Measuring the Total-Factor Green Efficiency in China’s Industrial Sectors: A Parametric Approach

At present, China’s industrial economy is facing a severe problem of green transformation, so the measurement of total-factor green efficiency has become one of the research hot spots. Combining Shephard’s distance function and metafrontier model, this study constructs a parametric total-factor green efficiency model in consideration of technology heterogeneity. Stochastic metafrontier analysis, which controls individual effects, is used to estimate metafrontier green efficiency. This study calculates the green efficiency of Chinese industrial sectors. Results show that there are significant differences in metafrontier green efficiency between high- and low-emission groups, and the efficiency level of the low-emission group is systematically higher than that of the high-emission group. Compared with pooled green efficiency and existing studies without considering technology heterogeneity, the metafrontier green efficiency is more intuitive and realistic. In order to achieve green industrial growth, this study suggests that the government should implement heterogeneous energy conservation and emission reduction policies for high- and low-emission groups, especially to encourage carbon-intensive industries to improve the use of existing group technologies, and to promote technology diffusion and spillover between high- and low-emission groups. Based on the reliable measurement of green efficiency, green productivity might be reliably explored as well in the future.


Introduction
In the past four decades of reform and opening up, China has made remarkable achievements in economic development. At the same time, the industrial economy has also achieved unprecedented development. China has not only become the "world factory" covering the whole industrial chain but also increased its industrial added-value production by nearly 60 times compared with 1978, with an average annual growth rate of 14.5% [1]. China's economic growth miracle has dramatically improved the welfare of its people and eliminated absolute poverty across the country by 2020. However, decades of rapid growth have also brought enormous environmental pressure, resulting in the frequent haze, extreme weather, and environmental degradation across the country in recent years, which is largely due to the traditional extensive mode of growth. is type of growth is characterized by "high input, high consumption, and high emissions" and is also the main culprit of various environmental and climate change problems. For this reason, since the 11th Five-Year Plan [2], energy conservation and emission reduction have become a mandatory target of the government's national economic plan and have been well implemented. At present, energy conservation and emission reduction have become the international consensus to deal with global warming. At the 75th Session of the United Nations General Assembly recently, the Chinese government stated that China will strive to achieve the carbon emission peak by 2030 and achieve carbon neutrality by 2060. On the other hand, economic growth has its inherent regularity. Since 2012, China's economic growth has been under great downward pressure and entered the "new normal" of medium-high growth [3]. erefore, how to ensure the sound and steady growth of China's economy and solving the problems of environment and climate change has become one of the core issues of China's sustainable economic growth in the new era.
Under this background, green growth has become a new economic growth model that attracts much attention [4]. Although there is no universally recognized and unified definition, its basic connotation is to achieve sustainable economic growth with minimum resource consumption and minimum environmental cost [5]. In other words, green growth is an environmentally inclusive growth model that ensures environmental friendliness while achieving economic growth. It is an alternative to the "pollution first, treatment later" model and a feasible solution to environmental and climate change issues. Studies have shown that industrial activities are the main source of environmental and climate change problems, and the green development of China's economy largely depends on the green transformation of the industrial economy.
ere are two main lines of research on measuring green growth. One is to construct a comprehensive evaluation indicator system, and the other is to construct relevant indexes of green growth under the input-output framework [5]. is study adopts the second research route, in which green growth is often expressed by green total-factor productivity or total-factor green efficiency. Chambers et al. [6] proposed an environmental regulation behavior analysis model based on directional distance function (DDF), which can asymmetrically deal with outputs and/or inputs. However, the directional distance function requires that the inputs or outputs vary in the same proportion (radial) and that input-and output-based choices (angular) are required for efficiency measurement. In order to overcome the above two defects, Chuang et al. [7]; Oh et al. [8]; and Du et al. [9] combined DDF to construct Malmquist-Luenberger totalfactor productivity index by taking undesirable output as an output variable to measure the green total-factor productivity that takes environmental factors into account. However, this method is carried out in a nonparametric framework and has two main shortcomings: (i) mathematical programming is nonlinear except in the case of constant return to scale; (ii) the model is deterministic, and statistical inference cannot be made unless bootstrapping is used [10].
On the other hand, Fare et al. [11] introduced a hyperbolic distance function to measure production performance through the ability to expand output and shrink input in a balanced way. In this case, the traditional radial distance function, which expands output or contracts input, is a special case of the hyperbolic distance function. Fare et al. [12] used the linear programming technique to construct a parametric (quadratic) directional distance function to assess the ability of firms to improve environmental efficiency by simultaneously increasing good output and reducing bad output, but this model is still affected by the second shortcoming of the nonparametric approach described above. Cuesta et al. [13] developed a stochastic hyperbolic distance function model, which utilized the transcendental logarithmic production function proposed by Christensen et al. [14]. Zhang and Ye [15] extended the hyperbolic distance function module of Cuesta et al. [13] to include the use of an elastic time-varying framework to capture neutral technical changes using technology (t) rather than time dummy variables. Duman and Kasman [16] applied the enhanced hyperbolic distance function proposed by Cuesta et al. [13] to investigate the environmental efficiency of EU members and candidate countries and analyzed its convergence. However, the hyperbolic distance function still needs to expand and decrease the good and bad outputs in equal proportion. Zhou et al. [17] proposed the carbon emission distance function under the DEA framework, which can investigate the maximum emission reduction potential of carbon emissions under the condition that other inputs and technologies remain unchanged, so as to flexibly measure carbon emission efficiency or green efficiency more. Lin and Du [18] proposed the green efficiency based on the carbon emission distance function under the SFA framework and investigated the green efficiency and productivity of each province in China. e SFA framework for green efficiency measurement gained many attention because it could provide statistical inference while the DEA framework generally does not. For example, Tan et al. [19] estimated the green efficiency of 36 industrial subsectors in China from 2001 to 2015. Lv et al. [20] used the SFA framework to evaluate the green productivity of 30 provinces in China from 1997 to 2017.
A common assumption in the above studies is that all DMUs share the same production technology, which may lead to biased measurement results because there may be inherent differences between different technology groups. Hayami and Ruttan [21] first proposed the concept of metafrontier to solve the problem of noncomparability of production performance of different groups. Battese and Rao [22] developed the stochastic metafrontier method (SMFA) by combining the coproduction concept with the SFA framework, but the method had problems with the data generation process (DGP). Battese et al. [23] proposed a different definition of the metafrontier function to solve the above DGP problem. ey also proposed a two-step standard estimation procedure, that is, the first step uses SFA to estimate the group frontier, and the second step uses linear or quadratic programming techniques to estimate the metafrontier. O 'Donnell et al. [24] further extended this method to the distance function and the DEA model. Based on the development of the metafrontier function and due to the advantage of providing statistical inference of SFA, Lin and Du [25] used the SMFA method to measure the totalfactor energy efficiency of 30 regions in China from 1997 to 2010. Along this line, Lin and Du [18] used the fixed-effects SMFA model to estimate the total-factor carbon emission efficiency and Malmquist carbon emission performance of 30 provinces in China during 2000-2010. Bai et al. [26] used the SMFA to measure the environmental performance and carbon emission reduction potential of 39 industrial sectors in China from 2005 to 2011. Zheng et al. [27] estimated the total-factor water efficiency of 30 provinces in China from 2001 to 2016 using the SFMA. All the above studies adopted the two-step method proposed by Battese et al. [23] and O 'Donnell et al. [24]. However, Huang et al. [28] pointed out that the statistical properties of the metafrontier estimated by the second step of the above two-step mixed approach are not clear, because the estimated results obtained from programming techniques may be "contaminated" by random disturbances. ey then proposed a two-step stochastic frontier approach that uses SFA estimation in both the first and second steps to address the limitations mentioned above. e two-step stochastic frontier approach attracted many attention and was applied in a wide range of efficiency studies. For example, Safiullah and Shamsuddin [29] applied the two-step stochastic frontier approach to measure the Islamic banks' cost efficiency and Alem et al. [30] evaluated Norwegian dairy farms' technical efficiency using this approach. In the field of energy and environmental studies, Lu et al. [31] used the two-step stochastic frontier approach to assess the environmental efficiency of China's 273 cities from 2002 to 2016. Zhang et al. [32] estimated the energy efficiency of Chinese cities from 2005 to 2015 using the two-step stochastic frontier approach. However, these studies seldom considered individual heterogeneity, which might cause biased results [18]. erefore, this study aims to provide a new parametric framework of total-factor green efficiency, based on the carbon emission distance function proposed by Zhou et al. [17] and Lin and Du [18] and the two-step stochastic frontier approach proposed by Huang et al. [28]. e new method can deal with both individual heterogeneity and technology heterogeneity, which has been seldom carried out in literature, especially in the measurement of green efficiency. Moreover, there are numerous studies assessing the energy or green efficiency in China from the province perspective while those from the industry perspective are very limited.
us, using this method, this study calculates the total-factor metafrontier green efficiency of China's 34 industrial sectors from 2000 to 2016, and the results show that the green efficiency is more reasonable and accurate after considering the technology heterogeneity and individual heterogeneity.
is study is arranged as follows: in section 2, the method of total-factor green efficiency considering technology heterogeneity is given, and the data source and parametric estimation are given. Section 3 is the analysis of the green efficiency of the Chinese industry. Section 4 is the conclusion. [17] proposed the Shephard emission distance function under the DEA framework. is function measures the largest reduction of bad output (carbon emissions) given good output. Lin and Du [18] parameterized this function and proposed a parametric measurement framework of total-factor green efficiency. Based on Lin and Du [18], this study will construct the total-factor green efficiency in consideration of technology heterogeneity among different groups of industrial sectors. Under the concept of metafrontier, there are two different kinds of environmental technologies: one is group technology, which is heterogeneous among different groups; the other is the metafrontier technology, which is the envelope function of different group technologies.

Research Methodology
An environmental technology that produces good output (Y) and bad output of carbon dioxide (C) is considered by putting in capital (K) and labor (L). e reason why energy input is not considered here is that China's industrial energy consumption structure is relatively stable, which has a very high correlation with carbon emissions and thus affects the effect of econometric analysis [18]. In this study, China's industrial sectors are divided into groups, and the group environmental technology is defined by the following: (1) where j � 1, 2, . . . , J denotes sectors, and P j stands for the group environmental technology.
Accordingly, the metafrontier environmental technology is defined by the following: where P * stands and the metafrontier environmental technology.
Referring to Zhou et al. [17] and Lin and Du [18], the Shephard emission distance function corresponding to group environmental technology and metafrontier environmental technology is given by the following: where θ ≥ 1 reflects the maximum reduction potential of carbon emissions given by the capital stock, labor, and technology. e group green efficiency (GGE) is defined by the following: e metafrontier green efficiency (MGE) is defined by the following: Since the metafrontier is an envelope function of the group frontiers, it can be obtained as follows: In other words, we get the following: O 'Donnell et al. [24] constructed a metafrontier ratio (MTR) to capture the potential gap between group frontier and metafrontier as follows: Discrete Dynamics in Nature and Society us, the metafrontier green efficiency can be regarded as the product of group green efficiency and metafrontier ratio as follows: Equation (9) reveals that for any decision-making unit, its green efficiency relative to the metafrontier consists of two parts: one is within the group, namely, group green efficiency (GGE), and the other is between groups, namely, metafrontier ratio (MTR). Accordingly, there are two basic ways to improve green efficiency. One is to approach the leaders of green efficiency within the group by tapping their own potential, such as management, innovation, and energy-saving investment. e other is to improve the group's overall potential green efficiency by improving the economic environment and conditions, such as infrastructure investment, environmental regulation, and technology diffusion. e above discussion shows that under the concept of metafrontier, the improvement of green efficiency requires not only the contribution of a single individual but also the joint efforts of its group.
Following Huang et al. [28] and Wang [33], this study first describes the carbon emission distance function in the translogarithmic function because of its flexibility, ease of calculation, and homogeneity [18,34]. In order to control individual effects, we adopt the fixed-effects SFA method proposed by Greene [35]. e group emission distance function is then given by the following: where α i measures the individual effects; D j it is the distance function of industry i at time t; t is also a technical variable; and ε j it is a random term and satisfies ε j it ∼ N(0, σ 2 εj ). For the convenience of expression, equation (10) is rewritten as follows: Since the carbon emission distance function is linearly homogeneous to carbon emission, it can be obtained as follows: After rearranging, we get the following: where > 0 is defined as the inefficiency term in stochastic frontier analysis and satisfies u j it ∼ N + (0, σ 2j u ). en, the group green efficiency can be estimated as follows: Oil processing and coking H07 Chemical materials and products H08 Nonmetallic mineral products H09 Ferrous metal smelting and pressing H10 Nonferrous metal pressing H11 Electricity production H12 Gas production L13 Nonferrous metal mining L14 Food processing L15 Food manufacturing L16 Beverage manufacturing L17 Tobacco manufacturing L18 Textile industry L19 Leather manufacturing L20 Timber and wood processing L21 Furniture manufacturing L22 Printing and intermediary replication L23 Culture, education, and sport activities L24 Medicine manufacturing L25 Chemical fiber manufacturing L26 Rubber and plastic manufacturing L27 Metal product manufacturing L28 General-purpose manufacturing L29 Special-purpose manufacturing L30 Transport equipment manufacturing L31 Electrical machinery and equipment L32 Communication equipment manufacturing L33 Measuring instrument manufacturing L34 Water production Note: H and L denote high-emission and low-emission groups, respectively.

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Discrete Dynamics in Nature and Society e second step is to estimate the metafrontier ratio (MTR). Referring to Huang et al. [28], it can be derived that: Equation (15) is substituted into equation (17) to get the following: where ε Referring to Huang et al. [28], the non-negative inefficiency term can be assumed as can also reasonably be assumed to be an asymptotically normal distribution with zero mean, but it may not be an independent normal distribution because of the inclusion of ε ij t ∧ . To solve this problem, a quasi-maximum likelihood estimator (QMLE) can be used. erefore, MTR can be predicted as follows: Finally, the metafrontier green efficiency (MGE) can be calculated according to equation (9) given equations (14) and (18).

Data.
e sample period of this study is 2000-2016. During this period, the National Industry Classification Standard (NSIC) was revised twice (2002 and 2011). In order to ensure the consistency of statistical coverage, we finally select 34 industrial sectors with good continuity of industry connotation for empirical analysis, as shown in Table 1. e capital stock and labor data of China's industrial sectors      [37], the carbon emissions are calculated by the following: where C ij represents the carbon emissions; AD ij represents energy consumption; NCV j is the net caloric value; CC j is carbon content; and O ij stands for the oxidation rate. It should be noted that the first two variables on the right-hand side of equation (19) measure the standard quantity of energy consumption. Since this study directly uses the final energy consumption of industrial sectors provided by China Energy Statistical Yearbook, there is no need to repeat the calculation. e coefficients of carbon content (CC j ) and oxidation rate (O ij ) are referred to Shan et al. [37]. Industrial sectors need to be grouped to reflect technology heterogeneity. We calculate carbon emission intensity first and then rank the sectors in terms of the annual average levels between 2000 and 2016. Together with the classification of light and heavy industries, the industries with more than 4 tons per10000 yuan are classified as the high-emission group, while those with less than 4 tons per 10000 yuan are classified as the low-emission group. e high-and low-emission groups consist of 12 and 22 industrial sectors, respectively. Table 2 presents the statistical description of variables in the high-and low-emission groups, respectively. Notice that the average carbon intensity of two groups (CI) is quite different, which to a certain extent supports the rationality of the use of carbon intensity as a grouping variable. Table 3 reports the estimation results of four different stochastic frontiers, in which models (1), (2), and (4) adopt the MLE estimation, and model (3) adopts the QMLE estimation. Models (1) and (2) are group estimates, model (3) is a metafrontier estimate, and model (4) is a pooled estimate. Here, the logarithmic likelihood ratio (LR) is used to test whether group heterogeneity is statistically significant, i.e., λ � −2 ln[L(H 0 ) − L(H 1 )] , ln[L(H)0)] represents the likelihood ratio value of the null hypothesis that all groups face the same frontier; Ln [L(H 1 )] represents the likelihood ratio value of the alternative hypothesis, that is, the sum of the logarithmic likelihood values of the highemission group and the low-emission group. As shown in Table 3, the logarithmic likelihood ratio test rejects the null hypothesis, indicating that the high-and low-group frontiers are statistically heterogeneous. In addition, the standard deviations of inefficiency (σ u ) and random disturbance (σ v ) in models (1)-(4) have a statistical significance of 1%-10%, indicating that the two-step stochastic metafrontier method is appropriate. In particular, lnCI, which measures inefficiency variables, was positive in each model. is is consistent with theoretical expectations, indicating the reliability of the model. Table 3, we calculate the group green efficiency of 12 sectors in the high-emission group and 22 sectors in the low-emission group. Figure 1 shows the trend of average group green efficiency of high-and low-emission groups. As defined, they are not comparable between groups. So, we analyze their individual trends here. In the high-emission group, the group green efficiency experienced a fluctuating process, with an increase during 2000 and 2002 but a decrease during    At the same time, it may also be related to the transition of China's economic growth rate, because during this period China entered the "new normal" stage characterized by medium-high speed. e traditional model of supporting high-speed growth could not be sustained, while the new growth mode was being shaped. In 2014, the group green efficiency showed a temporary improvement but then entered the decline range, because the long-term heavy industrialization and high investment in response to the financial crisis accumulated a large amount of excess capacity. e deterioration of economic efficiency led to the deterioration of group green efficiency. Comparatively, the low-emission group witnessed an increase-decrease-increase trend, which is relatively smooth. Table 4 reports the group green efficiency of China's industrial sectors. Since there is no comparability between high-and low-emission groups, we investigate sectoral performance within each group. On the one hand, in the high-emission group, H10 has the highest green efficiency, with an average value of 0.916. Meanwhile, H11 has the lowest group green efficiency of 0.754. In the low-emission group, the top three sectors are L32, L17, and L33, with average group green efficiency of 0.999, 0.997, and 0.997, respectively. e bottom three are L14, L15, and L16, with average group green efficiency of 0.889, 0.892, and 0.916, respectively.

Metafrontier Ratio.
e metafrontier ratio measures the gap between group frontier and metafrontier. It is the key indicator to transform the noncomparable group green efficiency into comparable metafrontier green efficiency. Figure 2 shows the trend of the metafrontier ratio of the high-and low-emission groups from 2000 to 2016. In the high-emission group, except for a transient increase in 2005 and 2016, the rest years show a continuous decline. In the low-emission group, with the exception of a few years (2004, 2008, 2010, and 2013), the metafrontier has been growing on.
is means that the low-emission group is gradually shrinking the gap to the metafrontier. From the perspective of comparison, the metafrontier of the low-emission group is systematically higher than that of the high-emission group. at is to say, the low-emission group is closer to the metafrontier. is conclusion is consistent with the reality that the low-emission group or light industry is generally considered to be more efficient in carbon emission. In other words, carbon-intensive sectors need to make more effective use of technology spillover mechanisms, such as stricter regulations and technology diffusion reservoirs, to shrink the technology gap to the metafrontier. Table 5 shows the metafrontier ratios of China's industrial sectors. Since the metafrontier ratios of the different groups are comparable, we can analyze them from a global view of point. Comparisons can be made from the perspective of the entire industrial sector. In terms of individual sectors, the three industries with the highest metafrontier ratios are L32, L17, and L31, with values of 0.9993, 0.9985, and 0.9968, respectively. We observe that they belong to the  Discrete Dynamics in Nature and Society low-emission group. e three industries with the lowest metafrontier ratios are H11, H02, and H03, which belong to the high-emission group.
We also observe that group green efficiency and metafrontier ratio are not always consistent. As shown in Table 6, H03 in the high-emission group appears in the top three for highest green efficiency and the bottom three for lowest metafrontier ratio. More generally, there is a big discrepancy between the top and bottom sectors in terms of group green efficiency and metafrontier ratio. In fact, this shows the difference between group technologies and metatechnology, which implies different possibilities for efficiency catch-up.
at is, sectors with low group green efficiency may get a free ride on technology spillover and environmental regulation of the group to improve the metafrontier ratio. On the other hand, some sectors with higher group green efficiency may deviate from the metafrontier if they do not effectively utilize technology spillover. In short, in order to improve the overall green efficiency, it is necessary not only to improve its own group green efficiency but also to promote the technological progress of this group and make comprehensive use of the technology spillover.

Metafrontier Green Efficiency.
As discussed above, the metafrontier green efficiency is comparable from a global view of point. In Figure 3, the overall metafrontier green efficiency suffered a general declining trend from 2000 to 2004, a rising trend during 2005-2011, and a slightly declining trend after 2012. is periodic shift is in line with those studies that considered the technology heterogeneity, e.g., Li and Lin [38]; Cheng et al. [39]; and Cheng and Jin [40]. However, this periodic shift is not very in line with those studies that either did not consider technology heterogeneity or did not consider individual heterogeneity, e.g., Sun and Huang [41]; Ouyang et al. [42]; and Luo et al. [43]. Moreover, the high-emission group witnessed a general declining trend of metafrontier  green efficiency while the low-emission group experienced an increasing trend. ese results are in line with the existing literature, e.g., Li and Lin [38]; Kang et al. [44]; and Liu et al. [45]. Table 7 reports the metafrontier green efficiency of China's industrial sectors. Among different industrial sectors, the top three sectors of metafrontier green efficiency are L32 (Communication equipment manufacturing), L17 (Tobacco manufacturing), and L31 (Electrical machinery and equipment), with values of 0.9988, 0.9955, and 0.9925, respectively. e bottom three sectors of metafrontier green efficiency are H11 (Electricity production), H02 (Oil and natural gas extracting), and H03 (Ferrous metal mining), with values of 0.197, 0.255, and 0.438, respectively. is is consistent with the metafrontier ratio, because the metafrontier ratio has more difference than group green efficiency between the high-and low-emission groups. erefore, the metafrontier ratio has a greater weight than group green efficiency in the calculation of metafrontier green efficiency. From the perspective of the industry distribution of best and worst metafrontier green efficiency, the calculation results in this study are reliable and follow the practical observations. Comparatively, those studies that did not consider technology heterogeneity and/or individual heterogeneity might suffer bias. For example, in Li and Cheng [46], the top three sectors of green efficiency include Communication equipment manufacturing (L32), Oil processing and coking (H06), and Leather manufacturing (L19). However, the Oil processing and coking (H06) is known as the high-emission and low green efficiency sector [38]. Printing and intermediary replication (L22) and Paper industry (H05) are the bottom two sectors in their study,  H01  H02  H03  H04  H05  H06  H07  H08  H09  H10  H11  H12  L13  L14  L15  L16  L17  L18  L19  L20  L21  L22  L23  L24  L25  L26  L27  L28  L29  L30  L31  L32  L33  L34 Pooled green efficiency Metafrontier green efficiency Discrete Dynamics in Nature and Society which is also anti-intuitive because none of them belong to the six high-emission industries recognized by the Chinese government [47].

Comparison between Metafrontier and Pooled Green
Efficiency. Figure 4 shows the average pooled green efficiency and metafrontier green efficiency from 2000 to 2016.
For the high-emission group, the pooled green efficiency is obviously higher than the metafrontier green efficiency, while for the low-emission group the pooled green efficiency is systematically lower than the metafrontier green efficiency. Nevertheless, from the global perspective, the average pooled green efficiency is very close to the metafrontier green efficiency. ese results indicate that the pooled green efficiency overestimates the efficiency level of the highemission group and underestimates the efficiency level of the low-emission group when technological heterogeneity is not considered. Figure 5 provides a further comparison at the sector level. Consistent with the situation of the high-and low-emission groups in Figure 4, in the high-emission group, the pooled green efficiency of each sector (except H01) is systematically higher than the metafrontier green efficiency, which is consistent with Figure 4. In the low-emission group, the metafrontier green efficiency of each sector is systematically higher than the pooled green efficiency, which is also consistent with Figure 4.
Finally, we provide Table 8 to compare the rankings of sectors between the metafrontier green efficiency and the pooled green efficiency. As shown, the rankings of metafrontier green efficiency among sectors and those of the pooled green efficiency are quite different. ere are only two sectors that have the same ranking, i.e., L31 and L32, both of which belong to the top three sectors of green efficiency. e biggest ranking difference appears in H05, which ranks 25th in the metafrontier green efficiency while ranks 8th in pooled green efficiency ranked. Since H05 ranks 11th in terms of carbon intensity (from high to low), we believe that the ranking of metafrontier green efficiency is more reliable than that of pooled green efficiency. Overall, there are 13 sectors with ranking differences within 3 while more than 60% of sectors have ranking differences greater than 3. Compared with existing studies that did not consider technology heterogeneity and/or individual heterogeneity (e.g., [45,46]), we find that their rankings of green efficiency are quite different from ours. Take the six high-emission sectors as an example, they are ranked the 34th (Electricity production, H11), 30th (Oil processing and coking, H06), 29th (Nonmetallic mineral products, H08), 27th (Chemical materials and products, H07), 26th (Ferrous metal smelting and pressing, H09), and 23rd (Nonferrous metal pressing, H10). In other words, all of them belong to the bottom group of sectors in terms of green efficiency. However, in Li and Cheng [46], only Chemical materials and products (H07) and Nonmetallic mineral products (H08) belong to the bottom group while Ferrous metal smelting and pressing (H09) belong to the middle group and Non-ferrous metal pressing (H10) and Oil processing and coking (H06) even belong to the top group.
is indicates that technology heterogeneity should be considered to get a better understanding of individual sectors' green efficiency performance.

Conclusions
In this study, we propose a new parametric measurement framework for total-factor green efficiency by combining the Shephard distance function [18] and the two-step stochastic frontier approach [28].
e new approach can not only flexibly evaluate green efficiency but also deal with both technology heterogeneity and individual heterogeneity. Using the comprehensive approach, we measure the metafrontier green efficiency of 34 industrial sectors in China.
It is found that the metafrontier green efficiency in China's industrial sectors has experienced a fluctuating change, with an overall trend of decline-increase-decline. At the same time, the metafrontier green efficiency levels of the high-and low-emission groups are significantly different. Moreover, the efficiency level of the low-emission group is systematically higher than that of the high-emission group. Note: ranking differences are calculated with reference to metafrontier green efficiency.

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Discrete Dynamics in Nature and Society Compared with pooled green efficiency without considering technology heterogeneity, the metafrontier green efficiency is more intuitive and realistic both at the group average level and at the sector level. Moreover, compared with those studies that did not consider technology heterogeneity and/ or individual heterogeneity, this study produces more reliable green efficiency of industrial sectors, which also follows the common economic sense. e results indicate that, in order to achieve green growth, the government needs to implement heterogeneous energy conservation and emission reduction policies for high-and low-emission groups. In particular, carbon-intensive industries should be encouraged to effectively improve the utilization of existing group technologies and to promote technology diffusion and spillover between groups. Overall, the new approach proposed in this study produces a reliable measurement of green efficiency, which is supported by various comparisons. Nevertheless, there are some limitations of this study. For example, the highemission and low-emission groups are equally divided on the basis of carbon intensity. In the future, a new grouping criterion that asymmetrically divides the industrial sectors into groups may be found with additional information. Besides, this study only considers the metafrontier green efficiency. In the future, green productivity based on the reliable measurement of green efficiency can be explored.
Data Availability e data that support the findings of this study are openly available in China Statistical Yearbook and China Industry Statistical Yearbook.

Conflicts of Interest
e authors declare that they have no conflicts of interest.