How Does Energy Misallocation Affect Carbon Emission Efficiency in China? An Empirical Study Based on the Spatial Econometric Model

Abstract

As an essential factor of production, energy is receiving increased attention. Yet, other than some fundamental policy suggestions towards China’s energy issues, there have been very few investigations into energy misallocation so far. The measurements of energy misallocation index and carbon emission efficiency were made based on the panel data from 30 provinces in China. To empirically study the impact of energy misallocation on carbon emission efficiency, a spatial econometric model was built. It is found that during the survey period, there was a certain degree of energy misallocation in all regions of China, and the differences between the regions were obvious. There is an inverted U-shaped relationship between the impact of energy misallocation and carbon emission efficiency in which intensified allocation distortion accelerates the arrival of the critical point that is not conducive to energy conservation and emission reduction. The results viewed by regions show that due to a low degree of misallocation, the impact of carbon emission efficiency in the east region is positive, while that of the central and west regions are mostly negative. Accordingly, it is necessary to accelerate the marketization process of the energy market and improve the ecological quality.

1. Introduction

An effective allocation of resources refers to one that maximizes the overall output of society and achieves optimum, while resource misallocation is the deviation from this optimum [1]. The extensive economic growth model leads to resource misallocation among regions and industries, which results in a series of structural problems such as inefficient resource consumption, overcapacity, and slowdown in growth. The report of the 19th National Congress of the Communist Party of China clearly pointed out: “We should pursue supply-side structural reform as our main task; and work hard for better quality; higher efficiency; and more robust drivers of economic growth through reform. We need to raise total factor productivity”. Therefore, for China’s economy to achieve sustainable development, the effectiveness of resource allocation must be improved while meeting the requirements of the ecological environment. As an essential factor of production, the impact of energy on national economy and the environment is particularly prominent. Therefore, does energy misallocation really exacerbate environmental degradation in China? And how does it affect carbon emission efficiency? Does regional disparity affect the relationship between energy misallocation and carbon emission efficiency? Studying these issues has important practical significance for the Chinese economy, which is at a critical stage of transformation and upgrading.

From the existing research we can see that many scholars have noticed the phenomenon of resource misallocation in China’s marketization process as comprehensive and in-depth studies were conducted on the extent, causes, and effects of factor misallocation. Many factors such as local protectionism and government intervention [2,3], ownership differences caused by administrative monopolies [4,5], firm-level policy distortions [6,7], and imbalanced development of transportation infrastructure [8] has been causing serious resource misallocation in China. Under the theoretical framework of measuring the degree of resource misallocation developed by Hsieh and Klenow [9], domestic and foreign scholars have examined the current situation of resource misallocation in China from the aspect of industry, region and ownership [10,11]. Essential productive factors involved in the existing fruitful studies include capital, labor, land, energy, etc. [12,13,14,15]. Although important findings have been made, there are few studies on energy misallocation. The main aspects of concern are: measuring the distortion of energy allocation and efficiency of allocation from the industry, enterprise and factor market level, and pointing out that the impact of energy misallocation cannot be ignored [16,17,18,19,20]. Some scholars have pointed out that factor market distortions pose a significant negative impact on energy efficiency and environmental protection [21,22]. In addition, there are studies that specifically analyze the different impacts of energy misallocation on the related industries or enterprises, which aim to guide policy makers into reducing the degree of factor misallocation and improving economic efficiency by formulating reasonable and effective resource tax rates and energy policies so that the harmonious development of the economy and the environment can be achieved [6,23,24]. Although important results have been achieved, there are still room for improvement in the existing studies: Firstly, there are many studies on resource misallocation in China, but studies on the energy misallocation are relatively scarce. Secondly, due to the lack of such research, the practical issue of how energy misallocation affects China’s carbon emission efficiency requires relevant interpretations and empirical tests so as to provide a theoretical basis for government departments to formulate relevant policies and measures. Therefore, the contributions of this paper are mainly: analyzing energy misallocation and revealing the internal mechanism through which it affects carbon emission efficiency; empirically examining the impact of energy misallocation on carbon emission efficiency by constructing a spatial econometric model based on the panel data of China’s provinces and the measurements of misallocation index and carbon emission efficiency in those provinces.

2. Influencing Mechanism

In the 40 years of reform and opening up, China’s degree of marketization has been significantly improved, but the existing mechanism still lead to resource misallocation [10,25]. Local governments impose too much intervention on the market when unilaterally pursuing local gross domestic product (GDP) growth and administrative achievements. Local governments have the pricing power over essential productive factors and control essential productive factor markets, which, to some extent, distorts the allocation of resources [6,26]. Energy, as a major production input factor, is the material basis for economic growth and social development. According to the Report on the Big Data of Energy in China 2018, judging by the data from the last decade, coal and oil accounted for 80~90% of the total primary energy consumption in China while the proportion of clean energy such as natural gas constantly increased, showing great potential. Fossil energy is the main part of energy consumption, and using fossil energy affects the eco system. Thus, carbon emission efficiency reflects the relationship between energy consumption and the environment. Therefore, the ways in which energy misallocation affects carbon emission efficiency are as follows:

(1) Energy misallocation is not conducive to the optimal inter-firm resource allocation and restrains the improvement of total factor productivity of the enterprises, or the improvement of carbon emission efficiency. The state-owned nature of natural resources indicates that local governments have the initial allocation right of resources, which means energy is not preferentially allocated to enterprises with high production efficiency according to market rules but to those with political connections, resulting in the inefficient use of resources [21]. For example, research by Nie Huihua and Jia Ruixue [27] found that resource misallocation is the main reason the total factor productivity of state-owned enterprises is lower than that of other enterprises. On the other hand, local governments, to simply pursue local GDP growth, also tend to prioritize energy allocation to local state-owned monopoly enterprises that generate more output value and fiscal revenue, and set barriers to keep out non-local enterprises, which is not conducive to fair inter-firm competitions. Intervention and control of the energy market leads to distortions in the allocation of factors. In particular, low-cost energy factors allow enterprises to obtain considerable profits by simply increasing factor inputs, resulting in excessive energy consumption [28,29] and hindered improvement of carbon emission efficiency and ecological quality.

(2) Energy misallocation inhibits the efficient flowing of production factors and restrains the industrial structure from upgrading, and affects carbon emission efficiency. According to Environmental Kuznets Curve, people would rather sacrifice the environment in exchange for economic growth in the period of rapid economic development. Under the extensive growth model, lowered prices allow enterprises to intensively consume energy, keeping the outdated production capacity that should be eliminated profitable. Therefore, the enterprises have no incentive to invest in the research and development of technology [28], which is not conducive to improving carbon emission efficiency. At the same time, under the current achievement assessment system, the distortion of energy allocation has caused a large number of factors to flow to energy-intensive, high-energy-consumption, high-pollution, high-yield heavy chemical industries and low-level processing industries, hindering technological innovation and transformation and upgrading towards knowledge-and technology-intensive industries [24,30]. Driven by economic growth and employment goals, local governments compete to attract investments and formulate preferential policies on supply and price of production factors. The reducing of energy prices not only lowers the environmental threshold of enterprises, but also costs enterprises with good environmental protection technologies their competitive advantages [31]. The extensive growth model deadlock as a result increases the energy consumption per unit of GDP and adversely affects the local carbon emission efficiency.

(3) Energy misallocation forces the production factors to the inferior industries with low rate of return, especially those with high energy consumption, exacerbating the adverse effects on carbon emissions efficiency. Distortion of energy allocation makes low-cost factors a major advantage of enterprises in export trade, enhances their competitiveness in the international market, and improves their level of diversification in export, especially product diversification level, trade breadth, and export probability, leading to rapid expansion of exports [28,32,33]. On the other hand, factor misallocation inhibits the improvement of technological complexity in export by hindering the positive effects of FDI and R&D inputs [33], while export enterprises transfer the due proceeds of domestic production factors to foreign consumers through low product prices [32]. Therefore, energy misallocation dose not increase the enterprise’s export profit margin. It is thus clear that energy misallocation is more about promoting the export of non-technology-and-knowledge-intensive products with the characteristics of high investment, high energy consumption, high pollution, and low profit. As a result, China is at the low-end of the global production value chain, which brings tremendous pressure on China’s ecological environment and seriously hinders the improvement of carbon emission efficiency.

In summary, the impact of energy misallocation on carbon emission efficiency by affecting the economic development level is the result of many factors in combination. Therefore, the specific impact needs to be empirically tested based on theoretical analysis.

3. Variable Measurement

3.1. Calculation of the Energy Misallocation Degree in Each Province

Drawing on the practices of Chen Yongwei and Hu Weiming [1], the energy misallocation degree is estimated. The specific misallocation index τ_Ei is as follows:

$${\gamma }_{Ei}=\frac{1}{1+{\tau }_{Ei}}$$

(1)

Among them, γ_Ei is the absolute distortion coefficient of energy prices. Generally, in the calculation it can be replaced by the relative distortion coefficient of the price:

$${\widehat{\gamma }}_{Ei}=\left(\frac{E_i}{E}\right)/\left(\frac{s_i{\beta }_{Ei}}{{\beta }_E}\right)$$

(2)

Among them, $s_i=\frac{p_i{y}_i}{Y}$ represents the share of region i’s output value in the entire economy, and weighted contribution proportion of energy to the output can be expressed as ${\beta }_E={\displaystyle {\sum }_i^N{s}_i}{\beta }_{Ei}$. In addition, (E_i/E) represents the actual proportion of energy consumption of region i in total energy consumption, E_i represents the energy consumption of region i, E represents the total energy consumption. While $\frac{s_i{\beta }_{Ei}}{{\beta }_E}$ represents the theoretical proportion of energy used in region i when energy is effectively allocated. The ratio of the two reflects the degree by which the actual energy consumption deviates from the consumption under effective allocation. If the ratio is greater than 1, it indicates that the actual energy allocation is above the theoretical level, resulting in excessive energy allocation. Otherwise, it means that the actual allocation of energy in the region is lower than the theoretical allocation under effective allocation, and the energy allocation is insufficient. For the development of the local economy and the improvement of political achievements, local governments may stimulate production by lowering energy prices and increasing its input, which affects the effective allocation of factor markets.

From Equations (1) and (2), we can see that to calculate the energy misallocation index τ_Ei, we must estimate the contribution proportion of energy to each region’s output β_Ei. In most of the existing studies, researchers use Cobb-Douglas(C-D) production function with constant return to scale and the translog production function to estimate the contribution proportion of factor to the output. The former is simple in form with the assumption that the unit factor replace elasticity is 1. The latter is more inclusive, but with an excessive collinearity because of the large number of estimation parameters. This deficiency will become more obvious if adding the energy factor. Therefore, this paper adopts the most basic C-D production function with energy factor incorporated into it. Y_it in Equation (3) represents each year’s total output in each of the provinces, K_it, L_it, and E_it represents each year’s capital, labor and energy input in each of the provinces, β_Ki, β_Li and β_Ei represents the contribution proportion of capital, labor, and energy to the output in each province. The specific form is as follows:

$$Y_{it}=A{K}_{it}^{{\beta }_{Ki}}{L}_{it}^{{\beta }_{Li}}{E}_{it}^{{\beta }_{Ei}}$$

(3)

This paper followed the practice of Bai et al. [34] and Pu et al. [35]. Let ${\beta }_{Ki}+{\beta }_{Li}+{\beta }_{Ei}=1$, take the logarithm of both sides of Equation (3):

$$\ln Y_{it}=\mathrm{lnA}+{\beta }_{Ki}\ln K_{it}+{\beta }_{Li}\ln L_{it}+{\beta }_{Ei}\ln E_{it}+{\mu }_i+{\lambda }_t+{\epsilon }_{it}$$

(4)

μ_i in Equation (4) is the individual effect, λ_t is the time effect and ε_it is the random error term. Then we have:

$$\ln (Y_{it}/L_{it})=\ln A+{\beta }_{Ki}\ln (K_{it}/L_{it})+{\beta }_{Ei}\ln (E_{it}/L_{it})+{\mu }_i+{\lambda }_t+{\epsilon }_{it}$$

(5)

The output variable (Y_it) is represented by the regional GDP of each province. Taking 2005 as the base year, data of other years are deflated and converted into actual GDP represented with the constant price in 2005. The capital input amount (K_it) is represented by the fixed capital stock of each province. This paper draws on and converts the data from the results of the 2005 capital stock estimated by Ye Mingque et al. [36]. Taking the year 2005 as the base year, the fixed capital stock from 2006 to 2016 were calculated with the perpetual inventory method. The labor input (L_it) is represented by the average annual employment of each province, that is, the arithmetic average of the number of employed people at the beginning of the year (the number of employed people at the end of the previous year) and the number of employed people at the end of the year. Energy input (E_it) is represented by the total energy consumption indicators of the provinces from 2005 to 2016.

This paper uses the panel data of each region from 2005 to 2016 to regress model Equation (5) and estimate β_Ei, the contribution proportion of energy to each region’s output, to calculate the energy misallocation index in each province. Due to different levels of regional development, the contribution proportion of energy to each region’s output may be different. Therefore, this paper uses the Least-Squares Dummy Variable (LSDV) to estimate the contribution proportion of energy to the output in the east, central, and west regions. LSDV introduces individual dummy variables in the regression equation, allowing each individual to have its own intercept term. The estimation results show that most of the provincial dummy variables are significant, which there is individual effect and the LSDV estimation method is applicable. See

Table 1. Regression results of the contribution proportion of energy to the output.

Estimated Coefficient	East	Central	West
${\beta }_{E\mathrm{i}}$	0.5609 ***	0.9608 ***	0.6468 ***
	(0.1675)	(0.0949)	(0.1066)
Number of samples	132	96	132

Note: The numbers outside the parentheses in the table are the regression coefficients, the numbers in parentheses are the standard errors, and *** indicates the significant level of 1%.

.

According to the formulas Equations (1) and (2), the energy misallocation index of each province is calculated. See

Table 2. Measured and calculated energy misallocation index of each province in 2005–2016 (partial).

Region		2005	2008	2010	2012	2014	2016
East	Beijing	0.4310	0.5758	0.6223	0.7004	0.7823	0.8793
	Tianjin	0.0695	0.0825	0.0279	0.0309	0.0566	0.0655
	Hebei	−0.4396	−0.4443	−0.4498	−0.4408	−0.4656	−0.4730
	Liaoning	−0.3396	−0.3385	−0.3360	−0.3166	−0.2857	−0.4755
	Shanghai	0.2599	0.2035	0.1740	0.1716	0.1721	0.1653
	Jiangsu	0.1987	0.1858	0.1909	0.1934	0.1619	0.1915
	Zhejiang	0.2340	0.2206	0.2447	0.2537	0.1673	0.1693
	Fujian	0.1809	0.1236	0.1435	0.1548	0.0907	0.1616
	Shandong	−0.1589	−0.1338	−0.1572	−0.1664	−0.1129	−0.1344
	Guangdong	0.3928	0.3362	0.3036	0.2819	0.2507	0.2687
	Hainan	0.2364	0.1042	0.0964	0.0352	−0.0212	−0.0628
Central	Shanxi	−0.3608	−0.3257	−0.3173	−0.3255	−0.4231	−0.4405
	Jilin	0.2909	0.2970	0.3203	0.3764	0.4642	0.5366
	Heilongjiang	0.3051	0.2035	0.1537	0.1403	0.1277	0.0315
	Anhui	0.5587	0.5295	0.6142	0.6518	0.5920	0.6026
	Jiangxi	0.8013	0.8854	0.9057	0.9726	0.7955	0.7719
	Henan	0.3766	0.3586	0.3504	0.3477	0.3731	0.4360
	Hubei	0.2389	0.2686	0.3326	0.3566	0.5094	0.5767
	Hunan	0.2930	0.3498	0.3649	0.4476	0.6199	0.6664
West	Inner Mongolia	−0.4845	−0.4116	−0.4071	−0.4151	−0.4094	−0.4599
	Guangxi	0.0441	0.0247	0.0241	0.0260	−0.0040	0.0048
	Chongqing	−0.1049	−0.1335	−0.1343	−0.0928	0.0263	0.0853
	Sichuan	−0.2025	−0.1992	−0.2000	−0.1685	−0.1377	−0.1160
	Guizhou	−0.5464	−0.5268	−0.5304	−0.5002	−0.4266	−0.3666
	Yunnan	−0.2666	−0.2719	−0.3082	−0.2924	−0.2722	−0.2479
	Shaanxi	−0.0991	−0.0478	−0.0522	−0.0331	−0.0627	−0.1179
	Gansu	−0.4350	−0.4387	−0.4352	−0.4406	−0.4783	−0.4809
	Qinghai	−0.5850	−0.5893	−0.5977	−0.6510	−0.6929	−0.6975
	Ningxia	−0.6918	−0.6494	−0.6278	−0.6433	−0.6785	−0.6990
	Xinjiang	−0.3966	−0.4387	−0.4668	−0.5629	−0.6469	−0.6882

.

The larger the absolute value of the index, the more serious the energy misallocation. When the index is greater than 0, it indicates that within the entire economy, the actual allocation of energy in the region is lower than the theoretical ratio under effective allocation, namely, insufficient energy allocation; otherwise, excessive allocation. There is a certain degree of misallocation in the energy markets in various regions of China, and the differences between regions are obvious. The absolute value of the misallocation index in the more developed east region is generally smaller than that in the central and west regions, indicating a low level of energy misallocation in this region. Furthermore, most of the provinces have an index greater than zero, indicating the actual energy input of those regions are lower than the theoretical ratio, namely, insufficient energy allocation. In the west region where the economy is relatively backward, the misallocation indexes of almost all provinces are less than zero, indicating that the actual energy input in this region is higher than the theoretical ratio, namely, excessive energy allocation. The index in the central region is generally higher than that in the east and west, indicating a serious energy misallocation situation. Judging from the energy misallocation in various regions, the demand for energy in the east region is high due to the high level of economic development, resulting in a lower energy allocation than the optimal allocation level matching its economic development. On the other hand, the east region has gradually changed its economic growth pattern from extensive to intensive emphasizing on the adoption of energy-saving and environmentally friendly technologies to promote industrial transformation and upgrading. Therefore, to alleviate the problem of “high energy consumption and high pollution”, the east region raises energy prices or increases the resource tax to curb the energy input of enterprises, resulting in insufficient energy allocation. In the central region, except for Shanxi Province, all the provinces show positive misallocation, indicating that the demand for energy in this region also exceeds the theoretical optimal allocation. This is related to a series of policies to promote regional development, such as the “Rise of Central China”. In the accelerated economic development stage, the demand for energy in this region increases rapidly, so the central region has a higher degree of positive misallocation. For the west region, to balance regional development and narrow the gap between regions, the state provides key support through the implementation of policies such as “Go-West Campaign”. Due to low technical level and low added value of enterprise output, the input production factors cannot fully contribute to the local economy, resulting in an energy factor allocation greater than the effective allocation under current output levels.

3.2. Calculation of Carbon Emission Efficiency in Each Province

Data Envelopment Analysis (DEA) is a method for evaluating the relative efficiency of several Decision-Making Units (DMUs) with the same type of inputs and outputs. Both the desired and undesired outputs are present in the actual production process. According to Fukuyama [37], two basic assumptions are met between output and undesired output: First, in the case of constant investment, output and undesired output increase and decrease by the same proportion, indicating that the reduction of undesired output requires the consumption of additional factor inputs. Second, the undesired output and the desired output reach zero at the same time, indicating that undesired output emerge simultaneous as the output. According to Tone [38], this paper uses the undesirable SBM (Slacks-Based Measure of efficiency)model to measure the carbon emission efficiency of each province. The model is as follows:

$$\begin{array}{c}\underset{\lambda ,s^{+},s^{-}}{\min \rho }=\frac{1-\frac{1}{m}{\displaystyle {\sum }_{i=1}^m\frac{s_i^{-}}{x_{i0}}}}{1+\frac{1}{n_1+n_2}\left[{\displaystyle {\sum }_{j=1}^{n_1}\frac{s_j^g}{y_{j0}^g}+{\displaystyle {\sum }_{j=1}^{n_2}\frac{s_j^b}{y_{j0}^b}}}\right]}\\ \{\begin{array}{l}{x}_0=X\lambda +S^{-},\\ y_0^g=Y^g\lambda -S^g,\\ y_0^b=Y^b\lambda +S^b,\\ \lambda \ge 0,s^{-}\ge 0,s^g\ge 0,s^b\ge 0\end{array}\end{array}$$

(6)

where m is the type of the input factor, n₁ is the type of the output, and n₂ is the type of the undesired output, and $x_0$, $y_0^g$, $y_0^b$, $s_i^{-}$, $s_j^g$, $s_j^b$ represent the input, the output, the undesired output, the input slack, the output slack, and the undesired output slack respectively. $X$, $Y^g$, $Y^b$, $S^{-}$, $S^g$, $S^b$ represent the input, the output, the undesired output, the input slack, the output slack, and the undesired output slack matrix for DMUs, λ represents the weight of each input factor, and ρ is the efficiency of the decision-making unit.

The output and input data of each province are the same data used in the calculation of the energy misallocation index. The undesired output data is the carbon dioxide emissions generated by the consumption of seven energy sources such as coal, coke, gasoline, kerosene, diesel, fuel oil, and natural gas in the end energy consumption, usually estimated by multiplying the actual consumption of each energy source with the corresponding carbon dioxide emission coefficient. The calculation formula NCV_i × CC_i × COF_i × 44/12 can be defined as the carbon dioxide emission coefficient, where NCV_i, CC_i, and COF_i represent the average low calorific value, the carbon content, and the carbon oxidation factor of the i-th energy source, respectively. These parameters are based on the data published in the appendix of IPCC (2006) and China Energy Statistical Yearbook. The carbon emission efficiency of each province, calculated with undesirable SBM model with constant return to scale, is as follows:

The results in

Table 3. Measured and calculated carbon emission efficiency of each province in 2005–2016 (partial).

Region		2005	2008	2010	2012	2014	2016
East	Beijing	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000
	Tianjin	0.7087	0.6553	0.6019	0.5893	0.5596	0.5317
	Hebei	0.3681	0.3577	0.3411	0.3348	0.3051	0.2876
	Liaoning	0.6246	0.4710	0.4393	0.4330	0.4074	0.2924
	Shanghai	1.0000	1.0000	1.0000	1.0000	0.6596	0.6476
	Jiangsu	0.5428	0.5436	0.5494	0.5449	0.5459	0.5443
	Zhejiang	0.7047	0.6086	0.5999	0.5862	0.5526	0.5468
	Fujian	0.7659	0.6351	0.5777	0.5394	0.5065	0.5052
	Shandong	0.5163	0.4895	0.4397	0.4225	0.4190	0.3961
	Guangdong	1.0000	1.0000	1.0000	1.0000	1.0000	0.6142
	Hainan	1.0000	1.0000	0.5738	0.4624	0.4038	0.3745
Central	Shanxi	0.3344	0.3447	0.3077	0.3006	0.2536	0.2295
	Jilin	0.4632	0.3945	0.3658	0.3744	0.3591	0.3379
	Heilongjiang	0.4304	0.3955	0.3644	0.3593	0.3280	0.2895
	Anhui	0.5074	0.4626	0.4533	0.4356	0.4042	0.3829
	Jiangxi	0.4127	0.4411	0.4427	0.4599	0.4389	0.4255
	Henan	0.4067	0.3930	0.3514	0.3299	0.3104	0.2993
	Hubei	0.3811	0.4053	0.4109	0.4117	0.4216	0.4137
	Hunan	0.4393	0.4699	0.4458	0.4491	0.4496	0.4363
West	Inner Mongolia	0.3293	0.3920	0.3785	0.3693	0.3265	0.2988
	Guangxi	0.5220	0.4733	0.3899	0.3526	0.3395	0.3289
	Chongqing	0.4060	0.3881	0.3925	0.4187	0.4391	0.4518
	Sichuan	0.3834	0.3966	0.3820	0.3950	0.3853	0.3782
	Guizhou	0.1999	0.2533	0.2572	0.2842	0.2955	0.2937
	Yunnan	0.2986	0.3166	0.2820	0.2807	0.2684	0.2528
	Shaanxi	0.4110	0.4116	0.3803	0.3829	0.3668	0.3390
	Gansu	0.2440	0.2715	0.2694	0.2788	0.2646	0.2357
	Qinghai	0.2111	0.2361	0.2298	0.2244	0.2005	0.1779
	Ningxia	0.1967	0.2347	0.2335	0.2405	0.2196	0.2011
	Xinjiang	0.4118	0.3474	0.3231	0.3014	0.2581	0.2133

show that there are large differences in carbon emission efficiency among provinces in China: the highest in the east, the second in the central region, and the lowest in the west. Among them, Beijing, Shanghai, and Guangdong have higher carbon emission efficiency, but most of the provinces in the east have a downward trend, and the changes in carbon emission efficiency of the central and west provinces is not obvious. The east region has relatively developed economy and certain energy-saving technologies that can promote the transformation and upgrading of the industry. Therefore, its carbon emission efficiency is high. However, in recent years, it has shown a downward trend. This region needs to make timely adjustments in respond to the environmental problems occurred in production and life to ensure the effective implementation of emission reduction policies. The carbon emission efficiency of the central provinces has not changed much. It is necessary to formulate phased emission reduction targets, implement effective energy conservation measures, and fully apply green technologies to economic construction. The carbon emission efficiency of the west region is relatively low, and there is much room for improvement in energy conservation and emission reduction. These provinces need to actively develop environmental protection technologies and formulate emission reduction targets that are consistent with the actual situation in the region. Inefficient carbon emission is still a real problem in the process of China’s socialist modernization. Only by improving regional carbon emission efficiency can we achieve sustainable economic development.

4. Model Construction and Data Description

4.1. Spatial Econometric Modeling

To investigate the impact of regional energy misallocation on carbon emission efficiency based on the spatial panel data econometric model constructed by Lesage and Pace [39], this paper sets the carbon emission efficiency CE_it as the dependent variable, the energy misallocation index τ_Eit as the independent variable, and constructs the following spatial econometric model:

$$C{E}_{\mathrm{it}}={\alpha }_0+\delta W*C{E}_{it}+\beta *{\tau }_{Eit}+\gamma *X_{it}+{\mu }_i+{\lambda }_t+{\epsilon }_{it}$$

(7)

$${\epsilon }_{it}=\phi W{\epsilon }_{it}+{\nu }_{it}$$

(8)

when $\delta \ne 0,\beta \ne 0,\phi =0$, it is a spatial lagged model (SLM) showing that the carbon emission efficiency of this region is not only related to the independent variables of the region, but also related to the carbon emission efficiency of adjacent regions. When $\delta =0,\beta \ne 0,\phi \ne 0$, it is a spatial error model (SEM) showing that the carbon emission efficiency of this province is not only related to the province’s independent variables, but also related to the carbon emission efficiency and independent variables of adjacent provinces.

In the model, the subscript i signifies the provinces, and the subscript t signifies the year, X_it is a series of control variables including: the GDP, the industrial composition (IC), the R&D investment (RD), the energy consumption structure (ES), the openness degree (OD), the infrastructure (IS), the percentage of urbanization (PU), and the degree of government intervention (GI), μ_i represents the non-observable individual effect, λ_t represents the time effect, ε_it is the random error terms, and W is the spatial weight matrix.

4.2. Data Description

The research samples selected in this paper are panel data of 30 provinces in China from 2005 to 2016 (excluding Hong Kong, Macao, Taiwan, and Tibet). The original data are from the China Statistical Yearbook, China Energy Statistical Yearbook and provincial statistical yearbooks. See

Table 4. Definitions of main variables.

Variable	Symbol	Definition
Carbon emission efficiency	CE	Each province’s estimated CO2 emission efficiency
Energy misallocation index	τE	Each province’s energy misallocation
Gross domestic product	GDP	Each province’s per capita GDP, unit: 10,000 yuan/person
Industrial composition	IC	Each province’s proportion of output value of secondary industry to the GDP
R&D investment	RD	Each province’s proportion of R&D input to the GDP
Energy consumption structure	ES	Each province’s proportion of coal consumption to the total energy consumption
Openness degree	OD	Each province’s proportion of total import and export trade to the GDP
Infrastructure	IS	Each province’s total mileage of roads and railways, unit: 10,000 km
Percentage of urbanization	PU	Each province’s proportion of urban population to the total population
Government intervention	GI	Each province’s proportion of government fiscal expenditure to the GDP

and

Table 5. Descriptive statistics of the main variables.

Variable	Obs	Average	Std	Min	Max
CE	360	0.4557	0.2088	0.1779	1.0000
гE	360	−0.0018	0.4034	−0.7036	0.9726
GDP	360	3.0356	1.7952	0.5254	9.1336
IC	360	0.4661	0.0784	0.1930	0.5862
RD	360	0.0139	0.0105	0.0017	0.0601
ES	360	0.6145	0.1328	0.1069	0.8254
OD	360	0.3058	0.3496	0.0134	1.6455
IS	360	13.1664	7.3161	0.8379	32.8761
PU	360	0.5238	0.1403	0.2687	0.8960
GI	360	0.2131	0.0942	0.0798	0.6269

.

5. Empirical Results and Analysis

5.1. Spatial Autocorrelation Test

The spatial autocorrelation index Moran’s I was employed to test whether regional economic variables have spatial correlation.

$$Moran’s I=\frac{{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{W}_{ij}(Y_i-\overline{Y})(Y_j-\overline{Y})}}}{S^2{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{W}_{ij}}}}$$

(9)

where $S^2=\frac{1}{n}{\displaystyle \sum _{i=1}^n(Y_i-\overline{Y}),\overline{Y}=}\frac{1}{n}{\displaystyle \sum _{i=1}^n{Y}_i}$, Y_i represents carbon emission efficiency of the i-th province, n is 30, W is the 0~1 spatial contiguity matrixes. When i province is adjacent to j province, W is 1, otherwise, W is 0. The range of Moran’s I is generally −1≤I≤1. When Moran’s I is greater than 0, there is a positive spatial correlation between regional economic variables. When Moran’s I is less than 0, there is a negative spatial correlation between regional economic variables. When Moran’s I is equal to 0, there is no spatial correlation.

Table 6. Moran’s I of carbon emission efficiency in China from 2005 to 2016.

Years	Moran’s I	E (I)	sd (I)	z	p-Value
2005	0.330	−0.034	0.121	3.021	0.001
2006	0.321	−0.034	0.120	2.959	0.002
2007	0.281	−0.034	0.119	2.649	0.004
2008	0.282	−0.034	0.119	2.668	0.004
2009	0.311	−0.034	0.117	2.965	0.002
2010	0.307	−0.034	0.116	2.946	0.002
2011	0.282	−0.034	0.115	2.749	0.003
2012	0.284	−0.034	0.115	2.769	0.003
2013	0.276	−0.034	0.112	2.760	0.003
2014	0.276	−0.034	0.113	2.758	0.003
2015	0.361	−0.034	0.111	3.561	0.000
2016	0.377	−0.034	0.111	3.693	0.000

Note: E (I) is the expected value of I, sd (I) is the standard deviation of I, z is the z statistics of I, P is the significance level.

shows that although the Moran’s I of carbon emission efficiency in China has a certain fluctuation during the 12 years, it is always greater than 0, indicating that there is a significant positive spatial correlation between the carbon emission efficiency of each province, as well as a strong spatial dependence on the whole. Provinces with relatively high carbon emission efficiencies tend to be close to other provinces with high carbon emission efficiency, and provinces with relatively lower carbon emission efficiencies tend to be adjacent to other provinces with lower carbon emission efficiency.

5.2. Selection of the Spatial Panel Data Econometric Model and the Related Inspection

According to the above spatial autocorrelation test results, to introduce the spatial econometric model for the empirical analysis. Moran’s I only verifies the existence of the spatial effect. Whether to adopt SLM or SEM is determined according to the criterion of Anselin [40], thus Lagrange Multiplier-lag (LM-lag) Test and Lagrange Multiplier-error (LM-err) Test are needed. If neither of these two passes the significance test, robustness test is required, namely, Robust LM-lag (R-LM-lag) Tests and Robust LM-error (R-LM-err) Tests. The test results are shown in

Table 7. Test results of model selection.

Test	Statistics	p-Value
LM-lag	4.4323	0.0350
R-LM-lag	17.5863	0.0000
LM-err	5.6588	0.0170
R-LM-err	18.8128	0.0000

.

The results show that both LM-lag and LM-err passed the test at the significance level of 5%, thus, SLM and SEM are both applicable. For the sake of comparison, this paper also lists the estimation results of the Ordinary Least-Squares Estimates, spatial random effects, spatial fixed effect, time period fixed effect, and spatial and time period fixed effect.

The results in

Table 8. Nationwide estimated results of the impact of energy misallocation on carbon emission efficiency.

	OLS	SLM				SEM
		Spatial Fixed	Time Fixed	S&T Fixed	Spatial Random	Spatial Fixed	Time Fixed	S&T Fixed	Spatial random
Intercept	0.718 ***	-	-	-	0.304 **	-	-	-	0.379 ***
	(9.696)	-	-	-	(2.225)	-	-	-	(2.868)
τE	0.089	0.599 ***	−0.034	0.606 ***	0.476 ***	0.602 ***	−0.009	0.626 ***	0.498 ***
	(1.227)	(4.319)	(−0.497)	(4.773)	(3.752)	(4.356)	(−0.127)	(4.839)	(4.191)
τE2	0.036	−0.515 ***	0.205 **	−0.405 ***	−0.413 ***	−0.518 ***	0.163 **	−0.425 ***	−0.430 ***
	(0.412)	(−3.478)	(2.454)	(−2.962)	(−2.941)	(−3.510)	(1.964)	(−3.034)	(−3.238)
GDP	−0.108 ***	0.131 ***	−0.033	0.113 *	−0.126 ***	0.135 ***	−0.030	0.098	−0.153 ***
	(−4.585)	(3.573)	(−1.078)	(1.790)	(−3.494)	(3.679)	(−0.966)	(1.573)	(−4.153)
IC	−0.411 ***	0.388 ***	−0.582 ***	−0.433 ***	0.227 **	0.357 ***	−0.642 ***	−0.408 ***	0.063
	(−5.276)	(3.459)	(−7.395)	(−2.887)	(2.057)	(3.159)	(−8.156)	(−2.677)	(0.581)
RD	2.111 ***	−1.135 ***	1.237 *	0.807 ***	−1.613	−1.229 ***	0.792	0.571 ***	−1.296
	(2.890)	(−4.167)	(1.814)	(2.873)	(−1.045)	(−4.195)	(1.156)	(3.299)	(−0.888)
ES	−0.439 ***	−0.465 ***	−0.409 ***	−0.621 ***	−0.501 ***	−0.476 ***	−0.427 ***	−0.630 ***	−0.565 ***
	(−8.603)	(−4.821)	(−8.804)	(−6.851)	(−5.796)	(−4.902)	(−9.171)	(−6.931)	(−6.793)
OD	0.251 ***	0.079 *	0.236 ***	0.069 *	0.216 ***	0.074 *	0.222 ***	0.054	0.194 ***
	(11.985)	(1.771)	(11.739)	(1.667)	(5.877)	(1.658)	(11.262)	(1.284)	(5.626)
IS	0.014 *	0.041 *	0.038 ***	0.069 **	0.006	0.041 *	0.039 ***	0.068 **	0.009
	(1.663)	(1.899)	(4.010)	(2.086)	(0.362)	(1.878)	(4.315)	(2.051)	(0.540)
PU	0.554 ***	0.695 ***	0.567 ***	1.003 ***	0.820 ***	0.743 ***	0.568 ***	0.971 ***	1.008 ***
	(4.280)	(2.921)	(4.639)	(4.276)	(3.714)	(3.103)	(4.647)	(4.131)	(4.719)
GI	−0.765 ***	−0.360 ***	−0.652 ***	−0.256 **	−0.534 ***	−0.378 ***	−0.612 ***	−0.293 **	−0.714 ***
	(−12.56)	(−2.989)	(−8.432)	(−2.080)	(−4.922)	(−3.087)	(−8.609)	(−2.432)	(−6.715)
W * dep. var.	-	0.054	0.089 **	0.258 ***	0.017	-	-	-	-
	-	(0.756)	(1.985)	(3.553)	(0.264)	-	-	-	-
spat. aut.	-	-	-	-	-	0.054	0.006	0.135 *	0.301 ***
	-	-	-	-	-	(0.727)	(0.079)	(1.727)	(4.431)
R2	0.853	0.931	0.877	0.944	0.919	0.931	0.875	0.942	0.920

Note: The results above are calculated in MATLAB. The numbers outside the parentheses in the table are the regression coefficients, *, ** and *** indicate passing the test at the significance level of 10%, 5%, and 1% respectively, the numbers in parentheses are t-statistic, -- indicates that the content is empty.

show that spatial lagged dependent variable term(W * dep.var) of the time period fixed effect and spatial and time period fixed effect of the SLM passed the significance level test. Spatial error autocorrelation term (Spat. aut) of the spatial and time period fixed effect and spatial random effects of the SEM passed the significance level test. At the same time, the Hausman test results show that the four models above are all applicable. According to the goodness of fit R², we can see that the SLM with spatial and time period fixed effect has the highest value of R². Therefore, this paper uses the SLM with spatial and time period fixed effect to explain the estimated results.

5.3. Analysis of the Empirical Results

Firstly, estimated coefficients of independent variables of energy misallocation index τ_E and τ_E² are positive and negative respectively, and both passed the test at the significance level of 1%, indicating that the relationship between energy misallocation and carbon emission efficiency is not a simple linear one, but a non-linear one with an inverted U-shape, that is, a slight degree of misallocation has positive impact on carbon emission efficiency, instead, a more severe distortion has a negative effect on carbon emission efficiency, which is consistent with the calculation results obtained earlier in this paper, namely, the energy misallocation in the east region is lower than that in the central and west regions, and the carbon emission efficiency in the east region is relatively higher. Therefore, the resource allocation equilibrium is only an ideal state. The only effective way to improve carbon emission efficiency is to limit the misallocation level to a reasonable range and improving the allocation efficiency.

As for other control variables, the estimated coefficients of GDP, RD, OD and IS are positive at different significance levels, indicating that the gross domestic production, R&D investment, foreign trade, and infrastructure construction all contribute to carbon emission efficiency. Economically developed regions have emphasized technology research and development, higher production levels, relatively completed infrastructure, and advanced production management technologies brought by foreign trade expansion, all of which promote the improvement of carbon emission efficiency. The estimated coefficients of IC and ES are negative at the significance level of 1%, and the coefficient is large, indicating that the growth of the secondary industry output and coal consumption significantly reduce the carbon emission efficiency. The secondary industry relies heavily on fossil energy and coal has always been the main proportion of China’s primary energy consumption. Its combustion use rate is low, so it has a negative impact on carbon emission efficiency. Therefore, using clean energy and promoting the industrial structure upgrading can effectively improve carbon emission efficiency. The estimated coefficient of GI is negative at the significance level of 5%, indicating that excessive government intervention will hinder the improvement of carbon emission efficiency. While unilaterally pursuing GDP growth, local governments use administrative means to control the economy and distorts the market mechanism, which is not conducive to fair competition among producers and results in inefficient allocation of resources and excessive consumption of energy. The estimation coefficient of PU is also significantly positive, and the coefficient is large, indicating that there is a positive effect between the percentage of urbanization and carbon emission efficiency. This is contrary to the expectations of this paper. The reason may be that the industrialization process promotes the optimization and upgrading of the industrial structure through technological innovation, thereby transforming the economic growth mode and optimizing the resource allocation, thus, the carbon emission efficiency is correspondingly improved. This is also consistent with the results obtained in the previous calculations, that is, the carbon emission efficiency of the east region with relatively high PU is also relatively higher.

5.4. Analysis of Regional Empirical Results

Due to the difference in the degree of misallocation in each region, this paper conducted empirical tests separately. To avoid the distortion of the estimated results caused by the insufficient sample size, the central and west regions were studied together. According to the LM statistic test results, the spatial panel lagged model should be selected for the analysis. See

Table 9. Regional estimated results of the impact of energy misallocation on carbon emission efficiency.

	East				Central and West
	Spatial Fixed	Time Fixed	S&T Fixed	Spatial Random	Spatial Fixed	Time Fixed	S&T Fixed	Spatial Random
Intercept	-	-	-	1.516 ***	-	-	-	0.319 ***
	-	-	-	(11.076)	-	-	-	(3.149)
τE	0.457 ***	−0.077	0.358 **	−0.036	0.123	−0.203 ***	0.157 **	0.023
	(3.081)	(−1.314)	(2.456)	(−0.511)	(1.404)	(−4.358)	(2.486)	(0.274)
τE2	-	-	-	-	−0.188 **	0.299 ***	−0.115 *	−0.084
	-	-	-	-	(−2.050)	(5.611)	(−1.743)	(−0.940)
GDP	−0.248 ***	−0.188 **	−0.325 **	−0.270 ***	−0.031	0.075 ***	0.335 ***	−0.040 *
	(−2.761)	(−2.558)	(−2.521)	(−4.417)	(−1.478)	(2.650)	(10.157)	(−1.899)
IC	0.676 **	−0.664 ***	0.098	−0.467 **	0.198***	−0.270***	−0.469***	0.209***
	(2.389)	(−3.265)	(0.302)	(−2.049)	(2.990)	(−3.464)	(−6.515)	(3.146)
RD	2.880*	−0.453	3.452	2.245	2.014 ***	2.306 ***	−1.524	1.640 **
	(1.812)	(−0.251)	(0.933)	(1.199)	(3.259)	(2.992)	(−1.209)	(2.496)
ES	−0.320	−1.323 ***	−0.629 ***	−1.208 ***	−0.268 ***	−0.170 ***	−0.244 ***	−0.210 ***
	(−1.451)	(−9.767)	(−2.820)	(−8.236)	(−3.921)	(−4.846)	(−4.624)	(−3.235)
OD	0.028	0.119 ***	0.009	0.182 ***	−0.005	0.063	−0.008	−0.031
	(0.458)	(3.876)	(0.143)	(6.120)	(−0.086)	(1.250)	(−0.171)	(−0.482)
IS	0.003	0.062 ***	−0.036	0.022	0.025 **	0.039 ***	0.048 ***	0.031 ***
	(0.059)	(3.278)	(−0.584)	(1.328)	(2.024)	(5.343)	(2.743)	(2.618)
PU	1.590 ***	1.256 ***	2.306 ***	1.047 ***	−0.012	0.043	0.184	0.117
	(3.810)	(5.957)	(5.241)	(4.704)	(−0.077)	(0.430)	(1.417)	(0.802)
GI	−2.726 ***	−2.738 ***	−2.224 ***	−2.941 ***	−0.074	−0.434 ***	−0.158 ***	−0.185 ***
	(−7.876)	(−9.051)	(−5.901)	(−9.628)	(−1.086)	(−7.731)	(−2.678)	(−2.835)
W * dep. var	0.123	0.100 **	0.211 **	0.139 ***	0.142 *	0.205 ***	0.200 **	0.170 **
	(1.406)	(2.005)	(2.554)	(2.750)	(1.762)	(3.196)	(2.563)	(2.129)
R2	0.941	0.934	0.951	0.911	0.887	0.757	0.943	0.874

Note: The results above are calculated in MATLAB. The numbers outside the parentheses in the table are the regression coefficients, *, ** and *** indicate passing the test at the significance level of 10%, 5%, and 1% respectively, the numbers in parentheses are t-statistic, -- indicates that the content is empty.

.

Except for the time period fixed effect model for the east region, the Hausman test P values of all the other models are 0, so the assumption of random effect model is rejected, and the fixed effect model is selected. In this paper, the spatial and time period fixed effect model is used to explain the estimated results of both the east region and the central and west regions. The degree of energy misallocation in the east region is relatively low, and the impact on carbon emission efficiency is significantly positive. However, the distortion degree of energy allocation should be corrected in a timely manner to prevent the occurrence of inverted U-shaped phenomena that affects the ecological environment in the east region. The misallocation index of the central and west regions is higher than that of the east, and the impact on carbon emission efficiency is inverted U-shaped. Targeted measures should be taken to alleviate the distortion of energy allocation and reduce its adverse impact on the local ecology.

Among other control variables, GDP has the opposite effects on carbon emission efficiency of the east and the central and west regions, indicating that gross domestic production have a favorable impact on environmental quality to a certain extent. With too fast and too heated development, people tend to ignore the series of environmental pollution problems that hinder the improvement of carbon emission efficiency. The impact of IC on the east region is not significant, and its impact on the central and west regions is significantly negative, indicating that the industrial structure of the east region is undergoing adjustment and upgrading, and the central and west regions still need to rely on the secondary industry with high energy consumption and high pollution to stimulate the local economy. PU has a significant positive impact on the carbon emission efficiency in the east region, and the coefficient is large, indicating that the technological innovation brought about by the urbanization process have a positive impact on the environmental quality. The urbanization process in the west region is slow, and its impact on carbon emission efficiency is not significant. The impact of ES and GI on the east and central and west is negative at the significance level of 1%. The impact on the east region is especially significant, indicating that the inefficient consumption of coal and the intervention by local governments hinder the improvement of carbon emission efficiency and affect the regional environmental quality; RD, OD, and IS have little impact on the two regions. In particular, the insignificant impact of RD in the east region indicates that the current R&D investment is far from reaching its due role and level, and further research investment is needed so that it can be effectively applied to production and life to promote sustainable development.

6. Conclusions and Policy Suggestions

Based on the 2005–2016 provincial panel data, this paper calculated the energy misallocation index and carbon emission efficiency of each region, constructed a spatial panel data econometric model, and empirically studied the impact of energy misallocation on carbon emission efficiency using Moran’s I index and SLM and SEM. The main conclusions are:

First, there are different levels of energy misallocation in the various regions of China during the surveying period, and there are significant differences between the regions. Most provinces in the east region have lower degree of misallocation. In addition, the misallocation indexes of most provinces in the central and west regions are generally higher than that of the east, and the misallocation of the west region is predominately negative. The reasons may be: Firstly, the level of marketization in the east region is relatively high, making the energy allocation less distorted. Secondly, the central region is currently in a period of rapid economic development, so the demand for energy is large, and the low energy efficiency has caused a high degree of misallocation in this region. Finally, the low technical level and the country’s various preferential policies and greater support in the west region may lead to inefficiency in the input and output. The current energy allocation in the west region is relatively excessive. Therefore, from the perspective of policy, we should accelerate the reform of the market-oriented mechanism for the price of resource products, reduce inappropriate government regulations and interventions, and give full play to the decisive role of market mechanisms in resource allocation. Government departments should play a better role of coordination and supervision, eliminate administrative barriers between regions, and make production factors flow rationally between regions according to price signals so that the distortion of energy markets may be reduced.

Second, there is a significant positive spatial correlation between the carbon emission efficiency of each province, showing a spatial spillover effect, namely, there are interactions between adjacent provinces. As far as the whole country is concerned, there is an obvious inverted U-shaped relationship between energy misallocation and carbon emission efficiency. It is necessary to prevent the distortion of allocation from accelerating the arrival of this critical point, which results in a reduction in carbon emission efficiency and is not conducive to energy conservation and emission reduction. The energy misallocation index in the east region is relatively small, and its impact on the carbon emission efficiency of the region is positive. We should be able to correct the further aggravation of factor allocation distortion in a timely manner. The energy misallocation index in the central and west regions is relatively large, and its impact on the carbon emission efficiency of the regions is negative, resulting in inefficient carbon emissions and deteriorating ecological environment. Accordingly, in the formulation and promotion of regional policies for the marketization of energy, the provinces of the three major regions need to consider the characteristics of their own province as well as the spatial spillover effects brought by the impact of distortions on carbon emissions in other provinces.

The enlightenment of these conclusions is: On one hand, the market-oriented reform of resource-based factors such as coal, oil, and natural gas should be accelerated, so that product prices can truly reflect the supply and demand relationship and the scarcity of energy. Environmental protection constraints should be strengthened and a sound environmental compensation system must be established to promote the internalization of environmental protection costs of production enterprises. In addition, the government departments should focus on the market-oriented reform of energy in light of the actual conditions of each region, especially the reform of the marketization process of factors in the central and western regions, and accelerate the development of market systems and institutional innovation in the western region, improve the technical level and economic foundation, break local protectionism, promote the free flow and efficient allocation of production factors, and formulate regional policies tailored to local conditions. On the other hand, local governments’ direct interventions in microeconomic activities should be reduced to prevent local governments from distorting the prices of production factors in pursuit of expanding local economic interests. The performance appraisal system for officials should be improved. The performance appraisal based solely on the pursuit of GDP growth should be changed. While focusing on maintaining growth, attention must be given to environmental protection. In addition, indicators such as ecological benefits and improvement of people’s livelihood must be taken as an important basis for assessment. In addition, the reform of resource taxation must be accelerated, environmental taxes must be incorporated into local taxes as new sources of income for local governments to improve the quality of public services.