Regional Ecological Security Evolution and Green Economy: An Empirical Study

How to maintain and improve ecological security in the process of green economy development is of great significance in terms of both theory and practice. Hence, in this paper, based on the framework of DPESAR (driving force-pressure-exposure-sensitivityadaptation-response), we establish a structural model using SPASS and Eviews6 software to identify the contributing factors for green economy development. We use panel data of Liaoning Province, China, from 1995 to 2017 to analyze the relationships among these factors and their indicators. Furthermore, we simulate and identify the ideal evolution status of the ecological security and green economy development up to the year of 2022. Our results show that first, those adjusted indicators of ecological security can greatly promote green economy development. Second, specific regulation indicators and scope can be obtained by identifying the evolutionary state of ecological security. *ird, the interactions among the government, firms, and the public should be considered to further develop regional ecological security and green economy.


Introduction
In recent years, how to promote green economy development while maintaining ecological security has become a hot topic for academics, industry practitioners, and policymakers. At present, much research has been done from different perspectives.
Wang and Wu [1] explore the regional ecological security gradual-change process and explain the gradual positive phase transition process from the "Rheology-Mutation" theory of safety science. Wu et al. [2] discuss the selection and weighting methods of regional ecological security evaluation indicators based on the principal component projection evaluation model. ey establish an evaluation model of regional ecological security and apply this model for Anhui Province, China. Li et al. [3] build the "Human Green Development Indicator," assuming equal importance of the two dimensions of social and economic sustainable development and sustainable development of ecological resources and environment. ey measure the green development indicator values of 123 countries and their rankings based on 12 element indicators. Zhou et al. [4] summarize the key economic development indicators and predicted the future green economy development for 2016-2020 in Liaoning Province of China. Wang and Liu [5] employ the Biennial Weight Modified Russell Model to study the effects and mechanisms of energy conservation and emission reduction on China's Green Total Factor Productivity under resource and environmental constraints. ey analyze whether energy conservation and emission reduction could achieve a win-win situation between environmental protection and China's economic development. Wang et al. [6] adopt the PSR framework to build a land ecological security evaluation indicator system of Yongzhou City from the perspectives of nature, society, and economy. ey adopt the range method and the entropy weight method to evaluate the land ecological security of Yongzhou City from 2003 to 2012. Peng et al. [7] reveal the driving mechanism behind the vulnerability of the ecological environment and the spatial clustering characteristics of the vulnerability of urban agglomerations. ey determine the Moran Index (MI) with spatial autocorrelation model and estimate the ecological environment vulnerability in 2005, 2011, and 2017. ey show that the driving forces of ecological environment vulnerability of Yangtze River city group have changed from natural factors to social-economic factors and then to policy factors. eir results show that the environmental protection investment has the greatest impact on ecological carrying elastic force, followed by the proportion of the tertiary industry.
Although the above-mentioned research has laid an important foundation for building and refining the relevant theories of ecological security, the research on the relationship between the evolutionary state of regional ecological security and the development of green economy has not attracted the attention of scholars, especially from the perspective of the dynamic evolution of ecological security. To fill this research gap, Liaoning Province, China, is taken as the research object in this paper, and the panel data comprising environmental economy and ecological security factors are obtained to establish a model on the relationship between ecological security evolution and green economy development. It is based on the ecological safety status indicator system with the DPESAR (driving force-pressureexposure-sensitivity-adaptation-response) framework from 1995 to 2017. e optimal control model for developing the green economy is identified through the adjustment of the control variables. In short, this paper makes a major contribution by providing managerial and policy insights for green economy development. e optimal control model of green economy constructed in this paper can also be used as a reference for the development of green economy in other countries and regions. e rest of this paper is organized as follows. Section 2 details the indicator selection and data processing in this research. In Section 3, we build a measurement model so that the evolution trend of the different levels of indicators can be identified. In Section 4, we build a structural equation model to study the mutual evolution among the indicators. After that, we set up an optimal control model and use it to identify the optimal state equations in Section 5. Finally, we summarize our conclusions and managerial insights in Section 6.

Original Indicator System and Data Normalization.
PSR [8], DPSIR [9], DPSER [10], and other ecological security evaluation indicator systems commonly used in the literature have several common shortcomings such as ambiguity of specific classification and application context differences. Hence, in this research, the area method is adopted in view of the actual situation in Liaoning Province in particular and China in general. Specifically, the economic, social, and environmental aspects are classified according to the main research directions of sustainable development, and then the specific goals are determined by the layered approach [11][12][13][14][15][16][17].
erefore, based on the framework of DPESAR, a total of 64 indicators are selected including resource and environment indicator, natural resources indicator, and environmental policies and investment. Following Ge et al. [18], to measure Level-1 comprehensive economic and environmental indicators, we adopt the six indicators of DPESAR for Level-2 indicators. e indicators are defined as follows: A(k) driving indicator, B(k) presser indicator, C(k) exposure indicator, D(k) sensitivity indicator, E(k) adaptation indicator, and F(k) response indicator. All data are based on the National Statistical Yearbook 1995-2017, the information provided by the local authorities, and Beijing EPS Data Company. e entropy evaluation method [19] is adopted to normalize the six secondary indicators (see Table 1).

Reliability Analysis.
e Spass17 statistical software is used to perform reliability analysis on the Level-3 indicators corresponding to each Level-2 indicator. e test results are shown in Table 2.
It can be seen from Table 2 that, in addition to the standardization-based Cronbach's alpha for the adaptation indicator E which is less than 0.050, the reliability of the remaining Level-2 indicators is above 0.7, which basically meets the reliability requirements. e lower reliability of the adaptation index E is because the main factors governing the regional climate are affected by global climate change. e last row in Table 2 is the reliability analysis for the five Level-2 indicators except the pressure indicator B. e pressure indicator B is excluded because it belongs to the control index, and the man-made interference factor is very strong. In recent years, it is basically not affected by other factors.
Excluding the unreasonable items marked in Table 2, the original indicator system is modified, then the new indicator is weighted by the entropy evaluation method, the new Level-2 indicator relative weight is obtained, and the normalized data processing is performed (see Table 3).

Establishment of the Measurement Model.
In order to clearly identify the evolution trend of the Level-2 indicators to the Level-3 indicators, it is necessary to build a measurement model. e Eviews6 software is used to perform regression analysis on the data shown in Table 3. Under the condition that the regression coefficient meets the significance level, it is maximized as much as possible. e driving force A(k) is firstly selected to analyze the influence of the Level-3 indicator A3(k) under the control of it (see Table 4) in this paper.
At the same time, the regression residual is detected by the stable test. For the same reason, other measurement models are also available.
erefore, the autoregression model with the optimal value of more than 80% is established as follows: 2 Mathematical Problems in Engineering    e maximum significance level and the optimum can be obtained after the regression analysis of (1)-(15) is conducted (see Table 5).
Since most of the data obtained are from the National Statistical Yearbooks and related regional organizations, there are errors in the data, and the randomness by various industries is strong. Hence, it is satisfactory that the adjusted optimum can reach 80% or more.

Explanations of the Measurement Model.
When discussing the measurement model, we need to understand why the Level-2 indicators may have a negative impact on the Level-3 indicators. It can be seen from the regression results of the measurement model that A3(k) can be completely affected by A(k) without the influence of other Level-2 indicators. In addition to being affected by A(k), A7(k), A8(k), and A9(k) are also negatively affected by the interaction of B(k) and F(k). is is because the proportion of tourism output to GDP is affected by the number of people employed in tourism, which is also restricted due to environmental protection. At the same time, the total export-import volume and the throughput of coastal ports are also affected by the government's investment policy and local economic protection.
B2(k) is positively affected by B(k) and A(k) because the improvement of industrial sewage discharge is related to the reduction of total solid waste production; the gradual decrease of the impact speed is related to the improvement of science and technology; B2(k) is negatively affected by C(k) because the pollution is increasing with the increase in environmental governance investment. B1(k) and B5(k) are positively affected by B(k) and are negatively affected by A(k); this is because the total solid waste reduction should be positively affected by the reduction of industrial sewage discharge and industrial waste gas emissions and negatively related to the increase in per capita GDP and the throughput of coastal ports.
Both C1(k) and C4(k) are positively affected by the square of A(k) because the urban green area and the growth of domestic tourists in Liaoning Province are driven by the per capita GDP, the annual growth rate of tourists, and the tourism output value, and the speed of the green industry development is increasing year by year.
D2(k) is negatively affected by C(k) because the reduction in dust fall quantity is related to the increase in the number of domestic tourists in Liaoning Province. D9(k) is negatively affected by the interaction between A(k) and B(k) because the increase in per capita water resources and per capita GDP is negative correlation to the acceleration of "three wastes" emissions.
F4(k) is positively affected by A(k), because the planned fixed-asset investment growth will increase with the natural population growth rate, the proportion of the population of urban and town, per capita GDP, investment, and other indicators; F4(k) is directly affected by F3(k), which is indirectly affecting F5(k). In recent years, F4(k) has been affected by F8(k) and F9(k) due to the economic policy of "One Belt and One Road." erefore, our results indicate that, in the process of institutional reform, it is necessary to focus on measuring the negative effect of the Level-2 indicators on the Level-3 indicators.
e elimination or reduction of this negative effect will greatly promote the ecological security of Liaoning Province and the development of a green economy.

Establishment of the Structural Equation Model
In order to study the mutual evolution among the Level-2 indicators, it is necessary to establish a structural equation model. e Eviews6 software is used to perform regression analysis on the data of the Level-2 indicators. Under the condition that the regression coefficient meets the significance level, it is maximized as much as possible. e nonlinear structural equations are obtained as follows: Firstly, after the cointegration test, it can be seen that the adaptation indicator E(k) is stable, so the role of the adaptation indicator is neglected when studying the relationship among the Level-2 indicators. Secondly, in order to establish the Level-2 indicators' optimal state equation of the system, the Eviews6 software is employed. After repeated tests, it is maximized as much as possible under the condition that the regression coefficient satisfies the significance level. e autoregression structural equations for A(k), C(k), and D(k) are obtained as follows:

Mathematical Problems in Engineering
When computing D(k + 1), an autoregressive structural equation of A(k) needs to be established in case that the normalized data of A(k) is needed: Hence, the data of A(k) can be calculated from the response indicator F(k). Regression results of (16)-(23) are shown in Table 6.
It can be seen from the structural equation (16) that A(k) is negatively affected by F(k), indicating that, under the past or existing system, the government decision-making has a negative impact on the driving-force indicators, so institutional reform shall be carried out. Moreover, it can be calculated based on the structural equation (17) that when D(k) > 0.2989, the government decision-making can play a positive role on the pressure indicator through the exposure indicator. is is because if the government's response indicator is biased towards economic development, it will result in a decline in investment in pollution control, which will inevitably lead to increasing emissions of "three wastes." It can be seen from structural equations (16) and (17) that the effect of increasing the driving-force indicator is beneficial to the indicators of exposure and sensitivity. It can be seen from the calculation of structural equation (18) that the drivingforce indicator A(k) has a negative effect on the government's response indicator. is is because the increase in the import and export volume of A(k) (including the tourism industry in B(k)) and the throughput of coastal ports (with the consumption of large-scale enterprises in the province) is difficult for the government to determine the economic growth rate in the province, especially under the premise that the system is not transformed. And when the resources are exhausted, the growth rate of GDP can only be reduced. It can be seen from the autoregressive structural equation of A(k) that the driving-force indicator can be completely controlled by the response indicator, which is an abnormal phenomenon. From the perspective of economic development, government intervention can only play an auxiliary rather than dominant role in the development of the natural environment.

e Optimal Control Model and Preliminary Prediction.
Since the adaptation status indicator is mainly determined by climatic factors in the natural environment, the climatic environment status of a region is affected by the global climate environment and geographic location. In the measurement model analysis earlier, the effect of the region on adaptation indicator only accounted for more than 20%. erefore, as the state variable, the adaptation indicator E is not affected by the local environmental control, so it is ignored in this paper. At the same time, since the sensitivity indicator C(k) is affected by the one-phase lag of the pressure indicator, the lagged item C(k − 1) is placed in the control vector when the objective function is established. According to the specific meaning of the Level-3 indicators, it is determined that the vector function x(k) � [C(k), C(k − 1), D(k)] T represents the indicator system state variable, u(k) � [A(k), B(k), F(k)] T represents the control variable of the indicator system, and the correlation matrix of the state indicator and the control indicator is (24) e objective function of building an ecological security indicator system is (25) e constraint equation of equation (24) is determined by equations (21)-(23) as where the regularity conditions need to be met: Considering that Q , R are both the positive definite matrix, the larger x(k) 2 and u(k) 2 , the larger the objective function. Under the premise that the control vector is given in the theoretical model, it is important to find out whether the maximum value can be obtained in the objective function and how to obtain the maximum value. According to the relevant regulations of China and Liaoning Province during 2016-2020, this paper obtains the control variable data for the next five years. at is, en the state equation is used to predict the trend in the next five years to determine whether it can achieve the desired result.
According to the official plan for 2016-2020, the threewaste emission shall be reduced by 20% each year. Specifically, the amount of agricultural fertilizers used reached the highest level. It shall be reduced by 20% per year. e increase in the number of employees in the tourism industry can drive the domestic and overseas market demand, expand green industries, and reduce dependence on industrial output. According to the national requirements and industry requirements for 2016-2020, the number of employees in the tourism industry should increase by more than 15% per year (20% is used in this paper). As a result, the main indicators of pressure growth from 2018 to 2023 can be obtained, which is listed in Table 7.
According to the calculation of the pressure indicator B(k), the data of the control indicator B(k) from 2018 to 2023 is obtained as shown in Table 8 under the assumption that the other Level-3 indicators remain unchanged.
According to the official targets for the five-year period of 2016-2020, the industrial removal rate of sulfur dioxide can be increased by 20% per year, and the regional GDP growth rate is set according to the national minimum standard of 6%. e growth rate of fixed assets investment is 20%, and other response control data are given according to the targets for the years of 2016-2020 and combined with the data of Liaoning Province in previous years. In this way, the F(k) indicators are obtained (see Table 9).
From Table 9, the normalized data is obtained according to the indicator system, and then the weights of the response indicators in Table 3 are combined to obtain the control indicator of F(k): Taking the data of 2015, 2016, and 2017 as the initial data, a numerical study was carried out using MATLAB, and the state change curve of Figure 1 was obtained. e results showed that it was very unsatisfactory. e indicator D(k) has been in a state of decline, indicating that the existing system must be changed. Otherwise, the ecological security It can be seen from the state equation of D(k) that there is one item (−0.582002C(k − 1)B(k)) for the decline. at is, there is a negative effect due to the interaction between the pressure indicator of the current year and the exposure indicator of the previous year. If the lagged effect of the exposure indicator C(k) can be eliminated by institutional reform and the negative effect coefficient of 0.582002 is adjusted to be 0.1 or less, a better result illustrated in Figure 2 can be obtained. erefore, this coefficient is very sensitive to the exposure and sensitivity indicators. However, indicator D(k) is still unsatisfactory.

Correction and the Optimal State Equation.
In order to achieve satisfactory results, the state equation needs to be corrected and optimized. is is because, in the process of economic development, the internal mechanism of the relevant indicators will not change greatly in a short time period. Moreover, the concept of a smooth transition of the green economy also requires the gradual reform of enterprises and governments. At the same time, the improvement of exposure indicator C(k) and sensitivity indicator D(k) shall meet the requirements of consistency. erefore, the reforms outlined in the official plan (called the 13th Five-Year Plan in China) only reduce or eliminate the negative effects in the evolution of the ecological security state to varying degrees, that is, the changes in the degree of effect.
en, according to (21)-(23), the state equation containing the influence factor is obtained as follows:   Table 9: F(k) indicators during the years of 2016-2020.
Industrial removal rate of sulfur dioxide (%) F1 0.728 Planned regional GDP growth rate (%) F3 6.5 Planned fixed-asset investment growth rate (%) F4 20 Planned public budget revenue growth (%) F5 6.5 Planned total revenue growth of tourism of more than (%) F6 11.18 Planned total retail sales of consumer goods growth rate (%) In this research, ideally, both the exposure indicator C(k) and the sensitivity indicator D(k) can be steadily improved through changing the values of the influence factors, which help promote the development of green economy. However, it can be seen that the faster the state curve x(k) � [C(k), C(k − 1), D(k)] T rises, the larger the optimal control target is. Since it is difficult to solve the theoretical optimal control model of (31), we turn to analyze the evolution of the state process brought about by the change of the influence factors α i , i � 1, 2, 3, 4, 5. e following results can be observed through simulations.
e increase or decrease of the influence factor α 1 does not change the evolution trend of the state process but consistently rises or lowers the curves of C(k) and D(k); the increase of the influence factor α 2 rapidly rises the curve of the exposure indicator C(k) and rapidly lowers the curve of the sensitivity indicator, and the two curves become steeper. Conversely, the decrease of the influence factor α 2 results in the lower of the C(k) curve and the rise of the curve of the sensitivity indicator D(k), the distance between the two curves becomes shorter, and the shape of the curve tends to be straight; the increase of the influence factor α 3 will cause both curves to rise. However, as α 3 increases, the D(k) curve rises rapidly. As α 3 decreases, the C(k) curve lowers rapidly. e increase (decrease) of the influence factorα 4 will cause both curves to rise (lower) at the same time, but D(k) curve changes faster and the factor is more sensitive. e increase (decrease) of the influence factor α 5 will cause the C(k) curve and the D(k) curve to lower (rise), while D(k) curve changes faster and the factor is more sensitive.
Based on the nature of the change of the above influence factors α i , i � 1, 2, 3, 4, 5, the following set of influence factor values was selected through simulations: e ideal simulation state evolution result is obtained as shown in Figure 3.
To ensure the realization of the expected goals, the value of the influence factor α 1 was increased by about 90% from its original value, which required the enforcement of government decision-making institutions to be strengthened; the value of the influence factor α 2 was increased by about 7% on the original basis, which required the mutual effort of enterprises and communities to reduce the effect of pollution. e value of the influence factor α 3 remains almost unchanged. e value of the influence factor α 4 was increased by about 62% on the original basis, which required the government to further develop tourism resources and increase the output value of the tourism industry. At the same time, the total amount of solid waste and the application amount of agricultural fertilizer shall be reduced. e value of the influence factor α 5 was also reduced by about 90% on the original basis, and it was necessary to eliminate the exposure indicator C(k) by the lag effect brought about by the pressure indicator. e ecological security indicators and green economy development issues can be effectively solved through the above calculations.

Conclusions
In this paper, we adopt the DPESAR indicator framework which is combined with the ecological security status and development of the green economy of Liaoning Province, China. We propose and refine a total of 64 Level-3 indicators of the evolution relationship between the ecological security and green economy development. Furthermore, we use the data on the ecological security and green economy from 1995 to 2017 to build a state equation model for this evolutionary relationship. In addition, the evolution of different state equations is explored, and the development of state indicators is improved through the adjustment of the control variables. Furthermore, the optimal control model for the development of the green economy is obtained. e main conclusions of this research are as follows. First, several Level-2 indicators have a negative effect on the Level-3 indicators. Hence, the interactions among the government, firms, and the public should be considered to identify the symptoms and eliminate or reduce such negative effects. Second, the driving-force indicator A(k) has a negative effect on the government's response indicators. is is because the inconsistency between the government and the public and firms can cause the government to make relatively arbitrary plans. Lastly, it can be seen from the optimal control model that the current economic system has no significant promotional effect on the development of green economy, and under the current situation, the decline of the sensitivity indicator will result in the deterioration of the ecological security. However, the efforts of the government can prevent the deterioration of the ecological environment or even improve it, thereby promoting the development of the green economy. erefore, our research shows that the key factors for the development of the measurement model and the structural model can be identified directly or indirectly. en the specific regulation indicators and scope can be obtained by studying the evolutionary state of ecological security. is can provide a theoretical basis for the ecological security and green economy development of different countries and regions.

Data Availability
e data used to support the study are available within the article.

Conflicts of Interest
e authors declare that they have no conflicts of interest.