China’s environmental governance efficiency evaluation based on novel cross-efficiency network DEA model

Abstract

This study evaluates the environmental governance efficiency (EGE) of 30 Chinese provinces using an enhanced neutral cross-efficiency network DEA model. Following the “attention-action-outcome” framework, EGE is divided into response efficiency (EGRE) and implementation efficiency (EGIE). Results show that while EGE exhibits a fluctuating upward trend, it remained low at 0.254 in 2022. EGIE outperforms EGRE on the whole but is more volatile. The eastern region achieves the highest efficiencies, while the western region performs the worst. Intra-group disparities significantly exceed inter-group disparities for all three types of efficiency. Moreover, the development disparities in EGIE have roughly exhibited a fluctuating downward trend since 2016. A quadrant analysis offers region-specific recommendations to improve EGE and support sustainable development.

Introduction

As the largest developing country in the world, China’s previous extensive development model has led to severe environmental pollution¹, posing severe challenges to people’s health and high-quality economic development². To address these dilemmas, the Chinese government has consecutively implemented a series of environmental governance measures. For example, in 2007, the central government formally incorporated environmental protection indicators into the performance evaluation system for local officials³; and in 2015, a new environmental protection law was enforced⁴. Additionally, the expenditure on energy conservation and environmental protection in government fiscal budgets has continually increased, from RMB 256.68 billion in 2011 to RMB 523.58 billion in 2022. Under the leadership of the government, both production activities and public lifestyles have gradually shifted towards greener practices⁵, leading to significant improvements in environmental quality. According to the China Statistical Yearbook, emissions of sulfur dioxide and nitrogen oxides decreased from 22.18 million tons and 24.04 million tons in 2011 to 2.44 million tons and 9.01 million tons in 2022, respectively.

From the perspective of governance outcomes, China’s environmental governance measures have achieved remarkable results, which can also be verified through numerous studies demonstrating the effectiveness of environmental governance measures. For instance, Zhou et al.⁶ found, based on data from the Yangtze River Delta region in China, that environmental regulations can effectively reduce haze pollution. Wang et al.⁷ utilized enterprise-level data from China to discover that environmental taxes contribute to decreasing wastewater discharge. However, the current situation of high input in environmental governance in China is unlikely to change in the short term. In this context, whether China’s environmental governance efficiency (EGE) has improved has become a research hot^8,9,10. Furthermore, as a pivotal force in the environmental governance system, the government plays an irreplaceable role¹¹. The report of the 19th National Congress of the Communist Party of China also explicitly stated that the government should play a leading role in the environmental governance system¹². Therefore, the efficiency of governmental environmental governance has also attracted the attention of some scholars^13,14. Unfortunately, existing research has confined government environmental governance merely to a sub-process ranging from government environmental governance measures to environmental governance outcomes, neglecting the significant role played by government environmental attention in environmental governance. According to the attention-based theory, organizational behavior is typically the result of an organization’s allocation and management of attention¹⁵. Consequently, the process of governmental environmental governance should encompass the logical chain of “governmental environmental attention - governmental environmental measures - environmental governance outcomes”. In other words, government environmental governance not only involves the implementation sub-stage of environmental governance, which encompasses the transformation from environmental governance measures to environmental governance outcomes, but also encompasses the response sub-stage of environmental governance, which entails the transformation from government environmental attention to government environmental governance measures. While some scholars have employed econometric models to validate the effectiveness of the above logical chain^16,17,18, research that analyzes it from an efficiency perspective remains scarce.

As a governance activity involving multiple inputs and outputs, Data Envelopment Analysis (DEA) has become a commonly used method for assessing the EGE¹⁴. However, existing studies have exclusively employed the DEA model under the self-assessment mode for analysis, which may lead to the dilemma where the assessment results are not accepted by other research subjects^19,20. As an effective complement to the self-assessment mode, the cross efficiency DEA model can obtain more reliable results by considering both self-assessment and peer-assessment simultaneously^21,22. Although scholars have proposed numerous cross efficiency DEA models, their application in the field of environmental governance remains limited. Furthermore, while DEA can handle multiple inputs and outputs simultaneously, it does not imply that more indicators selected are better^23,24. Reasonable indicator selection is crucial for obtaining reliable results^25,26,27. In this context, each selected indicator should play a role in efficiency assessment as much as possible. To put it another way, the weight assigned to each indicator in the efficiency assessment should be maximized as much as possible. Based on above considerations, this paper proposes a novel neutral cross network DEA model and applies it to the assessment of government EGE across 30 provinces in China.

The main contributions of this paper are twofold: Firstly, we analyze the EGE of the Chinese government by following the logical chain of “attention - action - outcome”, enriching the relevant research on EGE and contributing to a comprehensive understanding of the effectiveness of resource allocation in the Chinese government’s environmental governance. Secondly, we develop a novel cross efficiency network DEA model, thereby expanding the relevant research on DEA.

The structure of the paper is arranged as follows: The section two provides a literature review; the proposed model is presented in the section three; the validation of the model’s effectiveness and the empirical analysis of the efficiency of China’s government environmental governance are covered in the section four; and the section five gives conclusions and policy implications.

Literature review

To achieve the construction of ecological civilization, China has invested substantial resources in environmental governance²⁸. Although China’s environmental quality has significantly improved in recent years, whether these resources have been utilized efficiently has remained a topic of concern among scholars. In this context, different methods have been employed to evaluate the EGE. Early research tended to use the treatment rate of specific pollutant indicators to characterize EGE, as exemplified by Fu²⁹ and Pan et al.³⁰. However, these studies overlooked the resource inputs involved in environmental governance, failing to comprehensively reflect the environmental governance process. To address these issues, Stochastic Frontier Analysis (SFA) and Data Envelopment Analysis (DEA) have emerged as prevalent methods for analyzing EGE. For instance, Fan et al.³¹ employed SFA to evaluate the efficiency of solid waste collection services in 30 provinces in China. Li et al.³² utilized the DEA model to assess the EGE of 86 iron and steel enterprises in China. However, it should be noted that the reliability of SFA results is closely tied to the artificially specified functional form³³, and this method struggles to handle scenarios with multiple outputs³⁴. Consequently, the DEA model is widely adopted for assessing EGE.

The evaluation of EGE at the provincial level in China has received widespread attention from scholars. For instance, Tang et al.³⁵ used the SBM-DEA model to assess the EGE of 30 provinces in China. Similarly, Hou et al.³⁶ employed the super-efficiency SBM-DEA model to analyze the EGE of 30 provinces in China. Building on considerations of technological heterogeneity, Liu et al.³⁷ utilized the meta-frontier DEA model to evaluate the EGE of 30 provinces in China. Moreover, EGE has also been studied at the city level¹⁰, industrial sector level³⁸ and enterprise level³². Furthermore, as a crucial agent in environmental governance, whether governments have achieved effectiveness in this domain has also attracted considerable attention. For instance, Wang and Guo¹⁴employed the GML index based on DEA to evaluate the governmental EGE across 284 cities in China and explored the positive impact of digital technology on the efficiency. Yang et al.¹² further subdivided governments into central and local governments, analyzing the governmental EGE in 30 provinces of China.

In addition to evaluating EGE independently, some scholars have integrated economic production and environmental governance into a unified analytical framework, using network DEA models for analysis. For example, Wu et al. (2016) constructed a two-stage DEA model that includes shared inputs and resource feedback to evaluate the production efficiency and waste treatment efficiency of China’s industrial sectors⁸. Chen et al. (2022) developed a two-stage DEA model that accounts for heterogeneous emission reduction paths to assess the production and waste gas treatment efficiency of 106 Chinese cities³⁹. Tang et al.⁴⁰ used a network SBM-DEA model to analyze the production and solid waste treatment efficiency of 30 provinces in China. Wang and Feng⁴¹ further developed a network DEA model that includes production sub-stages and three types of pollutant treatment sub-stages (wastewater, waste gas, and solid waste).

It can be observed that scholars have conducted extensive research on EGE. However, research focusing on governmental EGE remains inadequate, and no studies have incorporated government environmental attention into the process of government environmental governance. For governments, environmental governance not only involves inputs (such as environmental regulations and financial support) and corresponding outputs but is also closely related to the speed of response in government actions. In other words, from the moment governments pay attention to environmental issues to the implementation of environmental governance measures, and ultimately to the improvement of environmental quality, this constitutes a relatively complete logical chain of environmental governance. Although a few studies have validated the “attention-action-outcome” research paradigm, for example, Bao and Liu¹⁶ found, based on provincial-level data in China, that emission reduction policies play a significant mediating role between governmental environmental attention and local pollutant emissions. Liu et al.¹⁷, using data from Chinese cities and enterprises, discovered that fiscal expenditure significantly mediates the relationship between governmental environmental attention and corporate carbon emissions. Similar studies also include Zhu et al.⁴² and Chen et al.⁴³. Nonetheless, there is a dearth of research that examines this paradigm from an efficiency perspective.

Additionally, although scholars have employed various DEA models to measure EGE, these models all belong to a self-evaluation mode, where each research subject selects a set of weights most favorable to itself to obtain evaluation results, making the corresponding results difficult to be accepted by other research subjects^19,44. To address this issue, the cross efficiency DEA model has garnered extensive academic attention⁴⁵. Unlike the self-evaluation mode, the cross efficiency DEA model considers the optimal weights for each research subject simultaneously, leading to more reasonable evaluation results^46,47. Unfortunately, the optimal weights obtained from DEA model for each research subject may not be unique^48,49, significantly limiting the application of the cross efficiency DEA model. To this end, scholars have proposed numerous secondary objective methods to obtain a unique optimal weight⁵⁰. Among them, aggressive cross efficiency and benevolent cross efficiency are two common secondary objective methods⁵¹. They seek to maximize and minimize the efficiency of the other evaluation subjects, respectively, while ensuring optimal self-evaluation efficiency for the evaluated subject⁵². Relevant studies include Lim (2012)⁵³ and Davtalab-Olyaie⁵⁴. The dilemma faced by decision-makers lies in choosing between the above two types of cross efficiency DEA models⁵⁵. In this situation, Wang et al.⁵⁶ proposed a neutral cross efficiency model, and similar studies also include Shi et al.⁵⁷ and Chen et al.⁵⁸. The aforementioned cross efficiency DEA models all treat the production system as a black box, neglecting the internal structure of the system, which may lead to biased efficiency results^59,60. Consequently, research based on the cross efficiency network DEA model has gradually gained popularity. For instance, Kao and Liu⁶¹ constructed a benevolent cross efficiency two-stage DEA model; Kremantzis et al.⁶² developed a benevolent cross efficiency two-stage DEA model that considers free intermediate output indicators; from optimistic and pessimistic perspectives, Gangi et al.⁶⁰ established a comprehensive benevolent cross efficiency two-stage DEA model; Örkcü et al.⁶³ extended the neutral cross-efficiency proposed by Wang et al.⁵⁶ to a network structure, and a similar approach also appearing in the research of Liu et al.⁶⁴. Furthermore, some scholars have integrated prospect theory⁶⁵ and regret theory⁶⁶ with network DEA, proposing corresponding cross efficiency network DEA models.

Despite the construction of different cross efficiency models from various perspectives, studies focusing on the maximization of indicator weights remain scarce. As a data-driven method for efficiency evaluation, the importance of indicator selection in DEA has been widely acknowledged^25,26. In this context, the selected indicators should be utilized to their fullest extent in efficiency evaluations. To this end, this paper proposes a novel neutral cross network DEA model and applies it to the efficiency assessment of governmental environmental governance in China, aiming to enrich DEA-related research and provide a clear understanding of the effective utilization of resources in governmental environmental governance in China.

Methodology

Self-evaluation network DEA model

Figure 1 shows a basic two-stage network structure. And each decision-making unit (DMU_j, j = 1, …, n) uses inputs (x_ij, i = 1, …, m) in the sub-stage 1 to produce intermediate outputs (z_pj, p = 1, … ,q). Moreover, these intermediate outputs are consumed to produce finial outputs (y_rj, r = 1, …, s).

Fig. 1

Two-stage network structure.

Kao and Hwang⁵⁹ developed an relational network DEA model to evaluate the efficiency of DMUs that consist of two sub-stages. The corresponding model has since become a widely adopted research paradigm for assessing the efficiency of DMUs with network structures^67,68. The specific model is presented as model (1).

$$\begin{aligned}&\theta _{{kk}} =\hbox{max} \theta_{{kk}}^{1} * \theta_{{kk}}^{2}=\hbox{max} \frac{{\sum_{{r=1}}^{s} { \pi_{{pk}}z_{{pk}} }}}{{\sum_{{r=1}}^{s} { \upsilon _{{ik}} x_{{ik}} }}}*\frac{{\sum_{{r=1}}^{s}{ \mu _{{rk}} y_{{rk}}}}}{{\sum_{{r=1}}^{s} { \pi _{{pk}}z_{{pk}} } }}=\hbox{max}\frac{{\sum_{{r=1}}^{s}{ \mu _{{rk}} y_{{rk}} }}}{{\sum_{{r=1}}^{s}{ \upsilon _{{ik}} x_{{ik}} } }} \hfill \\ &\begin{array}{ll}s.t.&\frac{{\sum_{{r=1}}^{s} { \mu _{{rk}}y_{{rj}} } }}{{\sum_{{r=1}}^{s} {\upsilon _{{ik}} x_{{ij}} } }}\leqslant 1,\quad j=1,\ldots,n \\ &\frac{{\sum_{{r=1}}^{s}{ \pi_{{pk}} z_{{pj}} }}}{{\sum_{{r=1}}^{s} { \upsilon _{{ik}} x_{{ij}}} }} \leqslant 1,\quad j=1,\ldots,n \\ &\frac{{\sum_{{r=1}}^{s} {\mu_{{rk}} y_{{rj}} }}}{{\sum_{{r=1}}^{s} { \pi _{{pk}}z_{{pj}} }}} \leqslant 1,\quad j=1,\ldots,n \\ & \upsilon _{{ik}} \geqslant 0;\quad\pi_{{pk}} \geqslant 0;\quad \mu _{{rk}}\geqslant 0;\quad\forall i,p,r\end{array}\end{aligned}$$

(1)

In model (1), θ_kk denotes the efficiency of DMU_k (k = 1, …, n), expressed as the product of the efficiencies of its two sub-stages ($\theta_{{kk}}^{1}$ and $\theta_{{kk}}^{2}$). The efficiency of each sub-stage is defined as the ratio of the weighted sum of outputs to the weighted sum of inputs, reflecting the extent to which inputs are transformed into outputs within each sub-stage. This is a widely adopted method for defining efficiency in production theory⁶⁹. Model (1) seeks to maximize the overall efficiency of the DMU_k (k = 1, …, n) under the condition that the overall efficiency of each DMU and the efficiencies of its two sub-stages do not exceed 1. Here, υ_ik, π_pk, and µ_rk represent the weights of inputs, intermediate outputs, and final outputs, respectively, which are decision variables. Through the C-C transformation, that is, letting $t=1/\sum_{{r=1}}^{s} {\upsilon_{{ik}}x_{{ik}} }$, and v_ik=t*υ_ik, w_pk=t*π_pk, u_rk=t_*µ_rk, Model (1) can be converted into the linear programming model presented below.

$$\begin{aligned}&\hbox{max}\,\theta _{{kk}} =\hbox{max} u_{{rk}} y_{{rk}} \hfill \\ &\begin{array}{ll} s.t.& \sum_{{r=1}}^{s} { v_{{ik}} x_{{ik}} } =1 \\ &\sum_{{r=1}}^{s} { u_{{rk}} y_{{rj}} } - \sum_{{p=1}}^{q} { w_{{pk}} z_{{pj}} } \leqslant0,\quad j=1,\ldots,n \\ &\sum_{{p=1}}^{q} { w_{{pk}} z_{{pj}} } - \sum_{{r=1}}^{s} {v_{{ik}} x_{{ij}} } \leqslant 0,\quad j=1,\ldots,n \\ &v_{{ik}} \geqslant 0;\quad w_{{pk}} \geqslant 0;\quad u_{{rk}}\geqslant 0;\quad \forall i,p,r \end{array} \end{aligned}$$

(2)

Assuming $v_{{ik}}^{*}$, $w_{{pk}}^{*}$, and $u_{{rk}}^{*}$ are the optimal solutions of Model (2), the overall efficiency and the efficiencies of the two sub-stages for DMU_k (k = 1, … , n) can be obtained through model (3). It can be observed that the system efficiency is equal to the product of the efficiencies of the two sub-stages.

$$\begin{aligned}\theta _{{kk}}^{*}&=\frac{{\sum_{{r=1}}^{s} { u_{{rk}}^{*} y_{{rk}} } }}{{\sum_{{r=1}}^{s} {v_{{ik}}^{*} x_{{ik}} }}},\quad k=1,\ldots,n \\ \theta_{{kk}}^{{1*}}&=\frac{{\sum_{{r=1}}^{s} {w_{{pk}}^{*} z_{{pk}} }}}{{\sum_{{r=1}}^{s} { v_{{ik}}^{*}x_{{ik}} } }},\quad k=1,\ldots,n\\ \theta _{{kk}}^{{2*}}&=\frac{{\sum_{{r=1}}^{s} { u_{{rk}}^{*} y_{{rk}} } }}{{\sum_{{r=1}}^{s} {w_{{pk}}^{*} z_{{pk}} } }},\quad k=1,\ldots,n \end{aligned}$$

(3)

Neutral cross efficiency network DEA model

The primary limitation of Model (1) is that the optimal solution may not be unique, which can lead to non-unique efficiency results and rankings⁷⁰. To address the issue, scholars have proposed various cross efficiency network DEA models, such as aggressive cross efficiency and benevolent cross efficiency^61,66. However, selecting between these two types of cross efficiency network DEA models poses a challenge for decision-makers⁵⁵. In this context, Örkcü et al.⁶³, building upon the work of Wang et al.⁵⁶, introduced a neutral cross efficiency network DEA model, as illustrated in model (4).

$$\begin{aligned}&\hbox{max}\, \gamma = {\mathop{\hbox{min}}\limits_{{i \in \{ 1,\ldots,m\}}}} \{ v_{{ik}} x_{{ik}} \} \\ &\hbox{max}\, \delta = {\mathop{\hbox{min}}\limits_{{p \in \{1,\ldots,q\} }}} \{ w_{{pk}} z_{{pk}}\} \\ &\hbox{max}\, \beta = {\mathop{\hbox{min} }\limits_{{r\in \{ 1,\ldots,s\} }}} \{ u_{{rk}}y_{{rk}} \} \\ &\begin{array}{ll} s.t.& \sum_{{r=1}}^{s} { v_{{ik}} x_{{ik}} } =1 \\ &\theta_{{kk}}^{*} =\sum_{{r=1}}^{s} {u_{{rk}} y_{{rk}} } \\ &\theta_{{kk}}^{{1*}} =\sum_{{p=1}}^{q} {w_{{pk}} z_{{pk}} } \\ &\sum_{{r=1}}^{s} { u_{{rk}}y_{{rj}} } - \sum_{{p=1}}^{q} {w_{{pk}} z_{{pj}} } \leqslant0,\quad j=1,\ldots,n;\quad j \ne k \\ &\sum_{{p=1}}^{q} { w_{{pk}}z_{{pj}} } - \sum_{{r=1}}^{s} {v_{{ik}} x_{{ij}} } \leqslant0,\quad j=1,\ldots,n;\quad j \ne k \\ &v_{{ik}} \geqslant 0;\quad w_{{pk}} \geqslant0;\quad u_{{rk}} \geqslant 0;\quad \forall i,p,r \end{array}\end{aligned}$$

(4)

Model (4) aims to maximize the product of each indicator’s weight and its observations, while maintaining the self-evaluated overall and sub-stage efficiencies of DMU_k (k = 1, …, n) unchanged. Since the efficiency of sub-stage 2 can be indirectly derived from the overall and sub-stage 1 efficiencies, it is not included as a constraint in Model (4).

A novel neutral cross efficiency network DEA model

Although Model (4) can avoid the dilemma faced by decision-makers in choosing between aggressive and benevolent cross efficiency network DEA models, it may result in relatively small or even zero weights for individual indicators. As evident from the objective function of Model (4), its optimal value is significantly influenced by the scale of the indicators. An increase in the scale of the indicators leads to a corresponding decrease in their weights. As mentioned above, the selection of indicators is crucial for obtaining valid efficiency results^26,27. In such circumstances, assigning small or even zero weights to the selected indicators is unreasonable. To address this issue, we propose an improved neutral cross efficiency network DEA model, as shown in model (5):

$$\begin{aligned}&\hbox{max}\,\gamma = {\mathop{\hbox{min}}\limits_{{i \in \{ 1,\ldots,m\}}}} \{ v_{{ik}} \} \\ &\hbox{max}\, \delta= {\mathop{\hbox{min} }\limits_{{p \in \{ 1,\ldots,q\} }}} \{w_{{pk}} \} \\ &\hbox{max}\,\beta ={\mathop{\hbox{min} }\limits_{{r \in \{ 1,\ldots,s\} }}} \{u_{{rk}} \} \\ &\begin{array}{ll} s.t.& \sum_{{r=1}}^{s} { v_{{ik}} x_{{ik}} } =1 \\ &\theta _{{kk}}^{*} =\sum_{{r=1}}^{s} { u_{{rk}} y_{{rk}} } \\ &\theta_{{kk}}^{{1*}} =\sum_{{p=1}}^{q} {w_{{pk}} z_{{pk}} } \\ &\sum_{{r=1}}^{s} { u_{{rk}}y_{{rj}} } - \sum_{{p=1}}^{q} {w_{{pk}} z_{{pj}} } \leqslant0,\quad j=1,\ldots,n;\quad j \ne k \\ &\sum_{{p=1}}^{q} { w_{{pk}} z_{{pj}} } - \sum_{{r=1}}^{s} { v_{{ik}} x_{{ij}} } \leqslant 0,\quad j=1,\ldots,n;\quad j \ne k \\ & v_{{ik}} \geqslant 0;\quad w_{{pk}} \geqslant0;\quad u_{{rk}} \geqslant 0;\quad \forall i,p,r \end{array}\end{aligned}$$

(5)

Unlike model (4), model (5) directly sets the weights of the evaluated DMU_k as the objective function. By maximizing the weights of different indicators, it aims to ensure that each indicator plays as significant a role as possible in the efficiency evaluation. According to Wang and Chin⁷¹, the multi-objective programming model can be transformed into a single-objective programming model as shown in Model (6).

$$\begin{aligned}&\hbox{max}\, \alpha _{1} *\gamma + \alpha_{2} *\delta + \alpha _{3} *\beta \\ &\begin{array}{ll} s.t.& \sum_{{r=1}}^{s} { v_{{ik}} x_{{ik}} } =1 \\ &\theta _{{kk}}^{*} =\sum_{{r=1}}^{s}{ u_{{rk}} y_{{rk}} } \\ &\theta_{{kk}}^{{1*}} =\sum_{{p=1}}^{q} {w_{{pk}} z_{{pk}} } \\ &\sum_{{r=1}}^{s} { u_{{rk}}y_{{rj}} } - \sum_{{p=1}}^{q} {w_{{pk}} z_{{pj}} } \leqslant0,\quad j=1,\ldots,n;\quad j \ne k \\ &\sum_{{p=1}}^{q} { w_{{pk}}z_{{pj}} } - \sum_{{r=1}}^{s} {v_{{ik}} x_{{ij}} } \leqslant0,\quad j=1,\ldots,n;\quad j \ne k \\ &\gamma -v_{{ik}} \leqslant 0,\quad i=1,\ldots,m \\ &\delta - w_{{pk}} \leqslant 0,\quad p=1,\ldots,q \\ &\beta - u_{{rk}} \leqslant0,\quad r=1,\ldots,s \\ &v_{{ik}}\geqslant 0;\quad w_{{pk}} \geqslant 0;\quad u_{{rk}} \geqslant 0;\quad \forall i,p,r\\ &\gamma ,\delta ,\beta \geqslant 0 \end{array} \end{aligned}$$

(6)

In the model, ${\upalpha}$₁, ${\upalpha}$₂, and ${\upalpha}$₃ represent the weighting coefficients for three objectives, satisfying ${\upalpha}$₁ + ${\upalpha}$₂ + ${\upalpha}$₃ = 1. After the optimal weight of each DMU is obtained by model (6), the cross efficiency matrix of different DMUs can be obtained by following model (7).

$$\begin{aligned}\theta _{{kj}}^{*}&=\frac{{\sum_{{r=1}}^{s} { u_{{rk}}^{*} y_{{rj}} } }}{{\sum_{{r=1}}^{s} {v_{{ik}}^{*} x_{{ij}} }}},\quad k=1,\ldots,n,\quad j=1,\ldots,n\\ \theta_{{kj}}^{{1*}}&=\frac{{\sum_{{r=1}}^{s} {w_{{pk}}^{*} z_{{pj}} }}}{{\sum_{{r=1}}^{s} { v_{{ik}}^{*}x_{{ij}} } }},\quad k=1,\ldots,n,\quad j=1,\ldots,n\\ \theta _{{kj}}^{{2*}}&=\frac{{\sum_{{r=1}}^{s} { u_{{rk}}^{*} y_{{rj}} } }}{{\sum_{{r=1}}^{s} {w_{{pk}}^{*} z_{{pj}} }}},\quad k=1,\ldots,n,\quad j=1,\ldots,n \end{aligned}$$

(7)

Finally, the cross efficiency of DMU_k (k = 1, …, n) can be obtained from following model (8). And it satisfies that the overall cross efficiency equals the product of the cross efficiencies of the two sub-stages.

$$\begin{aligned}E_{j}^{c} &= {\left[\prod_{{k=1}}^{n}{ \theta _{{kj}}^{*} } \right]}^{{1/n}} \\ E_{j}^{{1c}} &={\left[\prod_{{k=1}}^{n} { \theta _{{kj}}^{{1*}}} \right]}^{{1/n}} \\ E_{j}^{{2c}} &={\left[\prod_{{k=1}}^{n} { \theta _{{kj}}^{{2*}}} \right]}^{{1/n}} \end{aligned}$$

(8)

Since Charnes et al.⁷² put forward the first DEA model, named the CCR model, various types of DEA models have been successively proposed, such as the additive DEA model⁷³, the SBM model⁷⁴, the network DEA model⁵⁹, and game-theoretic DEA models⁷⁵. Compared with existing DEA models, our proposed model has certain advantages. Firstly, compared with single-stage DEA models, such as the additive model and the single-stage SBM model, the proposed model considers the internal structure of evaluated objects, enabling more accurate identification of internal causes for inefficiency of evaluated objects^39,59. Secondly, compared with network DEA models, such as efficiency decomposition model and network SBM model, the proposed model belongs to the category of cross-efficiency assessment model, which combines the ideas of self-evaluation and peer evaluation, thus being able to obtain more convincing results^46,47. Finally, compared with existing cross-efficiency assessment models, such as game cross-efficiency DEA models, the proposed model focuses on the importance of indicator weights and can effectively alleviate the situation where indicator weights are excessively small or zero.

Empirical analysis

Model verification

The data from 24 non-life insurance companies, as utilized by Kao and Hwang (2008), are employed to demonstrate the validity and superiority of our model. Similar to Örkcü et al.⁶³, Table 1 presents the Spearman correlation coefficients of the computational results from three models: the self-evaluation model proposed by Kao and Hwang⁵⁹, the neutral cross efficiency network DEA model proposed by Örkcü et al.⁶³, and our improved model. And the numbers in parentheses represent p-values. It can be observed that, for both overall cross efficiency (E) and the cross efficiencies of the two sub-stages (E1 and E2), the results obtained from the three models are correlated at a significance level of 1%. Furthermore, the results from our model exhibit a higher correlation with those from the model proposed by Örkcü et al.⁶³. This may be attributed to the fact that both models fall into the category of neutral cross efficiency network models. To a certain extent, the aforementioned results demonstrate the validity of our model.

Table 1 Correlation coefficients of Spearman.

Table 2 further presents the minimum weights of the indicators obtained from three different models using Matlab 2023b. Specifically, we employed the linprog function from the Optimization Toolbox in Matlab 2023b, which is widely used to solve linear programming problems, to compute the indicator weights. As previously mentioned, the rational selection of input and output indicators is crucial for obtaining reliable efficiency results^26,27. Therefore, the chosen indicators should play as significant a role as possible in the efficiency evaluation. According to Table 3, compared with the other two models, the model proposed in our paper assigns as large weights as possible to the indicators in the efficiency evaluation. In this context, it can be considered that our model possesses certain advantages over the other two models.

Table 2 Minimum weights of indicators.

Table 3 Descriptive statistics.

Research on government environmental governance efficiency

Indicators selection

Based on the “attention-action-outcome” research paradigm, we subdivide government environmental governance into two sub-stages: environmental governance response sub-stage and environmental governance implementation sub-stage. The former refers to the process where environmental issues attract the attention of the government, leading to the initiation of environmental governance measures. The latter refers to the process where the government, through its environmental governance measures, achieves improvements in environmental quality. In this situation, government environmental attention (GEA) is regarded as the primary input indicator. Drawing on existing research^16,42, we use the number of environment-related terms appearing in government work reports as a proxy for government environmental attention. Specifically, we select keywords related to environmental pollution, environmental protection, energy consumption, coordinated development and joint environmental governance. For detailed content, please refer to the studies by Liu et al.^3,17. Regarding intermediate outputs, these serve as both the outputs of the environmental governance response sub-stage and the inputs of the environmental governance implementation sub-stage. Governments typically provide support for environmental governance through legislation and funding. Therefore, the number of environmental laws and regulations (EL&R) and the amount of fiscal expenditure on energy conservation and environmental protection (FE) are considered as corresponding alternative indicators^12,14. Regarding final outputs, improvements in environmental quality typically manifest in two aspects: the reduction of pollutants and the increase in green areas. Therefore, indicators such as wastewater discharge volume (WD), waste gas emission volume (WG), industrial solid waste generation volume (SW), and urban green space area (GS) are selected accordingly^14,32. It is worth noting that data on wastewater discharge volume and waste gas emission volume are no longer disclosed after 2018. Drawing on existing research^12,76, we employ the entropy weight method to process data on chemical oxygen demand and ammonia nitrogen emissions, as well as SO2, nitrogen oxides, and particulate matter emissions, to obtain the corresponding indicators. The relevant data comes from China Statistical Yearbook, China Environmental Yearbook, China Environmental Statistical Yearbook, government work Report and Peking University law database. The descriptive statistics of each indicator are shown in Table 3.

It should be noted that the final outputs, including WD, WG, and SW, are non-desirable outputs with the characteristic of being better when lower. Therefore, referring to existing research^77,78, we perform a linear transformation on the corresponding indicators using the formula W^a = max(W) + 1 − W (where W represents WD, WG, and SW) to convert them into desirable outputs.

Government environmental governance efficiency at the National scale

Figure 2 presents the changes in government EGE of 30 provinces in China from 2011 to 2022. In the figure, the solid line represents the mean value, while the dashed line indicates the median value. It can be observed that during the study period, the average government EGE in China exhibited a fluctuating upward trend, increasing from 0.226 in 2011 to 0.254 in 2022. Despite the improvement in China’s EGE, there is still considerable room for further enhancement. Notably, significant declines in government EGE occurred in 2012, 2015, and 2020. The possible reasons for these declines are as follows: Since the 18th National Congress of the Communist Party of China in 2012, China’s economic development paradigm has gradually shifted from an extensive to an intensive model, with ecological civilization construction being established as a pivotal position of the country’s overall development strategy⁴. However, due to the long-standing inertia of China’s economic growth, it has been challenging for the government to achieve efficient environmental governance in the short term. The implementation of the new environmental protection law in 2015, often referred to as the strictest environmental legislation in history⁷⁹, set higher standards for environmental governance, posing a significant challenge to governmental environmental governance capability, which might lead to a temporary decline in government EGE. Additionally, the decrease in government EGE in 2020 could be due to the initial outbreak of the COVID-19 pandemic, which diverted substantial governmental attention and resources, thereby hindering the upward trend in government EGE.

Fig. 2

The trend of changes in government environmental governance efficiency.

The distribution of government EGE across different years, as illustrated by the violin plots, predominantly exhibits a “narrow top and wide bottom” pattern. This indicates that the government EGE of most provinces is concentrated at lower levels, a trend also reflected by the fact that the mean efficiency values consistently exceed the medians across the years. In other words, there is a suspicion that the current average government EGE of the Chinese government is being pulled upwards by a few high-performing provinces.

Figure 3 illustrates the efficiency and its changes in the two sub-stages of governmental environmental governance. It is observable that, on the whole, the government environmental governance implementation efficiency (EGIE) surpasses the government environmental governance response efficiency (EGRE), as represented by the dotted line in the figure. The plausible reason lies in the fact that, in comparison to the response sub-stage of environmental governance, the improvement in local environmental quality is more closely correlated with the implementation sub-stage of environmental governance, prompting local governments to prioritize the latter in their operational focus. However, as depicted in the line chart, during the study period, the EGIE exhibits greater fluctuations compared to the EGRE. This phenomenon may be attributed to the “campaign-style” environmental governance implemented by local governments. Serving as an “image project” that can both fulfill the interests of governments and officials and swiftly demonstrate governance effectiveness, campaign-style environmental governance has become a preferred approach for some local governments in implementing environmental governance. While such measure contributes to a rapid increase in EGE in the short term⁸⁰, our finding indicates that it fails to ensure the long-term stable development of EGE.

Fig. 3

Government environmental governance efficiencies of two sub-stages.

Government environmental governance efficiency at regional scale

Figure 4 illustrates the trends in changes of government EGE and its two sub-stages at the regional level. Considering the significant variations among different regions (eastern, central, and western) in China in terms of economic development, resource endowments, and technological levels⁸¹, achieving coordinated development among these regions has been a vital development strategy for China. Referring to Chen et al. (2021)⁸², the eastern region includes Beijing (BJ), Tianjin (TJ), Hebei (HB), Liaoning (LN), Shanghai (SH), Jiangsu (JS), Zhejiang (ZJ), Fujian (FJ), Shandong (SD), Guangdong (GD), and Hainan (HaN). The central region comprises Shanxi (SX), Jilin (JL), Heilongjiang (HLJ), Anhui (AH), Jiangxi (JX), Henan (HN), Hubei (HuB), and Hunan (HuN). The western region encompasses Inner Mongolia (IM), Guangxi (GX), Chongqing (CQ), Sichuan (SC), Guizhou (GZ), Yunnan (YN), Shaanxi (ShX), Gansu (GS), Qinghai (QH), Ningxia (NX), and Xinjiang (XJ). And drawing on existing research¹², the Theil index is utilized to explore the developmental disparities in government EGE among different regions, which can further disaggregate these disparities into intra-group and inter-group components, as depicted in the bar charts in Fig. 4.

Fig. 4

Government environmental governance efficiencies of different regions.

As evident from the average efficiency (indicated by the dotted lines in the line graph), China’s eastern region demonstrates superior performance in both overall efficiency and the efficiencies of the two sub-stages, whereas the western region exhibits poorer performance. This disparity is closely related to the varying degrees of emphasis placed on environmental issues and the governance capabilities across different regions. Compared to the central and western regions, the eastern region places a high priority on environmental issues⁸³, and the government enjoys significant advantages in policy formulation and enforcement⁸⁴, which are likely key factors in maintaining higher government EGE in the eastern region. Unlike the EGRE, the gap in EGIE among the three regions is relatively smaller, and notably, the EGIE in the western region surpasses that of the central region between 2016 and 2021. A possible explanation for this phenomenon is that the central region, characterized by a concentration of heavy industries⁸⁵, faces severe environmental governance challenges. In contrast, the majority of provinces in the western region rely on tourism as their main economic pillar⁸², which causes relatively less damage to the local ecological environment, making it easier to achieve high EGIE.

Additionally, a noteworthy finding is that the efficiency gap between the eastern and central regions is relatively small in the environmental governance response sub-stage, while the efficiency gap between the central and western regions is relatively small in the environmental governance implementation sub-stage. The underlying causes for this divergence are as follows. On the one hand, provincial governments in eastern and central China typically possess stronger fiscal revenues and financing capabilities⁸⁶. This enables them to proactively allocate corresponding fiscal resources towards environmental infrastructure inputs upon receiving clear policy signals. In contrast, some western provinces lack the fiscal capacity to swiftly implement their environmental intentions, resulting in a dilemma of “willingness constrained by capability”. On the other hand, eastern provinces possess greater expertise in applying complex environmental technologies⁸⁷. Conversely, both central and western regions rely more heavily on relatively basic, established technologies⁸⁸. These technologies yield diminishing marginal returns in addressing complex or emerging environmental problems, resulting in similar efficiency trends between central and western regions during the implementation of environmental governance.

From the bar charts in Fig. 4, it can be seen that for both the overall efficiency and the efficiencies of the two sub-stages, the intra-group disparities are significantly larger than the inter-group disparities. This indicates that internal inequality within regions has become a significant obstacle for China’s governmental environmental governance. Moreover, the developmental disparities in EGRE are significantly greater than those in EGIE. Furthermore, in terms of the trend of changes, except for individual years (2012 and 2015), the developmental disparities in government EGE in China exhibit a roughly U-shaped pattern. Specifically, after 2016, the developmental disparities in government EGE have shown a fluctuating upward trend, both in terms of intra-group and inter-group disparities. In other words, since the 13th Five-Year Plan, the developmental disparities in government EGE among different regions in China have increased, which should be a matter of concern. Unlike the changes in the developmental disparities of government EGE, the developmental disparities in the EGIE exhibit a roughly inverted U-shaped pattern, with disparities gradually narrowing since 2016. In comparison, the developmental disparities in the EGRE among different regions have not shown a clear trend of change. It is noteworthy that while intra-group disparity is the primary cause of developmental disparity in government EGE among different regions in China, which is also true for the developmental disparities of the two sub-stage efficiencies, the gradual increase in inter-group disparity in recent years deserves special attention, especially for government EGE and EGIE.

Government environmental governance efficiency at provincial scale

Figure 5 further presents the average government EGE of 30 provinces in China. It can be observed that there are significant differences in the government EGE among different provinces, with Jiangsu Province achieving the highest efficiency at 0.435, while Qinghai Province has the lowest efficiency, at only 0.07. As an economically developed province, Jiangsu not only possesses robust economic strength but also actively explores feasible solutions for the construction of ecological civilization⁸⁹. For instance, Jiangsu has taken the lead in initiating a paid-use and trading system for emission rights nationwide, as well as being the first to delineate ecological protection red lines, implement fiscal policies for pollution reduction and carbon emission mitigation, and establish a comprehensive system for compensation for ecological environment damage⁹⁰. These initiatives have provided robust institutional support for environmental governance, which may be a significant reason for the province’s high efficiency in environmental governance. In comparison, Qinghai Province, located on the Qinghai-Tibet Plateau, faces a complex and diverse geographical environment, a relatively weak economic foundation, and a severe shortage of environmental governance experience and technology⁹¹. Additionally, there is room for improvement in policy enforcement efforts and regulatory mechanisms⁹². These factors may collectively contribute to the relatively low governmental environmental governance efficiency. Furthermore, provinces that are geographically adjacent and receive significant national policy support may still exhibit notable differences in EGE. For instance, within the Beijing(BJ)-Tianjin(TJ)-Hebei(HB) region, the efficiency levels of Beijing, Tianjin, and Hebei exhibit a distinct tiered decline. Similarly, marked discrepancies exist among the EGEs of Shanghai(SH), Jiangsu(JS), Zhejiang(ZJ), and Anhui(AH) within the Yangtze River Delta region. This phenomenon may be partly attributed to the siphoning effect involving capital and skilled talent occurring between adjacent provinces⁹³, particularly when there are significant divergences in economic development and resource endowments. To provide a clear understanding of the EGE of each province and the efficiencies of its two sub-stages, we present the corresponding efficiency values in Table A1 of the supplementary material.

Fig. 5

Government environmental governance efficiencies of different provinces.

Indeed, the significant differences in EGE across provinces not only reflect the validity of decentralization theory in the field of environmental governance, but also highlight substantial variations in institutional capacity among provinces. Given that local governments possess superior information regarding local environmental conditions, they are able to design more flexible and targeted environmental policies⁹⁴. As a result, the central government has progressively devolved environmental management authority to local governments in recent years⁹⁵. Our findings indicate that some provinces have achieved relatively high environmental governance performance, which, to some extent, demonstrates the effectiveness of environmental decentralization. However, this study also reveals that the efficiency of environmental governance remains low in several provinces, a phenomenon that may be attributed to disparities in institutional capacity across provinces. According to institutional capacity theory, the successful realization of policy objectives hinges on whether the implementing agencies—such as governmental departments and regulatory bodies—possess sufficient capabilities. These capabilities are multidimensional, encompassing policy formulation and implementation, resource management, inter-agency cooperation and so on⁹⁶. Given the substantial body of existing research showing significant differences among Chinese provinces in terms of administrative efficiency and regulatory enforcement^97,98, the aforementioned findings can be considered reasonable.

Based on the average efficiency of the two sub-stages, the 30 provinces can be subdivided into four categories: high EGRE-high EGIE, low EGRE-high EGIE, low EGRE-low EGIE, and high EGRE-low EGIE, as illustrated in Fig. 6. An intuitive observation is that a certain number of provinces are distributed within each of the four quadrants, which further reflects the significant variations in government EGE among different provinces in China. It can be seen that six provinces fall into the first quadrant (I), accounting for 20% of the total sample, and except for Anhui Province, the remaining provinces all belong to the eastern region. These provinces can serve as benchmarks for improving the government EGE of surrounding provinces. In contrast, seven provinces are located in the third quadrant (III), with all except Shanxi Province belonging to the western region. It is worth mentioning that other western provinces are distributed in the second quadrant (such as Guangxi and Ningxia) and the fourth quadrant (such as Sichuan and Shaanxi), which to some extent provides a reference for improving the government EGE of provinces in the western region within the third quadrant. In other words, provinces located in the third quadrant have the option to prioritize either the enhancement of EGIE or the enhancement of EGRE, with reference benchmarks available for both choices. For those provinces that originally in the second and fourth quadrants (II and IV), it is important for them to strive to address their own shortcomings so as to achieve a balanced development between EGRE and EGIE.

Fig. 6

Distribution of different provinces.

It should be noted that even provinces within the same quadrant may exhibit specific differences in EGE. For example, although both Beijing (BJ) and Hebei (HB) belong to the fourth quadrant and are located in the Beijing-Tianjin-Hebei region, it can be seen from Fig. 6 that there is a significant disparity in their efficiency during the environmental governance implementation sub-stage. These findings offer more nuanced implications for the formulation and implementation of environmental governance policies across provinces. Specifically, while both Beijing and Hebei should prioritize improving their implementation efficiency in the coming period, the formulation and enforcement of relevant policies are more urgent for Hebei.

Conclusions and policy implications

The Chinese government has invested heavily in environmental governance to promote ecological civilization construction and achieve high-quality economic development. China’s environmental quality has significantly improved as a result of governance efforts. However, it remains a key concern for both the government and scholars whether these resources have been used efficiently. Based on the “attention–action–outcome” research framework, we divide the government’s environmental governance process into two sub-stages: environmental governance response sub-stage and environmental governance implementation sub-stage. Then, an improved neutral cross-efficiency network DEA model is proposed to analyze the environmental governance efficiency of 30 Chinese provinces from 2011 to 2022.

The effectiveness of the proposed model is confirmed. Then, empirical results indicate that: Firstly, the average environmental governance efficiency of the Chinese government exhibits a fluctuating upward trend during the study period. However, it only reached 0.254 in 2022. Secondly, on the whole, the efficiency of environmental governance implementation sub-stage is superior to that of environmental governance response sub-stage, but the former also demonstrates greater volatility. Thirdly, on average, the eastern region performs the best, while the western region performs the worst. This applies to both overall efficiency and the efficiencies of the two sub-stages. Fourthly, the development disparities in government environmental governance efficiency among provinces, both intra-group and inter-group disparities, have increased in recent years. However, the development disparities in government environmental governance implementation efficiency have roughly exhibited a fluctuating decline since 2016. In contrast, no clear trend is observed in the development disparities of government environmental governance response efficiency. Additionally, both overall efficiency and the efficiencies of two sub-stages show that intra-group disparities are much greater than inter-group disparities. Finally, the analysis based on the quadrant diagram provides a clear direction for enhancing the efficiency of government environmental governance across different provinces in China.

Based on the aforementioned research findings, the following policy recommendations can be provided for China’s environmental governance.

Firstly, the overall environmental governance efficiency of the Chinese government has shown a fluctuating upward trend, which indirectly demonstrates the effectiveness of governmental environmental governance measures. However, it is worth noting that, as of 2022, there is still considerable room for improvement. This suggests that simply increasing investment in environmental governance might no longer be the most optimal strategy, particularly in light of the significant progress made in China’s environmental quality. In this context, the Chinese government should focus on how to maintain environmental quality while making better use of environmental governance resources. Therefore, introducing third-party supervision mechanisms and enhancing the tracking and monitoring mechanisms throughout the environmental governance process can provide significant support for improving environmental governance efficiency.

Secondly, during the study period, the environmental governance implementation efficiency performed better compared to the response efficiency. This finding suggests that in China’s environmental governance, the effectiveness of the government’s environmental attention is lower than that of its environmental governance resources. Indeed, governmental attention is also a limited and scarce resource. Inadequate governmental environmental governance response efficiency can, to a certain extent, undermine the government’s credibility. Therefore, enhancing the environmental governance response capacity of the Chinese government should be an urgent issue that needs to be addressed. It is noteworthy that although the environmental governance implementation efficiency outperforms the response efficiency, the former also exhibited significant volatility during the study period. This indicates that the utilization of environmental governance resources by the Chinese government is far from achieving stable and sustainable development. In this context, establishing a long-term implementation mechanism for environmental governance and an efficient monitoring mechanism can contribute to the steady development of environmental governance implementation efficiency.

Thirdly, both overall efficiency and the efficiencies of the two sub-stages show that China’s eastern, central, and western regions have a gradually decreasing development trend, indicating that regional imbalanced development persists in environmental governance in China. This can also be reflected in the increasing development disparities in environmental governance efficiency across China in recent years. Consequently, striving to achieve regional balanced development remains a challenge for the Chinese government. Moreover, according to the decomposition results of development disparities, intra-group disparities are the primary cause of regional development disparities, compared to inter-group disparities. In other words, although there are significant gaps in environmental governance efficiency among China’s three major regions, the developmental differences among different provinces within each region should be the primary focus of the government. In this context, a development strategy based only on the three major regions may not be the best approach for environmental governance. Instead, regional environmental policies that focus on smaller geographical divisions can better reduce disparities within regions, thereby contributing to the balanced development of environmental governance efficiency among different regions in China. Additionally, compared to the environmental governance implementation efficiency, the regional development disparities in the environmental governance response efficiency have not shown a downward trend, which should garner more attention from the government.

Finally, the quadrant diagram analysis shows that the 30 provinces are roughly evenly distributed across the four quadrants. This observation not only highlights the significant differences in governmental environmental governance among provinces in China but also provides clear directions for further improvements in environmental governance efficiency for respective provinces. For provinces in the second and fourth quadrants that perform well in either environmental governance response efficiency or implementation efficiency, efforts should be directed towards strengthening their weaker aspects. Provinces situated in the third quadrant, where both sub-stages of environmental governance show room for improvement, should consider those in the second or fourth quadrants as benchmarks for the next phase of development. As for provinces in the first quadrant, they should proactively establish effective communication channels and cooperation mechanisms with provinces in other quadrants, aiming to facilitate the overall enhancement of environmental governance efficiency across China.

There are several limitations: Firstly, this paper focuses on provincial administrative units as the main research subjects, whereas cities have become fundamental units for population aggregation, economic growth, and environmental pollution. Provincial-level analyses may mask significant variations in environmental governance efficiency driven by nested governance structures, such as differences in municipal-level policy enforcement and inter-city resource allocation. For instance, cities within the same province might exhibit divergent efficiency trajectories due to localized institutional arrangements or economic priorities. With the advancement of China’s urbanization process, the aforementioned phenomenon may become further intensified. Thus, conducting analyses with cities as the research subjects might yield more nuanced insights. Secondly, the neutral cross-efficiency network DEA model developed in this paper is based on the multiplicative model proposed by Kao and Hwang (2008); expansions to other methods, such as additive models and leader-follower game models, are also worthy of investigation. Lastly, some production systems may possess more complex network structures; applying the modeling ideas presented in this paper to corresponding models is another potential direction for future research.