Applying the Super-EBM model and spatial Durbin model to examining total-factor ecological efficiency from a multi-dimensional perspective: evidence from China

Ecological efficiency mainly emphasizes the importance of balancing the relationships between natural resources, energy, the ecological environment and economic growth, which has aroused widespread concern worldwide. China’s rapid economic development has inevitably been accompanied by serious resource exhaustion, environmental pollution and ecological deterioration in the past several decades, which has brought huge challenges to China’s sustainable development. Therefore, establishing the evaluation framework of total-factor ecological efficiency (TFEE) and identifying its driving force have a great significance for improving China’s sustainable development capabilities. First, an ecological efficiency evaluation framework is established based on the theory of total-factor analysis. Second, the super efficient hybrid distance model considers undesirable output and measures TFEE nationwide in 30 provinces and four regions during the period 2003–2017. Finally, the spatial effect of TFEE and its influencing factors are examined by using a spatial Durbin model. The empirical results show that (1) nationwide and regional TFEEs have different degrees of decline during the study period. There were significant differences among the 30 provinces and four regions. Beijing, Tianjin and Shanghai are efficient, while the other provinces have not been as effective. The TFEEs of the four regions are not effective with an ordering of eastern > northeast > central > western. (2) Moran’s I index shows that the TFEE nationwide has a positive spatial autocorrelation with strong spatial agglomeration. However, the spatial distribution pattern of TFEE in China was unstable and labile. The Moran scatter plot indicates that China’s provincial TFEE has not only spatial dependence characteristics but also differences in spatial correlation. (3) Most factors are bound up with TFEE to various degrees: technological progress (TP), industrial agglomeration (IG) and human capital (HC) play a positive role, while industrial structure (IS), the level of urbanization (CITY) and energy intensity (EI) play a negative role. Additionally, environmental regulation (GZ) shows a U-type relationship with TFEE. The level of economic development (GDP) and foreign direct investment (FDI) cannot have a significant impact on TFEE at this stage. (4) The spatial Durbin model results show that TFEE has a significant spatial spillover effect, and the improvement of the TFEE of a province will increase the TFEE of neighbouring provinces. The confirmed spatial spillover effects of technological progress (TP), industrial structure (IS), the level of urbanization (CITY), industrial agglomeration (IG) and human capital (HC) can significantly impact the TFEE of neighbouring provinces. Among them, technological progress (TP), the level of urbanization (CITY) and human capital (HC) can significantly improve the TFEE of neighbouring provinces, and the level of economic development (GDP) and foreign direct investment (FDI) can significantly inhibit the improvement of TFEE in neighbouring provinces.


Introduction
Since the implementation of the reform and opening policy, China's economic development has had many remarkable achievements (Tu et al. 2019). From 1978 to 2018, China's gross domestic product (GDP) grew at an average annual rate of 9.5%. However, behind rapid economic growth, there are Responsible Editor: Eyup Dogan also negative effects, such as excessive consumption of natural resources and deterioration of the ecological environment. The development mode of "high pollution, high consumption, low efficiency" and a high coal energy structure has caused a resource crisis and has aggravated environmental and ecological destruction (Dong et al. 2020). The problems of resources and the ecological environment have severely restricted China's future sustainable development. Transforming the economic development approach, breaking the bottleneck restricting the sustainable development of China, supporting economic development with less resource consumption and reducing environmental pollution have become the focus of social concern. To clarify these obstacles caused by environmental pollution and ecological deterioration and to explore the path of sustainable development, the Chinese government proposed to vigorously promote the construction of an ecological civilization strategy. However, there are still difficult problems in finding the key to the coordination of the ecological environment and economic development. How to realize the coordination between economic development, resource and energy consumption and environmental protection from a comprehensive perspective, rather than unilaterally solving only individual problems, is an important question (Li et al. 2016). Ecological efficiency (EE) is of increased importance in response to the challenges posed by these problems.
American scholars Schaltegger and Sturm first proposed the concept of ecological efficiency in 1990 as a way to measure the impact of the environment on economic activities (Schaltegger and Sturm 1990). In the years since, a wave of research has followed. The World Business Council for Sustainable Development (WBCSD) was the first to promote ecological efficiency as a business concept (WBCSD 2000). BASE defines the concept of ecological efficiency from the perspective of products. The OECD expanded the concept to multiple fields, such as governments and industrial enterprises, and defined ecological efficiency as the efficiency of using ecological environmental and natural resources to meet the demand of human activities (OECD 1998). In addition to these institutions, scholars have also studied the concept of ecological efficiency. Mickwitz et al. (2006) pointed out that ecological efficiency involves multiple dimensions, such as the economy, society and ecological environment, and can be used to effectively measure the level of sustainable development. Litos et al. (2017) defined ecological efficiency as a way to achieve optimal value at a lower cost. Although there are certain differences in the definition of ecological efficiency across society, they all emphasize that ecological efficiency needs to take into account economic and ecological benefits and maximize economic benefits while minimizing the impact of negative environmental externalities.
Ecological efficiency has been widely recognized and accepted by academics and has become an important tool for studying and analysing the impact of economic activities on the environment. Currently, scholars in the ecological efficiency field have made great efforts to study the different dimensions involved. In this context, this article reviews the existing literature.
(1) Many scholars are working to improve the scientific basis and accuracy of measurement results and to develop appropriate EE evaluation methods. Michelsen et al. (2006) evaluated the production efficiency of Norweg-ian furniture based on nine criteria, including heavy metal output, photochemical smog production, total waste production, greenhouse gas emissions, energy consumption and material consumption. Ghimire and Johnston (2017) took life cycle cost, net present value and GDP as economic indicators and used 11 environmental indicators, including acidification, ecotoxicity, energy demand and metal consumption, to measure eco-efficiency. Arabi et al. (2015) used the SBM-DEA model combined with the Meta-Frontier-Malmquist index method to study the change of ecological efficiency of thermal power plants in Iran in the past 8 years. Hu and Liu (2015) used the SBM-DEA model to analyse the ecological efficiency of the Australian construction industry from 1990 to 2013 from the spatial and temporal dimensions. Angeles et al. (2017) studied the agricultural eco-efficiency of small farms in southeast Spain and made a regression analysis of the factors affecting their expected output efficiency. Halkos and Petrou (2019) used a DEA model to evaluate the environmental ecoefficiency of 28 EU member states with a directionaldistance function to deal with non-expected outputs. They concluded that Germany, Ireland and the UK had the highest environmental eco-efficiency, and the countries with higher environmental efficiency also had relatively high recycling rates. Robaina-Alves et al. (2015) constructed a new stochastic frontier model, which can combine data envelope analysis and composite errors from stochastic frontier methods to make ecological efficiency measurement results more scientific and accurate. Moutinho et al. (2020) analysed and predicted the ecological efficiency of 24 German cities through stochastic frontier model (SFA) and data envelopment model (DEA) and tested the factors influencing the ecological efficiency score at the city level through fractional regression. Kounetasa et al. (2020) applied a nonparametric model to estimate the eco-efficiency of the US states from 1990 to 2017 and analysed the regional convergence/divergence pattern in eco-efficiency in the USA. Li et al. (2011) put forward an energy efficiency assessment method for building manufacturing based on energy analysis and applied it to the ecological building rating of Beijing and Shanghai. Liu et al. (2018) evaluated the ecological efficiency of the circular economy system in Shanxi province by using the SBM-Undesirable model based on energy analysis and DEA. Liu et al. (2021) built an evaluation model of ecological efficiency based on energy analysis to achieve quantitative evaluation of an industrial production system. Yang and Yang (2019)  (2) With the emergence of various assessment methods, the research scope of ecological efficiency has gradually expanded. At present, the research process of ecological efficiency evaluation has been applied to enterprises, industries, regions and other fields. From the perspective of enterprises, Huppes et al. (2007) evaluated and analysed the ecological efficiency of natural gas and petroleum resource enterprises in the Netherlands through cost analysis. From the perspective of products, Van et al. (2011) analysed and studied the ecological efficiency of semihard cheese in different periods based on energy consumption, land consumption and temperature warming. Many examples are available from the perspective of industry. Yago et al. (2016) used life cycle theory to measure the ecological efficiency of wastewater treatment plants. Kharel and Charmondusit (2008) studied the ecological efficiency of mineral processing. Ingaramo et al. (2009) studied the ecological efficiency of wastewater in the sugar industry. Charmondusit and Keartpakpraek (2011) studied the ecological efficiency of 31 petroleum organizations in Thailand based on the definition of ecological efficiency proposed by WBCSD. Gössling et al. (2015) studied the ecological efficiency of tourism from the perspective of carbon dioxide equivalent emissions. Barak and Dahooei (2018) evaluated the safety of flight routes by using fuzzy data envelopment analysis and fuzzy multi-attribute data decision unit. Studies from the regional perspective are also numerous. Mickwitz et al. (2006) proposed a regional ecoefficiency index system with three dimensions of society, economy and nature. Salmi (2007) proposed the evaluation criteria of ecological efficiency from three aspects: nature, economy and society. Caneghem et al. (2010) analysed the changing trend of ecological efficiency in Flanders industrial zones from the perspective of economic decoupling and environmental impact. Wursthorn et al. (2011) studied how to achieve the unification of ecological efficiency evaluation indexes in Europe. Bianchi et al. (2020) used the Metafrontier Data Envelopment Analysis (DEA) model to comprehensively evaluate the ecological efficiency of 282 regions in Europe from the perspective of regional heterogeneity.
(3) With the improvement of ecological efficiency methods and the expansion of application fields, the research content of ecological efficiency is not limited to simple measurements but has gradually grown to explore the influencing factors of ecological efficiency. The research on the influencing factors of ecological efficiency is shown in Table 1.
This article reviews the existing research progress, identifies the current challenges and proposes improvement methods from these three aspects.
First, a scientific and reasonable evaluation system is essential for EE research. According to the definition of EE, the research on evaluation indicators has undergone a transformation from a single-factor framework to a total-factor framework. In the single-factor analysis framework, the ratio of economic development to environmental impacts is often used to measure EE. Because of the high complexity of the interactions between natural resources, the economy and the environment, the analysis results obtained by the single-factor framework may cause distortions of reality and be unable to provide the best choice for decision makers. To overcome the shortcomings of a single factor framework, many studies have tried to establish a total-factor analysis framework covering multiple input and output indicators. Therefore, on the basis of referring to the existing research, this article defines the totalfactor ecological efficiency (TFEE) and attempts to construct a TFEE evaluation index system that considers multiple inputs and multiple outputs.
As ecological efficiency mainly emphasizes that inputoutput factors should consider "ecological" characteristics, total-factor productivity emphasizes that input-output factors should cover multiple production factors, such as capital and labour. However, in actual production activities, the realization of capital proliferation is inseparable from labour factors of production, labour is often inseparable from material products and natural resources are a very important consumption. At the same time, production activities are inevitably accompanied by the emission of environmental pollutants under the current technological conditions. Therefore, in this article, on the premise that resources and environment are binding on economic growth, input (including capital, labour, land resources, energy, water), desirable output (economic development) and undesirable output (including CO 2 emissions, SO 2 emissions, waste water emissions, industrial solid wastes discharge) will be incorporated into the total-factor framework together. The resulting efficiency value will be designated total-factor ecological efficiency (TFEE).
Second, at this stage, the mainstream EE evaluation methods mainly include data envelopment analysis (DEA), stochastic frontier analysis, energy analysis, ecological footprint and lifecycle assessment. In these evaluation methods, DEA, as a nonparametric calculation method that can simultaneously consider multiple outputs and multiple inputs, has been widely accepted by academia. The advantage of the DEA method is that it can avoid the influence of subjective factors on the weight during the measurement so that the evaluation result of EE is more accurate. EE evaluation must consider not only desirable output but also undesirable output (e.g. environmental pollutants). Tone (2001) proposed the slack-based measure (SBM) model, which can simultaneously consider undesired output and slack variables and can efficiently avoid redundancy and shortage problems. However, the SBM model still has the problem of potentially losing proportionality with the original inputs or outputs. Tone and Tsutsui (2010) proposed the epsilon-based measure (EBM) model to overcome those defects by a hybrid distance function. In addition, the value of EE often has multiple evaluations prone to equal to 1. This makes it impossible for us to effectively rank decision-making units (DMUs) or to accurately reveal the heterogeneity between DMUs. Therefore, this article is first based on the EBM model considering undesirable output then refers to Andersen and Petersen (1993) to extend it into a Super-EBM (S-EBM) model.
Third, research on the influencing factors of EE has also received extensive attention by utilizing multitudinous econometric technology. According to previous research, the economic development level, industrial structure, technological progress, environmental regulations and urbanization level are the most important driving factors of EE Zhou et al. 2018). Traditional regression models have been widely used to examine the key influencing factors of EE. In terms of measurement model selection, most studies have chosen to use Tobit regression (Long et al. 2015;Liu et al. 2017;Wu et al. 2018;Wang et al. 2018), quantile regression (Moutinho et al. 2018) and panel regression models (Zhao et al. 2018) to test the influencing factors of EE. However, these regression models often overlook ubiquitous spatial effects such as spatial dependence and spatial heterogeneity. According to previous studies, spatial regression models are rarely used to study the driving factors of EE. This means that the spatial spillovers embedded in EE and the socioeconomic development of various regions are poorly understood. While the studies of driving factors of EE have garnered great attention internationally, a few studies have analysed the driving factors and the spatial spillover effects behind EE by using spatial regression models at China's provincial level. Despite the great contributions of previous studies, only a few studies have examined the relationship between anthropogenic factors and EE in neighbouring regions, including spatial spillover effects. Therefore, the driving factors of EE need to be further studied. Based on the above analysis, this article's possible contributions are as follows. First, we establish a TFEE evaluation index framework that considers multiple inputs and outputs (energy, land resources, water resources, labour and capital as inputs, GDP as desirable outputs, and CO 2 , SO 2 , wastewater and industrial solid waste as undesirable outputs). Second, the Super-EBM model considering undesirable outputs was proposed for measuring the TFEE of China's three-dimensional (national-regional-provincial) model from 2003 to 2017. This is the first time that the Super-EBM model considering undesirable outputs has been applied to provincial ecological efficiency evaluations in China, which can effectively improve the accuracy of TFEE measurement results. Finally, this article applied the ESDA model and spatial regression model to systematically and comprehensively test the spatial agglomeration characteristics, influencing factors and spatial spillover effect of TFEE. This revealed both a spatiotemporal variation and spatial correlation mechanism of TFEE from different perspectives with practical implications for policymaking and multiregional coordination development.

Study area
This article is based on 30 regions in China (22 provinces, four municipalities and four autonomous regions) from 2013 to 2017. The four regions of Tibet, Hong Kong, Macau and Taiwan are no longer within the scope of the study due to the difficulty of obtaining data. For the convenience of research, this article refers to these 30 regions collectively as provinces. In addition, this article divides the 30 provinces into four regions according to China's economic regions, as shown in Fig. 1.

Data and variable description
The data required in this article mainly come from the China Statistical Yearbook (2004), China Energy Statistical Yearbook (2004) and China Environment Yearbook (2004. At the same time, the data are also revised in conjunction with relevant statistics of 30 provinces. Because the water consumption of 30 provinces before 2002 cannot be obtained, and the construction land area after 2018 cannot be obtained either. Therefore, the research interval of this article is 2003-2017. In this article, the evaluation indicators of TFEE include input (ecological resource indicators), desirable output (economic indicators) and undesirable output (environmental pollution indicators). Referring to the existing literature (Ren et al. 2020;Bianchi et al. 2020;Liu et al. 2020a, b, c;Tang et al. 2020;Zhang and Li 2020;Tan and Wang 2021), the level of economic development (GDP), the level of urbanization (CITY), industrial structure (IS), energy intensity (EI), technological progress (TP), foreign direct investment (FDI), industrial agglomeration (IG), human capital (HC) and environmental regulation (GZ) were selected as the influencing factors of TFEE.
(1) Input indicators include energy consumption, total water consumption, construction land area, labour stock and capital stock. Energy consumption was directly obtained from the China Energy Statistics Yearbook. The labour, total water consumption and construction land area were directly obtained from the China Statistical Yearbook (2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018). The capital stock was calculated by the "permanent inventory method" based on year 2000 data (Zhang and Zhang 2003). The formula is as follows: Research method S-EBM model DEA, as a nonparametric analysis method, uses linear programming ideas to evaluate the relative effectiveness of comparable decision-making units. The DEA method was first introduced by American operation researchers Charnes and Cooper. Since its introduction, it has been widely used in many fields and has become one of the most popular methods for evaluating relative efficiency (Charnes et al. 1978). Generally, traditional DEA models are divided into two types: radial and nonradial. However, both radial DEA models (such as the CCR model) and nonradial DEA models (such as the SBM model) have some drawbacks. For the radial DEA model, the main disadvantage is that it ignores nonradial slack when reporting efficiency scores (Avkiran et al. 2008). For the nonradial DEA model, the main disadvantage is that the slack potentially loses proportionality with the original inputs or outputs (Tone 2001). In view of the shortcomings of the DEA models, Tone and Tsutsui proposed an EBM model considering hybrid distances. The EBM model can not only overcome the primary defects of two types of model measures but also combines the advantages of the two measures into a comprehensive framework that also considers undesirable outputs (Tone and Tsutsui 2010). In addition, the value of efficiency often has multiple evaluations prone to equal to 1. This makes it impossible for us to effectively rank decisionmaking units (DMUs) or to reveal the heterogeneity of DMUs. Therefore, we used the EBM model that considers undesired output and then extended it to a form of the Super-EBM (S-EBM) model by referring to Andersen and Petersen (Andersen and Petersen 1993). The model is shown in Eq. (1): where ω þ r and ω b− t are the weights of the desirable output and the weights of undesirable output, s þ r and s b− t are the slack variables of desirable output r and the slack variables of undesirable output t, b tj stands for the tth undesirable output of the DMU j and p denotes the total number of undesirable outputs.

Spatial econometric analysis methods
Spatial econometric analysis is usually divided into two steps. In the first step, a spatial autocorrelation test is used to test whether there is a spatial correlation among dependent variables because spatial econometric analysis is needed only when spatial autocorrelations exist. Geoda 1.6 is used for this analysis (see "Spatial autocorrelation test" section). The first step is to test whether there is a spatial correlation between the dependent variables through the spatial autocorrelation test because the existence of a spatial autocorrelation is a prerequisite for spatial econometric analysis. Geoda 1.6 is used for analysis (see "Spatial autocorrelation test" section). In the second step, according to the spatial autocorrelation results, an appropriate spatial econometric model should be chosen to examine the relationship between the dependent variable and the explanatory variable. MATLAB software is used for this analysis (see "Spatial econometric models" section).

Spatial autocorrelation test
This article first uses the global Moran's I index to test the spatial autocorrelation of TFEE in 30 provinces, as shown in Eq. (2): In Eq.
(2), n is the number of research objectives, Zi and Zj are observations of regions i and j, Wij represents the spatial weight matrix, S2 is the observed variance and Z is the average of the observations. The range of Moran's I index is [−1,1]. The closer to 1 or −1, the stronger the spatial correlation. If Moran's I index is positive, it indicates that agglomeration is present. If Moran's I index is negative, it indicates that the representation is spatially different. When Moran's I index is close to 0, it indicates that the spatial distribution is random and that there is no spatial correlation.
This article constructs a 0-1 spatial weight matrix to be referred to as W1.
The 0-1 spatial weight matrix mainly examines the adjacency relationship between spatial units. The definition of the element value is as follows:.

Spatial econometric models
The spatial econometric model can effectively solve the spatial dependence and correlation between the variables being investigated. Traditional spatial econometric models are divided into two types: spatial lag models (SLM) and spatial error models (SEM) (Anselin et al. 2004).
The SLM can be expressed as In Eq. (4), y represents the dependent variable, X represents explanatory variables, W represents the spatial weight matrix, ε is a random error term, ρ is the spatial regression coefficient and β is an estimated independent coefficient.
The SEM can be expressed as In Eq. (5), y represents the dependent variable, X represents explanatory variables, W represents the spatial weight matrix; ε is a random error term, λ is the spatial autocorrelation coefficient, β is an estimated independent coefficient and ν is a disturbance term.
In 2009, Pace and Lesage introduced an equation containing a spatial lag term, including dependent and independent variables ). This equation can effectively realize the complementary advantages of SLM and SEM and is named SDM The SDM can be expressed as In Eq. (6), y represents the dependent variable, X represents explanatory variables, W represents the spatial weight matrix, ε is a random error term, ρ is the spatial regression coefficient, β is an estimated independent coefficient and θ represents the spatial lag coefficient of the independent variable to be estimated. Since the new century, China's economy has shown a trend of rapid growth, people's living standards have been continuously improved and TFEE has also been developed. However, at the same time, the negative impact accumulated by China's past extensive development model of "three highs" (high investment, high consumption and high pollution) has also begun to intensively erupt. Ecological destruction and environmental pollution followed one after another, which seriously hindered the further improvement of TFEE. Therefore, the current level of China's TFEE is relatively high, but it shows a downward trend.

Regional perspective
From a regional perspective, the TFEE of the eastern region is the highest, with a 15-year mean of 0.8664, much higher than the other three regions and the national mean. The TFEE basically remained at a high level above 0.8000 during the study period. The TFEE of the northeast region is second, with a 15year mean of 0.7369, which is higher than the other two regions and the national mean. The TFEE varies greatly and is not stable enough during the study period. The TFEE of the central region is third, with a 15-year mean of 0.6245, which is lower than the national mean. The TFEE remained between 0.5500 and 0.6600 during the study period. The TFEE of the western region is the lowest, with a 15-year mean of only 0.5469, which is lower than the national mean. The TFEE is lower than 0.6000 during the study period. Together, the TFEE of the four regions showed a downward trend during 2003-2017. Among them, the downward trend of the northeast region was the most intense with an average annual growth rate of −2.70%. The downward trend of the eastern region was the gentlest with an average annual growth rate of −0.89%. The downward trend of the central and western regions is basically consistent with the national downward trend with average annual growth rates of −1.14% and −1.37%, respectively.
The TFEE of the four regions has not been effective. There are obvious differences between regions, with an ordering of eastern > northeast > central > western. The eastern and northeastern regions have superior geographical locations and have always been the economic development centre of China. It has strong capital, technology and talent advantages, making its TFEE always a leader in China. However, with the implementation of development strategies such as "Rise of Central China", "Development of the Western Region" and "Belt and Road", a westward shift of the economic centre of gravity and decline in the capacity of the ecological environment due to regional economic growth have occurred. The TFEE of the eastern and northeastern regions thus shows a downward trend. As the economic development transition region of China, the central region has abundant natural resources, but its economic foundation and scale are far inferior to those of the eastern and northeastern regions. Its resource utilization efficiency and capital conversion rate are low, and its policy advantages are not obvious, making its TFEE relatively low. The western region is restricted by transportation and other infrastructure, the development is relatively late, the economic  [2003][2004][2005][2006][2007][2008][2009][2010][2011][2012][2013][2014][2015][2016][2017] foundation is weak and the ecological environment carrying capacity is low, so the TFEE is the lowest.

Provincial perspective
From a provincial perspective, the TFEE means of Beijing, Shanghai and Tianjin are 1.0365, 1.0275 and 1.0121, respectively, and their TFEE was also greater than 1 from 2003 to 2017. The TFEE of these three provinces achieves the effective level. It shows that the TFEE of these provinces is above the frontier, and both input and output reach the best configuration. The TFEE of Guangdong is basically effective. Its TFEE mean is 0.9976, and the TFEE is greater than 1 from 2003 to 2016, but it was not effective in 2017. This shows that Guangdong's input and output are close to the effective state. Although the gap between the input and output is very small, the stability is not high enough. For the TFEE of Guangdong, there is still much room for improvement. The provinces with relatively high TFEE are Heilongjiang, Zhejiang, Fujian, Hainan, Shandong, Jiangsu, Liaoning and Inner Mongolia. Their mean TFEEs are above 0.7000, which is higher than the national mean. Among them, the TFEE of Heilongjiang, Fujian, Hainan, Liaoning, Inner Mongolia, and Shandong can be effective in a few years. The TFEE of Zhejiang and Jiangsu is relatively stable, maintaining between 0.7000 and 0.9000. This shows that although these provinces' inputs and outputs are ineffective, the gap between inputs and outputs is relatively small, and there is a relatively large room for improvement.
The TFEE means in the other 18 provinces are lower than the national mean. Among them, the TFEE means of Hebei, Anhui, Sichuan, Hunan, Jilin, Hubei, Henan, Jiangxi, Shanxi and Chongqing were higher than 0.6000.This shows that these provinces' inputs and outputs are ineffective, the gap between inputs and outputs is relatively large and there is a relatively limited room for improvement. The TFEE means of Shaanxi, Gansu, Yunnan, Guangxi and Xinjiang are less than 0.6000, and the TFEE means of Guizhou, Qinghai and Ningxia are less than 0.5000. This shows that these provinces' inputs and outputs are ineffective, and the gap between inputs and outputs is extremely large, making it difficult to improve. There are significant differences in the TFEE of the 30 provinces in China. There are 12 provinces with high TFEE, accounting for 40%. These provinces are mainly distributed in the eastern and northeast regions. There are 18 provinces with low TFEE, accounting for 60%. These provinces are mainly distributed in the central and western regions. Due to the overall environmental impact of China's development, the development trend of most provinces is similar to that of China as a whole, showing a downward trend.
Specifically, Chongqing, Inner Mongolia, Sichuan and Tianjin showed a growing trend, with a proportion of 13.33%. The four provinces' growth trends are relatively flat with average annual growth rates of only 0.53%, 0.39%, 0.18% and 0.05%. The other 26 provinces' average annual growth rates are negative, showing a downward trend, accounting for 86.66%. Hainan, Hebei, Liaoning, Heilongjiang, Fujian, Shandong, and Guangdong have a sharp downward trend. The average annual growth rates of Shandong and Guangdong are approximately −1.5%, and the average annual growth rates of the other 5 provinces are higher than −2.5%. The downward trends in Jilin, Shanxi, Shaanxi, Henan, Guangxi and Yunnan are more obvious, and the average annual growth rates of these provinces are higher than −1.0%. The downward trend in the other 13 provinces is relatively stable and consistent with the overall downward trend in China. The provinces with high TFEE have an unstable development trend, the average annual growth rate is relatively low and are mainly concentrated in the northeast and east regions. The provinces with low TFEE have a relatively stable development trend and a high average annual growth rate and are mainly concentrated in the central and western regions.

Spatial autocorrelation of TFEE
According to the TFEE of 30 provinces from 2013 to 2017, under the W1 matrix (0-1 distance), GeoDa1.6 software was used to estimate Moran's I index (Table 4) and draw its development trend chart (Fig. 3). Table 4 shows that the global Moran's I index of TFEE was positive with a high degree of consistency during the study period. The range of the global Moran's I index was between 0.2790 and 0.4530 with all years passing the 1% significance level test . The results show that the TFEE of China has a significant positive spatial autocorrelation, and high (low) adjacent provincial units are relatively agglomerated, showing a strong spatial agglomeration pattern. Figure 3 shows that the global Moran's I index shows a downward trend, the dynamics of up and down waves are obvious and the fluctuation frequency is high. There was a relatively drastic downward trend starting in 2003 that reached its lowest point in 2007. From 2008 to 2011, it showed a trend of rising volatility, and from 2012 to 2017, it showed a relatively stable upward trend. The results show that although China's TFEE is spatially significant, the degree of prominence of its agglomeration situation will vary due to differences in the spatial matrix. The wave dynamics of the global Moran's I index show that the spatial distribution pattern of China's TFEE is unstable and easy to change.
Although Moran's I index can scientifically reflect the spatial autocorrelation of TFEE, it has a certain limitation. When some provinces show a positive spatial autocorrelation and others show a negative spatial autocorrelation, these effects will offset each other, in which case Moran's I index may tend to 0 and show non-spatial autocorrelation. Therefore, the spatial characteristics and agglomeration of TFEE should be more scientifically and accurately reflected. We do this using Moran's I scatter plot and visualize it using ArcGIS software. We choose three representative years (2003, 2010 and 2017) to visualize Moran's I scatter plots of TFEE, which are summarized in Fig. 4.
As shown in Fig. 4, under the two spatial weight matrices, most provinces show H-H and L-L clusters and positive spatial autocorrelation. Under the W1 matrix, 23 provinces (76.6%), 22 provinces (73.33%) and 19 provinces (63.33%) were located in the first and third quadrants in 2003, 2010 and  Although the number of provinces in the first and third quadrants showing similar spatial correlation has decreased, the proportion still remains above 60%. While the number of provinces in the second and fourth quadrants showing dissimilar spatial association has increased, the proportion is still less than 40%. The provinces in the first and third quadrants are mostly concentrated in the eastern and western regions, while the provinces in the second and fourth quadrants are mostly concentrated in the central and northeastern regions. These results all show that the TFEE of China has both spatial dependence and varying characteristics.

Spatial econometric regression results
According to the above analysis, TFEE exhibits significant spatial correlation and dependence. However, using ordinary regression models can underestimate or overestimate some influencing factors. Therefore, we choose the spatial econometric model that can consider spatial effects to test the driving factors of TFEE. This article first selects the most appropriate spatial econometric model through related tests such as LM, LR and Wald. The results are shown in Tables 5 and 6. According to the test results of the fixed effects and random tests (Table 5), it can be seen that the probability value of the likelihood ratio statistic also rejects the null hypothesis of "spatial fixed effects combined insignificant" and "time fixed effects combined" under the 1% significance level test. Therefore, it is most reasonable to choose the spatial panel model with spatial and time fixed effects.
The LM, Wald and LR test results of the spatial panel model based on spatial and time fixed effects (Table 6) show that both LM lag and LM error passed the significance level test while robust LM lag and robust LM error did not. At the same time, the Wald test and LR test both rejected the null hypothesis. These results show that the spatial Durbin model cannot be simplified into a spatial lag model and a spatial error model. Therefore, this article finally chooses the spatial Durbin model with spatial and time fixed effects.
According to the regression results in Table 7, the coefficients of technological progress (TP), industrial agglomeration (IG) and human capital (HC) passed the significance level test and were significantly positive. The coefficients of industrial structure (IS), energy intensity (EI) and urbanization level (CITY) passed the significance level test and were significantly negative. The coefficients of environmental regulations (GZ) and its quadratic coefficients (GZ2) passed the significance level test and were significantly positive and significantly negative, respectively, showing a "U" shape. The coefficient of economic development level (GDP) and foreign direct investment (FDI) was positive, but it failed the significance level test. All driving factors will affect the TFEE through specific "polarization effect" and "trickle down effect", that is, the TFEE of neighbouring provinces will have a corresponding impact on the TFEE of the provinces. Each factor promotes the improvement of TFEE of the province which will also be transmitted to neighbouring provinces through the spatial spillover mechanism, thereby promoting the common improvement of TFEE of neighbouring provinces.
However, according to the related theory of LeSage and Pace (LeSage and Pace 2009), when the spatial lagging explanatory variable and the explained variable are included in the spatial econometric model, the estimated coefficient cannot directly reflect the marginal effect like the traditional econometric model. To obtain the average spillover effect on adjacent regions when the regional explanatory variables change, decompose it into direct effects (effects on this region), indirect effects (spillover effects on neighbouring regions) and total effects (comprehensive effect), and then proceed with statistical testing (Elhorst 2010;Elhorst and Fréret 2010). A more scientific and reasonable method is to analyse by observing direct effects and indirect effects. Therefore, this article uses direct effects and indirect effects to observe the impact of each driving factor on TFEE. The results are shown in Table 8.
(1) The regression results show that the direct effect coefficient of the economic development level is 0.0241. Although the coefficient direction is positive, it does not pass the significance test. This shows that economic development on the improvement of TFEE is not obvious. The traditional extensive development model consumes much fossil energy and produces more pollution emissions, which makes the environmental cost of economic development continue to rise. However, as the economy continues to develop, new energy sources, energy-saving and consumption-reducing technologies continue to emerge, and the negative environmental externalities at the initial stage of development are gradually offset. At this stage, the development model of China is gradually shifting from an extensive model to a high-quality model. In the process of transformation, although the negative environmental externalities are gradually offset, the policy, technology, management and other aspects are still not perfect. As a result, the TFEE cannot be easily improved. The indirect effect coefficient of the economic development level is −0.2503 and passes the 1% significance test. This shows that the level of economic development will produce significant negative spatial spillover effects. This may be because provinces with high economic development levels transfer industries with high input, high pollution and high energy consumption to neighbouring provinces with lower economic development levels during the process of economic development mode transformation, which inhibits the increase in TFEE in other provinces. At the same time, in provinces with a high level of economic development, the local government has higher environmental regulation requirements, and the local residents have higher environmental protection demands, which will force the high-polluting enterprises to move to the surrounding provinces with lower environmental regulation requirements and low environmental protection demands, thus inhibiting the improvement of TFEE in surrounding provinces.
(2) The direct effect coefficient of technological progress is 0.0243, and the indirect effect coefficient is 0.0707. Both passed the 1% significance test and were significantly positive. This shows that technological progress can not only significantly improve the TFEE of this province but also significantly promote the TFEE of neighbouring provinces. Technological progress can effectively promote the innovation of production technology, promote the popularization of advanced technologies such as energy savings, new energy, low-carbon and pollution control, help improve the utilization efficiency of resources and energy in the production process and reduce the production and discharge of pollutants. Therefore, technological progress is not only conducive to improving the TFEE of the province but also has a positive effect on the improvement of the TFEE of neighbouring provinces.
(3) The direct effect coefficient of the industrial structure is −0.2751 and passes the 1% significance test, showing that the industrial structure has an inhibitory effect on the improvement of TFEE. The higher the proportion of the secondary industry is, the higher the consumption of fossil energy. As the main producer of environmental pollution, fossil energy will generate four waste emissions (solid waste, CO 2 , SO 2 and wastewater) during economic operation, which will worsen the ecological environment. China's economic development is in a critical transition period, but the secondary industry, which is characterized by "three high" (high investment, high energy consumption and high pollution), still occupies the dominant position, and its negative impact on TFEE will continue to exist. The indirect effect coefficient of the industrial structure is −0.1735 and does not pass the significance test, showing that the industrial structure has no obvious negative spillover effect. The reason is that the industrial structure, as a significant bond between economic activities and the ecological environment, plays a crucial part in resource allocation, resource consumption and the types and quantities of pollutants discharged through structural adjustments that affect changes in input and output elements. However, these effects are limited by distance and have limited impact on the TFEE of neighbouring provinces. (4) The direct effect coefficient of industrial agglomeration is 0.3298 and passes the 1% significance test, showing that industrial agglomeration promotes the improvement of TFEE. Industrial agglomeration is an inevitable choice for the development of industrialization. In the initial stage of industrial agglomeration, the agglomeration effect brought about product exchange symbiosis, infrastructure and technology spillover sharing, which is conducive to the positive externality of the agglomeration. However, with the continuous expansion of industrial agglomeration, the congestion effect caused by resource shortages and environmental pollution will gradually offset the positive externalities of agglomeration. At this stage, the level of industrialization in China was still low, and industrial agglomeration was still in the growth stage. Industrial agglomeration will still promote the improvement of TFEE. The indirect effect coefficient of industrial agglomeration is 0.1172 and does not pass  the significance test. Industrial agglomeration will lead to industrial transfer in neighbouring provinces. The relocation of "high pollution, high consumption and high input" industries provides favourable conditions for the improvement of TFEE in neighbouring provinces. In addition, industrial agglomeration in the province drives the development of nearby enterprises to cluster. The positive effect of industrial agglomeration promotes the improvement of TFEE in neighbouring provinces. Since the level of industrial agglomeration in provinces was still low at the current stage, this spatial spillover effect could not be brought into full play, resulting in a situation in which although positive effects could be produced, the effects were not significant. (5) The direct effect coefficient of the urbanization level is −0.2780 and passes the 1% significance test, indicating that the urbanization level has an inhibitory effect on the improvement of TFEE. China's urbanization is in an accelerated stage, and urban problems begin to emerge. First, it has increased the pressure on land resources, water resources and energy. Second, a large number of agricultural populations have entered cities, increasing pollution and resulting in the continuous deterioration of urban ecological environment quality. Thus, improvement of TFEE is inhibited. The indirect effect coefficient of the urbanization level is 0.5992, passes the 1% significance level test and is significantly positive. This shows that the urbanization level has an obvious positive spillover effect; that is, the urbanization level in a province can promote the improvement of TFEE in neighbouring provinces. This may be because the higher the level of urbanization, the more infrastructure construction and the inflow of rural population will increase. These factors will aggravate the population, resources and environmental pressures of the provinces but can greatly alleviate the population, resources and environmental pressure of neighbouring provinces. Simultaneously, when the urbanization process in a province is relatively smooth, it will indirectly stimulate the speed of urbanization in neighbouring provinces, thereby promoting the improvement of TFEE in neighbouring provinces. (6) The direct effect coefficient of energy intensity is −0.1139 and passed the 1% significance tests, indicating that energy intensity has an inhibitory effect on improving TFEE. The higher the energy intensity is, the greater the pressure it brings to the environment, resulting in increasing pressure on China's ecological environment year by year and triggering a series of ecological and environmental issues, which seriously hinder the improvement of TFEE. In addition, the energy consumption structure of China's provinces is dominated by highly polluting coal, and the energy structure is unreasonable, which makes energy consumption pay a large ecological cost while promoting economic development, which greatly restricts the improvement of TFEE. The indirect effect coefficient of energy intensity is −0.0614 and does not pass the significance test, indicating that energy intensity cannot produce significant spatial spillover effects. (7) The direct effect coefficient of human capital is 0.4498, passes the 1% significance test and is significantly positive. This shows that human capital can promote the improvement of TFEE. Higher human capital not only contributes to technological innovation and promotes technological progress but also improves the management level and promotes institutional innovation, thereby improving the efficiency of natural resource utilization and achieving the purpose of promoting the improvement of TFEE. In recent years, with the rapid development of China, the education level of residents has also risen sharply, and human capital has made great progress, which has greatly promoted the improvement of TFEE. The indirect effect coefficient of human capital is 1.7663 and passes the 1% significance test, showing that human capital has an obvious positive spillover effect. That is, the human capital of the province can promote the improvement of the TFEE of neighbouring provinces. The promotion of human capital is conducive to the formation of talent aggregation phenomena, which makes the provinces present a trend of increasing talent, technology and other elements. When the elements gather to a certain scale, it will produce spillover effects of technology and knowledge, spread to neighbouring provinces and promote the improvement of TFEE in neighbouring provinces. (8) The direct effect coefficient of FDI is −0.0001 and does not pass the significance test. This shows that foreign direct investment cannot play an effective role in the TFEE of this province. China is at the bottom of the industrial chain in the process of introducing foreign capital. Most FDI enterprises are pollution-intensive enterprises. Through the linkage effects of upstream and downstream industries, polluting industries have shifted from developed countries to China, which has aggravated China's natural resource consumption and the deterioration of the ecological environment, making China become the developed countries' "pollution haven". However, the advanced production technology, technical equipment and management experience mastered by FDI enterprises can offset some of the negative effects brought about by FDI to a certain extent. This creates a situation where although there will be a negative impact, the effect is not significant. The indirect effect coefficient of FDI is −0.0277 and passes the 10% significance test showing that FDI has an obvious negative spillover effect. It may be that the cross-regional pollution-intensive industry chain of FDI has initially formed, and crossregional pollution spillover is more obvious. In addition, the technology and knowledge spillover effects of FDI can radiate only to provinces and cannot radiate to neighbouring provinces to offset the negative impact of cross-regional pollution. This led to the formation of the current situation. (9) The direct effect coefficient of the primary term of environmental regulation is −1.6651, passes the 10% significance test and is significantly negative. The direct effect coefficient of the secondary term of environmental regulation is 0.8282, passes the 10% significance level tests and is significantly positive. This shows that there is a Ushaped relationship between environmental regulation and TFEE. Before the U-shaped turning point, China's environmental pollution control investment level was low, and its effect on the improvement of the ecological environment was very limited. In addition, an increase in government investment in governance would squeeze out economic construction expenditures, which was not conducive to economic growth; therefore, the strengthening of environmental regulation will lead to a decline in TFEE. After the U-shaped turning point, the government's investment in the three waste treatment projects is at a relatively high level. The equipment and technology used for environmental pollution treatment have been greatly improved due to financial support. The effect of environmental pollution control began to appear, and environmental regulation began to promote the improvement of TFEE. The indirect effect coefficient of the primary term of environmental regulation is 4.9524, and the indirect effect coefficient of the secondary term of environmental regulation is −2.4643. Neither passed the significance test, indicating that the spatial spillover effect of environmental regulation is not significant and cannot have a significant impact on the TFEE in neighbouring provinces.

Robustness analysis
In this article, the robustness test of the empirical results of TFEE is carried out by replacing the spatial weight matrix. First, in the previous analysis, we mainly used the 0-1 matrix based on geographic location as the spatial weight matrix. In the robustness test, we used the nested matrix of geographic location and geographic distance (W2) and nested matrix of geographical location and economic distance (W3) to reexamine the above results. The regression results are consistent with Tables 8 and 9. The results show that the significance and signs of the coefficients of each variable are basically the same as the above. Tables 9 and 10 show the specific robustness test results.

Conclusions and policy implications
In this article, a TFEE model considering input, desirable output and undesirable output was constructed based on the totalfactor analysis framework. Next, a hybrid distance Super-EBM model considering undesirable output was proposed to evaluate China's TFEE in three dimensions (national-regional-provincial)from 2003 to 2017. Then, an ESDA model was conducted to reveal the spatiotemporal characteristics and spatial effects of TFEE. Finally, a spatial Durbin model (SDM) with spatial-temporal double fixed effects was selected to test the driving factors and spatial spillover effects of China's TFEE. To sum up, the following main findings can be drawn. First, from a national perspective, although China's TFEE is relatively high, China's overall TFEE showed a downward trend during 2003 to 2017. From a regional perspective, the TFEE of the four regions has not been effective, and there are obvious differences between regions, with an ordering of eastern > northeastern > central > western. From a provincial perspective, the TFEE of Beijing, Tianjin, Shanghai is efficient, is above the frontier and reaches the optimal configuration. The TFEE of other provinces has not been effective, their input and output are inefficient, the optimal configuration has not been achieved and there is still a room for improvement to varying degrees. In addition, the development trend of provinces with high TFEE is unstable, the average annual growth rate is low and they are mainly distributed in the northeast and eastern regions. The provinces with low TFEE have a relatively stable development trend and a high average annual growth rate, mainly distributed in the central and western regions. Second, the TFEE of China has a positive spatial autocorrelation and shows a strong spatial agglomeration. However, Moran's I index showed a fluctuating dynamic trend from 2003 to 2017, showing that the spatial distribution pattern of TFEE in China was unstable and easily changed. Furthermore, the Moran scatter plot indicates that the provinces of the first and third quadrants are mostly distributed in the eastern and western regions, while the provinces of the second and fourth quadrants are mostly concentrated in the central and northeastern regions. These results all show that China's provincial TFEE has both spatial dependence characteristics and spatial difference characteristics.
Third, the spillover effect of TFEE in provinces that would enhance the TFEE of neighbouring provinces is supported by the spatial Durbin model with spatial-temporal double fixed effects. The results show that most factors are related to TFEE to varying degrees. TP, IG and HC play a positive role in TFEE and can effectively improve the province's TFEE. IS, CITY and EI play a negative role in TFEE and inhibit the promotion of TFEE in this province. Furthermore, ER shows a U type of relationship with TFEE. Before the U-shaped inflection point, GZ inhibits TFEE, and after the U-shaped inflection point, it promotes TFEE. GDP and FDI cannot have a significant impact on TFEE at this stage. Finally, the spatial spillover effects of GDP, TP, CITY, HC and FDI are proven to exist. TP, CITY and HC will have a significant positive spatial spillover effect and promote the improvement of TFEE in neighbouring provinces. GDP and FDI will produce significant negative spatial spillover effects, inhibiting the improvement of TFEE in neighbouring provinces. The spatial spillover effects of IS, IG, EI and GZ are not significant. This shows that at this stage, these three factors will only have a significant impact on the TFEE of the local provinces and will not have a significant impact on the TFEE of neighbouring provinces.
Based on these conclusions, this article puts forward meaningful policy implications from four aspects: (1) National top-level design China should accelerate the transformation of the economic development mode and attach importance to resource consumption and environmental constraints in the process of economic development. Under the guidelines of sustainable development and ecological civilization construction, China should follow the laws of nature, attach importance to environmental protection and enhance the efficiency of resource utilization. The government should abolish the "GDP-only theory", improve the "green" assessment system based on TFEE and improve the environmental protection awareness of governments at all levels in the process of development.
(2) Regional and provincial differences Because the TFEE of China's regions and provinces shows significant differences, it is essential to break the regional blockade and benefit barriers, reduce system disorder impeding regional cooperation, strengthen regional cooperation, promote the free flow of capital, labour, technology, etc., achieve the gradient transfer of high-quality talents, high technology and advanced management mode and thereby reduce the regional difference of TFEE. In addition, China should actively promote "top-down" overall economic development planning, avoid homogeneous competition among provinces and speed up the formation of a new coordinated development mechanism for joint prevention and control of the ecological environment.
(3) Spatial distribution characteristics China's TFEE has significant positive spatial correlation and agglomeration characteristics. Therefore, for the central and western regions with low level TFEE agglomeration, while vigorously promoting technological and structural emission reduction, emphasis should be placed on the development of industries with high added value, low carbon and environmental protection. At the same time, central and western regions should actively carry out extensive and specialized division of labour and cooperation with the eastern and northeastern regions and accelerate the construction of industries closely related to the leading industries in the eastern and northeastern regions, to promote the optimization and upgrading of the industrial structure. Provinces with high TFEE in the eastern and northeast regions should provide corresponding technical assistance to the central and western regions, actively publicize and impart advanced experience in resource utilization and environmental protection and vigorously carry out technical exchanges and cooperation in the field of energy and environment.
(4) Influencing factors According to the test results of influencing factors and the spatial spillover effect of China's TFEE, this article proposes some pertinent policy suggestions.
① China should adhere to the strategy of upgrading and developing its industrial structure, resolutely close down and eliminate the "three high" (high investment, high energy consumption and high pollution) enterprises and take the market as the guide to let enterprises and industrial development survive. At the same time, China should actively guide the orderly transfer of industries to achieve scientific upgrading of industrial structure. ② China should adhere to the "innovation-driven development" strategy and explore the potential of technological innovation to improve the TFEE, promote the construction of an innovation system and accelerate the transformation of scientific and technological achievements. At the same time, enterprises should be encouraged to increase investment in research and development through fiscal, taxation, government procurement and other policies, to strengthen independent research and development, technology introduction and technological transformation investment, to reduce resource consumption in the production process, to reduce the intensity and total amount of pollutants discharged and to improve the TFEE. ③ China should strengthen environmental regulations, introduce more stringent and effective policies for resource and environmental management and regulate the structure and scale of energy, land and water resource utilization. At the same time, China should further refine all kinds of environmental protection rules and regulations, set specific, operable and quantifiable emission reduction targets for environmental protection and severely punish illegal enterprises and excessive emissions to reduce environmental pollution at the source. ④ With the construction of high-level industrial agglomeration areas as the entry point for future development, efforts should be made to improve the integration degree of traditional leading industries and appropriately develop emerging industries to continuously expand the regional industrial clusters to realize the interaction between industry and city and green development and to optimize the resource allocation between regions through coordination. ⑤ China should promote green low carbon energy consumption structure transition, encourage enterprises in the development and utilization of renewable energy sources, such as wind and tidal power, promote a clean coal utilization plan of action, the all-round in view of the special action efficiency key energy-consuming industries, speed up the building enterprise energy management system, energy management system throughout the whole process of production of the enterprise. ⑥ China will actively change the path of extensive urbanization. On the one hand, China will accelerate the formation of cluster development with central cities as the core and surrounding cities as the support to realize the intensive and economical use of resources and centralized management of pollutant discharge, accelerate the industrial and population agglomeration of the central cities and improve the comprehensive carrying capacity and radiation driving capacity of the central cities. On the other hand, China should realize the intensive use of land, optimize the energy consumption structure, improve the utilization rate of natural resources and reduce the total emission of pollutants to obtain the maximum economic benefits with minimum resource consumption and environmental damage. ⑦ On the one hand, China must change to a local government achievement appraisal system and guide government investment of foreign capital to pay attention not only to economic benefits but also to resources and environmental benefits, and improve the utilization rate of foreign capital by using preferential policies to guide foreign capital flows to the third industry, the high-tech industry, by raising taxes to limit excessive foreign flow to the excessively polluting manufacturing industry. On the other hand, China will issue detailed rules on finance, taxation and finance to encourage foreign-invested enterprises to transform domestic high-polluting industries and enterprises by introducing advanced technologies and equipment to promote the improvement of TFEE. ⑧ China should make great efforts to attract high-level, highly skilled talent and encourage talent from the region to return. At the same time, China should also increase investment in educational infrastructure, improve the equalization of educational resources, vigorously develop educational undertakings and improve the human capital level of residents.
Author contribution LC, ZY and ZS designed the whole study; LC and WJ conducted data collection, modeling and results analysis; LC wrote the paper. Data availability The data used in this article can be found in the "China Statistical Yearbook", "China Energy Statistical Yearbook" and "China Environment Yearbook".

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Competing interests The authors declare no competing interests.