Research on Green Economic Efficiency Measurement and Influencing Factors in Chengdu-Chongqing Twin-City Economic Circle--Analysis Based on Super-Efficient SBM and Tobit Model

. Based on the panel data of 16 cities in the Chengdu-Chongqing region from 2005 to 2020, this paper measures the green economic efficiency of each city in the Chengdu-Chongqing region using the super-efficient SBM model that takes into account non-desired outputs, and analyses the influencing factors of green economic efficiency in the Chengdu-Chongqing region using the Tobit model. The results show that the overall green economic efficiency of the Chengdu-Chongqing region is at a moderate level, but shows a fluctuating upward trend with the change of time. From the perspective of the influencing factors: the level of economic development, the level of science and technology, and the endowment structure have a significant positive contribution to the green economic efficiency of the Chengdu-Chongqing region; the environmental regulation does not have a significant contribution to the green economic efficiency due to the differences between cities; the industrial structure dominated by the secondary industry and the urbanisation rate have a significant negative inhibiting effect.


Introduction
The Chengdu-Chongqing region has an important ecological status in the western region of China and is an important part of the strategic pattern of "two screens and three belts" for ecological security in China. However, due to the large-scale investment of capital, labour and resources in the western development for more than 20 years, the rapid economic development of the Chengdu-Chongqing region has also paid a huge ecological and environmental price, and the sloppy economic growth has led to the destruction of ecological environment and the waste of energy resources. Therefore, promoting the development of green economy in Chengdu-Chongqing region and improving its green economic efficiency have an important supporting role for the construction of ecological civilization in China as well as promoting the Yangtze River Economic Belt strategy [1] . Therefore, this paper takes 16 cities in Chengdu-Chongqing twin-city economic circle as the research object, refers to scholars' measurement methods on green economic efficiency, combines the development status of Chengdu-Chongqing twin-city circle, determines input, expected output and non-expected output indicators, and measures the green economic efficiency value of Chengdu-Chongqing region. Secondly, the Tobit model is used to refine and analyse the factors affecting the green economic efficiency of Chengdu-Chongqing region and put forward relevant policy suggestions to promote the development of green economic efficiency.

Literature review
The term "green economy" was introduced by Pearce in 1989, but not clearly defined [2] ; the United Nations Environment Programme defined green economy in 2008 as a form of economy with harmonious ecological, economic and social development. In the field of green economy research, green economy efficiency measurement and factor analysis are highly representative. Among them, Yang Long, Hu Xiaozhen, and Zhu Dajian believe that green economic efficiency is derived on the basis of green economy and economic efficiency, and factors such as environmental pollution should be added to the traditional economic efficiency calculation [3] [4] . Golley and Guo, Bingnan et al. argue that green economic efficiency is a win-win indicator of environmental protection and economic development, and is an input-output efficiency that integrates the efficiency of economic operation, production efficiency, resource utilisation, environmental constraints and pollution emission intensity [5] [6] .Tone incorporates environmental pollution indicators into the input-output indicator system and proposed the SBM model to measure green economic efficiency [7] .
Birol analysed the degree of influence of technological progress on green economic efficiency [8] ; Yuli Nie and Huwei Wen found that the optimization and upgrading of industrial structure is conducive to improving the efficiency of resource utilization, and the green economic efficiency and the level of economic development show a relationship of first depression and then increase [9] . Wang xia, Xu Xiaohong, Wu Chuanqing, Zhou Xiyi Min and other scholars believed that the level of economic development, industrial structure, environmental pollution control, and the level of opening to the outside world have significant effects on the green economic efficiency of the Yangtze River Economic Belt, and there are spatial differences [10] [11] ; Wu Zunjie and Liu Haoran used the super-efficient SBM model to measure the green economic efficiency of the Yangtze River Economic Belt, Beijing-Tianjin-Hebei region, and their influencing factors were studied [12] [13] . In summary, there are abundant studies on green economic efficiency, but fewer studies have focused on the Chengdu-Chongqing region. Therefore, in this paper, the super-efficient SBM model with non-desired outputs is used to measure the green economic efficiency of 16 cities in the Chengdu-Chongqing region by directly incorporating non-desired indicators into the model. Secondly, the Tobit model is used to explore the factors affecting the green economic efficiency and provide references and suggestions for the development of the green economy in the Chengdu-Chongqing region.

Measurement method
(1) Super-efficient SBM model The super-efficient SBM model solves the problem that the efficiency value of the SBM model cannot be greater than one, allowing the results to be compared. In the super-efficient SBM model, which takes into account non-desired outputs, each city is considered as a production decision unit (DMU) and the green development efficiency of its production decision units is measured, assuming that each DMU has m inputs:  , and the set of production possibilities for the green economic efficiency measure is Equation (1) Based on the above possibility set, the super-efficient SBM model for measuring production decision units is(2)(3) x x y y z z y , , x y z in Equation (2) denotes the input, desired output, and non-desired output slack variables, respectively; j  is the envelope multiplier, which is the weight vector of inputs and outputs. *  is the green economic efficiency value to be measured, and the larger its value is, the higher the green economic efficiency is.

Selection of indicators and data sources
The input-output variables selected in this paper are shown in the following figure1. (1) Input indicators Labour input: In this paper, the total number of people employed in the city at the end of the year (10,000) is chosen as a measure of labour input.
Capital input: The level of economic development varies among regions in Chengdu and Chongqing, and there may be differences in price indices and depreciation rates of investment goods. Considering the availability and accuracy of data in each city, this paper uses the total annual fixed asset investment in billion yuan as the amount of capital input.
Energy input: Based on the existing literature, it is found that the total energy consumption can reflect the use of various energy sources more effectively and can avoid the errors caused by the differences in energy structures of different regions. Therefore, the indicator for energy input in this paper is chosen as the total regional energy consumption.
(2) Expected output index In this paper, the real GDP of 2005 as the base period is selected as the variable of expected output, in order to truly reflect the economic development level of Chengdu-Chongqing region.
(3) Non-desired output indicators In this paper, considering the availability of data and the accuracy of the results, industrial wastewater emissions (10,000 tons), industrial sulfur dioxide emissions (10,000 tons) and industrial smoke (dust) emissions (10,000 tons) from industrial production in Chengdu and Chongqing are selected as the indicators of non-expected output.
In this paper, 16 cities in the Chengdu-Chongqing region from 2005 to 2020 were selected as samples in this paper to measure their green economic efficiency, in which the measured input-output data were mainly obtained from the China Urban Statistical Yearbook, statistical yearbooks and statistical bulletins published by the statistical bureaus of various cities, etc. The descriptive statistics of each variable are shown in Table  1, and the missing data and abnormal data were complemented by the mean interpolation method and linear interpolation method.

Analysis of green economic efficiency results
In this paper, the green economic efficiency of the twincity economic circle in the Chengdu-Chongqing region from 2005 to 2020 is measured using Maxdea-Ultra9 software and the super-efficient SBM model, and the results are shown in the following Table2. Calculated from the average values in the table, the average value of green economic efficiency in the Chengdu-Chongqing region is about 0.63, indicating that its green economic efficiency is at a medium level and there is still room for improvement. Secondly, from the efficiency values of each city, the efficiency values of Chongqing and Zigong are greater than 1 and 0.9 respectively, indicating that their green economic efficiency development is at a high level, but the average efficiency values of most of the cities are lower than 0.8 and are between 0.3 and 0.7, indicating that the economic development and environmental protection and resource development and utilization of these cities have not reached a balanced state, and the green economic development efficiency needs to be improved.
Secondly, as there are large regional differences among the cities in the Chengdu-Chongqing twin-city economic circle, this paper draws a time trend graph to analyse their green economic efficiency from the perspective of time evolution. As can be seen in Figure 2 below, the average value of green economic efficiency is generally on a fluctuating trend. Secondly, the green economic efficiency of Chengdu and Chongqing are on the rise respectively, with the efficiency value of Chengdu being lower than the overall part before 2010 and exceeding the overall value and rising after 2010; the efficiency value of Chongqing has been greater than the overall value and rose significantly in 2020, with the efficiency value reaching about 1.8, indicating that Chongqing has a high level of green economic efficiency and a good balance between ecological environment and economic development. The higher the level of economic development, the more material and financial support can be provided for the development of green economy, the urban environment is treated, pollution emissions are reduced and the energy structure is optimised, which will lead to the continuous improvement of green economic efficiency. Therefore, this paper hypothesizes that a higher level of economic development has a positive promotion effect on the green economic efficiency of the Chengdu-Chongqing region.
(2) Industrial structure Different industries have different impacts on green economic efficiency. The secondary industry plays an important role in the national economic growth, and consumes a lot of energy and resources and emits a lot of pollutants. Therefore, this paper assumes that an increase in the industrial structure of the secondary industry has a negative inhibiting effect on the green economic efficiency of the Chengdu-Chongqing region.
(3) The level of science and technology An increase in the level of science and technology is conducive to an increase in total factor productivity, which leads to continuous innovation in green technology in the host city, improves the efficiency of resource utilization and ultimately promotes the improvement of green economic efficiency. Therefore, this paper assumes that the improvement of science and technology level has a positive contribution to the green economic efficiency of the Chengdu-Chongqing region.
(4) Level of urbanization Urbanisation on the one hand promotes coordinated economic and urban-rural development, which has a positive impact on green economic efficiency. On the other hand, in the process of urbanisation, a certain amount of environmental pollution and pollutant emissions are generated, which inhibits the development of green economic efficiency. Therefore, this paper assumes that the level of urbanisation has a significant impact on the development of green economic efficiency in the Chengdu-Chongqing region, but the direction is uncertain.
(5) Strength of environmental regulation Environmental regulation is an act of the government to restrain economic agents with high energy consumption and high pollutant emissions. Stronger government regulation can force enterprises to accelerate innovation in green technology, reduce pollutant emissions and promote the improvement of green economic efficiency. Therefore, this paper hypothesises that an increase in the intensity of environmental rules has a significant contribution to the development of green economic efficiency in the Chengdu-Chongqing region.
(6) Endowment structure This paper uses the capital-labour ratio to measure the structure of endowments. The capital-labour ratio can affect the ecological environment on the basis of the industrial structure. Its increase leads to a shift in economic structure from labour-intensive to capitalintensive, and its increased technological level leads to a greater ability to manage the environment and promote green economic efficiency. Therefore, this paper hypothesises that the endowment structure has a positive contribution to the development of green economic efficiency in the Chengdu-Chongqing region.

The construction of Tobit regression model
This paper adopts Tobit model to analyse the influencing factors of green economic efficiency in Chengdu-Chongqing region, the model is shown in (1) (2) below.
In the above equation,  is a constant term,  is a vector of regression coefficients,  is a random disturbance term, * it y is the green economic efficiency value of the ith city in year t, and * it X is a factor affecting green economic efficiency.

Variable descriptions and data sources
The level of economic development is measured by GDP per capita, the industrial structure by the share of value added in the secondary sector in GDP, the level of scientific and technological development by the number of patents granted, the level of urbanisation by the urbanisation rate of the resident population, the intensity of environmental regulation by the comprehensive utilisation rate of general industrial solid waste, and the structure of endowment by the capital-labour ratio.
All the above data were obtained from the China Urban Statistical Yearbook, the statistical yearbooks of cities and municipalities, statistical bulletins, and the Bureau of Ecology and Environment, and individual missing data were filled in by mean interpolation and linear interpolation. The descriptive statistics of the relevant variables are shown in Table 3.

Regression results analysis
This paper uses stata17.0 software for Tobit regression, and the p-value in the LR test is 0 less than 0.05, so this paper chooses the Tobit model with random effects. The regression results are shown in the following table4. 0.000 Note: The labels *, **, and *** in the above table indicate that they are significant at the 10%, 5%, and 1% significance levels, respectively.
The following analysis can be derived from the regression results in the table above: (1) The coefficient of GDP per capita is positive and significant, indicating that there is a significant positive promotion relationship between green economic efficiency and the level of economic development. The higher the level of economic development, the more material and financial resources the city can have to combat environmental pollution and strengthen environmental protection, making the green economic efficiency increasing, and the hypothesis holds.
(2) The coefficient of the industrial structure dominated by the secondary industry is negative and significant. The secondary industry is mainly manufacturing industry, especially in Chongqing, whose leading industry is industry, which consumes a lot of energy and resources, emits a lot of pollutants and makes environmental pollution increasingly serious, which reduces the development of green economic efficiency in Chengdu and Chongqing, and the hypothesis is valid.
(3) The coefficient of science and technology level is positive and significant, which is due to the continuous innovation and development of science and technology, which makes the input of production factors decrease continuously, the efficiency of resource utilization increases and waste decreases, which promotes the green economic efficiency, and the hypothesis holds.
(4) The coefficient of urbanization rate is negative and significant. From the above, it can be seen that the direction of the influence of urbanization level on green economic efficiency is uncertain. According to the analysis of the results in this paper, the environmental pollution and resource waste generated by urbanization in Chengdu and Chongqing regions outweigh its positive effect on promoting urban and rural economic development and inhibit the development of green economic efficiency. The hypothesis holds.
(5) The coefficient of environmental regulation is positive, but not significant. This may be due to the fact that cities in the Chengdu-Chongqing region differ greatly in the number of above-scale enterprises, their governance capacity, pollutant treatment technology and government regulation, making the general industrial solid waste utilization rate vary across cities and leading to insignificant results. (6) The coefficient of endowment structure is positive and significant because industries in the Chengdu-Chongqing region are constantly adjusting from labor-intensive to capital-and technology-intensive industries, and the capital-and technology-intensive industries are more inclined to tertiary industries such as services and tourism, and this transformation leads to less pollution and a better ecological environment, which promotes the improvement of green economic efficiency in the Chengdu-Chongqing region, and the hypothesis holds.

Research findings
In general, the green economic efficiency of the Chengdu-Chongqing region from 2005 to 2020 is at an intermediate level, and the average efficiency values of most cities are between 0.3 and 0.7, indicating that the green economic efficiency of the Chengdu-Chongqing region needs to be improved. The time trend graph shows that the average value of green economic efficiency is fluctuating upwards. Chengdu and Chongqing are in an increasing state respectively, and the efficiency value of Chongqing is always greater than the overall value, indicating that Chongqing has a higher level of green economic efficiency and a better balance between ecological environment and economic development.
Next, this paper analyzes the factors affecting green economic efficiency and finds that the level of economic development, the level of science and technology, and the structure of endowment have a significant role in promoting the development of green economic efficiency. The industrial structure dominated by secondary industry and urbanization have a significant inhibitory effect on the development of green economic efficiency. Among them, environmental regulation can promote green economic efficiency, but its effect is not significant due to the differences between cities.

Policy Recommendations
(1) Implementing a harmonious win-win situation between economic development and environmental protection Cities in the Chengdu-Chongqing region should adhere to economic development and pursue economic development benefits and environmental benefits with a new development concept. Secondly, the cities should support the transformation of enterprises to high-tech, information industry, high-end management services and other green aspects, so that technological development can optimize the resource utilization system and drive the improvement of green economic benefits.
(2) Optimize the industrial structure and promote the development of green economy According to the actual situation of each city, adjust the proportion of secondary industries, strictly control the growth of high energy-consuming and high-polluting industries, and fully implement clean production. Strengthen the proportion of high-tech industries, modern service industries, modern special agriculture and other strategic emerging industries, create green manufacturing demonstration units, and build a green manufacturing system.
(3) promote the development of new urbanization with the construction of ecological civilization as the core The cities in the Chengdu-Chongqing region should strengthen the construction of new urbanization, deeply promote urbanization with ecology and greenery as the core, and promote coordinated urban development. For example, under the premise of park city construction, Chengdu should focus on creating a series of green consumption models that run through the concept of green sustainable development, such as healthy retirement and even green catering, green tourism, green finance, etc. Each city should create its own city card according to its own characteristics and advantages, combined with green development.
(4) Increase government investment and improve scientific and technological innovation ability Each government in the Chengdu-Chongqing region should increase support for cutting-edge research in science and technology innovation, and improve the innovation mechanism with the government as the leader and enterprises as the main body. Improve the conversion rate of scientific and technological achievements, cultivate a number of high-tech industries with core competitiveness and science and technologybased small and medium-sized enterprises, and drive the joint development of scientific and technological achievements and related industries so that scientific and technological achievements can be continuously applied and updated.