Analysis of Carbon Emission Efficiency in the Yellow River Basin in China: Spatiotemporal Differences and Influencing Factors

Abstract

A good grasp of the carbon emission efficiency (CEE) of the provinces in the Yellow River basin (YRB) in China, and its influencing factors, can help promote the sustainable development of the region and smooth realization of the national carbon emission reduction target. Based on stochastic frontier analysis (SFA), this paper calculates the CEE of nine provinces in the YRB from 2005 to 2019, and then, analyzes its spatial and temporal characteristics. The spatial Durbin model (SDM) with two-way fixed effects is selected to investigate the influencing factors of the CEE in the YRB. The results suggest that: (1) the overall CEE of the YRB shows a slow upward trend, and although the gap in CEE between provinces is large, it is slowly narrowing; (2) there is a significant negative spatial autocorrelation in the CEE of the provinces in the YRB; and (3) technological innovation capability, energy consumption structure, population density, and urban greening level are the most significant factors affecting the CEE of the YRB. Both population density and urban greening level have a positive effect on the improvement of the CEE of the provinces themselves and of the whole YRB, and there is also a spatial spillover effect on the improvement of CEE due to population density. Technological innovation capability and energy consumption structure had a negative impact on the overall CEE of the province and the basin during the research period. This study may have some reference value for improving the CEE of the YRB.

1. Introduction

The YRB has the most energy resources among the seven major river basins in China, and has formed a distribution pattern of upstream hydropower, midstream coal, and downstream oil. Relying on its abundant energy resources, the construction and spatial layout of heavy industries with high energy consumption in the YRB have been gradually formed. In addition, the industries in this basin, such as the iron and steel, automobile, and petroleum chemical industries, have an important influence on China. As an important energy and chemical base, the provinces of the YRB are not only an important part of China’s economic development pattern, but also an important typical area of global warming [1]. The YRB is an important ecological corridor connecting the Qinghai–Tibet Plateau with the Loess Plateau and the North China Plain, in which the carbon emission from energy consumption has increased dramatically in recent years [2]. Under the traditional development model of “High energy consumption, High emission, High pollution”, the contradiction between economic development and ecological protection is gradually emerging and sharp. In 2019, the energy consumption of the nine provinces in the YRB reached 1638.65 million tons of standard coal, accounting for about 33.65% of the national energy consumption. Compared with the upper reaches, the middle and lower reaches are the main sources of carbon emission in the YRB, and the proportion of carbon emission in the middle reaches has always remained above 40% [3]. From 2000 to 2017, the CEE of the middle and lower reaches of the Yellow River (Shanxi, Inner Mongolia, Henan, and Shaanxi) was much lower than that of other economic regions in China [4]. The inefficient use of energy restricts intensive economic development and seriously affects environmental security [5].

In 2019, China regarded the ecological protection and high-quality development of the YRB as a major national strategy [6] and issued the “Outline of the Plan for Ecological Protection and High-quality Development of the Yellow River Basin” in 2021. In the context of green development, the YRB is facing unprecedented challenges and opportunities. The improvement of the CEE in the YRB contributes to its ecological protection and high-quality development, and provides an important regional force for China’s implementation of the Paris Climate Agreement. Therefore, to promote the development of a green economy in the YRB, we must accurately measure the CEE of the provinces in the basin, and analyze the temporal and spatial differences in and driving factors of the increase in CEE, so that we can make policy recommendations accordingly.

Based on the above research background and purpose, the possible contributions of this study are as follows. Firstly, this study selects 21 energy sources to calculate carbon dioxide emissions more accurately, and then, calculates the CEE of nine provinces in the YRB from the perspective of the river basin, which is based on the stochastic frontier model. Secondly, the spatial and temporal characteristics of CEE from 2005 to 2019 are systematically analyzed at the provincial unit level. Thirdly, an SDM with two-way fixed effects is introduced to investigate the influencing factors of CEE. Finally, this study gives a new economic explanation of CEE in the YRB. These findings may provide some suggestions for policymakers to improve CEE.

The structure of the remainder of this paper is as follows: the second part presents a literature review, the third part covers the materials and methods, the fourth part presents an empirical analysis, the fifth part presents the conclusions, the sixth part presents a discussion, and the last part covers policy recommendations.

2. Literature Review

As an important indicator to measure the development of a green economy, CEE can effectively explain the relationship between economic development and carbon dioxide emissions, which is the key to achieving carbon emission reduction [7]. In recent years, CEE has become a hot topic in the academic research field. There have been many relevant studies on CEE, and rich research results have been achieved. Previous research mainly focuses on efficiency evaluation, regional differences, and influencing factors.

(1) There are strong disputes among scholars on the definition and measurement of CEE. According to the number of input factors, CEE can be divided into single-factor CEE [8,9] and total-factor CEE [10,11]. Single-factor CEE is mainly expressed as the ratio of two-factor indicators, such as carbon productivity [12], carbon intensity [13,14], and carbon index [15]. The advantages of the single-factor CCE index are that it is convenient, simple, and easy to understand when evaluating regional CEE. However, the single-factor CCE index mainly measures the single proportional relationship between carbon emission and output (or input), ignoring the intrinsic correlation of capital, labor or other production inputs, and CEE [16]. It can easily cause deviation and one-sided calculation results. In addition, the diversification of measurement indicators is also prone to controversy [10]. Therefore, some scholars have carried out studies on CEE from the perspective of total factors. They considered that the measurement of carbon efficiency should be integrated into three frameworks: energy consumption, economic development, and carbon emissions [17]. Currently, data envelopment analysis (DEA) [18,19], SFA [20,21], and their extended models are widely used to calculate the total-factor CEE. As a non-parametric method, DEA is a data-oriented method, which uses the operations research method to construct a frontier that enveloping surfaces. It is used to estimate the total factor efficiency of homogeneous decision-making units (DMUs). DEA can obtain the weights of a set of optimal input and output variables through optimization methods based on objective data of evaluation objects, and determine the efficiency level of DMUs n the form of the ratio of input to output. DEA is widely used in the study of CEE due to its characteristics, such as the lack of need to set a specific production function form and to perform dimensionless data processing. However, this method may overestimate the level of technical inefficiency, requires high data quality, and does not have statistical characteristics.

SFA is a typical representative of the parametric method in frontier analysis. Compared with the non-parametric method, since the influence of random factors on output is considered, it can not only separate the influence of random factors, but also be free from the interference of measurement errors or other random errors, so errors can be avoided as far as possible. In addition, due to the introduction of random disturbance terms in the SFA model and its statistical characteristics, the estimated parameters can be tested, and the model itself can be tested, so the measured results are more real. In this paper, we choose the SFA model to measure the total-factor CEE of the provinces in the YRB.

(2) Existing studies on factors affecting CEE can be roughly divided into two categories. The first category is decomposition analysis, which allows us to quantify the factors driving CO₂ emissions [22]. The representative research methods include index decomposition analysis (IDA), structural decomposition analysis (SDA), and the logarithmic mean divisia index (LMDI) [23]. IDA is a method that divides changes in the target variables into several combinations of influencing factors, screens out the factors with greater influence, decomposes and quantifies their output, and thus, objectively determines the different degrees of influence of each factor on the target variables [24]. SDA is based on the input–output theory, in which the input–output table can connect multiple regions, and the research scope includes single and multiple economies [25,26]. LMDI can effectively solve the final residual value problem and prevent subjective randomness when estimating and determining parameters caused by the unexplained residual value [27].

Another category is the econometric model method. Based on the different perspectives, scholars use the Granger causality test, cointegration analysis, and panel data regression to test the relationships between economic development [28,29], industrial structure upgrading [30], technological progress [31], urbanization [32], international trade [33], renewable energy development [34], and CEE. Zhang et al. argued that factor mismatch has a significant inhibitory effect and a spatial spillover effect on CEE, which is an important reason for low carbon emission levels and the differences in CEE between different regions [35]. Chu et al. further found that there is a significant inverted U-shaped relationship between improper energy allocation and CEE in China [36]. For different categories and industries, the degree and direction of the impact of mismatched energy on CEE are also different [37]. By using the spatial mediation model and the spatial adjustment model, Dong et al. found that environment-related green technology innovation can significantly improve regional CEE, and it can indirectly affect CEE by affecting economic development and urbanization [38]. Yao et al. found that the development of digital finance can promote the efficiency of carbon emissions effectively. Its depth of use and degree of digitization play a promoting role, while the breadth of coverage plays a restraining role [39]. Based on the spatial Durbin panel model, Li et al. found that improving the technical level is an important way to promote the growth of CEE in the Yangtze River Delta region [40].

(3) Scholars also noticed that there may be regional differences and spatial effects in CEE, and gradually applied spatial econometrics to the study of CEE. Existing studies have shown that there are significant spatial autocorrelations and inter-provincial differences in China’s provincial CEE, and the average CEE of eastern coastal provinces is significantly higher than that of inland provinces [41]. The CEE of the power sector in the eastern region is relatively high, and it has a positive spillover effect on surrounding provinces [42]. The CEE of the construction industry is spatially high in the east and low in the west. The high–high (HH) agglomeration areas are mainly distributed in the coastal areas of the eastern Yangtze River delta, and the low–low (LL) agglomeration areas are mainly distributed in the northeast, southwest, and northwest regions [43]. The CEE of transportation shows a decreasing trend from east to west, and there is a significant accumulation of space; it forms the HH agglomeration area composed of the eastern coastal provinces (including Hebei, Tianjin, Shandong, and Jiangsu), and the LL agglomeration area composed of Central and Southern China, South China, and Northeast China (including Guangdong, Jiangxi, Hunan, and Hubei) [44].

To summarize, the existing literature on CEE has been relatively abundant and mainly focuses on industries, provinces, and economic zones. However, researchers have paid relatively insufficient attention to studying CEE from the perspective of watersheds, which play an important role in social and economic development. In 2016, China issued the “13th Five-Year Plan for Controlling Greenhouse Gas Emissions”, and clearly stated that strict control of carbon emissions in key river basins is one of the main goals and most important tasks in China’s greenhouse gas emission control from 2016 to 2021. Therefore, based on the defects of existing studies, this study selects 21 energy sources to calculate carbon dioxide emissions more accurately, calculates CEE based on the SFA model from the perspective of the river basin, and analyzes the spatial and temporal differences. Then, we investigate the influencing factors of CEE through a spatial model. Finally, we propose some countermeasures and suggestions for the improvement of the CEE of the YRB to promote the high-quality development of the basin.

3. Materials and Methods

3.1. Methods

3.1.1. Measurement of Carbon Emission Efficiency

SFA is a parametric method for estimating efficiency based on the frontier production function, which was independently proposed by Aigner et al. [45] and Meeusen et al. [46] in 1977. Compared with the nonparametric method, SFA calculates cross-period panel data based on considering the impact of random factors on output to ensure the results are more reliable and robust. Therefore, this paper selects SFA and uses the Frontier 4.1 program to measure the CEE of nine provinces in the YRB from 2005 to 2019. The benchmark model of SFA is as follows:

$$y_{it}=f\left(x_{it},\beta \right)\mathit{exp}\left(v_{it}-u_{it}\right),i=\mathrm{1,2},\dots ,N,t=1,\dots ,T$$

(1)

In Formula (1), $x_{it}$ and $y_{it}$, respectively, represent the input and output of sample 𝑖 in the 𝑡 period. $f\left(x_{it},\beta \right)$ is the frontier production function, where $\beta$ is the parameter to be evaluated. $v_{it}$ is the random error term, which obeys the normal distribution of $N\left(0,{\sigma }_v^2\right)$, and represents the influence of various external factors on output. $u_{it}$ is a non-negative technical inefficiency term, indicating the impact on output when technology is inefficient. In general, $v_{it}$ and $u_{it}$ are independent of each other.

This paper draws on the practice of Sun et al. [47] and Sun et al. [48], using the translog production function to calculate CEE based on the Battese and Coelli (1992) [49] model. The model is as follows:

$$\begin{gathered} ln\left(\frac{{GDP}_{it}}{{CO}_{2it}}\right)={\beta }_0+\left({\beta }_1-1\right)ln{CO}_{2it}+{\beta }_{2}ln{K}_{it}+{\beta }_{3}ln{L}_{it}+{\beta }_4{\left(ln{CO}_{2it}\right)}^2+{\beta }_5{\left(ln{K}_{it}\right)}^2+{\beta }_6{\left(ln{L}_{it}\right)}^2 \\ +{\beta }_7\left(ln{CO}_{2it}\right)\left(ln{K}_{it}\right)+{\beta }_8\left(ln{CO}_{2it}\right)\left(ln{L}_{it}\right)+{\beta }_9\left(ln{L}_{it}\right)\left(ln{K}_{it}\right)+{\nu }_{it-}{u}_{it} \end{gathered}$$

(2)

In Formula (2), ${GDP}_{it}$ and ${CO}_{2it}$, respectively, represent the actual gross domestic product (GDP) and carbon emissions of province 𝑖 in the 𝑡 period. $K_{it}$ is the fixed asset investment, and $L_{it}$ is the number of urban employed persons at the end of the year.

This paper refers to the practice of Zhang and Xu [50], which uses the physical consumption of 21 kinds of fossil fuel to calculate the emissions of CO₂. The main types of fossil fuel are raw coal, cleaned coal, other washed coal, briquettes, coke, coke oven gas, other gas, other coking products, crude oil, gasoline, kerosene, diesel oil, fuel oil, liquefied petroleum gas, refinery gas, other petroleum products, natural gas, gangue, blast furnace gas, converter gas, and liquified natural gas. The calculation formula is as follows:

$$C{O}_{2i}={\displaystyle \sum _{j=1}^{21}E{C}_{ij} \times }C{V}_j\times C{C}_j\times CE{F}_j\times O{R}_j\times \frac{44}{12}$$

(3)

In Formula (3), ${CO}_{2i}$ denotes carbon emissions in province 𝑖, and ${EC}_{ij}$ represents the jth fossil fuel consumption of province 𝑖. ${CV}_j$, ${CC}_j$, ${CEF}_j$, and ${OR}_j$, respectively, represent the calorific value, the carbon content, the carbon emission coefficient, and the oxidation rate of the jth fossil fuel.

Define:

$$y_{it}=\frac{{GDP}_{it}}{{CO}_{2it}}$$

(4)

Then, the expression of CEE is:

$${CEE}_{it}=\frac{E\left[f\left(x_{it}\right)exp\left(v_{it}-u_{it}\right)\right]}{E\left[f\left(x_{it}\right)exp\left(v_{it}-u_{it}\right)\left|u=0\right.\right]}=\frac{E\left[y_{it}\right]}{E\left[y_{it}\left|u_{it}=0\right.\right]}=e^{-u_{it}}$$

(5)

In Formula (5), the CEE is defined as the ratio of the actual expected output per unit of CO₂ to the expected output at the frontier of production. When $0<{CEE}_{it}<1$ and it is closer to 1, the CEE is higher, and the current production technology is more effective. When ${CEE}_{it}=1$, the CEE has reached the boundary of the production frontier, and the existing production technology can be fully exerted and reach the ideal level.

3.1.2. Kernel Density Estimation

We use the kernel density estimation method to depict the dynamic distribution characteristics of CEE in the YRB. Referring to the practice of Li and Racine [51], the specific formula for kernel density estimation is as follows:

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

(6)

where $X_i$ is the observed value; $N$ is the number of observations (number of provinces); $h$ is the bandwidth; and $K(·)$ is the kernel function. In this paper, the Gaussian kernel function is used to describe the evolution of CEE in the YRB. The expression is as follows:

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

(7)

Currently, the optimal bandwidth is $h^{\ast }=1.3643\delta n^{-0.2}S$, where $\delta =0.7764$, and $S$ is the sample standard deviation [52]. Due to spatial limitations, this paper takes 2005, 2008, 2011, 2014, 2017, and 2019 as measuring time points.

3.1.3. Spatial Econometric Model Construction

Spatial regression econometric models can effectively reveal the complex dependency structure between observation units. To enhance the accuracy of measuring the influencing factors of CEE, this paper introduces a spatial geographic weight matrix into the empirical model. Before constructing the model, general OLS regression is carried out with the spatial (robust) Lagrange multiplier (LM) test, spatial panel likelihood ratio (LR) test, and Wald test to select a suitable spatial econometric model.

The test results show that this paper should use the SDM with two-way fixed effects. Therefore, the specific spatial panel measurement model of CEE and its influencing factors in the YRB is set as follows:

$$\begin{gathered} {CEE}_{it}={\beta }_0+\rho W_i^{\prime }{CEE}_t+{\beta }_1{IS}_{it}+{\beta }_2{TIC}_{it}+{\beta }_3{ECS}_{it}+{\beta }_4{UR}_{it}+{\beta }_5\mathit{ln}PD+ \\ {\beta }_6{UGI}_{it}+{\beta }_7\mathit{ln}{ER}_{it}+\delta {\sum }_j{W}_{ij}{X}_{it}+{\alpha }_i+{\phi }_t+{\epsilon }_{it} \end{gathered}$$

(8)

In Formula (8), ${CEE}_{it}$ represents the carbon emission efficiency of province $i$ in period $t$; $\beta$ is the multi-dimensional coefficient vector, and $\rho$ is spatial autoregressive coefficient. $W_i^{\prime }$ is the $i$th row of the spatial weight matrix $W$; $\delta$ is the spatial spillover coefficient matrix of other explanatory variables in neighboring provinces to this province; $W_{ij}$ is the geographic distance weight matrix; and $X_{it}$ is the explanatory variable matrix, where ${\alpha }_i$ and ${\phi }_t$ denote the individual fixed effects and time fixed effects. ${\epsilon }_{it}$ is the random error term and follows a normal distribution.

$${\epsilon }_{it}=\lambda m_i^{\prime }{\epsilon }_t+k_{it}$$

(9)

where $\lambda$ is the spatial autoregressive coefficient of the error term, $m_i^{\prime }$ is the $i$th row of the spatial weight matrix $M$ of the disturbance term, and $k_{it}$ is the residual term and follows an independent and identical distribution.

The construction principle of $W_{ij}$ in this paper is as follows:

$$W_{ij}=\left\{\begin{array}{c}\frac{1}{d_{ij}}, \mathrm{i}\mathrm{f} i\ne j\\ 0, \mathrm{i}\mathrm{f} i=j\end{array}\right.$$

(10)

In Formula (10), $d_{ij}$ denotes the distance between the geographic centers of $i$ and $j$. Suppose the radius of the earth is $R$, the latitude and longitude of the geographic center point A of province $i$ are $a_1$ and $b_1$, and the latitude and longitude of the geographic center point B of province $i$ are $a_2$ and $b_2$. The calculation formula of $d_{ij}$ can be written as:

$$d_{ij}=R\times \mathrm{a}\mathrm{r}\mathrm{c}\mathrm{c}\mathrm{o}\mathrm{s}\left[\mathrm{c}\mathrm{o}\mathrm{s}{b}_1\mathrm{c}\mathrm{o}\mathrm{s}{b}_2\mathrm{c}\mathrm{o}\mathrm{s}{\left(a_1-a_2\right)+\mathrm{s}\mathrm{i}\mathrm{n}b}_1\mathrm{s}\mathrm{i}\mathrm{n}{b}_2\right]$$

(11)

3.2. Data and Variables

3.2.1. Influencing Factors

Many factors, such as resource endowment, production mode, and institutional environment, will affect CEE. The existing literature selects different influence variables according to their research focus. This paper selects seven aspects (industrial structure upgrading, technological innovation capability, energy consumption structure, urbanization rate, population density, urban greening level, and environmental regulation intensity) in each province as the influencing factors for the analysis, based on the experience of scholars and basin characteristics. The selection basis and processing methods of the influencing factors are shown in

Table 1. Description of the influencing factors.

Symbol	Variables	Reason for Selection	Processing Methods
IS	Industrial structural upgrading	The optimization and upgrading of the industrial structure will lead to changes in energy consumption structure and efficiency, which, in turn, will affect carbon emissions [53].	Production value of the tertiary industry/production value of the second industry
TIC	Technological innovation capability	Technological innovation can effectively promote clean energy to replace traditional energy, reduce carbon emissions [54,55], and have a positive effect on CEE [30].	R&D expenditure as a percentage of GDP in that year
ECS	Energy consumption structure	China’s energy consumption structure is still dominated by fossil fuels, such as coal, with low fuel utilization and high carbon emissions, which has a negative impact on the improvement of CEE [41]. With the optimization and rational development of the energy structure, regional CEE will also be effectively improved [56].	Coal energy consumption as a proportion of total energy consumption
UR	Urbanization rate	There is an inverted U-shaped relationship between urbanization and CEE [57]. Initially, the urbanization process and CEE developed in the same direction [58]. However, as the level of urbanization further increases and exceeds the critical value, it will have a negative impact on CEE [57].	(Urban population/total population) × 100%
lnPD	Population density	When the urban population density is higher, the carbon emissions of energy consumption and heat source emissions of the city will also increase accordingly [59].	ln(total population/provincial area)
UGL	Urban greening level	Urban greening can effectively reduce thermal comfort energy consumption and carbon emissions [60]. With the expansion of green space, its ability to cool the environment and reduce CO2 emissions will also be further improved in general [61], and thus, affect the efficiency of carbon emissions.	Green area per capita
lnER	Environmental regulation intensity	The strength of environmental regulations will directly affect the total amount of carbon emissions, which, in turn, will affect the efficiency of carbon emissions [62].	ln(environmental pollution control investment)

.

3.2.2. Data Sources

The YRB includes nine provinces: Shanxi, Inner Mongolia, Shandong, Henan, Sichuan, Shaanxi, Gansu, Qinghai, and Ningxia. In this paper, the data of the provinces in the YRB from 2005 to 2019 are selected. Tibet was not included in the study scope due to missing data. All data used in this paper are from China Statistical Yearbook, China Energy Statistical Yearbook, and China Science and Technology Statistical Yearbook. Capital input is expressed as a fixed asset investment. Labor input is shown as the number of urban employed persons at the end of the year. Among them, fixed asset investment as an economic indicator needs to deal with inflation through the consumer price index, and this paper takes 2005 as the base period. In the energy consumption statistics, since the consumption of all kinds of energy represents the the physical statistics in the original statistics, it must be converted to standard statistics in the calculation of carbon emissions.

4. Empirical Analysis

4.1. SFA Model Parameter Estimation

This study selects SFA and uses the Frontier 4.1 program to measure the CEE of nine provinces in the YRB from 2005 to 2019. The parameter estimation results of the model are listed in

Table 2. Parameter estimation results of the model.

Variables	Coefficient	t-Statistic
Constant	1.6400	1.6367
${\mathit{ln}CO}_2$	−0.5155 ***	−3.068
$\mathit{ln}K$	−0.2969	−1.4628
$\mathit{ln}L$	1.3376 ***	3.0596
$\mathit{ln}{CO}_2 \ast \mathit{ln}{CO}_2$	−3.1230 ***	−4.6190
$\mathit{ln}K \ast \mathit{ln}K$	2.0504	0.9380
$\mathit{ln}L \ast \mathit{ln}L$	−0.2257 ***	−3.3080
$\mathit{ln}{CO}_2 \ast \mathit{ln}K$	−8.6378 ***	−4.2134
$\mathit{ln}{CO}_2 \ast \mathit{ln}L$	0.1438 ***	5.7326
$\mathit{ln}K \ast \mathit{ln}L$	0.1181 **	2.0028
${\sigma }^2$	4.4995 ***	6.5662
$\gamma$	0.8575 ***	23.1398
log-likelihood function	128.2141
LR test of the one-side error	101.4605

Notes: *** indicates significance at the 1% level; ** indicates significance at the 5% level.

.

In Table 2, the coefficients of $\mathit{ln}{CO}_2$, $\mathit{ln}L$, $\mathit{ln}{CO}_2\ast \mathit{ln}{CO}_2, \mathit{ln}L\ast \mathit{ln}L, \mathit{ln}{CO}_2\ast \mathit{ln}K$, and $\mathit{ln}{CO}_2\ast \mathit{ln}L$ all pass the t-test at the 1% level, and the coefficient of $\mathit{ln}K\ast \mathit{ln}L$ passes the t-test at the 5% level. The coefficient of $\gamma$ is 0.8575 and passes the t-test, indicating that the deviation in actual output from the frontier is mainly due to the technical inefficiency term. The random error term in this model can be ignored. Therefore, using SFA is suitable for this study.

The parameter estimation value of the $\mathit{ln}{CO}_2$ is −0.5155, which shows that for every 1% increase in carbon emissions from the combustion of 21 types of fossil fuels, the GDP output per unit of carbon emissions will roughly decrease by 51.55%. However, the impact of changes in fixed-asset investment in each province over the years on GDP output per unit of carbon emissions is not statistically significant.

4.2. Analysis of Carbon Emission Efficiency

In this paper, the CEE of nine provinces in the YRB from 2005 to 2019 is calculated (

Table 3. The CEE of the YRB in 2005–2019.

Year	Shanxi	Qinghai	Sichuan	Gansu	Ningxia	Inner Mongolia	Shaanxi	Henan	Shandong	Mean
2005	0.3993	0.4617	0.6610	0.4068	0.3303	0.5686	0.4484	0.6893	0.9082	0.5415
2006	0.4071	0.4693	0.6668	0.4146	0.3380	0.5754	0.4560	0.6947	0.9100	0.5480
2007	0.4148	0.4768	0.6724	0.4223	0.3458	0.5821	0.4636	0.7000	0.9118	0.5544
2008	0.4225	0.4842	0.6780	0.4299	0.3536	0.5887	0.4711	0.7053	0.9136	0.5608
2009	0.4302	0.4916	0.6836	0.4376	0.3613	0.5953	0.4786	0.7104	0.9153	0.5671
2010	0.4378	0.4990	0.4452	0.4492	0.3691	0.6018	0.4860	0.7155	0.9170	0.5734
2011	0.4455	0.5063	0.6944	0.4528	0.3769	0.6082	0.4934	0.7206	0.9187	0.5796
2012	0.4531	0.5136	0.6997	0.4604	0.3847	0.6145	0.5007	0.7255	0.9203	0.5858
2013	0.4606	0.5208	0.7050	0.4679	0.3924	0.6208	0.5080	0.7304	0.9219	0.5920
2014	0.4682	0.5279	0.7101	0.4754	0.4002	0.6270	0.5153	0.7352	0.9234	0.5981
2015	0.4757	0.5350	0.7152	0.4829	0.4079	0.6332	0.5225	0.7399	0.9250	0.6041
2016	0.4831	0.5421	0.7203	0.4903	0.4156	0.6393	0.5296	0.7446	0.9265	0.6101
2017	0.4905	0.5491	0.7252	0.4976	0.4233	0.6453	0.5367	0.7492	0.9280	0.6161
2018	0.4979	0.5560	0.7301	0.5050	0.4310	0.6512	0.5437	0.7538	0.9294	0.6220
2019	0.5052	0.5628	0.7349	0.5122	0.4387	0.6571	0.5507	0.7582	0.9308	0.6279
Mean	0.4528	0.5131	0.6828	0.4603	0.3846	0.6139	0.5003	0.7248	0.9200	0.5854

). Figure 1 more intuitively shows the temporal and spatial differences in CEE in the YRB. As shown in Table 3 and Figure 1, in general, the CEE of the YRB is relatively low and has a steadily increasing development trend year by year, and there are differences between the nine provinces. The two provinces with the highest CEE are Shandong and Henan, with an average CEE of 0.9200 and 0.7248, respectively, located in the lower reaches of the YRB. Provinces in the upper and middle reaches of the YRB have relatively low CEE, among which Gansu and Ningxia are the lowest. The low-value area of the YRB is centered in Ningxia and spreads to the periphery along the mainstream of the Yellow River, while the high-value area is small in scale.

4.3. Kernel Density Estimation

A kernel density estimation distribution curve of CEE was drawn using the kernel density estimation method (Figure 2).

As shown in Figure 2, the distribution curve of CEE in the YRB from 2005 to 2019 continues to shift to the right with the increase in years, and the change in the right tail of the distribution curve is not obvious. This shows that the CEE of the provinces in the YRB is improving year by year. However, the number of high-CEE provinces has not increased, and the change range is small.

As shown in the ductility of the curve, the absolute distance between the two tails of the distribution curve of CEE in the provinces of the YRB decreases slightly year by year, which shows that the gap between the CEE of each province in the YRB is slightly reduced. The kurtosis of the curve gradually becomes steeper, which means that the growth rate of CEE in each province is slightly slower.

As shown in the shape of the curve, there is no multi-peak structure in the distribution curve. This shows that the CEE level of each province in the YRB is relatively uniform, and the phenomenon of multi-level differentiation is not obvious.

4.4. Spatial Model Selection and Estimated Results

4.4.1. Spatial Model Selection

Before the spatial regression, the spatial panel Lagrange multiplier (LM) method is used to test which spatial econometric model applies to the CEE and influencing factors of provinces in the YRB.

As shown in the test results in

Table 4. Spatial panel Lagrange multiplier (LM) test.

Test Type	Spatial Error Test			Spatial Lag Test
	Moran’s I	LM Test	Robust LM Test	LM Test	Robust LM Test
Statistic	3.949 ***	12.018 ***	43.328 ***	3.365 *	34.675 ***

Notes: *** indicates significance at the 1% level; * indicates significance at the 10% level.

, the value of Moran’s I is positive, and strongly rejects the original hypothesis that there is no spatial correlation at the 1% level, indicating that the model has spatial correlation. In addition, the LM error, R-LM error, and R-LM lag are all positive and pass the significance test at the 1% level; the LM lag is also positive and passes the significance test at the 10% level, indicating that the spatial error term and spatial lag term of the model should be considered in this paper. The SDM is more suitable than the spatial autoregressive model (SAR) and the spatial error model (SEM). Therefore, this paper uses the SDM to carry out the regression analysis on CEE and its influencing factors in the YRB.

Next, we use the Hausman test to determine whether this study should use the SDM with fixed effects or the SDM with random effects. The test results are shown in

Table 5. Hausman test.

Explanatory Variables	Coefficients		Difference
	Fixed Effects	Random Effects
IS	−0.0116458	0.0166735	−0.0283192
TIC	−4.406674	−2.908241	−1.498433
ECS	−0.0537973	−0.0114069	−0.0423904
UR	0.000026	0.0004261	−0.0004001
lnPD	0.5912818	0.0971622	0.4941196
UGL	0.0001787	0.0001498	0.0000289
lnER	0.006738	0.0149401	−0.0082022
${\chi }^2$	29.45 ***

Notes: *** Indicates significance at the 1% level.

.

In Table 5, ${\chi }^2=29.45$ and strongly rejects the original hypothesis at the 1% level, indicating that the estimation results of the fixed-effects and random-effects models are significantly inconsistent, and it is more appropriate to use the SDM with fixed effects in this study. According to the characteristics of the panel data, it is necessary to further test and select the categories of the fixed-effect model (individual fixed effects, time fixed effects, and two-way fixed effects). The test results are shown in

Table 6. Selection of fixed-effects categories.

H0	${\mathit{\chi }}^2$
Individual fixed effects are superior to two-way fixed effects	26.33 ***
Time fixed effects are superior to two-way fixed effects	172.18 ***

Notes: *** indicates significance at the 1% level.

.

In Table 6, the original hypotheses that individual fixed effects and time fixed effects are more appropriate than two-way fixed effects are both strongly rejected at the 1% level. Therefore, the SDM with two-way fixed effects is used in this paper.

To determine the accuracy and applicability of the model selected in this paper, the spatial panel LR test and Wald test are used to determine whether the SDM with two-way fixed effects will degenerate into SAR or SEM (

Table 7. Wald test and LR test.

	H0	${\mathit{\chi }}^2$
Wald test	SDM will degenerate into SAR	22.62 ***
	SDM will degenerate into SEM	13.61 *
LR test	SDM will degenerate into SAR	19.25 ***
	SDM will degenerate into SEM	14.18 **

Notes: *** indicates significance at the 1% level; ** indicates significance at the 5% level; * indicates significance at the 10% level.

).

In Table 7, the results of the Wald test and LR test significantly reject the original hypothesis to varying degrees, indicating that the SDM will not be converted to SAR or SEM. Therefore, this paper finally selects the SDM with two-way fixed effects to conduct a regression analysis on the influencing factors of CEE in the YRB.

4.4.2. Estimated Results

Considering the spatial factors, this paper uses the maximum likelihood estimation method (MLE) to estimate the parameters of Formula (8) and decompose the spatial spillover effect to gain a good grasp of the direction and extent of the specific impact of each factor. The estimated results are shown in

Table 8. Estimated results of SDM and spatial spillover effect decomposition.

Variables		CEE	Variables		CEE
Direct explanatory variables	IS	−0.0220	Direct effects	IS	−0.0103
	TIC	−5.1756 ***		TIC	−4.1406 ***
	ECS	−0.0690 ***		ECS	−0.0501 **
	UR	0.0001		UR	0.00002
	lnPD	0.9604 ***		lnPD	0.6908 ***
	UGL	0.0002 ***		UGL	0.0002 ***
	lnER	0.0090		lnER	0.0104
Spatial lag explanatory variables	IS	−0.1303	Indirect effects	IS	−0.0563
	TIC	−14.7843 **		TIC	−4.5553
	ECS	−0.2551 *		ECS	−0.0910
	UR	0.0008		UR	0.0005
	lnPD	3.3892 ***		lnPD	1.1678 ***
	UGL	0.0007 *		UGL	0.0003
	lnER	0.0030		lnER	−0.0052
ρ: −1.3180 *** R2: 0.4394			Total effects	IS	−0.0666
				TIC	−8.6959 ***
				ECS	−0.1411 **
				UR	0.0005
				lnPD	1.8586 ***
				UGL	0.0004 **
				lnER	0.0052

Notes: *** indicates significance at the 1% level; ** indicates significance at the 5% level; * indicates significance at the 10% level.

.

The regression results of the SDM in Table 8 show that $\rho =-1.3180$ is significant at the 1% level, indicating that there is an obvious negative spatial spillover effect among the nine provinces in the YRB. In other words, the improvement of the CEE of neighboring provinces will harm the local province’s CEE. This may be because energy consumption has a negative spatial spillover effect on the carbon dioxide emissions in the surrounding provinces and cities [63].

The impact of industrial structure upgrading on CEE is negative and insignificant in all effects. The reason industrial structure upgrading does not play a role in improving CEE is that the internal structure of the tertiary industry in the YRB is unreasonable. At present, the tertiary industries of the nine provinces in the YRB are mainly concentrated in traditional tertiary industries, such as commercial catering, accommodation, transportation, logistics, wholesale, and retailing. The development of high-tech industries dominated by information transmission, software and information services, and finance is slow. At this stage, the modern tertiary industry in the provinces of the YRB generally has problems with small size and low quality [64].

The direct effect and total effect of technological innovation capacity on CEE are significantly negative at the 1% level. When the proportion of R&D internal expenditure in GDP increases by one unit, the CEE of each province decreases by 4.1406. From the perspective of the total effect, when the proportion of internal R&D expenditure in GDP in the whole YRB increases by one unit, the CEE will decrease by 8.6959. This shows that the internal expenditure in R&D in the YRB has serious problems with unreasonable distribution. The current innovation studies and experiments of every province still mainly focus on expanding production scale and improving production efficiency, and there is a lack of innovation in low-carbon production technology to reduce carbon emissions in production processes.

The direct effect and total effect of the energy-consumption structure on CEE are significantly negative at the 5% level. Each increase in the proportion of coal energy consumption in total energy consumption by one unit will reduce CEE by 0.0501 in each province. When the proportion of coal energy consumption in total energy consumption increases by one unit in the whole YRB, the CEE will decrease by 0.1411. The energy-consumption structure of the nine provinces in the YRB is still dominated by coal, among which Shanxi, Inner Mongolia, Ningxia, Shandong, and other traditional coal-producing provinces in the basin are also major energy utilization provinces [65]. Many coal resources in the basin are directly used for the combustion of living and production activities, which, in turn, causes a large number of carbon emissions.

The influence of urbanization rate on CEE is positive and insignificant at all stages. Cities with a high urbanization rate are more inclined to develop high-tech industries [66], and urbanization is conducive to reducing transaction costs, improving transaction efficiency, expanding the market size [67], and thus, improving CEE. Our results show that the urbanization rate has no significant impact on the CEE of the YRB. This may be because although urbanization rate in this region has reached a stage of synergistic advancement with CEE, its change has little impact on CEE, and can even be ignored. Therefore, it is still necessary to further strengthen the green and low-carbon transformation of all aspects of the urbanization process in the YRB provinces [68].

The direct effect, indirect effect, and total effect of population density on CEE are all significantly positive at the 1% level. This shows that an increase in the population density of each province has a good promotional effect on the improvement of CEE; when the population density of each province increases by one unit, its CEE will also increase by 0.6908. This is because population density can effectively help provinces to attract outstanding technical talent, give full play to the capital advantages brought by this, and promote the improvement and innovation of the low-carbon production process. At the same time, if the population density of neighboring provinces increases by one unit, the CEE of this province will increase by 1.1678. Regarding the long-term total effect, for every one unit increase in population density in the whole YRB, CEE will increase by 1.8586. With an increase in population density in the YRB, an urban sharing economy and low-carbon lifestyles will also develop, which will promote the improvement of CEE to a certain extent. Meanwhile, its advanced concepts and models will also have a certain driving effect on the surrounding provinces.

The direct effect of urban greening level on CEE is positive and significant at the 1% level, which means that CEE will increase by 0.0002 for each unit of per capita green space increase in the provinces in the basin. The total effect is positive and significant at the 5% level, which means that CEE increases by 0.0004 for each unit of green space per capita in the entire YRB. This shows that the urban greening level can effectively offset and restrain carbon emissions through the carbon neutralization mechanism, and the construction of the ecological environment of the YRB plays an important role in promoting its high-quality sustainable development.

The effect of environmental regulation intensity on CEE is not significant, while the direct effect and total effect are positive, and the indirect effect is negative. The negative indirect effect indicates that with an increase in the intensity of environmental regulation in the province, some high-carbon emission companies may choose neighboring provinces for relocation to maintain high profits, forming a pollution refuge effect. It also shows that no province can be “stand-alone” regarding environmental governance. The realization of a reduction in carbon emissions needs to break through the administrative boundaries and strengthen inter-provincial cooperation and exchange. The current investment in environmental governance in the provinces of the YRB has had no significant impact on the improvement of CEE, which may be due to the lack of environmental protection regulations in the provinces from 2005 to 2019, or the fact that the current environmental regulations focus more on controlling industrial waste gas, industrial wastewater, and other wastes pollutant emissions.

5. Conclusions

This study adopted the stochastic frontier model to measure the CEE of nine provinces in the YRB from 2005 to 2019, and then, conducted kernel density estimation to visually analyze the overall state and spatiotemporal differences in the CEE of each province. Finally, this study selected an SDM with two-way fixed effects to investigate the influencing factors of provincial CEE in the YRB. The conclusions are as follows:

(1) The overall CEE of the YRB is on an upward trend, but there is still much room for improvement. There is a large gap in CEE among the nine provinces in the YRB. The lower reaches of the YRB have higher CEE, while the middle and upper reaches of the YRB are all at a low efficiency level.

(2) From the kernel density distribution curve, it can be found that the CEE levels of provinces in the YRB are relatively uniform and have a slow upward trend. The CEE of the nine provinces in the basin has shown little change, and the efficiency gap between the provinces has narrowed slightly at a slow pace. At the same time, the unbalanced phenomenon of “multi-level differentiation” does not exist in the CEE of the provinces in the YRB.

(3) There is a significantly negative spatial autocorrelation in the CEE of the provinces in the YRB. The CEE of the YRB is affected by a variety of factors, and each factor has a different effect. Technological innovation capability, energy consumption structure, population density, and urban greening level are the main significant factors affecting the CEE of the YRB. Both population density and urban greening level have a positive effect on the improvement of the CEE of the provinces themselves, and in the whole YRB. Among them, the sharing economy and low-carbon lifestyle brought about by an population density increase will also play a role in improving the CEE of neighboring provinces to a certain extent. Technological innovation capacity and energy-consumption structure had a negative impact on the overall CEE of the province and the basin during the research period.

6. Discussion

Improving CEE is a necessary way to achieve green and low-carbon economic development in China. Most of the relevant scholars conduct research on a macro- and meso-scale. The differences between Chinese regions are obvious, and the imbalance is serious. Therefore, it was necessary to carry out an in-depth study from a regional angle. This paper analyzes this issue from the perspective of the watershed, which can help mine more accurate characteristic information and enrich the existing research.

(1) China has a vast territory; different regions have different natural resource endowments, different levels of economic development, and different development modes. The overall CEE in the YBR is low, and is higher in the downstream provinces than in the middle and upper provinces. The spatial difference and imbalance in CEE are closely related to regional resource factor endowment and geographical advantage. The Western development strategy promotes the elimination of resource-based industries with high energy consumption and high emissions in the lower reaches of the Yellow River, and transfers them to the middle and upper reaches of the Yellow River with rich resources and few environmental constraints; this affects the improvement of CEE and the effect of green development in the upper reaches of the Yellow River [69]. The middle reaches are mostly coal-resource-based cities, which rely heavily on coal resources and face great pressure to reduce carbon emissions, thus making the urban CEE low [70].

Existing studies have studied the regional and industrial differences in CEE in China. From the perspective of the watershed, most studies focus on the exploration of a single watershed, and less attention is paid to the differentiation comparison among different basins. Jiang et al. [71] analyzed the spatial evolution characteristics of CEE in the Yangtze River basin and the YRB, and found that CEE in the Yangtze River basin presents a spatial distribution pattern with low CEE in the middle and high CEE at both ends, while the YRB presents an increasing spatial pattern in the order of the top, middle, and bottom reaches. The Yangtze River basin and the YRB have typical north–south differences, with different development bases and conditions, but both emphasize green, low-carbon, sustainable, and high-quality development. It is of great significance to regional and national development to adopt policies based on local conditions and classification to effectively improve CEE and promote green development. Therefore, future studies could study the spatiotemporal evolution characteristics and influencing factors of CEE from the perspective of watershed comparison, accurately identifying the causes of differences and the path to improving CEE, in order to facilitate the government’s precise policies.

(2) It is necessary to clarify the influencing factors to improve CEE. Many factors, such as natural conditions, resource endowment, mode of production, institutional environment, and economic basis, will affect CEE. The influencing factors of CEE vary in different regions and different research objects. The existing literature selects different influencing factors according to their research aims, mostly focusing on property right structure, economic development level, industrial structure, technological innovation, urbanization, foreign investment, environmental policy, government intervention, energy consumption structure, energy prices, etc. [72,73]. On the basis of relevant studies, this paper selects seven factors: industrial structure upgrading, technological innovation ability, energy consumption structure, urbanization rate, population density, per capita green space, and environmental regulation intensity, considering the geographical characteristics, resource endowment, and economic development of the provinces in the YRB, especially as it is the main coal production and power supply base in China [74]. Future studies could introduce more influencing factors for a comprehensive analysis.

(3) As the main methods of measuring CEE, SFA and DEA have achieved fruitful research results. Both methods have advantages and disadvantages. The advantages of SFA are obvious. Since the influence of random factors on output is considered and the influence of random factors can be separated when determining the efficiency frontier, the results will not be affected by measurement errors or other random errors, and the errors caused by the random bias of the deterministic model can be better overcome. Traditional SFA also has some disadvantages: it requires the assumption of production functions, which may cause multicollinearity problems. Setting the production function has certain subjectivity, and the results obtained using different settings are quite different. It cannot deal with the multi-input–multi-output problem. Researchers have made a series of improvements to SFA according to their specific research purposes. Herrala et al. [75] investigated the CEE of 170 countries based on stochastic cost frontier analysis. Zhou et al. [76] combined the Shepard distance function with SFA, so that the SFA model could simultaneously deal with the multi-input–multi-output problem. Kuosmanen adopted random non-parametric data envelope analysis (StoNED) by integrating SFA and DEA together, and found that it is more maneuverable, accurate, and flexible in efficiency measurement compared with SFA or DEA [77]. Battese et al. [78] introduced a meta-frontier model for different technology groups to solve the bias of efficiency evaluation results caused by heterogeneity among DMUs. Based on Zhang and Zhou’s [79] two-step stochastic frontier model, Zhang and Tu [80] made an improvement, taking into full consideration the technological heterogeneity between different industries and the unexpected output of enterprises, and calculated the total factor efficiency of the micro-enterprises in China.

This paper uses macro-level data, and some data are obtained through the estimation of basic data, which inevitably has noise; therefore, it is more appropriate to choose the random frontier boundary analysis method. In addition, under the framework of the stochastic frontier boundary, the definition of CEE in this paper is more intuitive, and it is more appropriate for evaluating the carbon dioxide emission performance in production activities, which is also an important reason for choosing the stochastic frontier boundary analysis method in this paper. In future studies, SFA could be improved or combined with other methods, and a comparative analysis could be carried out to select a suitable method that meets the authors’ research needs.

On this basis, our future research will mainly focus on two aspects. Firstly, different CEE measurement methods will be adopted for comparative analysis and further improvement to determine the most suitable and effective method for research objects and data acquisition problems, and to more accurately mine carbon emission characteristic information in specific regions. Secondly, the status, characteristics, and causes of CEE in various river basins will be compared and analyzed, and policies will be proposed that consider local, current, and appropriate circumstances to comprehensively promote the overall improvement of CEE in the whole country.

7. Policy Recommendations

Based on the above analysis and results, the following suggestions are put forward on how to effectively improve the CEE of the YRB:

(1)

The government needs to provide more support for the development of a low-carbon economy in the central and western regions through policy tools. Different provinces should develop differentiated efficiency improvement strategies, strengthen the regional flow and allocation of low-carbon economic development elements between high-value and low-value areas of CEE, achieve overall planning, and optimize resource allocation. The high-value area should play a leading role in radiation, to narrow the gap between the upper, middle, and lower reaches, and achieve common development.

(2)

The government should increase the support for energy conservation, emission reduction, and new energy development; optimize the rational allocation of technological innovation funds; actively guide the focus of scientific research projects to encourage technological innovation that is conducive to improving CEE levels; accelerate the research, development, and dissemination of energy-saving and emission reduction technologies; and accelerate the diffusion of advanced technologies from high-value areas to low-value areas.

(3)

Areas with low CEE should actively work towards advanced low-carbon technology and management experience, attach importance to the rationalization of industrial structure, and prioritize the development of high-tech industries, advanced manufacturing, high-end service industries, and other low-carbon industries to accelerate the transformation and upgrading of regional industrial structure.

(4)

The provinces in the YRB should take advantage of their natural geographical advantages, strengthen the development and utilization of clean energy, such as wind energy, hydro energy, and solar energy, reduce the proportion of fossil energy consumption, and improve the energy consumption structure.

(5)

Provincial managers should enhance the awareness of urban greening construction and further promote the improvement of regional greening construction and management levels through financial allocation and other means.

(6)

All provinces should continue to improve the reform of ecological and environmental supervision systems while increasing investment in environmental governance. We will accelerate the establishment of a cross-provincial model of joint law enforcement and punishment for environmental governance to prevent low-tech environmental pollution projects from being transferred to other provinces to evade environmental regulations.