# Analysis of Public Management Performance Evaluation Model Based on Fuzzy DEA Model

Authors: Chenguang Sun; Le Zhang; Zhihui Mao
Journal: Discrete Dynamics in Nature and Society
 (2022)

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## Abstract

The evaluation of public management performance is the key to identify the effectiveness of the work of public administration, and public policy is an important guarantee for the orderly promotion of the work of public administration; therefore, it is important to analyze the effectiveness of public management policies to evaluate public management performance. Taking environmental protection policies as an example, this paper constructs an environmental-economic DEA efficiency analysis model using the DEA method to conduct a comprehensive evaluation of EEE in different provinces of China. It is found that EEE is highly correlated with the regional economic development level and is highly influenced by policy fluctuations, but the overall EEE of different provinces from 2016 to 2020 tends to be consistent and has a certain degree of stability. The conclusions of this paper have important implications for policy guidance, emphasizing the need to focus on the coordination of economic development and environmental protection, and the need for the improvement of the environmental policy system to be continuously optimized in an incremental manner, taking into account the actual situation of local development.


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## Body

## 1. Introduction

Since the reform and opening up, China has made great achievements in economic development, becoming the world’s second largest economy, gradually grasping the right to speak in the world economic system and increasing its influence in the international community, but in contrast, the environmental pollution problem has become more and more serious [1], and both the central government and local governments are faced with the dilemma of economic development and environmental protection [2–4]. In 2020, China announced that it would strive to achieve carbon neutrality by 2060 and contribute to the international environmental protection cause, which has aroused widespread concern in the international community and is an important event that will affect China’s international reputation in the future. With the main theme of “reducing carbon emissions”, guiding environmental protection has become one of the top priorities of the Chinese government [5, 6]. The key to environmental protection lies in sound public policy guidance. At the macro level, the public administration is the core force in guiding enterprises to reduce carbon emissions, which is the key to promote the orderly implementation of public policies [7, 8]. At the microlevel, policy arrangements also help to benignly guide social forces and the general public to deeply participate in environmental protection. Therefore, it is of great theoretical and practical importance to analyze the policy efficiency of public administration in environmental protection from the perspective of performance evaluation.China’s environmental protection work began with the reform and opening up. In 1992, China regarded sustainable development planning as the core element of future planning. In 2006, carbon emission reduction was first introduced as a control indicator for domestic economic development. In 2015, strict environmental protection regulations began to be implemented. In 2018, Several Opinions on Delineating and Strictly Adhering to the Ecological Protection Red Line was promulgated and implemented, and the ecological red line became the the primary guide for the development of national land space. Along with the continuous iterations and updates of environmental protection policies, China has formed a top-down systematic environmental protection policy mechanism and has made some achievements in environmental protection. However, it is worth noting that economic development has brought environmental pollution problems far beyond policy constraints, with a number of vicious environmental pollution incidents coming to light frequently, sparking widespread concern among public opinion. In December 2016, the country ushered in unprecedented hazy weather, with a rare PM2.5 pollution belt forming in and around Beijing, Tianjin and Hebei. In short, the issue of environmental management has become one of the most important tasks of public administration.However, policy iterations have struggled to keep up with the pace of environmental pollution, leading public administrations to enact a series of air pollution control strategies that optimize structures, strengthen standards, and provide strong oversight one after another. To sustainably improve air quality, the State Council in 2018 versioned the Three-Year Action Plan for Winning the Blue Sky Defense War and advanced the work plan of the Blue Sky Protection Project. The total investment in air pollution treatment is rapidly rising, according to the “2018–2022 China Air Pollution Treatment Industry Market Research and Development Trend Forecast Research Report” reality, in 2020, the industrial sector air pollution treatment or more than 200 billion yuan, during 2018–2022, the treatment equipment will maintain high growth with an annual growth rate of 9.5%. In the trade-off between air pollution treatment and economic development, in order to improve the existing public policy system, improve the efficiency of policy implementation in public administration, and adapt to the requirements of environmental protection, China urgently needs a scientific assessment of the efficiency of current environmental policies [9, 10]. However, few studies have been conducted to systematically analyze and evaluate the efficiency of environmental policies, and there is a need for further comprehensive evaluation using appropriate methods to provide policy recommendations. Therefore, we focus on how to evaluate public management policies and how to conduct a comprehensive evaluation of public administration performance to ensure the economic efficiency of environmental protection policies. More importantly, given the vast size of China and the huge differences in the level of economic development among regions, it is necessary to evaluate public environmental protection policies in different regions in a fair manner. Therefore, this paper takes air pollution control public policy as a case object, adopts a fuzzy-set DEA model, and draws on performance evaluation theory to establish a policy evaluation system that simultaneously takes into account environmental protection and economic development, so as to provide a practical and reliable theoretical reference for public administrations such as the government.


## 2. Related Studies

Public policy refers to a series of measures and management programs enacted by a certain country or region for the management of public affairs. In order to optimize and improve public policies, it is necessary to build an evaluation system to measure and evaluate the scientific and effectiveness of public policies [11], and the information obtained from the evaluation of public policies is also an important basis for improving and adjusting public policies. The information from public policy evaluation is also an important basis for public policy improvement and adjustment [12].The evaluation of public policies mainly focuses on the evaluation of the effects of the policies after their promulgation and implementation, and is mainly based on scientific evaluation tools and instruments to observe the impact and consequences of the policies after their implementation, so as to evaluate the relevance of the policies and the rationality of their contents [13, 14]. Therefore, public policy evaluation is a specialized activity that assesses and judges the social effectiveness, implementation efficiency, and impact of public policies by scientific methods. It is the main reference for the government to formulate and improve policies, and it is also a key measure of the government’s administrative and social management capabilities and achievements, and an important indicator of the government’s governance [15, 16]. Public policy evaluation mainly focuses on information collection, analysis and evaluation of the effects of policy enactment, which can be divided into several levels according to the nature of the effects [17, 18], such as social benefits, economic benefits, cultural impacts, educational significance, etc. [19, 20], which are the results of a comprehensive evaluation of the objectives of the benefits of public policy design and the actual results and additional benefits. The research on public policy evaluation in international and domestic research fields is focused on three main items: system construction, practical issues and evaluation tools and methods [21].Although there is no uniformity in the research community regarding the concept of assessing policy performance, policy performance evaluation has attracted extensive attention from scholars. Performance evaluation encompasses both behavioral and outcome evaluations [22]. The last understanding is more widely used in studies related to policy performance [23], which emphasizes that public policy analysis is a necessary process in policy formulation and includes technical aspects of policy implementation, changes in policy goals, audience size, and changes in stakeholder behavior strategies. In addition, due to the complexity of public policy, the evaluation of public policy performance should be conducted from multiple perspectives [24], based on the rationale and logic of public policy, to assess the consistency between policy outcomes and expectations of policy goals [25]. Environmental policy is an important component of public policy and the top priority for Chinese public administration at the moment [26, 27]. Importantly, the implementation process of environmental policies requires a lot of public sector effort and involves several government departments, therefore, the coordination of authority before the departments under resource constraints is crucial, and the evaluation of the enforceability of the policy is related to whether the policy can be implemented. However, few studies have been conducted to evaluate the implementability of policies, and there is a lack of systematic research on the evaluation of environmental policy efficiency in particular. It is necessary to adopt a suitable method to evaluate the efficiency of environmental policies in China in order to provide a new theoretical perspective to evaluate the performance of public management in China.


## 3. Methodology

Figure1 shows the basic process of model construction, including the process of determining the evaluation objectives, selecting DMUs, constructing the index system and analyzing the results.Figure 1
DEA model construction process.


### 3.1. CCR Model

The CCR model is the closing model of DEA, which assumes that the payoffs of scale will not change for all decision units, and then the production efficiency of each decision unit over the segment. Assume that there aren evaluation units in the production possibility set, and each evaluation unit is a production system consisting of m inputs and s outputs, where xij (i = 1, 2, …, m) denotes the value of the i-th input indicator of the j-th evaluation unit DMUj, yrj (r = 1, 2, …, s) denotes the value of the r-th output indicator of the j-th evaluation unit vii=1,2,…,m represents the measure of the i-th input indicator of the production possibility set, and ur (r = 1, 2, …, s) represents the measure of the r-th output indicator of the production possibility set, both of which are variables. Thus, the planning model for measuring the efficiency of the evaluation unit DMUj0 is as follows [28].(1)max∑r=1suryrj0∑i=1mvixij0,s.t.∑r=1suryrj−∑i=1mvixij0≤0;j=1,2,…,n,ur≥0;i=1,2,…,m,vi≥0;i=1,2,…,s.The above model is a nonlinear programming model, which is difficult to compute. Thus, Charnes and Cooper proposed the Charnes-Cooper transformation, which allows the above nonlinear programming model to change to a model equal to equivalent linear programming model. That is,t=1/∑i=1mvixij0, ur = tur, ωi=tvi, thus obtaining the following model.(2)max∑r=1suryrj0,s.t.∑r=1suryrj−∑i=1mωixij0≤0;j=1,2,…,n,∑i=1mωixij0=1,ur≥0;i=1,2,…,m,vi≥0;i=1,2,…,s.Based on the dual theory of linear programming, the dual form of model (2) is obtained as follows.(3)minθ,s.t.∑j=1nλjxij+si−=θxij0;i=1,2,…,m,∑j=1nλjyrj−sr+=yrj0;r=1,2,…,s,λj,si−,sr+≥0;j=1,2,…,n.When its optimal value is 1, the evaluation unit is technically efficient; it is technically effective; when its optimal value is less than 1, the evaluation unit DMUj0 is technically inefficient. For the model in equation (3), when its optimal value is 1, the evaluation unit DMUj0 is weakly technically efficient; when its optimal value is 1 and satisfied, the evaluation unit DMUj0 is strongly technically efficient; if it is less than 1, the evaluation unit DMUj0 is technically inefficient.


### 3.2. BCC Model

The corresponding CCR model is based on the conjecture of constant returns to scale, so the technical efficiency calculated by the model includes the effect of the scale factor. In order to eliminate the scale factor from the technology level, scholars have developed a data envelopment analysis model based on the variable payoff to scale -BCC model [29].(4)max∑r=1suryrj0+μ0∑i=1mvixij0,s.t.∑r=1suryrj+μ0−∑i=1mωixij0≤0;j=1,2,…,n,∑i=1mωixij0=1,ur≥0;i=1,2,…,m,vi≥0;i=1,2,…,s,where μ0 is the scale factor, reflecting the scale efficiency of the decision unit. Moreover, the above nonlinear planning model is converted into a linear planning model equivalent to it using the Charnes-Cooper transformation. That is, t=1/∑i=1mvixij0, ur = tur, ωi=tvi, η0=tμ0, thus obtaining the following model.(5)max∑r=1suryrj0+η0,s.t.∑r=1suryrj+η0−∑i=1mvixij0≤0;j=1,2,…,n,ur≥0;i=1,2,…,m,vi≥0;i=1,2,…,s.According to the dual theory of linear programming, the dual form of model (5) is obtained as follows:(6)minθ,s.t.∑j=1nλjxij+si−=θxij0;i=1,2,…,m,∑j=1nλjyrj−sr+=yrj0;r=1,2,…,s,∑j=1nλj=1,λj,si−,sr+≥0;j=1,2,…,n.In order to distinguish the arithmetic data of the BCC model from those of the CCR model, scholars define the efficiency values derived from these models as pure technical efficiency. In subsequent studies, the concept of scale efficiency has been defined as the ratio of pure technical efficiency to technical efficiency, which reflects the difference between the current scale of production of the decision unit and the most efficient scale of production.


### 3.3. SBM-DEA Model

The SBM model differs from the traditional CCR and BBC models in that it directly incorporates the slack variables into the objective function, and the optimal solution shows that there are too many inputs or too few outputs for any production process. The optimal solution shows that there are too many inputs or too few outputs for any production process, and the amount of excess inputs or too few outputs is called the slack variable. The model is expressed as (7), (8).(7)minρ=1−1/m∑i=1msi−/xi01+1/s∑r=1ssr+/yr0,(8)s.t.x0=Xλ+s−,y0=Yλ−s+,λ≥0,s−≥0,s+≥0,λ is the weight attached to the efficiency measure of each decision unit, and s− and s+ represent the excess input and output deficit. The fraction of too much input and too little production is referred to as slack. In model (7), the decision unit is said to be SBM efficient when and only when the objective function value ρ∗=1. ρ∗=1 means that s−s−∗=s+∗=0, i.e., there is no excess input and no output deficit. For an invalid decision unit DMU0, x0 = Xλ + s+∗ and y0 = Yλ − s−∗. To make this decision unit effective for SBM, the input redundancy s−∗ needs to be subtracted and the output deficiency s+∗ needs to be added, a planning process known as SBM planning.


### 3.4. Environmental and Economic DEA Model

In the face of deteriorating environmental quality, both local and central governments are gradually raising the profile of environmental protection in their work. However, in the face of environmental challenges, governments are still forced to make trade-offs between environmental protection and local economic development. The government cannot sacrifice economic development to protect the environment in the face of pressure from citizens’ employment and government finances, nor can it sacrifice environmental quality to support economic development in the face of citizens’ growing demands for urban environment and air quality in recent years. The trade-off between economic development and environmental protection is inevitable, and it is therefore important to propose an assessment model that can simultaneously evaluate environmental and economic performance. With this need, Zhou and Wu used the model in equation (9) to assess environmental performance and estimated the environmental-economic efficiency of different countries or regions based on the SBM-DEA model [30].(9)λ∗=minλ,s.t.∑k=1kzkxnk≤xn0;n=1,2,…,N,∑k=1kzkymk≥ym0;m=1,2,…,M,∑k=1kzkujk=λuj0;j=1,2,…,J,Zk≥0;k=1,2,…,K,where xnk (n = 1, 2, …, N) denotes the n-th input indicator value of the k-th evaluation unit DMUk; ymk (m = 1, 2, …, M) denotes the m-th desired output indicator value of the k-th evaluation unit DMUk; umk (j = 1, 2, …, J) denotes the m-th undesired output indicator value of the kth evaluation unit DMUk. denotes the m-th undesired output indicator value of the kth evaluation unit DMUk. Based on this, this paper improves Wu’s model by adding slack variables to the objective function to describe the undesired output, and based on this, the conditional constraints on the undesired output are improved:(10)minρ∗=1−1/N∑n=1Nsn−/xn01+1/M∑m=1Msm−/ym0+suk−/λ∗u0,s.t.∑k=1kzkxnk+snk−=xn0;n=1,2,…,N,∑k=1kzkymk−smk+=ym0;m=1,2,…,M,∑k=1kzkujk+suk−=λuj0;j=1,2,…,J,Zk≥0;k=1,2,…,K.In the model, snk− denotes the input redundancy of input variables, suk− denotes the redundancy of nondesired output; smk + denotes the redundancy of desired output, where is the planning result of model (9). That is, all decision units in model (10) are effective in terms of environmental pollution. The planning result ρ∗ is the economic efficiency when all evaluation units are efficient in terms of environmental pollution, i.e., environmental-economic efficiency. When ρ∗ = 1 and sn−=su−=sm+=0, the evaluation unit is said to be environmentally and economically efficient.Whenλ∗ = 1, the evaluation unit is the environmental efficiency value, and ρ∗ = 1 is the economic efficiency value when λ∗ = 1. On this basis, the environmental-economic efficiency (EEE) can be calculated by assigning different weights to economic efficiency and environmental efficiency. EEE can be expressed by equation (11), and in the empirical study, local governments can assign different weights to environmental efficiency λ∗ and economic ρ∗ according to the local development characteristics and governance tendencies.(11)EEE=ω1λ∗+ω1ρ∗.In other words, the proposed environmental-economic model not only allows for the evaluation of multiple policy objectives simultaneously, but also allows for the setting of weights according to the local governments’ preferences for different policy outcomes. In the next section of the empirical analysis, the assumption that economic efficiency and environmental efficiency are equally important will be made, i.e.,ω1=ω2=0.5 (Figure 2). In conclusion, the model in this paper overcomes the shortcomings of traditional DEA models and provides a new methodological tool for studying environmental efficiency.Figure 2
EEE model.


### 3.5. Index System Construction and Data Sources

This paper argues that it is inevitable that each region in China invests capital, labor, and consumes energy in production activities, while generating GDP. Therefore, this paper selects capital stock, labor force and total energy consumption as input factors based on previous research. The provincial GNP is the desired output indicator, and the total air emission is the nondesired output indicator (Figure3).Figure 3
Index system.


#### 3.5.1. Capital Input

The impact of investment in production activities in different regions on output is not only based on current investment, but also on the capital stock formed by past investment, so this paper uses the capital stock to measure the input of capital factors. There are no direct statistics on capital in each region of China. Instead, the perpetual inventory method has been used in the literature to estimate the capital stock in different regions [30]. The estimation of the fixed capital stock Kn,t can be calculated by(12)Kn,t=Kn,t−1+In,t−Dn,t=1−dn,tKn,t−1+In,t,where Kn,t denotes the fixed capital stock of province n in year t; In,t denotes the new investment in fixed assets in province n in year t. In this study, the total value of fixed capital formation published in the China Statistical Yearbook in that year is used; Dn,t denotes the depreciation of fixed assets in province n in year t, and dn,t denotes the depreciation rate. In the empirical analysis of this paper, 10% is used as the depreciation rate, and 2000 is used as the base period. In other words, the fixed capital stock of each province and city region is estimated by (11), and the data from 2016 to 2020 are finally used as input variables for the study.


#### 3.5.2. Labor Input

Labor is a very basic factor of production, which is crucial for economic growth. In the classical growth theory stage of the economic growth system, the quantity of labor is considered to play an important role in economic growth. In both classical and neoclassical trade theories, labor endowment is also a central element. Labor and other productive resource factors play a key role in a country. This has an impact on comparative advantage, industrial structure and trade structure. China’s cheap labor force is very large and has become a key advantage for the country’s economic development. It also influences China’s industrial output and trade imports and exports. It plays a key role in the country’s economic growth. In order to provide a more realistic picture of the production life of a region, this paper uses labor force inputs including “urban unit workers”, “private enterprise workers”, and “urban and rural workers engaged in self-employment activities”. In this paper, the labor input includes “urban single-employee”, “private enterprise”, and “urban and rural self-employed”.


#### 3.5.3. Resource Consumption Input

Adequate energy input is the basic material basis to ensure the normal development of economic and social production and life, and to maintain the survival and development of human beings. Rough energy consumption patterns have led to a series of energy problems, which have become two bottlenecks limiting the economic development of China. It is imperative to conserve energy, reduce consumption, and improve energy efficiency. In this paper, resource consumption inputs are used as “total energy consumption” published in the China Energy Statistics Yearbook.


#### 3.5.4. Expected and Unexpected Outcomes

GDP is taken as the desired output of the production process. The nondesired output is the negative output of the production process, the less the better. In this paper, the nondesired output is the total emissions of each province as the target of environmental efficiency of each province. In the calculation, the total emissions include the sum of sulfur dioxide, nitrogen oxides, and soot emissions published in the China Statistical Yearbook. The emissions come from industrial processes, urban living, motor vehicle emissions, and emissions from centralized pollution control facilities. Since the total emissions as undesired output are the local emissions of the evaluation unit, the environmental efficiency evaluation results estimated by the model reflect the local emissions efficiency. In practice, the emission sources of urban pollutants in a certain area may come from other neighboring areas, which means that the local air quality is affected not only by the local air pollution emission efficiency, but also by the air pollution emission efficiency of the neighboring areas, so the local environmental efficiency assessed by the model cannot fully reflect the local air quality. Therefore, this paper concludes that although the proposed environmental-economic model does not fully reflect the air quality of a region, it is sufficient to assess the efficiency of air pollution control and economic development of the local government.Due to the lack of data for some regions, Tibet, Hong Kong, Macau, and Taiwan are excluded from the decision unit of this study. The raw data for the model variables are obtained from the China Statistical Yearbook and the China Energy Statistical Yearbook published by the National Bureau of Statistics.


## 3.1. CCR Model

The CCR model is the closing model of DEA, which assumes that the payoffs of scale will not change for all decision units, and then the production efficiency of each decision unit over the segment. Assume that there aren evaluation units in the production possibility set, and each evaluation unit is a production system consisting of m inputs and s outputs, where xij (i = 1, 2, …, m) denotes the value of the i-th input indicator of the j-th evaluation unit DMUj, yrj (r = 1, 2, …, s) denotes the value of the r-th output indicator of the j-th evaluation unit vii=1,2,…,m represents the measure of the i-th input indicator of the production possibility set, and ur (r = 1, 2, …, s) represents the measure of the r-th output indicator of the production possibility set, both of which are variables. Thus, the planning model for measuring the efficiency of the evaluation unit DMUj0 is as follows [28].(1)max∑r=1suryrj0∑i=1mvixij0,s.t.∑r=1suryrj−∑i=1mvixij0≤0;j=1,2,…,n,ur≥0;i=1,2,…,m,vi≥0;i=1,2,…,s.The above model is a nonlinear programming model, which is difficult to compute. Thus, Charnes and Cooper proposed the Charnes-Cooper transformation, which allows the above nonlinear programming model to change to a model equal to equivalent linear programming model. That is,t=1/∑i=1mvixij0, ur = tur, ωi=tvi, thus obtaining the following model.(2)max∑r=1suryrj0,s.t.∑r=1suryrj−∑i=1mωixij0≤0;j=1,2,…,n,∑i=1mωixij0=1,ur≥0;i=1,2,…,m,vi≥0;i=1,2,…,s.Based on the dual theory of linear programming, the dual form of model (2) is obtained as follows.(3)minθ,s.t.∑j=1nλjxij+si−=θxij0;i=1,2,…,m,∑j=1nλjyrj−sr+=yrj0;r=1,2,…,s,λj,si−,sr+≥0;j=1,2,…,n.When its optimal value is 1, the evaluation unit is technically efficient; it is technically effective; when its optimal value is less than 1, the evaluation unit DMUj0 is technically inefficient. For the model in equation (3), when its optimal value is 1, the evaluation unit DMUj0 is weakly technically efficient; when its optimal value is 1 and satisfied, the evaluation unit DMUj0 is strongly technically efficient; if it is less than 1, the evaluation unit DMUj0 is technically inefficient.


## 3.2. BCC Model

The corresponding CCR model is based on the conjecture of constant returns to scale, so the technical efficiency calculated by the model includes the effect of the scale factor. In order to eliminate the scale factor from the technology level, scholars have developed a data envelopment analysis model based on the variable payoff to scale -BCC model [29].(4)max∑r=1suryrj0+μ0∑i=1mvixij0,s.t.∑r=1suryrj+μ0−∑i=1mωixij0≤0;j=1,2,…,n,∑i=1mωixij0=1,ur≥0;i=1,2,…,m,vi≥0;i=1,2,…,s,where μ0 is the scale factor, reflecting the scale efficiency of the decision unit. Moreover, the above nonlinear planning model is converted into a linear planning model equivalent to it using the Charnes-Cooper transformation. That is, t=1/∑i=1mvixij0, ur = tur, ωi=tvi, η0=tμ0, thus obtaining the following model.(5)max∑r=1suryrj0+η0,s.t.∑r=1suryrj+η0−∑i=1mvixij0≤0;j=1,2,…,n,ur≥0;i=1,2,…,m,vi≥0;i=1,2,…,s.According to the dual theory of linear programming, the dual form of model (5) is obtained as follows:(6)minθ,s.t.∑j=1nλjxij+si−=θxij0;i=1,2,…,m,∑j=1nλjyrj−sr+=yrj0;r=1,2,…,s,∑j=1nλj=1,λj,si−,sr+≥0;j=1,2,…,n.In order to distinguish the arithmetic data of the BCC model from those of the CCR model, scholars define the efficiency values derived from these models as pure technical efficiency. In subsequent studies, the concept of scale efficiency has been defined as the ratio of pure technical efficiency to technical efficiency, which reflects the difference between the current scale of production of the decision unit and the most efficient scale of production.


## 3.3. SBM-DEA Model

The SBM model differs from the traditional CCR and BBC models in that it directly incorporates the slack variables into the objective function, and the optimal solution shows that there are too many inputs or too few outputs for any production process. The optimal solution shows that there are too many inputs or too few outputs for any production process, and the amount of excess inputs or too few outputs is called the slack variable. The model is expressed as (7), (8).(7)minρ=1−1/m∑i=1msi−/xi01+1/s∑r=1ssr+/yr0,(8)s.t.x0=Xλ+s−,y0=Yλ−s+,λ≥0,s−≥0,s+≥0,λ is the weight attached to the efficiency measure of each decision unit, and s− and s+ represent the excess input and output deficit. The fraction of too much input and too little production is referred to as slack. In model (7), the decision unit is said to be SBM efficient when and only when the objective function value ρ∗=1. ρ∗=1 means that s−s−∗=s+∗=0, i.e., there is no excess input and no output deficit. For an invalid decision unit DMU0, x0 = Xλ + s+∗ and y0 = Yλ − s−∗. To make this decision unit effective for SBM, the input redundancy s−∗ needs to be subtracted and the output deficiency s+∗ needs to be added, a planning process known as SBM planning.


## 3.4. Environmental and Economic DEA Model

In the face of deteriorating environmental quality, both local and central governments are gradually raising the profile of environmental protection in their work. However, in the face of environmental challenges, governments are still forced to make trade-offs between environmental protection and local economic development. The government cannot sacrifice economic development to protect the environment in the face of pressure from citizens’ employment and government finances, nor can it sacrifice environmental quality to support economic development in the face of citizens’ growing demands for urban environment and air quality in recent years. The trade-off between economic development and environmental protection is inevitable, and it is therefore important to propose an assessment model that can simultaneously evaluate environmental and economic performance. With this need, Zhou and Wu used the model in equation (9) to assess environmental performance and estimated the environmental-economic efficiency of different countries or regions based on the SBM-DEA model [30].(9)λ∗=minλ,s.t.∑k=1kzkxnk≤xn0;n=1,2,…,N,∑k=1kzkymk≥ym0;m=1,2,…,M,∑k=1kzkujk=λuj0;j=1,2,…,J,Zk≥0;k=1,2,…,K,where xnk (n = 1, 2, …, N) denotes the n-th input indicator value of the k-th evaluation unit DMUk; ymk (m = 1, 2, …, M) denotes the m-th desired output indicator value of the k-th evaluation unit DMUk; umk (j = 1, 2, …, J) denotes the m-th undesired output indicator value of the kth evaluation unit DMUk. denotes the m-th undesired output indicator value of the kth evaluation unit DMUk. Based on this, this paper improves Wu’s model by adding slack variables to the objective function to describe the undesired output, and based on this, the conditional constraints on the undesired output are improved:(10)minρ∗=1−1/N∑n=1Nsn−/xn01+1/M∑m=1Msm−/ym0+suk−/λ∗u0,s.t.∑k=1kzkxnk+snk−=xn0;n=1,2,…,N,∑k=1kzkymk−smk+=ym0;m=1,2,…,M,∑k=1kzkujk+suk−=λuj0;j=1,2,…,J,Zk≥0;k=1,2,…,K.In the model, snk− denotes the input redundancy of input variables, suk− denotes the redundancy of nondesired output; smk + denotes the redundancy of desired output, where is the planning result of model (9). That is, all decision units in model (10) are effective in terms of environmental pollution. The planning result ρ∗ is the economic efficiency when all evaluation units are efficient in terms of environmental pollution, i.e., environmental-economic efficiency. When ρ∗ = 1 and sn−=su−=sm+=0, the evaluation unit is said to be environmentally and economically efficient.Whenλ∗ = 1, the evaluation unit is the environmental efficiency value, and ρ∗ = 1 is the economic efficiency value when λ∗ = 1. On this basis, the environmental-economic efficiency (EEE) can be calculated by assigning different weights to economic efficiency and environmental efficiency. EEE can be expressed by equation (11), and in the empirical study, local governments can assign different weights to environmental efficiency λ∗ and economic ρ∗ according to the local development characteristics and governance tendencies.(11)EEE=ω1λ∗+ω1ρ∗.In other words, the proposed environmental-economic model not only allows for the evaluation of multiple policy objectives simultaneously, but also allows for the setting of weights according to the local governments’ preferences for different policy outcomes. In the next section of the empirical analysis, the assumption that economic efficiency and environmental efficiency are equally important will be made, i.e.,ω1=ω2=0.5 (Figure 2). In conclusion, the model in this paper overcomes the shortcomings of traditional DEA models and provides a new methodological tool for studying environmental efficiency.Figure 2
EEE model.


## 3.5. Index System Construction and Data Sources

This paper argues that it is inevitable that each region in China invests capital, labor, and consumes energy in production activities, while generating GDP. Therefore, this paper selects capital stock, labor force and total energy consumption as input factors based on previous research. The provincial GNP is the desired output indicator, and the total air emission is the nondesired output indicator (Figure3).Figure 3
Index system.


### 3.5.1. Capital Input

The impact of investment in production activities in different regions on output is not only based on current investment, but also on the capital stock formed by past investment, so this paper uses the capital stock to measure the input of capital factors. There are no direct statistics on capital in each region of China. Instead, the perpetual inventory method has been used in the literature to estimate the capital stock in different regions [30]. The estimation of the fixed capital stock Kn,t can be calculated by(12)Kn,t=Kn,t−1+In,t−Dn,t=1−dn,tKn,t−1+In,t,where Kn,t denotes the fixed capital stock of province n in year t; In,t denotes the new investment in fixed assets in province n in year t. In this study, the total value of fixed capital formation published in the China Statistical Yearbook in that year is used; Dn,t denotes the depreciation of fixed assets in province n in year t, and dn,t denotes the depreciation rate. In the empirical analysis of this paper, 10% is used as the depreciation rate, and 2000 is used as the base period. In other words, the fixed capital stock of each province and city region is estimated by (11), and the data from 2016 to 2020 are finally used as input variables for the study.


### 3.5.2. Labor Input

Labor is a very basic factor of production, which is crucial for economic growth. In the classical growth theory stage of the economic growth system, the quantity of labor is considered to play an important role in economic growth. In both classical and neoclassical trade theories, labor endowment is also a central element. Labor and other productive resource factors play a key role in a country. This has an impact on comparative advantage, industrial structure and trade structure. China’s cheap labor force is very large and has become a key advantage for the country’s economic development. It also influences China’s industrial output and trade imports and exports. It plays a key role in the country’s economic growth. In order to provide a more realistic picture of the production life of a region, this paper uses labor force inputs including “urban unit workers”, “private enterprise workers”, and “urban and rural workers engaged in self-employment activities”. In this paper, the labor input includes “urban single-employee”, “private enterprise”, and “urban and rural self-employed”.


### 3.5.3. Resource Consumption Input

Adequate energy input is the basic material basis to ensure the normal development of economic and social production and life, and to maintain the survival and development of human beings. Rough energy consumption patterns have led to a series of energy problems, which have become two bottlenecks limiting the economic development of China. It is imperative to conserve energy, reduce consumption, and improve energy efficiency. In this paper, resource consumption inputs are used as “total energy consumption” published in the China Energy Statistics Yearbook.


### 3.5.4. Expected and Unexpected Outcomes

GDP is taken as the desired output of the production process. The nondesired output is the negative output of the production process, the less the better. In this paper, the nondesired output is the total emissions of each province as the target of environmental efficiency of each province. In the calculation, the total emissions include the sum of sulfur dioxide, nitrogen oxides, and soot emissions published in the China Statistical Yearbook. The emissions come from industrial processes, urban living, motor vehicle emissions, and emissions from centralized pollution control facilities. Since the total emissions as undesired output are the local emissions of the evaluation unit, the environmental efficiency evaluation results estimated by the model reflect the local emissions efficiency. In practice, the emission sources of urban pollutants in a certain area may come from other neighboring areas, which means that the local air quality is affected not only by the local air pollution emission efficiency, but also by the air pollution emission efficiency of the neighboring areas, so the local environmental efficiency assessed by the model cannot fully reflect the local air quality. Therefore, this paper concludes that although the proposed environmental-economic model does not fully reflect the air quality of a region, it is sufficient to assess the efficiency of air pollution control and economic development of the local government.Due to the lack of data for some regions, Tibet, Hong Kong, Macau, and Taiwan are excluded from the decision unit of this study. The raw data for the model variables are obtained from the China Statistical Yearbook and the China Energy Statistical Yearbook published by the National Bureau of Statistics.


## 3.5.1. Capital Input

The impact of investment in production activities in different regions on output is not only based on current investment, but also on the capital stock formed by past investment, so this paper uses the capital stock to measure the input of capital factors. There are no direct statistics on capital in each region of China. Instead, the perpetual inventory method has been used in the literature to estimate the capital stock in different regions [30]. The estimation of the fixed capital stock Kn,t can be calculated by(12)Kn,t=Kn,t−1+In,t−Dn,t=1−dn,tKn,t−1+In,t,where Kn,t denotes the fixed capital stock of province n in year t; In,t denotes the new investment in fixed assets in province n in year t. In this study, the total value of fixed capital formation published in the China Statistical Yearbook in that year is used; Dn,t denotes the depreciation of fixed assets in province n in year t, and dn,t denotes the depreciation rate. In the empirical analysis of this paper, 10% is used as the depreciation rate, and 2000 is used as the base period. In other words, the fixed capital stock of each province and city region is estimated by (11), and the data from 2016 to 2020 are finally used as input variables for the study.


## 3.5.2. Labor Input

Labor is a very basic factor of production, which is crucial for economic growth. In the classical growth theory stage of the economic growth system, the quantity of labor is considered to play an important role in economic growth. In both classical and neoclassical trade theories, labor endowment is also a central element. Labor and other productive resource factors play a key role in a country. This has an impact on comparative advantage, industrial structure and trade structure. China’s cheap labor force is very large and has become a key advantage for the country’s economic development. It also influences China’s industrial output and trade imports and exports. It plays a key role in the country’s economic growth. In order to provide a more realistic picture of the production life of a region, this paper uses labor force inputs including “urban unit workers”, “private enterprise workers”, and “urban and rural workers engaged in self-employment activities”. In this paper, the labor input includes “urban single-employee”, “private enterprise”, and “urban and rural self-employed”.


## 3.5.3. Resource Consumption Input

Adequate energy input is the basic material basis to ensure the normal development of economic and social production and life, and to maintain the survival and development of human beings. Rough energy consumption patterns have led to a series of energy problems, which have become two bottlenecks limiting the economic development of China. It is imperative to conserve energy, reduce consumption, and improve energy efficiency. In this paper, resource consumption inputs are used as “total energy consumption” published in the China Energy Statistics Yearbook.


## 3.5.4. Expected and Unexpected Outcomes

GDP is taken as the desired output of the production process. The nondesired output is the negative output of the production process, the less the better. In this paper, the nondesired output is the total emissions of each province as the target of environmental efficiency of each province. In the calculation, the total emissions include the sum of sulfur dioxide, nitrogen oxides, and soot emissions published in the China Statistical Yearbook. The emissions come from industrial processes, urban living, motor vehicle emissions, and emissions from centralized pollution control facilities. Since the total emissions as undesired output are the local emissions of the evaluation unit, the environmental efficiency evaluation results estimated by the model reflect the local emissions efficiency. In practice, the emission sources of urban pollutants in a certain area may come from other neighboring areas, which means that the local air quality is affected not only by the local air pollution emission efficiency, but also by the air pollution emission efficiency of the neighboring areas, so the local environmental efficiency assessed by the model cannot fully reflect the local air quality. Therefore, this paper concludes that although the proposed environmental-economic model does not fully reflect the air quality of a region, it is sufficient to assess the efficiency of air pollution control and economic development of the local government.Due to the lack of data for some regions, Tibet, Hong Kong, Macau, and Taiwan are excluded from the decision unit of this study. The raw data for the model variables are obtained from the China Statistical Yearbook and the China Energy Statistical Yearbook published by the National Bureau of Statistics.


## 4. Results and Discussion

As shown in Table1, Beijing and Tianjin have been assessed as having a valid EEE among the 30 provinces and municipalities assessed. Hebei Province was assessed as EEE-valid in 2016, and its EEE score and EEE ranking decreased each year for the next four years, dropping from sixth place in China to 18th place in 2020. Shanghai’s EEE has improved over the five-year period, reaching EEE validity in 2018–2020. Other provinces EEE rankings are more stable and less volatile. The kernel density distributions of the x-axis and y-axis indicators are obtained by fitting the Kernel function accordingly. The kernel density distribution shows a relatively flat single-peaked feature, which indicates that the economic and environmental efficiency of most provinces converge to a steady-state level, while a few provinces are at more extreme (too high and too low) levels (Figure 4).Table 1
EEE evaluation in China.
Region2016–2020 mean value on EEE20162017201820192020Beijing1.001.001.001.001.001.00Tianjin1.001.001.001.001.001.00Shanghai0.970.950.881.001.001.00Shandong0.941.001.001.001.000.72Jiangsu0.891.000.741.001.000.73Guangdong0.851.001.001.000.650.60Zhejiang0.750.731.000.760.620.63Hunan0.740.690.770.650.611.00Fujian0.640.620.670.670.650.57Hebei0.611.000.550.540.500.46Hubei0.580.580.590.570.580.59Sichuan0.560.670.590.580.480.46Guangxi0.530.560.540.540.550.48Hainan0.530.570.540.530.510.49Jiangxi0.520.570.530.520.490.49Anhui0.520.580.540.520.500.46Shanxi (陕西)0.510.560.510.510.480.47Henan0.500.550.510.500.480.47Liaoning0.500.540.530.520.530.38Jilin0.470.530.480.470.430.42Chongqing0.460.490.460.450.460.45Neimenggu0.440.500.460.430.420.39Heilongjiang0.430.430.410.450.470.40Guizhou0.420.380.390.420.460.44Yunnan0.400.380.380.380.480.39Shanxi (山西)0.350.400.370.350.340.31Gansu0.350.390.370.360.330.32Qinghai0.330.350.340.340.330.30Xinjiang0.320.350.340.340.310.28Ningxia0.310.330.340.320.300.28Figure 4
EEE scatter plot.The heat map (Figures5–10) of EEE in China shows that the geographical variation of EEE in China in 2016–2020 is small in magnitude and maintains a steady state, with the highest EEE in Beijing-Tianjin-Hebei region, and the Yangtze River Delta and Pearl River Delta also in the top, but with lower EEE out of the marginal provinces. In other words, EEE is positively correlated with the level of economic development. However, there are some provinces with large fluctuations, such as Hunan Province, which saw a significant rise in EEE in 2020, but provinces such as Shandong, Jiangsu and Guangdong saw a large decline. 2020 saw a large change in the national environmental policy system, with the drawing of ecological red lines forming a compulsory constraint on regional development and construction, stimulating the effective implementation of environmental policies, which to some extent had a significant impact on regional EEE impact, in short, policy arrangements are the primary factor affecting EEE.Figure 5
2016 EEE value in China.Figure 6
2017 EEE value in China.Figure 7
2018 EEE value in China.Figure 8
2019 EEE value in China.Figure 9
2020 EEE value in China.Figure 10
2016–2020 EEE mean value in China.Figure11 similarly shows that the annual variation in EEE is small, with the top cities and cities with higher levels of economic development ranking high in EEE efficiency, but the environmental problems of resource-dependent provinces (e.g., Shanxi and Gansu) and economically underdeveloped provinces (e.g., Qinghai, Xinjiang, and Ningxia) should not be underestimated and require further attention.Figure 11
EEE value in different regions.


## 5. Conclusions

Environmental policy efficiency is the most important part of evaluating public management performance. This paper proposes an improved environmental-economic DEA model, which not only takes into account the environmental efficiency and economic efficiency of air pollution prevention and control policies, but also sets the corresponding weights according to the different policy objectives of the government, so as to obtain the evaluation results that meet the actual needs. Theoretically, this paper represents the first comprehensive evaluation of the performance and efficiency of public administration in China, analyzing intercity differences in the efficiency of public administration in China in terms of public policy. In the empirical study, the model is used to assess the overall efficiency of regional air pollution prevention and control in China, providing a methodological and data base for the subsequent assessment of policy efficiency. The study finds that when environmental and economic objectives are given the same policy preferences, environmental inefficiency is the main reason for the low environmental-economic efficiency of air pollution prevention and control in the region. Specifically, the heterogeneity of environmental economic efficiency in different Chinese provinces is highlighted, indicating that regional imbalances remain an important issue to be addressed in China’s environmental protection policy system. The findings of this study have important value for public policy making in China, suggesting that future environmental public policies in China should be tilted towards the backward regions. There are still some limitations in this paper. For example, the time span of this paper is 2016–2020, and a dataset with a longer time horizon could be selected in the future to analyze the efficiency of public management over time. Second, although the selection of input-output indicators is based on extensive literature, there is still a possibility that some indicators are overlooked and do not reflect the real world. [31].



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*Source: 8228763-2022-04-28.xml*