# How to Evaluate the Efficiency of Green Economy and Its Regional Differences: Evidence from China

Authors: Xin Duan; Miaomiao Tang; Kui Zhang
Journal: Discrete Dynamics in Nature and Society
 (2022)

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## Abstract

Green economy is environmentally friendly economy, which is important for the sustainable economic development and environmental protection. Based on the panel data of 30 provinces and cities in China, a three-stage super-efficient SBM-DEA (slack-based model-data envelopment analysis) model is constructed to evaluate the efficiency of green economy and analyze its regional differences. The results show that, first, the random error factor and external environmental conditions significantly affect the efficiency of green economy. Second, the green economic efficiency in China from 2010 to 2019 is stable and needs to be further improved. Third, through regional comparison, it is found that the green economy efficiency in eastern China is higher than those in central and western China and the green economy efficiency in northeast China is the lowest. Finally, green economy efficiency does not simply depend on the economic development, the regional differences of green economy efficiency results from the combined effects of different geographical resources endowment, different economic development characteristics, and different environmental protection policies in different regions of China. Based on the research findings, corresponding policy suggestions are put forward to improve the efficiency of green economy.


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## Body

## 1. Introduction

Since the reform and opening-up in 1978, China’s economy has grown rapidly, and its economic strength and people’s living standards have improved significantly. However, the economic growth of China used to be characterized by high input, high energy consumption, high emissions, and high pollution. The problems of resource waste and environmental pollution are becoming increasingly prominent, and the green economy is inefficient. With China’s GDP (gross domestic product) exceeding 100 trillion in 2020, it is estimated that the average economic loss of 190 cities caused by environment pollution in China in 2014–2016 was 0.3% of GDP [1]. At the same time, in recent years, the traditional driving force of China’s economy has gradually weakened, and the economic growth rate has shown a downward trend. China urgently needs to transform its economic development model, improve the efficiency of resource utilization, reduce pollution, and reduce social losses caused by environmental pollution. Green development is an important part of high-quality economic development and a necessary requirement to build a high-quality modern economic system [2, 3]. The Chinese government attaches great importance to the development of green economy and proposes to implement the concept of green development. At the same time, with the deepening of regional coordinated development strategy, scientific evaluation of green economic efficiency in different regions of China is the key to better implement the concept of green development. What are the levels about the green economic efficiency in each region of China? What are the characteristics of regional differences? In-depth studying these issues is of practical significance to improve the efficiency of green economy and promote regional coordinated development.This paper is structured as follows: Section2 is the literature review about efficiency of green economy. Section 3 illustrates the methods and data sources, followed by the research results in Section 4. Section 5 presents the conclusions, including policy implications.


## 2. Literature Review

The efficiency of green economy is an important indicator to measure whether economic development is sustainable under the dual pressure of resources and environment. Green economic efficiency was first put forward by Hall in 1989, who believed that economic development should not destroy the ecological environment by blindly pursuing growth of GDP, nor cause economic stagnation by depleting resources, and economic development must be limited within the range that natural resources can bear [4]. In recent years, many scholars have made a similar definition of the concept about green economic efficiency, and its connotation includes economic growth, resource consumption, and environmental pollution [5–7]. At present, the methods to evaluate green economic efficiency mainly include three types.The first type is data envelopment analysis (DEA) of nonparametric method. For example, Yang Qing et al. introduced the comprehensive environmental pollution index on the basis of the traditional DEA model to analyze the provincial green development efficiency in China and studied its evolutionary mechanism [8]. Ho, C-T Ho used hybrid model of GRA-DEA (gray relational data envelopment) to calculate the efficiency of green economy and analyzed the regional differences of the efficiency of green economy from the aspects of technical efficiency and scale efficiency [9]. Some scholars put forward its need to consider the unexpected output when studying the efficiency of green economy. In the early stage, variable or numerical conversion was generally adopted. For example, Scheel calculated the efficiency of green economy by incorporating environmental pollution into output variables [10]. Seiford took the negative number of the undesirable output and converted it to positive indicator through the intermediate number [11]. At present, it is common to consider the negative impact of undesired output on economic growth and introduce the undesired output and expected output into the model research by using slacks-based model (SBM). For example, Chen Fang et al. used “carbon emissions” as single nonexpected output index to measure the green economic efficiency of all provinces in China [12]. Xia Yongqiu et al. used the SBM to calculate China’s green economic efficiency by taking the industrial three wastes emission index as multiple undesired outputs and discovered that the national average annual green economic efficiency was 0.7, yielding an inverted U-shaped evolution process [13]. The second type is SFA (stochastic frontier analysis). Zhang Caiqing and Chen Panyu used the SFA model to measure the panel data of the Yangtze River Economic Belt and found that the overall level of green economic efficiency was in a state of inefficiency [14]. Zhang Sheng et al. took panel data of 21 prefecture-level cities in Guangdong Province as samples and used stochastic frontier model and logarithmic Cobb–Douglas production function to analyze the growth of green economic efficiency [15]. Wu DJ used stochastic frontier model to estimate the efficiency of China’s marine green economy and tested the effects of per capita GDP, urbanization rate, industrial structure, foreign trade, and energy consumption structure on the efficiency of China’s marine green economy [16]. The third category is three-stage DEA model. On the basis of combining the characteristics of parametric method and nonparametric method, the three-stage DEA model is introduced which considers how to separate the random errors in the nonparametric method. Waldhoff S et al. used the three-stage model to study the damage caused by four greenhouse gases such as carbon dioxide and methane to the efficiency value of global green economy [17]. Kupika et al. studied the efficiency of green economy in central Zimbabwe and took the interview results of experts on green economy and climate change as the source data of the second stage of the study; then, the results are more authentic and reliable [18]. Wu MR measured the green technology innovation efficiency of 30 provinces in China from 2008 to 2017 by constructing a three-stage super-efficiency DEA model including undesired output. The study found that the overall performance of regional green technology innovation efficiency in China was poor in the past decade, and there was still a lot of room for improvement [19]. In addition, other methods such as cluster analysis, technique for order preference by similarity to an ideal solution model, and translogarithmic random boundary analysis model are also shown in the literature about green economic efficiency [20–26].


## 3. Research Design

### 3.1. Research Methods

DEA is a nonparametric technical efficiency analysis method first proposed by Charnes et al. which is used to evaluate the relative efficiency of decision-making units with multiple inputs and outputs [27]. Due traditional DEA model has the defect of the input data and output data are enlarged or reduced the same proportion [28]. Tone introduced super-efficiency SBM to remedy this defect, but ignored uncontrollable factors such as external environment and random interference [29]. Fried et al. studied how to introduce environmental factors and random factors into DEA model and proposed three-stage DEA model [30]. Considering the characteristics of statistical data, random error, and the impact of environmental factors, this paper combines DEA model and super-efficiency SBM to establish a three-stage super-efficiency SBM-DEA model.The specific steps are as follows.In the first stage, the super-efficiency SBM is adopted to consider both expected output and unexpected output. The model to calculate the initial efficiency value is shown in(1)ρ=min1/t∑i=1tx¯/xik1/s1+s2∑r=1s1yd¯/yrkd+∑q=1s2yu¯/yqku,Subject  tox¯≥∑j=1≠knxijλj,i=1,…,t,yd¯≥∑i=1+tnyijdλj,r=1,…,Si,yu¯≥∑j=1≠knyqjuλj,q=1,…,S2,λj≥0,j=1,…,n,j≠0,x¯≥xk,i=1,…,t;yd¯≥ykd,r=1,…,S1;yu¯≥yku,q=1,…,S2,where X= (Xy), (i = 1,…,t, j = 1,…,n), 1,…,s; j = 1,…,n), Yd = (y drj), (i = 1,…,s1; j = 1,…,n), Yu = (yuqj), (i = 1,…,s2; j  = 1,…,n). t represents inputs, n represents departments, s represents outputs, S1 represents expected outputs, and S2 represents unexpected outputs. The constant vector λ represents the weight of decision-making unit. P represents the efficiency value.In second stage, in order to exclude the influence of random error and environmental factors, the random frontier SFA method is adopted in the second stage to find out the random errors and environmental factors with the greatest influence. The regression expression of random frontier is shown in(2)Sik=fZi;βk+vik+μik,where i = 1, 2, 3, …, t; k = 1, 2, 3, …, n; and Sik are the slack variable and represent the input difference of the i-th input in the k-th decision unit. Zk is the environment variable. β is the parameter to be estimated corresponding to environmental variables. f (Zi;βk) has a stochastic machine and is used to represent the influence of environmental factors on Sik. Vik stands for random error, roughly normal distribution. Uik represents the inefficiency of management, presenting a truncated normal distribution. Vik and Uik are independent of each other, and Vik + Uik is a mixed error term. According to the values of Vik and Uik, the input index and output index of efficiency value are adjusted, and the adjusted results are shown in(3)Xik∗=Xik+maxfZk;βn^−fZk;βn^+maxvik−vik,Xik is the original input, and the new input value X∗ik is obtained by (3).In the third stage,X∗ik value excluding the influence of environmental and random factors in the second stage is brought into the super-efficiency SBM to calculate the relative efficiency, and the result obtained is more objective and accurate.


### 3.2. Design of Index System

On the basis of comprehensive consideration of the scientific, systematic, and operable selection of indicators, this paper builds an index system of green economy efficiency (see Table1). The index system constructed in this paper consists of input variables, output variables, and external environment variables.Table 1
Index system of green economic efficiency.
Destination layerCriteria layerIndicator name (unit)The input variablesCapital inputCapital stock (100 million yuan)Labor inputTotal number of employed persons (ten thousand)Energy inputWater supply (100 million cu·m)Electricity consumption (100 million kw·h)Land for construction (1000 hectares)The output variableDesirable outputGDP (100 million yuan)Undesirable outputIndustrial wastewater discharge (ten thousand tons)General solid waste emissions (ten thousand tons)Industrial sulfur dioxide emissions (ten thousand tons)The extraneous variableEconomic developmentNatural logarithm of per capital GDP (ten thousand yuan)Self-dependent innovationProportion of technology and education expenditure in GDP (%)Environmental investmentProportion of energy conservation and environmental protection expenditure in GDP (%)Industrial structureProportion of secondary industry in GDP (%)Open door to the outside worldProportion of total imports and exports to GDP (%)


#### 3.2.1. Input Variables

According to the production function, labor, capital, and land are essential inputs, and energy consumption is the main source of nondesired output. This paper takes labor, capital, land, and energy as input factors. Referring to the research of Zeng Gan et al., labor input is expressed by the average annual number of employees per unit, capital input is expressed by the actual capital stock, land input is expressed by built-up area, and energy input is expressed by water supply and total social electricity consumption [26]. Since the data of actual capital stock cannot be obtained directly, this paper uses the perpetual inventory method proposed by Pittman to calculate the capital stock [31]. The calculation formula is as follows: Kt = (1−δ) Kt−1 + It, where Kt and Kt-1 represent the capital stock of period t and t−1, respectively. δ is the depreciation rate. This paper refers to the practice of Zhang Jun et al. [32] and takes δ = 9.6%, It = I0/(δ+ g), I0 is the fixed assets investment in 2005, and g is the average growth rate of new fixed assets in the whole society from 2010 to 2019.


#### 3.2.2. Output Variables

In this paper, output variables are composed by GDP and industrial waste. The expected outputs used include gross domestic product (GDP), industrial added value, total retail sales of social consumer goods, green coverage area of built-up areas, etc. In this paper, GDP is selected as expected output. When measuring output, not only social benefits but also ecological benefits should be considered. In order to avoid single undesired output index and improve the accuracy of measurement results, this paper selects industrial sulfur dioxide emissions, industrial wastewater emissions, and industrial smoke (powder) dust emissions as undesired output.


#### 3.2.3. External Variables

The factors that drive and restrict the efficiency of the green economy focus on several aspects, such as economic development, technology innovation, investment environment, industrial structure, and opening to the outside world on the basis of comprehensive consideration of the scientific, systematic, and operable selection of indicators. In this paper, the per capital GDP, the proportion of technology and education expenditure in GDP, the proportion of environmental protection expenditure in GDP, the proportion of secondary industry in GDP, and the proportion of total import and export in GDP are selected as external variables.


### 3.3. Data Source

The data in this paper are from China Statistical Yearbook (2010–2019), China Environmental Statistical Yearbook(2010–2019), and China Energy Statistical Yearbook (2010–2019). In order to facilitate regional comparison, 30 provinces and cities are divided into eastern region, northeastern region, central region, and western region.


## 3.1. Research Methods

DEA is a nonparametric technical efficiency analysis method first proposed by Charnes et al. which is used to evaluate the relative efficiency of decision-making units with multiple inputs and outputs [27]. Due traditional DEA model has the defect of the input data and output data are enlarged or reduced the same proportion [28]. Tone introduced super-efficiency SBM to remedy this defect, but ignored uncontrollable factors such as external environment and random interference [29]. Fried et al. studied how to introduce environmental factors and random factors into DEA model and proposed three-stage DEA model [30]. Considering the characteristics of statistical data, random error, and the impact of environmental factors, this paper combines DEA model and super-efficiency SBM to establish a three-stage super-efficiency SBM-DEA model.The specific steps are as follows.In the first stage, the super-efficiency SBM is adopted to consider both expected output and unexpected output. The model to calculate the initial efficiency value is shown in(1)ρ=min1/t∑i=1tx¯/xik1/s1+s2∑r=1s1yd¯/yrkd+∑q=1s2yu¯/yqku,Subject  tox¯≥∑j=1≠knxijλj,i=1,…,t,yd¯≥∑i=1+tnyijdλj,r=1,…,Si,yu¯≥∑j=1≠knyqjuλj,q=1,…,S2,λj≥0,j=1,…,n,j≠0,x¯≥xk,i=1,…,t;yd¯≥ykd,r=1,…,S1;yu¯≥yku,q=1,…,S2,where X= (Xy), (i = 1,…,t, j = 1,…,n), 1,…,s; j = 1,…,n), Yd = (y drj), (i = 1,…,s1; j = 1,…,n), Yu = (yuqj), (i = 1,…,s2; j  = 1,…,n). t represents inputs, n represents departments, s represents outputs, S1 represents expected outputs, and S2 represents unexpected outputs. The constant vector λ represents the weight of decision-making unit. P represents the efficiency value.In second stage, in order to exclude the influence of random error and environmental factors, the random frontier SFA method is adopted in the second stage to find out the random errors and environmental factors with the greatest influence. The regression expression of random frontier is shown in(2)Sik=fZi;βk+vik+μik,where i = 1, 2, 3, …, t; k = 1, 2, 3, …, n; and Sik are the slack variable and represent the input difference of the i-th input in the k-th decision unit. Zk is the environment variable. β is the parameter to be estimated corresponding to environmental variables. f (Zi;βk) has a stochastic machine and is used to represent the influence of environmental factors on Sik. Vik stands for random error, roughly normal distribution. Uik represents the inefficiency of management, presenting a truncated normal distribution. Vik and Uik are independent of each other, and Vik + Uik is a mixed error term. According to the values of Vik and Uik, the input index and output index of efficiency value are adjusted, and the adjusted results are shown in(3)Xik∗=Xik+maxfZk;βn^−fZk;βn^+maxvik−vik,Xik is the original input, and the new input value X∗ik is obtained by (3).In the third stage,X∗ik value excluding the influence of environmental and random factors in the second stage is brought into the super-efficiency SBM to calculate the relative efficiency, and the result obtained is more objective and accurate.


## 3.2. Design of Index System

On the basis of comprehensive consideration of the scientific, systematic, and operable selection of indicators, this paper builds an index system of green economy efficiency (see Table1). The index system constructed in this paper consists of input variables, output variables, and external environment variables.Table 1
Index system of green economic efficiency.
Destination layerCriteria layerIndicator name (unit)The input variablesCapital inputCapital stock (100 million yuan)Labor inputTotal number of employed persons (ten thousand)Energy inputWater supply (100 million cu·m)Electricity consumption (100 million kw·h)Land for construction (1000 hectares)The output variableDesirable outputGDP (100 million yuan)Undesirable outputIndustrial wastewater discharge (ten thousand tons)General solid waste emissions (ten thousand tons)Industrial sulfur dioxide emissions (ten thousand tons)The extraneous variableEconomic developmentNatural logarithm of per capital GDP (ten thousand yuan)Self-dependent innovationProportion of technology and education expenditure in GDP (%)Environmental investmentProportion of energy conservation and environmental protection expenditure in GDP (%)Industrial structureProportion of secondary industry in GDP (%)Open door to the outside worldProportion of total imports and exports to GDP (%)


### 3.2.1. Input Variables

According to the production function, labor, capital, and land are essential inputs, and energy consumption is the main source of nondesired output. This paper takes labor, capital, land, and energy as input factors. Referring to the research of Zeng Gan et al., labor input is expressed by the average annual number of employees per unit, capital input is expressed by the actual capital stock, land input is expressed by built-up area, and energy input is expressed by water supply and total social electricity consumption [26]. Since the data of actual capital stock cannot be obtained directly, this paper uses the perpetual inventory method proposed by Pittman to calculate the capital stock [31]. The calculation formula is as follows: Kt = (1−δ) Kt−1 + It, where Kt and Kt-1 represent the capital stock of period t and t−1, respectively. δ is the depreciation rate. This paper refers to the practice of Zhang Jun et al. [32] and takes δ = 9.6%, It = I0/(δ+ g), I0 is the fixed assets investment in 2005, and g is the average growth rate of new fixed assets in the whole society from 2010 to 2019.


### 3.2.2. Output Variables

In this paper, output variables are composed by GDP and industrial waste. The expected outputs used include gross domestic product (GDP), industrial added value, total retail sales of social consumer goods, green coverage area of built-up areas, etc. In this paper, GDP is selected as expected output. When measuring output, not only social benefits but also ecological benefits should be considered. In order to avoid single undesired output index and improve the accuracy of measurement results, this paper selects industrial sulfur dioxide emissions, industrial wastewater emissions, and industrial smoke (powder) dust emissions as undesired output.


### 3.2.3. External Variables

The factors that drive and restrict the efficiency of the green economy focus on several aspects, such as economic development, technology innovation, investment environment, industrial structure, and opening to the outside world on the basis of comprehensive consideration of the scientific, systematic, and operable selection of indicators. In this paper, the per capital GDP, the proportion of technology and education expenditure in GDP, the proportion of environmental protection expenditure in GDP, the proportion of secondary industry in GDP, and the proportion of total import and export in GDP are selected as external variables.


## 3.2.1. Input Variables

According to the production function, labor, capital, and land are essential inputs, and energy consumption is the main source of nondesired output. This paper takes labor, capital, land, and energy as input factors. Referring to the research of Zeng Gan et al., labor input is expressed by the average annual number of employees per unit, capital input is expressed by the actual capital stock, land input is expressed by built-up area, and energy input is expressed by water supply and total social electricity consumption [26]. Since the data of actual capital stock cannot be obtained directly, this paper uses the perpetual inventory method proposed by Pittman to calculate the capital stock [31]. The calculation formula is as follows: Kt = (1−δ) Kt−1 + It, where Kt and Kt-1 represent the capital stock of period t and t−1, respectively. δ is the depreciation rate. This paper refers to the practice of Zhang Jun et al. [32] and takes δ = 9.6%, It = I0/(δ+ g), I0 is the fixed assets investment in 2005, and g is the average growth rate of new fixed assets in the whole society from 2010 to 2019.


## 3.2.2. Output Variables

In this paper, output variables are composed by GDP and industrial waste. The expected outputs used include gross domestic product (GDP), industrial added value, total retail sales of social consumer goods, green coverage area of built-up areas, etc. In this paper, GDP is selected as expected output. When measuring output, not only social benefits but also ecological benefits should be considered. In order to avoid single undesired output index and improve the accuracy of measurement results, this paper selects industrial sulfur dioxide emissions, industrial wastewater emissions, and industrial smoke (powder) dust emissions as undesired output.


## 3.2.3. External Variables

The factors that drive and restrict the efficiency of the green economy focus on several aspects, such as economic development, technology innovation, investment environment, industrial structure, and opening to the outside world on the basis of comprehensive consideration of the scientific, systematic, and operable selection of indicators. In this paper, the per capital GDP, the proportion of technology and education expenditure in GDP, the proportion of environmental protection expenditure in GDP, the proportion of secondary industry in GDP, and the proportion of total import and export in GDP are selected as external variables.


## 3.3. Data Source

The data in this paper are from China Statistical Yearbook (2010–2019), China Environmental Statistical Yearbook(2010–2019), and China Energy Statistical Yearbook (2010–2019). In order to facilitate regional comparison, 30 provinces and cities are divided into eastern region, northeastern region, central region, and western region.


## 4. Results

Green economic efficiency is the comprehensive economic efficiency considering the cost of resources and environment, and it is an important index to measure the level of green development. The evaluation results of green economic efficiency by using three-stage DEA model are more consistent with reality.


### 4.1. SBM Analysis of Initial Super-Efficiency in the First Stage

According to the index system of green economic efficiency (Table1), input and output variables are selected and the super-efficiency SBM is adopted to calculate the efficiency of green economy about 30 provinces and cities in China from 2010 to 2019. The results are in Table 2 and Figure 1.Table 2
Green economic efficiency in all regions from 2010 to 2019.
RegionProvince year2010201120122013201420152016201720182019Eastern ChinaBeijing1.2221.2121.2051.2051.2081.2121.2051.2021.1951.316Tianjin1.1061.0931.0961.0981.1041.0971.1091.0981.0951.000Hebei0.4690.5040.4500.4290.4080.4060.4180.4440.4400.463Shanghai1.0941.0341.0271.0281.0201.0261.0401.0731.0621.041Jiangsu1.0441.0761.0800.6280.5890.6280.6201.0051.0191.040Zhejiang0.5730.6010.5970.5510.5450.5510.6151.0000.6031.025Fujian1.0161.0071.0010.5300.5371.0021.0231.0221.0321.045Shandong0.5910.5890.5650.5370.5250.5170.4990.5170.5061.005Guangdong1.0581.0561.0491.0421.0341.0240.6830.5700.6320.531Hainan0.5710.6100.6000.5410.5420.4700.4600.4700.4310.430Mean0.8740.8780.8670.7590.7510.7930.7670.8400.8010.890Central ChinaShanxi0.4000.4320.3810.3510.3240.3170.3050.3300.3360.270Anhui0.4180.4410.4290.4020.3990.3970.4000.4070.3840.586Jiangxi0.4380.4430.4290.4080.4060.3940.3960.3810.3830.395Henan0.4570.4490.4400.4100.4150.4090.4190.4200.4360.506Hubei0.5000.5060.5140.4750.4670.4850.5050.4880.4901.019Hunan0.5560.5850.6131.0061.0041.0151.0201.0171.0101.017Mean0.4620.4760.4680.5090.5020.5030.5080.5070.5070.632Northeastern ChinaLiaoning0.4600.4570.4600.4360.4250.4250.3060.3230.3400.303Jilin1.0041.0090.4611.0061.0051.0071.0000.4070.3900.246Heilongjiang0.4230.4330.4140.3970.4010.3780.3530.3350.3240.235Mean0.6290.6330.4450.6130.6100.6030.5530.3550.3510.261Western ChinaInner Mongolia0.5081.0301.0381.0331.0221.0130.4150.3280.3380.355Guangxi0.3950.4370.4200.4020.4010.4080.4090.3650.3540.317Chongqing0.4350.4630.4930.4660.4790.4820.5220.5140.4741.020Sichuan0.4560.4750.4950.4690.4650.4480.4630.4550.4510.601Guizhou0.3360.3390.3470.3510.3520.3790.3960.3780.3780.398Yunnan0.3530.3410.3530.3720.3610.3680.3590.3530.3440.572Shanxi1.0081.0221.0100.4890.4810.4590.4390.4380.4510.440Gansu0.3080.3130.3080.2890.2720.2570.2410.2310.2400.212Ningxia0.2560.2750.2690.2570.2460.2470.2540.2530.2580.236Qinghai0.3210.3340.3370.3140.3090.3050.2980.2870.2940.250Xinjiang0.3090.3070.2940.2730.2630.2480.2280.2260.2380.235Mean0.4260.4850.4880.4290.4230.4200.3660.3480.3470.421NationwideMean0.6000.6300.6010.5740.5680.5790.5470.5410.5270.597Figure 1
The variation of green economic efficiency in different regions from 2010 to 2019.From Table2 and Figure 1, there are obvious regional differences in China’s green economy efficiency from 2010 to 2019, the eastern region has the highest green economy efficiency, with an average efficiency level of 0.822, the green economic efficiency in central China is 0.507, the average value of green economic efficiency in northeast China is 0.505, and western China has the lowest green economic efficiency, with an average of 0.415. This is because the eastern region is at the forefront of China's reform and opening up. Its unique geographical advantages and good policies given to the eastern region by the central government have made its economic development in a leading position. In addition to technology and education, capital and other elements gathered have promoted the economic transformation and upgrading in the eastern region, so the green economic efficiency is much higher than other area. The central region and the western region benefit from the strategy of western development and the rise of the central region. After accepting the industrial transfer from the east region, the economic production efficiency is greatly improved. Moreover, most of the industries are pollution industries, so there is big gap in green economic efficiency between central region, western region, and eastern region. The economic level of northeast region was once in the forefront of the country. However, in recent years, its economic structure problems have been exposed continuously, and the lack of cultivation of new economic industries has led to a sustained downturn in economic development. As a result, its green economic efficiency has declined rapidly and has been surpassed by the central region and western region.


### 4.2. SFA Regression Analysis in the Second Stage

In second stage, the relaxation variable of the input index calculated from the super-efficiency SBM in the first stage was taken as the dependent variable and the external environmental variables. In Table1, they were taken as the independent variables to establish the SFA regression model. The results are listed in Table 3.Table 3
Second-stage random frontier regression results.
Real capital stockNumber of employed personsTotal water supplyTotal electricityBuilt-up areaConstant term−12.383 (−1.269)14.022∗∗∗ (3.317)216.090∗∗∗ (4.291)393.651 (1.331)527.305∗∗∗ (4.737)Ln (PGDP)6.102∗∗∗ (2.692)−6.278∗∗∗ (−5.258)−50.192∗∗∗ (−3.316)198.886∗∗ (1.997)−75.046∗∗ (−1.991)Expenditure on technology and education share of GDP58.311∗∗∗ (3.367)−42.968∗∗∗ (−3.559)−214.090∗ (−1.729)241.913 (0.255)−340.536∗∗ (−1.979)Expenditure on energy conservation and environmental protection share of GDP58.186 (0.871)−127.887∗∗∗ (−2.942)−1318.317∗∗∗ (−2.931)−3171.728∗∗∗ (−3.085)−3302.647∗∗∗ (−2.664)The second industry share of GDP−113.504∗∗∗ (−9.851)17.128∗∗∗ (3.042)−61.826 (−0.956)−1248.703∗∗∗ (−2.825)−587.677∗∗∗ (−3.539)Total import and export share of GDP21.690∗∗∗ (4.235)−0.505 (−0.209)−137.415∗∗∗ (−3.450)−832.836∗∗∗ (−3.447)−108.409 (−1.141)σσσ2222337.279∗∗∗ (3.173)56.104∗∗∗ (5.105)28005.398∗∗∗ (15442.383)707671.550∗∗∗ (37838.040)222112.090∗∗∗ (89727.844)γγγ0.978∗∗∗ (135.076)0.579∗∗∗ (4.471)0.901∗∗∗ (105.085)0.778∗∗∗ (40.306)0.916∗∗∗ (120.750)The log function value−1085.726−952.783−1664.048−2266.027−1960.665LR unilateral check value145.28839.257348.971172.724368.040Note.∗∗∗, ∗∗, and ∗ show significance at the 1% level, 5% level, and 10% level, respectively.It can be found from Table3 firstly the relationship between economic development and capital, labor, energy, and land is significant. The increase in labor, water supply, and land inputs can promote the economic development. Capital investment is not conducive to the level of economic development, but it is consistent with the actual situation of the current transformation development in China. At present, China’s economy has not completely transformed into a green economic development model, which is basically driven by the supply of land and high consumption of water. Secondly, the improvement of technology and education can promote the utilization rate of labor force, water supply, and land factors. Thirdly, except for the negative impact of environmental investment on capital factors, environmental investment has positive impact on employed persons, total water supply, total electricity, and built-up area, and it shows that the increase of energy conservation and environmental protection expenditure can improve ecological environment, reduce pollutant emissions, improve energy utilization rate, increase energy conversion, and promote the efficiency of green economic development. Fourth, the industrial structure can promote the input of capital, energy, and land factors, and this shows that the development of China’s secondary industry has not been free from the dependence on energy consumption, land, and capital. At the same time, in recent years, the intelligent level of China’s secondary industry has been improved, and the demand for human capital has been weakening. Finally, the coefficient of capital investment relaxation caused by opening to the outside world is positive, which also indicates that capital is waste and more redundancy is generated in the process of capital introduction by opening to the outside world. The regression coefficient of the investment relaxation on land and energy is negative, which indicate that the improvement of the level of opening-up not only increases the consumption of land and energy, but also promotes employment.In conclusion, there are differences in the influential factors of economic efficiency in different regions and the direction and magnitude of their influence, which can lead to deviations in the assessment of the efficiency of the green economy. Therefore, it is necessary to eliminate the influence of environmental variables and recalculate green economy efficiency.


### 4.3. Efficiency Analysis after Input Adjustment in the Third Stage

After adjusting the original input value, the input data and original output data after eliminated random errors and environmental variables are substituted into the super-efficiency SBM again. The calculation results are listed in Table4.Table 4
Green economic efficiency in all regions from 2010 to 2019.
RegionProvince year2010201120122013201420152016201720182019Eastern ChinaBeijing1.2221.2121.2051.2051.2081.2121.2051.2021.1951.316Tianjin0.5760.6051.0111.0171.0221.0181.0020.5960.5670.271Hebei1.0021.0051.0111.0051.0000.5500.5421.0361.0070.427Shanghai1.0761.0191.0141.0220.7530.7391.0181.0631.0561.030Jiangsu1.0411.0551.0671.0271.0181.0241.0261.0371.0351.058Zhejiang1.0141.0091.0111.0061.0021.0161.0181.0161.0141.012Fujian0.5650.5150.5730.6571.0060.6281.0030.6641.0051.016Shandong1.0881.0811.0861.0911.0781.0901.0821.0821.0691.015Guangdong1.0791.0701.0661.0721.0591.0501.0521.0571.0541.048Hainan0.1920.2100.2180.2170.2230.2110.2100.2060.1960.179Mean0.8860.8780.9260.9320.9370.8540.9160.8960.9200.837Central ChinaShanxi0.3460.3720.3700.3540.3410.3520.3190.3330.3390.293Anhui0.4220.4200.4430.4760.4890.4690.4440.4620.4590.503Jiangxi0.3670.3640.3830.4090.4250.4060.3810.3790.3790.374Henan0.6270.6460.6520.6241.0070.6081.0010.6680.7340.594Hubei0.5010.4820.5180.5750.5810.5900.6080.6010.6771.011Hunan0.4950.5120.5490.5701.0031.0111.0231.0031.0020.582Mean0.4600.4660.4860.5010.6410.5730.6290.5740.5980.559Northeastern ChinaLiaoning0.5940.5530.5810.6220.5990.5690.3920.3950.3860.340Jilin0.3520.3380.3840.3860.3840.3680.3800.3510.3410.231Heilongjiang0.3740.3510.3550.3830.3940.3650.3250.3270.3260.240Mean0.4400.4140.4400.4640.4590.4340.3660.3570.3510.270Western ChinaInner Mongolia0.4470.4341.0140.5090.4470.4150.4220.3410.3340.291Guangxi0.3270.3600.3690.4040.4170.4190.3940.3540.3580.334Chongqing0.3500.3800.4370.4540.4590.4590.4790.4780.4560.434Sichuan0.5610.5540.6220.7150.6230.5921.0070.6070.6461.006Guizhou0.2830.2610.2900.3280.3340.3560.3680.3660.3620.334Yunnan0.3470.3160.3530.4020.4090.3950.3550.3750.3730.414Shanxi0.4280.4341.0040.5440.6130.4880.4550.4750.4870.407Gansu0.2220.2080.2300.2490.2540.2390.2090.2100.2130.204Ningxia0.0870.0950.1030.1060.1100.1130.1160.1110.1080.103Qinghai0.0840.0900.0970.1000.1100.1080.1030.1030.1050.099Xinjiang0.2180.2090.2200.2320.2420.2320.2070.2150.2210.225Mean0.3050.3040.4310.3680.3650.3470.3740.3310.3330.350NationwideMean0.5410.5360.6040.5890.6180.5680.6010.5670.5800.541Overall, as shown in Table4 and Figure 2, the efficiency value in the third stage compared with efficiency value calculated in the first stage has significant changed, indicating that external environmental factors and random factors can promote the efficiency of green economy. The adjusted efficiency value from 2010 to 2019 is more stable, which is different from the large fluctuation of the efficiency value in the first stage. It shows that thanks to the gradual improvement and implementation of the national green economic efficiency policy, the continuous increase of environmental protection input, and the gradual enhancement of residents’ environmental awareness, the green economic efficiency develops steadily. In addition, the green economic efficiency in the third stage of each province and city has changed greatly from 2010 to 2019, and the regional imbalance shows that green economic efficiency is highest in the eastern region, second in the central region, third in the northeast region, and lowest in the western region. It is concluded that geographical advantage plays an important role in the efficiency of green economy. Beijing, Tianjin, the Yangtze River Delta, and the Pearl River Delta serve as “leading regions.” The province of Jiangxi, Chongqing, Gansu, and Guizhou has the function of connecting the east region with the west region, connecting the north region with the south region. The northwest region and northeast region are marginal regions with the lowest green economic efficiency. Secondly, the efficiencies of green economy in different regions are influenced by a variety of factors, and differences of geographical environment and economic development have significant effect.Figure 2
Average change of efficiency in the third stage from 2010 to 2019.


## 4.1. SBM Analysis of Initial Super-Efficiency in the First Stage

According to the index system of green economic efficiency (Table1), input and output variables are selected and the super-efficiency SBM is adopted to calculate the efficiency of green economy about 30 provinces and cities in China from 2010 to 2019. The results are in Table 2 and Figure 1.Table 2
Green economic efficiency in all regions from 2010 to 2019.
RegionProvince year2010201120122013201420152016201720182019Eastern ChinaBeijing1.2221.2121.2051.2051.2081.2121.2051.2021.1951.316Tianjin1.1061.0931.0961.0981.1041.0971.1091.0981.0951.000Hebei0.4690.5040.4500.4290.4080.4060.4180.4440.4400.463Shanghai1.0941.0341.0271.0281.0201.0261.0401.0731.0621.041Jiangsu1.0441.0761.0800.6280.5890.6280.6201.0051.0191.040Zhejiang0.5730.6010.5970.5510.5450.5510.6151.0000.6031.025Fujian1.0161.0071.0010.5300.5371.0021.0231.0221.0321.045Shandong0.5910.5890.5650.5370.5250.5170.4990.5170.5061.005Guangdong1.0581.0561.0491.0421.0341.0240.6830.5700.6320.531Hainan0.5710.6100.6000.5410.5420.4700.4600.4700.4310.430Mean0.8740.8780.8670.7590.7510.7930.7670.8400.8010.890Central ChinaShanxi0.4000.4320.3810.3510.3240.3170.3050.3300.3360.270Anhui0.4180.4410.4290.4020.3990.3970.4000.4070.3840.586Jiangxi0.4380.4430.4290.4080.4060.3940.3960.3810.3830.395Henan0.4570.4490.4400.4100.4150.4090.4190.4200.4360.506Hubei0.5000.5060.5140.4750.4670.4850.5050.4880.4901.019Hunan0.5560.5850.6131.0061.0041.0151.0201.0171.0101.017Mean0.4620.4760.4680.5090.5020.5030.5080.5070.5070.632Northeastern ChinaLiaoning0.4600.4570.4600.4360.4250.4250.3060.3230.3400.303Jilin1.0041.0090.4611.0061.0051.0071.0000.4070.3900.246Heilongjiang0.4230.4330.4140.3970.4010.3780.3530.3350.3240.235Mean0.6290.6330.4450.6130.6100.6030.5530.3550.3510.261Western ChinaInner Mongolia0.5081.0301.0381.0331.0221.0130.4150.3280.3380.355Guangxi0.3950.4370.4200.4020.4010.4080.4090.3650.3540.317Chongqing0.4350.4630.4930.4660.4790.4820.5220.5140.4741.020Sichuan0.4560.4750.4950.4690.4650.4480.4630.4550.4510.601Guizhou0.3360.3390.3470.3510.3520.3790.3960.3780.3780.398Yunnan0.3530.3410.3530.3720.3610.3680.3590.3530.3440.572Shanxi1.0081.0221.0100.4890.4810.4590.4390.4380.4510.440Gansu0.3080.3130.3080.2890.2720.2570.2410.2310.2400.212Ningxia0.2560.2750.2690.2570.2460.2470.2540.2530.2580.236Qinghai0.3210.3340.3370.3140.3090.3050.2980.2870.2940.250Xinjiang0.3090.3070.2940.2730.2630.2480.2280.2260.2380.235Mean0.4260.4850.4880.4290.4230.4200.3660.3480.3470.421NationwideMean0.6000.6300.6010.5740.5680.5790.5470.5410.5270.597Figure 1
The variation of green economic efficiency in different regions from 2010 to 2019.From Table2 and Figure 1, there are obvious regional differences in China’s green economy efficiency from 2010 to 2019, the eastern region has the highest green economy efficiency, with an average efficiency level of 0.822, the green economic efficiency in central China is 0.507, the average value of green economic efficiency in northeast China is 0.505, and western China has the lowest green economic efficiency, with an average of 0.415. This is because the eastern region is at the forefront of China's reform and opening up. Its unique geographical advantages and good policies given to the eastern region by the central government have made its economic development in a leading position. In addition to technology and education, capital and other elements gathered have promoted the economic transformation and upgrading in the eastern region, so the green economic efficiency is much higher than other area. The central region and the western region benefit from the strategy of western development and the rise of the central region. After accepting the industrial transfer from the east region, the economic production efficiency is greatly improved. Moreover, most of the industries are pollution industries, so there is big gap in green economic efficiency between central region, western region, and eastern region. The economic level of northeast region was once in the forefront of the country. However, in recent years, its economic structure problems have been exposed continuously, and the lack of cultivation of new economic industries has led to a sustained downturn in economic development. As a result, its green economic efficiency has declined rapidly and has been surpassed by the central region and western region.


## 4.2. SFA Regression Analysis in the Second Stage

In second stage, the relaxation variable of the input index calculated from the super-efficiency SBM in the first stage was taken as the dependent variable and the external environmental variables. In Table1, they were taken as the independent variables to establish the SFA regression model. The results are listed in Table 3.Table 3
Second-stage random frontier regression results.
Real capital stockNumber of employed personsTotal water supplyTotal electricityBuilt-up areaConstant term−12.383 (−1.269)14.022∗∗∗ (3.317)216.090∗∗∗ (4.291)393.651 (1.331)527.305∗∗∗ (4.737)Ln (PGDP)6.102∗∗∗ (2.692)−6.278∗∗∗ (−5.258)−50.192∗∗∗ (−3.316)198.886∗∗ (1.997)−75.046∗∗ (−1.991)Expenditure on technology and education share of GDP58.311∗∗∗ (3.367)−42.968∗∗∗ (−3.559)−214.090∗ (−1.729)241.913 (0.255)−340.536∗∗ (−1.979)Expenditure on energy conservation and environmental protection share of GDP58.186 (0.871)−127.887∗∗∗ (−2.942)−1318.317∗∗∗ (−2.931)−3171.728∗∗∗ (−3.085)−3302.647∗∗∗ (−2.664)The second industry share of GDP−113.504∗∗∗ (−9.851)17.128∗∗∗ (3.042)−61.826 (−0.956)−1248.703∗∗∗ (−2.825)−587.677∗∗∗ (−3.539)Total import and export share of GDP21.690∗∗∗ (4.235)−0.505 (−0.209)−137.415∗∗∗ (−3.450)−832.836∗∗∗ (−3.447)−108.409 (−1.141)σσσ2222337.279∗∗∗ (3.173)56.104∗∗∗ (5.105)28005.398∗∗∗ (15442.383)707671.550∗∗∗ (37838.040)222112.090∗∗∗ (89727.844)γγγ0.978∗∗∗ (135.076)0.579∗∗∗ (4.471)0.901∗∗∗ (105.085)0.778∗∗∗ (40.306)0.916∗∗∗ (120.750)The log function value−1085.726−952.783−1664.048−2266.027−1960.665LR unilateral check value145.28839.257348.971172.724368.040Note.∗∗∗, ∗∗, and ∗ show significance at the 1% level, 5% level, and 10% level, respectively.It can be found from Table3 firstly the relationship between economic development and capital, labor, energy, and land is significant. The increase in labor, water supply, and land inputs can promote the economic development. Capital investment is not conducive to the level of economic development, but it is consistent with the actual situation of the current transformation development in China. At present, China’s economy has not completely transformed into a green economic development model, which is basically driven by the supply of land and high consumption of water. Secondly, the improvement of technology and education can promote the utilization rate of labor force, water supply, and land factors. Thirdly, except for the negative impact of environmental investment on capital factors, environmental investment has positive impact on employed persons, total water supply, total electricity, and built-up area, and it shows that the increase of energy conservation and environmental protection expenditure can improve ecological environment, reduce pollutant emissions, improve energy utilization rate, increase energy conversion, and promote the efficiency of green economic development. Fourth, the industrial structure can promote the input of capital, energy, and land factors, and this shows that the development of China’s secondary industry has not been free from the dependence on energy consumption, land, and capital. At the same time, in recent years, the intelligent level of China’s secondary industry has been improved, and the demand for human capital has been weakening. Finally, the coefficient of capital investment relaxation caused by opening to the outside world is positive, which also indicates that capital is waste and more redundancy is generated in the process of capital introduction by opening to the outside world. The regression coefficient of the investment relaxation on land and energy is negative, which indicate that the improvement of the level of opening-up not only increases the consumption of land and energy, but also promotes employment.In conclusion, there are differences in the influential factors of economic efficiency in different regions and the direction and magnitude of their influence, which can lead to deviations in the assessment of the efficiency of the green economy. Therefore, it is necessary to eliminate the influence of environmental variables and recalculate green economy efficiency.


## 4.3. Efficiency Analysis after Input Adjustment in the Third Stage

After adjusting the original input value, the input data and original output data after eliminated random errors and environmental variables are substituted into the super-efficiency SBM again. The calculation results are listed in Table4.Table 4
Green economic efficiency in all regions from 2010 to 2019.
RegionProvince year2010201120122013201420152016201720182019Eastern ChinaBeijing1.2221.2121.2051.2051.2081.2121.2051.2021.1951.316Tianjin0.5760.6051.0111.0171.0221.0181.0020.5960.5670.271Hebei1.0021.0051.0111.0051.0000.5500.5421.0361.0070.427Shanghai1.0761.0191.0141.0220.7530.7391.0181.0631.0561.030Jiangsu1.0411.0551.0671.0271.0181.0241.0261.0371.0351.058Zhejiang1.0141.0091.0111.0061.0021.0161.0181.0161.0141.012Fujian0.5650.5150.5730.6571.0060.6281.0030.6641.0051.016Shandong1.0881.0811.0861.0911.0781.0901.0821.0821.0691.015Guangdong1.0791.0701.0661.0721.0591.0501.0521.0571.0541.048Hainan0.1920.2100.2180.2170.2230.2110.2100.2060.1960.179Mean0.8860.8780.9260.9320.9370.8540.9160.8960.9200.837Central ChinaShanxi0.3460.3720.3700.3540.3410.3520.3190.3330.3390.293Anhui0.4220.4200.4430.4760.4890.4690.4440.4620.4590.503Jiangxi0.3670.3640.3830.4090.4250.4060.3810.3790.3790.374Henan0.6270.6460.6520.6241.0070.6081.0010.6680.7340.594Hubei0.5010.4820.5180.5750.5810.5900.6080.6010.6771.011Hunan0.4950.5120.5490.5701.0031.0111.0231.0031.0020.582Mean0.4600.4660.4860.5010.6410.5730.6290.5740.5980.559Northeastern ChinaLiaoning0.5940.5530.5810.6220.5990.5690.3920.3950.3860.340Jilin0.3520.3380.3840.3860.3840.3680.3800.3510.3410.231Heilongjiang0.3740.3510.3550.3830.3940.3650.3250.3270.3260.240Mean0.4400.4140.4400.4640.4590.4340.3660.3570.3510.270Western ChinaInner Mongolia0.4470.4341.0140.5090.4470.4150.4220.3410.3340.291Guangxi0.3270.3600.3690.4040.4170.4190.3940.3540.3580.334Chongqing0.3500.3800.4370.4540.4590.4590.4790.4780.4560.434Sichuan0.5610.5540.6220.7150.6230.5921.0070.6070.6461.006Guizhou0.2830.2610.2900.3280.3340.3560.3680.3660.3620.334Yunnan0.3470.3160.3530.4020.4090.3950.3550.3750.3730.414Shanxi0.4280.4341.0040.5440.6130.4880.4550.4750.4870.407Gansu0.2220.2080.2300.2490.2540.2390.2090.2100.2130.204Ningxia0.0870.0950.1030.1060.1100.1130.1160.1110.1080.103Qinghai0.0840.0900.0970.1000.1100.1080.1030.1030.1050.099Xinjiang0.2180.2090.2200.2320.2420.2320.2070.2150.2210.225Mean0.3050.3040.4310.3680.3650.3470.3740.3310.3330.350NationwideMean0.5410.5360.6040.5890.6180.5680.6010.5670.5800.541Overall, as shown in Table4 and Figure 2, the efficiency value in the third stage compared with efficiency value calculated in the first stage has significant changed, indicating that external environmental factors and random factors can promote the efficiency of green economy. The adjusted efficiency value from 2010 to 2019 is more stable, which is different from the large fluctuation of the efficiency value in the first stage. It shows that thanks to the gradual improvement and implementation of the national green economic efficiency policy, the continuous increase of environmental protection input, and the gradual enhancement of residents’ environmental awareness, the green economic efficiency develops steadily. In addition, the green economic efficiency in the third stage of each province and city has changed greatly from 2010 to 2019, and the regional imbalance shows that green economic efficiency is highest in the eastern region, second in the central region, third in the northeast region, and lowest in the western region. It is concluded that geographical advantage plays an important role in the efficiency of green economy. Beijing, Tianjin, the Yangtze River Delta, and the Pearl River Delta serve as “leading regions.” The province of Jiangxi, Chongqing, Gansu, and Guizhou has the function of connecting the east region with the west region, connecting the north region with the south region. The northwest region and northeast region are marginal regions with the lowest green economic efficiency. Secondly, the efficiencies of green economy in different regions are influenced by a variety of factors, and differences of geographical environment and economic development have significant effect.Figure 2
Average change of efficiency in the third stage from 2010 to 2019.


## 5. Conclusions

By using the three-stage super-efficiency SBM-DEA model and constructing the index system of green economic efficiency, this paper evaluates the green economic efficiency of China from 2010 to 2019 and analyzes its regional differences. The conclusions are drawn. Firstly, random error factors and external environmental conditions can significantly impact on the efficiency of China’s green economy and they can promote the efficiency of green economy. Although economic development can improve the utilization rate of labor force and energy, the investment of capital factors is not conducive to the development of economy, leading to a result that it is easy to produce a lot of redundancy. Industrial structure can enhance the demand for capital and increase consumption of energy and land. Technology and education have positive effect on the utilization rate of land, labor, and energy, but negative effect on capital. Secondly, excluding random error and external environment, the efficiency of China’s green economy rose steadily from 2010 to 2019. Third, from the perspective of regional differences, green economic efficiency in the eastern region is higher than that in the central and western regions, with the lowest in the northeast region. The province of Beijing, Guangdong, and Shandong has the highest green economic efficiency, and the province of Ningxia, Qinghai, and Hainan has the lowest green economic efficiency; in addition, the green economic efficiency of developed regions is not necessarily high. These regional differences are mainly due to the joint effects of different geographical resources endowments, different economic development characteristics, and different environmental protection policies.Based on the research findings, the policy suggestions are proposed. First, strengthen technology and education investment to enhance the development of technology and education, and the development of technology and education is not only beneficial to the transformation and upgrading of economic development, and to create more employment opportunities. Second, further speed up opening to the outside world and strengthen the capital investment in the field of environmental protection, which is beneficial to the transformation of economic development, and develop green economy. Third, allocate economic resources appropriately and bridge the development gap in different regions.



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*Source: 4902406-2022-09-23.xml*