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

Authors: Zhenghuan Wang
Journal: Discrete Dynamics in Nature and Society
 (2022)

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## Abstract

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.


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## Body

## 1. 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. This 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]. Therefore, 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.There 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]. This 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 total-factor 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. The 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. They 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 total-factor 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. They 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. The 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].Therefore, 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]. The 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. Thus, 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.This study is arranged as follows: in section2, 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.


## 2. Research Methodology

### 2.1. Method

Zhou [17] proposed the Shephard emission distance function under the DEA framework. This 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.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). The 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)Pj=Kj,Lj,Yj,Cj:Kj,Ljcan produceYj,Cj,where j=1,2,…,J denotes sectors, and Pj stands for the group environmental technology.Accordingly, the metafrontier environmental technology is defined by the following:(2)P∗=K,L,Y,C:K,Lcan produceY,C,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:(3)DCjKj,Lj,Yj,Cj=supθ|Kj,Lj,Yj,Cjθ∈Pj,DC∗K,L,Y,C=supθ|K,L,Y,Cθ∈P∗,where θ≥1 reflects the maximum reduction potential of carbon emissions given by the capital stock, labor, and technology. The group green efficiency (GGE) is defined by the following:(4)GGE=1DCjKj,Lj,Yj,Cj.The metafrontier green efficiency (MGE) is defined by the following:(5)MGE=1DC∗K,L,Y,C.Since the metafrontier is an envelope function of the group frontiers, it can be obtained as follows:(6)DC∗K,L,Y,C≥DCjK,L,Y,C.In other words, we get the following:(7)MGE≤GGE.O ‘Donnell et al. [24] constructed a metafrontier ratio (MTR) to capture the potential gap between group frontier and metafrontier as follows:(8)MTR=DC∗K,L,Y,CDCjK,L,Y,C=MGEGGE.Thus, the metafrontier green efficiency can be regarded as the product of group green efficiency and metafrontier ratio as follows:(9)MGE=GGE×PGE.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. The 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. The 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]. The group emission distance function is then given by the following:(10)lnDitj=αi+αklnKitj+αllnLitj+αtt+0.5αkklnKitj2+0.5αlllnLitj2+0.5αttt2+αkllnKitjlnLitj+αtktlnKitj+αtltlnLitj+βylnYitj+0.5βyylnYitj2+βclnCitj+0.5βcclnCitj2+βyclnYitjlnCitj+γkylnKitjlnYitj+γlylnLitjlnYitj+γtytlnYitj+δkclnKitjlnCitj+δlclnLitjlnCitj+δtco2tlnCitj+εitj,where αi measures the individual effects; Ditj is the distance function of industry i at time t; t is also a technical variable; and εitj is a random term and satisfies εitj∼N0,σεj2. For the convenience of expression, equation (10) is rewritten as follows:(11)lnDitj=TLKj,Lj,t,Yj,Cj+εitj.Since the carbon emission distance function is linearly homogeneous to carbon emission, it can be obtained as follows:(12)lnDC,itjKitj,Litj,t,Yitj,Citj=lnCitj+lnDH,itjKitj,Litj,t,Yitj,1.After rearranging, we get the following:(13)−lnCitj=αi+αklnKitj+αllnLitj+αtt+0.5αkklnKitj2+0.5αlllnLitj2+0.5αttt2+αkllnKitjlnLitj+αtktlnKitj+αtltlnLitj+βylnYitj+0.5βyylnYitj2+γkylnKitjlnYitj+γlylnLitjlnYitj+γtytlnYitj+εitj−uitj,where uitj=lnDC,itjKitj,Litj,t,Yitj,Citj>0 is defined as the inefficiency term in stochastic frontier analysis and satisfies uitj∼N+0,σu2j.Then, the group green efficiency can be estimated as follows:(14)GGEit∧=Eexp−uitj|εitj∧.The second step is to estimate the metafrontier ratio (MTR). Referring to Huang et al. [28], it can be derived that:(15)−lnTLitj=−lnTLit∗−uitj∗,(16)−lnYitj=−lnTLitj+εitj=−lnTLitj∧+εitj∧.Equation (15) is substituted into equation (17) to get the following:(17)−lnTLitj∧=lnTLit∗+εitj∗,where εitj∗=vitj∗−uitj∗ and vitj∗=εitj−εitj∧.Referring to Huang et al. [28], the non-negative inefficiency term can be assumed as i.i.d. uitj∗∼Nμ,σuj∗2; vtij∗ 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 εtij∧. To solve this problem, a quasi-maximum likelihood estimator (QMLE) can be used. Therefore, MTR can be predicted as follows:(18)MTRit∧=Eexp−uitj∗|εitj∗∧.Finally, the metafrontier green efficiency (MGE) can be calculated according to equation (9) given equations (14) and (18).


### 2.2. Data

The 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 Table1. The capital stock and labor data of China’s industrial sectors from 2000 to 2008 are quoted by Chen [36]. The data from 2009 to 2016 are extrapolated according to Chen’s method, and the original data required are from China Statistical Yearbook and China Industry Statistical Yearbook. All nominal values are deflated at 1990 constant price. Referring to Shan et al. [37], the carbon emissions are calculated by the following:(19)Cij=ADij×NCVj×CCj×Oij×4412,where Cij represents the carbon emissions; ADij represents energy consumption; NCVj is the net caloric value; CCj is carbon content; and Oij 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. The coefficients of carbon content (CCj) and oxidation rate (Oij) are referred to Shan et al. [37].Table 1
China’s industrial sectors and group codes.
CodeSectorsH01Coal mining and washingH02Oil and natural gas extractingH03Ferrous metal miningH04Nonmetal miningH05Paper industryH06Oil processing and cokingH07Chemical materials and productsH08Nonmetallic mineral productsH09Ferrous metal smelting and pressingH10Nonferrous metal pressingH11Electricity productionH12Gas productionL13Nonferrous metal miningL14Food processingL15Food manufacturingL16Beverage manufacturingL17Tobacco manufacturingL18Textile industryL19Leather manufacturingL20Timber and wood processingL21Furniture manufacturingL22Printing and intermediary replicationL23Culture, education, and sport activitiesL24Medicine manufacturingL25Chemical fiber manufacturingL26Rubber and plastic manufacturingL27Metal product manufacturingL28General-purpose manufacturingL29Special-purpose manufacturingL30Transport equipment manufacturingL31Electrical machinery and equipmentL32Communication equipment manufacturingL33Measuring instrument manufacturingL34Water productionNote:H and L denote high-emission and low-emission groups, respectively.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. The high- and low-emission groups consist of 12 and 22 industrial sectors, respectively. Table2 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 2
Statistical description of main variables.
VariableUnitHigh-emission groupLow-emission groupObservationsMeanStandard deviationObservationsMeanStandard deviationY108 yuan2041419.151580.143742426.983737.28K108 yuan20415648.8423092.153745401.286579.41L104 persons204297.49237.93374346.02337.35EPJ2045849.659835.75374323.48304.07C104 tons20440414.3777756.413741316.991339.65CITon/104 yuan20423.8334.683741.000.86


### 2.3. Estimation

Table3 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=−2lnLH0−LH1, ln[L(H)0)] represents the likelihood ratio value of the null hypothesis that all groups face the same frontier; Ln [L(H1)] represents the likelihood ratio value of the alternative hypothesis, that is, the sum of the logarithmic likelihood values of the high-emission 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 (σu) and random disturbance (σv) 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. This is consistent with theoretical expectations, indicating the reliability of the model.Table 3
Estimated results of different stochastic frontier functions.
Model(1) High-emission group(2) Low-emission group(3) Metafrontier(4) PooledMethodsMLEMLEQMLEMLElnK−2.717∗∗∗(0.713)3.308∗∗∗(0.737)3.275∗∗∗(0.025)0.815∗∗(0.413)lnL0.402(0.914)−1.020∗(0.616)−0.988∗∗∗(0.023)−1.492∗∗∗(0.462)lnY1.473∗(0.767)−0.728(0.726)−0.896∗∗∗(0.027)−0.409(0.399)t0.191#(0.127)−0.529∗∗∗(0.092)−0.511∗∗∗(0.002)−0.144∗∗(0.057)lnK2−0.216∗∗(0.106)−0.295∗∗(0.118)−0.318∗∗∗(0.007)−0.108#(0.066)lnL2−0.232(0.269)−0.098(0.103)−0.093∗∗∗(0.003)0.079(0.087)lnY2−0.174#(0.118)0.195∗∗∗(0.069)0.200∗∗∗(0.003)0.031(0.054)t20.008∗∗∗(0.003)−0.002(0.002)−0.002∗∗∗(0.000)0.006∗∗∗(0.001)lnKL0.628∗∗∗(0.218)0.409∗∗(0.186)0.430∗∗∗(0.006)0.117(0.113)lnKY0.400∗∗∗(0.153)−0.242∗∗(0.102)−0.208∗∗∗(0.008)−0.037(0.070)lnLY−0.452(0.392)−0.125(0.128)−0.156∗∗∗(0.006)−0.014(0.097)tlnK0.023(0.029)0.094∗∗∗(0.024)0.096∗∗∗(0.001)0.024#(0.014)tlnL−0.052(0.045)−0.062∗∗∗(0.018)−0.061∗∗∗(0.000)−0.034∗∗∗(0.012)tlnY−0.036#(0.025)0.026∗(0.014)0.022∗∗∗(0.001)0.013∗(0.008)σulnCI0.843∗∗∗(0.264)2.905#(1.799)2.583∗∗∗(0.121)0.392∗∗∗(0.065)_Cons−5.460∗∗∗(0.939)−6.340∗∗∗(2.174)−6.229∗∗∗(0.104)−2.526∗∗∗(0.174)σv_Cons−3.872∗∗∗(0.356)−3.572∗∗∗(0.084)−14.387∗∗∗(0.518)−4.675∗∗∗(0.317)σu0.678∗∗∗(0.195)0.942∗∗∗(0.345)1.839∗(1.089)0.137∗∗∗(0.039)σv0.005∗∗∗(0.000)0.001∗∗∗(0.000)0.008∗∗∗(0.001)0.002∗∗∗(0.000)Likelihood51.93129.43917.3691.40LR test179.92 (P−value = 0.000)Observations578204374578Note: (1) #,∗, ∗∗, and ∗∗∗ represent statistical significance of 15%, 10%, 5%, and 1%, respectively. (2) The numbers in brackets are standard deviations.


## 2.1. Method

Zhou [17] proposed the Shephard emission distance function under the DEA framework. This 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.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). The 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)Pj=Kj,Lj,Yj,Cj:Kj,Ljcan produceYj,Cj,where j=1,2,…,J denotes sectors, and Pj stands for the group environmental technology.Accordingly, the metafrontier environmental technology is defined by the following:(2)P∗=K,L,Y,C:K,Lcan produceY,C,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:(3)DCjKj,Lj,Yj,Cj=supθ|Kj,Lj,Yj,Cjθ∈Pj,DC∗K,L,Y,C=supθ|K,L,Y,Cθ∈P∗,where θ≥1 reflects the maximum reduction potential of carbon emissions given by the capital stock, labor, and technology. The group green efficiency (GGE) is defined by the following:(4)GGE=1DCjKj,Lj,Yj,Cj.The metafrontier green efficiency (MGE) is defined by the following:(5)MGE=1DC∗K,L,Y,C.Since the metafrontier is an envelope function of the group frontiers, it can be obtained as follows:(6)DC∗K,L,Y,C≥DCjK,L,Y,C.In other words, we get the following:(7)MGE≤GGE.O ‘Donnell et al. [24] constructed a metafrontier ratio (MTR) to capture the potential gap between group frontier and metafrontier as follows:(8)MTR=DC∗K,L,Y,CDCjK,L,Y,C=MGEGGE.Thus, the metafrontier green efficiency can be regarded as the product of group green efficiency and metafrontier ratio as follows:(9)MGE=GGE×PGE.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. The 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. The 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]. The group emission distance function is then given by the following:(10)lnDitj=αi+αklnKitj+αllnLitj+αtt+0.5αkklnKitj2+0.5αlllnLitj2+0.5αttt2+αkllnKitjlnLitj+αtktlnKitj+αtltlnLitj+βylnYitj+0.5βyylnYitj2+βclnCitj+0.5βcclnCitj2+βyclnYitjlnCitj+γkylnKitjlnYitj+γlylnLitjlnYitj+γtytlnYitj+δkclnKitjlnCitj+δlclnLitjlnCitj+δtco2tlnCitj+εitj,where αi measures the individual effects; Ditj is the distance function of industry i at time t; t is also a technical variable; and εitj is a random term and satisfies εitj∼N0,σεj2. For the convenience of expression, equation (10) is rewritten as follows:(11)lnDitj=TLKj,Lj,t,Yj,Cj+εitj.Since the carbon emission distance function is linearly homogeneous to carbon emission, it can be obtained as follows:(12)lnDC,itjKitj,Litj,t,Yitj,Citj=lnCitj+lnDH,itjKitj,Litj,t,Yitj,1.After rearranging, we get the following:(13)−lnCitj=αi+αklnKitj+αllnLitj+αtt+0.5αkklnKitj2+0.5αlllnLitj2+0.5αttt2+αkllnKitjlnLitj+αtktlnKitj+αtltlnLitj+βylnYitj+0.5βyylnYitj2+γkylnKitjlnYitj+γlylnLitjlnYitj+γtytlnYitj+εitj−uitj,where uitj=lnDC,itjKitj,Litj,t,Yitj,Citj>0 is defined as the inefficiency term in stochastic frontier analysis and satisfies uitj∼N+0,σu2j.Then, the group green efficiency can be estimated as follows:(14)GGEit∧=Eexp−uitj|εitj∧.The second step is to estimate the metafrontier ratio (MTR). Referring to Huang et al. [28], it can be derived that:(15)−lnTLitj=−lnTLit∗−uitj∗,(16)−lnYitj=−lnTLitj+εitj=−lnTLitj∧+εitj∧.Equation (15) is substituted into equation (17) to get the following:(17)−lnTLitj∧=lnTLit∗+εitj∗,where εitj∗=vitj∗−uitj∗ and vitj∗=εitj−εitj∧.Referring to Huang et al. [28], the non-negative inefficiency term can be assumed as i.i.d. uitj∗∼Nμ,σuj∗2; vtij∗ 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 εtij∧. To solve this problem, a quasi-maximum likelihood estimator (QMLE) can be used. Therefore, MTR can be predicted as follows:(18)MTRit∧=Eexp−uitj∗|εitj∗∧.Finally, the metafrontier green efficiency (MGE) can be calculated according to equation (9) given equations (14) and (18).


## 2.2. Data

The 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 Table1. The capital stock and labor data of China’s industrial sectors from 2000 to 2008 are quoted by Chen [36]. The data from 2009 to 2016 are extrapolated according to Chen’s method, and the original data required are from China Statistical Yearbook and China Industry Statistical Yearbook. All nominal values are deflated at 1990 constant price. Referring to Shan et al. [37], the carbon emissions are calculated by the following:(19)Cij=ADij×NCVj×CCj×Oij×4412,where Cij represents the carbon emissions; ADij represents energy consumption; NCVj is the net caloric value; CCj is carbon content; and Oij 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. The coefficients of carbon content (CCj) and oxidation rate (Oij) are referred to Shan et al. [37].Table 1
China’s industrial sectors and group codes.
CodeSectorsH01Coal mining and washingH02Oil and natural gas extractingH03Ferrous metal miningH04Nonmetal miningH05Paper industryH06Oil processing and cokingH07Chemical materials and productsH08Nonmetallic mineral productsH09Ferrous metal smelting and pressingH10Nonferrous metal pressingH11Electricity productionH12Gas productionL13Nonferrous metal miningL14Food processingL15Food manufacturingL16Beverage manufacturingL17Tobacco manufacturingL18Textile industryL19Leather manufacturingL20Timber and wood processingL21Furniture manufacturingL22Printing and intermediary replicationL23Culture, education, and sport activitiesL24Medicine manufacturingL25Chemical fiber manufacturingL26Rubber and plastic manufacturingL27Metal product manufacturingL28General-purpose manufacturingL29Special-purpose manufacturingL30Transport equipment manufacturingL31Electrical machinery and equipmentL32Communication equipment manufacturingL33Measuring instrument manufacturingL34Water productionNote:H and L denote high-emission and low-emission groups, respectively.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. The high- and low-emission groups consist of 12 and 22 industrial sectors, respectively. Table2 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 2
Statistical description of main variables.
VariableUnitHigh-emission groupLow-emission groupObservationsMeanStandard deviationObservationsMeanStandard deviationY108 yuan2041419.151580.143742426.983737.28K108 yuan20415648.8423092.153745401.286579.41L104 persons204297.49237.93374346.02337.35EPJ2045849.659835.75374323.48304.07C104 tons20440414.3777756.413741316.991339.65CITon/104 yuan20423.8334.683741.000.86


## 2.3. Estimation

Table3 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=−2lnLH0−LH1, ln[L(H)0)] represents the likelihood ratio value of the null hypothesis that all groups face the same frontier; Ln [L(H1)] represents the likelihood ratio value of the alternative hypothesis, that is, the sum of the logarithmic likelihood values of the high-emission 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 (σu) and random disturbance (σv) 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. This is consistent with theoretical expectations, indicating the reliability of the model.Table 3
Estimated results of different stochastic frontier functions.
Model(1) High-emission group(2) Low-emission group(3) Metafrontier(4) PooledMethodsMLEMLEQMLEMLElnK−2.717∗∗∗(0.713)3.308∗∗∗(0.737)3.275∗∗∗(0.025)0.815∗∗(0.413)lnL0.402(0.914)−1.020∗(0.616)−0.988∗∗∗(0.023)−1.492∗∗∗(0.462)lnY1.473∗(0.767)−0.728(0.726)−0.896∗∗∗(0.027)−0.409(0.399)t0.191#(0.127)−0.529∗∗∗(0.092)−0.511∗∗∗(0.002)−0.144∗∗(0.057)lnK2−0.216∗∗(0.106)−0.295∗∗(0.118)−0.318∗∗∗(0.007)−0.108#(0.066)lnL2−0.232(0.269)−0.098(0.103)−0.093∗∗∗(0.003)0.079(0.087)lnY2−0.174#(0.118)0.195∗∗∗(0.069)0.200∗∗∗(0.003)0.031(0.054)t20.008∗∗∗(0.003)−0.002(0.002)−0.002∗∗∗(0.000)0.006∗∗∗(0.001)lnKL0.628∗∗∗(0.218)0.409∗∗(0.186)0.430∗∗∗(0.006)0.117(0.113)lnKY0.400∗∗∗(0.153)−0.242∗∗(0.102)−0.208∗∗∗(0.008)−0.037(0.070)lnLY−0.452(0.392)−0.125(0.128)−0.156∗∗∗(0.006)−0.014(0.097)tlnK0.023(0.029)0.094∗∗∗(0.024)0.096∗∗∗(0.001)0.024#(0.014)tlnL−0.052(0.045)−0.062∗∗∗(0.018)−0.061∗∗∗(0.000)−0.034∗∗∗(0.012)tlnY−0.036#(0.025)0.026∗(0.014)0.022∗∗∗(0.001)0.013∗(0.008)σulnCI0.843∗∗∗(0.264)2.905#(1.799)2.583∗∗∗(0.121)0.392∗∗∗(0.065)_Cons−5.460∗∗∗(0.939)−6.340∗∗∗(2.174)−6.229∗∗∗(0.104)−2.526∗∗∗(0.174)σv_Cons−3.872∗∗∗(0.356)−3.572∗∗∗(0.084)−14.387∗∗∗(0.518)−4.675∗∗∗(0.317)σu0.678∗∗∗(0.195)0.942∗∗∗(0.345)1.839∗(1.089)0.137∗∗∗(0.039)σv0.005∗∗∗(0.000)0.001∗∗∗(0.000)0.008∗∗∗(0.001)0.002∗∗∗(0.000)Likelihood51.93129.43917.3691.40LR test179.92 (P−value = 0.000)Observations578204374578Note: (1) #,∗, ∗∗, and ∗∗∗ represent statistical significance of 15%, 10%, 5%, and 1%, respectively. (2) The numbers in brackets are standard deviations.


## 3. Results and Discussion

### 3.1. Group Green Efficiency

With estimation results in Table3, 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 2003 and 2005. This is because the heavy industrialization process occurred during this period, resulting in a large amount of energy consumption and pollution discharge. The energy conservation and emission reduction have become a mandatory target of the government’s 11th Five-Year Plan, so the group green efficiency has undergone an improvement since 2006. However, the group green efficiency of the high-emission group deteriorated from 2011 to 2013, which may be related to the four-trillion stimulus measures taken in response to the global financial crisis. Large-scale investment flowed to the heavy industry, resulting in the deterioration of group green efficiency of the high-emission group. 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. The 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. The 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.Figure 1
Trends in group green efficiency of different groups.Table4 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. The bottom three are L14, L15, and L16, with average group green efficiency of 0.889, 0.892, and 0.916, respectively.Table 4
Group green efficiency of China’s industrial sectors.
Code20002001200220032004200520062007200820092010201120122013201420152016AverageH010.8230.8490.8660.8040.9320.9290.9200.9130.9260.7980.8610.8200.7950.7890.9500.9410.9310.873H020.6020.7200.8220.7940.8530.9080.8960.9340.8650.9170.8830.9300.8980.8390.8930.8030.8610.848H030.9120.9200.9410.9350.8950.9060.9100.9230.9090.9360.8090.9090.9250.9020.9050.9220.9190.911H040.9510.9520.9520.9230.8950.8080.8060.8060.8580.8700.9140.9320.9000.9430.9410.9350.9210.900H050.8320.8700.8650.8910.8350.8390.8670.8890.8820.8850.9320.9280.9450.9550.9620.9620.9570.900H060.8980.9390.9380.8880.8230.8780.8910.8390.8250.8700.8120.7050.6920.6500.6530.5370.5600.788H070.8770.9090.9040.9080.8500.8290.8390.8630.8980.9110.9370.9140.9170.9200.9120.8740.8810.891H080.8200.8440.8670.8090.6750.6840.7670.8250.8640.8820.9170.8700.8680.9110.9170.9120.9100.844H090.8920.9060.9230.9100.9110.8440.8440.8240.8450.7940.8160.7790.7520.7470.7220.7260.6590.817H100.8910.9290.9180.9210.9100.9000.8760.8820.8960.9060.9330.9290.9330.9420.9360.9330.9300.916H110.7270.8180.8500.8620.8290.8470.8320.8290.8490.8310.7860.7360.6970.6010.5840.6000.5410.754H120.6150.5310.7250.6990.8230.7710.8750.7910.7890.9430.9490.9580.9660.9160.9580.9530.9220.834L130.9400.9440.9340.9170.8380.8550.8390.9200.9440.9580.9740.9670.9730.9800.9810.9820.9870.937L140.8970.8980.9030.9300.7570.7790.8060.7820.7830.8670.9410.9560.9640.9700.9650.9570.9560.889L150.8070.8410.8770.9110.8030.8190.8160.8640.8590.8800.9330.9360.9580.9610.9670.9700.9640.892L160.9470.9530.9500.9470.7740.7740.8100.8400.8520.8970.9680.9710.9730.9740.9750.9780.9800.916L170.9910.9920.9920.9930.9960.9960.9970.9980.9990.9990.9990.9990.9990.9991.0001.0001.0000.997L180.9310.9350.9360.9350.8740.8870.9130.9300.9420.9530.9630.9600.9720.9790.9870.9880.9890.946L190.9690.9780.9800.9820.9700.9750.9520.9660.9740.9800.9880.9900.9890.9920.9940.9950.9950.981L200.9050.9310.9320.9170.8100.8310.8740.9150.9260.9400.9650.9650.9720.9810.9870.9890.9940.931L210.9550.9650.9670.9670.9910.9910.9820.9840.9840.9870.9900.9920.9940.9950.9960.9960.9970.984L220.9730.9790.9800.9800.9890.9900.9850.9880.9880.9910.9920.9950.9960.9960.9950.9950.9960.989L230.9870.9880.9890.9900.9870.9900.9840.9880.9900.9920.9930.9960.9860.9880.9870.9890.9880.989L240.9770.9820.9820.9830.9730.9760.9730.9740.9760.9840.9860.9860.9870.9900.9930.9940.9950.983L250.8920.8340.8390.9120.8960.8850.9220.9400.9490.9630.9680.9570.9580.9660.9760.9760.9730.930L260.9640.9710.9760.9760.9590.9580.9500.9620.9630.9730.9800.9830.9870.9900.9930.9940.9950.975L270.9180.9310.9380.9530.9610.9650.9530.9600.9630.9720.9810.9850.9790.9810.9880.9890.9900.965L280.9430.9510.9530.9640.9570.9440.9410.9460.9470.9540.9670.9400.9800.9860.9880.9880.9890.961L290.9000.9210.9440.9420.9580.9620.9610.9690.9750.9790.9790.9860.9910.9920.9920.9940.9950.967L300.9590.9710.9760.9860.9850.9830.9830.9870.9870.9900.9920.9930.9930.9940.9960.9970.9980.987L310.9920.9940.9940.9950.9930.9940.9920.9940.9950.9960.9970.9970.9980.9980.9990.9990.9990.996L320.9980.9990.9990.9990.9990.9990.9990.9990.9991.0001.0001.0001.0001.0001.0001.0001.0000.999L330.9890.9910.9910.9920.9960.9970.9970.9970.9980.9980.9980.9990.9990.9990.9991.0001.0000.997L340.9310.9380.9230.8960.8940.8840.8740.9350.9350.9460.9060.9620.9340.9650.9800.9750.9770.933High0.8200.8490.8810.8620.8530.8450.8600.8600.8670.8790.8790.8670.8570.8430.8610.8420.8330.856Low0.9440.9490.9520.9580.9260.9290.9320.9470.9510.9640.9750.9780.9810.9850.9880.9880.9890.961All0.9000.9140.9270.9240.9000.8990.9070.9160.9220.9340.9410.9390.9370.9350.9430.9370.9340.924


### 3.2. Metafrontier Ratio

The 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. Figure2 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. This 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. That is to say, the low-emission group is closer to the metafrontier. This 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.Figure 2
Trends in metafrontier ratio of different groups.Table5 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 low-emission group. The three industries with the lowest metafrontier ratios are H11, H02, and H03, which belong to the high-emission group.Table 5
Metafrontier ratio of China’s industrial sectors.
Code20002001200220032004200520062007200820092010201120122013201420152016AverageH010.7420.7720.7910.7830.8010.8310.8390.8780.8820.9470.9290.9810.9970.9830.9540.9140.8860.877H020.9870.7150.5290.4140.3630.3440.2890.2410.2440.2200.1920.1700.1660.1560.1330.1420.1260.319H030.8940.9990.6430.6290.4750.4090.4270.3980.3770.4030.3360.3340.3510.3590.3590.3580.3940.479H040.3470.3550.3660.4420.5610.9990.7430.8260.7340.7570.7480.7140.6830.6660.6280.6920.8170.652H050.9970.9870.9840.9620.9130.9560.9240.9010.8420.8040.7680.7750.7450.7140.6850.6700.6620.841H060.9940.9300.9480.8670.7280.6010.5440.5630.5260.4630.4670.4620.4510.4450.4360.4430.4520.607H070.9950.9820.9520.8850.7700.8120.8200.7340.6410.6710.6110.6060.6110.5880.5440.5450.4750.720H080.9950.8650.8320.8160.8100.7980.7550.6900.6390.6560.6020.6090.6300.5600.5070.4920.4550.689H090.8900.8940.7990.8510.8280.9210.9810.9840.8970.9360.8400.7400.6940.6090.5300.4560.4250.781H100.9970.9910.9590.9720.9280.9380.9330.9070.8570.8670.8440.8070.7970.7500.7290.7100.6800.863H110.2710.2930.3040.3070.4030.2980.3050.3130.2830.2610.2380.2160.1900.1680.1510.1460.1370.252H120.1400.2400.1770.2130.2330.2980.2680.3840.6350.5710.7060.8380.7050.9980.9440.7570.9980.536L130.9430.9410.9350.9310.9330.9420.9500.9550.9670.9750.9790.9810.9850.9870.9930.9950.9990.964L140.9700.9690.9710.9740.9740.9780.9800.9820.9810.9890.9890.9940.9960.9980.9970.9980.9970.985L150.9680.9690.9760.9730.9750.9800.9830.9860.9850.9880.9870.9900.9910.9890.9900.9980.9980.984L160.9860.9860.9890.9900.9870.9900.9910.9940.9940.9950.9940.9950.9950.9950.9940.9970.9980.992L170.9990.9990.9980.9980.9990.9990.9980.9970.9970.9990.9990.9980.9990.9980.9991.0001.0000.999L180.9910.9910.9910.9920.9870.9910.9920.9920.9910.9920.9920.9960.9980.9970.9950.9970.9980.993L190.9960.9990.9970.9990.9870.9930.9930.9950.9940.9950.9950.9980.9980.9960.9920.9900.9900.994L200.9580.9650.9650.9610.9630.9710.9740.9790.9810.9850.9880.9950.9970.9980.9990.9970.9960.981L210.9590.9640.9670.9720.9780.9850.9890.9940.9900.9910.9910.9950.9990.9990.9980.9980.9960.986L220.9800.9940.9930.9970.9960.9990.9990.9990.9960.9950.9930.9920.9940.9910.9910.9910.9900.994L230.9950.9980.9990.9970.9870.9910.9900.9930.9940.9940.9930.9960.9970.9960.9990.9980.9950.995L240.9750.9780.9830.9850.9880.9930.9920.9930.9920.9930.9920.9920.9930.9940.9950.9990.9990.990L250.9970.9770.9800.9780.9830.9930.9940.9950.9900.9850.9820.9900.9900.9870.9880.9920.9980.988L260.9890.9880.9910.9920.9910.9920.9920.9930.9910.9920.9910.9960.9960.9970.9960.9980.9990.993L270.9700.9740.9750.9730.9690.9740.9760.9800.9780.9820.9820.9880.9940.9930.9990.9910.9920.982L280.9690.9730.9760.9810.9810.9850.9870.9890.9890.9910.9920.9950.9980.9970.9970.9990.9980.988L290.9600.9630.9680.9740.9740.9790.9820.9840.9850.9880.9890.9940.9970.9970.9980.9980.9980.984L300.9780.9820.9860.9880.9880.9930.9940.9950.9940.9960.9930.9950.9960.9950.9930.9980.9990.992L310.9920.9940.9950.9970.9950.9970.9970.9970.9960.9970.9960.9980.9990.9980.9980.9991.0000.997L320.9990.9990.9990.9990.9990.9990.9990.9990.9991.0000.9991.0001.0001.0001.0001.0001.0000.999L330.9690.9700.9710.9880.9880.9940.9960.9980.9980.9960.9980.9990.9990.9990.9990.9991.0000.992L340.9250.9380.9580.9660.9780.9700.9880.9940.9880.9890.9840.9870.9860.9790.9740.9880.9990.976High0.7710.7520.6900.6780.6510.6840.6520.6520.6300.6300.6070.6040.5850.5830.5500.5270.5420.635Low0.9760.9780.9800.9820.9820.9860.9880.9900.9900.9910.9910.9940.9950.9940.9950.9960.9970.989All0.9030.8980.8780.8750.8650.8790.8700.8710.8630.8640.8550.8560.8500.8490.8380.8310.8370.864We also observe that group green efficiency and metafrontier ratio are not always consistent. As shown in Table6, 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. That 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.Table 6
Comparison between group green efficiency and metafrontier ratio.
GroupTop and bottom industriesGrouped green efficiencyCommon frontier ratioHigh-emission groupTop threeNonferrous metal pressing H100.916Coal mining and washing H010.877Ferrous metal mining H030.911Nonferrous metal pressing H100.863Nonmetal mining H040.900Paper industry H050.841Bottom threeElectricity production H110.754Electricity production H110.252Oil processing and coking H060.788Oil and natural gas extracting H020.319Ferrous metal smelting and pressing H090.817Ferrous metal mining H030.479Low-emission groupTop threeCommunication manufacturing L320.999Communication equipment manufacturing L320.999Tobacco manufacturing L170.997Tobacco manufacturing L170.999Measuring instrument manufacturing 330.997Electrical machinery and equipment L310.997Bottom threeFood processing L140.889Nonferrous metal mining L130.964Food manufacturing L150.892Water production L340.976Beverage manufacturing L160.916Timber and wood processing L200.981


### 3.3. Metafrontier Green Efficiency

As discussed above, the metafrontier green efficiency is comparable from a global view of point. In Figure3, 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. This 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. These results are in line with the existing literature, e.g., Li and Lin [38]; Kang et al. [44]; and Liu et al. [45].Figure 3
Trends in the metafrontier green efficiency of different groups.Table7 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. The 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. This is consistent with the metafrontier ratio, because the metafrontier ratio has more difference than group green efficiency between the high- and low-emission groups. Therefore, 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, which is also anti-intuitive because none of them belong to the six high-emission industries recognized by the Chinese government [47].Table 7
Metafrontier green efficiency of China’s industrial sectors.
Code20002001200220032004200520062007200820092010201120122013201420152016AverageH010.6100.6560.6850.6300.7460.7720.7720.8020.8170.7560.8000.8050.7920.7760.9070.8600.8250.765H020.5940.5150.4350.3290.3090.3130.2590.2260.2110.2020.1690.1580.1490.1310.1180.1140.1080.255H030.8150.9190.6050.5880.4260.3700.3880.3670.3430.3770.2720.3030.3240.3240.3250.3300.3620.438H040.3300.3380.3480.4080.5020.8070.5990.6660.6300.6580.6830.6650.6140.6280.5910.6470.7530.580H050.8300.8580.8510.8570.7630.8020.8010.8010.7430.7120.7160.7190.7040.6810.6590.6440.6330.751H060.8920.8730.8890.7700.5990.5280.4850.4720.4340.4030.3790.3260.3120.2890.2850.2380.2530.496H070.8730.8930.8610.8040.6550.6730.6880.6340.5750.6110.5730.5530.5600.5420.4960.4760.4190.640H080.8160.7310.7220.6600.5460.5460.5790.5690.5520.5790.5520.5300.5470.5100.4650.4490.4140.574H090.7940.8090.7370.7740.7550.7780.8290.8110.7570.7430.6860.5760.5220.4550.3830.3310.2800.648H100.8880.9200.8800.8950.8450.8440.8170.8000.7680.7860.7880.7500.7430.7060.6830.6620.6330.789H110.1970.2400.2590.2640.3340.2520.2540.2590.2400.2160.1870.1590.1320.1010.0880.0870.0740.197H120.0860.1270.1280.1490.1920.2300.2350.3040.5010.5390.6690.8030.6810.9140.9040.7220.9200.477L130.8860.8890.8730.8540.7820.8060.7970.8790.9120.9340.9530.9480.9590.9670.9740.9770.9850.904L140.8700.8710.8770.9060.7380.7620.7900.7680.7690.8570.9310.9500.9610.9680.9620.9550.9530.876L150.7810.8150.8550.8860.7830.8030.8020.8520.8460.8690.9210.9260.9490.9510.9570.9690.9620.878L160.9340.9400.9390.9370.7640.7660.8030.8340.8460.8930.9620.9660.9690.9690.9690.9760.9770.909L170.9900.9910.9900.9910.9950.9950.9950.9950.9950.9980.9980.9970.9980.9970.9990.9990.9990.996L180.9220.9270.9280.9270.8630.8790.9050.9230.9340.9460.9550.9560.9700.9750.9820.9850.9880.939L190.9650.9770.9770.9810.9570.9680.9440.9610.9680.9750.9840.9880.9870.9880.9860.9850.9850.975L200.8670.8980.8990.8810.7810.8070.8510.8970.9080.9250.9530.9600.9690.9780.9860.9870.9890.914L210.9160.9310.9360.9400.9690.9760.9700.9780.9740.9780.9810.9870.9930.9940.9940.9950.9930.971L220.9540.9730.9720.9780.9850.9890.9840.9870.9840.9860.9860.9870.9900.9860.9860.9870.9860.982L230.9810.9870.9880.9860.9740.9810.9740.9800.9840.9860.9860.9930.9830.9840.9860.9860.9830.984L240.9530.9610.9650.9690.9610.9690.9660.9670.9680.9770.9780.9780.9800.9850.9880.9920.9930.974L250.8900.8150.8230.8910.8810.8790.9170.9360.9390.9480.9510.9470.9490.9530.9640.9680.9710.919L260.9540.9600.9670.9680.9500.9510.9430.9550.9530.9650.9710.9780.9830.9870.9890.9920.9940.968L270.8900.9070.9140.9280.9310.9400.9300.9400.9420.9540.9630.9730.9730.9740.9860.9800.9820.947L280.9130.9250.9300.9460.9390.9300.9280.9360.9370.9450.9590.9350.9770.9830.9850.9870.9870.950L290.8640.8870.9140.9180.9330.9410.9440.9540.9610.9670.9690.9800.9880.9890.9910.9920.9930.952L300.9380.9540.9630.9750.9730.9760.9780.9830.9820.9860.9860.9880.9890.9890.9890.9950.9970.979L310.9840.9880.9890.9920.9880.9900.9880.9910.9910.9930.9930.9960.9970.9970.9970.9980.9990.993L320.9980.9980.9980.9980.9980.9980.9980.9980.9990.9990.9991.0001.0001.0001.0001.0001.0000.999L330.9590.9620.9620.9800.9850.9910.9930.9960.9960.9940.9960.9980.9980.9990.9990.9990.9990.988L340.8610.8790.8850.8660.8750.8580.8640.9290.9230.9350.8920.9500.9210.9440.9540.9630.9760.910High0.6440.6570.6170.5940.5560.5760.5590.5590.5480.5480.5400.5290.5070.5050.4920.4630.4730.551Low0.9210.9290.9340.9410.9090.9160.9210.9380.9410.9550.9670.9720.9770.9800.9830.9850.9860.950All0.8230.8330.8220.8180.7850.7960.7930.8040.8020.8120.8160.8160.8110.8120.8100.8010.8050.809


### 3.4. Comparison between Metafrontier and Pooled Green Efficiency

Figure4 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. These results indicate that the pooled green efficiency overestimates the efficiency level of the high-emission group and underestimates the efficiency level of the low-emission group when technological heterogeneity is not considered.Figure 4
Comparison of metafrontier and pooled green efficiency in different groups.Figure5 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.Figure 5
Comparison of metafrontier and pooled green efficiency in different sectors.Finally, we provide Table8 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. There 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. The 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. This indicates that technology heterogeneity should be considered to get a better understanding of individual sectors’ green efficiency performance.Table 8
Comparison of rankings of metafrontier and pooled green efficiency.
SectorsMGEMGE rankPGEPGE rankDifference of rankH010.765240.736306H020.255330.76228−5H030.438320.76627−5H040.580280.80519−9H050.751250.8288−17H060.496300.645333H070.640270.759292H080.574290.77325−4H090.648260.702315H100.789230.81913−10H110.197340.69932−2H120.477310.548343L130.904200.81016−4L140.876220.774242L150.878210.81614−7L160.909190.779234L170.99620.83564L180.939150.787227L190.97580.8375−3L200.914170.81315−2L210.971100.7912111L220.98260.826104L230.98450.7692621L240.97490.822123L250.919160.809171L260.968110.8374−7L270.947140.8347−7L280.950130.82511−2L290.952120.806186L300.97970.8592−5L310.99330.84130L320.99910.88310L330.98840.82895L340.910180.804202Note: ranking differences are calculated with reference to metafrontier green efficiency.


## 3.1. Group Green Efficiency

With estimation results in Table3, 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 2003 and 2005. This is because the heavy industrialization process occurred during this period, resulting in a large amount of energy consumption and pollution discharge. The energy conservation and emission reduction have become a mandatory target of the government’s 11th Five-Year Plan, so the group green efficiency has undergone an improvement since 2006. However, the group green efficiency of the high-emission group deteriorated from 2011 to 2013, which may be related to the four-trillion stimulus measures taken in response to the global financial crisis. Large-scale investment flowed to the heavy industry, resulting in the deterioration of group green efficiency of the high-emission group. 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. The 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. The 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.Figure 1
Trends in group green efficiency of different groups.Table4 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. The bottom three are L14, L15, and L16, with average group green efficiency of 0.889, 0.892, and 0.916, respectively.Table 4
Group green efficiency of China’s industrial sectors.
Code20002001200220032004200520062007200820092010201120122013201420152016AverageH010.8230.8490.8660.8040.9320.9290.9200.9130.9260.7980.8610.8200.7950.7890.9500.9410.9310.873H020.6020.7200.8220.7940.8530.9080.8960.9340.8650.9170.8830.9300.8980.8390.8930.8030.8610.848H030.9120.9200.9410.9350.8950.9060.9100.9230.9090.9360.8090.9090.9250.9020.9050.9220.9190.911H040.9510.9520.9520.9230.8950.8080.8060.8060.8580.8700.9140.9320.9000.9430.9410.9350.9210.900H050.8320.8700.8650.8910.8350.8390.8670.8890.8820.8850.9320.9280.9450.9550.9620.9620.9570.900H060.8980.9390.9380.8880.8230.8780.8910.8390.8250.8700.8120.7050.6920.6500.6530.5370.5600.788H070.8770.9090.9040.9080.8500.8290.8390.8630.8980.9110.9370.9140.9170.9200.9120.8740.8810.891H080.8200.8440.8670.8090.6750.6840.7670.8250.8640.8820.9170.8700.8680.9110.9170.9120.9100.844H090.8920.9060.9230.9100.9110.8440.8440.8240.8450.7940.8160.7790.7520.7470.7220.7260.6590.817H100.8910.9290.9180.9210.9100.9000.8760.8820.8960.9060.9330.9290.9330.9420.9360.9330.9300.916H110.7270.8180.8500.8620.8290.8470.8320.8290.8490.8310.7860.7360.6970.6010.5840.6000.5410.754H120.6150.5310.7250.6990.8230.7710.8750.7910.7890.9430.9490.9580.9660.9160.9580.9530.9220.834L130.9400.9440.9340.9170.8380.8550.8390.9200.9440.9580.9740.9670.9730.9800.9810.9820.9870.937L140.8970.8980.9030.9300.7570.7790.8060.7820.7830.8670.9410.9560.9640.9700.9650.9570.9560.889L150.8070.8410.8770.9110.8030.8190.8160.8640.8590.8800.9330.9360.9580.9610.9670.9700.9640.892L160.9470.9530.9500.9470.7740.7740.8100.8400.8520.8970.9680.9710.9730.9740.9750.9780.9800.916L170.9910.9920.9920.9930.9960.9960.9970.9980.9990.9990.9990.9990.9990.9991.0001.0001.0000.997L180.9310.9350.9360.9350.8740.8870.9130.9300.9420.9530.9630.9600.9720.9790.9870.9880.9890.946L190.9690.9780.9800.9820.9700.9750.9520.9660.9740.9800.9880.9900.9890.9920.9940.9950.9950.981L200.9050.9310.9320.9170.8100.8310.8740.9150.9260.9400.9650.9650.9720.9810.9870.9890.9940.931L210.9550.9650.9670.9670.9910.9910.9820.9840.9840.9870.9900.9920.9940.9950.9960.9960.9970.984L220.9730.9790.9800.9800.9890.9900.9850.9880.9880.9910.9920.9950.9960.9960.9950.9950.9960.989L230.9870.9880.9890.9900.9870.9900.9840.9880.9900.9920.9930.9960.9860.9880.9870.9890.9880.989L240.9770.9820.9820.9830.9730.9760.9730.9740.9760.9840.9860.9860.9870.9900.9930.9940.9950.983L250.8920.8340.8390.9120.8960.8850.9220.9400.9490.9630.9680.9570.9580.9660.9760.9760.9730.930L260.9640.9710.9760.9760.9590.9580.9500.9620.9630.9730.9800.9830.9870.9900.9930.9940.9950.975L270.9180.9310.9380.9530.9610.9650.9530.9600.9630.9720.9810.9850.9790.9810.9880.9890.9900.965L280.9430.9510.9530.9640.9570.9440.9410.9460.9470.9540.9670.9400.9800.9860.9880.9880.9890.961L290.9000.9210.9440.9420.9580.9620.9610.9690.9750.9790.9790.9860.9910.9920.9920.9940.9950.967L300.9590.9710.9760.9860.9850.9830.9830.9870.9870.9900.9920.9930.9930.9940.9960.9970.9980.987L310.9920.9940.9940.9950.9930.9940.9920.9940.9950.9960.9970.9970.9980.9980.9990.9990.9990.996L320.9980.9990.9990.9990.9990.9990.9990.9990.9991.0001.0001.0001.0001.0001.0001.0001.0000.999L330.9890.9910.9910.9920.9960.9970.9970.9970.9980.9980.9980.9990.9990.9990.9991.0001.0000.997L340.9310.9380.9230.8960.8940.8840.8740.9350.9350.9460.9060.9620.9340.9650.9800.9750.9770.933High0.8200.8490.8810.8620.8530.8450.8600.8600.8670.8790.8790.8670.8570.8430.8610.8420.8330.856Low0.9440.9490.9520.9580.9260.9290.9320.9470.9510.9640.9750.9780.9810.9850.9880.9880.9890.961All0.9000.9140.9270.9240.9000.8990.9070.9160.9220.9340.9410.9390.9370.9350.9430.9370.9340.924


## 3.2. Metafrontier Ratio

The 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. Figure2 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. This 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. That is to say, the low-emission group is closer to the metafrontier. This 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.Figure 2
Trends in metafrontier ratio of different groups.Table5 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 low-emission group. The three industries with the lowest metafrontier ratios are H11, H02, and H03, which belong to the high-emission group.Table 5
Metafrontier ratio of China’s industrial sectors.
Code20002001200220032004200520062007200820092010201120122013201420152016AverageH010.7420.7720.7910.7830.8010.8310.8390.8780.8820.9470.9290.9810.9970.9830.9540.9140.8860.877H020.9870.7150.5290.4140.3630.3440.2890.2410.2440.2200.1920.1700.1660.1560.1330.1420.1260.319H030.8940.9990.6430.6290.4750.4090.4270.3980.3770.4030.3360.3340.3510.3590.3590.3580.3940.479H040.3470.3550.3660.4420.5610.9990.7430.8260.7340.7570.7480.7140.6830.6660.6280.6920.8170.652H050.9970.9870.9840.9620.9130.9560.9240.9010.8420.8040.7680.7750.7450.7140.6850.6700.6620.841H060.9940.9300.9480.8670.7280.6010.5440.5630.5260.4630.4670.4620.4510.4450.4360.4430.4520.607H070.9950.9820.9520.8850.7700.8120.8200.7340.6410.6710.6110.6060.6110.5880.5440.5450.4750.720H080.9950.8650.8320.8160.8100.7980.7550.6900.6390.6560.6020.6090.6300.5600.5070.4920.4550.689H090.8900.8940.7990.8510.8280.9210.9810.9840.8970.9360.8400.7400.6940.6090.5300.4560.4250.781H100.9970.9910.9590.9720.9280.9380.9330.9070.8570.8670.8440.8070.7970.7500.7290.7100.6800.863H110.2710.2930.3040.3070.4030.2980.3050.3130.2830.2610.2380.2160.1900.1680.1510.1460.1370.252H120.1400.2400.1770.2130.2330.2980.2680.3840.6350.5710.7060.8380.7050.9980.9440.7570.9980.536L130.9430.9410.9350.9310.9330.9420.9500.9550.9670.9750.9790.9810.9850.9870.9930.9950.9990.964L140.9700.9690.9710.9740.9740.9780.9800.9820.9810.9890.9890.9940.9960.9980.9970.9980.9970.985L150.9680.9690.9760.9730.9750.9800.9830.9860.9850.9880.9870.9900.9910.9890.9900.9980.9980.984L160.9860.9860.9890.9900.9870.9900.9910.9940.9940.9950.9940.9950.9950.9950.9940.9970.9980.992L170.9990.9990.9980.9980.9990.9990.9980.9970.9970.9990.9990.9980.9990.9980.9991.0001.0000.999L180.9910.9910.9910.9920.9870.9910.9920.9920.9910.9920.9920.9960.9980.9970.9950.9970.9980.993L190.9960.9990.9970.9990.9870.9930.9930.9950.9940.9950.9950.9980.9980.9960.9920.9900.9900.994L200.9580.9650.9650.9610.9630.9710.9740.9790.9810.9850.9880.9950.9970.9980.9990.9970.9960.981L210.9590.9640.9670.9720.9780.9850.9890.9940.9900.9910.9910.9950.9990.9990.9980.9980.9960.986L220.9800.9940.9930.9970.9960.9990.9990.9990.9960.9950.9930.9920.9940.9910.9910.9910.9900.994L230.9950.9980.9990.9970.9870.9910.9900.9930.9940.9940.9930.9960.9970.9960.9990.9980.9950.995L240.9750.9780.9830.9850.9880.9930.9920.9930.9920.9930.9920.9920.9930.9940.9950.9990.9990.990L250.9970.9770.9800.9780.9830.9930.9940.9950.9900.9850.9820.9900.9900.9870.9880.9920.9980.988L260.9890.9880.9910.9920.9910.9920.9920.9930.9910.9920.9910.9960.9960.9970.9960.9980.9990.993L270.9700.9740.9750.9730.9690.9740.9760.9800.9780.9820.9820.9880.9940.9930.9990.9910.9920.982L280.9690.9730.9760.9810.9810.9850.9870.9890.9890.9910.9920.9950.9980.9970.9970.9990.9980.988L290.9600.9630.9680.9740.9740.9790.9820.9840.9850.9880.9890.9940.9970.9970.9980.9980.9980.984L300.9780.9820.9860.9880.9880.9930.9940.9950.9940.9960.9930.9950.9960.9950.9930.9980.9990.992L310.9920.9940.9950.9970.9950.9970.9970.9970.9960.9970.9960.9980.9990.9980.9980.9991.0000.997L320.9990.9990.9990.9990.9990.9990.9990.9990.9991.0000.9991.0001.0001.0001.0001.0001.0000.999L330.9690.9700.9710.9880.9880.9940.9960.9980.9980.9960.9980.9990.9990.9990.9990.9991.0000.992L340.9250.9380.9580.9660.9780.9700.9880.9940.9880.9890.9840.9870.9860.9790.9740.9880.9990.976High0.7710.7520.6900.6780.6510.6840.6520.6520.6300.6300.6070.6040.5850.5830.5500.5270.5420.635Low0.9760.9780.9800.9820.9820.9860.9880.9900.9900.9910.9910.9940.9950.9940.9950.9960.9970.989All0.9030.8980.8780.8750.8650.8790.8700.8710.8630.8640.8550.8560.8500.8490.8380.8310.8370.864We also observe that group green efficiency and metafrontier ratio are not always consistent. As shown in Table6, 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. That 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.Table 6
Comparison between group green efficiency and metafrontier ratio.
GroupTop and bottom industriesGrouped green efficiencyCommon frontier ratioHigh-emission groupTop threeNonferrous metal pressing H100.916Coal mining and washing H010.877Ferrous metal mining H030.911Nonferrous metal pressing H100.863Nonmetal mining H040.900Paper industry H050.841Bottom threeElectricity production H110.754Electricity production H110.252Oil processing and coking H060.788Oil and natural gas extracting H020.319Ferrous metal smelting and pressing H090.817Ferrous metal mining H030.479Low-emission groupTop threeCommunication manufacturing L320.999Communication equipment manufacturing L320.999Tobacco manufacturing L170.997Tobacco manufacturing L170.999Measuring instrument manufacturing 330.997Electrical machinery and equipment L310.997Bottom threeFood processing L140.889Nonferrous metal mining L130.964Food manufacturing L150.892Water production L340.976Beverage manufacturing L160.916Timber and wood processing L200.981


## 3.3. Metafrontier Green Efficiency

As discussed above, the metafrontier green efficiency is comparable from a global view of point. In Figure3, 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. This 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. These results are in line with the existing literature, e.g., Li and Lin [38]; Kang et al. [44]; and Liu et al. [45].Figure 3
Trends in the metafrontier green efficiency of different groups.Table7 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. The 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. This is consistent with the metafrontier ratio, because the metafrontier ratio has more difference than group green efficiency between the high- and low-emission groups. Therefore, 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, which is also anti-intuitive because none of them belong to the six high-emission industries recognized by the Chinese government [47].Table 7
Metafrontier green efficiency of China’s industrial sectors.
Code20002001200220032004200520062007200820092010201120122013201420152016AverageH010.6100.6560.6850.6300.7460.7720.7720.8020.8170.7560.8000.8050.7920.7760.9070.8600.8250.765H020.5940.5150.4350.3290.3090.3130.2590.2260.2110.2020.1690.1580.1490.1310.1180.1140.1080.255H030.8150.9190.6050.5880.4260.3700.3880.3670.3430.3770.2720.3030.3240.3240.3250.3300.3620.438H040.3300.3380.3480.4080.5020.8070.5990.6660.6300.6580.6830.6650.6140.6280.5910.6470.7530.580H050.8300.8580.8510.8570.7630.8020.8010.8010.7430.7120.7160.7190.7040.6810.6590.6440.6330.751H060.8920.8730.8890.7700.5990.5280.4850.4720.4340.4030.3790.3260.3120.2890.2850.2380.2530.496H070.8730.8930.8610.8040.6550.6730.6880.6340.5750.6110.5730.5530.5600.5420.4960.4760.4190.640H080.8160.7310.7220.6600.5460.5460.5790.5690.5520.5790.5520.5300.5470.5100.4650.4490.4140.574H090.7940.8090.7370.7740.7550.7780.8290.8110.7570.7430.6860.5760.5220.4550.3830.3310.2800.648H100.8880.9200.8800.8950.8450.8440.8170.8000.7680.7860.7880.7500.7430.7060.6830.6620.6330.789H110.1970.2400.2590.2640.3340.2520.2540.2590.2400.2160.1870.1590.1320.1010.0880.0870.0740.197H120.0860.1270.1280.1490.1920.2300.2350.3040.5010.5390.6690.8030.6810.9140.9040.7220.9200.477L130.8860.8890.8730.8540.7820.8060.7970.8790.9120.9340.9530.9480.9590.9670.9740.9770.9850.904L140.8700.8710.8770.9060.7380.7620.7900.7680.7690.8570.9310.9500.9610.9680.9620.9550.9530.876L150.7810.8150.8550.8860.7830.8030.8020.8520.8460.8690.9210.9260.9490.9510.9570.9690.9620.878L160.9340.9400.9390.9370.7640.7660.8030.8340.8460.8930.9620.9660.9690.9690.9690.9760.9770.909L170.9900.9910.9900.9910.9950.9950.9950.9950.9950.9980.9980.9970.9980.9970.9990.9990.9990.996L180.9220.9270.9280.9270.8630.8790.9050.9230.9340.9460.9550.9560.9700.9750.9820.9850.9880.939L190.9650.9770.9770.9810.9570.9680.9440.9610.9680.9750.9840.9880.9870.9880.9860.9850.9850.975L200.8670.8980.8990.8810.7810.8070.8510.8970.9080.9250.9530.9600.9690.9780.9860.9870.9890.914L210.9160.9310.9360.9400.9690.9760.9700.9780.9740.9780.9810.9870.9930.9940.9940.9950.9930.971L220.9540.9730.9720.9780.9850.9890.9840.9870.9840.9860.9860.9870.9900.9860.9860.9870.9860.982L230.9810.9870.9880.9860.9740.9810.9740.9800.9840.9860.9860.9930.9830.9840.9860.9860.9830.984L240.9530.9610.9650.9690.9610.9690.9660.9670.9680.9770.9780.9780.9800.9850.9880.9920.9930.974L250.8900.8150.8230.8910.8810.8790.9170.9360.9390.9480.9510.9470.9490.9530.9640.9680.9710.919L260.9540.9600.9670.9680.9500.9510.9430.9550.9530.9650.9710.9780.9830.9870.9890.9920.9940.968L270.8900.9070.9140.9280.9310.9400.9300.9400.9420.9540.9630.9730.9730.9740.9860.9800.9820.947L280.9130.9250.9300.9460.9390.9300.9280.9360.9370.9450.9590.9350.9770.9830.9850.9870.9870.950L290.8640.8870.9140.9180.9330.9410.9440.9540.9610.9670.9690.9800.9880.9890.9910.9920.9930.952L300.9380.9540.9630.9750.9730.9760.9780.9830.9820.9860.9860.9880.9890.9890.9890.9950.9970.979L310.9840.9880.9890.9920.9880.9900.9880.9910.9910.9930.9930.9960.9970.9970.9970.9980.9990.993L320.9980.9980.9980.9980.9980.9980.9980.9980.9990.9990.9991.0001.0001.0001.0001.0001.0000.999L330.9590.9620.9620.9800.9850.9910.9930.9960.9960.9940.9960.9980.9980.9990.9990.9990.9990.988L340.8610.8790.8850.8660.8750.8580.8640.9290.9230.9350.8920.9500.9210.9440.9540.9630.9760.910High0.6440.6570.6170.5940.5560.5760.5590.5590.5480.5480.5400.5290.5070.5050.4920.4630.4730.551Low0.9210.9290.9340.9410.9090.9160.9210.9380.9410.9550.9670.9720.9770.9800.9830.9850.9860.950All0.8230.8330.8220.8180.7850.7960.7930.8040.8020.8120.8160.8160.8110.8120.8100.8010.8050.809


## 3.4. Comparison between Metafrontier and Pooled Green Efficiency

Figure4 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. These results indicate that the pooled green efficiency overestimates the efficiency level of the high-emission group and underestimates the efficiency level of the low-emission group when technological heterogeneity is not considered.Figure 4
Comparison of metafrontier and pooled green efficiency in different groups.Figure5 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.Figure 5
Comparison of metafrontier and pooled green efficiency in different sectors.Finally, we provide Table8 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. There 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. The 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. This indicates that technology heterogeneity should be considered to get a better understanding of individual sectors’ green efficiency performance.Table 8
Comparison of rankings of metafrontier and pooled green efficiency.
SectorsMGEMGE rankPGEPGE rankDifference of rankH010.765240.736306H020.255330.76228−5H030.438320.76627−5H040.580280.80519−9H050.751250.8288−17H060.496300.645333H070.640270.759292H080.574290.77325−4H090.648260.702315H100.789230.81913−10H110.197340.69932−2H120.477310.548343L130.904200.81016−4L140.876220.774242L150.878210.81614−7L160.909190.779234L170.99620.83564L180.939150.787227L190.97580.8375−3L200.914170.81315−2L210.971100.7912111L220.98260.826104L230.98450.7692621L240.97490.822123L250.919160.809171L260.968110.8374−7L270.947140.8347−7L280.950130.82511−2L290.952120.806186L300.97970.8592−5L310.99330.84130L320.99910.88310L330.98840.82895L340.910180.804202Note: ranking differences are calculated with reference to metafrontier green efficiency.


## 4. 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]. The 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. 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. The 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 high-emission 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.



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*Source: 5634702-2022-05-09.xml*