Research on eco-efficiency of provinces along the Belt and Road in China based on DEA methods and AI prediction algorithms

Abstract

Under the strategic goals of promoting ecological civilization and advancing regional coordinated development, China’s Belt and Road provinces face dual pressures from economic growth and environmental protection. Therefore, a scientific assessment of eco-efficiency is crucial for achieving regional sustainable development. This study aims to systematically examine eco-efficiency and its spatiotemporal evolution across Belt and Road provinces, while also projecting future development trends. To achieve this, the study employs the super-efficiency Epsilon-Based Measure model to measure static efficiency and integrates the Global Malmquist–Luenberger index to analyze dynamic changes. Utilizing Kernel Density Estimation and Moran index to reveal spatial characteristics. A new information-preferred damped cumulative gray model with artificial intelligence is introduced to provide high-precision predictions. The study finds: (1) The overall eco-efficiency level remains low with a declining trend, exhibiting significant regional variations. (2) The technological progress index is a central driver of eco-efficiency. (3) Spatial heterogeneity in eco-efficiency is particularly pronounced, exhibiting spatial clustering characteristics. (4) The forecast indicates that overall eco-efficiency will show an upward trend in the future. Based on the above conclusions, this study puts forward corresponding policy suggestions. These recommendations are of great significance for promoting the sustainable improvement of eco-efficiency in the provinces along the Belt and Road in China.

Introduction

Against the backdrop of the global green transition becoming a shared trend in economic development, how to reduce resource consumption and ecological pressure while maintaining economic growth has become a core challenge facing all nations¹. Being the predominant developing state and progenitor of the Belt and Road (B&R) Initiative, China bears an international obligation to advance development that is high-quality, environmentally sustainable, and inclusive². The B&R Initiative is a significant strategic platform for enhancing cooperation with countries along the routes and collectively building and sharing benefits³. The provincial regions within its radiation range are the vanguard positions for policy implementation, project execution, economic development, and ecological civilization construction⁴. Against the backdrop of advancing the dual carbon goals and the high-quality development strategy, promoting green transformation in regions along the B&R has become a key lever for coordinating domestic and international affairs. Eco-efficiency (EE) serves as an important indicator for measuring the coordination relationship among resource input, output, and environmental impact in economic activities^5,6. This region spans 18 provinces and serves as both a strategic fulcrum for economic growth and a crucial ecological security barrier. Its sustainable development directly impacts the effectiveness of the nation’s overall ecological civilization construction.

However, while carrying the burden of promoting economic growth, these regions are also facing severe resource and environmental pressures. During rapid economic development, certain provinces and regions have placed excessive emphasis on the speed of development. The profound repercussions of resource depletion and contaminant discharge on ecosystem integrity have been systematically overlooked, leading to increasingly prominent ecological and environmental problems. Although the eastern coastal regions possess technological and capital advantages, their environmental capacity has reached saturation. Central and western regions heavily rely on resource-based industries, with energy consumption and pollution emissions per unit of GDP significantly exceeding the national average, indicating relatively weak foundations for green transformation. More critically, disparities in green development levels between regions continue to widen. This reality urgently requires taking EE as the key point to ensure regional economic growth while achieving the coordinated unity of resource circularity and ecological protection⁷. In this context, conducting an in-depth analysis of EE in provincial regions situated along the B&R becomes particularly significant and imperative.

The concept of EE originated in the field of ecological economics⁸. It serves to evaluate the link between the efficiency of resource utilization and the environmental consequences of economic activities. The central concept lies in achieving optimal economic output with minimal environmental burden, given specific resource and capital inputs. In the context of an expanding focus on sustainability, EE serves as a vital indicator reflecting both ecological progress and the pursuit of high-quality development. It has gradually received great attention from scholars and policymakers around the world. The assessment methods of EE mainly include the ratio method⁹, parameter estimation method^10,11, comprehensive index method^12,13,14,15, and data envelopment analysis (DEA) method^16,17. Among various efficiency evaluation methods, the DEA model stands out for its widespread use in academia, attributed to its high adaptability and the fact that it does not necessitate the specification of a production function in advance. Such as the research by Emrouznejad et al. on the systematic review of literature on EE in the netzero and DEA models has provided new directions for future studies¹⁸. Wang et al. conducted a study on the tourism EE of China using the super-efficiency SBM model. They found that the overall tourism EE in China first increased and then decreased¹⁹. He and Liu proposed an improved Meta-frontier SBM-DNDEA method to evaluate the industrial EE in China, and found that the EE level was not very high²⁰. Wang et al. conducted a study on the health EE of cities in the Yellow River Basin of China using the super-efficiency SBM method²¹. The concept has gained significant traction in the realm of environmental performance assessment, finding application at the corporate level. For instance, Liu et al. developed a fairness model for non-expected outputs and successfully applied it to the assessment of coal-fired power plants in China, revealing their generally poor performance²². Przychodzen and Przychodzen found that ecological innovative enterprises have higher asset return rates and equity return rates, but their profit retention rates are relatively low²³. At the industrial level, Lorenzo-Toja et al. combined Life Cycle Assessment with DEA to study the EE of wastewater treatment plants in Spain²⁴. Heidenreich et al. employed the DEA model to investigate the EE of smallholder crops in sub-Saharan Africa²⁵. Lai et al. believed that the digital economy can significantly enhance the EE of cities²⁶. Wang et al. researched the impact of green innovation and industrial structure on the EE of Chinese cities²⁷. At the regional level, Yao et al. based on the super-efficiency SBM model and using the panel data of 30 provinces in China, found that urbanization in terms of population and ecology had a positive impact on EE, while urbanization in terms of society and space showed a significant negative impact²⁸. Yang et al. conducted an EE study focusing on cultivated land utilization and found that the EE of cultivated land utilization in the Yangtze River Economic Belt showed a trend of first decreasing and then increasing²⁹. Xiao et al. employed a two-stage network DEA model and found that the EE of China’s resource-based cities has been continuously improving³⁰. Yin et al. regarded environmental pollution as an undesired outcome and conducted an empirical study on China’s provincial capital cities using an improved super-efficiency DEA model. It provides valuable suggestions for the sustainable development of Chinese cities³¹. Zhang et al. employed the super-efficiency SBM model and found that the EE of the five major urban clusters in China has been showing a gradually increasing trend³². At the national level, Wang et al. based on the SBM model, found that the ecological efficiency of 17 European countries was generally low³³. Li et al. utilized the DEA model to investigate the performance relationships among energy, economy and environment in the BRICS countries. The study revealed that China and Brazil performed better than the other BRICS countries³⁴.

Driven by ongoing technological progress, AI algorithms rely on powerful data processing capabilities and the advantages of pattern recognition. It is gradually applied to the field of efficiency evaluation and is widely used in data optimization, trend prediction, and resource allocation. The accuracy of the efficiency measurement has been effectively improved. For example, Mergoni et al. discussed the DEA-AI model in the review of DEA models, which promoted the future development of the DEA field³⁵. Zhu et al. discussed the application of four machine learning algorithms in combination with the DEA model for the measurement and prediction of listed companies in China’s manufacturing industry. They found that the DEA model combining a Genetic Algorithm with a backpropagation neural network was the most optimal³⁶. Amirteimoori et al. developed a novel artificial intelligence framework for assessing environmental efficiency in Iranian forests by integrating Artificial Neural Networks, Gene Expression Programming, and the Artificial Immune System. Their findings demonstrated a notable enhancement in overall EE using this approach³⁷. By employing K-means-based unsupervised learning, Wang et al. investigated disparities in grain production efficiency, introducing an innovative perspective for related research³⁸. Chen et al. proposed an AI-based model to assess the utility of renewable energy and energy efficiency in economic development. The results showed a 97.32% gain in energy efficiency and a notable increase in renewable energy use³⁹. Furthermore, in a study of energy efficiency in manufacturing firms, Liu et al. noted that firm performance can enhance the contribution of AI to energy efficiency⁴⁰. By combining machine learning with the DEA approach, Mirmozaffari et al. proposed a novel evaluation method and utilized it to measure the EE of 22 cement producers in Iran⁴¹. With the continuous development and maturity of AI algorithms, their application has been widely expanded to the field of efficiency assessment and optimization in various industries. For example, Bagheri et al. and Farzzaneh et al. highlighted that AI technologies contribute significantly to enhancing energy efficiency in smart buildings^42,43. In addition, AI is widely used in a variety of fields, including industrial production, transportation, healthcare, education, and environmental governance. It contributes increasingly to the sustainable use of resources, the optimization of operational systems, and the alleviation of environmental stress.

In summary, this study identifies deficiencies in the extant research on EE by systematically reviewing the existing literature. Firstly, the current construction of the EE input indicator system generally focuses on traditional factors such as labor, capital, land, and energy. Emerging data elements within the digital economy are seldom taken into full consideration. Secondly, the majority of extant studies concentrate on the analysis at the level of a particular province, city, or region. To date, there has been a paucity of EE studies for provinces along the B&R in China. Thirdly, in terms of measurement methods, most of them use traditional DEA models. Although some studies have introduced slack variables, they tend to ignore the proportionality between inputs and outputs. And most of the model efficiency values are limited to 1, which makes it difficult to make further ranking comparisons. In addition, most current literature remains constrained to static measurement techniques, lacking the adoption of holistic multi-model frameworks for capturing the complex, multidimensional nature of EE. For example, few studies have systematically examined the spatial-temporal evolution and spatial autocorrelation characteristics of EE among provinces along the B&R. Fourthly, concerning the use of AI algorithms in efficiency evaluation, most studies mainly focus on the efficiency improvement or data optimization level. This study attempts to predict future input-output indicators based on AI algorithms, combined with historical data, and then carry out EE measurement. Aimed at detecting data irregularities and facilitating strategic decision-making for the optimal and anticipatory allocation of ecological resources.

Based on the above issues, this study proposes the following objectives. Firstly, this study aims to systematically construct a multidimensional evaluation framework integrating data elements to achieve a comprehensive analysis of EE across provinces along the B&R. Secondly, it measures the static efficiency of provinces along the B&R, analyzing the dynamic evolution mechanism of their EE, and employing spatial analysis methods to reveal their spatial and temporal evolution characteristics. Thirdly, this study predicts the future trend of EE. This will provide quantitative evidence for formulating differentiated and forward-looking green transformation strategies.

To achieve the objectives above, firstly, this study employs a non-directional super-efficiency Epsilon-Based Measure (EBM) model to conduct a static measurement of EE. This approach is chosen because the model can simultaneously handle both radial and non-radial slack variables, making it suitable for scenarios involving non-expected output. Secondly, the Global Malmquist–Luenberger (GML) index model is introduced to decompose efficiency variations, aiming to identify the core factors driving the dynamic changes in EE. Thirdly, by using the Kernel Density Estimation (KDE) and Moran index models, the spatial distribution pattern and clustering characteristics of EE can be revealed, which is suitable for analyzing regional interaction and spatial spillover mechanisms. Finally, this study innovatively combines the DEA model with AI algorithms. A new paradigm integrating efficiency assessment and trend prediction is constructed. Through a new information-preferred damped cumulative gray model (NDGM(1,1)) model, the future input and output indicators are predicted with high precision. Incorporating historical efficiency enables a comparative analysis that overcomes the traditional DEA model’s excessive reliance on historical data.

This study enriches the theoretical framework of sustainable development at the production function level by incorporating data elements into the EE assessment framework. Through the integration of multiple analysis methods, this provides a new analytical perspective and theoretical explanation for understanding the spatial and temporal evolution patterns of regional EE. At the same time, making predictions about EE can provide quantitative support for the government in formulating medium- and long-term green development strategies. It also helps identify potential regional collaboration opportunities and policy risk points. Therefore, this research not only has theoretical value but also has significant policy and practical significance.

In light of the above, this study makes the following key contributions. (1) This study incorporates data elements into the input framework of EE, establishing a more comprehensive scientific evaluation system. It also partially fills the gap in research on EE across provinces along the B&R in China. (2) The system integrates the super-efficiency EBM model, GML index, KDE, spatial autocorrelation analysis, and the AI-enhanced NDGM(1,1) prediction model. It achieves four-dimensional linkage analysis of the static level, dynamic evolution, spatial and temporal evolution characteristics, and future trends of EE. It overcomes the defect of existing studies that are mostly limited to a single perspective. To provide a replicable new paradigm for regional green sustainable performance assessment. (3) Based on empirical results, this study not only provided in-depth theoretical explanations but also distilled practical policy recommendations. These conclusions have provided an important scientific basis and empirical support for promoting the green and high-quality development of the B&R.

Research design

The super-efficiency EBM model

Traditional DEA models are typical radial models⁴⁴. However, radial models require input and output indicators to expand or contract in the same proportion. Efficiency values tend to be overestimated when slack variables are not adequately accounted for in the model. With further research, in response to the overestimation caused by ignoring slack variables, Tone proposed the non-radial, non-directional Slack-Based Measure (SBM) model^45,46. The model effectively addresses the issue of neglecting non-proportional adjustments in the radial model. Although the SBM model accounts for slack variables, it overlooks the proportionality between input and output variables. To overcome the shortcomings of purely radial or non-radial models, Tone and Tsutsui proposed the EBM model⁴⁷. Compared with traditional DEA models (such as SBM, PEBM, directional distance, network DEA and two-stage DEA), the EBM model possesses both radial and non-radial characteristics. It not only retains the input-output ratio information but also can fully capture the slack variables. Thus, it avoids the problems of overestimation of efficiency in radial models and information loss in purely non-radial models. It is more suitable for handling multi-index and non-proportional adjustment EE evaluations. The EBM model expression is given below:

$$\begin{gathered} {\beta ^*}=\hbox{min} \frac{{\theta - {\varepsilon _x}\sum\limits_{{i=1}}^{m} {\frac{{\omega _{i}^{ - }S_{i}^{ - }}}{{{x_{ik}}}}} }}{{\varphi +{\varepsilon _y}\sum\limits_{{r=1}}^{q} {\frac{{\omega _{r}^{+}S_{r}^{+}}}{{{y_{rk}}}}} }} \hfill \\ s.t.\left\{ \begin{gathered} \sum\limits_{{j=1}}^{n} {{x_{ij}}{\lambda _j}+S_{i}^{ - }=\theta {x_{ik}},i=1, \cdots ,m} \hfill \\ \sum\limits_{{j=1}}^{n} {{y_{rj}}{\lambda _j} - S_{r}^{+}=\varphi {y_{rk}},r=1, \cdots ,q} \hfill \\ \sum\limits_{{j=1}}^{n} {{\lambda _j}=1,{\lambda _j} \geqslant 0,S_{i}^{ - },S_{r}^{+} \geqslant 0} \hfill \\ \end{gathered} \right. \hfill \\ \end{gathered}$$

(1)

Although the above model can measure EE relatively accurately. However, it is impossible to distinguish and compare multiple decision-making units (DMUs) with an efficiency value of 1 simultaneously. It also cannot solve the problem of non-expected output that may occur during the production process. Therefore, the EBM model is modified in this study. Setting up the provinces along the B&R as n DMUs$DM{U_j}\left( {j=1, \cdots ,n} \right)$. where each DMU has m inputs ${x_{ij}}$, q desired outputs, and p non-expected outputs ${u_{tj}}$.This study constructs a super-efficiency EBM model that integrates both radial and non-radial components while accounting for non-expected outputs⁴⁸. Furthermore, this model is set as non-directional, which not only reduces redundancy and insufficient output, but also conforms to the characteristic of jointly optimizing EE and output. In terms of the assumption of scale returns, this study selects constant returns to scale (CRS) to reflect the comparison of scale benchmarks among different provinces under similar development constraints. The model expression is given below:

$$\begin{gathered} {\beta ^*}=\hbox{min} \frac{{\theta - \frac{{{\varepsilon _x}}}{{\sum\limits_{{i=1}}^{m} {\omega _{i}^{ - }} }}\sum\limits_{{i=1}}^{m} {\frac{{\omega _{i}^{ - }S_{i}^{ - }}}{{{x_{ik}}}}} }}{{\varphi +\frac{{{\varepsilon _y}}}{{\sum\limits_{{r=1}}^{q} {\omega _{r}^{+}} }}\sum\limits_{{r=1}}^{q} {\frac{{\omega _{r}^{+}S_{r}^{+}}}{{{y_{rk}}}}+\frac{{{\varepsilon _u}}}{{\sum\limits_{{t=1}}^{p} {\omega _{t}^{{u+}}} }}\sum\limits_{{t=1}}^{p} {\frac{{\omega _{t}^{{u+}}S_{t}^{{u+}}}}{{{u_{tk}}}}} } }} \hfill \\ s.t.\left\{ \begin{gathered} \sum\limits_{{j=1,j \ne k}}^{n} {{x_{ij}}{\lambda _j}+S_{i}^{ - }=\theta {x_{ik}},i=1, \cdots ,m} \hfill \\ \sum\limits_{{j=1,j \ne k}}^{n} {{y_{rj}}{\lambda _j} - S_{r}^{+}=\varphi {y_{rk}},r=1, \cdots ,q} \hfill \\ \sum\limits_{{j=1,j \ne k}}^{n} {{u_{tj}}{\lambda _j} - S_{t}^{{u+}}=\varphi {u_{tk}},t=1, \cdots ,p} \hfill \\ \sum\limits_{{j=1}}^{n} {{\lambda _j}=1,{\lambda _j} \geqslant 0,S_{i}^{ - },S_{r}^{+},S_{t}^{{u+}} \geqslant 0} \hfill \\ \end{gathered} \right. \hfill \\ \end{gathered}$$

(2)

where ${\beta ^*}$denotes the EE. If ${\beta ^*}>1$, it indicates that DMU is valid, and the larger its value, the better. ${x_{ik}}$, ${y_{rk}}$, and ${u_{tk}}$ denote the i inputs, r desired outputs, and t non-expected outputs of the k DMUs, respectively. $S_{i}^{ - }$, $S_{r}^{+}$, and $S_{t}^{{u+}}$ denote slack variables for inputs, desired outputs, and non-expected outputs, respectively. $\omega$ is the weight. $\theta$ and $\varphi$ denote the radial components of the EBM model. ${\lambda _j}$ denotes linear combination factor. $\varepsilon$ represents the significance of the efficiency value in the non-radial part, and its value range is $0 \leqslant \varepsilon \leqslant 1$.

The GML index model

Since the super-efficiency EBM model is a typical static analysis method. It isn’t easy to portray the evolution of EE in the time series. To compensate for this deficiency, this study introduces the GML index model to measure the dynamic changes of EE⁴⁹. The GML index model employs a global reference and selects a non-directional vector, which aligns with the direction specified by the super-efficiency EBM model. Compared with the traditional Malmquist index model, the GML index model uses the technological frontier of the entire sample period as the reference set. This way, the shortcomings of the Malmquist index, such as insufficient transitivity and the inability to solve problems, in cross-period comparisons have been overcome. Particularly suitable for analyzing long panel data. The formula is as follows:

$$\begin{gathered} GM{L^{N,N+1}}\left( {{X^N},{Y^N},{C^N},{X^{N+1}},{Y^{N+1}},{C^{N+1}}} \right)=\frac{{1+{E^G}\left( {{X^N},{Y^N},{C^N}} \right)}}{{1+{E^G}\left( {{X^{N+1}},{Y^{N+1}},{C^{N+1}}} \right)}} \hfill \\ =\frac{{1+{E^N}\left( {{X^N},{Y^N},{C^N}} \right)}}{{1+{E^{N+1}}\left( {{X^{N+1}},{Y^{N+1}},{C^{N+1}}} \right)}} \times \frac{{\frac{{1+{E^G}\left( {{X^N},{Y^N},{C^N}} \right)}}{{1+{E^T}\left( {{X^N},{Y^N},{C^N}} \right)}}}}{{\frac{{1+{E^G}\left( {{X^{N+1}},{Y^{N+1}},{C^{N+1}}} \right)}}{{1+{E^{T+1}}\left( {{X^{T+1}},{Y^{T+1}},{C^{T+1}}} \right)}}}} \hfill \\ =E{C^{N,N+1}} \times T{C^{N,N+1}} \hfill \\ \end{gathered}$$

(3)

where $GM{L^{N,N+1}}$ represents the degree of change in total factor productivity (TFP) in the decision unit $N+1$ period relative to the N period. If $GML>1$, it indicates an increase in TFP, otherwise, it indicates a decrease. ${E^G}$ is the global directional distance function. The GML index consists of two parts: technological efficiency (EC) and technological progress (TC).

The KDE model

This study applies KDE to reveal the temporal and spatial distribution characteristics of EE among different regions⁵⁰. The probability density function of a random variable is:

$$f\left( g \right)=\frac{1}{{Mn}}\sum\limits_{{i=1}}^{M} {K\left( {\frac{{{g_i} - \overline {g} }}{n}} \right)}$$

(4)

where $f\left( g \right)$ is the density function of the random variable g. M is the number of provinces. n is for bandwidth. $K\left( u \right)$ is a kernel function. ${g_i}$ is the observed value for i study subjects. $\overline {g}$ is the mean value. In addition, this study uses a Gaussian function with random variable g obeying a normal distribution for kernel estimation of the spatiotemporal evolution of efficiency. The specific formula is as follows:

$$K\left( g \right)=\frac{1}{{\sqrt {2\pi } }}\exp \left( { - \frac{{{g^2}}}{2}} \right)$$

(5)

The Moran index model

This study adopts Moran’s I method to explore the spatial autocorrelation characteristics of EE in provinces along the B&R in China at the global and local levels, respectively⁵¹.

$$Global{\text{ }}Moran's{\text{ }}I=\frac{{n\sum\limits_{{u=1}}^{n} {\sum\limits_{{v=1}}^{n} {{W_{uv}}\left( {{Z_u} - \mathop Z\limits^{ - } } \right)\left( {{Z_v} - \mathop Z\limits^{ - } } \right)} } }}{{\left( {\sum\limits_{{u=1}}^{n} {\sum\limits_{{v=1}}^{n} {{W_{uv}}} } } \right)\sum\limits_{{u=1}}^{n} {{{\left( {{Z_u} - \mathop Z\limits^{ - } } \right)}^2}} }}\left( {u \ne v} \right)$$

(6)

$$Local{\text{ }}Moran's{\text{ }}I=\frac{{n\left( {{Z_u} - \mathop Z\limits^{ - } } \right)\sum\limits_{{v=1}}^{n} {{W_{uv}}\left( {{Z_v} - \mathop Z\limits^{ - } } \right)} }}{{\sum\limits_{{u=1}}^{n} {{{\left( {{Z_u} - \mathop Z\limits^{ - } } \right)}^2}} }}$$

(7)

n is the number of provinces. ZZ is EE. ${W_{uv}}$ is the spatial weight adjacency matrix.

The predictive model of AI algorithms

Gray predictive models are a crucial component of gray systems theory. It is widely used to address data prediction problems involving small samples, uncertainty, and incomplete information. Among them, the GM(1,1) model is the most basic and widely used model type in gray prediction models⁵². However, the traditional GM(1,1) model has a certain lag when dealing with problems with strong dynamic changes and rapidly updated data. It often fails to comprehensively incorporate the effects of the latest data fully. Consider that the input-output indicators of the provinces along the B&R have been changing over time. The latest data are more direct and sensitive to trends in EE. Therefore, on the basis of the traditional gray accumulation model, a mechanism for prioritizing the accumulation of new information is introduced to improve the responsiveness to new data. At the same time, damping coefficients are added to adjust the overall prediction trend to enhance the model fit and prediction accuracy. Based on this, this study uses the NDGM(1,1) model proposed by Zhao et al.⁵³, to forecast the input-output indicators for the next five years in each province and region. The model not only combines the adaptability of the gray model to small sample data, but also strengthens the dynamic responsiveness to the latest information. This approach enables a more precise capture of the dynamic trends in input and output variables, thereby offering robust support for the prospective evaluation of EE. The specific model construction equations are as follows:

Step 1: Let the original nonnegative time series be:

$${R^{\left( 0 \right)}}=\left\{ {{r^{\left( 0 \right)}}\left( 1 \right),{r^{\left( 0 \right)}}\left( 2 \right), \cdots ,{r^{\left( 0 \right)}}\left( n \right)} \right\}$$

(8)

Creating a new information prioritized damped cumulative generation for the original sequence yields ${R^{\left( {q,p} \right)}}$.

$${R^{\left( {q,p} \right)}}=\left[ {{r^{\left( {q,p} \right)}}\left( 1 \right),{r^{\left( {q,p} \right)}}\left( 2 \right),S,{r^{\left( {q,p} \right)}}\left( n \right)} \right]$$

(9)

$${R^{\left( {q,p} \right)}}\left( x \right)=\sum\limits_{{i=1}}^{x} {\left( {{q^{x - i}}\frac{{{r^{\left( 0 \right)}}\left( i \right)}}{{{p^{i - 1}}}}} \right)} \left( {x=1,2,S,n} \right)$$

(10)

Where ${R^{\left( {q,p} \right)}}\left( x \right)$ is an improved new sequence.

Step 2: The gray differential equation for the NDGM (1, 1) model is established as:

$$\frac{{d{r^{\left( {q,p} \right)}}}}{{dt}}+g{r^{\left( {q,p} \right)}}=h$$

(11)

Where g and h are distributed as development coefficients and gray action quantity. Then, the parameters g and h are estimated using the least squares method, and the matrix is constructed. The purpose of this is to make the gray equations predict the data more regularly and obviously.

$$\left[ \begin{gathered} \widehat {g} \hfill \\ \widehat {h} \hfill \\ \end{gathered} \right]={\left( {{H^T}H} \right)^{ - 1}}{H^T}W$$

(12)

$$W=\left[ {\begin{array}{*{20}{c}} {{r^{\left( {q,p} \right)}}\left( 2 \right) - {r^{\left( {q,p} \right)}}\left( 1 \right)} \\ {{r^{\left( {q,p} \right)}}\left( 3 \right) - {r^{\left( {q,p} \right)}}\left( 2 \right)} \\ \vdots \\ {{r^{\left( {q,p} \right)}}\left( n \right) - {r^{\left( {q,p} \right)}}\left( {n - 1} \right)} \end{array}} \right],H=\left[ {\begin{array}{*{20}{c}} { - {\varphi ^{^{{\left( {q,p} \right)}}}}\left( 2 \right)}&1 \\ { - {\varphi ^{^{{\left( {q,p} \right)}}}}\left( 3 \right)}&1 \\ \vdots & \vdots \\ { - {\varphi ^{^{{\left( {q,p} \right)}}}}\left( n \right)}&1 \end{array}} \right]$$

(13)

$${\varphi ^{^{{\left( {q,p} \right)}}}}\left( x \right)=0.5\left\{ {{r^{\left( {q,p} \right)}}\left( x \right)+{r^{\left( {q,p} \right)}}\left( {x - 1} \right)} \right\},\left( {x=2,3,S,n} \right)$$

(14)

Step 3: The time response function of the NDGM (1, 1) model is:

$${\widehat {r}^{\left( {q,p} \right)}}\left( x \right)=\left( {{r^{\left( 0 \right)}}\left( 1 \right) - \frac{h}{g}} \right){e^{ - g\left( {x - 1} \right)}}+\frac{h}{g},x=1,2,S,n,S,n+nc$$

(15)

Here, $nc$ denotes the number of predicted data.

Step 4: The fitted and predicted values can be obtained by accumulating the inverse new information priority damping on the time response values.

$${\widehat {r}^{\left( 0 \right)}}\left( {x+1} \right)={p^x}{\widehat {r}^{\left( {q,p} \right)}}\left( {x+1} \right) - p{q^x}{\widehat {r}^{\left( {q,p} \right)}}\left( x \right),x=1,2,3,S,n,S,nc$$

(16)

Among them, ${\widehat {r}^{\left( 0 \right)}}\left( 1 \right)={r^{\left( 0 \right)}}\left( 1 \right)$

Step 5: The predictive performance of gray models is typically evaluated using the mean absolute percentage error (MAPE), where a smaller value indicates a closer alignment between predicted and actual outcomes.

$$MAPE=\frac{1}{n}\sum\limits_{{x=1}}^{n} {\frac{{\left| {{{\widehat {r}}^{\left( 0 \right)}}\left( x \right) - {r^{\left( 0 \right)}}\left( x \right)} \right|}}{{{r^{\left( 0 \right)}}\left( x \right)}}} \times 100\%$$

(17)

Study area and data source

This study carries out EE measurement and analysis based on the 18 key provinces delineated in the Vision and Action for Promoting the Construction of the Silk Road Economic Belt (SREB) and the 21st Century Maritime Silk Road (24CMSR). Because there is much missing data in the Statistical Yearbook of the Tibet region, it is excluded from the research scope. To further explore the similarities and differences in EE between regions, this study divides the regions along the B&R into two regions based on the above. The specific provincial distribution is shown in Fig. 1. Considering that the B&R Initiative was formally proposed in 2013, and that the data for some provinces in 2023 is not yet complete. Therefore, this study selects 2013–2022 as the study period to construct a 10-year panel dataset. The main sources of data include: China Statistical Yearbook, China Environmental Statistical Yearbook, China Population and Employment Statistical Yearbook, Wind database, and provincial statistical yearbooks of previous years. For individual years or individual indicators that are missing, this study uses interpolation to make reasonable completions to ensure the continuity of the data and the feasibility of the model.

Fig. 1

Distribution of the study area.

Construction of the indicator system

Drawing on prior studies of EE, this research systematically establishes the input-output indicator system by aligning the technical specifications of the DEA model with data availability and representativeness (see Table 1). Drawing upon foundational economic growth theory, labor and capital are incorporated as core input factors in the indicator system. The number of employed persons at the end of the year was chosen to represent labor input³¹. The total social fixed asset investment was chosen to represent capital input⁵⁴. In light of China’s intensified ecological and environmental constraints, the promotion of land-use greening has emerged as a policy priority, particularly as the nation grapples with a significant mismatch between energy supply-demand structure. The following input indicators were further introduced in this study. The urban built-up area was chosen to represent land input³⁰. The energy consumption was chosen to represent energy input²⁸. While earlier EE research has primarily considered labor and capital as key inputs, this study extends the scope to include additional relevant variables. Considering the impact of technology penetration on EE in the digital economy. Therefore, the number of Internet access ports was selected as the data input indicator for this study⁵⁵. To reflect the extent of digital infrastructure development and respond to the need for synergistic technology-environment development. With regard to output indicators, the desired output is represented by the. Considering that the Statistical Yearbook provides nominal GDP, most studies ignore the inflation factor, resulting in distorted measurements. In this paper, nominal GDP was deflated to obtain real GDP using 2013 as the base period⁵⁶.

In terms of non-expected outputs, taking into account policy relevance and data coverage. Three typical industrial pollutants were selected: industrial wastewater, sulfur dioxide, and smoke (dust) emissions. From the perspective of policy relevance, these three pollutants are all core monitoring indicators within China’s environmental monitoring system. They are designated as key monitoring targets in the Air Pollution Prevention and Control Action Plan and the Water Pollution Prevention and Control Action Plan, as well as the emission reduction targets for the 12th and 13th Five-Year Plans, demonstrating a clear policy direction. In terms of data coverage, these three categories of pollutants offer the advantages of strong data continuity, broad coverage, and good inter-provincial comparability. They represent the most representative environmental emission indicators at the provincial level, with readily accessible data. Therefore, they are also widely applied in studies related to EE. Given the non-expectant output of the EBM model, this study employed weak disposability. And the entropy weighting method was used to weight them and construct a comprehensive pollution emission index as a non-expected output indicator⁵⁷.

Table 1 EE evaluation index system.

To examine the correlations among the three types of non-expectant output variables, this study employed the Spearman correlation test (see Table 2). The results indicated that although there was a significant positive correlation among the three indicators, they did not reach the level of complete collinearity (maximum ρ = 0.750 < 0.80). Therefore, it is reasonable to select these three types of pollutants as non-expectant output.

Table 2 Spearman correlation test for non-expectant output variables.

Robustness and sensitivity analyses

In this study, the non-directional, CRS-conditioned super-efficiency EBM model was adopted as the benchmark for the research. To test the sensitivity of the results to the assumptions regarding the directionality and scale returns of the model. Three alternative DEA models were constructed: input-directed CRS, output-directed CRS, and non-directional variable returns to scale (VRS). Spearman correlation tests were conducted on these models (see Table 3).

Table 3 Spearman correlation test for the three models.

The results indicated that under the same CRS assumptions, both input-oriented (ρ = 0.973) and output-oriented (ρ = 0.952) approaches maintained high consistency with the main model. It indicates that the research conclusion is not sensitive to the direction setting and has strong robustness. However, under the non-directional VRS condition, the average Spearman correlation coefficient with the main model was only 0.351, indicating a significant reduction in the correlation. This difference is not due to the instability of the model, but rather reflects the fundamental difference in the essence of efficiency between CRS and VRS. The efficiency under CRS conditions incorporates scale effects and is more suitable for evaluating the comprehensive EE of a region at a given development scale. Under the VRS condition, only pure technical efficiency is measured, and the scale effect is excluded. When the sample size is limited, it is prone to result in generally higher efficiency levels and significantly alter the shape of the efficiency frontier, thereby making the ranking results overly sensitive to the model setup. Therefore, in this study, a non-directed CRS was selected as the main model. Although there were certain differences in Spearman rankings under the alternative model settings, the overall efficiency level, regional pattern, and temporal evolution trend remained consistent, further verifying the robustness of the research conclusion.

To verify the robustness of the selection of data input indicators, this study conducted a sensitivity analysis by using the number of mobile phone users as a substitute indicator. The EE was recalculated based on the alternative indicators. The Spearman correlation coefficient between the two is shown in Fig. 2.

Fig. 2

Data indicators replace the Spearman correlation test.

The results indicated that efficiency scores under the two data metrics maintained a high degree of consistency, exhibiting a significant positive correlation. Annual correlation coefficients ranged from 0.580 to 0.985, with an average correlation of 0.884. This indicates that the substitution of data input indicators will not alter the time variation trend, regional structure, or main conclusions of EE. Therefore, the number of internet access ports as a choice for data input indicators is robust.

The conceptual framework of this study is shown in Fig. 3.

Fig. 3

Conceptual framework.

Research results

The results of the super-efficiency EBM model

To evaluate the EE of provinces along the B&R in China during 2013–2022, this study applied the super-efficiency EBM model incorporating non-expected outputs. The calculation results are presented in Table 4.

Table 4 EE in provinces along the B&R, 2013–2022.

According to Table 4, the average of the static measurement of EE of provinces along the B&R in China from 2013 to 2022 was 0.623, relatively inefficient relative to the production frontier. It had not yet reached the level of effective efficiency. This indicates that input-output efficiency in the field of ecology and environment has been low during this period. There is still redundancy of resource inputs at the current level of outputs, leading to low resource utilization. At the provincial level, both standard deviation (SD) and coefficient of Variation (CV) had shown a continuous upward trend. Especially after 2016, the fluctuations had intensified. CV rose from 17.4% in 2013 to 39.3% in 2022, indicating that the EE differences among provinces had continued to widen. Thus, it can be seen that the EE differences among various provinces are significant. The top four provinces in terms of EE mean were Guangdong, Shanghai, Zhejiang, and Fujian in that order. Guangdong had the highest value of 0.992, while the remaining three provinces had values of 0.979, 0.878, and 0.877, respectively. These provinces were all above average in terms of EE. This phenomenon is not only related to its location in the eastern coastal area of China and its strong economic foundation. It can also be systematically explained by the theory of New Economic Geography (NEG). According to NEG, the developed coastal areas have higher market potential, transportation accessibility, and industrial agglomeration degree. Capital, technology, and talent are highly concentrated spatially. This leads to significant agglomeration economies and technological spillover effects. Industrial agglomeration further strengthens knowledge dissemination, innovation diffusion, and scale, making green technologies more readily adopted. At the same time, environmental regulations are more stringent, and through regulatory promotion effects, the environmental governance capacity is enhanced. The combined effect of these mechanisms enables eastern coastal provinces to maintain high resource utilization efficiency, governance level, and industrial greenness in the long term, thus maintaining a continuously leading EE.

The four provinces with the lowest EE averages were Ningxia, Xinjiang, Qinghai, and Gansu, with values of 0.447, 0.446, 0.423, and 0.420, respectively. EE in these areas was relatively low and below average. This phenomenon is not only located in the western part of China, but can also be explained by the resource curse hypothesis and the path dependence theory. The resource curse hypothesis theory posits that resource-rich regions, despite possessing abundant mineral or energy endowments, tend to develop excessive reliance on resource-intensive industries. This leads to an unbalanced industrial structure, insufficient innovation incentives, and capital flowing away from high-productivity and green industrial sectors. Consequently, these regions become trapped in a path dependence cycle of inefficient development. These regions have relatively low levels of economic development and are in the ascending phase of the Environmental Kuznets Curve (EKC). That is, an increase in pollution accompanies economic growth, while environmental governance and technical capabilities are insufficient to counteract this pressure, resulting in a long-term low level of EE. The remaining provinces, except for Jilin, Heilongjiang, Guangxi, and Hainan, had above-average EE averages.

According to the results shown in Fig. 4, from the perspective of the time trend, the EE showed a W-shaped fluctuation pattern throughout the period from 2013 to 2022. From a theoretical perspective, in the early stage of the B&R Initiative, some regions placed greater emphasis on economic growth. The decline in EE is in line with the characteristics of the EKC curve during the phase of economic pressure. As technological investment increased and environmental regulations tightened, EE gradually recovered. The renewed decline between 2019 and 2020 may have been influenced by multiple factors, including the impact of COVID-19 and fluctuations in industrial activity. At the regional level, 21 CMSR was significantly more EE than SREB. This not only reflects disparities in economic development but also highlights the amplified role of spatial agglomeration effects in green transformation, as emphasized by the NEG. Overall, the trend of EE changes in the B&R region over the period 2013–2022 was consistent with that of the SREB region. The results imply that the suboptimal overall EE of the B&R region is significantly attributable to the low EE levels observed within the SREB region.

Fig. 4

Trends in regional EE.

The results of the GML index model

To capture the temporal dynamics of EE, this study adopts the GML index model. Figure 5 shows that from 2013 to 2022, the average GML index of China’s B&R provinces was 1.012. This represented an average annual increase in EE of 1.2%. Although the overall GML had improved, the growth rate was relatively small. The GML reflects the dynamics of EE. To further explore the reasons for the changes, it can be decomposed into EC and TC. From the decomposition results, EC showed a decreasing trend over the study period, averaging 0.991 and decreasing at an annual rate of 0.9%. TC was above 1 in all but a few years, averaging 1.024 and increasing at an annual rate of 0.9%. This suggests that the increase in EE in the regions along the B&R is mainly due to TC. Therefore, strengthening technological innovation will become a key path to promoting the sustainable improvement of EE.

Fig. 5

GML index and decomposition results.

According to Fig. 6, at the regional level, the SREB region recorded an average GML of 1.003. The average annual growth rate was only 0.3%, which was relatively small, although it had improved. In comparison, the 21CMSR region’s GML average was 1.024, increasing at an annual rate of 2.4%, demonstrating more significant growth. This indicates that the 21CMSR region has achieved relatively successful practical experience in green development and ecological environmental protection, facilitated by the B&R Initiative. It provides a useful reference for the ecological transformation of the SREB region. It is noteworthy that although the two regions differ significantly in industrial structure, economic development, and environmental governance capacity. However, both of their EE improvements are mainly attributed to TC. This is in line with the findings from the regional analysis of the B&R. It further highlights the key role of TC in enhancing EE.

Fig. 6

Regional GML index and decomposition results.

At the provincial level, except for Hainan, Gansu, Qinghai, and Ningxia, the GML of most provinces along the B&R Initiative was greater than 1. These regions have demonstrated tangible improvements in environmental protection, green innovation, and workforce management. Interestingly, for the provinces where GML was less than 1, their EC was also lower than 1. Owing to disparities in economic development levels and the resource endowment of each province, the GML index and its decomposition indicators also show significant differences. Among them, the GML index in Yunnan was the highest, at 1.050, increasing at an annual rate of 5%. This growth was mainly attributed to the continuous improvement of the EC. In comparison, the GML value in Qinghai was the lowest, at only 0.958, with an average annual decrease of 4.2%. The EC was 0.943, and the TC was also low. Reflecting its declining EE, it was mainly subject to the influence of both EC and TC factors.

Characterization of spatial and temporal evolution

Dynamic evolution characteristics of distribution

To more effectively characterize the dynamic evolution of absolute differences in EE in provinces along the B&R in China. In this study, the KDE model was used to analyze the distribution of EE. The results are shown in Fig. 7. In terms of the overall evolution trend, the main peak of the KDE curve showed an overall shift to the left during the sample period. This reflected an overall decrease in its EE level. Looking at the characteristics of the peak change, it was observed that the height of the main peak of the KDE curve had continued to decrease over the period 2013–2017. It was shown that the distribution of EE between regions had become more dispersed, and the absolute differences were widening, showing a clear trend of polarization. And since 2018 until 2022, the height of the main peak had gradually increased, accompanied by the gradual weakening of the secondary peak. It was shown that the differences in EE between regions began to narrow, and the distribution tended to concentrate. There was some degree of dynamic convergence between regions. Further analysis of the shape of the KDE curve reveals that most years were characterized by a bimodal or multimodal distribution. And it was accompanied by an obvious trailing phenomenon on the right side. It shows that although the level of EE is higher in some provinces and regions. However, overall, there is still a significant uneven development of EE among provinces and regions. That is, the spatial heterogeneity of EE is still more prominent.

Fig. 7

Results of KDE.

Spatial correlation analyses

In this study, the Moran index was introduced to explore potential spatial autocorrelation in the EE of B&R provinces. According to Fig. 8, the global Moran index for EE in provinces along China’s B&R remained positive throughout the period from 2013 to 2022. The lowest passed the 10% significance level test in all years except 2014. From 2013 to 2022, the global Moran index of EE showed a notable upward trend, rising by 72% from 0.326 to 0.561. A significant positive spatial correlation was observed in the EE of B&R provinces, highlighting pronounced spatial clustering effects. Although there were some fluctuations during this period, the overall trend showed a gradual increase from weak to strong. This indicates that the EE in the regions is gradually forming a more closely related pattern in space.

Fig. 8

Results of the global Moran index.

To further explore the local spatial agglomeration relationship between provinces. The local Moran index was used to analyze the EE. For space reasons, four key years, 2013, 2016, 2019, and 2022, were selected for this study. Figure 9 shows that the EE of provinces along China’s B&R was mainly distributed in the first and third quadrants. It showed that the overall spatial agglomeration presents H-H and L-L types. Regions with higher or lower levels of EE were relatively concentrated. Specifically, there were individual provinces where the type of agglomeration had changed significantly. Among them, Shanghai, Zhejiang, and Fujian were consistently located in the first quadrant. This reflected the long-standing and stable advantages of these regions in terms of environmental protection and efficient resource utilization. Since 2019, Guangdong has returned to the first quadrant, demonstrating a continuous improvement in EE. Guangxi and Hainan were consistently in the L-H agglomeration type, indicating that their EE was low and that neighboring regions were relatively high. Yunnan, which was also in the 21 CMSR region, had been in the fourth quadrant since 2013 and had fallen into the third quadrant in subsequent years. This change suggested that there had been no significant improvement in its EE. Neighboring provinces were developing rapidly in this area, and the regional gap had widened. In contrast, most of the provinces in the SREB region were concentrated in L-L agglomerations or H-L agglomerations, reflecting that the overall level of EE was still low. It was noteworthy that the type of Chongqing agglomeration fluctuated considerably and showed some instability. As one of the important industrial bases and economic centers in China, Chongqing has a relatively fast economic development and a complex industrial structure. In some years, Chongqing might have placed greater emphasis on economic growth, resulting in a decline in EE. For instance, in 2016, it fell back to the L-L agglomeration. In other years, Chongqing may have strengthened its ecological protection and resource utilization efficiency, which had led to a rebound in EE, such as in 2013 and H-H or H-L agglomeration in 2019 and 2022.

Fig. 9

Results of the local Moran index.

Future EE projections

To better advance the sustainable growth of EE across B&R provinces, and to observe the trend changes in the next five years from 2023 to 2027. In this research, future values of input and output indicators for each province were estimated using the NDGM(1,1) model, and EE was subsequently calculated through the super-efficiency EBM model. Given the excessive MAPE and substantial error in predicting total social fixed asset investment in Guangdong province, this study does not include this province in the analysis for the time being. The results of the MAPE values for each province are shown in Fig. 10.

Forecasting results are typically deemed highly accurate when the MAPE value falls below the 10% threshold, as suggested by relevant benchmarks. Figure 8 demonstrates that the MAPE values of the 16 provinces were less than 10%. Among them, Chongqing had the lowest MAPE value (0.969%), and Liaoning had the highest (3.847%). The total mean value was 2.049%, which was significantly lower than the standard threshold, indicating a very high prediction accuracy. It was proved that the NDGM(1,1) model used in this study was scientifically sound, and the model predicted the data more accurately.

Fig. 10

Average value of MAPE by province, 2023–2027.

Table 5 Projected results of EE by Province for 2023–2027.

As shown in Table 5, it is expected that in the next five years, the EE of the four provinces of Liaoning, Shanghai, Fujian, and Chongqing will reach the DEA effective state, indicating that their resource allocation and environmental outputs have reached an optimal level of efficiency. Among them, although the EE of Zhejiang Province declined slightly, it remains at a relatively high level overall, with a mean value of 0.749. In contrast, the EE of the remaining provinces ranges from 0.256 to 0.719. The findings once again underscore the pronounced regional variation in EE across the B&R provinces. As shown in Fig. 11, Qinghai still has the lowest EE of all provinces. Although the EE of the provinces along the B&R improves year by year from 2023 to 2027, the overall efficiency is not high. The average for the 16 provincial areas is only 0.564 and has declined from past levels of development. Overall, EE in the provinces along the B&R will still take a long time if it is to reach a high level.

Fig. 11

Trend changes in EE by province, 2023–2027.

As shown in Fig. 12, A gap between historical and predicted EE values can be identified among the provinces in the B&R. Overall, the average EE predicted for the next five years (0.564) is slightly lower than the historical average for 2013–2022 (0.623), with a decrease of 9.4%. This suggests that EE is expected to decline in most provinces during the period 2023–2027, but the overall decline is relatively limited. In terms of trends, EE shows a W-shaped fluctuation in the historical phase. In the forecast phase, it shows a continuous upward trend. The forecast points to a sustained rise in EE across provinces, with a gradual trend toward more optimal levels. Looking at specific provinces, EE is expected to continue to rise in some provinces. For example, Liaoning improved from 0.662 to 0.817, Fujian from 0.877 to 0.935, and Chongqing from 0.638 to 0.975, representing increases of 0.155, 0.058, and 0.337, respectively. Among them, Chongqing saw the biggest improvement, showing its effectiveness in ecological and environmental management and efficient resource utilization. In addition, Shanghai’s EE has only improved from 0.979 to 1.006, but it is still at an effective level, as its raw level is close to the efficiency frontier. In contrast, most provincial forecasts are lower than historical values. Inner Mongolia, in particular, saw its EE drop from 0.627 to 0.479, a decrease of 23.6%, making it the region with the largest decrease. Although the decline in the remaining provinces was relatively small, mostly around 10%, the downward trend in EE cannot be ignored.

Fig. 12

Comparison of EE between historical and predicted values.

Discussion

This study comprehensively employs super-efficiency EBM, GML index, spatial analysis methods, and AI algorithms prediction models. A multi-dimensional and systematic assessment of the EE of the provinces along the B&R in China from 2013 to 2022 is conducted. Compared to the study of Jiang et al., we introduce data elements into the input indicator system and are no longer limited to the traditional selection of indicators⁵⁴. The research results show that EE exhibits a significant spatial differentiation pattern with higher levels in the east and lower levels in the west. This is consistent with the conclusion of You et al., further proving the existence of a significant imbalance in regional EE⁵⁸. This study introduces the NEG theory, providing a more systematic explanatory framework at the theoretical level for this spatial pattern. The higher efficiency of the eastern coastal provinces is not only due to their geographical advantages. It also deeply reflects the technological spillover effect brought about by the agglomeration economy and the higher intensity of environmental regulations. This is consistent with the research conclusion of Hu and Li on technology agglomeration promoting EE⁵⁹. The relatively low EE in the western provinces can be explained by the resource curse and the theory of path dependence. And it can also be further linked to the locking effect of the EKC. This study further reveals that these regions may not simply be in the ascending phase of the EKC. Instead, it is locked onto a development path that relies on the consumption of resources. Despite the continuous implementation of policies such as the Western Development Strategy, the insufficient capacity for green technological innovation and the lagging reform of the factor market remain issues. This makes it even more difficult to break through the resource curse. Therefore, it should not be assumed that economic growth can automatically improve environmental quality. Instead, for specific regions, precise industrial policies should be implemented, and green technologies should be introduced to actively break the path dependence, rather than passively waiting for the arrival of the EKC inflection point.

The decomposition results of the GML index indicate that TC is the core driving force for improving EE. This discovery is highly consistent with the conclusion of Liu et al. regarding the Yellow River Basin in the Mesopotamia region of China⁵⁷. Further highlighting the crucial role of green technological innovation in promoting sustainable development. The current improvement of EE in the provinces along the B&R mainly relies on the outward shift of the frontier production boundaries. For instance, advancements in new energy technologies and pollution control techniques, rather than relying on the improvement of existing resource allocation efficiency. From the perspective of innovation economics, this indicates that, compared to static adjustments in resource allocation, promoting the research and dissemination of green technologies may have a greater leverage effect on improving EE.

The distributional characteristics of EE, as revealed by the KDE model, correspond to the earlier static findings and reflect a decreasing trend. The Moran index results show that the EE of the provinces along the line exhibits significant spatial clustering, mainly manifested as the H-H type and L-L type distributions. This is similar to the results of Liu et al., further confirming the existence of strong spatial correlation provinces along the B&R⁵⁵. This feature is in line with the theory of spatial spillover. The green technologies, management experiences and institutional advantages of high-efficiency regions can generate positive spillover effects through diffusion among neighbors and policy imitation. On the contrary, low-efficiency regions, due to their weak foundation, lagging policies and limited absorption and learning capabilities, are difficult to obtain effective spillovers and thus continue to remain in a low-efficiency state.

The NDGM(1,1) model prediction indicates that the EE will show a steady upward trend in the future. This is largely consistent with the long-term expectations of the EKC hypothesis. As the dual-carbon strategy is further implemented, the green transformation experience of the eastern region is expected to be disseminated to the central and western provinces through policy diffusion and industrial linkage. However, the predicted average value is slightly lower than the historical average. This indicates that the green transition is not a quick process and still requires continuous advancement and long-term investment.

Conclusions and recommendations

Conclusions

This study systematically measures and analyzes the EE of provinces along the B&R in China from 2013 to 2022. Firstly, to ensure a comprehensive evaluation, a robust EE index system is constructed, combining standard production factors with distinctive variables from the digital economy domain. Secondly, the super-efficiency EBM and the GML index models are used to analyze the EE statically and dynamically. The results show an overall decreasing trend in EE over the period 2013–2022, with an average value of only 0.623, which has not yet reached the effective level set by the DEA model. Of these, the 21CMSR region has an overall higher level of efficiency than the SREB region. The results of the GML index decomposition show that the external environment mainly influences changes in EE, and TC is a key factor in its improvement. Thirdly, the study of its spatial and temporal evolution characteristics reveals that a noticeable leftward movement of the main peak in the KDE curve indicates a declining trend in the distribution, with more prominent spatial heterogeneity characteristics. Findings derived from the Moran index suggest that EE is not randomly distributed but shows clear spatial agglomeration among provinces, which is mainly manifested as H-H type and L-L type agglomeration patterns. Finally, this study innovatively incorporates the DEA with AI algorithms to predict future EE with the help of the NDGM(1,1) model. The projections show that EE in Liaoning, Shanghai, Fujian, and Chongqing is expected to be on the frontier in the next five years, with a continuous upward trend in the overall efficiency mean.

Recommendations

Drawing upon the aforementioned results, this study puts forward the following policy suggestions. To help the sustainable improvement of EE in the provinces along the B&R in China, and to contribute to the promotion of green and sustainable development of China’s regional ecology and economy.

• (1) Developing differentiated governance strategies tailored to local conditions to resolve regional imbalances. Given the overall EE level of the provinces along the B&R in China, it was relatively lower compared to the production frontier. There were significant differences in EE among various provinces. Local governments should formulate practical ecological and environmental protection policies based on their unique resource endowments, economic foundations, geographical advantages, and industrial structures. They should adopt tailored approaches and focus efforts precisely on specific areas. For the eastern region, its role as a green innovation source area should be strengthened by establishing a cross-provincial platform for the transfer of green technologies. Actively export clean production standards and environmental governance technologies to the central and western regions. For western regions, establish a special fund for green transition to break the resource curse and path dependency. The policy focus should shift from the sole assessment of GDP to the evaluation of green total factor productivity. Strengthen supervision over the allocation of funds for high-energy-consuming and high-emission projects, and avoid further entanglement in inefficient tracks.

• (2) Accelerating green technology innovation and actively introducing high-level technical talents. The decomposition results of the GML index indicate that TC is the core driving force for improving EE. The central and local governments should establish a special fund for green technology research and development under the B&R. This fund should focus on supporting original breakthroughs in areas such as new energy, pollution control in a coordinated manner, and the circular economy. At the same time, the government should introduce corresponding loan incentives to encourage enterprises to conduct green technology research and development and to introduce new technologies. Encouraging enterprises, universities, and research institutions to carry out collaborative innovation research and development in the fields of clean energy, energy conservation, and emission reduction, as well as the circular economy. Furthermore, high-level technical talents are the key to driving technological progress. All regions should establish high-level research platforms, improve the talent incentive mechanism, and attract green technology talents from both at home and abroad. Thereby driving the overall advancement of technological progress along the B&R routes.

• (3) Promoting regional synergy to achieve green transformation and upgrading. Given the significant H-H and L-L spatial clustering characteristics in the provinces along the B&R. All regions should actively respond to the green transformation policies. Promoting regional cooperation and complementarity in terms of division of labor. Strengthening the construction of a collaborative and interactive mechanism between the eastern and western regions in the field of green ecological governance. For instance, efficient regions should share their green governance experiences with less efficient regions. Exploring a mechanism for paired assistance between certain provincial regions. Promoting the efficient cross-regional flow and coordinated allocation of policy, technology, capital, and human resources, and accelerating the absorption of positive spillover effects in the western regions. Achieving a collaborative framework where stronger regions support weaker ones and eastern regions drive western development, thereby enhancing overall EE.

• (4) Enhancing the prediction and regulation of AI algorithms in EE improvement. This study verified the feasibility and accuracy of the NDGM(1,1) model in predicting EE. In the future, each province should enhance the deep integration of AI technology with ecological environment protection and governance. Constantly promoting the application of AI algorithms in areas such as dynamic prediction of EE, pollution emission monitoring, and optimization of resource allocation. Local governments should establish an AI-based dynamic monitoring and early warning platform to assess the changes in EE of each province in real time, providing data support for policy adjustments. In combination with remote sensing monitoring and big data analysis technologies, strengthen the dynamic supervision of environmental behaviors in key areas and key industries. Utilizing the prediction results to identify areas where EE may decline in advance. Developing targeted intervention plans to achieve the transformation from post-event governance to pre-event prevention.

While this study has yielded valuable findings regarding the EE of provinces along the B&R and offered novel insights for future investigations, some limitations remain. Firstly, this study only considers the provinces along the B&R and fails to explore the efficiency at the city level. In the future, further research can focus on typical city clusters along the B&R. Additionally, the effects of environmental variables and random disturbances are not considered, which may introduce bias in the measurements. In the future, we can consider combining the EBM model and the SFA model to form a three-stage EBM model. Thirdly, the NDGM(1,1) model used in this study may generate a non-parametric frontier that is sensitive to extreme values in the prediction results. It may produce deviations in years with significant data fluctuations. Future research could consider introducing more robust, improved grey models or combining machine learning methods to enhance the prediction accuracy.