Impact of spatial misallocation of electric power resources on economic efficiency and carbon emissions in China

The relationship between resource misallocation and productivity has become a hot topic in recent years, but few studies examined the impact of spatial misallocation of electric power resources (SMEPRs) on economic efficiency and carbon emissions. Here, we constructed a calculation model of SMEPRs that can measure both the misallocation degree and direction and uncovered the spatiotemporal evolvement mechanism of SMEPRs. On this basis, we explored the impact of SMEPRs on regional economic efficiency and carbon emissions using panel data from 29 provinces in China from 1988 to 2017. The results demonstrate that the high level of SMEPRs in China shows complex spatiotemporal characteristics and significantly affects the regional economic efficiency and carbon emissions. Specifically speaking, first, SMEPRs present the characteristics of the coexistence of excessive and insufficient allocation among provinces and regions, the increasing extent of misallocation in the eastern and western regions, and the gradual decline in the central region; second, SMEPRs have a strong negative effect on the regional economic efficiency and carbon emissions by affecting regional industrial structures, which indicates that SMEPRs are an important factor restricting the high-quality development of regional economies. The research is conducive to the development of resource misallocation theory. Moreover, the research observations offer fresh insights to upgrading the high-quality and green development of China’s power sector and promoting regional economic transformation and ecological sustainability.


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Since the reform and opening-up policies were implemented, China has experienced 40 years of rapid growth, and 26 its economy has become the second-largest in the world. China accounts for more than 30% of global economic growth 27 and has increasingly become a driving force for growth (Freeman, 2019). However, the presence of a high level of 28 economic growth does not necessarily mean that high-quality economic development is taking place. At present, 29 problems such as extensive economic growth, unbalanced regional development, and serious environmental pollution 30 still plague China's economic and social development, which largely constrains the sustainability of economic growth 31 (Xu and Tan, 2020;Zhou et al., 2020;Wu et al., 2018). As such, the report of the 19th National Congress of the 32 Communist Party of China put forward the concept of high-quality development. And this has become the foundation of 33 China's economic and social development in the new era. This also means that China has shifted from pursuing the 34 "high-speed" economic growth of the past to focusing on "high-quality" economic development. Both the classic 35 theories of development economics and the latest research results show that the effectiveness of resource allocation is a 36 key factor affecting the likelihood of realizing high-quality development (Kong et al., 2021). The misallocation of 37 resources across regions, industries, and various sectors leads to inefficient resource allocation and affects the 38 short-term total output. It also affects the long-term output combination of the economy and seriously challenges the 39 sustainability of economic growth (Hsieh and Klenow, 2009). As a country in transition, China has been confronted 40 with the serious problem of spatial misallocation of resources. And this is due to the existence of factors such as 41 regional market segmentation, government intervention, and enterprise ownership differences. In particular, electric 42 power resources are indispensable production factors to satisfy the development of all sectors of the national economy. 43 Since the power system reform in 2015, China has made some achievements in the construction of the power resource 44 market. For example, the power supply structure has been improved, and the power production capacity has been 45 controlled. Nevertheless, the market-oriented pricing and allocation mechanism of electric power resources have not 46 been realized. Meanwhile, thermal power generation is still the main mode of power production in China, which is the 47 main cause of air pollution and carbon dioxide emissions . Moreover, in the critical period of China's 48 high-quality economic development and the transformation of old and new kinetic energy, the allocation of electric 49 power resources is deserved to be discussed. Moreover, this has important theoretical and practical significance for 50 improving the spatial allocation efficiency of electric power resources and realizing the coordinated development of the 51 regional economy (Zheng et al., 2020). 52 In recent years, given the adverse effects of spatial resource misallocation, scholars have carried out many fruitful 53 discussions on the ideal method for measuring it (Hsieh and Klenow, 2009;Chen and Hu, 2011), its formation 54 mechanisms (Haley et al., 2013;Wu et al., 2018), and its economic effects (Brandt, 2012;Hao et al., 2020). However, 55 some defects are mainly reflected in the following three issues: First, In terms of research objects, most studies focus on 56 essential production factors such as capital, land, and labor. There are also some studies discussing the problem of 57 energy misallocation (Chu et  Given that this study is focused on SMEPRs, directly measuring the distortion of factor input helps analyze the 153 spatiotemporal heterogeneity of SMEPRs. Accordingly, based on the HK model, we will introduce a discussion of 154 factor misallocation into traditional growth accounting and then construct a model for calculating SMEPRs. 155 3.1.1 Production problems in the Province N 156 We first considered the production problem of the Province N . This paper focuses on the misallocation of electric 157 power resources among provinces, so we assumed that the elasticity of factors is heterogeneous among various 158 provinces. Based on the Cobb-Douglas production function, it was assumed that each province included three factors of 159 production: capital ( K ), labour ( L ), and electric power resources ( E ). Similar to the HK model, we supposed that the 160 factor prices faced by each province were distorted. And the distortion was supposed to be reflected in the form of price 161 taxes. Specifically, the prices of capital, labour, and electric power resources faced by province i in period t would 162 be ( )

Aggregate production functions and resource constraints 178
The total output t Y (the final product of the society is the value of the economy, and the price is 1) of the whole 179 economy during period t is determined by the output of each province: 180 181 where ( ) F  is assumed to be constant returns to scale, therefore, 183 According to Euler's theorem: 184 This implies that, from the perspective of output value, the output value of the whole economy in period t is 186 equal to the total output value of each province. When the total amount of production factors in period t is given 187 exogenously, the following resource constraints exist: 188

Competitive equilibrium 190
Given the above setting, we can define competitive equilibrium with distortions when the productivity levels, 191 distorted "taxes," and the total amount of factors in the economy in period t are all given. K L E P P P P F satisfies the optimal first-order conditions for N provinces, 193 2 Given that goods in China are now much more market-oriented than factors of production, it is assumed that there is no price distortion in the product market.
(3)-(5); the constant returns to scale of the aggregate production function, (6) and (7); and the resource constraints, (9 For further analysis, we defined two types of "distortion coefficients," which are as follows: 197 The absolute distortion coefficient of electric power resources in period t in Province i is defined as follows: In the equilibrium of competition, the output value of Province i in the whole economy during period t is The contribution value of electric power resources weighted by output is the absolute value of the output elasticity of electric power resources in Province i . Then, the relative distortion 202 coefficient of the electric power resource price can be defined as follows: 203 where Eit  is the absolute distortion coefficient of electric power resources in period t in Province i .

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When determining the allocation of factors between provinces, we must note that what matters is the "relative," not 206 the "absolute" distortion of factor prices. This can be observed in optimal conditions. If the absolute distortion of 207 electric power resources in all provinces changes simultaneously, it increases the price of electric power resources by 208 the same proportion. In this case, the relative price of electric power resources in each region remains unchanged, and 209 the allocation of electric power resources among provinces also remains unchanged. Suppose there is no 210 factor-distortion "tax" on the whole economy. In that case, we can assume that the relative distortion of the price of 211 electric power resources in all provinces is 1, meaning no resource misallocation. 212 In the face of actual data, it was impossible to carry out actual measurements due to the lack of important 213 information about the actual price of electric power resources. Therefore, the relative distortion coefficient of electric 214 power resources, which can be obtained from equations (10) and (12), was adopted in this study: 215 the power resource cost in period t in Province i is high. As a result, the actual allocation of electric power 226 resources in such a province is bound to be lower than the theoretical level. And the allocation of electric power 227 resources is insufficient. Through equation (14), we can express the invisible factor price distortion coefficient visibly 228 and establish a connection between factor cost distortion and SMEPRs. 229

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In the face of the infinite growth of human needs, resources are always limited within time and space. In the 231 context of the absolute growth of human needs, the relative insufficiency of resources results in scarcity. A scarcity of 232 resources indicates that the limited resources must be allocated to various fields to achieve the best use. If the limited 233 resources cannot be allocated reasonably and effectively, a situation of low efficiency in economic activities in the 234 medium and long term arises, which hinders the long-term sustainable development of the economy (Hsieh and Klenow,235 2009; Chu et al., 2016). In the specific context of electric power resources, the unreasonable allocation leads to 236 distortions in the electricity market. This may result in the underestimation of electric power prices in areas with 237 abundant power resources. Further, this makes backward production capacity remain profitable and induces regional 238 energy-intensive enterprises to form a lock-in effect of extensive growth. And this weakens the willingness and 239 motivation of enterprises to engage in further technological innovation, which, in turn, restricts the improvement of 240 industrial productivity and aggravates regional environmental pollution. More importantly, as the most significant 241 contributor to carbon emissions, its excessive accumulation inevitably directly leads to the growth of regional carbon 242 emissions (Teng et al., 2017). 243 The former industrial structure theory is often based on the assumption of complete competition in the factor 244 market. The various industrial sectors have the same factor prices, but the resource allocation within each sector is also 245 completely effective. This hypothesis is inconsistent with the actual situation in China, which is in a transitional stage. 246 The unbalanced development of China's three industries and changes in the industrial structure exist alongside resource 247 misallocation. In the specific context of electric power resources, the regional allocation policy of electric power 248 resources changes the comparative advantages of each region. For the sake of long-term sustainable development, 249 energy-intensive firms are more inclined to choose production in areas where the required resources are relatively 250 abundant, and the factor costs are relatively low. The richer the regional power resources, the stronger the intention of 251 electric power consuming enterprises to expand. This is also more attractive to energy-intensive firms, which leads to 252 the excessive accumulation of energy-intensive firms in areas with abundant power resources. In response to electric 253 power shortages, areas with few electric power resources usually prioritize ensuring residential power consumption, 254 while "power rationing" is adopted for industrial firms. And thus force energy-intensive firms to move away. In doing 255 so, such firms become over-aggregated in areas with abundant power resources. In this way, the proportion of industries, 256 especially heavy chemical ones, in the regional economy increases, and the development space of tertiary industries 257 becomes squeezed. A large volume of evidence shows that the share accounted of secondary industries plays a 258 significant role in increasing carbon emissions in various regions (Elliott and Shanshan, 2008). Meanwhile, due to 259 resource dependence, the SMEPRs will inhibit the innovation motivation of enterprises and hinder the upgrading of the 260 industrial structure. And the dependency would further result in inhibiting the promotion of regional economic 261 efficiency and carbon reduction processes. In summary, we propose the following theoretical analysis framework: 262 "spatial misallocation of electric power resources → regional industrial structure → economic efficiency and carbon 263 emissions," as shown in Figure 1.
where i and t represent the province and year, respectively, Control is the control variable,  is the 280 individual effect,  is the time effect, and  is the random disturbance term.  (1 ) The missing data were supplemented by interpolation, and the price variables were deflated to the base period level in 307

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According to the calculation model of SMEPRs, the closer EM is to 1, the smaller the degree of the SMEPRs 309 will be; the more it deviates from 1, the greater the degree of SMEPRs will be. Thus, EM is a moderate index. To

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(1) Economic efficiency 319 TFP comprehensively reflects the overall efficiency of converting input into output over a specific period and can 320 measure provincial economic efficiency well (Feng et al., 2018). For this reason, we used TFP to measure regional 321 economic efficiency. Moreover, the specific calculation method was as follows: The Manquist Index method based on 322 data envelopment analysis (DEA) was used to calculate TFP. Specifically, capital stock, labour input, and electric power 323 consumption were selected as input indicators, and the GDP of each province was selected as the output indicator. The 324 data sources for the relevant indicators were the same as those in Section 4.2.1. 325 (2) Carbon emissions 326 The existing literature has generally used the amount of carbon emissions and carbon emissions intensity (i.e., the 327 amount of carbon emissions per unit of GDP) to characterize carbon emissions. There is currently no direct official data 328 on carbon emissions, which are generally calculated based on statistical data from various provinces. There are three 329 main calculation methods. The first is to use the consumption of coal, oil, natural gas, and other primary energy sources Macao, and Taiwan (China) 5 for empirical analysis. Table 3 reports the descriptive statistics and collinearity test results  371 for the main variables. First, based on the overall level, the mean value of EM is 2.018, indicating that the overall 372 level of SMEPRs is excessive. The mean value of variable LN CEI is 1.684. It is much higher than that of developed 373 countries such as the US and Japan and countries such as Brazil and Mexico, whose per capita GDPs are like that of 374 China (Li and Qin, 2019). This means that the current pressure to reduce carbon emissions in China is still high. The 375 average TFP value is 0.991, which is under 1, indicating that the most efficient production conditions have not been 376 reached overall. Second, from the dispersion level, there are varying degrees of differences in carbon emissions, 377 economic efficiency, and the level of SMEPRs among provinces. This difference also proves that there are many 378 problems in China's rapid development. For example, the difference between the provinces with the highest (Inner 379 Mongolia) and lowest carbon emissions intensity (Hainan) is about 125 times. The difference between the provinces 380 with the highest TFP and the province with the lowest is 5.5 times. The province with the highest degree of 381 over-allocation of electric power resources (Guizhou) has a value of 13.925, while that with the greatest 382 under-allocation (Hainan Province) has only 0.185. Finally, the dispersion coefficients of the control variables are 383 mostly relatively high. This indicates that the levels of urbanization and technological development are significant 384 differences among provinces. And this is consistent with the imbalances in China's regional economic development. 385 Moreover, we investigated the variance expansion factor of the explanatory variables and found that the VIF value of 386 each variable is under 10, and the mean value is under 2. Therefore, it can be concluded that there was no 387 multicollinearity among the explanatory variables. 388 Insert Table 3 here.   term. According to the calculation steps above, the estimated elastic coefficients of each production factor can be 414 obtained, as shown in  The results are shown in Appendix C. The results of SMEPRs was divided into three categories. The spatial allocation 422 degree of electric power resources is greater than or equal to 0 and less than 0.8 is insufficient allocation, greater than or 423 equal to 0.8 and less than 1.2 is reasonable allocation 6 , and greater than or equal to 1.2 is excessive allocation.  in the top 10 in China's total economic output. However, they are also the provincial power grid with the most outgoing 477 power, whose power consumption does not match the economic development. Hebei, Shandong, Henan, and Yunnan are 478 the four provinces that have always remained within a reasonable range. Six provinces have changed from irrational to 479 rational allocation. Heilongjiang, Shanghai, Jiangxi, Shaanxi, and Gansu have changed from excessive to rational 480 allocation, and Jiangsu has changed from insufficient to rational allocation. This mainly stems from the "West-East 481 Power Transmission" project, which has promoted the flow of electric power resources. The provinces that have 482 evolved from rational to irrational allocation include Liaoning, Jilin, and Hunan, and all of which have changed from 483 rational to insufficient allocation. Guangdong went from insufficient to excessive. Given that Guangdong was included 484 in the first batch of reform and opening-up policies in manufacturing provinces, since participating in the "West-East 485 Power Transmission" project, it has become the province with the greatest amount of investment. It has received the 486 most power from the West. 9 Therefore, in the allocation of electric power resources, not only the electric power 487 demand of the province must be considered, but also the province's economic development to avoid over-allocation. 488 Insert Fig. 5 here.

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To investigate the transmission mechanism that SMEPRs affects economic efficiency through the industrial 492 structure, we chose the proportion of the added value of secondary industries to the GDP as the mediator to conduct the 493 mediation effect test. Table 8 reports the two-dimensional fixed-effects estimation results using the panel data model. 494 Wooldridge's "robust Hausman test" was used to select the fixed-or random-effects model. Table 9 reports the test 495 results obtained by bootstrap sampling with TFP as the explained variable and IS as the intermediary variable.

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The regression results in column (1) of Table 7 show that EM harms TFP. Its estimated coefficient is -0.043, but  Table 7 show that the estimated coefficient of EM is 34.652, which is significant 501 at the 1% level. A possible reason for this result is that the electric power price in a specific province can be easily 502 distorted and underestimated when the degree of electric power resources allocation is high. As a result, industrial 503 enterprises, especially energy-intensive ones, are attracted to agglomerate. And the added value of secondary industries 504 increases as a percentage of the GDP. For example, the power resources in Shanxi Province are over-allocated, and the 505 misallocation degree is always serious. Correspondingly, the industrial structure in Shanxi is relatively simple, and the 506 heavy chemical industry accounts for a relatively high proportion of the total. 507 Column (2) of Table 7 shows the regression results after adding the intermediary variables. It can be seen that the 508 estimated coefficient of EM is still negative, but it is not statistically significant. The estimated coefficient of IS is 509 0.0011, which is significant at the 1% level. Previous studies have shown that industrial agglomeration can promote 510 TFP growth to some extent (Geppert et al., 2008). Combined with the results in Table 8, the bootstrap test shows that 511 the mediation effect of electric power resource allocation on TFP through industrial structure is significant. The signs of 512 direct and indirect effects are opposite, but the direct effect EM of TFP is not significant. The result indicates that the 513 impact of the level of power resource allocation on TFP is not direct but is formed through the mediator of industrial 514 structure. In addition, the opposite sign of direct and indirect effects indicates that the excessive allocation of electric 515 power resources inhibits the improvement of TFP. But the industrial structure, as a mediator, weakens the negative 516 impact of the excessive allocation of electric power resources on TFP to some extent. This result is consistent with the 517 conclusion that resource misallocation hinders the improvement of economic efficiency. At the same time, the above 518 results reveal the internal transmission mechanism of resource misallocation affecting TFP. That is, the SMEPRs will 519 inhibit the adequate flow of production factors, and excessive electric power resources will cause the accumulation of 520 energy-intensive enterprises. They often rely excessively on the advantages of electric power resources and lack 521 sufficient motivation to carry out technological innovations, thereby inhibiting the increase in TFP. 522 Insert Tables. 8 and 9 here. 523 524

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To investigate the transmission mechanism underlying how SMEPRs affects carbon emissions through the regional 526 industrial structure, we chose the proportion of the added value of secondary industries to the GDP as the mediator to 527 conduct the mediation effect test. Table 10 reports the two-dimensional fixed-effects estimation results using the panel 528 data model. Wooldridge's "robust Hausman test" was used to select the fixed-or random-effects model. Table 11  529 reports the test results obtained by bootstrap sampling with LNCE and LNCEI as the explained variables and IS 530 as the intermediary variable. 531 The regression results in columns (1) and (3) of Table 9 show that the regression coefficients of LNCE and 532 LNCEI to EM are 2.698 and 2.822, respectively, and they are significant at the 1% level. A possible reason is that 533 the power sector is the largest contributor to carbon emissions, and an excessive accumulation in the sector leads to the 534 growth of regional carbon emissions. The regression results in column (5) of Table 10 show that the estimated 535 coefficient of EM is 34.652, which is significant at the 1% level. Moreover, as shown in columns (2) and (4) of Table   536 10, the regression coefficients of LNCE and LNCEI to EM are 2.182 and 2.370, respectively.  Accordingly, dummy variables were substituted for explanatory variables in the stepwise regression analysis. 561 Table 12 reports the two-dimensional fixed-effects regression results under the ordinary panel data model. The 562 spatial allocation of electric power resources affects TFP, LNCE , and LNCEI through the industrial structure. And 563 the explanatory variable is a dummy variable. In Table 12 Tables 13 and 14. Comparing Tables 8-11 with Tables 13  589 and 14, we found that the signs and significance levels of the regression coefficients of all the variables are consistent 590 with the previous ones. Therefore, the regression results based on the new intermediary variables show that the 591 conclusions of this study are robust. Owing to space limitations, the details are not repeated. 592 Insert Tables. 13 and 14  Based on the fact that the electric power market has not yet been fully market-oriented in China, this paper 597 constructed a calculation model for SMEPRs. The degree, direction and trend of SMEPRs had been analyzed. On this 598 basis, it has empirically investigated the influence and transmission mechanism of SMEPRs with regional economic 599 efficiency and carbon emissions. The main conclusions are as follows. 600 First, the level of SMEPRs in China is relatively high and presents significant spatiotemporal heterogeneity. In 601 terms of spatial dimensions, the average level of SMEPRs is medium-to-high overall. In comparison, the degree of 602 SMEPRs is the highest in the western region, followed by the eastern region, and it is the lowest in the central region. In 603 terms of the time dimension, the fluctuation trend of the average level of SMEPRs from 1988 -2017 was relatively 604 stable. Nevertheless, there was also significant heterogeneity among the regions. Among them, the degree of SMEPRs 605 in the eastern and western regions appeared to be on the rise, while, in the central region, there appears to be a trend of 606 improvement. This conclusion indicates that the governance related to China's electric power resource misallocation 607 problem needs to be implemented following local conditions and trends. 608 Second, SMEPRs has a significant negative impact on regional economic efficiency. But this effect is indirect and 609 mainly occurs through the industrial structure. Specifically, the excessive allocation of electric power resources inhibits 610 the growth of economic efficiency. However, since industrial agglomeration can promote the improvement of TFP, the 611 industrial structure as an intermediary variable weakens the negative impact of the excessive allocation of electric 612 power resources on TFP. This conclusion shows that SMEPRs is an important factor that restricts the high-quality 613 development of regional economies. 614 Third, SMEPRs has a significant direct impact on regional carbon emissions and has an indirect impact through the 615 industrial structure. The more serious the over-allocation of electric power resources is, the higher the proportion of the 616 added value of the secondary industries in GDP. And the regional carbon emissions and carbon emissions intensity will 617 increase accordingly. This suggests that regional industrial layouts and structural optimization should be considered in 618 the governance process of SMEPRs. Furthermore, this should be taken as the focus to improve economic efficiency and 619 reduce carbon emissions. 620

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According to the conclusions of this study, the problem of SMEPRs in China is still serious and will likely 622 continue to be in the future. And it currently has a significant negative impact on regional economic efficiency and 623 carbon emissions. Therefore, we propose the following policy implications. 624 Efforts should be made to continue deepening reforms to the power system and gradually promote a national 625 electricity market. China should strive to break the current inter-provincial monopoly in the electricity market. 626 Moreover, the unrestricted flow and optimal allocation of electric power resources across the country should be 627 promoted. First, it will be necessary to provide a solid platform for achieving cross-regional allocation optimization. In 628 particular, the construction of power grid infrastructure should be accelerated, especially in the construction of ultra 629 high voltage direct current transmission channels and alternating current synchronous power grids. Enhance the 630 transmission capacity of cross-regional power grids. Second, it will be necessary to provide a sound system and 631 mechanism to guarantee the optimal allocation of electric power resources across regions. Concretely, efforts should 632 also be made to establish a national power system and construct power transmission channels and other coordination 633 mechanisms. To accelerate the promotion of the national power resource interconnection and break provincial and 634 regional monopolies. Eventually, a unified, open, and orderly competitive national electricity market system will be 635 formed. Finally, it must be pointed out that cross-regional transactions are restricted by transmission channel capacity 636 constraints and market access restrictions. It would be not easy to achieve a truly unified national electricity market in 637 the short term. Therefore, the government should follow geographical proximity and resource complementarity 638 principles to build several inter-provincial regional electricity markets. The regional electricity market will gradually 639 become integrated, and a unified national electricity market will be formed. technological transformations and upgrades. The backward, inefficient, and environmentally unfriendly industry will be 649 gradually eliminated, and the regional industrial structure will be continuously optimized. For provinces with 650 insufficient power resource allocation (such as Beijing, Tianjin), on the one hand, clean power industries such as wind 651 and photovoltaic power should be actively developed. And distributed photovoltaic facilities should be built according 652 to local conditions. On the other hand, it will be necessary to coordinate the regional industrial layout and fully play to 653 regional advantages. High-end manufacturing with high technology, high information intensity, and strong driving 654 ability should be actively developed to promote regional industrial upgrading and restructuring. 655

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This paper measured the spatial misallocation of electric power resources in China. Furthermore, its spatiotemporal 657 patterns and its impact on economic efficiency and carbon emissions were analyzed. This deepens our understanding of 658 the SMEPRs and its impact, but there are also some limitations. For example, the calculation model of SMEPRs was 659 based on the assumption of constant return to scale, and the results might be sensitive to small changes. In future 660 research, we will try to pay more attention to these problems.                  Spatial misallocation of electric power resources