City Green Economy Evaluation: Empirical Evidence from 15 Sub-Provincial Cities in China

City green economy plays an important role in the development of low-carbon economy and the achievement of sustainable development of economy, society and ecological environment. From the perspective of economy, society, environment and resources, the evaluation of the green economy in urban areas tends to offer us a new insight into the green economy of cities. This paper is about the creation of a novel urban green economy evaluation model and its application. First of all, we established a city green economy evaluation index system based on R cluster analysis and coefficient of variation. Secondly, based on the nonlinear weighted utilizing entropy weight method, a city green economy evaluation model is established based on inferior constraints. Thirdly, by comparing the differences between evaluation rankings under inferior constraints and non-inferior constraints, the advantageous factors and the disadvantageous ones in urban green economy development are obtained. The proposed model has been verified with the data on 15 sub-provincial cities in China. Empirical analysis results show that: (1) The proposed approach can accurately find out the advantageous and disadvantageous factors for each sub-provincial city; (2) In the evaluation of green economy development, the order of importance of the three criterion layers is X1 Economy development > X2 Social livelihood of the people > X3 Resources and environment; (3) Local governments should implement differential, reasonable policies in order to improve their green economy development. Moreover, our research is not only significant for developing green economy in China’s sub-provincial cities, but also serves as a reference for the development of green economy in other cities in the world.


Introduction
The development of green economy is an inevitable choice for the sustainable development of economy, society and ecological environment [1,2]. Green economy development is needed to alleviate the conflict among economic development and energy consumption, resource utilization and the environmental protection [3,4]. In order to promote green economy development worldwide, many international authority organizations have developed a variety of green economy development policies [5][6][7][8][9]. At the same time, the Chinese government also puts forward a proposal that everyone should firmly establish and implement the green economy development concepts of innovation, coordination, green, open, shared during the thirteenth five-year period [10]. Under this background, the city green economy evaluation is urgent need of extracting the advantageous factors and the bottleneck factors in green economy development, which can help the authorities to make or adjust corresponding green economy development policies. during 2005-2020 by using standard system dynamic models [25]. In order to assess agricultural sustainability development level, Wang et al. established an evaluation system including agricultural economic profitability and environmental sustainability [26]. Chen et al. calculated the indices' weights by using the AHP method, and then established an industrial green development evaluation model. Empirical results by using the data on China's 30 provinces concluded that China's industrial green development level has the characteristic of typical regional differentiation with a ladder-like distribution from the east and middle to the west [27]. Wang et al. measured Dalian's level of green industry development from three aspects of green production, green consumption and green environment and constructed a green industry evaluation model by using the fuzzy control method to assess the level of Dalian's green industry development [28]. Nalan et al. assessed the green economy development conditions in Turkey. The study showed that Turkey also had a large potential for renewable energies, and most policy-makers, potential consumers and energy firm managers lacked the knowledge about renewable energy technologies [29]. Liang et al. created an index system to evaluate the performance of the low-carbon industry by using an expert scoring method [30]. Chi et al. proposed a path selection model for green city by utilizing scenarios analysis method. By taking Dalian as an example, empirical results showed that weak intervention scenario was the optimal industrial development path of the twelfth five-year plan for Dalian [31]. Mundaca et al. used an indicator-based method to evaluate the progress with respect to social-economic, energy and environmental issues derived from RE stimulus programs linked to the American Reinvestment and Recovery Act. The evaluation results showed that stimulus programs had a positive effect on the RE sector [32].
The above studies have made great progress in illustrating the depth and breadth of research on associated green development issues. However, research on city green economy development issues is still insufficient. Current research must be improved in at least two aspects. First of all, most of the current index systems focus on evaluating sustainable development or green industry development. There is still no authoritative evaluation index system of city green economy development. Secondly, during the comprehensive evaluation of green economy, most evaluation models are designed to solve the assessment ranking problems, but they cannot be used to find out the advantageous factors and the disadvantageous factors influencing city green economy development.
To fill in the above gaps, our study advances in three aspects. First, this paper creates a novel city green economy evaluation model by introducing the inferior constraint fuzzy comprehensive evaluation method into city green economy evaluation. The proposed model not only can calculate the evaluation ranking of city green economy development, but also can find out the advantageous and disadvantageous factors of city green economy development. Second, we propose that economy, society, environment and resources should be taken into account in city green economy development assessment. Then we establish an evaluation index system of city green economy development by combining R cluster analysis with coefficient of variation quantitative reduction approaches. The index system includes 23 indicators, which involves three criterion layers: X 1 Economic development, X 2 Social livelihood of the people and X 3 Resources and environment. Third, using the green economy development data on 15 sub-provincial cities in China, empirical results present the corresponding advantageous and disadvantageous factors for each sub-provincial city. The study can help the authorities to make or adjust corresponding green economy policies.
The rest of the paper is organized as follows. Section 2 introduces the design and methodology of this study. Section 3 presents the data and empirical analysis of our green economy evaluation model for 15 sub-provincial cities in China. Section 4 is the conclusions and future work.

Index Explainations of the Evaluation System
Evaluation index system of city green economy development should be based on fundamental principles, such as low-carbon, resource efficient, socially inclusive, comprehensive, coordinated, sustainable development and data accessibility. Through investigating the literature and combining these high frequency indicators of international authoritative organizations [5][6][7][8][9][10][12][13][14][15][16][17][18][19], the established first criteria layer is comprised of X 1 Economic development, X 2 Social livelihood of the people and X 3 Resources and environment. On this basis, a mass-election evaluation index system composed of six secondary criteria layers and 82 tertiary indices are created, as shown in Table 1. The detailed index set and its explanation are presented in Appendix Table A1. Table 1. Index reduction process of green economy evaluation.  The assessment of city green economy development should give full consideration to the unification of economic development speed, benefits and structure. Especially in the process of current Chinese economic development, economic growth and green transformation are equally important [33]. Out of the above considerations, two aspects of the indices X 1 1 Economic growth and X 11 1 Economy structure are designed under the first criteria layer X 1 Economic development. (1) In order to evaluate the contribution degree of the primary industry, secondary industry, and tertiary industry to city's economic development, nine indices are established, such as X 1,2 Per capita GDP, X 1,7 Value added of the tertiary sector and X 1,9 Value added of the construction industry. The three indices of X 1,4 Government revenue, X 1,10 Budgetary revenue of local government and X 1,12 Total investment in fixed assets are used to assess the city's fiscal revenue and investment situation. To evaluate the city's financial industry development, three indices are developed, they are X 1,18 Balance of loans and deposit in RMB and foreign currencies in financial institutions, X 1,19 Balance of loans in RMB and foreign currencies in financial institutions and X 1,23 Value added of the financial industry. Statistics from the National Development and Reform Commission show that logistics industrial has become one of the pillar industries in economic development [34]. To assess the contribution degree of logistics industry on Chinese sub-provincial city economic development, four indices are presented, i.e., X 1,20 Freight volume, X 1,21 Airport passenger throughput, X 1,22 Freight turnover and X 1,24 Added value of the logistics industry. Under the second criterion layer of X 1 1 Economic growth, there are five other indices are designed to describe the impact of merchandise trade on economic growth, such as X 1,15 Total retail sales of consumer goods; (2) Since the reform and opening, China's rapid economic development has made remarkable achievements. At the meantime, China's ecological environment and consumption of energy and resources have paid a heavy price. The economic green transformation and upgrading is the inevitable choice for the sustainable development of China's economy. Based on the above considerations, five parts of the indices are designed under the criterion layer of X 11 1 Economic structure. The proportions of the primary industry, secondary industry, and tertiary industry to GDP are used to evaluate the economic restructuring development level, such as X 1,25 The ratio of the added value of the primary sector to GDP, X 1,27 The ratio of industrial added value to GDP and X 1,28 The ratio of the added value of the tertiary industry to GDP. X 1,31 The ratio of private economic value added to GDP reveals the contribution degree of private economy to the regional economy development. X 1,32 The ratio of county economic aggregate to GDP reflects the development of the county economic sector. X 1,33 The ratio of value added of financial industry to GDP indicates the contribution degree of financial industry to the regional economy development. X 1,34 The ratio of logistics industry added value to GDP reflects the impact of the logistics industry on Chinese sub-provincial city economic development. X 2 Social livelihood of the people criteria: The ultimate purpose of economic development is to achieve a better quality of life and improve people's welfare. In the criterion layer of X 2 Social livelihood of the people, two areas are considered: X 1 2 People's livelihood improvement and X 11 2 Social undertakings. (1) In the evaluation of people's livelihood improvement, income distribution, health care, employment and population situation should be considered. The income distribution is measured by five indices, such as X 2,5 Per capita disposable annual income of urban households and X 2,8 The average annual growth rate of per capita disposable income of urban households. The health care is evaluated utilizing six indices, for instance X 2,10 Number of basic endowment insurance urban contributors and X 2,15 Number of beds in hospitals (10,000 units). X 2,3 Registered unemployment rate in cities and towns and X 2,4 Annual new employment in cities and towns are used to assess the city's employment level. The two indices of X 2,1 Census register population and X 2,2 Natural population growth rate are developed to assess the population situation; (2) Regarding the social undertakings, three parts of indices are designed: basic education, food safety and social security. The five indices are used to evaluate the basic education level of the sub-provincial cities, such as X 2, 16 The ratio of government expenditure on education to general budget expenditure and X 2,20 High school education gross enrollment ratio. X 2,21 Acceptance rate of foodstuffs sample survey is developed to assess the food safety status. The other four indices are presented to assess the city's social security level, such as X 2,22 Number of public transportation vehicles per 10,000 persons (District) and X 2,23 Daily supply of tap water. X 3 Resources and environment criteria: To consider low-carbon, resource efficient and environmentally friendly, a resource and environment index is designed from two parts: X 1 3 Resource carrying and X 11 3 Environmental quality.
(1) In order to reflect impacts of the bearing capacity of land resources, the ecological carrying capacity and the population bearing capacity on the city green economy and sustainable development, four indices are used: X 3,1 Protection area of cultivated land, X 3,5 Forest coverage rate, X 3,6 Coverage rate of green area in completed construction area and X 3,7 Public green space per capita. At the same time, regarding the influence of energy consumption on urban green economic development, five indices, such as X 3,4 Energy consumption elasticity coefficient, are developed to specify the energy consumption; (2) X 11 3 Environmental quality is the basic index to indicate the impact of city development on the environment, and environmental quality is mainly reflected from four aspects: atmospheric emissions, wastewater discharge, urban solid waste emissions and urban air quality status. On this basis, seven indices, such as X 3,10 Nitrogen dioxide content in air, are presented to assess the influence of waste gas emissions on the city environment; X 3,14 Treatment rate of living waste water and X 3,16 Urban wastewater discharge are the main indices to describe city water consumption and sewage recycling utilization status; the three indices: X 3,12 Industrial soot emissions, X 3,17 Decontamination rate of urban refuse and X 3,19 Comprehensive use of industrial solid wastes are developed to measure urban solid waste emissions and recycling efficiency; X 3,18 Fairly good air quality day is used to evaluate the urban air quality status.
The above 82 indices are used to establish the mass-election index system, which reflects the principles of comprehensive, coordinated, sustainable development and data accessibility. In the following section, we will carry out index reduction based on the mentioned indices.

Index Reduction of City Green Economy Development Evaluation
(1) Standardization of index data In order to eliminate the influence of the differences between indices dimensions and units on index reduction, the original green economy evaluation data must be converted into numbers within the interval [0, 1]. According to the features of indices, the evaluation index can be divided into four types: positive index, negative index, interval index and medium index. The positive indices are indices showing that the greater their green economy evaluation values are, the better the city green economy development is, such as "X 1,2 GDP Per capita". The negative indices are indices showing that the less their values are, the better the city green economy development is, such as "X 2,3 Registered unemployment rate in cities and towns". The interval indices are indices which are reasonable only when the original index data are within certain range, such as "X 1,26 Consumer price index (CPI)". The ideal range of "X 1,26 Consumer price index (CPI)" [35] is [101,105]. It indicates that neither deflation nor inflation exists, when the CPI is within range [101,105]. The moderate indices are indices showing that the closer their values to a certain ideal value are, the better city green economy development is. For example, the ideal value of the moderate index "X 1,29 Urbanization rate" is 75% [36]. Index types are shown in Table 1.
Index data standardization process for the four types of indices is as follows. Let p ij denote the standardized score of the j th city on the i th index. Let v ij denote the index original data of the j th city on the i th index. Let n denote the number of cities. The standardization equations of positive indices and negative indices are represented by Equations (1) and (2) respectively.
Let q 1 denote the left boundary of the ideal interval and let q 2 denote the right boundary of the ideal interval. Then the standardized score equation of the interval indices is expressed in Equation (3).
Let v i0 denote the ideal value of the i th index. The standardized equation of the moderate indices is shown as Equation (4).
(2) Indices cluster analysis In this subsection, R cluster analysis is utilized to cluster the indices, which reflect the same information in one class. It ensures that the different categories of indices reflect different data characteristics, and eliminate the information chaos of index system [22]. The steps of R cluster analysis are as follows.
Step 1: Treat m indices as n categories.
Step 2: Combine any pair of evaluation indices in those m indices into one class, with no change in indices left. There are m(m´1)/2 kinds of combination. Calculate the sum of square deviation S i of each class of indices according to formula (5). If cluster m evaluation indices into l categories, let S i denote the i th class's sum of square deviation, let m i be the number of the i th class's indices, let X pjq i be the standardized sample value vector (j = 1, 2, . . . , m i ) of the j th evaluation index in the i th class's indices, let X i be the average vector of the i th class of indices. The sum of square deviation S i of the i th class's indices is shown as Equation (5) [22].
Step 3: Calculate total sum of squares of deviations by formula (6), re-classify the indices in the way of indices' combination that would minimize the total sum of squares of deviation. Then S " Step 4: Repeat Step 3 until the final classification number equals l. It should be pointed out that the initial clustering number l is determined by subjective for the indices in the same second criterion layer.
Step 5: Test whether clustering number l is reasonable or not by using the nonparametric K-W test method. If the significance level of each class is greater than 0.05 [22], it means that the similar indices in the same class have no significant differences in values. The clustering number l is reasonable. Otherwise, the clustering number l is not reasonable, and we need to return to Step 4 to adjust the clustering number l.

(3) Calculation of the index information content
In this subsection, coefficient variation method is used to screen the index with the highest information content loading in each class, which ensures that the selected index has the greatest influence on the city green economy evaluation. The coefficient variation of index reflects the identification ability in the city green economy evaluation. The greater the coefficient of variation is, the greater the distribution of variation and the information content are in the city green economy evaluation, and the stronger the index information distinguishing ability is.
Let b i denote the coefficient of variation the i th index, let n denote the number of sub-provincial cities, let p ij denote the standardized data of the i th index in the j th city, then we get (4) The judgment of reasonability of the established index system As we know, index data variance reflects index information content [22,37]. This paper uses the ratio of the selected index system original data variance and the mass-election index system original data variance to judge the reasonability of the established index system. An index system is considered reasonably if the established index system is able to contribute more than 90% of original information by using less than 30% of indices in the mass-election index set.
Let S denote the covariance matrix of the indices' data, let trS denote the trace of the covariance matrix, let s denote the number of indices in the established index system, and let h denote the number of mass-election index set. The contribution rate In of the selected index system to the mass-election index set is given by [22] In " trS s /trS h (8)

A City Green Economy Evaluation Model Based on Inferior Constraint
In this section, we introduce a novel city green economy evaluation model by combining the entropy weight method with the inferior constraint fuzzy comprehensive evaluation technology. Firstly, the weightings of the selected indices in Section 2.2 can be calculated by using the entropy weight method. Secondly, a green economy evaluation model is established based on inferior constraint. Thirdly, the evaluation rankings of 15 sub-provincial cities under inferior constraints and non-inferior constraint are obtained. By comparing the differences between evaluation rankings under inferior constraints and non-inferior constraint, the advantageous factors and the disadvantageous factors impacting the sub-provincial cities green economy development can be worked out. A step-by-step instruction is as follows.

Weightings Determination Based on Entropy Weight Method
Let f ij denote the subordinate degree weight of the i th index in the j th city, let p ij denote the standardized score of the i th index in the j th city, let n denote the number of cities and m denote the number of evaluation indices. The subordinate degree function f ij of the index p ij is Then, the entropy H i of the i th evaluation index can be calculated by Equation (10).
Subsequently, the entropy weight w i of the i th evaluation index is [38]: where m ř i"1 w i " 1.

A City Green Economy Evaluation Model
Now we outline the steps to build the city green economy evaluation model.
Step 1 is to calculate the superior vector and the inferior vector. Let V α and V β denote the superior vector and the inferior vector of evaluation index sample values respectively. We have [39] where v i α denotes the best sample value of the i th evaluation index in all cities, and v i β denotes the worst sample value (i = 1, 2, ..., m).
Step 2 is to calculate the superior subordinate degree and the inferior subordinate degree. Corresponding to the superior vector V α and the inferior vector V β , the superior subordinate degree x α and the inferior subordinate degree x β can be got.
where x i α denotes the best subordinate degree of the i th evaluation index in all cities, i.e., x i α = 1, and x i β denote the worst subordinate degree, i.e., x i β = 0.
Step 3 is to establish the inferior constraint. If we select t evaluation indices from m evaluation indices (1 ď t ď m), the worst evaluation value vector of the t evaluation indices in all n cities is called an inferior constraint. The inferior constraint vector x Sk that is comprised of t evaluation indices is given by: Step 4 is to calculate the superiority of weight. Let x j denote the subordinate degree vector of the j th city, then x j " px j1 , x j2 , . . . , x jm q T The Euclidean distance d(x j , x α ) between the subordinate degree vector x j of the j th city and the superior subordinate degree x α can be calculated by Equation (18).
Let y j α denote the subordinate degree of the j th city belonging to the superior vector V α , and then, the superiority of weight D(x j , x α ) belonging to the superior vector V α is given by: In Equation (19), the superiority of weight D(x j , x α ) describes the distance between the subordinate degree vector x j of the j th city and the superior subordinate degree x α .
Step 5 is to calculate the inferiority of weight. In the same way, the Euclidean distance d(x j , x β ) between the subordinate degree vector x j and the inferior subordinate degree x β can be got.
Let y i β denote the subordinate degree of the j th city belonging to the inferior vector V β . Then, the inferiority of weight D(x j , x β ) belonging to the inferior vector V β can be obtained by Equation (21).
And then, the Euclidean distance d(x j , x Sk ) between the subordinate degree vector x j and the inferior constraint vector x Sk is given by Equation (22).
Let y β jS k denote the subordinate degree of the j th city belonging to the inferior constraint vector x Sk . Thus, the inferiority of weight D(x j , x Sk ) of the j th city belonging to the inferior constraint x Sk is Equation (23) describes the distance between the subordinate degree vector x j and the inferior constraint vector x Sk .
Step 6 is to establish the inferior constraints evaluation model. We set the objective function to be the minimal weighted sum of squares of the superiority of weight D(x j , x α ), the inferiority of weight D(x j , x β ) and the inferiority of weight D(x j , x Sk ) [39]. Then where L = the number of inferior constraints + 1. Equation (24) is applied to evaluate the city green economy development. On the right side of the equal sign, (D(x j , x α )) 2 denotes the square of the superiority of weight D(x j , x α ) of the j th city, (D(x j , x β )) 2 denotes the square of the inferiority of weight D(x j , x β ) of the j th city, and (D(x j , x Sk )) 2 denotes the square of the inferiority of weight D(x j , x Sk ) of the j th city. Equation (24) indicates that the smaller the distance between the j th evaluation city and the ideal city is, the better the green economy development of the j th city would be.
Step 7 is to present a method of how to obtain a global optimal solution. Substitute Equation (18) to Equation (23) into Equation (24), and we can solve the derivatives of Equation (24) with respect to variables y j α , y j β and y β jS k respectively. The three derivative equations constitute a system of equations. Solve the system of equations, and the optimal solution y α jS containing the inferior constraint x Sk can be obtained. That is The third item of denominator in Equation (25) reflects the influence of the inferior constraint vector x Sk on the city green economy evaluation results. Equation (25) illustrates that the smaller the distance d 2 (x j , x Sk ) between the subordinate degree vector x j and the inferior constraint vector x Sk is, the bigger the denominator would be, and the smaller the optimal solution value y α jS would be, and this means that the inferior constraint x Sk is the bottleneck factor of the j th city green economy development. On the contrary, the bigger the distance d 2 (x j , x Sk ) between the subordinate degree vector x j and the inferior constraint vector x Sk is, the smaller the denominator would be, the bigger the optimal solution value y α jS would be. It indicates that the inferior constraint x Sk is the advantageous factor of the j th city green economy development. (25), the optimal solution y α jS without containing the inferior constraint x Sk is shown in Equation (26).
Equation (26) indicates that the smaller the distance d 2 (x j ,x α ) between the subordinate degree vector x j and the superior subordinate degree vector x α is, the better the green economy development of the j th city would be. Conversely, the bigger the distance d 2 (x j ,x β ) between the subordinate degree vector x j and the inferior subordinate degree vector x β is, the better the green economy development of the j th city would be.

Key Factor Extraction of the City Green Economy Evaluation Model
This part is about the extraction of the common key factors influencing the sub-provincial cities' green economy development. Through comparing the differences d* between 15 sub-provincial cities' evaluation rankings under inferior constraints and non-inferior constraints, the differences d* can be divided into five categories by using Wald cluster analysis. These indices corresponding to the first classification are the common key factors, because they have the greatest influence on the sub-provincial cities' green economy development.
When selecting the advantageous factors and the disadvantageous factors influencing a sub-provincial city's green economy development after comparing the differences between a sub-provincial city's evaluation raking under the inferior constraint x* and non-inferior constraint, we can determine whether index x* is the advantageous factor of the sub-provincial city green economy development, or disadvantageous factor. If the evaluation rank rank inferior under the inferior constraint x* is less than the evaluation rank rank non-inferior under the non-inferior constraint (i.e., rank inferior´r ank non-inferior < 0), index x* is called an advantageous factor of green economy development. Conversely, if the evaluation rank rank inferior under the inferior constraint x* is greater than the evaluation rank rank non-inferior under the non-inferior constraint (i.e., rank inferior´r ank non-inferior > 0), index x* is called an disadvantageous factor of green economy development. For instance, in the following empirical analysis of Section 3.3.4, we select the index "X 1,10 Budgetary revenue of local government" as an inferior constraint. As mentioned below, the Dalian's evaluation rank rank non-inferior under the non-inferior constraint equals 11, while its evaluation rank rank inferior under the inferior constraint "X 1,10 Budgetary revenue of local government" equals 9. When rank inferior´r ank non-inferior = 9´11 =´2 < 0, it indicates that index "X 1,10 Budgetary revenue of local government" is an disadvantageous factor of green economy development for Dalian.

Sample Selection and Data Collection
In order to judge the city green economy development level, and find out the insufficiency and difference existing in the development of green economy, in July 2011, the WWF launched "2050 Shanghai Low-carbon Development Road Map Report", and began the low carbon development research in Shanghai [40]. In September 2011, the Beijing Committee of Communist Party and the Beijing Municipal People's Government issued "Green Beijing Development Construction Planning in Twelfth Five-year Period" [19]. On the basis of Green Beijing and Low-Carbon Shanghai, this paper selects all of 15 sub-provincial cities in China as empirical samples. The 15 sub-provincial cities includes Dalian, Haerbin, Changchun, Shenyang, Jinan, Qingdao, Nanjing, Hangzhou, Ningbo, Xiamen, Guangzhou, Shenzhen, Wuhan, Chengdu and Xi'an, as shown in Table 2.
The original data of green economy evaluation index of the 15 sub-provincial cities are derived from the corresponding sub-provincial cities' statistics in Yearbook 2013 [41,42], as shown from Column 5 to Column 19 in Table 2.

Application of Index Reduction Model
(1) The index data standardization According to the index type in Column 6 in Table 1, take the original data of positive indices v ij from Column 5 to 19 in Table 2 into Equation (1), the original data of negative indices v ij into Equation (2), the original data of interval indices v ij into Equation (3), and the original data of moderate indices v ij into Equation (4), the standardized data p ij of indices are obtained. The results are shown in Column 20 to 34 in Table 2.
(2) R cluster analysis In order to explain the process of R cluster analysis, the 24 indices of the first secondary criterion layer "X 1 1 Economic growth" gathering are divided into six categories as an example. Substitute the corresponding indices' data into Equation (5) and Equation (6), and the cluster results are obtained. From Column 4 in Table 3, the eight indices of X 1,1 , X 1,7 , X 1,11 , X 1,15 , X 1,18 , X 1,19 , X 1,21 and X 1,24 are the similar R cluster indices. Take the eight indices' data into SPSS17.0 software, the significance level Sig of K-W test that equals 0.563 can be got. Obviously, the significance level 0.563 is greater than 0.05, which means that the eight indices in the same class have no significant differences in values.
Similarly, we can obtain the significance levels of the rest of five classes indices which are greater than 0.05. It indicates that the clustering number six is reasonable for the first criterion layer. In the same way, we can get the corresponding cluster results for the rest of the five secondary criterion layers, as shown in Table 3. Table 3. Index reduction based on R cluster analysis and coefficient of variation.
(2 Substitute the standardized data in Table 2 into Equation (7), and the coefficients of variation of 82 indices can be obtained, as shown in Column 6 in Table 3. In the same clustering category in Table 3, we retain the index which has the biggest coefficient of variation, and delete the rest indices. The results are shown in Column 7 in Table 3. At last, we select 23 indices of city green economy evaluation, as shown in Table 4.
(4) The reasonability judgment of the established index system Take the corresponding original data of the 23 selected indices and the original data of the 82 mass-election indices into Equation (8), and the contribution rate In of the selected index system to the mass-election index set is In = trS s /trS h = 1.066ˆ10 14 /1.122ˆ10 14 = 95.01%. It means that the reduction index system indicates 95.01% original information with 28.05% indices (28.05% = 23/82).
It should be pointed out that there are some locally oriented indices in the established green economy evaluation index system, such as X 1,24 Added value of the logistics industry. Statistical data from the National Development and Reform Commission show that logistics industrial has become one of the pillar industries in economic development [34], so we use X 1,24 to reflect the contribution degree of the logistics industry to Chinese sub-provincial city economic development. Combining the above empirical analysis, the eight indices are the similar R cluster indices, i.e., X 1,1 , X 1,7 , X 1,11 , X 1,15 , X 1,18 , X 1,19 , X 1,21 and X 1,24 , and the index of X 1,24 has the biggest coefficient of variation, so it should be retained.

The Determination of Index Weight
In Table 2, take the standard score data of the retained 23 indices into Equation (9) to Equation (11), the entropy weights of the 23 indices and the corresponding weights of the criterion layers can be obtained, as shown in Table 4.
Known from Table 4, the ranking results of weights in descending order is X 1 = 0.506 > X 2 = 0.256 > X 3 = 0.238. It means that the order of importance of the three criterion layers is X 1 Economy development > X 2 Social livelihood of the people > X 3 Resources and environment. In other words, in the evaluation of green economy for sub-provincial city, economy development is at the core position, which means achieving a minimum negative impact on the environment and resources consumption while improving the economic growth and increasing social welfare. Table 4. Green economy evaluation index system for sub-provincial cities.   Table 4 into Equation (18), the Euclidean distance d 2 (x 1 , x α ) between the subordinate degree vector x 1 of Dalian and the superior subordinate degree x α can be obtained: = 0.710. In the same way, we can calculate the Euclidean distances d 2 (x j , x α ) between the rest of 14 sub-provincial cities subordinate degree vectors and the superior subordinate degree x α , as shown in the first Row in Table 5. (2) Calculate Euclidean distance between the evaluation cities and the inferior subordinate degree Substitute the data from Column 5 to Column 6 in Table 4 into Equation (20), and the Euclidean distance d 2 (x 1 , x β ) between the subordinate degree vector x 1 of Dalian and the inferior subordinate degree x β can be obtained: = 0.138. In the same way, we can calculate the Euclidean distances d 2 (x j , x β ) (j = 2, ..., 15), as shown in the second Row in Table 5.
(3) Calculate Euclidean distance between the evaluation cities and the inferior constraint vector For example, we select the index "X 1,10 Budgetary revenue of local government" as an inferior constraint. Then we can obtain the inferior constraint vector x S 1 = {x S 1,1 } = {0}. Substitute the data in Table 4 into Equation (22), and the Euclidean distance d 2 (x 1 , x S1 ) between the subordinate degree vector x 1 of Dalian and the inferior constraint vector x S1 can be obtained: 112. Likewise, we can calculate the Euclidean distances d 2 (x j , x Sk ) between the rest of 14 sub-provincial cities subordinate degree vectors and the inferior constraint vector x Sk , as shown in Row 3 to Row 25 in Table 5.
(4) Calculate the subordinate degree of green economy evaluation First, we calculate the subordinate degree and the evaluation rankings without inferior constraint. Take the data d 2 (x 1 , x α ) = 0.710 and d 2 (x 1 , x β ) = 0.138 into Equation (26), and the Dalian optimal subordinate degree y α 1 without containing the inferior constraint can be obtained:  Table 6, we can obtain the corresponding evaluation rankings of 15 sub-provincial cities in a descending order, as shown in Row 2 in Table 6. Second, we calculate the subordinate degree and the evaluation rankings containing inferior constraint. Take the data of Row 1 to Row 3 and Column 3 in Table 5 into Equation (25), and the Dalian optimal subordinate degree y α 1S containing the inferior constraint can be obtained:  Table 6. According to the data in Table 6, we can obtain the corresponding evaluation rankings of 15 sub-provincial cities under 23 different inferior constraints in a descending order, as shown in Row 4, Row 6, ..., and Row 48 in Table 6.

Extract the Common Key Factors of Sub-Provincial Cities' Green Economy Development
On the basis of the evaluation rankings' data from Row 2 and Row 4 in Table 6, the rankings' differences d* of 15 sub-provincial cities' evaluation rankings under inferior constraint X 1,10 can be calculated: d*(X 1,10 ) = |9´11| + |15´8| + . . . + |13´12| = 32. Similarly, we can calculate the rankings' differences d* of 15 sub-provincial cities containing the rest of 22 inferior constraints, as shown in Column 3 and Column 6 in Table 7. Table 7. The rankings' differences of green economy development with and without inferior constraint.
(2) Inferior Constraint  Table 7, the 23 indices have different effects on green economy evaluation of sub-provincial cities. The maximal rankings' differences d* equals 76, and the minimal rankings' differences d* equals 28. Divide the 23 rankings' differences d* into five categories. The classification results are illustrated in Table 8. From Table 8, the six indices corresponding to the first classification are the most important factors, i.e., the common key factors. They have the greatest influence on the sub-provincial cities' green economy development. Table 8. Common key factors of sub-provincial cities' green economy development. The second classification X 1,20 Freight volume, X 2,7 Urban households per capita consumption expenditure, X 2, 16 The ratio of government expenditure on education to general budget expenditure, X 3,18 Fairly good air quality day 3 The third classification X 1,12 Total investment in fixed assets, X 1,28 The ratio of the added value of the tertiary industry to GDP, X 3,3 Comprehensive energy consumption of industrial enterprises above designated size, X 3,21 Ammonia and nitrogen emissions of major pollutants 4 The fourth classification X 1,13 Total foreign trade value, X 1,32 The ratio of county economic aggregate to GDP, X 2,1 Census register population, X 2,22 Number of public transportation vehicles per 10,000 persons (District), X 2,24 Urban per capita housing area, X 3,7 Public green space per capita, X 3,12 Industrial soot emissions 5 The fifth classification X 1,10 Budgetary revenue of local government, X 1,31 The ratio of private economic value added to GDP

Select Advantageous and Disadvantageous Factors of Sub-Provincial Cities' Green Economy Development
According to the evaluation rankings' data from Row 2 and Row 4 in Table 6, the ranking difference d Dalian (X 1,10 ) under inferior constraint X 1,10 can be obtained: d Dalian (X 1,10 ) = 9´11 =´2. Similarly, we can calculate the rankings' differences d j (X i ) of 15 sub-provincial cities containing the 23 inferior constraints, as shown in Table 9. Table 9. Ranking difference rank inferior -rank non-inferior for 15 sub-provincial cities' green economy development.  We put the numbers in a descending order for each sub-provincial city by combining the data from Table 9. The indices corresponding to the maximal value and the second largest value are the most important advantageous factors of green economy development, labeled as "++". The indices corresponding to the minimal value and the second smallest value are the most important disadvantageous factors of green economy development, labeled as "--". Take Dalian as an example. Known from the third Column in Table 9, the maximal value of ranking difference rank inferiorŕ ank non-inferior equals 4, and the second largest value of ranking difference rank inferior´r ank non-inferior equals 3. The two corresponding indices X 1,28 and X 3,22 are the most important advantageous factors for Dalian green economy development, labeled as "++". Similarly, we can obtain two indices X 1,22 and X 3,21, the most important disadvantageous factors for Dalian green economy development, labeled as "--", as shown in Table 10. It means that Dalian municipal government can improve its green economy development by raising "X 1,22 Freight turnover" and lowering "X 3,21 Ammonia and nitrogen emissions of major pollutants". In the same way, we can obtain the most important advantageous factors and the most important disadvantageous factors for the 15 sub-provincial cities, as shown in Table 11. Table 10. The key labels for sub-provincial cities' green economy development.  Table 11. The advantage and disadvantage of 15 sub-provincial cities' green economy development.

Conclusions and Policy Implications
In order to help the authorities to make or adjust corresponding green economic development policies, we conduct the city green economy evaluation. First of all, this paper creates an index reduction model by using R cluster analysis to delete the repeated information indices and utilizing coefficient of variation to screen indices which have the greatest influence on city green economy evaluation. Secondly, on the basis of the nonlinear weighted by utilizing entropy weight method, a city green economy evaluation model based on inferior constraint is established. Thirdly, the cities' green economy evaluation rankings under inferior constraints and non-inferior constraints are obtained. By comparing the differences between evaluation rankings under inferior constraints and non-inferior constraints, we extract the advantageous factors and the disadvantageous factors of cities green economy development. The proposed model is verified by the data from 15 sub-provincial cities in China. Empirical analysis results are provided below. (1) The proposed approach can accurately find out the advantageous factors and the disadvantageous factors for each sub-provincial city; (2) The established green economy evaluation index system reflects 95.01% of original information by 28.05% of initial indicators, which includes 23 indices, such as "X 1, 28 The ratio of the added value of the tertiary industry to GDP", "X 2,24 Urban per capita housing area" and "X 3,7 Public green space per capita"; (3) In the evaluation of green economy development, the order of importance of the three criterion layers is X 1 Economy development > X 2 Social livelihood of the people > X 3 Resources and environment; (4) The six indices of X 1,22 Freight turnover, X 1,24 Added value of the logistics industry, X 2,9 The average annual growth rate of rural residents per capita net income, X 2,14 Number of doctors (10,000 persons), X 3,1 Protection area of cultivated land and X 3,22 Reduction of chemical oxygen demand emissions of main pollutants have the greatest influence on the green economy development of sub-provincial city.
The contributions of this paper lie in three aspects. First, the evaluation of the green economy of cities from the economy, society, environment, and resource perspective, instead of a more traditional economy development perspective, seems to offer a new insight into the green economy of the cities. Second, this paper builds an index system, which is suitable for city green economy development. Third, our research not only has practical significance for developing green economy in the 15 sub-provincial cities in China, but also provides a reference for development of green economy in other cities in the world.
Policy implications derived from the empirical findings are provided as follows. (1) The central government should establish the performance evaluation system for sub-provincial cities' green economic development. In this evaluation system, economy, society, environment, resources and some other relevant factors must be involved; (2) Due to the fact that different sub-provincial cities have different advantage and disadvantage factors in green economy development, local governments should implement differential, reasonable policies based on the bottleneck factors and advantage factors; (3) In order to locate the bottleneck factors and adjust the corresponding green economic development policies timely, local governments should conduct the dynamic performance evaluation of green economy development.
Although some results and insights have been gathered from this exploratory study, there are some limitations and room for further investigation. For our case, only empirical related data of the 15 sub-provincial cities of China are utilized. Policy and implications are derived from the analysis results, which may not be generalized enough for all cities in China. When investigating sustainability issues, there are also concerns about more relevant data. In addition, some new variables such as green innovation, green policy, global resource limits, climate change can be taken into consideration. Generalizing this technique to incorporate additional characteristic indicators is not too difficult and researchers can easily extract the impacts of these additional characteristic indicators through cases and empirical studies.

Conflicts of Interest:
The authors declare no conflict of interest. Table A1. The characteristic of indices for city green economy evaluation.

X 1,Average growth rate of GDP per annum
The index is the average growth rate of GDP beyond one-year period in the whole city, it is a dynamic indicator that reveals the change in the level of economic development in a given period.

X 1,Government revenue
The government revenue is the money income made by the government, including the central government, in a given period. It is one of the main ways that the government can achieve its aim of economic policies and provide public products and services.

X 1,Value added of the primary sector
The value added of the primary sector is the added value of products that are made by agriculture, forestry, animal husbandry and fishery industry. It is the foundation of the national economy. The budgetary revenue of local government is a kind of budget management funds that is dominated by the government. It can help to organize and coordinate economic activities, and complete set economic goals effectively.

X 1,Sales value in wholesale and retail sale trade
The sales value in wholesale and retail sale trade is the total amount of goods that are sold to outside enterprises and individuals. It reflects the development of the tertiary sector.

X 1,Total investment in fixed assets
The total investment in fixed assets is the construction and purchase workload of fixed assets in currencies. It is a comprehensive index that can reflect the scale, speed and other factors of investment in fixed assets.

X 1,Total foreign trade value
The total foreign trade value is the sum of the value of foreign merchandise trade and the value of trade commercial services. It is an important economic indicator that can measure the foreign trade situation of a country or a region. The value of export is the total amount of shipping in the goods and services out of the jurisdiction of a country. It is an important economic indicator that can measure the foreign trade situation of a country or a region.

X 1,Total retail sales of consumer goods
The total retail sales of consumer goods is the amount of retail sales of wholesale, retail trade, accommodation and catering industry and other industries directly sold to urban and rural residents and social group. It reflects the improvement of people's living standards in a certain period.

X 1,Foreign investment in actual use
The foreign investment in actual use is the actual arrival of foreign funds after signing the contract between China and a foreign country. It reflects the level of utilization of foreign investment in China.

X 1,Gross industrial output value of enterprises above designated size
The gross industrial output value of enterprises above designated size is the gross value of industrial corporate enterprises whose main business income reached 2000 million Yuan. It reflects the structure of industrial output value.

X 1,Balance of loans and deposit in RMB and foreign currencies in financial institutions
The index is the sum of the balance of deposits and loans in local and foreign currencies in financial institutions. It is the sum of a bank's assets and liabilities. It reflects the money supply in the green economic development.

X 1,Balance of loans in RMB and foreign currencies in financial institutions
The balance of loans in RMB and foreign currencies in financial institutions is the loan in local and foreign currencies that the borrower has not yet returned to the lender. It reflects banks' asset condition under the background of current economic development.

X 1,Freight volume
The freight volume is the actual shipping quantities of goods in transportation enterprises in a certain period. It reflects the contribution degree of transportation enterprises to the city economic development.

X 1,Airport passenger throughput
The airport passenger throughput is the number of passengers who buy tickets into and out of a certain region within one year. It indicates the development of the tertiary industry indirectly.

X 1,Freight turnover
The freight turnover is the total freight traffic that is calculated by the combination of actually completed freight and traffic distance and achieved by different kinds of transport tools. It reflects the transportation and production achievements comprehensively.

X 1,Value added of the financial industry
The value added of the financial industry is the final achievement that is calculated in market prices and made by a city's resident units who engage in financial production activities in a certain period. It indicates the development status of financial industry in the economic activity.

X 1,Added value of the logistics industry
Added value of the logistics industry is the final achievement of logistics activities made by logistics industry in monetary measures. Statistics from the National Development and Reform Commission show that logistics industrial has become one of the pillar industries in economic development [34]. This index reflects the contribution degree of the logistics industry to Chinese sub-provincial city economic development.

X 11
1 Economic structure X 1, 25 The ratio of the added value of the primary sector to GDP The ratio of the added value of the primary sector to GDP is the ratio of the added value of products that are made by the nature to GDP. It reflects the economic structure changes in a region in economic transformation and upgrading period. A consumer price index (CPI) measures the changes in the price level of a market basket of consumer goods and services purchased by households. It is an important index to observe regional inflation in the transformation of economic structure.

X 1,The ratio of industrial added value to GDP
The index is the ratio of the achievement of industrial production in monetary terms in the reporting period to GDP. It also reflects the economic structure changes in a region in economic transformation and upgrading period.

X 1,28
The ratio of the added value of the tertiary industry to GDP The ratio of the added value of the tertiary industry to GDP is the ratio of the added value of service industry to GDP. It indicates the economic structure changes in a region in economic transformation and upgrading period.

X 1,Urbanization rate
The urbanization rate is the ratio of people in cities and towns to the total population. It not only reflects the process of aggregation of people shifting from rural to urban areas, but also indicates the intensive degree of economic development in economic structure transformation and upgrading period [43].

X 1,The ratio of the third industry practitioners to the proportion of all employees
The ratio of the third industry practitioners to the proportion of all employees is the ratio of people who engage in the service industry to the total employees. It reflects the employment structure in regional economic development.

X 1,The ratio of private economic value added to GDP
The ratio of private economic value added to GDP is the ratio of the price of the product and service minus the cost of producing in the private sector to GDP. It indicates the contribution degree of private economy to the regional economy development. 32 X 1,32 The ratio of county economic aggregate to GDP The ratio of county economic aggregate to GDP is the ratio of the price of the product and service in the county economic sector to GDP. It reflects the development of the county economic sector.

X 1,The ratio of value added of financial industry to GDP
The index is the ratio of the final achievement that is calculated in market prices and made by a country's resident units who engage in financial production activities in a certain period to GDP. It indicates the contribution degree of financial industry to the regional economy development.

X 1,The ratio of logistics industry added value to GDP
The ratio of logistics industry added value to GDP is the ratio of the final achievement of logistics activities made by logistics industry in currencies to GDP. It reflects the contribution degree of the logistics industry to Chinese sub-provincial city economic development.

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X 2 Social livelihood of the people X 1 2 People's livelihood improvement X 2,1 Census register population The census register population is the total amount of citizens who have registered in the public household management authority in their habitual residence. The index reflects the population bearing capacity in the region during the sustainable development.

36
X 2,2 Natural population growth rate The natural population growth rate is the ratio of the natural population increase to the average number of population in a given period. It shows the degree and the trend of the population growth.

X 2,3 Registered unemployment rate in cities and towns
The registered unemployment rate in cities and towns is the ratio of the amount of registered urban unemployment population to the labor force in the end of the reporting period. It is the main index to evaluate the employment status of a city.  The ratio of government expenditure on education to general budget expenditure is the ratio of the actual cost spent on education in the budget management made by the government on the general budget expenditure. It reflects the government's financial support for education.  The gross enrollment rate of high school is the ratio of children who have enrolled in schools on the total number of the school-age children. It reveals the popularity of primary education. 54 X 2,20 Gross enrollment rate of high school The gross enrollment rate of high school is the ratio of high school students who have enrolled in schools on the total number of the high school age students. It is the essential index to measure the educational development level. 55 X 2,21 Acceptance rate of foodstuffs sample survey The acceptance rate of foodstuffs sample survey is the ratio of food selected and examined by the government on the total amount of food in the production. It shows that the government lays emphasis on food safety. The index is the total amount of arable land in certain areas. It reflects the bearing capacity of land resources in economic development.

X 3,2 Coal consumption
The coal consumption is the consumption of coal for the use of production and life in a region in a given period. It indirectly reveals the impact of energy consumption on urban green economic development.

X 3,3 Comprehensive energy consumption of industrial enterprises above designated size
The comprehensive energy consumption of industrial enterprises above designated size is the total amount of energy consumption of industrial enterprises whose main business income reached 2000 million Yuan. It reflects the resource carrying capacity in city's economic development.

X 3,4 Energy consumption elasticity coefficient
The energy consumption elasticity coefficient is the ratio of the growth of energy consumption on the growth of GDP. The index is used to evaluate city energy consumption and energy savings status.

X 3,5 Forest coverage rate
The index refers to a city forest area accounts for the percentage of land area. It reflects the bearing capacity of forest resources in green economic development.

X 3,6 Coverage rate of green area in completed construction area
This index is the percentage of green coverage area in completed construction area. It reveals the ecological carrying capacity in green economy development.      Table A5. Cont.