Regional Di ﬀ erences in the Spatial Characteristics and Dynamic Convergence of Environmental E ﬃ ciency in China

: This study uses the undesirable output and super-e ﬃ ciency slacks-based measure combined with window (WIN-US-SBM) data envelopment analysis (DEA) to evaluate the environmental e ﬃ ciency (EE) in 30 Chinese provinces, from 2005 to 2016, explores regional di ﬀ erences in the EE, and uses the dynamic spatial Durbin model (DSDM) to analyze regional di ﬀ erences in e ﬀ ects of important factors on the convergence of EE. It reveals that EE in the eastern area is higher than EE in the central and western areas, and a positive spatial autocorrelation exists in the interregional EE. The di ﬀ erence in provincial EE gradually narrows over time and tends to converge to its own steady-state level. Economic growth reduces EE for the central and western areas and improves e ﬃ ciency for the eastern area; economic growth from surrounding areas indirectly promotes local EE for the eastern area. Foreign direct investment (FDI) promotes EE in the eastern and central areas, and FDI in the adjacent areas has a positive e ﬀ ect on local EE for the eastern area. Export reduces EE for all areas, and export in surrounding areas indirectly promotes local EE for the central area. Industrialization reduces EE in the western area, and industrialization in the surrounding areas increases local EE for the eastern area. Energy e ﬃ ciency promotes EE for the central area, urbanization increases EE for the central area, and urbanization of the surrounding areas reduces local EE for the eastern area.


Introduction
Fossil energy consumption has led to heavy pollution in a wide range of areas in China over recent years, and it has attracted international attention. Regional development is seriously unbalanced for the vast territory of China. The eastern area is located in the coast, with pleasant climate, fertile soil, convenient transportation, and natural development advantages. Most of the central and western areas are inland with relatively underdeveloped transportation and many unfavorable factors for economic and social development. The economic base, industrial structure, export, foreign direct investment (FDI), population density, and urbanization have significant heterogeneity, in different areas of China. Pollutants easily spread across regions and an interaction effect exists among the regional economies, which influences regional environmental efficiency (EE). What are the characteristics of spatial changes in EE among different regions in China? Will the EE gap between regions tend to converge or diverge, and will it continue to exist or even expand in China? What factors affect the spatial convergence degree of EE in different areas? The answers are important to understand the current regional EE Sustainability 2020, 12, 7423 2 of 18 status and for taking measures to improve future EE. In this regard, this study explores regional differences in EE and discusses the effects of important factors, such as GDP per capita, industrial structure, export, FDI, energy efficiency, and urbanization, on the convergence of EE. Thus, this study provides a theoretical basis for formulating effective countermeasures of sustainable development for relevant decision-making departments.
The remainder of this article is organized as follows: In Section 2, we review existing research and point out the novelty of our study; in Section 3, we describe the model and method used in this study; in Section 4, we present the data sources; in Section 5, we outline the empirical results and discussion; and in Section 6, we present our conclusions and put forward relative policy suggestions.

Literature Review
EE refers to the ability to create more goods and services with less negative impact on the environment [1,2]. It measures the performance for an enterprise, an industry, or a region from an environmental perspective and provides references for government decision makers to formulate environmental policies to delay the trend of environmental degradation [3,4]. At present, many studies have used stochastic frontier analysis (SFA) and data envelopment analysis (DEA) to evaluate EE. For example, Wang et al. [5] used the SFA method to calculate EE of the Chinese coal industry from 2007 to 2014. SFA is a typical parametric method, suitable for multi-input and single-output model, but susceptible to the influence of production function form [6]. A DEA does not need dimensional processing of data and specific model form, which avoids subjective weights [3]. Fossil energy consumption inevitably produces undesirable outputs. Because of such pollutants and waste, many studies have adopted the DEA model which contains desirable and undesirable outputs for analyzing EE [7][8][9].
Nowadays, many studies have explored EE at an industrial or provincial level [2,4,10,11]. For example, at the industrial level, Chang et al. [12] used a non-radial DEA model based on the slacks-based measure (SBM) to examine EE in the Chinese transportation industry. Ullah and Perret [13] used the DEA method to explore EE in the Pakistani cotton growing industry. Zhou et al. [14] applied an integrating entropy weight method and the SBM model to analyze the current situation and trend of EE in the Chinese power industry from 2005 to 2010. At the provincial level, Yang et al. [15] estimated the EE for 30 provinces in China through the environmental super-efficiency DEA model, and examined regional differences in EE. Piao et al. [16] used three kinds of DEA models and combined them with the Malmquist-Luenberger productivity index to estimate EE and its dynamic change trend in Chinese provinces from 2005 to 2014. Chen et al. [17] used the DEA to evaluate the provincial EE in China and tested the hypothesis of EE and suggested that improving the EE was important for reducing environmental risks. Zhu et al. [18] constructed an extended DEA model, and used window DEA combined with undesirable output and super-efficiency slacks-based measure (WIN-US-SBM) model, to explore the impact on eco-efficiency in Western Taiwan Straits Economic Zone.
Meanwhile, some studies have explored the impact of various factors on EE. For instances, Li et al. [19] estimated the EE of 29 provinces in China, and found that the trade dependence, industrial structure, and local fiscal expenditure had different effects on the EE in different regions. Zhang et al. [20] studied the influencing factors for EE with the Tobit regression model, and found that the per capita GDP, population density, innovation capacity, environmental awareness, and industrial structure promoted the EE, whereas the energy intensity curbed the EE. Yang and Li [21] used the regression method to examine the impact of various factors on Chinese industrial EE and found that both FDI and export had a negative effect on the industrial EE.
For the study of convergence, many studies have focused on the convergence of energy intensity [22,23] and energy efficiency [24][25][26]. Some studies discussed the convergence of air pollutant emissions [27,28]. The analysis of convergence has been gradually extended to the field of resources and environment [29,30]. Cameron et al. [31] analyzed the convergence of EE in industrialized countries Sustainability 2020, 12, 7423 3 of 18 and found that there was a significant convergence of EE in industrialized countries, among which Switzerland had the highest EE, whereas other countries played the role of catching up to Switzerland.
Some studies have adopted a nonlinear time-varying factor model developed by Phillips and Sul [32] which took into account the individual heterogeneity. Gonzalez-alvarez et al. [33] used the Phillips and Sul's method to consider the evolution of non-renewable, unclean and total energy intensity and estimated the existence of convergent clubs. Castillo-Giménez et al. [34] discussed the convergence in municipal waste treatment in the European Union (EU)-27. Some studies used the traditional σ-convergence and β-convergence to discuss the efficiency convergence. Long et al. [35] used absolute and conditional β-convergence to study the eco-efficiency in Chinese cement enterprises, and found the eco-efficiency was convergent in China. Yu et al. [36] studied the industrial ecological efficiency in 30 provinces of China and found absolute and conditional convergences in the industrial eco-efficiency.
Previous studies have shown the spatial differences in EE among different regions in China, which were mainly because of the heterogeneity of resource endowment, technological progress, and other factors among different regions [18]. In summary, the existing studies had the following shortcomings. First, the general DEA method only used cross-sectional data, without considering the influence of time factor on the fluctuation of EE. Second, the current studies only evaluated the differences in regional development and failed to study the evolution of absolute differences with each region. Third, the existing studies seldom applied the dynamic spatial panel model to study the effects of factors on the convergence of EE. Considering the research gap, this study further investigates the following aspects: First, we take the pollutants as the undesirable output, and use the WIN-US-SBM method to comprehensively evaluate the regional EE in China. The WIN-US-SBM method is an improvement on the traditional DEA and can evaluate the efficiency of each decision-making unit (DMU) on a section, as well as the variation trend of the efficiency of all decision-making units (DMUs) on time series. Compared with Zhu et al. (2019), first, we expand the time range and increase the types of undesirable outputs. Second, we use the DSDM to study spatial EE convergence from the perspective of regional differences, explain the change trend and dynamic characteristics of EE in different provinces of China, and analyze the convergence or divergence of regional EE. This study provides new insight in this relative research area.

The WIN-US-SBM Method
The traditional radial DEA method cannot distinguish the efficiency difference between effective DMUs, because it does not consider the slack variable problem. Tone [37] put forward the SBM model to avoid the slack variable problem. The difference is that the input-output relaxation is directly introduced into the objective function in the SBM model, which is helpful for estimating the efficiency in a non-radial way on the basis of input-output data. Tone [38] proposed a super-efficiency and undesirable output SBM model. This model comprehensively considered the relationship between input and output/pollutants, and allowed the efficiency value to be greater than 1. The super-efficiency and undesirable output SBM model could evaluate the efficiency of DMU caused by the slack variable problem. Suppose the production system has n DMUs, according to the studies of Tone [38] and Cooper et al. [39], the formula of super-efficiency and undesirable output SBM model is expressed as Equation (1).
where i, r, t, and k stand for ith input, rth desirable output, tth undesirable output, and kth DMU, respectively; x ik , y g rk and y b tk represent input, desirable output, and undesirable output, respectively; m stands for the input (x) number; q 1 stands for the number of desirable output (y g ); q 2 stands for the number of undesirable output (y b ); s − i , s g+ r and s b− t are the slack variables in the input and output; λ is the weight vector; and ρ * represents the relative efficiency.
Since the original DEA method is mainly used for cross-sectional analysis, each DMU is observed only once and cannot be compared across periods, which greatly limits its application scope. In order to solve this problem, Charnes et al. [40] proposed the DEA window analysis. It uses the moving average method to estimate the relative efficiency in a DMU and investigates efficiency trends. The DEA window model regards the same DMU in different periods as different DMUs, thereby increasing the DMU number, which is conducive to exploring the efficiency change trend of each DMU and obtaining more efficiency evaluations. The DEA window model can be used to compare the performance in a DMU with its own performance during different periods, and with the performance in other DMUs during the same period [41]. Suppose the window width is d and the time period is T, the number of windows is established as T − d + 1. If the number of initial DMUs is n, then the number of evaluated DMUs is d × n × (T -d + 1). We combined the window DEA with the super efficiency SBM model and undesirable output. Compared with Zhu et al. [18], we expanded the time range (2005-2016) and increased the types of undesirable output. In the T (T = 1, . . . , T) period and N DMU, r types of input are used to get s types of output; suppose the input vector is X t n = x 1t n . . . x rt n T and the output vector is Y t n = y 1t n . . . y rt n T , if the window starts from time t (1 ≤ t ≤ T) and its width is d (1 ≤ d ≤ T − d + 1), the input and output matrices are expressed as Equations (2) and (3), respectively.
where δγ denotes the γth year in the δth window and x δγ ik , y g,δγ rk and y b,δγ rk represent input, desirable output, and undesirable output at the γth year in the δth window, respectively. Other variable definitions are consistent with Equation (1).
We choose window width d as 3, according to the study by Halkos and Polemis [42]. Thus, the first window contains the years 2005, 2006, and 2007. When the window slides, the original year is dropped and a new year is added, and the last window contains the years 2014, 2015, and 2016.

Global Spatial Autocorrelation
Moran [43] proposed a global Moran's I index, as shown in Equation (5).
where w ij is the element of spatial adjacency weight matrix. The commonly used spatial adjacency matrix is set as follows: if region i adjacent to j, then w ij = 1; otherwise, w ij = 0. In addition, n denotes the total regional number; x i and x j denote the EE in region i and region j, respectively; x represents the EE average; and the Moran's I index ranges from −1 to 1. The Moran's I index shows a positive spatial autocorrelation if it is between 0 and 1, and the greater the index is, the stronger the positive spatial autocorrelation is. Otherwise, it is a negative spatial autocorrelation, and the smaller the index is, the stronger the negative spatial autocorrelation is. In particular, there is no spatial autocorrelation if the index is 0.

Local Spatial Autocorrelation
Anselin [44] proposed the local Moran's I index to test whether the high or low observed values in local areas tend to agglomerate in space, which is expressed as Equation (6)

The Convergence Model
The main convergence model includes Phillips and Sul's model [32] and traditional σ-convergence and β-convergence. The shortcoming of the Phillips and Sul's method is that it cannot explore the influence of spatial factors on convergence. In this study, spatial factors were introduced into the analysis of EE convergence by combining spatial factors with traditional σ-convergence and β-convergence, and the regional differences in the spatial characteristics of EE convergence are discussed. This is helpful to clarify the convergence (divergence) of EE among provinces in China. If convergence exists in the interprovincial EE, the gap is narrowed between the provinces with low EE and provinces with high EE; otherwise, the gap of EE is further enlarged.
(i) The σ-Convergence σ-convergence is mainly used to analyze the dispersion degree of each sample distribution. If the σ value in different areas tends to go up, the σ-convergence exists. According to Yu et al. [45], the coefficient variation (CV) of EE is used to measure σ-convergence, which is shown as Equation (7): where, CV represents the coefficient variation of EE in year t, n is the total provincial number, EE it is the EE for province i in year t, and EE t represents the average EE of each province in year t.
(ii) The Absolute β-convergence The absolute β-convergence can test if the interprovincial EE approaches the same steady-state level, that is, if the provinces with low EE have a "catch-up effect" on the provinces with high EE. It is used to investigate whether or not EE is negatively correlated with its initial level. This model is expressed as Equation (8).
where, EE i,t and EE i,t−1 represent the EE values for region i in year t and year t − 1, respectively; ln(EE i,t ) − ln(EE i,t−1 ) stands for the EE growth rate for region i from year t − 1 to year t; β is the coefficient of convergence; α denotes the constant term; and ε it represents the random error term. The absolute β-convergence exists if the β value is less than 0.
(iii) The conditional β-convergence The conditional β-convergence means that different regions have their own steady-state levels. If the β value is less than 0, the conditional β-convergence exists. This model is expressed as Equation (9).
where X i,t−1 represents the control variable and λ represents the coefficient of control variable. The definition of other variables is the same to Equation (8).

Spatial Convergence Test
In this study, the spatial effect is considered in the convergence effect analysis. The spatial econometric models include spatial lag model (SLM), spatial error model (SEM), and spatial Durbin Sustainability 2020, 12, 7423 7 of 18 model (SDM). As a general form of SLM and SEM, the SDM contains the spatial lag of dependent and independent variables, which can be used to test the influence of independent variables on dependent variables in local and surrounding areas. Thus, the SDM was used in this study.
The SDM of absolute β-convergence is expressed as Equation (10): The SDM of conditional β-convergence is expressed as Equation (11): where denotes the growth rate of EE in region i from year t − 1 to year t, W represents the adjacent spatial weight matrix, and X represents control variables. We take into account the variables including the FDI, export, industrialization, energy efficiency, urbanization, and so on. Beta (β) is the regression coefficient, which reflects the test result of β-convergence; ρ denotes the spatial autoregressive coefficient; ε it denotes the random error; θ 1 represents the control variable coefficient; λ and θ 2 represent the spatial lag coefficients of ln EE i,t−1 and the control variable, respectively. Subscripts i and t represent the province and year, respectively. Vallés and Zárate [46] suggested that the environmental issues needed to be considered from a dynamic perspective, as pollutants in one year depend on the previous year's emissions. The dynamic panel data model reflects the dynamic lag effect by introducing the lag dependent variables. The EE change is a dynamic process, therefore, it takes into account the time lag effect, that is, the early development status can affect future development. Therefore, the dynamic panel model was extended to study the convergence of regional EE, and the spatial and time dimensions were considered to ensure the accuracy and reliability of empirical results [47]. The DSDM of absolute β-convergence is expressed as Equation (12): The DSDM of conditional β-convergence is expressed as Equation (13): where ∆EE i,t−1 represents the one year lagged ∆EE i,t and α represents the dynamic effect of ∆EE.

Data Sources
The sample interval was selected from 2005 to 2016. In this study, 30 provinces of China were considered exclusive of Hong Kong, Macao, Taiwan, and Tibet for the data absence. China can be divided into three areas based on the geographical and administrative location, i.e., the eastern, central, and western areas [25], as shown in Table 1. studies by Halkos and Tzeremes [7], Chang et al. [12], Pan et al. [48], and Wang and Wei [49]. The data for these wastes and pollutants came from the China Statistical Yearbook, China environment protection database and the emission inventory by Tsinghua University [50]. The data for energy use in the provinces came from the China Energy Statistical Yearbook. The data for labor (the number employed at the end of each year) came from the Provincial Statistical Yearbook for all provinces. The "perpetual inventory method" was generally used to estimate the actual capital stock for each year [51]. In order to measure the actual level of FDI and export, we used the index of FDI dependence and export dependence, expressed by the proportion of total FDI and total export to GDP in different provinces, respectively. The industrialization indicator was measured by the proportion of secondary industry output value. The original data for GDP per capita, export, FDI, industrial output, and built-up urbanization area came from the China Statistical Compilation, China Statistical Yearbook, and the China Provincial Statistical Yearbook. The variable definitions are shown in Table 3. In order to eliminate the impact of exchange rate and price on variable values, all currency data were converted into standard prices using the price index based on the year 2005 (2005 = 100).   (Figure 1). The average EE in the eastern area (0.7786), western area (0.2176), and central area (0.2130) reached the highest level in 2016. The eastern area is developed in the economy and high in production efficiency, so it has a high EE [4]. Due to its geographical location, Sustainability 2020, 12, 7423 9 of 18 the central and western areas fall behind the eastern area in economic development [52], and the EE is relatively low.    Table 5 shows that the Moran's I value is positive at the significance level of 5% after 2007. This reveals that the spatial distribution of EE has a significant positive correlation in China. The EE in each province presents a spatial agglomeration, that is, the provinces with high EE or with low EE tend to agglomerate. After 2012, the EE generally increased. This is because a comprehensive plan was declared for pollution prevention and control in the 12th Five-Year Plan period (2011)(2012)(2013)(2014)(2015). China increased the investment in environmental protection in order to achieve the target of emission reduction, and remarkable achievements in the emission reduction of major pollutants have been achieved, which effectively improves the EE.    Table 5 shows that the Moran's I value is positive at the significance level of 5% after 2007. This reveals that the spatial distribution of EE has a significant positive correlation in China. The EE in each province presents a spatial agglomeration, that is, the provinces with high EE or with low EE tend to agglomerate. After 2012, the EE generally increased. This is because a comprehensive plan was declared for pollution prevention and control in the 12th Five-Year Plan period (2011-2015).

Global Autocorrelation Test
China increased the investment in environmental protection in order to achieve the target of emission reduction, and remarkable achievements in the emission reduction of major pollutants have been achieved, which effectively improves the EE.   [53], which leads to large amounts of fossil energy use and serious pollution. Thus, the environment efficiency in these provinces is relatively low, and presents the L-L agglomeration.

Analysis of σ-Convergence
As shown in Figure 3 , the western area had a high economic growth rate and achieved great achievements in environmental construction, which results in EE convergence in the western area.
As shown in Figure 3, the CV in the eastern area generally shows a downward trend from 2005 to 2008 and the coefficient tends to be stable after 2008. This indicates that the absolute σ-convergence exists in the eastern area from 2005 to 2008. The reason may be that the 2008 Beijing Olympic Games accelerated the transfer and diffusion of advanced energy-saving and emission-reduction technologies among provinces. There is no obvious fluctuation of the variation coefficient in the central area. In the western area, the variation coefficient fluctuates from 2005 to 2010, and the coefficient generally declines after 2010, that is, the trend of absolute σ-convergence exists after 2010. During the 12th Five-Year Plan period (2011-2015), the western area had a high economic growth rate and achieved great achievements in environmental construction, which results in EE convergence in the western area.

Analysis of Absolute β-Convergence
The Hausman test results show that the p value is less than 0.05 nationally and regionally, therefore, the fixed effect model should be used. The likelihood ratio (LR) is used to test the spatial, time, and double fixed effects. It is found that the p value is less than 0.01 for the eastern, central, and western areas under the adjacent spatial weight matrix, therefore, the spatial and time fixed effects should be adopted. Table 6 shows that the spatial autocorrelation coefficients (ρ) for all areas are positive. This reflects the obvious spatial agglomeration characteristics of EE regionally. Note: Standard errors in parentheses * p < 0.10, ** p < 0.05, *** p < 0.01.
The regression coefficients of the first lag period of EE growth in the eastern and central areas are significantly positive. This indicates that a significant "time inertia" for the EE growth exists in the eastern and central areas, and the economic and environmental conditions in the early period have a significant impact on the EE growth in the current period.
The coefficient of β for the central area is negative but not significant during the whole period (Table 6), that is, no absolute β-convergence exists in the central area during 2005-2016. The coefficients of β for the eastern and western areas are significantly negative during the whole period. This shows that EE is absolutely β-convergent in the eastern and western areas, that is, EE growth has a negative correlation with its initial level. The possible reasons are that the economic foundation and production conditions in the eastern area are relatively better, and that the environmental protection process has been continuously promoted [54]. The Western Development Strategy has accelerated the infrastructure and environmental protection construction in the western area, which effectively improves the ecological environment quality of the western area [25]. Therefore, the EE gap between the provinces is narrowed, and EE tends to the same steady-state level in the western and eastern areas.

Analysis of Condition β-Convergence
The β coefficients for the eastern, central, and western areas are all significantly negative, indicating that there is a significant conditional β-convergence in regional EE after the control variables are added (Table 7). This means that the EE level of each province in the three areas changes towards its own steady-state level. The coefficient is larger in the conditional β-convergence than in the absolute β-convergence. This indicates that the convergence of EE is more obvious after introducing control variables. Note: Standard errors in parentheses * p < 0.10, ** p < 0.05, *** p < 0.01.
The coefficient of "lnY" in the eastern area is significantly positive in the DSDM model, whereas it is significantly negative for the central area in the SDM model. The coefficient of "lnY" is significantly negative in the western area. Zhou et al. [55] suggested that economic growth had reduced China's EE. Our empirical results indicate that economic growth reduces EE for the central and western areas and improves EE for the eastern area. The eastern area is economically developed due to its geographical location [56]. More attention is paid to the quality of economic development in the eastern area, which is conducive to the improvement of technology and energy efficiency. Thus, the EE is improved in the eastern area. The economic development for central and western areas mainly depends on the consumption of a large number of natural resources, resulting in a large amount of pollutants [57]. Thus, economic growth has a reducing effect on EE in the central and western areas.
The coefficient of "lnFDI" is positive in all areas. Especially, it is statistically significant at a 10% level in the eastern and central areas. This indicates that increased FDI dependence obviously increases the EE in the eastern and central areas. For instance, in the DSDM model, the coefficient of "lnFDI" is 0.0799 at a 1% significance level in the eastern area. This shows that the EE increases by 0.0799% with a 1% increase in FDI dependence for the eastern area. In recent years, the introduction of environmentally friendly FDI into China has been on the rise, and this has promoted economic growth through advanced technology and management experience [58,59]. The inflow of clean FDI leads to the optimization and upgrading of industrial structure, improves the allocation and utilization efficiency of resources, and reduces the resource consumption per unit output and pollutant emissions. Meanwhile, the foreign capital inflow can lead to fierce market competition, eliminate inefficient production, and improve energy efficiency [60]. This is consistent with the research of Zhou et al. [61]. Their results showed that FDI had a positive effect on EE. The structure of FDI has been gradually upgraded to strategic emerging, high-tech, and modern service industries, so the inflow of FDI is conducive to the rise of EE.
The coefficient of "lnEX" is negative in all areas. This indicates that the increase in export dependence reduces the EE. This result conforms to the studies by Wang et al. [5] and Yang and Li [21]. Although Chinese export structure has been continuously optimized, most exports are labor intensive and pollution intensive [62]. Clothing, steel, plastic products, engineering machinery, and other products are important exports in China [63]. For example, seven categories of labor-intensive export valued at 2.9 trillion RMB yuan in 2016, accounting for 20.8% of China's total export value (China Foreign Trade Situation Report, 2017). The production of these products consumed a lot of energy [64,65]. Therefore, increased export dependence reduced EE in all areas. The coefficient of "lnEX" was higher in the eastern area than that in the central and western areas, indicating that the increased export dependence in the eastern area had a stronger negative impact on EE. The total export of the eastern area accounted for more than 85% of China's total from 2005 to 2016, therefore, the increase in export dependence had a strong negative impact on EE for the eastern area.
The coefficient of "lnIND" is significantly negative in the western area, indicating that the increased proportion of industrialization reduces EE. The upgrading effect from labor and capital-intensive industry to high-end and knowledge-intensive industry is not obvious. Large-scale industrial production consumes a lot of energy and discharges a large amount of pollutants, which reduces the EE [66]. Yang and Li [21] showed that EE decreased with an increase of industrialization proportion. This is consistent with the results of our study.
The coefficient of "lnE" in the central area is significantly positive at a 1% statistical level. It indicates that the increased energy efficiency (decreased energy intensity) promotes EE. The emissions of major pollutants mainly come from fuel combustion. Energy efficiency promotion (energy intensity decline) reduces energy consumption per unit output, thereby saving the energy use and improving the EE [67].
In the SDM model, the "lnURE" coefficient in the central area is significantly positive, showing that the increased urbanization level for the central area can promote EE. With the expansion of urbanization scale and adjustment of urban structure in the central area, the layout of cities have been better planned, which effectively promotes the improvement of energy and industrial structure [68], thereby contributing to the improvement of EE.
As for the indirect effect on EE, Table 6 shows that the effect coefficient of W* (lnY) is positive at a significance level of 1% in the eastern area in the DSDM model. This indicates that the economic growth of the adjacent areas has a positive influence on the local EE in the eastern area. With the economic growth of the surrounding areas, the living standard of the people continues to improve and they adopt a more environmentally friendly lifestyle [69], which is conducive for reducing pollutants and indirectly improving EE for the eastern area.
In the SDM model, the coefficient of "W*lnFDI" in the eastern area is significantly positive at a significance level of 5%, which indicates that the increase in FDI dependence in adjacent provinces has a positive effect on the local EE for the eastern area (positive spillover effect). The coefficient of "W*lnFDI" in the eastern area is 0.227. This means that increased FDI dependence in the adjacent areas increases the local EE by 0.227% for the eastern area. This is because of the high degree of industrialization in the eastern area. The increased FDI in the surrounding areas leads to the transfer of a large number of labor-intensive and capital-intensive industries from eastern to surrounding areas [70,71]. This is conducive for improving EE in the eastern area.
The coefficient of "W*lnEX" is significantly positive in the central area. The increased export dependence in the surrounding areas promotes the local EE for the central area. Because processing commodity export is the main mode in the central area, emissions of the industrial "three wastes" in the central area are also increasing rapidly with the development of the export mode, which results in a lot of pollutants. The export of labor-intensive processing trade in the central area shifts to the surrounding areas, which reduces the pollutants and improves EE.
In the DSDM model, the coefficient of "W*lnIND" in the eastern area is significantly positive at a significance level of 1%. The increase in industrial proportion in the adjacent areas increases the local EE for the eastern area. The industrial production consumes a lot of fossil energy and emits pollutants for the eastern area. The eastern region transferred some industrial enterprises with high pollution and energy consumption to neighboring areas [72]. In this case, the increased industrialization level in the surrounding areas has a positive effect on local EE in eastern area.
In the DSDM model, the coefficient of "W*lnURB" is significantly negative in the eastern area. The urbanization in the eastern area consumes a lot of energy. With rapid development of the real estate industry and wide use of automobiles, urbanization leads to a lot of pollutant emissions in the surrounding area, the pollution generated by urbanization spreads to the neighboring areas, and therefore this has a negative impact on the environment efficiency [73,74].

Conclusions and Policy Implications
This study uses the WIN-US-SBM model to evaluate EE in China's different areas from 2005 to 2016, conducts a spatial econometric analysis of autocorrelation, and uses the DSDM to analyze the influencing factors on the spatial convergence of environment efficiency. The following conclusions are drawn based on the empirical analysis: (1) Significant regional differences exist in EE, EE is obviously higher in the eastern area than EE in the central and western areas, and a positive spatial autocorrelation exists in the Chinese interregional EE. (2) The gap between provincial EE exists in the central area, and the provincial EE gradually converges to the same steady-state level for the eastern and western areas; the difference in provincial EE gradually narrows over time and tends to converge to its own steady-state level. (3) Economic growth reduces EE for the central and western areas, but improves EE for the eastern area; an increase in economic growth from surrounding areas indirectly promotes local EE for the eastern area; FDI promotes EE in the eastern and central areas, and increased FDI dependence in adjacent areas has a positive effect on local EE for the eastern area; export dependence reduces EE for all areas, and an increase in export dependence in surrounding areas indirectly promotes the local EE for the central area; industrialization reduces EE in the western area, and industrialization in surrounding areas increases local EE for the eastern area; energy efficiency promotes EE for the central area; urbanization increases EE for the central area, and urbanization of the surrounding area reduces local EE for the eastern area.
This study uses a new model to evaluate provincial EE, and mainly analyzes the status of EE convergence and influencing factors on the spatial convergence of EE. Future research should further investigate the interactions and correlations among the influencing factors and EE. To explore the influence factors of provincial EE and simulate future provincial EE for different scenarios is worthy of further study. The empirical research points to the following policy implications: (1) With regard to Chinese regional EE characteristics, EE in the eastern area is obviously higher. Thus, effective measures should be taken to enhance EE in the central and western areas; the areas should learn developmental experiences from the eastern area. (2) Because positive spatial autocorrelation exists in inter-regional EE, governments in different areas should enhance their awareness of joint defense and control and strengthen cooperation in the field of environmental protection; the local governments should strengthen the cooperation among different provinces. The areas with high EE should play a leading role; the areas with low EE should actively learn environmental management experience from the areas with high EE. The linkage mechanism of environmental policies should be established, and therefore realize experience sharing and complementary advantages among different provinces. (3) It is necessary to balance the economic growth with environmental protection to further narrow the gap in EE among different areas. The eastern area should continue to maintain its high-quality development, and the central and western areas should focus more on EE in economic development. The government should formulate a policy to attract FDI based on coordination of regional economic, environmental, and social developments. In particular, the central area should adjust the quality of FDI, and attach importance to the introduction of high-quality FDIs which promotes industrial upgrading and clean technologies, to further enhance the energy efficiency. A reasonable export strategy should be formulated to actively improve the export structure, increase the green product export, decrease the pollution-intensive product export, and improve the added value of exported products. The regional government, especially for the western area, should transform traditional industries, eliminate backward production capacity, and vigorously develop a third industry, and therefore accelerate the transformation of industry. The eastern area should accelerate the adjustment of industrial structure and actively build a green industrial system. The central area should optimize energy structure, adjust energy layout, improve energy efficiency, and reduce pollutants by vigorously developing and utilizing new clean and renewable energy such as wind energy, biomass energy. and solar energy. The eastern area should accelerate the adjustment of urban structure and control excessive urban expansion to make the city layout appropriate; the central area should moderately accelerate the urbanization development, in order to make the balanced development of urbanization in China.