounting for spatial spillover effects and spatial dependence. Emir et al. (2018) found that the carbon intensity of EU countries can be converged to within 5-7 clubs. Li and Wang (2021) explored the spatial distribution and convergence of China's provincial carbon intensity employing spatial panel techniques. To sum up, researches on the spatial convergence of carbon productivity by different scholars differ in results due to different industries, regions, and time samples, but it is undeniable that these studies lay the foundation for this paper.
Through the review of the existing literature, we find the following deficiencies: at present, there is little research on the carbon productivity of the steel industry in China's provinces and regions, and existing studies of the evolution characteristics of carbon productivity mostly focus more on analyzing the differences in distribution and convergence between regions from the perspective of time change; the study of convergence also mainly adopts the traditional classical convergence models, lacking the consideration of spatial factors such as spatial heterogeneity and dependence, leading to it difficult to reveal the real change laws of the spatiotemporal dynamic evolution of carbon productivity. Consequently, the abovementioned deficiencies motivate this paper; the purpose of this paper is to explore the distribution and convergence of China's provincial steel industry carbon productivity from a spatial perspective and to examine which driving factors will contribute to the SICP of China. In order to achieve these goals, this paper makes the following potential marginal contribution: (1) this paper extends the research of carbon productivity to the Chinese provincial steel industry level, and measures the SICP in 29 provinces in China from 2006 to 2019 by establishing an SBM model containing undesired output and the Global-Malmquist-Luenberger index.
(2) The GML index of carbon productivity is decomposed into Technology Efficiency Change index (EC) and Technology Progress Change Index (TC) to explore the main driving force to promote SICP improvement in different provinces and at different time periods, and analyze the regional heterogeneity of SICP. (3) On this basis, this paper introduces spatial effects into the analysis framework of traditional convergence models, and constructs a spatial convergence model to systematically investigate the spatial convergence of SICP, and further analyzes the main factors affecting the convergence rate and regional differences of SICP. The empirical results can provide a reference for the measurement of SICP, help to understand the spatial convergence characteristics of SICP, and provide a scientific basis for formulating relevant policies.

Accounting method for CO 2 emissions in the steel industry
There are many widely used methods for calculating carbon emissions in the steel industry at home and abroad. The main international methods are the national greenhouse gas inventory CO 2 emission calculation method proposed by the Intergovernmental Panel on Climate Change (IPCC) and the World Steel Association (WSA). China has also successively issued the "Provincial Greenhouse Gas Inventory Compilation Guidelines" and "Greenhouse Gas Emission Accounting and Reporting Requirements" (abbreviated "Guidelines" and "Requirements," respectively). Depending on the data basis and purpose of the calculation, different calculation methods are selected. This article uses the algorithm given in "Requirements." This method can not only reflect the overall CO 2 emission situation of steel enterprises, the setting of carbon emission factors is more in line with the amount of steel production status in China, but also more consistent with the data types and accounting objectives collected in this paper.
Based on the carbon emission estimation method of the "Requirements," carbon emissions are the sum of fossil fuel combustion, production process emissions, and company purchases of electricity and heat, and then deduct carbon emissions from carbon sequestration products (crude steel). The calculation formula is as follows: In formula (1), E CO2 is the total carbon dioxide emissions; E fos is the fuel combustion emissions; E pro is the process emissions; E neh is the net power and heat emissions; E seq is the carbon dioxide implied by carbon fixing products.
In formula (2), AD i is the activity level data of i-th fossil fuel, and EF i is the carbon emission factor of i-th fossil fuel; A li and A do are respectively the quantity of limestone and dolomite in the steel production process, EF li and EF do are the corresponding carbon emission factors; A ne and A nh are the electricity purchased by the company and the heat purchased, respectively, EF ne is the average carbon emission factor of the power grid in the area where the company is located, and EF nh is the average annual heating carbon emission factor. A sp is the output of crude steel; EFsp is the carbon emission factor of crude steel.
The fuel calorific value and carbon emission factor data used in the formula come from steel production enterprises in Part 5 of the "Requirements" and the "Guide" (Li and Wang 2021).

Slack-based measure, SBM
Non-parametric data envelopment analysis (DEA) uses mathematical optimization to study the relative efficiency between multi-output and multi-input decision units (DMU), which was first proposed by famous operational research scientists Charnes, Cooper, and Rhodes in 1978. It takes each evaluation sample as a production decision unit, and each production decision unit has its input and output. The data of these input and output observations are linearly programmed to obtain a relatively effective production front. The efficiency value of the production decision unit is measured by comparing and analyzing the degree to which the decision unit deviates from the relatively effective production front surface. The DEA has proved to be an effective tool and widely used in the evaluation of efficiency and productivity in various economies. Conventional DEA models only consider the desired input and production to evaluate the efficiency of economic units. However, in the efficiency evaluation considering resource and environment constraints, the expected input and output, as well as the non-expected input and output, generally exist at the same time, and the traditional DEA efficiency evaluation does not completely conform to the actual situation. As a result, the direction distance function (DDF) which can distinguish the expected output from the non-expected output is widely used in the efficiency evaluation of economic growth with resource and environment problems, but one obvious disadvantage of the DDF is that the improvement of non-zero slacks are ignored. The nonradial and non-angle Slacks-Based Measure (SBM) model solves this problem by introducing slack variables into the objective function, and has been widely used in efficiency measurement. The SBM model of non-expected output is shown in Formula (3): Formula (3) is a SBM model containing non-consensual output based on the condition of constant returns to scale is the input and output value of t period, s x n , s y m , s b i represents the slack variable of input and output. The slack variable greater than 0 in constraints indicates that the actual input and non-expected output are larger than the input and output at the boundary, while the actual expected output is smaller than the output at the boundary. Therefore, s x n , s y m , s b i indicates the amount of overuse of input, over-emission of non-expected output and insufficient production of expected output. The objective function * about s x n ,s y m ,s b i is strictly regressive and 0 < * ≤ 1 . Production is considered to be fully efficient only when the evaluated production unit meets * = 1 s x n = 0s y n = 0s b i = 0 , and * < 1 indicates that the evaluated production unit has efficiency loss and there is room for improvement in input and output.

Global-Malmquist-Luenberger index
Malmquist productivity index was proposed in 1953 and used to study productivity changes, and is widely used in the research of dynamic efficiency trends. "Dynamic" is one of the important attributes of the steel industry, so the measurement angle of static efficiency is not appropriate. The total factor productivity considering resource and environment problems can be measured by Malmquist-Luenberger productivity index, which not only takes the advantage that Malmquist productivity index does not need to set production function in advance but also analyzes the problem of non-expected output optimization and can be integrated with other models according to research needs, but ML productivity index has the problems of non-transportability and non-circularity, it can only judge the productivity near the production period, and cannot measure the long-term trend of productivity level. Oh (2010) found that constructing Global-Malmquist-Luenberger (GML) productivity index on the basis of global production set can solve these problems; at the same time, it can effectively avoid the problems of linear programming without solution and technical regression. Therefore, this paper chooses to use the Global-Malmquist-Luenberger productivity index based on the SBM model (SBM-GML index); the formula is as follows: Decompose: where GML t+1 t represents the change of the overall efficiency value. When the GML t+1 t > 1 , it indicates that the efficiency value of the t + 1 period increases relative to the t period, which reflects the growth rate attribute of the GML, that is, dynamic. GML t+1 t can be further decomposed into global technical efficiency change index ( EC t+1 t ) and technological progress change index ( TC t+1 t ). EC t+1 t indicates the degree to which the production decision-making unit approximates the global production front surface from t to t + 1 period; when the EC t+1 t > 1 , the approximation is improved; otherwise, it deteriorates. TC t+1 t refers to the movement effect of the production front surface, whose value is greater than 1, which indicates the expansion degree of the production front surface from the t period to the t + 1 period to the global technical front surface, while less than 1 is the opposite.

Convergence analysis σ convergence
There are many indicators to measure the degree of dispersion to judge the σ convergence of carbon productivity, such as standard deviation, coefficient of variation, and σ coefficient. Although these indexes differ in formula, the basic principle is the same. If the index decreases gradually with the passage of time, it indicates the existence of σ convergence, and vice versa. In this paper, the σ coefficient is used to judge whether the SICP of China has σ convergence. The formula is: where σ stands for the σ coefficient, the ln CP i and the ln CP 2 represent SICP and the average of square of SICP, the Ln denotes the logarithm, the i denotes the province, and the N represents the number of provinces. β convergence β convergence is most widely used in convergence research. The classical β convergence is divided into absolute β convergence and conditional β convergence. The classical β convergence model is constructed as follows: Among them, CP i,t and CP i,t+1 are the SICP in the t,t + 1 year of i province, σ is a constant term, and the β is judgment coefficient of convergence. When < 0 significant, the SICP converges; otherwise, it tends to diverge.
i,t is a random disturbance term and the k is the regression coefficient of the control variable X. When k ≠ 0 , the model is absolute β convergence. When k ≠ 0 , the model is conditional β convergence. Absolute β convergence refers to the negative correlation between the growth rate of carbon productivity in different regions and the initial level with the passage of time, and the carbon productivity in each region converges to the same level. Conditional β convergence means that the SICP in each region will converge to their steady-state level over time due to the differences in industrial structure, energy consumption intensity, human capital, and so on. In addition, the natural logarithm of non-percentage data is taken in regression analysis, which reduces the dispersion of data. The classical β convergence examines the convergence of SICP in time evolution, while ignoring spatial factors may lead to biased of the estimated results (Hou and Yao 2019). Therefore, this study introduces spatial measurement into classical β convergence analysis, and constructs the following spatial lag model (SLM), spatial error model (SEM), and spatial Doberman model (SDM): (1). SLM β convergence: (2). SEM β convergence: (3). SDM β convergence: where Formula (8) is the SLM β convergence model, which is also called the spatial auto-regressive model. It adds the spatial auto-correlation term of the explained variable, which is suitable for studying the situation of mutual influence and interdependence between adjacent areas due to spillover effects. The Formula (11) is the SEM β convergence model, which contains the spatial autocorrelation term of the error term, which reflects that the spatial dependence between regions is caused by some missing variables that affect the adjacent region. SLM and SEM emphasize the endogeneity of spatial effect, and the spatial effect between regions may also come from exogenous variables. SDM model solves this problem well; it not only contains the spatial lag term of the explained variable, but also introduces the spatial lag term of the independent variable, which takes into account the influence of the spatial spillover effect of the independent variable on the dependent variable (Li et al. 2019a(Li et al. , 2019b. Like β classical convergence model, whether the value of the k is zero determines whether the model β absolute convergence or conditional convergence. ij is the element in the W of spatial weight matrix constructed by adjacency weight matrix, is the space lag coefficient, which reflects the direction and degree of space overflow, i,t is the spatial autocorrelation error term; X k,i,t represents the control variable for conditional convergence analysis, ln X k,i,t is the independent variable spatial lag term, k is the coefficient of ln X k,i,t , which is used to investigate the effect of independent variables (influencing factors) in adjacent areas on dependent variable observations (carbon productivity). k is the regression coefficient of the spatial interaction effect between the spatial weight matrix ij and the control variable X k,i,t . i,t is a random disturbance term.

Carbon productivity in steel industry
Before establishing a SBM model containing non-expected outputs, the elements of input and output need to be determined. Generally speaking, when studying carbon productivity or energy efficiency, scholars will use GDP or industry output value as expected output, and carbon emissions as non-expected output to model (Li et al. 2019a(Li et al. , 2019b. On the basis of the previous literature, combined with the characteristics of the steel industry, and considering the accessibility of the research data and the consistency of statistical caliber, 29 provinces of China (excluding Hong Kong, Macao, Taiwan, Tibet, and Hainan, where data are missing) were studied as decision-making units between 2006 and 2019. The index description and data units are shown in Table 1.
Three points need to be explained: Firstly, select fixed assets investment in the steel industry as a measure of capital investment and convert it to the same price in 2006 according to the fixed assets price index over the years; secondly, in the steel industry, the main energy inputs include coal, gasoline, fuel oil, coke, diesel, and electricity. Thirdly, there are eight provinces (Jiangsu, Shanghai, Guizhou, Hebei, Zhejiang, Guangxi, Sichuan, and Shandong) where relevant data is not available. The energy consumption of these eight regions is estimated using the energy structure of similar provinces, referring to the treatment methods of Lu (2016). Table 2 shows that in terms of output indicators, the standard deviation of gross output of the steel industry in 29 provinces from 2006 to 2019 is large, indicating that the total scale and total level of CO 2 emissions vary greatly, and the standard deviation of emissions is also high. Therefore, it can be seen that the relationship between total scale, total level, and CO 2 emissions is close. From the analysis of input index, there are great differences in fixed assets investment, year-end employment, and total energy consumption, which provide a research basis for the measurement of carbon productivity and the analysis of influencing factors steel industry.

Selection of conditional β convergence control variables
Industrial structure Industrial structure refers to the proportion of agriculture, industry, and service industry in the national economy, and the carbon productivity of different industries is different. This paper uses the ratio of tertiary industry to regional GDP in various provinces of China to express industrial structure (IS), reflecting the structural effect of carbon productivity.

Economic development level (PGDP)
The level of economic development has always been one of the important factors affecting carbon productivity. Economic developed areas not only have higher income levels but also pay more attention to environmental governance and energy-saving technology development (Mikayilov et al. 2018). Per capita GDP is adopted in this paper to reflect the level of economic development.

Enterprise size (ES)
Based on the existing literature, this paper selects fixed assets per capita to measure the size of the enterprise, which reflects the scale effect of carbon productivity. Generally speaking, large enterprises have more advantages than small and medium-sized enterprises in energy-saving technology innovation, and tend to form economies of scale more easily.
Human capital (EDU) This paper uses the per capita years of education. According to experience, people with higher education are more innovative and more environmentally conscious.

Energy consumption intensity (EI)
This paper uses the ratio of total primary energy consumption to GDP to measure the energy saving and consumption reduction of enterprises. The evolution of this ratio reflects the change of energy use efficiency and is an index of environmental effect.

Research and development (RD)
In general, increasing R&D can improve the productivity of enterprises. This paper uses the proportion of experimental researchers to the labor force to reflect the technical effect of carbon productivity.

Data sources
According to the principle of availability, validity, and maneuverability of the data, the panel data of 29 provinces in Chinese from 2006 to 2019 (except Tibet and Hainan) were selected to calculate the SICP and the spatial convergence of each province. The relevant data of the variables involved are derived from China Statistical Yearbook, China Energy Statistics Yearbook, China Environmental Statistics Yearbook and the national data website.

Carbon productivity in the steel industry and its decomposition
This paper uses the non-expected SBM model under the condition of constant returns to scale, based on the input-output index system of iron and steel industry, and uses the MaxDEA Pro software to measure the SICP in 29 regions from 2006 to 2019. The measurement results are shown in Table 3.
Observing Table 3, it can be found that SICP presents the following characteristics: Firstly, SICP in 24 provinces showed an overall growth trend, accounting for 82.8% of the total sample, indicating that the development of China's steel industry is relatively optimistic, and certain results have been achieved in energy conservation and emission reduction. The growth trend varies significantly between the different provinces; according to the analysis results, the province with the highest average ranking of the SICP is Beijing; the average growth rate reached 18%, followed by Shanghai (1.176), Chongqing (1.166), Gansu (1.116), and Hubei (1.103), with the average growth rate of 10% or above. The main reason for this is that the state has implemented targeted supporting policies for the development of these provinces, and industrial development level in these provinces is at the forefront of the country, which in turn promotes steel industry development and promotes the transformation and upgrading of industrial structure, effectively improving their industry green development level. The SICP of the five provinces of Fujian, Heilongjiang, Jiangxi, Sichuan, and Ningxia showed a downward trend. The province with the largest average decline was Heilongjiang (6%). These provinces are mainly located in the old industrial bases of China's central and western regions and northeast China have been in a development mode of high investment, high pollution, and low efficiency, which not only wastes a lot of resources but also forms serious environmental pollution. From the regional perspective, the carbon productivity in the three major regions varies significantly, showing a trend of "the highest in the east, the second in the west, and the lowest in the middle." The average carbon productivity in the eastern region is 1.063, which is higher than the overall average level, indicating that the steel enterprises in the eastern region pay more attention to the optimization of operation and management mode, allocation of input and output factors, and resource utilization efficiency. Although the SICP in the central and western regions is relatively low, the overall growth trend is still present, indicating that with the transformation of China's economic structure, environmental protection policies, the rise of central China and the implementation of the western development strategy, in order to keep up with the pace of economic development and solve the problem of overcapacity facing the steel industry, the central and western regions have also begun to focus on the steel industry reform, strengthen the supply-side structural reform, increase investment in research and development, and rely on policy support to promote the technological progress in the steel industry. Figure 1 intuitively shows that the driving factors for SICP changes in various provinces in China are different. Twenty-six provinces, including Beijing, Tianjin, and Hebei, are jointly promoted by EC and TC; Shanghai is driven by technological progress, and the growth of its SICP is entirely driven by TC; Heilongjiang and Ningxia belong to the type of technological progress and efficiency degradation; EC dropped by 1% and 4% respectively, indicating that the steel enterprises in these provinces still have the characteristics of extensive operation, the level of resource allocation is low, the scale of enterprise development is small or there is invalid scale expansion, the management mechanism is imperfect, the low utilization rate of factor resources and other factors have become the main bottleneck for the improvement of carbon productivity. Therefore, how to improve the efficiency of resource utilization and reduce environmental pollution has become a problem that must be solved in the development of inefficient provinces, and it is also a problem that needs to be solved to improve the carbon productivity of China's steel industry. It can be seen from Fig. 2 that from 2006 to 2019, the changes in China's SICP were not stable. Except for the decline in 2011-2012 and 2018-2019, the overall growth trend showed an average growth rate of 5.4%, indicating that the utilization efficiency and technology of resources and energy in China's iron and steel industry have improved during the sample period. It is observed that the growth rate of SICP varies in different periods. The largest increase in 2006-2007 (20.9%); followed by 2017-2018, an increase of 12.6%, which is closely related to a series of related policies issued by the government, such as the "Opinions on Resolving Excessive Capacity in the Iron and Steel Industry and Realizing Difficult Development" issued by the State Council in 2016, and the "Iron and Steel Industry Adjustment and Upgrade Plan (2016-2020)" issued by the Ministry of Industry and Information Technology, indicating that Chinese steel companies have made great efforts in improving internal management, organization, and control efficiency, but they are not good in technology introduction and change. Of course, the role of technological progress should not be underestimated. If there is no advancement in technology, it will be difficult for SICP to achieve breakthrough improvements. Looking further at Fig. 2, it is obvious that in the 11 stages of SICP improvement, there are 9 stages that are simultaneously

convergence and ˇ convergence
The above analysis indicates that there are obvious regional differences in carbon productivity in China's provincial steel industry. Next, this paper will further investigate the spatial convergence of SICP.

Spatial autocorrelation analysis
Before studying the spatial convergence of SICP, it is necessary to examine the spatial correlation of China's SICP, and this paper uses the Moran's I index to show the degree of Spatial auto-correlation. As shown in the Table 4, the global Moran's I index of SICP from 2006 to 2019 is positive and significant at 1% except 2006 and 2007, indicating a significant spatial positive correlation in SICP. Spatial dependence exists because neighboring provinces are relatively similar in terms of resource endowments and economic development levels, and because of the development of transportation and communications, the exchanges between provinces are becoming more frequent. In addition, it can be seen from the data that the global Moran's I index shows a trend of rising volatility, which indicates that the dependence between provinces is still increasing. All data are calculated by the Geoda095i software.

β Convergence
With regard to spatial β convergence, the Moran's I index method has been used above to prove the spatial correlation of SICP in each province, and it has been concluded that there is a significant positive correlation between the SICP in neighboring provinces. Since the regression result is influenced by the fixed effect, combined with the model selection principle proposed by (Paul 2010), when the time span of the spatial panel data is long, the use of fixed effects can make the model fit better. Therefore, this paper uses LR test to determine whether to select the fixed effect. As shown in Table 5, both the entity-fixed effect and the time-fixed effect passed the test at the significance level of 1%, which also indicates that the hypothesis of random effect is rejected, so the spatial convergence model of the Time-entity double fixed effect is selected. Moreover, the optimal spatial measurement model can be selected based on the statistics of LogL, sigma 2 , and R 2 . The smaller the value of sigma 2 , the larger the statistical value of LogL and R 2 , indicating that the model has better explanatory power. In order to prove the necessity of considering the spatial effect, Table 6 lists the regression results of the classical convergence model and the spatial convergence model at the same time. In the three spatial β convergence models of SLM, SEM, and SDM, the statistical values of LogL and R 2 of SLM and SEM are smaller than those of the SDM model, and the sigma 2 value of SDM is the smallest.   This shows that whether it is absolute β convergence or conditional β convergence, the goodness-of-fit of the SDM model is the highest, and the model's explanatory ability is stronger. In summary, the SDM spatial measurement model under double fixed effect is the most suitable for detecting the convergence of SICP. Some convergence characteristics can also be observed from Table 6: (1). Regardless of whether it is an absolute or conditional convergence model, the regression coefficient β of all lnCP i,t is less than zero at the 1% significance level, which indicating that the SICP as a whole has convergence characteristics, that is, regions with lower SICP have a "catch-up effect" on regions with higher carbon productivity. The existence of absolute β convergence suggests that the growth rate of low carbon productivity regions is faster than that of high carbon productivity regions, which reduces the difference in SICP between provinces. The existence of the conditional β convergence for carbon productivity indicates that each region is tending to its own steady-state level. In addition, the spatial effect coefficient in all spatial convergence models is significantly greater than 0, which indicates that there is a positive spatial spillover effect in the overall SICP. (2). Comparing the classical and spatial β convergence models, it can be seen that the addition of spatial effects speeds up the convergence speed. The convergence speed of the SDM model in absolute β convergence (0.386) is about 3 times that of the classical convergence model (0.126), and the conditional β convergence of the SDM model (0.480) is about 4 times the classical model (0.129), which shows that the spatial effect is one of the important factors in the convergence of SICP, has an accelerated effect on the convergence speed, neglecting the spatial effect will lead to the deviation of the result. The possible reason is that the uneven distribution of SICP in each province, coupled with economic development and the improvement of transportation and communication facilities, makes the resource and technology exchanges in the neighboring areas more frequent, and the resulting spatial spillover effect narrows the efficiency differences between regions and shortens the convergence period. (3). Comparing the absolute convergence and conditional convergence model, it can be observed that the conditional convergence model after adding the control variable performs better in both convergence speed and goodness-of-fit, because the conditional convergence model takes into account the factors leading to the inter-provincial heterogeneity, such as industrial structure and economic development level, which accelerates the convergence speed of SICP, thus making the test results of the model more accurate. (4). Comparing β convergence results with the σ convergence results above, the existence of β convergence and the absence of σ convergence suggest that although the low SICP is growing faster than that of the provinces with high carbon productivity, the absolute difference in carbon productivity between provinces has not narrowed.
From the regression results of the control variables of the conditional convergence model in Table 6, five of the six variables have significant effect on the SICP, and the symbols of SDM and classical convergence model regression coefficients are basically the same, but there are some differences in significance level and influence degree. According to the measurement results of the SDM model, we can draw the following conclusions: (1). The coefficient of IS is significantly positive, implying that the increase in the proportion of tertiary industry contributes to the growth of SICP in the region. Under the premise of realizing the goal of China's macro-economic regulation, the utility of the equivalent amount of financial investment in the tertiary industry is the greatest, which shows that the power of the tertiary industry to the economy is constantly improving. The tertiary industry has the least dependence on energy consumption, and vigorously developing the tertiary industry can not only drive sustained economic growth but also play an important role in promoting carbon productivity, so under the new normal of economy, we should actively promote the optimization and upgrading of industrial structure, fully release the potential of the tertiary industry in energy conservation and emission reduction, improve energy efficiency, and explore ways and means to make the tertiary industry a new growth point of regional economy.
(2). The positive impact of PGDP on carbon productivity at the 1% level of significance indicates that PGDP growth plays an important role in accelerating carbon productivity. Economic growth can provide technical, financial and human support for the improvement of coal utilization levels, and in more developed regions, while promoting industrial development, environmental regulation will be strengthened and more attention will be paid to the restrictions on CO 2 emissions (Wang and Wei 2020). Regions with different levels of economic development have different requirements for carbon intensity. In China, economically devel-oped provinces bear a relatively heavy responsibility for carbon reduction, while underdeveloped provinces such as Xinjiang, Hainan, have relatively light energy conservation and emission reduction tasks. Because of the positive correlation between PGDP and carbon productivity, all regions should insist on combining energy conservation and emission reduction with economic growth, pay attention to the sustainability of economic development, and realize the green development of national economy. (3). The estimated coefficient of ES is positive, but it fails the significance test, which shows that the expansion of enterprise scale can be beneficial to the improvement of carbon productivity to a certain extent, has a positive scale effect, but has not yet produced the ideal improvement effect on the SICP, which may be due to the fact that the company has not paid attention to the improvement of resource allocation and regeneration efficiency while expanding its scale, and has not promoted the formation of the integrity of the industrial chain, resulting in limited improvement in carbon productivity. (4). The improvement of EDU has a significant positive effect on the growth of SICP. Human capital is one of the important factors to improve the productivity of enterprises. This paper is based on the number of years of education per capita to measure human capital, the number of years of education reflects people's level of education, and higher stock of human capital can improve regional productivity and technological innovation ability; at the same time, citizens' awareness of environmental protection will be enhanced with the improvement of education level. In addition, the level of human capital also directly reflects the strength of a region's ability to absorb advanced knowledge and technology at home and abroad and to accept management experience. Therefore, increasing human capital will help the steel industry to increase carbon productivity. (5). EI has a negative effect on SICP at a significant level of 5%, which indicates that the lower the value of EI, the higher the energy efficiency per unit of output in the production process. EI is an index used to evaluate the efficiency of energy comprehensive utilization, which reflects the economic and environmental benefits of energy utilization and is the goal of "win-win" for governments and producers. Coal plays a dominant role in China's industrial energy consumption, and the proportion of coal consumption in total energy consumption is much higher than the world average, and it is well known that coal's carbon production efficiency is relatively low, which puts great pressure on China's energy conservation and emission reduc-tion efforts. The higher the intensity of energy consumption, the stronger the dependence of enterprises on energy. Therefore, increasing the development of clean energy, actively promoting improvement within the sector, and increasing the input of labor, capital, and technological innovation will not only help to reduce energy intensity in the production process and improve core competitiveness but also help to decouple economic growth and energy use, thus further ensuring energy security. (6). The regression coefficient of R&D investment is significantly positive, indicating that the SICP has a positive technical effect, that is, the increase in R&D investment in science and technology can bring about the growth of regional carbon productivity. The strength of R&D investment directly reflects the innovation ability of an enterprise, and innovation is the soul of enterprise production and development.
Research and development investment is an important way to promote technological, ideological, and institutional progress, on the one hand, to improve steel production efficiency, expand economic output while reducing production costs; on the other hand, it also helps to improve regional environmental governance capacity, improve energy efficiency, and achieve energy conservation and emission reduction targets, thereby promoting the regional SICP.
Taking into account the existence of regional heterogeneity, Table 7 further presents the regression results of conditional β convergence in the eastern, central, and western regions, and at the same time, in order to facilitate comparative analysis, the classical β convergence results are also included in the table. From a regional perspective, the β convergence coefficients of the three regions are negative and pass the significance test, indicating that there is a conditional β convergence for the SICP in each region. The coefficient of spatial effect is greater than 0 at the 1% significance level, and the convergence speed of the β convergence model, which is added to the spatial effect, is greater than that of the classical convergence model, which shows that the SICP in each region shows a strong spatial correlation and positive spatial spillover effect. Although the differences of SICP in the provinces within the three regions have narrowed over time, the rate of spatial convergence has shown an increasing order in the central (0.157), western (0.208), and eastern (0.228). Convergence is the slowest in the central region, possibly due to its inland location, low level of market development and backwardness from the east in terms of transport, communications, and other infrastructure, which leads to a slow reduction in efficiency differentials among the provinces of the central region. Most provinces in the eastern region are early implementers of energy technology reform; industrial infrastructure is more mature; steel enterprises have a high level of personnel quality and advanced technology, management system, thus speeding up the process of scale of the industry and convergence speed.
From the regression results of the control variables in each region, IS has a positive effect on the SICP in the east and west, and the impact on the central region is not significant, which may be due to the smaller growth rate of the central tertiary industry in the sample period than that of the eastern and western regions, and the annual growth rate of the proportion of the tertiary industries in the eastern, central, and western regions was 4.9%, 1.24%, and 1.36%, respectively. PGDP has a significant positive impact on the central and western regions, suggesting that when other conditions are equal, higher levels of economic development will help increase regional carbon productivity. EDU has a positive effect on the SICP in all three regions, which indicates that the carbon production efficiency of the region will improve with the level of education, and form a strong positive space spillover effect. In summary, EC, EI, and R&D investment have a differential impact on the growth of carbon productivity in the eastern, central, and western steel industry, but the effect is not significant; industrial structure, economic development level, and human capital are the main factors that cause the heterogeneity of carbon productivity in three regions.

Conclusions and recommendations
This paper used the SBM model containing undesired output and the Global-Malmquist-Luenberger index to calculate the SICP of 29 provinces in China from 2006-2019, and decomposed the GML index into EC and TC. On this basis, Moran's I index was used to verify the spatial correlation of SICP, and the spatial convergence model was used to analyze the characteristics of σ convergence and β convergence of SICP and their influencing factors.
We can draw some major conclusions from the above analysis: (1). The level of SICP of the whole country and subregions is still at a low level, but the overall trend is increasing. SICP in Beijing and Shanghai provinces was at a relatively high level during the sample inspection period. There are obvious spatial imbalances in carbon productivity in different regions; from 2006 to 2019, the SICP in the eastern coastal provinces was significantly higher than that in the western and central provinces, and the overall situation was "eastern > western > central." From the decomposition results of the GML index, it can be seen that in addition to Heilongjiang and Ningxia, both EC and TC contribute to the improvement of carbon productivity. On the whole, the improvement of SICP mainly depends on technical efficiency. The average annual growth of TC index is 5.92%, and the efficiency improvement brought by TC is relatively low; the average annual growth rate of EC index is 7.09%, indicating that the efficiency of resource allocation and management in the steel industry has improved, and the positive impact on SICP is more significant.
(2). There is a significant positive spatial autocorrelation between carbon productivity in the iron and steel industry in China. The SICP in a certain province will affect the neighboring provinces through the spatial spillover effect, and the spatial autocorrelation of SICP in various regions in China shows a fluctuating upward trend over time.
(3). The carbon productivity of the steel industry remained stable with no convergence characteristics, indicating that the inter-provincial differences in SICP have not narrowed over time; The σ coefficient of the central region shows a slow downward trend, indicating that a slower σ convergence in the central region; There is σ divergence in the western region, and inter-provincial SICP differences are gradually expanding. According to the measurement results of spatial β convergence, China's SICP has absolute β convergence and conditional β convergence on the whole, which indicates that the growth rate of low carbon productivity regions is faster than that of high carbon productivity regions, and there is a "catch-up effect," SICP in each region is tending to its own steady-state level at the same time. Moreover, due to the addition of control variables such as industrial structure, economic development level, and energy consumption level, conditional β convergence performs better in terms of convergence speed and goodness-of-fit. At the regional level, the SICP in the eastern, central, and western regions all have β convergence characteristics, with the eastern region having the fastest rate of convergence and the central region the slowest. In addition, the spatial factors have an accelerated effect on the convergence rate of SICP, and due to the existence of the spatial spillover effect, the spatial differences in SICP across China and in various regions have gradually narrowed over time. (4). The industrial structure, economic development level, human capital, and R&D have a significant positive effect on the growth of SICP, indicating that the higher the regional economic development level, the more conducive to the introduction of outstanding talents, and at the same time, it can effectively promote the adjustment and upgrading of the industrial structure. At the same time, it can effectively promote the adjustment and upgrading of regional industrial structure and technological innovation, improve pro-duction efficiency, and contribute to the improvement of industry carbon productivity. Energy consumption intensity is not conducive to the improvement of SICP. Some iron and steel enterprises are highly dependent on energy in the production process, excessively pursue an absolute increase in economic benefits, and ignore the pressure it brings to the external environment. The expansion of enterprise scale can improve SICP to a certain extent, but the effect is not significant. The differential influence of the above factors on the growth of SICP in various regions is an important reason for the difference in the spatial convergence of SICP in each region.
Based on the conclusions above, several feasible measures are proposed: First, pay attention to the issue of carbon emission reduction, and promote the low-carbon development of the steel industry (Li et al. 2016a(Li et al. , 2016b. It is necessary for the government and enterprises to reduce carbon dioxide emissions in the steel production process through technological innovation. Specifically, high SICP provinces such as Beijing and Shanghai should give full play to the advantages of industrial restructure and urgent demand; provinces with low SICP such as Heilongjiang, Fujian, and Sichuan should increase scientific and technological innovation, encourage the research and development and popularization of new processes and equipment, and expand new ways of energy conservation and emission reduction; in response to the slow convergence rate in the central region, we can optimize the industrial structure and solve overcapacity by increasing the proportion of the tertiary industry, take improving SICP as the development goal, and achieve win-win development of economic growth and carbon emission reduction.
Second, it is necessary to attach great importance to the spatial relevance and unbalanced characteristics of spatial development of SICP in various provinces and regions in China, and actively exert the positive spillover effect of steel carbon productivity. Explore and establish exchanges and cooperation systems with neighboring provinces, and gradually shift the high-quality development industries in the eastern region to the central and western regions, and encourage regions with higher SICP levels to drive regions with lower levels to achieve spatial inter-operability and optimization of production resources, and promote the coordinated development of carbon productivity in the steel industry. Due to the existence of spatial convergence, when local governments pay attention to their own steel production, they should also fully consider their differences with the surrounding areas. Enterprises and the government should dare to break down regional and institutional barriers, actively learn from the business management experience of neighboring provinces based on their own endowments, and narrow the differences in low-carbon development of steel and iron in regions, so as to promote the improvement of overall carbon productivity.
Third, there are significant differences in the steel production efficiency and degree of convergence in various provinces. Therefore, local governments should formulate appropriate low-carbon development policies for the steel industry in order and classification according to local conditions. Regions with a high level of SICP, such as the eastern provinces, should pay more attention to developing green industry, exert resources and geographical advantages, constantly strengthen independent innovation, seek innovation and accumulation of original theories and original technologies; for regions with a low level of technological innovation, it is necessary to reduce carbon emissions on the basis of economic development, increase R&D investment and promote technological innovation cooperation between regions by introducing high-end technological innovation elements, thereby achieving the improvement of carbon productivity in the steel industry. In addition, provinces need to focus on the accumulation of human capital and promote the steady growth of the steel industry, to further improve green development level of steel industry in the province, and ultimately achieve the improvement of the steel industry green level of all regions.

Limitations
Limited to the lack of personal knowledge and ability, this article has some shortcomings that need to be improved: limited to the lack of personal knowledge and ability, this article has some shortcomings that need to be improved. The first is data integrity. This article uses provinces as the research unit, and some data cannot be obtained completely. For example, the energy input data in the steel industry of some provinces (Jiangsu, Shanghai, Guizhou, Hebei, Zhejiang, Guangxi, Sichuan and Shandong) cannot be obtained. We refer to the common processing methods of previous scholars and use the energy structure of similar regions to estimate the energy consumption of these regions. Future research can use more accurate provincial data to analyze China's SICP. Second, the principle of constructing the spatial weight matrix is relatively simple. This article uses the logic of whether the provinces are adjacent in space as the principle of judgment. In fact, the provinces contain more complex geographic information. Subsequent use of the second-order adjacent method can be used to improve the construction of the spatial weight matrix to more truly reflect the spatial correlation. Finally, there are many factors that affect the spatial convergence of SICP. Due to the limitations of models and data, this article cannot comprehensively analyze all the influencing factors, and more accurately analyze the reasons for the regional differences in SICP.
Author contribution All authors contributed equally to this work. R.T. wrote the initial manuscript draft, and X.W. performed several significant revisions.

Data Availability
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Declarations
Ethics approval and consent to participate Not applicable.

Consent for publication Not applicable.
Competing interests The authors declare no competing interests.