Assessment and Forecast of Green Total Factor Energy Efficiency in the Yellow River Basin—A Perspective Distinguishing the Upper, Middle and Lower Stream

Abstract

As the fifth-longest river globally, the Yellow River is of great importance to the world’s ecological protection. Due to its location as an essential ecological barrier and economic zone, it is imperative to balance energy support and ecological management in the basin. In this process, improving energy efficiency is crucial solution. Distinguished into upstream, midstream, and downstream, we measured the trajectory of green total factor energy efficiency over the past fifteen years using the Super-Epsilon-based model. Further, we identified the heterogeneity of energy efficiency within different river basins with the help of kernel density estimation. We used it to analyze the geographical and policy reasons affecting energy efficiency fluctuations. Finally, we constructed high, medium, and low GDP growth scenarios, and used a long short-term memory neural network model to predict energy efficiency forecasts in each scenario. The study results clarified that the overall energy efficiency showed an upward trend since 2013. Among them, the most significant improvement in energy efficiency was observed upstream, while the energy efficiency in the middle and lower stream showed a decreasing trend. Regarding future development trends, an economic growth rate of 6.5% was most favorable for energy efficiency compared to 6% and 7%. This finding reminded us to be alert to the ecological condition of the lower Yellow River basin. In addition, maintaining an appropriate economic growth rate is helpful for the balance between development and ecology.

1. Introduction

Strengthening the construction of ecological civilization and pollution control has become an essential driving force for sustainable development nowadays [1]. The Yellow River basin is an important river in the world. With the geographical features of abundant water supply, plateau, and a sediment protection belt, the Yellow River has become the world’s ecological barrier. However, with the deterioration of natural conditions [2] and over-exploitation, the Yellow River basin has experienced ecological fragility and water shortage in recent years [3]. The ensuing environmental problems, such as large-scale pollution [4], climate warming, rapid population growth, and urban focus [5], further challenge the soil properties [6] of the Yellow River basin. These problems constrain the high-quality development of resources [7] and pose a severe threat to the ecological sustainability of the whole basin and even the world.

To achieve economic growth and ecological protection simultaneously, increasing green total factor productivity is a feasible way. As the driving force of the economy and society, energy is closely related to the sustainable development of the ecological environment. Therefore, the key to achieving low-carbon goals lies in relying on technology to improve the efficiency of energy resource utilization [8]. With 70% of China’s coal production and 40% of its energy production, the Yellow River basin is rich in natural resources and is a vital coal supply base for China, the world’s largest carbon emitter [9]. Therefore, improving the integrated energy efficiency not only contributes to pollution control in China but also has implications for the solution of environmental sustainability issues on a global scale. Most of the existing literature focusing on the Yellow River’s energy efficiency are mainly at provincial and industry levels, focusing on evaluation indicators, influencing factors, and time-series change patterns. However, the development of different basins of the Yellow River is heterogeneous, and there are apparent differences between different geographical locations in energy utilization types and water nutrients [10]. Therefore, when researching the Yellow River basin, it is important to break the boundaries of regional divisions and recognize the differences between upstream, middle, and downstream.

The motivation of this study is to serve the ecological sustainability of the Yellow River basin by identifying the driving factors restricting energy efficiency and clarifying the future scenarios of energy efficiency. Based on this, this study will systematically investigate the energy eco-efficiency of the Yellow River basin in China from the perspective of distinguishing upstream, middle, and downstream. Firstly, this study distinguished bad output (undesirable output) and expected output and used the method of Tone K [11] to transform again, and finally adopted a Super-Epsilon-based model (Super-EBM) to calculate the green total factor energy efficiency of the Yellow River basin. The corresponding temporal and spatial evolution trend would also be further analyzed through the GIS method [12]. Secondly, this study deeply analyzed the spatial drivers of green total factor energy efficiency to identify the key indicators in the domain. Finally, this study used a long short-term memory (LSTM) neural network prediction model to make short-term forecasts of green total factor energy efficiency trends in the future. Further, by setting a high, baseline, and low GDP development scenarios, we explore the most suitable economic environment for energy efficiency development. The study results would have specific policy inspirational effects on the improvement of the Yellow River basin’s ecological environment.

The structure of this article is as follows. Section 2 is a literature review. Section 3 is materials and the principle of methods. Section 4 is the measurement and prediction of green total factor energy efficiency. Section 5 is the conclusion of the full text.

2. Literature Review

Covering 750,000 square kilometers, the Yellow River basin has formed an energy distribution situation of hydropower in the upstream, coal in the midstream, and oil in the downstream. Due to the misalignment between resource distribution and productivity layout, research on comprehensive energy efficiency is the key to resolving the conflict between development and environmental protection. However, research on the Yellow River basin mostly focus on hydrological and ecological characteristics. For example, Chen et al. [13] established an environmental numerical model using the spatial principal component analysis (SPCA) model to analyze the ecological environment vulnerability and its changes in the Yellow River basin. Lei [14] and Zhao [15] assessed local environmental conditions in terms of precipitation and vegetation cover, respectively. Quan [16] evaluated the sustainable development of the entire Yellow River ecosystem under the conditions of climate change and the operation of hydropower projects. However, there are few studies on energy efficiency in the Yellow River basin. The existing studies around energy efficiency include measuring of energy efficiency, analysis of energy efficiency influencing factors, and energy efficiency prediction. This study will focus on these three aspects for the literature review.

2.1. Research on Energy Efficiency Measurements

The calculation of energy efficiency has successively gone through a single-factor energy efficiency stage, a total factor energy efficiency stage, and a green total factor energy efficiency stage. Single-factor energy efficiency, or energy intensity, means the amount of energy required to be consumed per unit of output. This measure is a relatively simple and direct way to portray energy consumption efficiency and is easy to apply. For example, Adom et al. [17] analyzed the impact of green finance policies on energy intensity by first converting fossil fuels, such as coal, oil, and natural gas, consumed into standard coal, summing them up, and measuring energy intensity as a ratio to GDP. Chen et al. [18] measured energy intensity as the ratio of the total value of energy inputs to the national output of the region. Wang and Qi [19] measured energy intensity using the ratio of primary energy consumption to real GDP and examined the effect of industrial structure distortions on energy intensity. Huang et al. [20] used energy consumption ratio to regional GDP as the energy consumption intensity when analyzing the heterogeneous effects of local R&D and foreign technology spillovers on energy intensity. Philip et al. [21] defined energy intensity as the sum of a firm’s fuel and electricity costs as a percentage of the firm’s sales revenue. In general, the calculation of single-factor energy efficiency is more straightforward and advantageous in analyzing long-time horizons and in the study of different energy types. However, single-factor energy efficiency ignores capital and labor inputs in the production process. Therefore, it cannot better measure the level of technology in energy use, nor can it overcome the substitutability of energy inputs and other input factors (capital, labor, etc.).

Combining literature reviews and social background, we define green total factor energy efficiency as: the optimal amount of energy input required by best production practices and specific outputs, under the condition that other production factors (such as labor, capital), other than energy input, remain unchanged and the undesired output is reduced as much as possible in ratio to the actual input. The evaluation standard is the larger the value, the higher the energy efficiency, and the higher the quality of economic development. Total factor energy efficiency constructs an optimal production frontier that includes energy inputs and measures energy efficiency in terms of the distance of actual production from the optimal frontier [22]. Since total factor energy efficiency measurement includes both capital, labor and energy inputs, it is calculated using the data envelopment analysis (DEA) method [23]. The DEA method calculates the level of technology without setting up a production function and is widely used when studying regional energy efficiency differences. There are numerous studies using data envelopment analysis. Olanrewaju [24] pioneered comprehensive exponential decomposition analysis-artificial neural network-data envelopment analysis (IDA-ANN-DEA) and used it for quantitative energy assessment based on mathematical programming problems. Ramakrushna [25] used a non-parametric data envelopment analysis (DEA) method to assess the growth return behavior of the Indian automotive industry. Yu [26] used the Dynamic Spatial Panel Model (DSPM) to empirically test the mechanism and influence of urban spatial structure on total factor energy efficiency. Chen et al. [27] used a three-level frontier surface relaxation measure to empirically analyze the total factor energy efficiency of 19 manufacturing sub-industries in nine Chinese provinces from 2001 to 2011.

With the development of the economy, academia has also begun to incorporate environmental factors into calculating total factor productivity and total factor energy efficiency. Academia began to introduce resource and environmental factors into the measurement model of energy efficiency. Productivity theory and empirical research considering resource and environmental factors have gradually become hot topics in the academic community. At the beginning of the research, some scholars, such as Comin [28] and Hulten [29], introduced resource and environmental factors as input variables into the model. However, this method does not conform to the actual input–output relationship and leads to biases in the productivity evaluation results. In addition, some scholars [30] convert pollutant output into ordinarily expected output through the use of harmful output methods, linear data conversion, nonlinear data conversion, and other data conversion function methods. These transformation methods still do not meet the basic requirements of efficiency evaluation and violate the actual production process. It was not until Chung [31,32] and other scholars applied the directional distance function to evaluate environmental productivity that the above problems were solved. The main idea of the method was based on the weak disposability of non-desired outputs, such as pollutants, a DEA environmental productivity evaluation framework based on the directional distance function is constructed. Since then, many scholars have used this function to measure total factor productivity considering non-desired outputs and called it environmental total factor productivity (also known as green total factor productivity, ecological total factor productivity, etc.).

2.2. Study of the Factors Influencing Energy Efficiency

Based on the summary of previous studies, the existing literature on energy efficiency influencing factors mainly focuses on three aspects: first, technological progress; second, structural factors [33], including industrial structure, economic structure, energy consumption structure, etc.; third, institutional factors include energy prices, degree of opening to the outside world, environmental control, fiscal system, etc. [34]. Ma and Stern [35] analyzed the role of technological change, industry structure change, and fuel substitution in improving energy efficiency. The research results affirm the positive effect of production transfer between industries. Yu [36] found that the information technology revolution represented by the internet is an important driving force for improving green productivity. Gilbert [37] analyzed the changing law of energy efficiency in the United States and confirmed that the increase in per capita income and the increase in energy prices played an important role in reducing energy intensity. Liao et al. [38] decomposed changes in energy intensity from two levels of sector structural effect and efficiency effect. The research results emphasize the importance of optimizing the department’s structure and reducing the proportion of investment. Djula Borozan [39] assessed the impact of various environmental variables on technology and energy efficiency in EU countries. Tobit regression analysis showed that technical and energy efficiency determinants are different. Human capital and innovation are significant for improving the regional efficiency of ecological performance. Voigt et al. [40] took the energy intensity of 40 countries worldwide as a sample to study the impact of technological changes and changes in economic structure on energy efficiency. After sorting out the heterogeneous results between different economies, the research affirmed the impact of changes in industry mix and technological changes in improving energy efficiency. He et al. [41] found that fundamental agricultural innovations that lead to higher production and environmental safety are the keys to improving efficiency. Chai et al. [42] decomposed the direct and indirect effects of changes in the final demand structure on energy efficiency by calculating the input–output table. Lin and Chen [43] pointed out that factor market distortion is the threshold of the spillover effect of exports and FDI, which will lead to a decline in exports and FDI, and further inhibit the growth of green total factor productivity. Environmental regulation can indeed increase green total factor productivity, but it is difficult for environmental regulation to promote green through technological innovation. Zhao et al. [44] found that technological progress, energy prices and economic development positively impact TFEE. The impact of technological progress was found to be the most important.

2.3. Research on Energy Forecasting Methods

The existing forecasting methods in the energy field can be roughly divided into time series forecasting, multi-factor modelling forecasting, and machine learning forecasting. Among them, the time series forecasting method fits the future trend by analyzing the historical characteristics of the data. Multi-factor modelling predicts by analyzing the complex connections within the system. Machine learning realizes comprehensive data learning through algorithm editing. Among them, deep learning has broad applicability in solving multi-class data with its powerful data analysis, prediction and classification capabilities [45]. In predicting energy efficiency, scholars have conducted a series of extensive research [46]. For example, Liimatainen et al. [47] analyzed energy efficiency by adding fuel data to national freight statistics, and proposed a framework for modelling and analyzing road freight energy. Forecast trends indicated that the Finnish government’s goal of increasing energy efficiency by 9% by 2016 would not be achieved. Bashmakov [48] made long-term predictions of the energy efficiency of Russian buildings. Based on the results, the researchers set up ten policy options for improving energy efficiency, aiming to reduce the fossil fuel consumption of buildings by more than half. Tomasz et al. [49] used the Takagi–Sugeno Fuzzy Model to predict the energy efficiency of buildings undergoing thermal upgrades. The results confirm that this model has higher accuracy than other artificial neural networks and rough set models. Work by Altintas et al. [50] is based on the principle of thermodynamics as an audit and forecasting tool and predicts the system’s energy efficiency by applying different ANN architecture types. Rossi et al. [51] combined machine learning algorithms with advanced statistical analysis to build a machine learning model based on gradient boosting regression algorithm to predict the factory’s energy efficiency. Li et al. [52] proposed a new method for predicting energy efficiency (SFA-GARCH), and based on this method, predicted China’s energy efficiency level in the past ten years. The results confirm that the improved method has good predictive performance. Muzychuk et al. [53] designed the energy-GRP ratio based on statistical methods, predicted the energy intensity of the Irkutsk region, and proposed measures to improve energy efficiency. Nazari et al. [54] predicted the energy efficiency of solar distiller through Artificial Neural Network (ANN) and a neural network optimized by Imperialist Competition Algorithm (ICA). According to the test data, the root mean square error (RMSE) value of energy efficiency is 1.37. In the robustness test [55], the average relative error, mean square error, etc., are all powerful measurement tools.

2.4. Summary of the Literature and Innovation Points

By combing through the existing literature, we have the following gaps in current research. (1) When solving energy efficiency in today’s society, it is urgent to pay attention to differences in economic development levels and technical differences between industries. (2) With the dual carbon goals and the policy requirements of economic sustainability, it is crucial to study the system impacts, including energy, economy, environment, technology, etc., to clarify the law of energy efficiency development. (3) In the field of energy forecasting, machine learning forecasting methods have been the most popular methods in recent years. Ordinary recurrent neural network (RNN) is difficult to train, which makes it difficult to handle long-distance dependencies in practical applications. LSTM machine learning models have long-term memory capabilities for sequence modeling problems and are simple to implement.

In response to the above findings, the innovations of this study are as follows. First, based on the definition of total factor energy efficiency, this study measures green total factor energy efficiency in the context of sustainable development. This concept is more consistent with China’s actual law of energy efficiency than the traditional energy efficiency. Secondly, this study fully combines the characteristics of an input–output efficiency index system, redundancy of decision units, efficiency ranking and other factors to improve the traditional EBM model continuously. A new efficiency value analysis model applicable to this study, the super efficiency EBM model with non-expected output, is constructed. We measured the green total factor energy efficiency of 96 prefecture-level cities in the basin with this method. Furthermore, the spatio-temporal efficiency evolution was analyzed according to the overall and upstream, midstream, and downstream basin distribution. Finally, this study predicts the green total factor energy efficiency values of the Yellow River basin and the upstream and midstream and downstream in 2020–2025 by using the LSTM prediction model and setting three scenarios for economic growth rates.

Overall, this study covers the analysis of the historical status of energy efficiency in the Yellow River basin and the forecast of future trends. The study distinguishes the upstream, midstream, and downstream and explores the heterogeneity of the development status of energy efficiency. The study results of the will be significant for a comprehensive assessment of the green ecological status of the Yellow River basin.

3. Materials and Methods

3.1. Super-Epsilon-Based Model (Super-EBM)

The measurement methods of total factor energy efficiency in existing research can be summarized into two categories: parametric and non-parametric. Among them, the parameter method needs to set the production function, and different settings often lead to different results. The non-parametric method has the unique advantages of avoiding subjective influence and reducing the complexity of the calculation process, because its input and output variables do not need to be correlated, which means that it does not need to estimate the parameters in advance. Among the non-parametric measurement methods, DEA is the most commonly used method at the beginning. In the process of using the method, the original production function in microeconomics was replaced by the envelope, and the input and output of decision-making units (DMU) were mapped to space and built a non-parametric envelope frontier line to make the effective point on the production frontier. With the later development, the traditional radial DEA model ignores the input and output slack variables. If this is used as a performance indicator in the evaluation and decision-making unit, it is likely to have a misleading effect on the decision maker. Based on this, the EBM model is proposed by Tone [11] through the study of the radial and non-radial relaxation ratio, which fully considered the differences of the relaxation variables of each element. Based on the assumption that the return to scale is not changed, the mathematical programming mode of the initial-oriented EBM model is as Equation (1) follows:

$${\gamma }^{*}=min\theta -{ϵ}_x{{\displaystyle {\displaystyle \sum }}}_{i=1}^m\left({\omega }^{-}{S}_i^{-}/x_{ik}\right)$$

(1)

$$s.t.{{\displaystyle {\displaystyle \sum }}}_{i=1}^n{\lambda }_j{x}_{ij}+S_i^{-}=\theta x_{ik},i=1,\dots ,m$$

(2)

where: ${{\displaystyle {\displaystyle \sum }}}_{j=1}^n{\lambda }_j{y}_{rj}\ge y_{rk},r=1,\dots ,s$; ${\lambda }_j\ge 0,S_i^{-}\ge 0$.

Among them, $x_{ik}$ and $y_{rk}$ are the input and output of decision-making unit k, and m and r are the input and output quantities. When studying the national green total factor energy efficiency, this paper fully combines the indicator system characteristics, data characteristics, decision-making unit redundancy, efficiency rankings and other factors of green total factor energy efficiency, and continuously improves the initial EBM model, and finally builds. This research is a new green all-factor energy efficiency analysis model. The specific improvement of the model includes the following three aspects. First, this study adds radial improvement parameters, and analyzes the target values of input and output variables when the efficiency is optimal, so that the slack variable not only conforms to the EBM planning, but also includes input and output constraints. The specific equation is: ${{\displaystyle \sum }}_{i=1}^n{\lambda }_j{x}_{ij}+S_r^{+}=\phi y_{rk},r=1,\dots ,s$. Among them, $S_r^{+}$ is the output slack variable, and $\phi$ is the output radial improvement parameter. The model involves constraints, objective functions, etc. The undirected EBM model can be expressed as Equation (3):

$$min\frac{\theta -{ϵ}_x{{\displaystyle \sum }}_{i=1}^m\left({\omega }_1^{-}{S}_i^{-}/x_{ik}\right)}{\phi -{ϵ}_y{{\displaystyle \sum }}_{r=1}^q\left({\omega }_i^{+}{S}_r^{+}/y_{rk}\right)}$$

(3)

$$\{\begin{array}{c}s.t.{{\displaystyle \sum }}_{i=1}^n{\lambda }_j{x}_{ij}+S_i^{-}=\theta x_{ik}, i=1,\dots ,m\\ {{\displaystyle \sum }}_{j=1}^n{\lambda }_j{y}_{rj}-S_r^{+}=\phi y_{rk},r=1,\dots ,s\\ {\lambda }_j\ge 0,S_i^{-}\ge 0,S_r^{+}\ge 0\end{array}$$

(4)

Secondly, this study adds undesired output, such as smoke and dust emissions, sulfur dioxide, wastewater, and other pollutants. This fully illustrates the importance of dealing with pollutant indicators. This research distinguishes bad output (undesirable output) and expected output, and uses the method of Tone K [56] to transform again, and finally generates an undirected model (Undesirable-EBM) that can deal with undesirable output. On the one hand, adding the non-desired output constraint yields Equation (5):

$${{\displaystyle \sum }}_{j=1}^n{\lambda }_j{b}_{ij}+S_t^{b^{-}}=\phi b_{tk},t=1,\dots ,p$$

(5)

where $b_{tk}$ is the t-th undesired output of the k-th decision-making unit ($t=1,\dots ,p$); $S_t^{b^{-}}$ is the undesired output slack variable, and the undesired output radial programming parameter expects the output to remain consistent. On the other hand, adding a weighted undesired output inefficiency term to the denominator of the objective function can result in Equation (6):

$${ϵ}_b{{\displaystyle \sum }}_{i=1}^p\left({\omega }_t^{b-}{S}_t^{b-}/b_{tk}\right)$$

(6)

where ${ϵ}_b$ represents the importance of the non-radial part of the undesired output in the calculation of the efficiency value; ${\omega }_t^{b-}$ represents the relative importance of each undesired output index, which satisfies ${{\displaystyle \sum }}_{i=1}^p{\omega }_t^{b-}=1$. The objective function is expressed as Equation (7):

$$\frac{\theta -{ϵ}_x{{\displaystyle \sum }}_{i=1}^m\left({\omega }_1^{-}{S}_i^{-}/x_{ik}\right)}{\phi +{ϵ}_y{{\displaystyle \sum }}_{r=1}^q\left({\omega }_i^{+}{S}_r^{+}/y_{rk}\right)+{ϵ}_b{{\displaystyle \sum }}_{t=1}^p\left({\omega }_t^{b-}{S}_t^{b-}/b_{tk}\right)}$$

(7)

The entire undirected Undesirable-EBM model can be expressed as Equation (8):

$${\gamma }^{*}=min\frac{\theta -{ϵ}_x{{\displaystyle \sum }}_{i=1}^m\left({\omega }_1^{-}{S}_i^{-}/x_{ik}\right)}{\phi +{ϵ}_y{{\displaystyle \sum }}_{r=1}^q\left({\omega }_i^{+}{S}_r^{+}/y_{rk}\right)+{ϵ}_b{{\displaystyle \sum }}_{t=1}^p\left({\omega }_t^{b-}{S}_t^{b-}/b_{tk}\right)}$$

(8)

$$\{\begin{array}{c}s.t.{{\displaystyle \sum }}_{i=1}^n{\lambda }_j{x}_{ij}+S_i^{-}=\theta x_{ik}, i=1,\dots ,m\\ {{\displaystyle \sum }}_{j=1}^n{\lambda }_j{y}_{rj}-S_r^{+}=\phi y_{rk},r=1,\dots ,s\\ {{\displaystyle \sum }}_{j=1}^n{\lambda }_j{b}_{ij}+S_t^{b^{-}}=\phi b_{tk}, t=1,\dots ,p\end{array}$$

(9)

Among them, ${\lambda }_j\ge 0,S_i^{-}\ge 0$, $S_r^{+}\ge 0$, $S_t^{b^{-}}\ge 0$. The efficiency calculation result ${\gamma }^{*}$ is between [0, 1]. The larger the score, the higher the efficiency of the decision-making unit; if ${\gamma }^{*}$ = 1, it indicates that the decision-making unit is technically effective compared to other decision-making units, located at the forefront of production.

Third, super efficiency is added to this study in order to make a more accurate assessment of urban green total factor energy efficiency. When analyzing and evaluating a city’s green all-factor energy efficiency, it is necessary to construct the frontier of the evaluation of industrial land efficiency.

The constraint formula of the input variable is shown in Equation (10):

$${{\displaystyle \sum }}_{j=1,j\ne k}^n{\lambda }_j{x}_{ij}-S_i^{-}\le \theta x_{ik}$$

(10)

The constraint formula of the expected output variable is shown in Equation (11):

$${{\displaystyle \sum }}_{j=1,j\ne k}^n{\lambda }_j{y}_{rj}+S_r^{+}\ge \phi y_{rk}$$

(11)

The constraint formula of the undesired output variable is shown in Equation (12):

$${{\displaystyle \sum }}_{j=1,j\ne k}^n{\lambda }_j{b}_{ij}-S_t^{b^{-}}\le b_{tk}$$

(12)

Therefore, the objective function is adjusted to Equation (13):

$$min\frac{\theta +{ϵ}_x{{\displaystyle \sum }}_{i=1}^m\left({\omega }_1^{-}{S}_i^{-}/x_{ik}\right)}{\phi -{ϵ}_y{{\displaystyle \sum }}_{r=1}^q\left({\omega }_{\Gamma }^{+}{S}_{\Gamma }^{+}/y_{rk}\right)+{ϵ}_z{{\displaystyle \sum }}_{t=1}^p\left({\omega }_t^{b-}{S}_t^{b-}/b_{tk}\right)}$$

(13)

Therefore, the improved EBM model constructed in this paper can be fully expressed as Equation (14):

$$min\frac{\theta +{ϵ}_x{{\displaystyle \sum }}_{i=1}^m\left({\omega }_1^{-}{S}_i^{-}/x_{ik}\right)}{\phi -{ϵ}_y{{\displaystyle \sum }}_{r=1}^q\left({\omega }_{\Gamma }^{+}{S}_{\Gamma }^{+}/y_{rk}\right)+{ϵ}_z{{\displaystyle \sum }}_{t=1}^p\left({\omega }_t^{b-}{S}_t^{b-}/b_{tk}\right)}, i=1,\dots ,m$$

(14)

$$\{\begin{array}{c}\begin{array}{c}s.t.{{\displaystyle \sum }}_{j=1,j\ne k}^n{\lambda }_j{x}_{ij}-S_i^{-}\le \theta x_{ik},r=1,\dots ,s\\ {{\displaystyle \sum }}_{j=1,j\ne k}^n{\lambda }_j{y}_{rj}+S_r^{+}\ge \phi y_{rk}, r=1,\dots ,s\end{array}\\ \begin{array}{c}{{\displaystyle \sum }}_{j=1,j\ne k}^n{\lambda }_j{b}_{ij}-S_t^{b^{-}}\le b_{tk}, t=1,\dots ,p\\ \lambda \ge 0,S^{-}\ge 0,S^{+}\ge 0,S^{b^{-}}\ge 0\end{array}\end{array}$$

(15)

Among them, $x_{ij}$ represents the input index variable data matrix; $y_{rj}$ is a variable data matrix, which represents the output index; there are two green total factor energy efficiencies, namely $\phi ,\theta$ (GDP, wastewater, waste gas and solid waste).

3.2. Kernel Density Estimation

The kernel density estimation method is a non-parametric method for estimating the distribution function, which plays an important role in measuring local density changes and exploring spatial hot spots [57]. Its essence is to estimate a more reasonable density function through the kernel density estimation value, which mainly measures the influence of a kernel on the surrounding area. The commonly used kernel functions of the kernel density estimation method include Gaussian kernel function [58], fourth power kernel function, and Epanechnikov kernel function [59]; but, relatively speaking, Epanechnikov kernel function has a better combination method, and the efficiency loss is small, so this paper selects Epanechnikov kernel function Analyze the spatial characteristics of the development level of green all-factor energy efficiency in the Yellow River basin, as shown in Equation (16):

$$f\left(x\right)=\frac{1}{nh}{{\displaystyle \sum }}_{i=1}^{n}K(\frac{X_i-x}{h})$$

(16)

$$K\left(x\right)=\frac{3}{4}\left(1-x^2\right)I\left(\left|x\right|\le 1\right)$$

(17)

In the formula, $f\left(x\right)$ is the kernel estimated value, the larger $f\left(x\right)$, the more dense the points in the area; n is the estimated number of cities and states; h is the bandwidth, which measures the smoothness of the density function; $K\left(x\right)$ is kernel function; $I(·)$ is indicative function, $I(·)$ is 1 when the conditions in brackets are satisfied, otherwise $I(·)$ is 0.

3.3. Long Short-Term Memory Forecasting Technique

In 1997, Hochreiter et al. [60] proposed long short-term memory neural network (LSTM), and it has been further improved in the following years. For problems such as the disappearance of gradients in long sequence sample training and prediction, the LSTM model has unique advantages. Compared with ordinary neural networks (RNN) [61], LSTM has a more complete neural unit structure. Figure 1 shows the operation process of the LSTM neural unit at time step $t$. During the training process of sample data, it will pass through the forget gate, input gate and output gate in sequence, and at the same time process the sample data information and enter the storage unit. At each step $t$, each gate structure receives the input $x\left(t\right)$ at this time, from the $h\left(t-1\right)$ output by the output unit at the time $t-1$ in the previous step. Therefore, these gates are similar to a kind of filter, each of which achieves a different purpose: the main function of the forget gate is to filter information data; the input gate controls which information can be input; The output gate controls which information can be output to the next neuron. The specific structure of the model is as Figure 1 follows:

The LSTM neural network is similar to the traditional feedforward network. As shown in Figure 2, the process of forward calculation is carried out in the direction of the black arrow, and the backward propagation of the error is carried out by the reverse arrow. The main points of the model include determining the network structure and loss function, obtaining gradient information, and updating parameters. In this way, when the gradient reaches the accuracy we require, we can determine the parameters of the model, complete the modeling of the LSTM model, and apply it to prediction or classification.

The specific calculation steps of the LSTM neural unit at time “t” are as follows:

Step 1: The LSTM neural unit will read $h\left(t-1\right)$ and $x\left(t\right)$ through the forget gate $f\left(t\right)$, where $x\left(t\right)$ represents the current time step, that is, the information currently input to the LSTM neural unit; $h\left(t-1\right)$ represents the previous time step, that is, the information output by the storage unit in the previous LSTM neural unit. The input information is processed, and the information that has no value is removed.

Step 2: Determine the amount of information entering the storage unit. This part includes two steps: First, determine the information that needs to be updated through the $sigmoid$ layer, and each $tanh$ layer forms a vector as the candidate update information to enter the storage unit; second, combine the $sigmoid$ and $tanh$ layers to update the storage unit.

Step 3: Update the information of the storage unit.

Step 4: Use the output information and the storage unit information to confirm the output gate.

3.4. Index Selection and Data Source

This study attempts to construct the Super-Epsilon-based model (Super-EBM) to calculate the green total factor energy efficiency, including undesired output. The multi-input and multi-output indicators involved are introduced as follows.

Input variables include the following categories: (1) Capital stock (units of 100 million yuan). This study draws on the calculation method of perpetual inventory method adopted by Shan Haojie [62] to calculate capital stock during 2004–2019. To ensure the consistency of the input and output variables, the capital stock we have chosen is converted to 2004 as the base period, and 10.96% is used as the annual depreciation rate of each province. (2) Labor input (unit: ten thousand people). In order to reduce the error, we choose the average number of employees at the end of the previous year and the following year as the number of employees in the current year. (3) Energy input (unit: 10,000 tons of standard coal). Energy input indicators are expressed by the annual energy consumption of each prefecture-level city. Because of the different types of energy consumption in each prefecture-level city, based on the availability of data, the raw coal, gasoline, diesel, electricity, etc., which are mostly consumed by each city, are converted into standards, and regarded as the total energy consumption. We divide output variables into expected and unexpected. Among them, the expected output variable is represented by GDP, and the basic unit is set to 100 million yuan. For undesired output, the three industrial wastes (wastewater, waste gas, waste) are selected.

The data in this study are mainly derived from the “China Statistical Yearbook” [63], “China Urban Construction Statistical Yearbook” [64] and “China Energy Statistical Yearbook” [65], et al. In the research process, we took the Yellow River basin as the main object, and selected panel data of 96 cities in 9 provinces around it from 2004 to 2019 as the research basis. For individual data missing from the overall data, this study uses exponential smoothing, trend, and mean methods to supplement the data. It is worth noting that the same indicator may have different statistical calibers between different provinces (cities), or different indicator names for statistical data with the same connotations, such as urban labor force and industrial employees. In response to this, this study has conducted multiple checks on this type of indicator data to ensure the consistency of the statistical content of the data to the greatest extent.

4. Results and Discussion

4.1. Spatial Evolution of Green All-Factor Energy Efficiency

In this study, the green total factor energy efficiency of 96 prefecture-level cities in the Yellow River basin is measured during 2004–2019 using the super efficiency EBM model. It is worth stating that this study needs to explore and analyze the heterogeneity of different river basins of the Yellow River. The division of upstream, midstream, and downstream is in line with the realistic characteristics of energy efficiency development in the Yellow River basin and is crucial for heterogeneity exploration of the study results. The obtained energy efficiency results for each region during 2004–2019 are shown in Figure 3. Among them, yellow represents energy efficiency between 0.0001–0.4333, red represents energy efficiency between 0.4334–0.7166, purple represents energy efficiency between 0.7167–0.9999, and blue represents energy efficiency between 1.0000–1.2577.

The sample was divided into two types of green total factor energy efficiency effectiveness and ineffectiveness according to the efficiency calculation results. From the energy efficiency distribution shown in Figure 3, we find that energy efficiency effectiveness undergoes a series of spatial evolution within each region. (1) From the upstream, midstream and downstream, the cities with effective green total factor energy efficiency in the upstream gradually formed a clustering trend toward the southeast from 2011 to 2019; the effective units of green total factor energy efficiency in the midstream were mainly concentrated in the central region; the effective units of green total factor energy efficiency in the downstream experienced a gradual decrease and finally formed two major block regions in the east and south. (2) From the provincial perspective, the effective provinces of green all-factor energy efficiency gradually shifted from the north to the south during the study period, while the distribution of effective green all-factor energy efficiency units in the central region remained stable, and the number of effective units in the eastern region was more stable but the distribution area changed more.

The reasons for the above multilateral differences in green total factor energy efficiency in the Yellow River basin mainly stem from the differences in economic development patterns due to its geographical characteristics and resource endowments. The upstream area of the Yellow River has a large drop-off, which is conducive to the use of abundant hydro resources for power generation. Hydropower development will play a catalytic role in local economic and social development and poverty alleviation. Reasonable mediation between hydropower development and ecological protection is the key to improve the efficiency of comprehensive hydropower utilization. The central part is in the Loess Plateau, Inner Mongolia Plateau and Middle and Lower Yellow River Plain region of China, which is rich in coal resources and belongs to the stable energy exporting area. The eastern part is the area where the Yellow River enters the sea and is an important energy production base and energy consumption area in China. Due to the continuous optimization of the energy utilization structure, the green total factor energy efficiency shows a trend of gradual improvement.

4.2. Basin Distribution Difference of Green Total Factor Energy Efficiency

In this paper, the kernel density estimation method is used to further identify the absolute difference of the green total factor energy efficiency of the Yellow River basin. The specific dynamic diagram of the evolutionary trends, including distribution location, distribution dynamics, distribution extension, and polarization trends, is shown in Figure 4. Among them, the distribution location refers to the distribution quantity of energy efficiency in each year. Distribution situation refers to the distribution size of energy efficiency in each year. Distribution ductility refers to the relative position gap between the highest value and the lowest value. Polarization trend refers to the absolute difference between the highest value and the lowest value.

From the position of temporal distribution, the main peak position of green total factor energy efficiency in the Yellow River basin as a whole and in the upstream and downstream regions has an overall rightward moving trend, implying that green total factor energy efficiency started to rise slowly in 2014–2019. The main peak position of green total factor energy efficiency in midstream does not change significantly, implying that the development of green total factor energy efficiency in midstream region is more stable. In terms of the magnitude of change, the upstream region has the largest change in green total factor energy efficiency, followed by the midstream and the smallest upstream.

In terms of the distribution pattern of the main peaks, a comparison using the starting and ending years as a criterion reveals that the absolute differences in green total factor energy efficiency within the overall, upstream, and downstream regions of the Yellow River basin show a decreasing trend, while the midstream region shows a widening trend. Specifically, the width of the main peak of the distribution of green total factor energy efficiency in the Yellow River basin as a whole and in the upstream area tends to increase, indicating that the absolute difference is increasing. The height of the main peak distribution in the downstream region increases and the width gradually decreases, which means that the absolute difference in the downstream region tends to decrease. The peak of the main peak of the distribution in the midstream region shows a decreasing trend and the width gradually increases, which means that the absolute difference within the midstream region increases year by year.

In terms of polarization trends, the green total factor energy efficiency levels in the Yellow River basin as a whole, upstream and midstream regions are polarized, while the green total factor energy efficiency levels in the downstream region are characterized by multipolar polarization. Specifically, there is a bimodal or multiple peak in the eco-efficiency distribution in the downstream region, indicating that there is a weak multipolar differentiation in the level of green total factor energy efficiency. The eco-efficiency distribution in the Yellow River basin as a whole, upstream and midstream regions all consist of main and side peaks arranged in a stepped pattern, but the degree of polarization is significantly different. For the Yellow River basin as a whole and the upper reaches, it indicates that there is a more disorderly gradient effect of green total factor energy efficiency level; the distribution of green total factor energy efficiency in the middle reaches shows a weak polarization trend.

4.3. Energy Efficiency Prediction Based on LSTM Method

This section uses a long short-term memory neural network (long short-term memory LSTM) model with strong error transferability and good convergence to predict, and 15 internal and external driving factors, such as labor force, industrial structure, and economic development level, are used as input indicators, with green total factor energy efficiency as the output indicator. At the same time, taking into account the economic and energy-related policies of various regions in the Yellow River basin, this study has set up three scenarios: a baseline scenario, a high-growth scenario, and a low-growth scenario, to predict the trend of green total factor energy efficiency in the Yellow River basin. Figure 5 shows the framework of the model.

The original data come from the “China City Statistical Yearbook” [63] and EPS database. The research selects the level of labor (labor), industrial structure (ind), urbanization (urban), human capital (hum), energy intensity (energy), government intervention (gov), foreign direct investment (fdi), and land in the Yellow River basin. Input (land), fixed capital stock (k), economic development level (gdp), environmental pollution (pollution), factor endowment structure (kl), financial development level (fin), population density (density), and infrastructure level (road), are input indicators for predicting green total factor energy efficiency. The source data of each influencing factor are shown in the Appendix A.

First of all, this research intercepts the sample data of each region according to a certain proportion. We distribute all samples, of which 80% of the data samples are trained, and the remaining 20% are used for testing. The purpose is to bring them into the LSTM model for training and predict.

Second, we use stochastic gradient descent (SGD) to optimize the parameters. By setting the initial learning rate (${\in }_0$) and initial parameters (${\theta }_0$), according to the formula: $g_t\leftarrow g_{t-1}+\frac{1}{n}{\nabla }_{\theta }{{\displaystyle \sum }}_i\zeta \left(f\left(x^{\left(t\right)},\theta \right),y^{\left(t\right)}\right)$, to calculate the gradient estimation. Convert the above parameter update process until ${\theta }_t$ reaches the accuracy we need, or reaches the number of iterations we set, output ${\theta }_t$.

In order to reflect the effectiveness of various mixed time series models in forecasting, this study selects the mean average percent error term as the evaluation index. This error is a weighted average of the mean absolute error. The specific formula is as follows, where $\widehat{x_t}$ represents the predicted value and $x_t$ represents the true value. We adopt 1-MAPE to denote the prediction accuracy. After comparing the historical data with the fitted data, the prediction accuracy of the model is shown in Figure 6. From the accuracy shown in Figure 6, the average accuracy of the forecast data within each watershed is around 85%. In addition, the minimum precision for each year is above 70%. This demonstrates the reliability of the model’s predicted effect:

$$\mathrm{MAPE}=\frac{1}{n}{{\displaystyle \sum }}_{t=1}^n\left|\frac{\widehat{x_t}-x_t}{x_t}\right|$$

(18)

Finally, we set future development scenarios based on the primary factors affecting energy efficiency. We use GDP as the limited value of the situation to set three simulation scenarios: the baseline scenario where the average annual GDP growth rate is set to 6.5%, the high-growth scenario of 7% and the low-growth scenario of 6%. For the remaining driving factors, we use average growth rates to simulate future development goals. The predicted values of energy efficiency after substituting into the model are shown in

Table 1. Predicted value of energy efficiency at different GDP growth rates.

GDP Growth Rate	Stream	2020	2021	2022	2023	2024	2025
6.0%	Overall	0.6957	0.7003	0.7047	0.7087	0.7122	0.7153
	Upstream	0.6148	0.6133	0.6074	0.6010	0.6065	0.6042
	Middle stream	0.6511	0.6429	0.6676	0.6813	0.6751	0.6823
	Downstream	0.7933	0.8039	0.8119	0.8195	0.8274	0.8346
6.5%	Overall	0.7093	0.7556	0.7755	0.7941	0.8010	0.7787
	Upstream	0.6481	0.6687	0.6787	0.6806	0.6860	0.6956
	Middle stream	0.6642	0.6681	0.6686	0.6657	0.6663	0.6673
	Downstream	0.7093	0.7556	0.7755	0.7941	0.8010	0.7787
7.0%	Overall	0.6875	0.6578	0.6448	0.6301	0.5963	0.5871
	Upstream	0.6115	0.5943	0.5808	0.5593	0.5523	0.5624
	Middle stream	0.6378	0.6371	0.6361	0.6344	0.6347	0.6346
	Downstream	0.7918	0.8145	0.8266	0.8317	0.8305	0.8181

.

4.4. Energy Efficiency under Different GDP Growth Scenarios in Each Basin

This section analyzes the energy efficiency forecasts under different GDP growth rates in detail.

The first is the low growth scenario of 6%. Figure 7 reflects the change trend of green total factor energy efficiency in the Yellow River basin and the upper, middle, and lower reaches of the Yellow River basin from 2020 to 2025 when the GDP growth rate is 6%. It can be found that the overall green total factor energy efficiency of the Yellow River basin, the middle and the lower reaches are on the rise. The downstream area has the largest increase, while the mid-stream area shows a downward trend. In a horizontal comparison, the downstream is higher than the overall value, while the midstream and downstream areas is lower than the overall value. On the whole, the 6% economic growth rate is conducive to the improvement of the efficiency of the downstream regions, but it is not conducive to the efficiency development of the whole and the middle and upper reaches.

Figure 8 reflects the change trend of green total factor energy efficiency in the Yellow River basin and the upper, middle, and lower reaches of the Yellow River basin from 2020 to 2025 when the GDP growth rate is 6.5%. It can be found that the overall green total factor energy efficiency of the Yellow River basin as a whole, upstream, midstream, and downstream has shown an overall upward trend. The rate of increase was overall > upstream > downstream > midstream regions, increasing by 9.78%, 7.33%, 1.34% and 0.47%, respectively. In a horizontal comparison, the upstream is higher than the overall value, while the midstream and downstream areas is lower than the overall value. On the whole, the economic growth rate of 6.5% is conducive to the improvement of the efficiency of the whole region. Among them, the improvement effect in the upstream area is the most obvious. This shows that maintaining a stable GDP growth rate of 6.5% in the Yellow River basin will play a positive role in improving the overall green total factor energy efficiency of the upper, middle, and lower reaches of the river.

Figure 9 reflects the changing trend of green total factor energy efficiency in the Yellow River basin from 2020 to 2025 when the GDP growth rate is 7%. From the change curve, it can be found that from 2020 to 2025, only the downstream regions will show an upward trend, while the overall, upstream, and midstream regions will show a downward trend. In a horizontal comparison, the downstream regions have the highest energy efficiency, and the upstream regions have the lowest energy efficiency. On the whole, the economic growth rate of 7% is conducive to the improvement of the efficiency of downstream regions. However, it has a significant inhibitory effect on the energy efficiency of the upstream and midstream. In other words, controlling the GDP growth rate at a high growth rate of 7% is not conducive to the coordinated improvement of the Yellow River basin as a whole and the green total factor energy efficiency of the upper, middle, and lower reaches.

5. Conclusions

Green total factor energy efficiency can reflect the sustainable relationship between a region’s economy and environment from the perspective of multi-input and multi-output. In this study, the green total factor energy efficiency of the Yellow River basin was measured using the Super-EBM method. By distinguishing upstream, midstream, and downstream, the study explores the historical evolution of energy efficiency in a heterogeneous manner. Further, in order to find the most suitable economic development scenario for energy efficiency improvement, this study uses the LSTM neural network model to make short-term predictions of green total factor energy efficiency under different GDP growth rate scenarios. There are several conclusions were drawn, as follows.

(1) Energy efficiency in the Yellow River basin has undergone a series of evolutions during the period 2004–2019. Overall, the energy efficiency of the Yellow River basin decreased during 2004–2012 and gradually increased during 2013–2019. This phenomenon is closely related to the time point of industrial transformation and upgrading. Energy efficiency in the upstream has tended to increase and agglomerate since 2010. The energy efficiency in the middle stream started to cluster towards the central part. The energy efficiency in the downstream is characterized by a decline. The reason for this phenomenon is due to the richness of clean electricity in the upstream on the one hand, and the dense industry in the downstream area on the other.

(2) The energy efficiency of the Yellow River basin has different performances under the high-speed scenario, baseline scenario and low speed scenario of economic development. Among them, the overall increase in green total factor energy efficiency in the Yellow River basin is the largest under the benchmark growth scenario of 6.5% growth rate. Under the low growth scenario of 6% and the high growth scenario of 7%, the energy efficiency of the Yellow River basin decreases to different degrees. The greatest decline is observed under the high-speed scenario.

This enlightens us that ecological problems in the lower reaches of the Yellow River basin should be paid more attention to in the future development. Given the relationship between economic growth and energy efficiency, the improvement of energy efficiency is inseparable from the support of the economy [66]. However, too fast, or too slow, growth rate is not conducive to the improvement of the overall energy efficiency and the protection of the ecological environment. It is suggested that the policy to adopt a growth rate of 6.5% in line with the law of social development is most conducive to achieving both the environment and the economy. A growing number of trends prove that economic growth is not the only important constraint on energy efficiency. Therefore, there is still room for further improvement in the exploration of the future value of the Yellow River basin in this study.