The Influence of Energy Price Distortion on Region Energy Efficiency in China’s Energy-Intensive Industries from the Perspectives of Urban Heterogeneity

Abstract

As typical representatives of China’s industrial sectors, energy intensive industries are the focus of energy conservation. This study constructs a trans-log production function and stochastic frontier analysis model to analyze the impact of energy price distortion on total factor energy efficiency in energy intensive industries on the city level. The results reveal that the phenomenon of energy price distortion existed in all cities from 2003 to 2019, with an average degree of −0.175; and the total factor energy efficiency in China’s energy intensive sectors showed an upward trend, with an average efficiency of 0.729. Further deep analysis of affecting mechanisms concluded that the price distortion showed a significant restraining effect on improving energy efficiency, while the improvement of urban agglomeration systems had an opposite effect. In addition, energy consumption structure, foreign trade, and infrastructure construction are positively correlated with energy efficiency. Therefore, promoting the market-oriented reform of China’s energy market is of great significance to improve city energy efficiency and build a resource-conserving society.

1. Introduction

As basic industries for national economic development, energy intensive industries (EIIs) have made important contributions to accelerate economic growth but input plenty of fossil energy in the production process. According to the statistics of China Energy Statistic Yearbooks, energy input of China’s EIIs in 2003 was 813.96 million tons of standard coal (mtce), which increased to 2472.09 mtce in 2019, 3.04 times larger than that in 2003. The average growth rate of energy input in EIIs increased by 7.25%, higher than that in the whole industry (6.63%) and on a national level (6.72%). Meanwhile, the quantities of energy input are impacted by energy prices, as the essence of market resource allocation is to realize the allocation of production factors in different sectors according to the change of prices [1]. If energy prices are too high, enterprises will shift production inputs from energy to non-energy (labor and capital) alternatives. If energy prices are too low, production inputs are converted in the opposite direction. State-owned energy enterprises, benefiting from government policy support and market share advantages, occupy a dominant position in the energy pricing mechanism. The result is that large amounts of energy are purchased by companies below equilibrium prices, creating energy price distortion (EPD). Price distortion will lead to misinformation in the energy market, which cannot accurately reflect the relationship between supply and demand, resulting in low allocation efficiency [2]. The national 14th Five-Year Plan calls for comprehensively improving the utilization of resources, promoting a clean and efficient use of coal and other fossil energy, and resolutely curbing the blind development of projects with high energy consumption and high emissions. Therefore, for China’s EIIs, solving the dilemma of EPD and the resulting unbalanced resource allocation efficiency is extremely urgent.

In addition, energy efficiency of EIIs is limited by spatial characteristics and regional economic development level. On one side, the development of EIIs presents obvious spatial agglomeration characteristics due to economies of scale and market segmentation. However, the spatial gathering brings the expansion of production scale and the change of the factor input within the region, and then produces a negative crowding effect, which affects the effective allocation of production resources. Under the influence of energy market-oriented reform lag and unbalanced energy prices, the excessive input of energy factors will aggravate the negative crowding effect. On the other side, due to gaps in regional economic development, energy efficiency in high-income areas is higher than that in low-income areas. Therefore, this paper conducts theoretical research and empirical analysis to explore the impact mechanism on energy utilizing performance of China’s EIIs, considering the characteristics of spatial heterogeneity from city perspective: first, the characteristics of distorted price in different energy products with the data of 34 representative large and medium-sized cities are deeply analyzed; second, a spatial economic theoretical model is established to explore the impact of distorted prices on total factor energy efficiency (TFEE) and is further empirically tested by city data; finally, policy guidance for improving cleaner production of China’s EIIs is proposed.

The contribution and novelty of this paper reflects in the following: first, the level of distorted prices of fossil energy was estimated at the city level, and the changing trend can be found to reflect practical properties that EIIs faced; second, the characteristics of heterogeneity in TFEE of EIIs were further analyzed and third, in order to find the inherent impacting mechanism, the variable of EPD is integrated into the panel stochastic frontier model as a non-efficiency item to test the impaction of price distortion on energy efficiency at the city and urban agglomeration level. Therefore, as the paper focuses on finding the heterogeneous features of fossil fuel distortion, the constructive policies could be proposed for future energy conservation at city level.

Other parts are arranged as follows: the second part systematically reviews the existing literature on TFEE; in the third part, the methodology of evaluating regional energy efficiency is described, and the main variables and related data used are described in the following part. The fifth part gives the empirical results and further analysis. The final part provides the conclusions and practical recommendations for improving energy efficiency and cleaner production in China’s EIIs.

2. Literature Review

2.1. Measurement of Energy Price Distortions

In recent years, as energy resource gains more and more attention, domestic and foreign scholars have discussed the impact of price distortion on efficiency. Ouyang et al. [3] and Kong et al. [4] proved that factor price distortions affect the efficiency of resource allocation at the provincial and enterprise levels, respectively. Perfect market price mechanism promotes efficiency [5]. Qiao et al. [6] explored renewable energy companies and found that distortions in capital and labor prices had a negative impact on innovation efficiency. The distortion of fossil (coal, oil, and natural gas) energy prices had a negative impact on the efficiency of the green economy [7]. In South Korea, Bongseok [8] pointed out that EPD in the manufacturing industry led to a reduction in the market allocation efficiency. At the same time, the existence of price distortion is not conducive to economic development. Ju et al. [9] established the relevant index to measure distortion of China’s energy products and pointed out that EPD hindered economic development. Shi and Sun [10] proved that regulatory price distortion is not conducive to output growth and has a negative impact on the economy. Regarding the distortion of electricity prices for Colombian residents, McRae and Wolak [11] showed that the implementation of fixed charges can increase the economic benefits of electricity prices. Eliminating price distortions is conducive to environmental protection. Cui and Wei [12] pointed out that the regulation of coal pricing would cause price distortions and environmental degradation. When studying the electricity demand of residents in Sri Lanka, Athukorala et al. [13] proved that the policy of controlling price is ineffective in the presence of distortions. Wang et al. [14] evaluated the degree of oil price distortion in China’s transportation sector, and concluded that eliminating oil price distortion could reduce CO₂ emissions. Through reviewing existing studies, we found that few studies focus on the changing status of the distortion level. Therefore, this article further analyzes the temporal and spatial evolution characteristics of abnormal energy price and its impact on energy input and utilization.

Considering the estimating methods of price distortion, Shi and Sun [10], and Ju et al. [9] used the energy price of the United States as the benchmark to calculate EPD in China; Lin and Du [15] adopted the product factor marketization index and composite index to establish factor market distortion index; Yin et al. [16] defined distortion as the degree to which the product marketization index deviated from the factor marketization index. As the index method can be artificial interference and so lead to measurement errors, most studies measured the distortion by economic models such as the shadow price model [7,17,18] and the production function model [2,6,19,20]. The shadow price method can reflect the whole energy pricing process and take into account external influences such as environmental cost. Comparatively, the advantages of production function model are that it reflects the practical producing process and does not require complex cost data. Relative to the C-D production function, the trans-log production function does not require the assumption of unit substitution elasticity to avoid the possibility of estimation error. Considering that EPD was formed in production activities, the trans-log production function was adopted to measure marginal output elasticity of energy.

2.2. Measurement of Energy Efficiency

As the research of energy efficiency has always been the focus, many scholars adopted various methods to study TFEE. The main estimation methods could be divided into two categories: data envelope analysis (DEA) and stochastic frontier analysis (SFA). DEA is formulated to estimate relative effectiveness through linear programming model. The optimal input or output ratio of decision-making units relative to the production frontier can be obtained based on distance between the actual production points of all decision-making units and the optimal frontier. Through the DEA model, many scholars had conducted research on energy utilizing performance at the regional or provincial perspective [14,21,22]. Some other literatures analyzed energy efficiency at the industrial sector or enterprise level, such as Qi [23] and Khodadadipour et al. [24]; a few scholars measured energy efficiency at the urban level [25,26]. Other scholars used DEA to discuss the differences of energy efficiency at the national level by regional comparison [27,28].

DEA assumes that all deviations from the optimal linear boundary are purely inefficient results. Using DEA to study energy efficiency may be overestimated or underestimated. However, SFA could solve the evaluation error by building the economic model. Considered as a parametric method, SFA contains random phenomena in production activities. The method was applied in panel data by Pitt and Lee [29] and gradually became one of the mainstream measurement methods of total factor productivity. In studies of energy efficiency, most scholars adopted the SFA method to estimate energy efficiency of different industrial sectors, such as Hu [30] (energy industry), Xie et al. [31] (transport sector), Longo et al. [32] (wastewater Sector), Haider and Mishra [33] (steel industry) and Macharia et al. [34] (manufacturing sector). Some other scholars developed SFA to study the influencing factors of energy efficiency. Haider and Bhat [35] measured the energy efficiency of India’s paper industry, and the results showed that energy saving potential, industrial structure and capital intensity had a positive impact on the energy effective utilizing level, while labor productivity had no significant impact. Sun et al.’s [36] study across countries found that both green innovation and institutional quality had significant positive effects on energy efficiency. Macharia et al. [33] pointed out that export status, R&D, senior management experience and female ownership could improve the energy efficiency of Kenya’s manufacturing industry. In order to make better use of existing information, Haider and Mishra et al. [33] used Bayesian SFA and found that innovation capabilities had improved the energy efficiency of Indian steel companies. In order to avoid estimation bias, Ouyang et al. [37] combined the meta-frontier method and SFA and showed that improvement in energy technology was conducive to improving efficiency. Considering economy, safety, and ecology, Ratanakuakangwan and Morita [38] used SFA with inefficiency effects to estimate the efficiency of power plants and showed that increasing the carbon tax would reduce efficiency. Therefore, as the SFA model considers both random shocks and inefficiencies, it is more applicable than DEA to study the impacting mechanism in China’ EIIs.

2.3. Research on the Relationship between Price Distortion and Energy Efficiency

Raising energy prices is an important measure to improve the energy utilization level. Higher energy prices will encourage producers to reduce the usage of energy and increase the input of other production factors. In China, energy prices have been kept low due to government subsidies [39]. To promote energy efficiency, it is important to understand the impact of low prices. Ouyang and Sun [17] believed that energy prices were distorted due to government controls, leading to a downward trend in energy saving potential. EPD will hinder the improvement of energy efficiency, and so energy price marketization is the key to improving the efficiency level [3]. Through market-oriented reform, the level of electricity price distortion was alleviated and energy efficiency was improved [40]. Tan et al. [19] also found that correcting price distortions was conducive to improving energy efficiency in industrial sectors. EPD shows an indirect impact on energy efficiency by affecting other factors. Through the mediating effect, Sha et al. [7] found that EPD inhibited the development of technological innovation, which had a negative impact on energy utilization performance.

In conclusion, although the study on energy efficiency has made good achievements, the existing research objectives solely focus on the national, industrial, or enterprise level, and few studies focus on studying the relationship between energy price and energy efficiency at the city level. Furthermore, energy prices and their direction of change are determined by the quantity of supply and demand in the market. On the one hand, there are differences in resource endowments in Chinese cities, energy production costs, and local government policies (such as resource taxes), which lead to differences in supply. On the other hand, the economic growth rate, industrial structure and energy consumption structure of each city are different, resulting in differences in energy demand. Therefore, there are significant differences in energy prices among cities. It is necessary to discuss the impacting mechanism of price distortion on energy efficiency at the city level. Therefore, we adopted the trans-log production function to measure EPD. Then, SFA is used to measure inefficiency futures in EIIs at the city level to explore the impact of EPD on energy utilization level.

3. Methodology

The production function method is one of the most common estimation methods used to measure price distortions. In order to control individual heterogeneity and measure dynamic changes in EPD over time, a trans-log production function model is constructed to estimate the output elasticity of energy and the distorted degree of energy price between actual price and the marginal output.

SFA is a parametric method that contains random noise, and the method could build the model, including the inefficiency terms and its influencing factors to directly identify the influence of various factors on production efficiency. Based on Battese and Corra [41], the basic form of stochastic frontier production functions is described as follows:

$$\begin{gathered} Y_i=f(x_i)\exp ({\nu }_i-{\mu }_i) \\ \begin{array}{l}{\nu }_i~iidN(0,{\sigma }_{\nu }^2)\\ {\mu }_i~iid{N}^{+}({\mu }_{\mathrm{i}},{\sigma }_{\mu }^2)\end{array} \end{gathered}$$

(1)

where $\nu$ and $\mu$ are independent of each other, and both the two variables are independent with explanatory variables.

Assuming that there are three input factors including capital ($K$), labor ($L$) and energy ($E$) in the production process. Considering the dynamic changes of technique progress, a time term T is added into the formula. The trans-log form of stochastic frontier production functions can be expressed as:

$$\begin{array}{l}Ln{Y}_{it}={\beta }_0+{\beta }_{1}Ln{K}_{it}+{\beta }_{2}Ln{L}_{it}+{\beta }_{3}Ln{E}_{it}+{\beta }_{4}Ln{K}_{it}\ast Ln{L}_{it}+{\beta }_{5}Ln{K}_{it}\ast Ln{E}_{it}\\ +{\beta }_{6}Ln{L}_{it}\ast Ln{E}_{it}+\frac{1}{2}{\beta }_7{(Ln{K}_{it})}^2+\frac{1}{2}{\beta }_8{(Ln{L}_{it})}^2+\frac{1}{2}{\beta }_9{(Ln{E}_{it})}^2+{\beta }_{10}T\ast Ln{K}_{it}\\ +{\beta }_{11}T\ast Ln{L}_{it}+{\beta }_{12}T\ast Ln{E}_{it}+{\beta }_{13}T+{\beta }_{14}{T}^2+{\nu }_{it}-{\mu }_{it}\end{array}$$

(2)

Finally, energy input efficiency can be expressed as:

$$T{E}_{it}=\frac{E\left[y_{it}|{\mu }_{it}=0\right]}{E\left[y_{it}\right]}=\exp (-{\mu }_{it})=e^{-{\mu }_{it}}$$

(3)

$${\mu }_{it}=-\ln (T{E}_{it})$$

(4)

$${\sigma }^2={\sigma }_{\mu }^2+{\sigma }_{\nu }^2$$

(5)

$$\gamma ={\sigma }^2/({\sigma }_{\mu }^2+{\sigma }_{\nu }^2),\mathrm{and}\gamma \in \left[0,1\right]$$

(6)

Considering the production process is unified, the form of the production function with price distortion is the same as Equation (2). According to the model, the input-output elasticity of energy can be calculated as:

$$\gamma =\frac{dY/Y}{dE/E}=\frac{d\ln Y_{it}}{d\ln E_{it}}={\beta }_3+{\beta }_{5}Ln{K}_{it}+{\beta }_{6}Ln{L}_{it}+{\beta }_{9}Ln{E}_{it}+{\beta }_{12}T$$

(7)

Therefore, the marginal output of energy can be expressed as:

$$M{P}_{E_{it}}=\gamma \frac{Y_{it}}{E_{it}}=({\beta }_3+{\beta }_{5}Ln{K}_{it}+{\beta }_{6}Ln{L}_{it}+{\beta }_{9}Ln{E}_{it}+{\beta }_{12}T)\frac{Y_{it}}{E_{it}}$$

(8)

After energy price ($P_E$) is obtained, the degree of EPD can be expressed as:

$$D_{E_{it}}=\frac{P_{E_{it}}-M{P}_{E_{it}}}{M{P}_{E_{it}}}$$

(9)

When $D_{E_{it}}=0$, there are no distortions in energy prices; $D_{E_{it}}<0$ indicates that the energy prices are below the market equilibrium price; $D_{E_{it}}>0$ indicates that energy prices are above the market equilibrium price.

4. Variables and Data Description

The paper constructs urban panel data and discusses the effects of distorted price on TFEE in China’s EIIs. The main EIIs include: the chemical raw materials and chemical products manufacturing, non-metallic mineral products, ferrous metal smelting and rolling processing industry, non-ferrous metal smelting, and the rolling processing industry. Due to the consistency and availability of data, we adopt the data of 34 large and medium-sized cities in China during 2003–2019. The selected cities are considered as the most important cities in China’s economic growth and infrastructure construction in national planning [42]. The cities show a leading role in energy consumption patterns, technological innovation, and policy implementation. Under the guidance of national policies, the cities are firstly chosen to change economic development mode, such as optimizing industrial structure and developing a circular economy. Therefore, discussing the energy conservation and emission reduction status of EIIs in these cities is conducive to finding key policy measures to improve urban energy efficiency.

The raw data are derived from 2004–2020 China Statistical Yearbook, China Energy Statistical Yearbook, China Environmental Statistical Yearbook, Statistical Yearbook of Cities and CEIC Database. The data are deflated at 2003 price levels.

Table 1. Variables and data description.

Variable	Short	Sample Size	Mean	Standard Deviation	Min	Max
Gross industrial output (100 million yuan)	Y	578	946.471	994.181	28.160	6188.640
Capital input (100 million yuan)	K	578	335.049	367.963	16.299	2270.290
Labor input (person)	L	578	9.413	6.754	0.960	29.740
Energy input (million tons of standard coal)	E	578	6.966	7.866	0.092	45.553
Energy price (yuan/ton standard coal)	PE	578	2109.121	1767.685	78.654	10,845.497
Energy consumption structure	ens	578	0.585	0.210	0.018	0.952
Trade dependence (yuan/yuan)	exp	578	0.250	0.291	0.002	1.851
Infrastructure construction(square meters/ten thousand people)	infr	578	88,872.718	68,253.127	15,284.144	639,993.903
Beijing-Tianjin-Hebei urban agglomeration	BTH	Beijing, Tianjin, Shijiazhuang
Yangtze River Delta urban agglomeration	YRD	Shanghai, Nanjing, Hangzhou, Ningbo, Hefei
Pearl River Delta urban agglomeration	PRD	Guangzhou, Shenzhen
Urban agglomeration in the Middle Reaches of the Yangtze River	MYR	Wuhan, Changsha, Nanchang

presents the relevant information of main variables, and the EPD are calculated at a later stage.

4.1. Industrial Output (Y)

This paper adopts the variable of gross industrial output value of EIIs in each city as output. The data come from statistical yearbooks of each city. Industrial price index is used to diminish the influence of inflation and produce the real value.

4.2. Capital Input (K)

Considering the availability of data, the fix capital stocks are calculated based on perpetual inventory method: (1) Taking the net value fixed assets in 2003 as the initial capital stock; (2) Taking the difference of net fixed assets between adjacent years as the new fixed assets every year; (3) Adopting the price index of fixed asset investment to conduct price adjustment (adjust to 2003 price level); and (4) Putting the data into Equation (10) to solve the average annual capital stock.

$$K_{it}=K_{i{t}_0}+{\displaystyle \sum _{t_0+1}^t(\Delta k_{it}/I_{it})}$$

(10)

In Equation (10), $K_{it}$ represents the annual average capital stock of city $i$ in year $t$, $K_{i{t}_0}$ represents the net fixed assets value o in city $i$ in 2003, $\Delta k_{it}$ represents the difference in net fixed assets value of neighboring years in city $i$, $I_{it}$ represents the fixed-asset investment price index in year t.

4.3. Labor Input (L)

The annual number of employees in EIIs is taken to measure labor input, and the data are derived from city statistical yearbooks. Lacking relevant information in Chengdu Statistical Yearbook, the proportion of industrial labor input of Chengdu city in Sichuan province is adopted to produce the labor in Chengdu’s EIIs.

4.4. Energy Input (E) and Energy Prices (PE)

The comprehensive energy consumption of EIIs at the city level is taken to measure energy input. The input of each energy resource could be added up by Equation (11).

$$E={\displaystyle \sum _{j=1}^m(e_j\times c_j)}$$

(11)

In Equation (11), $E$ is the total energy consumption, $m$ is the kind of energy product, $e_j$ is the input of the $j$ energy product, and $c_j$ is the coefficient to discount standard coal.

Many scholars choose raw material, fuel, and power purchase price index to represent energy price, which is hard to reflect the actual price effectively. In this paper, taking the input structure of each energy resource as weight, the price of each energy resource is added up by Equation (12).

$$P_E={\displaystyle \sum _{j=1}^m(p_j\times {\eta }_j)}$$

(12)

where $P_E$ is the total energy price, $p_j$ is the price of the $j\mathrm{th}$ energy product, and ${\eta }_j$ is the energy consumption proportion of the $j\mathrm{th}$ energy product in total products.

4.5. Indicators Related to Energy Efficiency

4.5.1. Energy Consumption Structure (ens)

All kinds of energy are used with different efficiencies, so differences maybe exit in effects of energy input structure on the efficiency. Considering that coal-related energy products show a dominant position in energy consumption, the consumption ratio of coal in energy is taken to express the distribution of energy, which reflects the utilization of energy products in China’s EIIs.

4.5.2. Trade Dependence (exp)

Trade dependence is a key indicator of open economy. The degree of economic openness shows an indirect influence on energy efficiency through bringing new energy-saving technology, enlarging trade scale and promoting economic structure, and trade dependence is conducive to the improvement of energy efficiency. Here, trade dependence is expressed by the proportion of export of EIIs in city GDP.

4.5.3. Infrastructure Construction (infr)

The obsolescence of infrastructure means that industries need more energy inputs to maintain normal levels of output. Perfect transportation and other infrastructure can help to reduce the cost in the process of resource allocation, including time cost and economic cost, to better allocate and utilize resources. This index is measured by the square meters of roads per 10,000 people and treated logarithmically.

4.5.4. Urban Agglomeration Variable

The development level of EIIs varies greatly in different regions. Considering the characteristics of different regions, this study takes urban agglomerations in the Beijing-Tianjin-Hebei (BTH) agglomeration, the Yangtze River Delta (YRD), the Pearl River Delta (PRD) and in the middle reaches of the Yangtze River (MYR) as examples to analyze the impacts of urban agglomerations on energy efficiency.

5. Empirical Results

5.1. Estimating Energy Price Distortion

A flexible energy price system will realize independent energy consumption and help to enhance the utilization level of energy allocation and usage. Regarded as an effective means to improve energy utilization performance, energy price marketization has played a very important role. However, the energy pricing system in China has been controlled for a long time and there is price distortion between the price energy-intensive enterprises faced and the actual price needed. Here, the distance of EPD is calculated by Equation (2).

The city fixed effect method was adopted to estimate coefficients of trans-log production function in Equation (2). According to the parameter estimation results of partial linear coefficient model (

Table 2. Parameter estimation of trans-log price distortion model.

Coef.	Coef. Value	Std. Err.	Coef.	Coef. Value	Std. Err.
${\beta }_0$	−0.675	0.628	${\beta }_8$	−0.044	0.096
	(−1.07)			(−0.46)
${\beta }_1$	2.230 ***	0.348	${\beta }_9$	0.072 ***	0.026
	(6.40)			(2.74)
${\beta }_2$	−1.522 ***	0.288	${\beta }_{10}$	0.022 ***	0.011
	(−5.28)			(2.01)
${\beta }_3$	0.648 ***	0.151	${\beta }_{11}$	−0.010	0.009
	(4.28)			(−1.17)
${\beta }_4$	0.384 ***	0.089	${\beta }_{12}$	−0.002	0.004
	(4.34)			(−0.58)
${\beta }_5$	−0.084 ***	0.039	${\beta }_{13}$	0.038	0.038
	(−2.16)			(1.00)
${\beta }_6$	−0.040	0.041	${\beta }_{14}$	−0.005 ***	0.001
	(−0.98)			(−7.30)
${\beta }_7$	−0.473 ***	0.105
	(−4.51)

Note: z value is in the parentheses. *** is the significance levels of 1%.

), the regression coefficients of most variables are significant. Therefore, the model is reliable and could be used to measure the marginal production and price distortion of energy.

The coefficients in Table 2 are calculated to obtain the estimated value of energy output elasticity in each period. On this basis, Equation (8) is used to estimate the marginal output of energy in each city. Finally, Equation (9) is used to estimate the degree of distorted price, and

Table 3. Energy price distortion of China’s EIIs at city level.

City	Energy Price Distortion	City	Energy Price Distortion
Beijing	0.61	Qingdao	−0.473
Tianjin	0.706	Zhengzhou	−0.479
Shijiazhuang	−0.217	Wuhan	0.709
Taiyuan	0.327	Changsha	−0.286
Hohhot	−0.453	Guangzhou	−0.571
Shenyang	0.203	Shenzhen	0.026
Dalian	−0.315	Nanning	−0.536
Changchun	−0.811	Chongqing	−0.285
Harbin	−0.384	Chengdu	0.352
Shanghai	0.11	Guiyang	0.091
Nanjing	0.372	Kunming	−0.511
Hangzhou	−0.614	Xi’an	−0.587
Ningbo	−0.185	Lanzhou	−0.337
Hefei	−0.596	Xining	−0.617
Fuzhou	−0.282	Yinchuan	0.847
Xiamen	−0.369	Urumqi	−0.207
Nanchang	−0.712	Average	−0.175
Jinan	−0.483

reports the results in detail.

Although the degree of distortion was different in cities, China’s EIIs faced certain EPD. The estimating result was similar when Tan et al. [43] adopted the profit function method. The difference between the two lies in the selection of energy price indicators. The former used raw material, fuel, and electricity purchase price indexes to represent energy prices, which would cause measurement errors and cannot reflect energy transaction prices. In this study, EPD is defined as the extent to which the real price deviates from the marginal output, and the production function is used to measure the marginal output. In order to reflect the real energy cost, this paper took the price of energy products including coal, oil, and electricity to integrate the price index, which could reflect the real distorted level.

The estimating results show that there is regional heterogeneity in EPD, which is consistent with the conclusion of Sha et al. [7]. However, the former used the marginal opportunity cost pricing method to calculate the theoretical price. Because the marginal analysis requires that the independent variables are carried out continuously and gradually, it does not meet the actual conditions. In this paper, the law of production function is chosen to follow the production activities of the factors. The fundamental reason of heterogeneity lies in the imbalance of regional economic development [7]. On average, China’s EIIs in most cities faced negative EPD, which means that energy prices are underestimated and EIIs will input more energy. Seen from city differences, the highest positive price distortion was in Yinchuan (0.847). Because Yinchuan’s energy consumption structure is dominated by coal, the high coal price leads to the high energy price. The highest negative EPD was found in Changchun (−0.811), an important city in the old industrial base of northeast China. With a high proportion of national controlled enterprises in Changchun, the city was characteristics with the slow market-oriented reform of the energy market, and so the highest EPD. The lowest degree of negative distortion was found in Ningbo (−0.185), which is located in eastern Yangtze River Delta. In Ningbo’s EIIs, differential electricity prices have been implemented to improve the resource price formation mechanism; production factors, government procurement, and public resources have been gradually allocated by the market. The lowest degree of positive distortion was found in Shenzhen (0.026), with the highest economic openness and the first batch of electricity price reform pilot projects.

Furthermore, in order to catch the aggregation characteristics of EPD, the changes of EPD in representative urban agglomerations were described in

Table 4. The characteristics of energy price distortion in urban agglomerations from 2003 to 2019.

	2003	2005	2007	2009	2011	2013	2015	2017	2019	AVE
Average energy price distortion of EIIs	−0.555	−0.375	−0.365	−0.298	−0.156	−0.112	−0.105	0.114	0.184	−0.175
BTH	−0.475	−0.243	−0.087	0.108	0.730	1.151	0.569	0.568	0.901	0.366
YRD	−0.529	−0.407	−0.371	−0.263	−0.053	−0.311	−0.208	−0.235	−0.161	−0.183
PRD	−0.613	−0.629	−0.432	−0.122	−0.491	−0.353	−0.352	1.055	−0.295	−0.314
MYR	−0.514	−0.220	−0.250	−0.374	−0.162	0.186	0.253	0.867	−0.042	−0.070

and Figure 1. During the studying period, EPD eased from −0.555 in 2003 to 0.184 in 2019. It shows that energy market reform has been gradually and effectively implemented, which benefited from the policy of price mechanism reform during the 13th Five-Year Plan period. From the empirical results, the distortion trend of energy prices in urban agglomerations is roughly the same as that of average energy prices, showing a state of fluctuation and rising. Different from the other urban agglomerations, it is important to note that the positive distortion in BTH has deepened since 2009. As the BTH is close to the political center of China, the formulation and implementation of relevant policies are more rapid. It is also conducive to the smooth implementation of energy market reform. Therefore, with the sharp rise in the prices of energy and raw materials such as oil, coal and non-ferrous metals, the positive price distortion has been exacerbated. Although the degree of distortion in the other three regions is negative, all of them have been alleviated to varying degrees.

5.2. Estimating the Impacts of Energy Price Distortion

The EPD would affect energy input and energy efficiency. Therefore, after obtaining the index of EPD, the SFA is further adopted to estimate the impacting factors of TFEE (

Table 5. Parameter estimation of stochastic frontier model.

Coef.	Coef. Value	Std. Err.	Coef.	Coef. Value	Std. Err.
${\beta }_0$	0.521	0.619	${\beta }_{12}$	0.007	0.004
	(−0.84)			(−1.56)
${\beta }_1$	1.515 ***	0.351	${\beta }_{13}$	0.054 ***	0.037
	(−4.32)			(−1.45)
${\beta }_2$	−0.371	0.269	${\beta }_{14}$	−0.005 ***	0.001
	(−1.38)			(−6.15)
${\beta }_3$	0.580 ***	0.142	BTH	0.205 ***	0.046
	(−4.08)			(−4.47)
${\beta }_4$	0.243 ***	0.086	YRD	0.240 ***	0.040
	(−2.84)			(−5.95)
${\beta }_5$	−0.147 ***	0.039	PRD	0.283 ***	0.068
	(−3.79)			(−4.17)
${\beta }_6$	0.091 ***	0.041	MYR	0.292 ***	0.048
	(−2.18)			(−6.07)
${\beta }_7$	−0.309 ***	0.109	dis	0.175 ***	0.022
	(−2.83)			(−7.93)
${\beta }_8$	−0.120 *	0.072	ens	−0.340 ***	0.078
	(−1.66)			(−4.35)
${\beta }_9$	0.060 ***	0.026	exp	−1.232 ***	0.185
	(−2.33)			(−6.65)
${\beta }_{10}$	0.022 **	0.011	lninfr	−0.299 ***	0.039
	(−0.74)			(−7.68)
${\beta }_{11}$	−0.019 **	0.008
	(−2.24)

Note: z value is in the parentheses. ***, ** and * are the significance levels of 1%, 5% and 10%, respectively.

).

Table 5 reports the results of SFA model. According to the regression results, the significance of the independent variable is basically controlled within 5%, and the significance of the control variables is controlled within 1%. As most variables in the models are significant, the estimating results of this paper are reliable. It should be noted that in the SFA, the non-efficiency term $U_{it}$ is a negative indicator of efficiency, that is, if the influence of a variable on $U_{it}$ is positive, the influence on efficiency is negative.

The regression coefficient of EPD is positive, which indicates that EPD has an inhibitory effect on energy utilization performance. The finding is consistent with the conclusion drawn by Tan et al. [19]. The difference between the two articles lies only in the definition of price distortion. Specifically, the distorted price of energy increases by 1%, and the TFEE decreases by 0.175%. First, EPD directly affects energy efficiency by affecting resource allocation. EPD causes actual prices to deviate from marginal output, resulting in market allocation failure and resource waste [3]. However, due to price control, energy prices in China are controlled at lower prices than in a perfectly competitive market. On the other hand, EPD indirectly affects energy efficiency by affecting technological innovation and energy consumption structure [7]. Technological innovation is one of the most effective ways to improve energy efficiency [44]. EPD means that lower costs are input for enterprises to obtain production materials, which reduces the enthusiasm of producers to carry out technological research and development. In addition, changing in the relative prices in energy products can lead to transition in energy consumption structure, and further affect energy efficiency. Seen from other impacting factors, the coefficients of energy consumption structure, trade dependence, and infrastructure construction coefficient are all negative, which means that optimizing energy consumption structure, promoting foreign trade, and improving infrastructure construction can promote energy efficiency [43,45,46].

The TFEE level of EIIs at the city level can be calculated by Equation (7) through the estimating results of the SFA model (

Table 6. Energy efficiency of China’s EIIs at city level.

City	Energy Efficiency	City	Energy Efficiency
Beijing	0.582	Qingdao	0.894
Tianjin	0.834	Zhengzhou	0.731
Shijiazhuang	0.589	Wuhan	0.550
Taiyuan	0.729	Changsha	0.650
Hohhot	0.697	Guangzhou	0.922
Shenyang	0.732	Shenzhen	0.975
Dalian	0.752	Nanning	0.635
Changchun	0.791	Chongqing	0.533
Harbin	0.571	Chengdu	0.521
Shanghai	0.934	Guiyang	0.544
Nanjing	0.865	Kunming	0.726
Hangzhou	0.873	Xi’an	0.747
Ningbo	0.886	Lanzhou	0.649
Hefei	0.792	Xining	0.515
Fuzhou	0.786	Yinchuan	0.586
Xiamen	0.975	Urumqi	0.753
Nanchang	0.692	Average	0.729
Jinan	0.763

). Energy efficiency of China’s EIIs in different cities is significantly different, which indicates unbalanced regional development. The average degree of energy efficiency is 0.729, showing great potential for efficiency improvement. Xiamen showed the highest energy efficiency (0.975) with the implementation of distributed energy project policy and technological transformation and upgrading. Xining showed the lowest energy efficiency (0.515) with the old extensive growth mode of “high input and low efficiency”.

Table 7. Energy efficiency of China’s EIIs in representative urban agglomerations.

	2003	2005	2007	2009	2011	2013	2015	2017	2019	Average
Average energy efficiency of EIIs	0.669	0.718	0.756	0.717	0.746	0.740	0.721	0.728	0.752	0.729
BTH	0.700	0.752	0.757	0.683	0.659	0.578	0.603	0.635	0.637	0.668
YRD	0.819	0.902	0.919	0.874	0.881	0.872	0.841	0.867	0.873	0.870
PRD	0.956	0.965	0.962	0.939	0.956	0.947	0.945	0.920	0.950	0.950
MYR	0.563	0.567	0.603	0.621	0.669	0.624	0.619	0.586	0.617	0.614

and Figure 2 show the TFEE level of four selected urban agglomerations. As can been seen, energy efficiency generally shows an upward trend, which is related to the overall institutional environment in which China promotes green ecological development. In order to accelerate the green transition, China has promulgated relevant laws such as ‘Circular Economy Promotion Law’, and ‘Energy Conservation Law’, which highlighted the developing direction of EIIs directly, improved technical support capabilities, and promoted the green development of China’s EIIs. In addition, the EIIs in each urban agglomeration express special features. Compared with the other two urban agglomerations, PRD and YRD show a higher level of economic development, a strong ability to attract foreign investment, more complete infrastructure, and diversified types of energy consumption. BTH is the only urban agglomeration whose energy efficiency was declined during the inspection period. The reason may be correlated with severe urban administrative obstacles and poor policy coordination in the region. In addition, the overall level of economic development in BTH lags behind that in PRD and YRD; the regional infrastructure network has not yet been formed, and the restrictive effect on the process of urban agglomeration economic integration is still obvious. MYR is in the middle stage of urban agglomerations development; the integrated development mechanism of urban agglomerations needs to be improved. Although enterprises in MYR have received technology transfer from the eastern regions, the energy efficiency is still relatively lower. Therefore, the energy efficiency in mature urban agglomerations is significantly higher than that in developing urban agglomerations.

6. Conclusions and Policy Proposals

As energy conservation and clean growth in China’s EIIs is extremely urgent, the study analyzed the affecting mechanism of EPD on improving energy efficiency. Based on trans-log production function model, the distorted energy price at city level was estimated first. Following this, the direct and indirect impact of price distortion was further estimated by SFA model. Empirical results show that: (1)The average EPD index China’s EIIs faced was −0.175, and had been eased overall (from −0.555 in 2003 to 0.184 in 2019); (2) The negative distortion means that energy prices were underestimated in most cities and showed obviously heterogeneous characteristics; (3) During the studying period, TFEE in EIIs showed an upward trend (from 0.669 in 2003 to 0.752 in 2019), and the average energy efficiency was 0.729; (4) The development of urban agglomerations had a significant impact on energy efficiency. The more mature the urban agglomeration system, the higher the efficiency; and (5) EPD showed an obvious inhibitory effect on energy utilization performance, and energy efficiency would increase by 0.175% for 1% cut of EPD. Meanwhile, the increase in energy consumption structure, trade dependence, and infrastructure construction had a positive effect on energy efficiency.

Based on the conclusions, the following suggestions for improving energy efficiency in EIIs are proposed:

(1)

Promoting market-oriented pricing for energy products.

The purpose of energy market reform is to reduce the direct intervention of the government in the energy market, make the market become the leading force of resource allocation, and ease EPD. Therefore, the government needs to ease the control on the energy market and encourage active participation of energy markets. For EIIs, the limit on the price adjustment range of refined oil products should be removed, the price adjustment period should be shortened; more experimental policies such as industrial electricity price adjustment could be implemented to further optimize the production process to consider environmental external costs. The role of the government should be positioned in the market supervision to ensure the market-oriented pricing.

(2)

Improving energy efficiency based on urban heterogeneity.

The level of energy utilization shows characteristics of urban heterogeneity, and the policies for cities to improve energy efficiency in EIIs should be different. Western cities such as Xining have obvious advantages in energy resources, with abundant new energy resources such as solar energy and biomass energy. Therefore, western cities can reduce primary energy consumption by developing clean energy. Then, cutting backward production capacities could help enterprises to change production mode; studying and imitating policies should be important for low-efficiency cities to learn techniques and gain experience in improving energy efficiency. Cities with high energy efficiency should continuously adjust industrial structure and implement technological innovation to seize the forefront of world industrial development.

(3)

Relying on the advantages of urban agglomerations to improve energy efficiency.

Compared with other urban agglomerations, BTH needs to break the restriction of administrative division on resource allocation system. In addition, the government should improve the infrastructure of the entire region to improve the efficiency of resource allocation. For MYR, guiding the urbanization process of related cities and promoting the complementary resource, industrial collaboration, and interactive development of cities should be effective ways to improve the energy utilization level and reduce energy inputs in EIIs. The EIIs in YRD and PRD presented relatively high efficiency. However, it is vital to improve information infrastructure, enhance the exchange capacity of inter-city internet, and realize the mutual sharing of information. Besides that, energy intensive enterprises should also innovate technological capabilities to maintain their leading position.

(4)

Improving energy efficiency in a multi-pronged manner.

As energy efficiency is affected by a series of economic factors, it is necessary to consider a multi-pronged approach to improve energy efficiency in China’s EIIs, such as improving energy consumption structure, enlarging foreign trade, improving infrastructure construction, and so on. First, the government should encourage enterprises to use clean new energy to increase the proportion of non-fossil energy consumption. In addition, various forms of biomass energy and geothermal energy should be developed according to regional advantages. Second, enlarging foreign trade is definitely helpful for energy saving and clean production. Third, it is necessary to build a comprehensive transportation hub and improve the construction of the highway network to activate the market. Although market-oriented reform is of great importance to influence energy input and utilization, more attention should be paid to improving energy utilization performance in China’s EIIs from the supply and demand side of energy products.