Dynamic evaluation method of urban green growth level in Anhui province: a comprehensive analysis of 16 cities’ panel data from 2013-2017

Considering that green growth development is an increasingly important environmental trend, this paper develops an urban green growth development index and applies it to Anhui Province in China and its 16 cities. Previously, such analyses have taken place mostly at the provincial level, and research on cities is relatively rare. To fill the gap, this paper constructs an urban green growth economy evaluation index based on economic technology, social development, ecological environment, and energy emissions. Using the vertical and horizontal pull-off method to comprehensively evaluate the green growth development levels of 16 cities in Anhui province from 2013 to 2017, the residual expectation coefficient is used to measure and analyze differences in the development levels. The results show that Hefei and Huangshan emit a medium-high level of carbon, and the other 14 cities belong in the high-carbon category. Furthermore, cluster analysis shows that the green growth development levels of the 16 cities fall into four groups. There is a wide disparity between the groups, and the differences between groups are significantly larger than the differences within groups.


INTRODUCTION
Green growth is becoming an important trend in the sustainable development of the global economy and society at large. To a significant extent, green growth and a low-carbon economy have important links. The low-carbon economy is a new economic form and development model for the comprehensive development of economic society and the ecological environment. It is guided by the science of sustainable development through technological and institutional innovation, the development of new energy sources, industrial transformation, and other means that will change energy consumption patterns and structures, improve energy efficiency, and minimize greenhouse gas emissions [1,2]. With the rapid development of China's economy since its economic reform, the rural population has migrated to cities, and urbanization has accelerated. In 2017, China's urbanization rate was 58.52%. By 2050, China's urbanization rate is predicted to reach 70% [3,4]. The high urbanization rate will increase energy consumption and emissions of carbon dioxide (CO2). According to Chinese government statistics, cities hold more than half of the world's population but consume 75% of the world's energy and generate 80% of the greenhouse gas emissions [5][6]. In this context, cities shoulder the responsibility of energy conservation and emissions reduction, which are essential to green growth.
Anhui province has abundant energy resources and a large population. The industrial structure is dominated by the second industry. The energy structure is dominated by coal. The recent accelerated increase in the economic development of Anhui has led to a continued increase in energy consumption, significantly raising greenhouse gas emissions. This has intensified the conflict between the environment and energy resources. Anhui should develop green growth economies for the cities to adjust the province's industrial structure, optimize its energy consumption structure, and develop a sustainable economy [7][8][9].

LITERATURE REVIEW
Since the British government published the Energy White Paper in 2003, the concept of green growth has emerged as a frequent topic of discussion among governments and scholars. In researching the development level of green growth, foreign scholars have paid more attention to policies, path choices, models, and carbon emission technologies [10][11][12]. For example, Kaya Yoichi proposed the KAYA model and Mahony extended the KAYA model, which states that population, energy consumption per unit of energy, energy intensity per unit of GDP, and per capita GDP will affect the carbon emissions of a region or country [13]; Kerkhof, from the perspective of household expenditure, Calculate household carbon dioxide in the Netherlands, Norway, Switzerland, and the United Kingdom in 2000 to identify factors affecting CO2 emissions within or between countries [14]. In China, scholars have tended to construct an evaluation system and use empirical methods for research [15][16][17]. The evaluation methods include the analytic hierarchy process, principal component, factor analysis, TOPSIS, and entropy weighting [18][19][20]. For example, Li Ziliang used a fuzzy analytic hierarchy to construct a comprehensive evaluation system including the overall level of carbon emission, system level of carbon emission, the control level of carbon emission, and an index level of carbon emission to evaluate the green growth in China [21]. Using principal component, factor analysis, and clustering methods, Zheng Shihua constructed and evaluated the provincial green growth development level and divided the development level of China's provincial green growth into four zones: low-carbon, significantly low-carbon, relatively high-carbon, and high-carbon [22]. Yuan Xiaoling constructed a regional green growth evaluation index system from the aspects of low carbon emissions and developmental capability. He applied the TOPSIS method to empirically analyze the 29 provinces and the eastern, central, and western regions of China [23]. Ma Jun considered the development status of the six provinces in the eastern coastal region. Linear weighting was used to calculate the comprehensive green growth value, and the Delphi method was used to determine the weights [24]. Zhang Xin and Wu Wenheng established an urban green growth evaluation index system from the dimensions of economy, society, technology, energy emissions, and the ecological environment, and used factor analysis to empirically study the development level of the green growth in 10 cities in Shaanxi province. The results show that these cities exhibit small-and medium-sized urban distribution patterns [25]. Zhu Xia and Lu Zhengnan implemented the DPSIR (Driving force-Pressure-State-Impact-Response) model and established a green growth evaluation index system with 27 indicators, applying the entropy weight and principal component projection methods to lower a comprehensive evaluation of the level of carbon economic development of the 13 prefecture-level cities in Jiangsu Province [26]. The above literature shows that evaluations of green growth development are mostly at the provincial level; research on cities and dynamic analyses are relatively rare, and most of the data are cross-sectional. Therefore, to fill this gap in the literature, this article dynamically analyzes cities.

Indicator selection
Based on the above principles and systemic ideas for constructing green growth in cities, relevant domestic and foreign indicators are compounded, and the urban green growth evaluation index system is constructed in accordance with the actual situation of 16 cities in Anhui. There are four primary indicators: economic and technological, social development, energy emissions, and ecological environment. Apart from these, there are 17 secondary indicators. See Table 1 for details.

Vertical and horizontal pull-off method
The vertical and horizontal pull-off method [27][28][29] is a comprehensive evaluation method for determining index weights based on time-series data tables. Assume n pairs of evaluation objects S1,S2,…,Sn and m evaluation indicators x1, x2,…,xm in chronological order t1, t2,…, tN form the original data , thus generating a time-series data table. Vertical and horizontal to the open class method was chosen as the evaluation method is simple in principle, have clear intuitive meaning and geometric meaning, and is more suitable for dynamic comprehensive evaluation problem, this method can both in transverse moment ( = 1,2, …, ) the differences between each system, and can reflect the overall distribution of each system on the longitudinal, and both for cross section data, or for sequential solid data, the comprehensive evaluation results are comparable, and is not influenced by subjective factors.
Without loss of generality, the original data here are consistent with dimensionless processing indicators, that is, the evaluation indicators in the original data x1, x2,…,xm. After the indicator type is consistently processed, it is a very large indicator. The series { } ,is standard data after dimensionless processing.
For time ( = 1,2, …, ) , the comprehensive evaluation function is: The principle of determining the weight is to maximize the difference between the evaluation objects in the time-series data table. The difference can be expressed by the sum of the squares of the total deviations: Since the raw data is standardized, Thus, order symmetric matrices; = ( = 1,2, …, ), and , ( = 1,2, …, ).

If
= 1 , when w is the eigenvector corresponding to the largest eigenvalue =  ( ) , of the matrix H, 2 takes the maximum value, and =  ( ). If > 0 , it must be that H >0, and there is a positive (normalized) weight coefficient vector w.
If one of the components w sought is negative, w can be found by the following planning problem. Choose w to make .

Requirement coefficient
The residual expectation coefficient [30] is a new indicator reflecting the degree of regional disparity. It overcomes the shortcomings of the Searle index and can compare data of different regions at different times while retaining the decomposability of the Xaar index. Assume that the probability of an occurrence of event A is P(A)=P. It is generally believed that the lower the probability of occurrence of an event, the greater is the amount of information generated. Therefore, the amount of information generated from event A occurring is defined as log (1 ). If there are n events with probabilities of occurrence P1, P2,…, Pn, the corresponding expected information is calculated as: The closer the values of the probabilities P1,P2,…,Pn, the greater the value of E. If P1 = P2 = … = Pn = 1/n, then = log ( ) . Define the residual expectation coefficient: According to the principle of decomposition of the Xaar index, the overall difference is divided into the differences between the parts and within the parts, and the difference within each part is equal to the weighted sum of the differences within each part.

Data collection and processing
The indicator data studied in this paper are sourced mainly from the statistical yearbooks and bulletins of Anhui and the 16 cities from 2013 to 2017. Some data are calculated, such as R&D expenditure as a percentage of GDP, industrial output, soot emissions, and industrial SO2 emissions per unit of GDP. Due to the different dimensions and magnitudes of each evaluation index, there is incommensurability, and the indicators need to be standardized. Positive indicator: Negative indicator:

Calculation and analysis
According to the steps of the vertical and horizontal pull-off method, the symmetric matrix = ( = 1,2,3 Substituting the calculated weight coefficient in formula (2), the comprehensive scores of green growth development levels of the 16 cities are obtained. The results are shown in Table 2. The green growth evaluation rating standards are shown in Table 3. Refer to the domestic and international literature on green growth evaluation grade standards for more details [18,24,[31][32][33][34][35].  Tables 2 and 3, the development level of the green growth in Hefei and Huangshan in 2013-2017 is comprehensive. The scores are all above 0.675, but none exceed 0.875, which corresponds to medium-high carbon emissions. The other 14 cities exhibit green growth development within the range of 0.42-0.675 in these five years, and, thus, they are all classified as high-carbon.
For further analysis, the scores of the green growth development level of the 16 cities in 2013-2017 are used as clustering variables, and system clustering analysis is conducted using SPASS22.0 software. System cluster strategy is to each object as a cluster, and then merge these atomic clusters for more and more variety, until all objects in a cluster, or an end conditions are met. The clustering method is easy to define the similarity of distance and rules, and has few restrictions. There is no need to specify the cluster number in advance; in addition, the hierarchical relationship of the classes can be visually demonstrated through the pedigree chart. The 16 cities can be divided into four groups, as shown in Figure 1. The first group of cities -high-carbon cities with a high level of green growth development -represents Hefei, Huangshan, and Bengbu. The development of the green growth in Hefei and Huangshan ranked first, second or third in each of these five years, and the low-carbon development level is greater than 0.65. Hefei is the capital of Anhui, with a developed economy, highly ranked colleges and universities, and advanced technology. Most of the indicators are developing well, and the low-carbon development level is high. Forest resources in Huangshan are abundant, tourism and tertiary industries are developed, carbon emissions are the low, and ecological environment and energy emission indicator values have remained strong. At the same time, the ecological environment indicators and energy emission indicators of Bengbu are developing very well.
The second group of cities have a moderately high level of green growth development. The specific cities are Bozhou, Wuhu, Tongling, and Chizhou. Their low-carbon economies rank between 4 and 10, and their green growth scores are around 0.56. Some of the green growth indicators in these cities are too low, such as the forest coverage rate and the green area of per capita parks of Wuhu; the proportion of R&D expenditures in Bozhou and Chizhou; and the proportion of Tongling's tertiary industry in GDP.
The third group of cities -Huaibei, Xuancheng, Suzhou and Lu'an-exhibit a moderately low level of green growth development. Green growth rankings are relatively low, with levels in the middle and lower ranges. The green growth indicators of these five cities are uneven, most of the indicators are low, and they only trend well in one dimension.
The fourth group of cities -Chuzhou, Fuyang, Huainan, Anqing and Maanshan -exhibit a low level of green growth development, and have done so historically. The economy and technology of these cities are underdeveloped except for Maanshan, and they are below average in economic technology, social development, ecological environment, and energy emissions. There is a sizeable disparity between this group and the other three groups and Maanshan's energy emission indicators have been at the bottom in these five years.

Calculation and analysis of the differences in the development levels of green growth economies
The residual expectation coefficient is an index describing the difference and mutual relationship between the two levels of urban green growth economies. Based on the above classification results, this paper compares the differences in the development levels of urban green growth economies from the differences between and within groups.
We define the differences between groups uG and the differences within the groups uW according to equations (7) and (8). The results are shown in Table 4. From the overall difference, we see that the gap between the development levels of green growth in various cities and towns in 2013-2017 has basically maintained an upward trend, and the extent of the increase is accordingly expanding. This shows that the gap between the green growth development levels of various cities and towns is expanding as a whole.
From the differences between and within groups, we observe that change basically maintained in a small fluctuation range before rebounding sharply in 2017. From the perspective of intra-group differences, the trend of change is basically the opposite of the difference between groups, rising until 2016 before beginning to decline. Again, from the data in Table 3, there is a certain gap between groups and within groups. The differences between groups are almost greater than the differences within groups from 2013 to 2017. The impact of differences between groups also indicates that the total difference in the development levels of green growth economies in different cities is caused mainly by differences between groups. In the future, exchanges, learning, and cooperation should be strengthened between cities at various levels.

Conclusions
Based on the relevant literature and the actual situation of each city, this research constructs an evaluation index of urban green growth development levels. Using the vertical and horizontal pull-off method to comprehensively evaluate the green growth development levels of 16 cities in Anhui province from 2013 to 2017, the residual expectation coefficient is used to measure and analyze differences in the development levels.
The results show that of the 16 cities in Anhui, the green growth development level of Hefei and Huangshan from 2013 to 2017 is characterized as medium-high carbon, and the other 14 cities belong in the high-carbon category. Furthermore, the green growth development levels of the 16 cities are clustered into four groups. From the overall difference, the disparity between the green growth development levels of the 16 cities from 2013 to 2017 was expanding. There is a wide disparity between the groups, and the differences between groups are significantly larger than the differences within the groups.

Suggestions
The industrial structures and economic development models of the 14 cities that emit high levels of carbon should be revised to promote the transition to green growth. Considering the challenges cities and towns face, they should adjust and optimize the industrial structure, promote technological innovation, and adopt a new model of economic development.
Targeted strategies should be adopted according to local conditions. The cities with a less developed green growth economy should improve the income guarantee and welfare system, and develop new energy sources and a green circular economy. The strategies for the third and fourth groups of cities should help them form the characteristics of the urban industrial structure while increasing investment in environmental protection and improving environmental quality.
The relevant decision-makers in these cities should broaden the opportunities for green growth exchanges. Various cities in Anhui can conduct symposiums and seminars and host expert field visits on the development of the green growth economy; exchange experiences and lessons from developing the green growth in all levels of cities; and promote the green growth in all levels of Anhui. The disparity in development levels indicates the need for common development.
Cities should establish and improve a green growth system. The economic system may be one of the most important factors as Anhui develops green growth, such as with the establishment of a carbon emission restraint mechanism, the construction of a green growth energy technology development mechanism, and the improvement of the taxation system and laws related to the development of the green growth.

CONTRIBUTIONS AND LIMITATIONS
With green growth development is increasingly important considering recent environmental trends, This study develops an urban green growth development index and applies it to Anhui Province in China and its 16 cities. Previously, such analyses have taken place mostly at the provincial level, few studies investigate the dynamic nature of such indices, and research on cities is relatively rare. At the same time, considering the imbalance of regional development, there may be some inadequate explanations of some issues. Future research needs to further consider the uncertainties existing in the calculation process, such as the uncertainty of weight, the uncertainty of normalized treatment, the uncertainty of clustering method, etc., and build more detailed aspects of the model to cover further aspects of issues associated with green growth.