Total factor energy efficiency in regions of China: An empirical analysis on SBM-DEA model with undesired generation

3.1.1 Energy efficiency measurement

Data Envelopment Analysis (DEA), a non-parametric technical efficiency analysis method, was first proposed by the American Charners, Cooper and Rhodes in 1978. DEA has a wide range of applications and relatively simple principles (Tinbergen, 1942). Especially when analyzing the situation of multiple inputs and multiple outputs, DEA has unparalleled special advantages. So the paper will adopt a decision making-unit (DMU) that measures multiple inputs and outputs. That is called Non-directional, non-radial SBM—DEA model (Tone, 2001; Olmos et al., 2012). The traditional and basic DEA model includes CCR model (Constant Return Scale, CRS) and BBC model (Variable Return Scale, VRS). Those two models are tools for measuring and evaluating the efficiency of DMU with multiple-input, multiple-output, and the same types.$$\mathrm{m}\mathrm{i}\mathrm{n}\rho =\theta$$

In the equation (1), θ represents the efficiency value of the jth decision unit, and 0 < θ < 1. When θ $=$ 1, it is the optimal solution, indicating that the decision unit (${\mathrm{D}\mathrm{M}\mathrm{U}}_{\mathrm{j}}$) is in a relatively valid state at this time. The BBC model is based on the CCR model to increase the constraint ${\sum }_{\mathrm{j}=1}^{\mathrm{k}}{\lambda }_{\mathrm{j}}=1(\lambda \ge 0)$. Both CCR and BBC models take radial and angular measures, Tone (2001) proposed a non-radial, non-angled, slack-based measure (SBM) efficiency assessment model that can improve radial (input–output proportional changes to achieve effective) models that are not considered for input–output slack problem (The DMU has invested too much or the output is too little to cause invalidity). That is, if there is excessive input or insufficient output, using the radial DEA model to measure factor efficiency will result in an overestimation of the efficiency of the DEA model; if there are multiple aspects of the input or output of the evaluation object, the use of the angle DEA model may produce deviations in the efficiency measurement results (Lin and Tan, 2016). Based on formula (1), SBM model adds ${\mathrm{S}}_{\mathrm{n}}^{\mathrm{x}}$to indicate the excess amount of input and ${\mathrm{S}}_{\mathrm{m}}^{\mathrm{y}}$indicates the deficiency of output, which is the slack variable considered by SBM model. At this time, the efficiency evaluation model of ${\mathrm{D}\mathrm{M}\mathrm{U}}_{\mathrm{k}}$ could be expressed as:$${\rho }^{\ast }=\mathrm{m}\mathrm{i}\mathrm{n}\frac{1-\frac{1}{\mathrm{N}}{\sum }_1^{\mathrm{N}}\frac{{\mathrm{s}}_{\mathrm{n}}^{\mathrm{x}}}{{\mathrm{x}}_{\mathrm{k}\mathrm{n}}^{\mathrm{t}}}}{1+\frac{1}{\mathrm{M}}{\sum }_1^{\mathrm{M}}\frac{{\mathrm{s}}_{\mathrm{m}}^{\mathrm{y}}}{{\mathrm{y}}_{\mathrm{k}\mathrm{m}}^{\mathrm{t}}}}$$

Among them, ${\mathrm{x}}_{\mathrm{k}\mathrm{n}}^{\mathrm{t}},{\mathrm{y}}_{\mathrm{k}\mathrm{m}}^{\mathrm{t}}$ is the input–output value of period t of the production unit, ${\mathrm{S}}_{\mathrm{n}}^{\mathrm{x}},{\mathrm{S}}_{\mathrm{m}}^{\mathrm{y}}$represents the slack vector of the input–output (Patterson, 1996). Tone proved that it is technically effective when the slack amount of the CCR model is zero and the efficiency value is greater than or equal to the SBM efficiency value. With the gradual deepening of the study of TFEE, Tone built an SBM model with undesired outputs in 2003:$${\rho }^{\ast }=\mathrm{m}\mathrm{i}\mathrm{n}\frac{1-\frac{1}{\mathrm{N}}{\sum }_1^{\mathrm{N}}\frac{{\mathrm{s}}_{\mathrm{n}}^{\mathrm{x}}}{{\mathrm{x}}_{\mathrm{k}\mathrm{n}}^{\mathrm{t}}}}{1+\frac{1}{\mathrm{M}+1}({\sum }_1^{\mathrm{M}}\frac{{\mathrm{s}}_{\mathrm{m}}^{\mathrm{y}}}{{\mathrm{y}}_{\mathrm{k}\mathrm{m}}^{\mathrm{t}}}+{\sum }_1^{\mathrm{I}}\frac{{\mathrm{s}}_{\mathrm{i}}^{\mathrm{b}}}{{\mathrm{b}}_{\mathrm{k}\mathrm{i}}^{\mathrm{t}}})}$$

Equation (3) is an SBM—DEA model with constant scale returns and contains undesired outputs. ${\mathrm{x}}_{\mathrm{k}\mathrm{n}}^{\mathrm{t}}{,\mathrm{y}}_{\mathrm{k}\mathrm{m}}^{\mathrm{t}},{\mathrm{b}}_{\mathrm{k}\mathrm{i}}^{\mathrm{t}}$ are input and output values in period t, ${\mathrm{S}}_{\mathrm{n}}^{\mathrm{x}},{\mathrm{S}}_{\mathrm{m}}^{\mathrm{y}},{\mathrm{S}}_{\mathrm{i}}^{\mathrm{b}}$is a slack variable of input–output. When these variables are greater than or equal to 0, they indicate excessive use of energy inputs, underproduction of expected outputs, and excessive emissions of undesirable outputs. The objective function $\rho$ is strictly decreasing with respect to the slack variable (Kuosmanen, 2012; Lei, 2010; Li and Cheng, 2008). The value of $\rho$is in the range of 0 to 1, and it can reach 1, when $\rho =1$, the corresponding ${\mathrm{S}}_{\mathrm{n}}^{\mathrm{x}},{\mathrm{S}}_{\mathrm{m}}^{\mathrm{y}},{\mathrm{S}}_{\mathrm{i}}^{\mathrm{b}}$ are 0, indicating that the decision unit is fully effective. When the ρ value is<1, it also shows that there is energy waste in the decision-making unit and the efficiency is lost (Li, 2012; Ma, 2017; O’Donnell et al., 2008). The input or output can be further improved. The difference between formula (3) and the basic formula (1) is that slack variables are added to the objective function. While solving the problems of input and output relaxation, the problems associated with unintended output could also be solved.

3.1.2 Spatial correlation test

Spatial autocorrelation is a spatial statistical method, which is mainly used to verify the interactions among regions. Among them, the global Moran index ($\mathit{Mora}{n}^{\prime }I$) is a commonly used spatial autocorrelation method (Honma, 2014). Its calculation formula is as follows:

In the formula ${\mathrm{S}}^2$=$\frac{1}{\mathrm{n}}{\sum }_{\mathrm{i}=1}^{\mathrm{n}}\left({\mathrm{E}}_{\mathrm{i}}-\stackrel{-}{\mathrm{E}}\right)$ , $\stackrel{-}{\mathrm{E}}$=${\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{E}}_{\mathrm{i}}$, S is the total factor energy efficiency value. Standard deviation, i and j denote the i-th and j-th provinces, ${\mathrm{E}}_{\mathrm{i}},{\mathrm{E}}_{\mathrm{j}}$ represent observations in province i, j. In this paper, they represent the total factor energy efficiency of the provinces respectively. ${\mathrm{W}}_{\mathrm{i}\mathrm{j}}$ is the (i, j) element of the binary contiguous space weight matrix. When the i-th province shares the common border with the j-th governorate, they are considered to be adjacent and named the number 1, that is${\mathrm{W}}_{\mathrm{i}\mathrm{j}}$ = 1; When the i-th region and the j-th region do not have a common boundary, they are considered non-adjacent and assigned the number 0, that is, ${\mathrm{W}}_{\mathrm{i}\mathrm{j}}$ = 0. The value of Moran^’ I is between (-1, 1), and Moran^’ I > 0 indicates positive spatial correlation among regions, which shows that provinces with higher total factor energy efficiency are adjacent, and provinces with lower total factor energy efficiency are adjacent to provinces with the same situation (Sun, 2002; Wang et al., 2019). Moran^’ I < 0 indicates negative spatial correlation between regions, which shows that provinces with higher total factor energy efficiency are surrounded by provinces with lower ones, or provinces with lower efficiency are surrounded by higher ones (Borozan and Djula, 2018). Moran^’ I = 0 indicates that there is no spatial correlation between regions, which shows that total factor energy efficiency values in provinces have nothing to do with each other.

The significance test of ${\mathrm{M}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{n}}^{\text{'}}\mathrm{I}$ is mainly performed by obeying the standard normal distribution Z statistic. Z is calculated as follows:

In the formula $\mathrm{E}\left(\mathrm{I}\right)=-\frac{1}{\mathrm{n}-1}$,

${\mathrm{s}}^2\mathrm{d}=\mathrm{V}\mathrm{A}\mathrm{R}\left(\mathrm{I}\right)=\frac{{\mathrm{n}}^2{\mathrm{w}}_1+\mathrm{n}{\mathrm{w}}_2+3{\mathrm{w}}_0^2}{{\mathrm{w}}_0^2({\mathrm{n}}^2-1)}$,

${\mathrm{w}}_0={\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\sum }_{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{w}}_{\mathrm{i}\mathrm{j}},{\mathrm{w}}_1=\frac{1}{2}{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\sum }_{\mathrm{j}=1}^{\mathrm{n}}{({\mathrm{w}}_{\mathrm{i}\mathrm{j}}+{\mathrm{w}}_{\mathrm{i}\mathrm{j}})}^2,{\mathrm{w}}_2$=$\sum {({\mathrm{w}}_{\mathrm{i}\bullet }+{\mathrm{w}}_{\bullet \mathrm{j}})}^2$.

3.2.1 Data sources

This paper uses the panel data of 30 provinces (without Tibet because it lacks energy data) and cities in Mainland China for the period of 2005–2016 (Borozan et al., 2018; Brian and Bengt, 2010). In this process, it learns from the concrete ideas of the eight integrated economic zones of the Development Research Center of the State Council, divides the 30 provinces and cities in the sample, and explores the differences in the energy efficiency between regions and the correlations between provinces in one region (Ceylan and Gunay, 2010). In the measurement of total factor energy efficiency, the data used are all derived from the China Statistical Yearbook of the “China Statistical Yearbook 2005” to the “China Statistical Yearbook 2017” for 12 years, the “2016 China Energy Statistical Yearbook”, and Statistical Yearbook in various provinces and cities during 2005–2017 years, and some other data are supplemented through the website of the National Bureau of Statistics and the websites of provincial and municipal statistics bureaus (Chen and Cheng, 2010).

3.2.2 Variable selection

First, selects the input indicators.

3.2.3 Second, selects the output indicators.

4.1.1 Analysis of time dimension difference characteristics

The time dimension mainly analyzes changes in the total factor energy efficiency from 2005 to 2016 across China. The results are shown in Table 2.

From Table 2, the average annual total factor energy measurement value in China for 12 years is only 0.4559 under the consideration of environmental constraints. With the existing technology and the constant investment scale, there is still a 50% increase in this value (Zhang, 2014). This provides a theoretical upside for the further transformation and upgrading of China’s energy production capacity and the reform of the supply side. Fig. 1 shows the changes of energy efficiency over time in the eight economic zones, and the average value of the national energy efficiency measurement of total factors is transformed into Fig. 2.

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Fig. 1

The trend of average energy efficiency of all factors in China from 2005 to 2016.

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Fig. 2

Trends of total factor energy efficiency values in the eight regions.

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In Fig. 1, the overall situation is still consistent with the National Energy Efficiency Trends Chart. The Southern Coastal Economic Zone, Eastern Coastal Economic Zone, and the Northern Coastal Economic Zone are above the mean curve. The integrated economic zone in the middle reaches of the Yangtze River and the Northeast Comprehensive Economic Zone are below the average. Southwest Comprehensive Economic Zone, the Yellow River Integrated Economic Zone, and Northwest Comprehensive Economic Zone are far below the average curve, which shows that the energy efficiency of these areas is even higher. From the curve in the Fig. 2, the southern coastal economic zone of China has experienced a significant decline in 2008, and the overall situation is still at a relatively high level. At the same time, there was a slight increase in 2009 in the Middle Yangtze River Economic Zone and the Southwestern Comprehensive Economic Zone.

At the same time, there was a slight increase in 2009 in the Middle Yangtze River Economic Zone and the Southwestern Comprehensive Economic Zone. According to the data, in 2009, the expected output of these provinces is that the increase in GDP is growing faster than the input, and the undesired output of carbon dioxide and sulfur dioxide emissions is relatively reduced. The Northeast region has been declining from 2005 to 2016. It shows that although there is support for the policy of northeast old industrial bases, the northeast region may not follow the green economic development model very well, and although the trend of economic regression has changed, it also sacrifices local resources and environment.

4.1.2 Analysis of spatial dimension difference characteristics

The spatial dimension mainly discusses the spatial differences in the energy efficiency values of eight regions during 2005–2016 to explore the regional differences under environmental constraints. China has significant differences in geographical conditions, resource endowments and other situations. (Fig. 3).

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Fig. 3

Diagram of total factor energy efficiency in the eight regions.

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From Fig. 3, the TFEE of the eastern coastal economic zone and the southern coastal economic zone are relatively high, going 0.7379 and 0.7266 respectively. That is due to the fact that cities in the southeastern coastal areas have developed economies with a relatively high level of openness. At the same time, they have high levels of industrial integration, advanced science and technology, and ample capacity for innovation. The northern coastal integrated economic zone reached 0.6024, mainly because the northern coast includes Beijing, the capital city of China. At the same time there is the coastal city of Tianjin, which has also higher value than the national average of 0.4753. However, the northern coast is not the highest one in the eight regions, mainly because the northern coast also includes Hebei Province and Shandong Province. Although these two provinces have a relatively high level of economic development, they are also accompanied by higher investment and pollution. In particular, Hebei Province has moved into many heavy industrial enterprises in recent years, causing an increase in undesired output. The total factor energy efficiency of the integrated economic zone in the middle reaches of the Yangtze River is 0.4239, which is lower than the national average, followed by the Northeast Comprehensive Economic Zone. It also shows that there are shortages in terms of factors for production such as capital, labor, and technology research and development. The rejuvenation of traditional old industrial bases and measures for the rise of central China are not obvious in the Northeast and the middle and lower reaches of the Yangtze River in the short term or in some important cities. In particular, the Northeast Economic Zone has historical problems in ideology, concepts, and institutional mechanisms have not been solved innovatively, resulting in the failure of improvement in the energy efficiency of all factors. The comprehensive economic zone in the middle Yellow River and the Southwest, Northwest have energy efficiency values below 0.4, and there is room for improvement of 60%. There is still a large gap between the energy efficiency of the region and the southeast coastal areas’. This is related to the original economic system in the west and the transfer of some polluting enterprises. Above all, the spatial changes in energy efficiency values in the eight economic regions of China are: Eastern Coastal Comprehensive Economic Zone Southern Coastal Economic Zone > Northern Coastal Integrated Economic Zone > Middle Yangtze River Integrated Economic Zone > Northeast Integrated Economic Zone > Greater Southwest Comprehensive Economic Zone > Middle Yellow River Integrated Economic Zone > Greater Northwest Comprehensive Economic Zone. It shows a clear spatial aggregate distribution