1. Introduction
With the development of economy and technology, environmental problems such as global warming and land desertification have emerged one after another. In addition, many unstable factors in the international community have exacerbated environmental problems, which have gradually become a hot issue in the world. Therefore, as an important factor in environmental issues, climate change has become one of the most urgent environmental issues facing the international community and governments. In September 2020, President Xi announced to the world at the general debate of the 75th United Nations General Assembly that China would strive to achieve carbon peaking by 2030 and carbon neutrality by 2060. On 15 March 2021, President Xi presided over the ninth meeting of the Central Finance and Economics Commission and delivered an important speech, emphasizing the need to integrate carbon peaking and carbon neutrality into the overall layout of ecological civilization construction, so as to achieve goals of peak carbon by 2030 and carbon neutrality by 2060 on schedule. The introduction of the “double carbon” target reflects China’s importance, and China has elevated the achievement of the “double carbon” target to a national strategy. At the same time, along with the increasing energy consumption and environmental pollution caused by economic growth, people have gradually realized the importance of a low-carbon economy. Considering the development of different regions, the first and foremost aspect of the government’s development of a low-carbon economy is to carry out regional energy conservation and emission reduction efforts to improve the efficiency of regional carbon emissions.
As countries pay more attention to carbon emission reduction, how to measure the carbon emission efficiency has gradually become a popular area of academic research. From the definition of carbon emission efficiency, there is no authoritative definition in academia yet, and it is mainly divided into single-factor and full-factor perspectives of carbon emission efficiency. From the single-factor perspective, the main measurement indicators are carbon dioxide emissions per unit of GDP per capita or carbon dioxide emissions per unit of GDP [
1,
2] and carbon emissions from energy consumption in terms of tons of standard coal [
3]. More scholars now use carbon productivity to represent single-factor carbon emission efficiency, which is defined as the economic output created per unit of carbon emissions, usually expressed as GDP per unit of carbon emissions [
4,
5,
6]. From the perspective of total-factor efficiency, the main indicator is the comprehensive efficiency of carbon emissions [
7,
8] or the total-factor efficiency of carbon emissions [
9], which reflects the characteristic of total-factor efficiency that combined with economic development and other indicators, and it can measure the efficiency of carbon emissions more accurately and comprehensively.
There are two main methods to measure total-factor carbon emission efficiency, SFA and DEA, with the DEA being the most popular. Lei and Yang [
10] used the SFA model and added seven variables that have an influence on carbon emission efficiency to the model to measure the carbon emission efficiency of 30 Chinese provinces from 1996 to 2011. Although some measure efficiency using the SFA method, more scholars use DEA to measure it. This is mainly because the DEA method does not require the setting of a specific functional form, thus avoiding the structural bias of the SFA method due to the mis-setting of the production function. Tyteca [
11] used the CCR model in DEA to evaluate environmental performance from the perspective of inputs and outputs. Ma et al. [
12] used the BCC model to measure the carbon emission performance of the logistics industry in 30 Chinese provinces. Moutinho et al. [
13] used CCR and BCC models to measure the economic and environmental efficiency of 26 different European countries from 2001 to 2012. Considering the inability of the traditional CCR and BCC models to measure panel data, the DEA window analysis model is proposed. Iftikhar et al. [
14] used the DEA window analysis model to assess the energy and CO2 emission efficiency of major economies. Yang et al. [
15] also used DEA window analysis to evaluate urban sustainability in Taiwan. Sueyoshi et al. [
16] evaluated the environmental performance of provinces in China from 2003 to 2014 by using a DEA window analysis model. Vlontzos et al. [
17] similarly used a DEA window analysis model to assess the efficiency of greenhouse gas emissions in the process of agricultural production in EU countries. Furthermore, there is literature that considered the effect of external drivers with stochastic noise, and then measured carbon emission efficiency through a three-stage DEA [
18]. This method used SFA proposed by Aigner et al. [
19] in addition to the DEA model to calculate the effects of external drivers and random errors on carbon emission efficiency, so that the calculation of emission efficiency can be more accurate. Hua et al. [
20] evaluated the provincial carbon dioxide emission performance in China by using a three-stage DEA and linear function transformation method. Zhang et al. [
21] studied the carbon emission efficiency of the construction industry in China based on a three-stage DEA model. While radial DEA models are mostly used in traditional DEA, nonradial SBM can measure efficiency values more accurately, which can be better applied in the carbon emission efficiency measurement. Iqbal et al. [
22] used an undesirable output SBM model to measure energy consumption, carbon emissions, and economic environmental efficiency in the top 20 industrial countries from 2013 to 2017. Anser et al. [
23] studied environmental efficiency using a comparative radial DEA and nonradial DEA, and the results showed that in the measurement of environmental performance analysis, the nonradial DEA had higher discriminability than radial DEA. Based on the aforementioned studies, we fully integrate the three-stage DEA and the SBM-undesirable models to measure carbon emission efficiency in 30 provinces of China.
Most studies stopped at the exploration of carbon emission efficiency measurement and influencing factors, and there is a lack of research on carbon emission efficiency prediction. In all fields of forecasting methods, there are few studies combining DEA with neural network models. The idea of combining DEA and neural networks was first proposed by Athanassopoulos and Curram [
24], using DEA as a preprocessing method for screening training cases and ANNs as a tool for learning nonlinear forecasting models. In particular, in the field of carbon emissions, some scholars used neural network models in their predictions [
25,
26], but these models were not combined with DEA. Some studies compared neural network models with econometric models in terms of prediction accuracy. Zhou and Kuang [
27] found that neural network models, especially the LSTM model, have higher accuracy in prediction than the traditional VAR model. Econometric models are commonly used in forecasting economics research, and such models are mainly based on linear relationships. While neural network models, which use gradient descent to search for the optimal global solution as well as have activation function and feedback mechanism, can better capture the nonlinear relationships, so they have obvious advantages in dealing with nonlinear, discontinuous and high-dimensional data [
28]. Ouyang et al. [
29] compared the prediction effectiveness of LSTM model with four models, namely, multilayer perceptron, support vector machine, K-nearest neighbor and GARCH, and the empirical results showed that LSTM model has higher prediction accuracy. It can effectively predict the dynamic trends of financial time series data in the long and short terms.
The important scientific contributions of this paper include the following: (1) Most of the carbon emission efficiency measurement methods are the undesirable SBM model and the traditional three-stage DEA model. In this paper, considering that the two models have different advantages, we combine the two to measure the carbon emission efficiency, which expands the modeling methods in this field. (2) This paper uses the SFA model regression to verify that six external drivers, including the intensity of finance in environmental protection, level of economic development, industrial structure, level of urbanization, degree of openness and level of science and technology innovation, have significant effects on the value of carbon emission efficiency, and proposes relevant policy recommendations based on the regression results. (3) In this paper, we use the LSTM model to forecast the labor force, capital stock, total energy consumption, gross regional product and carbon dioxide emissions in the next five years, and then measure the carbon emission efficiency of 30 provinces in China from 2020 to 2024. The empirical results show that the model has good prediction effect and can effectively predict the carbon emission efficiency. (4) This paper combines the data envelopment analysis method with a neural network model, which is a methodological expansion in the field of performance evaluation and prediction, and achieves good empirical results with certain generalization ability, further enriching the research ideas in this field.
In this paper, we construct an input–output evaluation index system containing nonexpectation indicators in a total-factor perspective, measure carbon emission efficiency values using a three-stage SBM-undesirable model, explore the external drivers of carbon emission efficiency through SFA regression, and finally forecast the carbon emission efficiency of thirty Chinese provinces in the next five years using an LSTM model. Based on the empirical study, this paper analyzes the current state of carbon emission in 30 provinces of China from 2006 to 2019, explores carbon emission reduction path in China, and then offers targeted policy recommendations to promote low-carbon development. The structure of this paper is as follows: in the second part, we introduce the basic models and methods involved in this study; in the third part, we design a system of evaluation and select some important external drivers; in the fourth part, we conduct carbon emission efficiency measurement, regression analysis of external drivers and prediction based on the above designed system and selected model. We also conduct an empirical analysis and discussion of the results; in the fifth part, we summarize main research findings and put forward corresponding recommendations based on these findings for the reference of relevant institutions.
2. Description of the Methodology
2.1. SBM-Undesirable Model
In 1978, Charnes, Cooper, and Rhodes created the first theoretical approach of DEA, the CCR model, which is named after the initials of these three individuals’ last names. They extended the concept of single-input, single-output engineering efficiency to multiple-input, multiple-output relative efficiency evaluation [
30]. The CCR model measures the relative efficiency of the decision-making unit (DMU) under the assumption of constant returns to scale. However, in practice, returns to scale are generally variable. Banker et al. [
31] then proposed for the first time to evaluate the relative efficiency of a DMU using the variable returns to scale as a criterion, which is the BCC model.
Since the DEA-CCR and BCC models cannot measure the full range of slack variables, there are defects in efficiency evaluation. For improvement, Tone [
32] proposed the SBM model, which took into account the slack of input–output and made the efficiency measurement more accurate. To solve the problem that the SBM model cannot measure the efficiency of DMUs with undesirable outputs, Tone [
33] then proposed an SBM model that considers undesirable outputs. The mathematical programming formula is:
Each DMU in the model consists of three variables, input, desired output and undesirable output, , and , respectively. is the objective function, which is strictly decreasing and satisfies . , , are the input slack variable, desirable output slack variable and undesirable output slack variable, respectively. For a particular DMU, it is efficient when and only when and , , . Conversely, the DMU is relatively inefficient.
2.2. Three-Stage DEA Model
Fried et al. [
18] proposed that the traditional DEA model did not remove the effects of managerial inefficiency, external drivers and random noise on the efficiency values, and they discussed how to introduce the above factors into the DEA model, which is the three-stage DEA model.
The three-stage DEA model solves the problem through three main stages. In the first stage, the traditional DEA model is used to evaluate the initial efficiency based on the original input–output data. In this paper, the SBM model, which considers undesirable outputs, is used in this stage to overcome the shortcomings of the traditional DEA model.
In the second stage, the main focus is on the SFA regression of slack variables, composed of management inefficiency, external drivers and random noise, and the slack variables are decomposed into the above three effects. If the first stage is input oriented, then the decomposition of the input slack variables is required. Next, we adjust the initial input variables according to the results, and the input-oriented SFA regression function is:
In Equation (2), refers to the nth slack value of input of DMUi; Zi denotes the external driver variable, is the coefficient of the environment variable; refers to the mixed error term, denotes random noise, and denotes management inefficiency.
The purpose of the SFA regression is to remove the effects of external drivers and random noise on efficiency, adjusting all DMUs to the same external environment with the following adjustment formula:
where
denotes adjusted input value;
is the input value before adjustment;
refers to the adjustment for external drivers; and
denotes the adjustment for random noise of DMU
i.
In the third stage, the adjusted input–output are remeasured applying the SBM model considering undesirable outputs. By the above process, the efficiency values at this time have removed the influence of external drivers and random noise, so as to obtain relatively accurate carbon emission efficiency values.
2.3. LSTM Model
The LSTM model, first proposed by Hochreiter and Schmidhuber [
34], is a special form of recurrent neural network (RNN). The LSTM model is unique because it improves the RNN model by adding the gate structure, allowing the LSTM model to remove or add information to the nodes to change the state of the information flow. This feature also enables the LSTM model to learn better with regard to long-term information, and the core structure of the model is shown in
Figure 1.
Specifically, ht-1 represents the result of the previous iteration, and Xt represents the new data vectors. Firstly, the LSTM model determines which messages to discard by passing through σ layer, known as the forgetting gate layer. This layer describes the situation of each information vector by outputting a number between 0 and 1, where 0 is not allowed to pass and 1 means pass. Subsequently, the σ layer, called the update gate layer, and the tanh layer determine which new information we will store in the unit node state, thus updating the learning outcome state C. Finally, the effective information is exported by the σ layer, called the output gate layer. This process can obtain a better prediction model by several iterations.
5. Main Conclusions and Recommendations
5.1. Main Conclusions
The main conclusions of this paper are as follows: (1) From the static analysis results, we know that the average value of carbon emission efficiency in China from 2006 to 2019 is 0.642 in the first stage and 0.696 in the third stage, which are ineffective, and there is much room to improve. From the provincial perspective, five provinces reach the effective carbon emission before the adjustment, namely, Beijing, Shanghai, Guangdong, Hainan, Qinghai. After the adjustment, Shanghai, Hainan and Qinghai are no longer in the effective frontier, and their average efficiency value has decreased. There are 12 provinces with higher efficiency values than the average after the adjustment, one more than before the adjustment. From the perspective of the four major economic regions, the adjusted carbon emission efficiency ranking is Eastern Region > Western Region > Central Region > Northeast Region, and only the eastern region has an efficiency value higher than the average.
(2) From the perspective of dynamic analysis, from 2006 to 2019, the carbon emission efficiency values of Beijing and Guangdong before and after adjustment are still maintained at 1 every year, reaching the effective frontier. In the third stage, the influence of external drivers and random noise is removed, so that all DMUs are adjusted to the same external environment, at which time Shanghai, Hainan and Qinghai no longer maintain the carbon emission efficiency of 1 in the first stage. According to the analysis of variance, the average annual fluctuation of carbon emission efficiency in China becomes smaller after the adjustment, and there are large differences between provincial areas.
(3) Based on the results of SFA regression analysis, it can be seen that the six external drivers selected in this paper have significant effects on the input slack variables, so it is necessary to eliminate the effects of external drivers. Among them, the intensity of finance in environmental protection and the degree of openness have negative effects on the slack variables, and the enhancement of these indicators is favorable to the improvement of carbon emission efficiency. The increases in urbanization level and the secondary industry have positive effects on the slack variables, which are not beneficial to the improvement of carbon emission efficiency. The economic development will consume the capital stock but promote employment, as well as increase energy consumption. The impact of science and technology innovation level on the total input slack variables is negative.
(4) We analyzed the annual average carbon emission efficiency values of each province under the three-stage SBM-undesirable model, and classified them into five levels. Beijing and Guangdong are effective regions. Jiangsu, Zhejiang, Shanghai, Hainan and Qinghai are less effective regions. Gansu, Liaoning, Heilongjiang, Guangxi Zhuang Autonomous Region, Shanxi, Guizhou and Hebei are inefficient regions. Sichuan, Hubei, Yunnan, Anhui, Hunan, Henan, Jilin, and Inner Mongolia Autonomous Region are the medium efficient regions, and the remaining provinces are the medium- high efficient regions.
(5) The prediction results of carbon emission efficiency values based on the LSTM model show that eight provinces will reach effective carbon emission in the next five years, namely, Beijing, Shanghai, Jiangsu, Zhejiang, Fujian, Guangdong, Hainan, and Qinghai, but the gap between provinces still exists. In addition, the overall national carbon emission efficiency is gradually improving, and the values of all regions will also improve, with the greatest improvement in the central region.
5.2. Recommendations
This paper proposed the following suggestions based on the results of efficiency value and predicted efficiency value combining the regression of six external-driven factors.
- (1)
Carbon emission efficiency in China is highly differentiated across regions, and there are still disparities among provinces after five years of prediction. Additionally, the adjusted carbon emission efficiency ranking is Eastern Region > Western Region > Central Region > Northeast Region. Therefore, it is essential to develop distinctive strategic policies that take advantage of the region’s own strengths. Specifically for the four major economic regions, the eastern region has the highest carbon emission efficiency and exceeds the average level in China. Hence, the eastern region should take advantage of its own strengths, continue to maintain a high-quality level of economic development, and promote the steady improvement of carbon emission efficiency. The western region should pay more attention to the adoption of technology, strengthen the construction of urbanization, and form an urban development path with ecological livability as the basic feature. The central region should increase local financial support for environmental protection, promote the construction of clean energy centers, and promote low-carbon urban development. The northeast region, as the region with the lowest carbon emission efficiency, should focus on reducing high energy-consuming industries, promoting the transformation of regional industrial structure by importing advanced technologies and talents, and enhancing the quality and efficiency of industries through upgrading technologies and equipment.
- (2)
We should focus on the structural layout of the industry and develop new business models driven by technological innovation. In recent years, China still has the problem of unreasonable industrial structure and overcapacity. Based on the results of this paper, it can be seen that the percentage of secondary industry has a negative impact on the carbon emission efficiency level, especially in Heilongjiang and Hebei, where the secondary industry is the predominant industry, the carbon emission efficiency value is relatively low. Therefore, similar provinces should optimize their industrial structure, emphasize technological innovation, and upgrade their carbon emission technologies. The government should integrate the three major industries to reduce carbon dioxide emissions by focusing on the development of strategic new industries in order to reduce industrial energy consumption and drive the development of new business models. In this way, it will promote the level of carbon emission efficiency and realize the sustainable path of low-carbon economic development.
- (3)
From the empirical results in the paper, it can be seen that opening up to the outside world has a positive effect on carbon emission efficiency. Beijing, Shanghai, Jiangsu, Zhejiang, Fujian, Guangdong, and Hainan are currently at a high level of efficiency. At the same time, all of these regions are at a high level of openness to the outside world and will achieve effective carbon emission efficiency values in the next five years. Therefore, provinces should be aware of the characteristics of the development of foreign cities similar to their own provinces and absorb advanced foreign technologies by recognizing these characteristics. The provincial situation should be considered to open the road to the outside world and form an effective docking with the outside, not only the cooperation and exchange of foreign regions, but also the coordinated development of other domestic provinces. In this way, we can form a low-carbon development of internal and external circulation channel to promote low-carbon development. Ultimately, by optimizing the opening structure, the internal and external cycles of low-carbon development can be realized.