Inuencing Factors Analysis on Provincial Difference of Rural Energy Eciency in China Employing Super Eciency SBM Model and Global Malmquist-Luenberger Index

11 Given the current circumstance of increasingly severe resource and environmental 12 deterioration, the progress of Chinese rural energy efficiency has a remarkable 13 impression on Chinese future high - quality development. Energy consumption in rural 14 areas accounts for a considerable proportion, so it is imperative to make a specific and 15 accurate assessment of rural energy efficiency. This paper abandons the traditional 16 method of regional division and separates China into eight economic zones. First of all, 17 this paper applies Super - SBM model to calculate the rural energy efficiency and 18 constructs a Global Malmquist - Luenberger (GML) Index based on 2008 - 2018 panel 19 data. Subsequently, GML is decomposed into technical efficiency change index 20 (GMLEC) and technological progress change index (GMLTC) to analyze green 21 total - factor productivity (GTFP) in rural areas. Eventually, the GML and its 22 decomposition terms of eight economic zones are explained by practicing a cumulative 23 multiplication method from 2008 to 2018. The consequences of employing panel data of region prove that: (1) There is a severe regional imbalance of Chinese rural energy 25 efficiency. (2) The rural energy efficiency in the northwest and southwest (western 26 region) is higher than the Middle Yangtze River and the Middle Yellow River (central 27 region). (3) GMLTC has a significant impact on GTFP.


Introduction 31
With the advancement of the economy and technology, China has constantly shifted 32 from high-speed development to high-quality development. Policymakers continuously 33 pay attention to the significance of sustainable development and have formulated 34 enforceable carbon reduction tactics and targets. China is not only a developing country 35 but also a predominantly agricultural country in the traditional sense. Rural areas 36 account for a large proportion of the country, so it is imperative to make a specific and represent the inputs, desirable outputs, and unexpected outputs, respectively. Can be 112 represented by vectors as ∈ ， ∈ 1 ， ∈ 2 ；x、 、 are matrices； 113 The production possibility set as Eq.(1): 115 Where λ is the non-negative weight vector assigned to input and output, and the SBM 117 model is constructed as follows: 118 Where represents the objective function, and its efficiency value can be larger than 1, 129 refer to inputs, desirable outputs, and undesirable outputs, respectively. 130 The slackness intricacy can be effectively shunned by utilizing the Super-SBM model 131 with undesirable outputs. Consequently, an authentic evaluation is provided by the 132 model, and DMUs are ordered effective. 133 134

Global Malmquist-Luenberger Index 135
The Malmquist index is one of the most well-known methods to measure productivity 136 variations. Sten Malmquist (Malmquist, 1953) initially recommended this approach to 137 investigate the fluctuations in consumption over a while. The Malmquist index proposal 9 had a strong response at that time, but it was unexpected that there was almost no 139 associated investigation for quite an extended time after that. According to (Chung et al.,140 1997) the ML productivity index from t period to t+1 period can be constructed as 141 Eq.(6): 142  ;, 1 ,;  The advantage of the GML principally according to the following four circumstances: 157 First of all, GML refers to the equivalent frontier and determines a sole Malmquist 158 index. Furthermore, the computation of efficiency variation still exerts its boundaries, 159 the efficiency values obtained are comparable. Thirdly, the evaluated DMU must be 160 incorporated in the global production possibility set, it does not exist the situation that 161 VRS without solution. Eventually, the reference of each stage is a mutual frontier, 162 which is transitive and multiplicative. According to Oh (2010), the GML index from t to 163 t+1 defined as: 164 In the Eq.(7), it decomposes GML into GMLEC and GMLTC. If +1 > 1, 166 which signifies that compared with the t period, DMU is closer to the productive 167 frontier in the + 1 period; if +1 > 1, it means that DMU has technological 168 progress in the + 1 period; if +1 > 1, it implies that the rural energy efficiency 169 is progressing. This article employs the GML productivity index to measure the 170 dynamic efficiency of energy efficiency in rural regions of China and discover the 171 factors that can control energy efficiency.

Indicators and data 175
The research intention of this article is the rural districts of 30 provinces in China. 176 The input-output data from 2008 to 2018 are elected as the investigation individuals. 177 According to the data's availability and representativeness, the relevant data come from Where CO2 is the emission of each province, represents all kinds of fossil energy, 191 including raw coal, coke, petrol, kerosene, diesel oil, fuel oil, liquefied petroleum gas 192 (LPG), and natural gas.
is the consumption of type energy, NCV is average low 193  Table 2. 215 Table 3 presents statistics descriptions of the input and output variables.  Table 4. 226 Table 5  The average energy efficiency of rural areas along the southern coastal and eastern 306 coastal is greater than 1 during the research period, it indicates DMUs are perpetually in 307 an effective state. Initially, the temperatures of the two regions are warmer than the 308 northern coast. Hence, these areas consume relatively less energy on heating in winter. 309 Additionally, the economy of the southern coastal and eastern coastal is relatively 310 developed and technical level is comparatively advanced, which promotes the energy 311 efficiency of the local rural areas. On the contrary, the contrast to previous research is 312 Zhejiang province. Preceding researchers have analyzed Zhejiang's energy efficiency 313 from rural and urban fields. Therefore, the performance of energy efficiency is 314 preeminent in Zhejiang. The reason is that city regions have performed an outstanding 315 contribution to raising energy efficiency. Conversely, we only explore rural areas' 316 aspects, excluding the influence of city on the outcomes, and conclude that the rural 317 energy efficiency of Zhejiang is relatively poor. This conclusion is different from Feng 318 and Wang (2017). We notice that the rural energy efficiency decreases in Zhejiang 319 province, resulting from output and input joint action. From the input perspective, the 320 gap between urban and rural areas is increasingly widening with the economy's 321 development, rural living situations and social welfare are far inferior to those of urban 322 residents, which leads to a large number of rural labor force flow to urban regions. As a 323 result, the productivity in rural areas is insufficient, and population aging is terrible. 324 From the point of output, Zhejiang has more numerous rural coastal areas, and fishing is 325 the leading industry. As an essential component of agriculture, the fishery has a 326 significant industrialization degree and more frequent machinery utilization rate. 327 Simultaneously, the fishery is deeply dependent on energy and resources and 328 significantly impacts the environment. Consumption of massive resources and energy is 329 the principal reason for numerous undesirable outputs. Fig.5 reveals that diesel oil and 330 LPG account for a considerable proportion of energy expenditure in the rural of 331 consumption needed to obtain each unit of expected output, continually stimulate 334 technological innovation, boost clean energy use, narrow the gap between rural and 335 urban areas, and diminish regional imbalances. 336 337

Dynamic analysis of green total factor productivity in rural areas 338
The GML and its decomposition items of the eight comprehensive economic zones 339 are displayed in Table 6. The GMLEC values of the northern coastal, eastern coastal 340 and southern coastal areas fluctuate around 1. Notably, during the entire investigation 341 period (2008-2018), GMLEC=1 indicates that the rural energy efficiency has been in an 342 effective state in the southern coastal. Additionally, GMLTC dramatically influences 343 GML in southern coastal. Therefore, when GMLTC is more massive than 1, GML is 344 more numerous than 1. Likewise, the eastern and northern coastal have a similar nature, 345 which demonstrates that technological progress is the foremost factor affecting rural 346 energy efficiency in Chinese coastal zones (Feng and Wang, 2017;Ouyang et al., 2021). 347 During the entire research phase, the GMLTC of the northeast was higher than 1. The decomposition term of GML is calculated similarly. The trend of GML and its 366 decomposition components in each area are exhibited in Fig.6. 367 According to the Eleventh Five-Year Plan's division method, China is divided into 368 eight major economic zones. The innovation of this investigation is that we concentrate on the rural areas of China, 399 and we abandon the traditional method of dividing the east, central and west (east, 400 central, west and northeast) in terms of regional distribution. According to the Eleventh 401 Five-Year Plan's division method, we classify China into eight major economic zones. 402 Moreover, we can discover the similarities and contrasts between regions through a 403 more comprehensive investigation, which can also provide novel ideas for 404

policymakers. 405
We notice that Chinese rural energy efficiency exhibits a decreasing inclination from 406 coastal to inland areas. On the contrary, the changing trend of GTFP manifests a similar 407 fluctuation shape in the southern coastal, the Middle Yangtze River, the Middle Yellow 408 River and southwest economic zones. Another similar fluctuation is presented in the 409 northern coastal, northeast, eastern coastal and northwest economic zones. If we obey 410 the traditional division process, it will lead to incomplete research and then ignore some 411 conclusions, for example, the general judgment that the western region should expose fluctuation trend of GTFP in southwest and northwest regions is discrepant. Likewise, 414 the trends of GTFP in the eastern coastal and southern coastal are not similar. 415 Additionally, we also notice a significant gap between urban and rural areas in Zhejiang 416 province. The research points out that Zhejiang's rural energy efficiency is not excellent 417 in China, and exists excessive energy consumption, this phenomenon is related to the 418 geographical location, sorts of energy consumption and industrial structure of Zhejiang. 419 The conclusion is distinct from preceding research consequences, but Zhejiang performs 420 more satisfying if the input and output of cities are taken into account (Ouyang et al., 421 2021). Consequently, it is meaningful to subdivide China into eight economic zones to 422 consider the regional energy efficiency discrepancies. In order to promote Chinese 423 energy efficiency, policymakers should concentrate on rural areas in the future. Paying 424 more attention to the optimization of energy structure and upgrading of industrial 425 structure in rural areas, enhancing the level of science and technology in agriculture, 426 improving the utilization rate of resources in rural areas, reducing the waste of resources, 427 breaking the original urban-rural pattern, and establishing a system of urban-rural 428 integration while minimizing regional imbalances. 429 One limitation of this paper is that our study only reveals the characteristics of 430 imbalance in China's diverse regions. For future research, we suggest further 431 exploration of spatial interaction and interpreting the interaction mechanism among 432 disparate regions. 433 24 434

Conclusion 435
As we all know, the advancement of a low-carbon economy has become the subject 436 of the eras. We calculate the energy efficiency of rural regions using the Super-SBM (2) The coastal area is subdivided into the northern coast, the eastern coast and the 448 southern coast. With the evolution of the economy and technology, the eastern and 449 southern coasts preserve excellent energy efficiency, and the average energy efficiency 450 is between 1.0 and 1.4. The northern coastal is only slightly better than the northwest 451 and northeast. Although they belong to coastal areas, they exhibit diverse characteristics.
there are remarkable discrepancies in rural energy efficiency and GTFP. Contrasted with 454 the previous studies on energy efficiency, the investigation results about regional 455 imbalances are more impressive, which provides a new idea for policymakers. This kind 456 of investigation idea possesses particular research value and significance. 457 (3) Research on the spatial distribution of rural energy efficiency reveals regional 458 imbalances and urban-rural gaps in China. As a result, rural resources inequality with 459 cities, and numerous laborers and talents flow to cities. Therefore, it is unavoidable to 460 advance the coordinated development of the regional economy, spontaneously support 461 low energy consumption industries, and actively promote cross-regional exchanges and 462 cooperation. 463 (4) The decomposition term of GML index reveals that GMLTC contributes more 464 significantly to promoting GTFP than GMLEC. Availability of data and materials 480 The corresponding data required for emergy value estimation chiefly originates from 481 "Shandong Statistical Yearbook", "China Energy Statistical Yearbook", "China 482 Statistical Yearbook" and the national data website 483 484 Authors Competing Interests 489 The authors declare that they have no competing interests 490