Total‐factor generation performance analysis of China's thermal power industry using meta‐frontier nonradial distance function approach

Thermal power is the main source of China's electricity supply. Improving total‐factor generation performance (TFGP) is essential for the development of this industry in the current deteriorating operating environment. This study adopts the meta‐frontier nonradial direction distance function approach to measure the static and dynamic TFGPs of the thermal power industry in China's 30 provinces in 2011–2019, and then discusses the regional distribution characteristics and the impact factors using spatial econometric model and Tobit regression method, respectively. Empirical results show that: (I) The TFGPs in central and west China are relatively close, but both are remarkably lower than that in east China. (II) The TFGPs in central and west China have generally remained stable since 2011, whereas that in west China has declined mainly because this region is more susceptible to the situation of electricity supply‐demand. (III) A significant spatial positive correlation exists among provincial TFGPs. High TFGP provinces are mostly in the eastern seaboard region and low TFGP provinces are in southwest China. (IV) Economic development, power structure, fuel prices, and environmental regulation have positive impacts on China's TFGP, while the impacts of technological innovation and energy endowment are not significant.

However, thermal power, as an industry with high consumption and high pollution, is difficult to adapt to the current complex business environment. In 2020, thermal power plants consumed 52.15% of China's total coal production, and emitted 29.2% of NO x , 13.3% of particulate matter, and 31.8% of industrial SO 2 . 3 In recent years, China's electric power industry has been experiencing large-scale overcapacity because of the continuous significant investment in power sources and the slowdown in electricity consumption growth. Since 2015, the annual average utilization hours of China's thermal power equipment have always been significantly less than 4500 h, which is usually considered the indicator of electricity supply-demand equilibrium. 4 In addition to the macro power supplydemand situation, the micro-operating environment of thermal power enterprises is also deteriorating. For one thing, with the accumulation of technological progress, scale effect, and learning effect, the generation cost of wind power and photovoltaic power has been rapidly decreasing, and thus, the cost advantage of thermal power is rapidly disappearing. 5 For another, China's energy-related carbon emissions maintained a growth trend in recent years, as shown in Figure 1. 6 The Chinese government has promised to achieve carbon peaking by 2030 and carbon neutrality by 2060. To achieve the aforementioned goals, China officially launched the national carbon trading market in 2021, and thermal power plants were introduced as the first participants. 7 The operation of this market increased the environmental costs of the thermal power industry. Besides, the large-scale market transactions of electricity are forcing the thermal power industry to concede tens of billions of yuan from its annual profits. 8 Under the combined effect of these multiple factors, China's electric power industry is in an unprecedented business plight. Since the second half of 2018, for the first time in the country's history, many thermal power enterprises have successively applied for bankruptcy liquidation. 9 As the external operating environment of China's thermal power industry cannot be fundamentally changed in the foreseeable future, improving generation performance is the key to the survival and development of this industry. Given this, this research measures the static and dynamic generation performance of China's thermal power industry by using a total-factor integrated production framework, identifies the key factors in its improvement, describes the regional distribution characteristics of it, and then offers implications for energy policy adjustment.
The main contributions of the research findings are as follows: (1) The improved nonradial directional distance function (NDDF) combined with the Malmquist index used in this research offers a research framework for the total-factor generation performance (TFGP) analysis of thermal power industry. This framework can not only evaluate the performance level but also explain the evaluation results from the different dimensions.
(2) Combining spatial correlation algorithm with meta-frontier theory, the regional difference in TFGP can be explored. This offers a model foundation for the design of regional differentiated energy policies. (3) The above models are applied to China to find policy implications to improve the TFGP of thermal power industry.
The rest of the paper is structured as follows. Section 2 reviews the studies related to this research. Section 3 introduces the research methods and data sources. Section 4 offers the empirical results, which are discussed in Section 5. Finally, conclusions and policy implications are presented in Section 6.

| China's thermal power generation performance
Given the huge scale of China's thermal power industry and its importance to the socioeconomic system, the generation performance of this industry has attracted extensive attention for a long time. Early studies on this issue concentrated on standard coal consumption rate (consumption amount of standard coal equivalent used to generate 1 kWh of electricity). 10,11 This indicator is usually called generation efficiency and has the capability to measure the level of technology together with management to a certain extent. However, the power generation process uses both energy and nonenergy inputs (e.g., labor and capital). In the complex operating environment, focusing only on energy inputs cannot fully reflect the generation performance of the thermal power industry.
To comprehensively understand the generation performance level of the thermal power industry, more inputs and outputs were involved in the followup studies. Some research concentrates on the analysis of the external factors affecting the generation performance of the thermal power industry. For example, Meng et al. 12 used polynomial functions and partial least squares algorithm to evaluate the impacts of China's market-oriented reforms on the generation efficiency and scale of the thermal power industry. Wang et al. 13 adopted a modified data envelopment analysis (DEA) method combined with the materials balance principle to forecast the possible impacts of pollution taxes on ecological and cost efficiencies of China's thermal power industry. Zhao and Ma, 14 Bai et al., 15 and some other researchers also performed similar investigations. The focus of the above studies is the impacts of certain socioeconomic environment changes on the operation status. However, the complex external business environment faced by the thermal power industry cannot be changed in a short time. Improving power generation performance is the key to the survival and development of this industry. Therefore, some other researchers studied the total-factor production performance of thermal power industry. For example, Wu et al. 16 built an integrated enhanced Russell measure based on DEA to analyze the comprehensive environmental productivity of China's thermal power industry and offered policy implications to guide the industry's green development. Chen and Jin 17 derived a Tornqvist-type productivity index and recommended its application in the productivity measurement of China's thermal power industry to prompt the lowcarbon transformation of this industry. In addition, Wang et al. 18 and Song and Wang 19 also conducted the total-factor productivity analysis of this industry. The total-factor productivity level has the ability to measure the competitiveness of the thermal power industry. However, capital and some other input variables which are used to calculate the total-factor productivity are fixed investment. That is, they cannot be adjusted, especially reduced at least over the short term. This makes the policy implications drawn from the total-factor productivity analysis of this industry usually lack operability. Given this, this research used the TFGP as the core indicator and identified the key directions of its improvement to help China's electric power industry through the present hard time.
Besides, the regional difference is usually ignored by some researchers mentioned above when analyzing the generation performance of China's thermal power industry. 12,[14][15][16] However, because of the difference in economic development level, natural endowment conditions, and other factors, the development pattern of China's thermal power industry varies among regions. [20][21][22] Considering that "provinces as entities" is the main regulation framework in China's electricity sector, 23 this study used provinces as decisionmaking units (DMUs) to investigate the regional difference in the TFGP analysis of China's thermal power industry.

| Performance analysis method
In essence, the calculation of TFGP is a comprehensive evaluation problem of a system with multi-input and multi-output indicators. The DEA model 24 is a traditional method for this issue and has been successfully used in hotels, 25,26 education, 27 finance, 28 and other industrial sectors. However, different from the aforementioned research objects, the thermal power industry has nonnegligible undesirable outputs (e.g., CO 2 ), which should be introduced into the TFGP measurement. This requirement is beyond the ability of the classical DEA model. 29,30 For undesirable output indicators, common approaches include converting the undesirable output into inputs for the production function 31 and converting undesirable output into desirable output, but these methods are inconsistent with production function theory. Another approach is to calculate desirable and undesirable outputs separately and then take their ratios. 32 This approach ignores the interaction between desirable and undesirable outputs. To address the shortcomings of the above methods, Chung et al. 33 proposed a directional distance function (DDF). The combination of DDF and DEA provides a feasible analytical framework for measuring the efficiency of a system that has both desirable and undesirable outputs. 34 Using this idea, some researchers have attempted to evaluate the generation performances of the thermal power industry in China and other countries. 35,36 However, DDF is in essence a radial algorithm. That is, it requires desirable and undesirable outputs to change at the same speed. In this case, when input or/and output has nonzero slack variables, the efficiency calculation deviates from the real level. To overcome the limitations of the radial function, Tone 37 used a slacks-based measure (SBM) to solve the problem of possible computational deviation. However, the SBM was proposed without considering the undesirable output, although it was adopted to calculate the eco-efficiency of China's thermal power plants. 38,39 Another method to address the aforementioned problem is NDDF. 40 This algorithm perfectly overcomes the impact of undesirable outputs on the DEA result and is especially suitable for the performance evaluation of the energy system. 41,42 Thus, this study adopts the idea of NDDF to design the TFGP measurement model of China's thermal power industry.
In view of the heterogeneity among observations, Battese and Rao 43 and O'Donnell et al. 44 proposed an idea to measure the observation efficiencies under the group frontier and meta-frontier, respectively. This idea was used by Walheer, 45 Xi et al., 46 and other research 47,48 to measure the technical gap of different groups. Given this, this research applied the metafrontier NDDF to assess the system efficiency with undesirable outputs, which not only avoids the shortcomings of the radial function, but also reflects the relative performance among different regions. However, this method cannot describe the relationship among different groups, although it can measure their relative performances. Thus, this study introduced the spatial correlation analysis method to explore the geographical distribution characteristics of the TFGP in China's provincial thermal power industry. This method has the capability to construct the relationship between data through spatial location, and then describes the degree of interdependence of things in space. 49 In summary, some literature investigated the TFGP of thermal power performance based on the input-output perspective, but their results cannot clearly demonstrate the key directions of performance improvement. Many other assessments of TFGP applied the SBM method, but ignored the problems of undesirable output and regional heterogeneity. Few literature used the meta-frontier nonradial direction distance function (MNDDF) model to measure the TFGP of the thermal power industry. To refine the research framework and provide more data support for policy formulation, this research measured the static and dynamic TFGP based on the MNDDF method, and calculated the driving indicators of dynamic changes to obtain the improvement directions of TFGP. Then, the spatial distribution characteristics of TFGP were measured by the spatial econometric model and its influencing factors were investigated by the Tobit regression method.

| Meta-frontier nonradial distance function
This research supposes there are N DMUs and each DMU uses capital (K), labor (L), and fossil energy (F) inputs to generate electricity (E) and undesirable output CO 2 (C). The technology production set can be defined as follows: (1) According to the production theory proposed by Fare et al., 34 the technology production needs to meet the following assumptions, including the closed and bounded set (i.e., limited inputs produce limited outputs), strongly disposable inputs and desirable outputs, and weakly disposable and null-jointly of outputs. The technology production set of the thermal power industry defined in Equation (1) is usually expressed by a nonparametric DEA model in empirical analysis. This study assumes the technology production set with constant returns to scale that can be expressed as the following equation: (2) In Equation (2), z n is the strength variable that ensures the production function has convex characteristics. To cope with the undesirable output variable, the NDDF is defined as ( , , , , ; ) = sup{ : (( , , , , ) In Equation (3), w = (w K , w L , w F , w E , w C ) T denotes a standardized weight vector, which is related to the number of input and output indicators. In this study, the calculation of the TFGP of the electric power industry includes three inputs, one desirable output, and one undesirable output variable; thus, w = (1/9,1/ 9,1/9,1/3,1/3) T ; g = (−g K , −g L , −g F , g E , −g C ) denotes the direction vector; and β = (β K , β L , β F , β E , β C ) T ≥ 0 denotes a scale vector, which represents the optimization of inputs, desired outputs, and undesired outputs. The preceding NDDF can be solved by the following equation: In this Equation (4), when   D x y b g ( , , ; ) = 0, it means that the DMU is at the best production frontier. This study assumes the optimal solutions of energy inputs and desirable output to be β F * and β E *, and then TFGP in theory can be defined as 44 In the above NDDF model, all DMUs are located in the unified production frontier and have similar production technologies. However, the characteristics of economic and technological development are quite different among regions in China. In view of this, the present study introduced the following meta-frontier NDDF model to investigate the regional difference of TFGP in China's electric power industry. All DMUs were divided into H groups, and group h contains N h DMUs. The following three production technology sets are established and each of them satisfies the production relationship defined in Equation (1).
can produce( , )}, In Equation (6), T h C is the production technology frontier of group h in period t (t = 1,2, …, T), which is defined as the contemporaneous production technology frontier of group h. T I h represents the production technology frontier of group h in all periods, which is defined as the inter-temporal production technology frontier of group h. T Meta I represents the production technology frontier of all DMUs in all periods, which is defined as the global production technology frontier.
Similarly, the inter-temporal and global NDDFs were defined as and respectively.
Based on the assumption that β*(.) is the optimal solution of Equations (7)-(9), the following TFGP-related indicators are defined: In Equation (10), CTFGP, ITFGP, and GTFGP use contemporaneous group frontier, group frontier, and meta-frontier as the benchmarks, respectively. As GTFGP is calculated based on the same benchmark for all DMUs, it is usually considered as the most important TFGP indicator.
The results of Equation (10) can be used to calculate the technology gap among groups. Following the idea of Oh 50 and Cheng et al., 51 GTFGP is decomposed as In Equation (11), TE denotes the generation performance of the thermal power industry. BPR denotes the ratio of group-frontier performance to contemporaneous performance, reflecting the technology gap between the specific group contemporaneous technology and group technology. TGR denotes the ratio of meta-frontier performance to group-frontier performance, which reflects the technology gap between the group technology and meta-frontier technology. Both BPR and TGR range from 0 to 1, and large values imply a minor technology gap.
In Equation (12), MNMI measures the change of the GTFGP. MNMI> (or <) 1 implies the increase (or decrease) of it. EC refers to the performance change index, reflecting the degree of performance change. Here, EC> (or <) 1 indicates that power generation performance is closer (or farther) to the contemporaneous best production frontier. BPC refers to the best practice gap change index, which reflects the change of technology gap between contemporaneous technology and group technology. Here, BPC> (or <) 1 indicates that contemporary technology is close to (or away from) inter-temporary technology, implying the technological progress degree. TGC refers to the technology gap change index, which reflects the change of the technology gap between group-frontier and meta-frontier. Here, TGC> (or <) 1 indicates a decrease (increase) in the technology gap between group-frontier and meta-frontier, implying the technology catch-up.

| Spatial correlation analysis
A spatial correlation measurement method was used to recognize the geographical distribution characteristics of TFGP in China's thermal power industry. The steps of this method are as follows: Step 1: Establishing the spatial weight matrix, and defining the spatial location information of each province in the form of a matrix.
where w ij denotes the spatial weight between province i and province j.
In Equation (13), the binary adjacency method is used to set the spatial weight matrix. If a common edge exists between provinces, it is defined as adjacency, and the corresponding weight coefficient is accordingly set to 1, otherwise it is 0. Of all provinces in China, Hainan is an exception. It is very close to Guangdong province, but strictly speaking has no common edge. To facilitate the following analysis, Hainan and Guangdong provinces are considered as adjacent in this study.
Step 2: Global spatial autocorrelation analysis. The global Moran I index is used to determine whether provincial TFGPs of the thermal power industry have spatial autocorrelation and their action directions.
where I t is the global Moran I in period t.
, is the mean TFGP of all provinces in the period t. GTFGP i,t and GTFGP j,t are the GTFGP values of provinces i and j in period t, respectively.
the number of considered provinces.
The value range of global Moran's I is [−1,1]. When I is larger than 0, it means that the TFGPs of China's thermal power industry in different provinces have spatial positive correlation; when I is less than 0, it implies spatial negative correlation; when I is equal to 0, it means that spatial correlation does not exist. The closer the absolute value of I is to 1, the more obvious the spatial correlation is.
Step 3: Local spatial autocorrelation analysis. The global Moran I index can be decomposed into the sum of the local Moran I index, which can measure the spatial correlation of a specific province to its neighbors. It is defined as If I i,t > 0, it means that the TFGPs of the thermal power industry in a province and its neighbors present a spatial agglomeration. That is, the provinces with high (low) TFGPs are surrounded by the provinces with high (low) TFGPs, which presents "high-high" ("low-low") agglomeration. If I i,t < 0, it means that the TFGPs of the thermal power industry in a province and its neighbors present spatial differentiation. That is, the provinces with high (low) TFGPs are surrounded by the provinces with low (high) TFGPs, showing a "high-low" ("low-high") correlation.

| Tobit regression
This research uses the nonradial distance function method to analyze the TFGP of the thermal power industry from the input-output perspective, but some important factors such as coal price, industrial structure, and technological development cannot be involved in the above analytic system. Therefore, it is necessary to use some measurement methods to further analyze the influencing factors of the generation performance. Since the TFGP of thermal power industry calculated by the nonradial distance function method are between 0 and 1, using ordinary least squares estimation will lead to biased and inconsistent results. Therefore, the Tobit regression method based on maximum likelihood estimation is used to solve the censored dependent variables. The Tobit regression model is defined as follows 52 : where Y* is the latent variable; X is the explanatory variables, that is, the impact factors of the efficiency; η is the regression coefficients of the explanatory variables; μ is the stochastic error, which follows the distribution of N(0, σ 2 ).

| Data selection
China has been implementing the Five-year Plan administrative mechanism shortly after the foundation of the People's Republic. That is, the government adjusts its development policies every five years. In the period of the 12th Five-year Plan, large-scale overcapacity in power generation began to appear in China. In view of this, the time span of samples selected in this study begins at 2011, the first year of the 12th Five-year Plan, and ends at 2019. As introduced above, provinces are basic DMUs in this study. Among all of China's 34 provinces, autonomous regions, municipalities, and special administrative regions (collectively called provinces in the following study), Taiwan is the only one that is not controlled by the Chinese central government. Hong Kong and Macao are special administrative regions with far more autonomy than other provinces. Besides, the scale of the thermal power industry in Tibet is small. For these reasons, these provinces were not considered in this research. According to the research in this area, 53  The statistics of variables needed for the TFGP analysis were mainly from three sources. The installed capacity of thermal power (input variable) and power generation (desirable output variable) were provided by China Electric Power Statistical Yearbook. 4 The labor (input variable) was the number of employees in the thermal power industry, which was selected from the China Population and Employment Statistical Yearbook. 54 The fossil energy consumption of thermal power plants (input variable) was derived from the China Energy Statistical Yearbook. 55 As CO 2 emissions (undesirable output) were not directly released by any statistical yearbooks, they were obtained by conversion. 56 where u = 1,2,3 represents the fossil energy type, which refers to coal, oil, and natural gas, respectively; 44/12 is the conversion factor between carbon and carbon dioxide; M u is the consumption of fossil energy; and N u is the carbon emission factor of fossil energy. According to the findings of the Energy Research Institute of National Development and Reform Commission, N u for coal, oil, and natural gas were 0.7329, 0.565, and 0.445, respectively. 57 To investigate the impact factors on generation performance of China's thermal power industry, referring to the conclusions in previous research 18,58-61 and considering the availability of data, we chose the following explanatory variables to construct the Tobit regression model.  62,63 The data came from the China Statistical Yearbook. 64 2. Technological innovation (TI). This research measured technological progress by using the ratio of internal expenditures of R&D investment to GDP of the province. 65,66 The data were also derived from the China Statistical Yearbook. 64 3. Energy endowment (EE). Thermal power generation in China is mainly fueled by coal resources, and the differences in coal resources largely affect the productivity of the thermal power industry. Referring to the research of Qin et al., 67 we used the ratio of coal production and consumption to represent the energy endowment and the data came from China Energy Statistical Yearbook. 55 4. Power structure (PS). The power structure directly determines whether the thermal power industry has primary or secondary responsibility for power generation in the province, thus affecting the development mode of this industry. According to Qin et al., 67 the power structure was represented by the proportion of thermal power to total power generation, and the data was derived from the China Electric Power Statistical Yearbook. 68 5. Fuel prices (FP). Coal prices are closely related to the production costs of the thermal power industry. The coal price indicator was used to represent the energy price, 69,70 and the data were expressed in terms of the China Electricity Coal Index (CECI). 71 6. Environmental regulation (ER). Environmental regulation policies are related to the province's attention to pollutant emissions. The intensity of environmental regulation may affect the pollutant abatement efficiency of thermal power industry. We used the ratio of pollution control investment to GDP to represent the environmental regulation intensity, 62,70 Table S1. To investigate the overall levels of the aforementioned five indicators, Table 1 lists their mean values in the sample period.
Introducing the CTFGP, ITFGP, and GTFGP calculations listed in Supporting Information: Table S1 into Equation (12), the dynamic change of TFGP and its factor decomposition results were obtained, listed in Supporting Information: Table S2. Table 2 shows the mean values of the preceding results in 2011-2019.

| Spatial correlation results
Introducing the GTFGP calculations listed in Supporting Information: Table S1 into Equation (14), the Moran I index was obtained. Besides, the p value was also calculated to measure the reliability. The results are listed in Table 3.
Based on Equation (15), the calculation of the global Moran's I index can be decomposed into the sum of each local indicator. Supporting Information: Table S3 lists these decomposition results. Table 4 shows the means of deviation and local Moran I index of each province in the sample period.

| Tobit regression results
Using the panel data from 2015 to 2019 and Equation (16), the external factors affecting the TFGP of China's thermal power industry were explored. The regression results are listed in Table 5. Through the calculation results in Table 5, ED, PS, FP, and ER have a significant positive effect on TFGP while TI and EE don't have an effect on GTFGP. Table 1 shows the mean values of generation performances based on contemporaneous group frontier (CTFGP), group frontier (ITFGP), and meta-frontier (GTFGP). The decomposition results (TE, BPR, and TGR) of GTFGP are also listed in it.

| Static TFGP analysis
GTFGP is the core indicator of the TFGP level. Among the three major regions of China, the GTFGPs in the central and west regions are relatively close, but both are remarkably lower than that in the east region (Table 1). Some west provinces have abundant coal resources and built many large-scale thermal power bases. Thermal power plants in the western region have the largest mean generation capacity per unit and therefore have the advantage of economies of scale. Currently, the mean generation capacity per unit in the western region is 17.75 Mw, noticeably higher than this indicator in east (14.02 Mw) and central (12.53 Mw). 4 However, the low operation rate decreased their TFGP. Compared to the western region, the eastern provinces have the highest operation rate among thermal power plants and thus, the TFGP was increased. Relatively, the central region has a balanced performance. 4 Another notable phenomenon is that the central region has the highest TE and lowest BPR scores. This condition implies T A B L E 1 Mean values of TFGP level (GTFGP) and its factor decomposition results.

Region
Province  Figure 2 displays the decomposition results of GTFGP in each province, which can reveal the reasons for the TFGP level.
According to the calculations listed in Table 1, Jiangsu and Yunnan have the highest and lowest GTFGP levels, respectively. Figure 2 shows that the scores of TE and TGR are the major reasons for this difference. These results can be explained by the difference in the utilization rate of the thermal power generation equipment. Yunnan has abundant renewable energy sources, especially hydropower. The main role of thermal power in this province is to make up for the seasonal shortage of hydropower generation. Given this condition, thermal power plants only supply 9.39% of the electricity demand in this province and the annual average utilization hours are only 1766, far less than the national average (4291 h) and ranks the lowest among all provinces. From the perspective of fairness, thermal power enterprises make a sacrifice for the smooth operations of the electric power system and therefore should receive sufficient compensation. However, China at present has no power ancillary service market. This causes the thermal power enterprise to have large survival pressures. Different from Yunnan, Jiangsu is one of the most developed provinces of China, which has large-scale electricity demand. Besides the external input, thermal power plants in this province provide most (93.35% in the sample period) of the electricity supply, as there are few other energy sources there. This makes the annual average utilization hours of thermal power equipment as high as 5087 h in the sample period, ranking first among all provinces. 4 Besides Jiangsu, provinces that have high GTFGP scores for similar reasons are Zhejiang and Shandong. Figure 2 also shows that Jilin and Liaoning provinces have remarkably low BPR scores. The two provinces are China's traditional industrial base but have faced development difficulties in recent years. Since the beginning of the sample time span (2011), the GDP of these two provinces has only increased by 10.96% and 12.07%, respectively. During the same period, the GDP growth rate for the entire country is as high as 104.50%. 55 However, because of ineffective supervision, investment in the power sources in these two provinces was not adjusted accordingly. During 2011-2019, their installed generating capacity of them increased by 35.44% and 57.94%, respectively. 4 As a result, the overcapacity of thermal power has been becoming increasingly serious, T A B L E 2 Mean values of TFGP change (GTFGP) and its factor decomposition results. and the BPR score then presents a decreasing trend year by year. To cut the aforementioned overcapacity, a ponderable measure is flexibility transformation. That is, some small and medium-sized thermal power units raise their power changing speed of generation through technical transformation. Supported by power ancillary services marked, their major function is not power generation but coping with peak load demand.

| Dynamic TFGP analysis
According to Equation (12)   demonstrates the annual change of MNMI and its decomposition results in each region. Figure 3 reveals an interesting fact: three regions have a distinct difference in the volatility of MNMI. Specifically, this indicator is the most unstable in west China and is steady in east China. According to Equation (12) and the results shown in Figure 3, TGC is the major factor resulting in the above results.
The geographical distribution of energy sources in China is uneven, and the power centers are usually not load centers. This condition makes the interprovincial power transmission inevitable. Nearly all of the eastern provinces of China are power importers. In most years, approximately 20% of electricity consumption in these provinces is provided by other regions. By contrast, most of the western provinces of China are power exporters, and approximately 25% of the electricity they generate is supplied to other regions. 4 When the growth speed of electricity consumption slows down because of the changes in the socioeconomic environment, similar to what happened in 2015 and 2016, power grid enterprises in eastern provinces reduced their electricity imports to ensure the smooth running of the local power generation enterprises. Accordingly, the TFGP of the thermal power industry in the western provinces decreased because of the insufficient rate of operation. When the opposite scenario occurred in 2018, grid enterprises in the eastern provinces enlarged the electricity imports and then raised the TFGP of the thermal power industry in the western provinces. Relatively, the TFGP of the thermal power industry in the eastern provinces can always remain stable because of the fixed operating hours.
The aforementioned behaviors of the power grid enterprises are usually affected by the local governments and not totally due to financial reasons. In fact, because of the difference in energy resource endowment, electricity prices in the western provinces are usually remarkably lower than those in the eastern provinces, and these price gaps are large enough to offset the electricity transmission cost. 73 These "interprovincial barriers" caused by local protectionism 74 should be removed to ensure the healthy development of the whole thermal power industry.

| Spatial correlation analysis
Using the calculations of deviations and local Moran I listed in Table 4, this study recognized the local agglomeration effects at a confidence level of 90%. Figure 4 demonstrates the agglomeration results. Table 3 shows that the values of global Moran's I index are all larger than 0 with high confidence, indicating the significant spatial positive correlation of TFGP in the thermal power industry among the 30 provinces. That is, the provinces with similar TFGP levels tend to be clustered geographically. Figure 4 further reveals that high TFGP provinces gather in the eastern seaboard region and low TFGP provinces are located in southwest China. Figure 4 also confirms the existence of three outliers: Liaoning, Henan, and Guizhou. As explained previously, Liaoning and its neighbor Jilin have largescale overcapacity of thermal power, which decreases the utilization rate of power generation equipment and then lowers the TFGP. Unlike the neighbors, Guizhou is the only province that has abundant coal resources in south China. The share of thermal power in this province is far higher than that in its neighbors. Fewer renewable powers make the thermal power plants in Guizhou take less responsibility for ancillary services and then maintain the high TFGP. The low TFGP of Henan is mainly due to its special electricity consumption structure. Henan is one of the most populous provinces in China, but its economy is not well developed. This condition makes the electricity consumption share of households in Henan significantly higher than those in most of the other provinces. Compared with other electricity consumers, households usually have a power load curve with the largest peak-valley difference. In China, the dispatch department of the power system usually meets the above change of load demand by the thermal unit startup, shutdown, and output adjustment. Given this condition, the share increase in residential electricity consumption can greatly lower the operational efficiency of the thermal power industry. Remarkably, with urbanization advancement and income increase, the electricity consumption share of China's household has been increasing in the past decade. In 2011, this indicator was 11.96%, but in 2020, it increased to 14.55%. 4 Obviously, this condition is expected to continue to hinder the TFGP improvement of China's thermal power industry in the foreseeable future. To raise the people's living standards, the Chinese government has been adopting cross subsidy to lower the residual electricity price since the People's Republic was founded in 1949. 75 However, the rebound effect supported by the cross subsidy has greatly increased household electricity consumption. 76 Considering that China's social economy has rapidly developed for many years, reducing or even canceling this subsidy should be considered to improve the TFGP of the thermal power industry. Table 5 displays the Tobit regression results for TFGP in relation to its potential impact factors. Its examination can reveal some intriguing facts. Table 5 shows that ED, PS, FP, and ER have a significant positive effect on TFGP. The above results indicate that economic development has enabled the power system to upgrade equipment, develop gas-fired generation, and adopt advanced management models. The greater share of thermal power generation allows thermal units to undertake fewer power auxiliary services so as to improve the TFGP of the thermal power industry. Higher fuel prices allow power systems to minimize fuel consumption and correspondingly reduce pollutant emissions. Environmental regulation is the most critical impact factor, indicating that increased investment in pollutant treatment can effectively reduce pollutant emissions and thus improve the TFGP. The effects of TI and EE on TFGP were not significant and these results are consistent with Qin et al. 67 They argue that the relationship between energy production and energy consumption is weak. The latter is because the energy market is highly distorted under the background of market-oriented reform, and technological progress will not significantly affect power generation performance.

| CONCLUSIONS AND POLICY IMPLICATIONS
At present, China's thermal power industry is facing increasing pressures from the business environment. Thus, improving the TFGP is essential for its survival and development. This study adopted an NDDF and its extended method to measure the TFGPs of the thermal power industry in China's 30 provinces in 2011-2019 and then investigated their regional distribution characteristics and impact factors using the spatial econometric model and a Tobit regression method, respectively.
Empirical results revealed the following facts: (I) Among all provinces considered, Jiangsu and Yunnan have the highest and lowest TFGPs levels, respectively. These results can be explained by the difference of the share of thermal power generation. Thermal power plants with larger shares undertake fewer power ancillary services and therefore have higher TFGP. The mean TFGPs in west, central, and east China are 0.7813, 0.8010, and 0.9146, respectively. Relatively, the TFGPs of the former two regions are close but both are remarkably lower than that in the last region. Coal resource endowment enables the west region to build many large-scale thermal power plants and therefore acquire the advantage of economies of scale. However, the low operation rate hinders the rise of its TFGP. By contrast, the east region has the highest operation rate, and therefore the TFGP increased accordingly. Relatively, the central region has balanced performance. (II) The geometric mean changes of TFGP in west, central, and east China are 0.9992, 0.9985, and 0.9838, respectively. That is, the TFGPs of the thermal power industry in central and west China generally remained stable, whereas that in west China declined. Due to the existence of interprovincial barriers in trans-provincial electricity transmission, the TFGP level in the west region, as an electricity exporter, is more susceptible to the electricity supply-demand situations, thereby resulting in the above decline. (III) The global Moran I index in different years is all larger than 0 with high confidence, indicating a significant spatial positive correlation of TFGPs in the thermal power industry among the 30 provinces. That is, provinces with similar TFGP levels tend to be clustered geographically. Specifically, high-TFGP provinces gather in the eastern seaboard region and low-TFGP provinces are in southwest China. The TFGP of Guizhou is remarkably higher than that of the surrounding provinces, mainly because Guizhou has less renewable energy to make thermal power plants bear less responsibility for power auxiliary services. In contrast, the TFGP of Henan is significantly lower than that of the neighboring provinces, due to the significantly higher share of household electricity consumption in Henan and hence lead to a larger peak-valley difference in power load curve. (IV) The influencing factors regression results reveal that economic development, power structure, fuel prices, and environmental regulation are significantly related to China's TFGP, and the impacts of technological innovation and energy endowment are not significant.
The following policy directions to prompt the development of China's thermal power industry are proposed: (I) Thermal power plants have been on an increasingly ancillary service, and it is essential to build a power ancillary service market to compensate them. The main policies include increasing the variety of products in the electricity auxiliary market, relaxing the market entry conditions, and changing the cost-sharing mechanism for electricity auxiliary services. (II) For Jilin, Liaoning, and other provinces that have severe overcapacity of thermal power generation, flexibility peaking transformation of some small and medium-sized thermal power units should be supported. With the support of power ancillary service market, their major function is not power generation but coping with the peak load demand. (III) Interprovincial barriers hinder the transprovincial electricity transmission and then lower the allocation efficiency of the thermal power resources. These interprovincial barriers should be removed to ensure the healthy development of the whole thermal power industry. A feasible approach is encouraging the market to play the main role of resource allocation and gradually remove the nonmarket-based administrative intervention. (IV) Cross subsidy raises residential electricity demand and indirectly causes the TFGP of the thermal power industry to decline. Thus, this subsidy has to be reduced.
As possible extensions, future research can be considered in such directions. Firstly, the current study considers the thermal power system as a whole and ignores the internal structure when assessing the generation performance. In the future, the overall and stage performances of thermal power systems can be explored under the network structure. Second, the current research only considers CO 2 as an undesirable output of the thermal power industry. In the future, more types of pollutants should be involved when data are available.