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Sector Sustainability on Fossil Fuel Power Plants across Chinese Provinces: Methodological Comparison among Radial, Non-radial and Intermediate.

Sector Sustainability on Fossil Fuel Power Plants across Chinese Provinces: Methodological Comparison among Radial, Non-radial and Intermediate Approaches under Group Heterogeneity

Toshiyuki Sueyoshi a, Aijun Lib*, Yaping Gaob a

New Mexico Institute of Mining & Technology, Department of Management, 801 Leroy Place, Socorro, NM, 87801, USA.

b

The Center for Economic Research, Shandong School of Development, Shandong University, Jinan, 250100, China.

This paper can be cited in the following form. Sueyoshi, T., Li, A., Gao, Y., 2018. Sector Sustainability on Fossil Fuel Power Plants across Chinese Provinces: Methodological Comparison among Radial, Non radial and Intermediate Approaches under Group Heterogeneity. Journal of Cleaner Production. 187, 819-829.

Abstract: Data Envelopment Analysis (DEA) has been widely applied to the performance analysis of energy and environment. For empirical applications, different DEA approaches often produce different empirical results, implying that there is a methodological bias. The methodological concern is important for DEA applications, in particular when designing environmental and climate policies. To document the research importance, this study compares empirical differences from using the three approaches (i.e. radial, non-radial and intermediate approaches), after considering group heterogeneity and two disposability concepts (natural and managerial disposability). As an application, these DEA approaches are used to examine the sector sustainability of fossil fuel power plants in China’s coastal and inland provinces. Our conclusions are threefold. First, Chinese provinces have paid attention to their operational efficiencies for economic developments under governmental catching-up policy. Second, coastal provinces outperform inland ones in terms of their operational efficiencies. Thus, there is a regional imbalance between the two province groups. The Chinese government needs to allocate resources and technology (e.g. clean coal technology) to inland provinces so that their fossil fuel power plants can attain high operational efficiencies, so enhancing the level of sector sustainability. Finally, these power plants in all provinces have been operating under governmental regulations and international pressure on air pollution. As a consequence, this study cannot find any major difference in their environmental efficiencies. Keywords: China; DEA Environmental Assessment; Fossil Fuel Power Plants; Carbon Dioxide Emissions; Provincial Gap

1. Introduction It is widely observed that many policy issues are concerned with China’s power sector, since these fossil fuel power plants are large contributors to energy consumption and CO2 emissions. In 2014, fossil fuel power plants accounted for 35.18% of China’s primary energy or equivalently 7.89% of the world’s total (IEA, 2016). In particular, those power plants accounted for 51.60% of China’s coal consumption or equivalently 26.64% of the world’s total. In term of CO2 emissions, power generation accounted for 48.15% of China’s total CO2 emissions or equivalently 13.62% of the world’s total (IEA, 2016). Thus, it attracts keen interest by the researchers, academics and even policymakers, regarding how to reduce the amount of CO2 emissions and to attain a high level economic success, so enhancing high sustainability in Chinese fossil fuel power plants. To prepare for policy suggestions on Chinese fossil fuel power plants, this study assesses the unified (operational and environmental) performance of these power plants at a provincial level. An important feature of this study is that we incorporate group (regional) heterogeneity into Data Envelopment Analysis (DEA). Then, we consider the group heterogeneity within the framework of natural and managerial disposability concepts.

To combat environmental issues, Sueyoshi and Goto (e.g. 2012a, 2012b, 2015, 2016) have introduced the concepts of natural and managerial disposability, where

disposability implies inefficiency elimination in DEA. Natural disposability treats operational efficiency as the first priority and environmental efficiency as the second priority. By contrast, managerial disposability treats environmental efficiency as the first priority and operational efficiency as the second priority. For environmental issues, sector prosperity and environmental protection are two common goals. In this study, sector prosperity is reflected in terms of the amount of desirable outputs and environmental protection is reflected in terms of undesirable outputs. In this regard, many studies argue that there is a conflict between these two goals (e.g. Lin and Li, 2013; Li et al., 2014; Li et al., 2017; Zhang et al., 2017).

Thus, the disposability concepts can achieve sector prosperity and environmental protection, simultaneously. As a result of the two disposability concepts, this study may assess the sector sustainability of China’s fossil fuel power plants. In addition to the disposability concepts, it is necessary for us to consider the group (regional) heterogeneity issue, because China is a large transitional developing economy with significant differences across regions1. Methodologically, this study uses the three DEA approaches (i.e. radial, non-radial and intermediate approaches) for our empirical investigation. Until now, the available DEA approaches for environmental assessment can be roughly classified into radial, non-radial and intermediate approaches (see Sueyoshi and Yuan, 2017; Sueyoshi et al., 2017b; Sueyoshi and Goto, 2018). For empirical applications, one important drawback

is methodological bias, meaning that different DEA approaches often produce different empirical results in empirical applications. This methodological concern is important for DEA applications, in particular when designing environmental and climate policies. To document the research importance, this study compares empirical differences from using these three approaches, after considering group heterogeneity and two disposability concepts (natural and managerial disposability). The purpose of this study can be separated into the following three research tasks: First, this study examines whether there are substantial empirical differences from using three different DEA approaches under the two disposability concepts. Second, we investigate whether there is group (regional) heterogeneity in fossil fuel power plants between coastal and inland provinces by performing the Mann–Whitney rank sum test. Finally, this study proposes a policy direction for enhancing the sector sustainability of Chinese fossil fuel power plants. All the abbreviations used in this study are summarized as follows: DMU: Decision Making Unit, GUEM: unified efficiency under group-frontier and managerial disposability, GUEN: unified efficiency under group-frontier and natural disposability, RTS: Returns to Scale, tce: tons of coal equivalent, UEN: unified efficiency under natural disposability, UEM: unified efficiency under managerial disposability, URS: Unrestricted. The rest of this study has the following structure: Section 2 reviews the literature. Section 3 discusses the methodology used in this study. Section 4 discusses a data set

on Chinese fossil fuel power plants. Section 5 discusses empirical results. Section 6 presents the conclusions along with future extensions.

2. Literature Review DEA environment assessment was usually classified into radial and non-radial categories. See, for example, Tapia et al. (2017), Liu et al. (2017) and Bi et al. (2018) for recent applications, using the two approaches for energy and environmental assessment. An intermediate approach was proposed as the third alternative in 2017. There were three groups of previous studies, directly linked to DEA environmental assessment. The first group of studies was related to DEA studies. The methodology was first proposed by Charnes et al. (1978). Since then, DEA has been widely used for efficiency assessment. DEA has many positive features (e.g. non-parametric approach and a high level of computational tractability) and negative features (e.g. sensitivity to atypical observations and methodological bias). For detailed discussion on DEA features, Reader can turn to Cooper et al. (2004), Coelli et al. (2005) and Sueyoshi and Goto (2018). In the history of DEA, many studies made contributions as found in Chambers et al. (1996), Barros et al. (2012), Zhou et al. (2012), Zhang et al. (2013), Zhang et al. (2014), Yao et al. (2015), Sueyoshi et al. (2017c) and Li et al. (2017), for example. A literature survey on DEA applied to energy and environment can be found in Sueyoshi et al. (2017a) and Sueyoshi and Goto (2018) that contained more than 800 previous studies during the past four decades. In the same vein for DEA developments, an intermediate approach has been recently proposed as a new alternative (Sueyoshi and

Yuan, 2017). Sueyoshi et al. (2017a) compared the three (radial, non-radial and intermediate) approaches and argued that intermediate approach had several unique features which could not be found in radial and non-radial approaches. The second group, closely related to this study, is concerned with the two concepts on disposability. This study finds that there are two groups of disposability concepts, where disposability means elimination of inefficiency. The traditional disposability concepts refer to as weak and strong disposability, initially proposed by Färe et al. (1989). These concepts have dominated previous DEA studies on environmental assessment. The other group was natural and managerial disposability, proposed by Sueyoshi and Goto (e.g., 2012a, 2013a, 2013b, 2016, 2018) and Sueyoshi and Yuan (e.g., 2015, 2016, 2017). This study fully utilizes the new disposability concepts. Here, it is noteworthy that the two groups of disposability concepts do not conflict with each other. For example, weak disposability can be a special case (i.e. under undesirable congestion) of natural disposability. See Sueyoshi and Goto (2018) for a description on undesirable congestion. Hence, we acknowledge the contribution of the traditional disposability concepts. Meanwhile, the concept of managerial disposability allows for a possible occurrence of green technology innovation on desirable congestion, while the traditional concepts do not. Furthermore, the concepts of natural and managerial disposability allow for simultaneous achievement of economic prosperity and environmental protection, so being able to attain a high level of sustainability by DEA environmental studies. Thus, the natural and managerial disposability concepts were developed to express new strategies for environmental

protection. See Sueyoshi et al. (2017b) and Sueyoshi and Goto (2018) for a detailed discussion on the new disposability concepts. The third (final) group, closely related to this study, is DEA environmental studies on the heterogeneity. Table 1 summarizes the recent DEA environmental studies about the heterogeneity. This table provides us with three interesting findings. First, there were generally two methods to consider the heterogeneity in DEA studies. One of them was to adopt group heterogeneity, implying that there were significant differences among different groups. Among them, six studies belonged to the research category. The other research included environmental variables, where they reflected the heterogeneity among observations. In Table 1, four studies belonged to the category. Second, there were four studies about electricity generation or electricity network and seven studies about energy consumption. Thus, their important research concerns discussed how to improve the level of unified efficiency in energy or power sectors. Finally, six studies were related to China, implying that the nation was a research focus. Position of this study: The position of this study is summarized as the following three contributions. First, until now, only two studies have discussed the intermediate approach. It is true that Sueyoshi et al. (2017a) have compared the three (i.e. radial, non-radial and intermediate) approaches. However, no study has applied the intermediate approach to Chinese fossil fuel power plants. Second, their study did not recognize an existence of group (regional) heterogeneity in China. Sueyoshi et al. (2017b) and Sueyoshi and Goto (2018), both covering more than 700 articles during

the past four decades, have never discussed the concept of group heterogeneity. Finally, this study compares the three approaches, after incorporating the natural and managerial disposability concepts, to obtain policy implications on Chinese fossil fuel power plants. A rank sum test is used to statistically examine whether a regional difference exists in China. It is easily envisioned that the statistical test, linked to group heterogeneity, provides us with a new analytical capability on the three DEA approaches applied to fossil fuel power plants and other policy issues in China and other industrial nations.

3. Methodology This study compares empirical differences from using the three approaches under the framework of group heterogeneity, after referring to models in Sueyoshi and Goto (2015 and 2016), Sueyoshi and Yuan (2017) and Sueyoshi et al. (2017a). Nomenclatures used in this study are summarized as follows: URS: Unrestricted,

X : A column vector of m inputs, G : A column vector of s desirable outputs, B : A column vector of h undesirable outputs, d ix : An unknown slack variable of the i-th input, d rg : An unknown slack variable of the r-th desirable output, d b : An unknown f slack variable of the f-th undesirable output,  : An unknown column vector of intensity (or structural) variables.  s : a very small number (e.g.  s = 0.0001 in this study) and  :a small number (e.g.  = 0.1 in this study). 3.1 Natural and Managerial Disposability Concepts This study considers the environmental performance of fossil fuel power plants across provinces in China. Every province is considered as a Decision Making Unit

(DMU). In every DMU, the production technology transforms an input vector ( X  S

into a desirable output vector ( G

) and an undesirable output vector ( B 

h 

m 

)

).

The axiomatic form of production technology (T) on a production and pollution possibility set (P) is expressed as follows:

T  P( X ) : X can produce G and B 

m 

(1)

Similar to many DEA studies, this study utilizes many conventional assumptions of the production technology such as convexity and a bounded set on P. Different from many existing DEA studies, this study uses the natural and managerial disposability concepts. Axiomatically, the production and pollution possibility set can be expressed under natural and managerial disposability as follows: n n n   G , B : G  G  , B  B  , X  X n n ,       j j j j   j 1 j 1 j 1 PvN  X    n &   j  1 and  j  0  j  1,..., n    j 1  n n n   G , B : G  G  , B  B  , X  X j  j ,     j j j j   j 1 j 1 j 1 PvM  X    n    j  1 and  j  0  j  1,..., n    j 1 

(2)

(3)

The above expressions on the production and pollution possibility set incorporate the assumption of variable Return to Scale (RTS)1 or Damages to Scale (DTS)2, since n

they incorporate the constraint, or

 j 1

j

1.

Equations (2) and (3) indicate that there is a difference between the two disposability concepts. The difference depends on the signs of input inequalities. For natural disposability, DMUs attain production frontiers by decreasing a directional vector of inputs. In contrast, DMUs reach production frontiers by increasing a

directional vector of inputs under managerial disposability. Meanwhile, both natural n

n

j 1

j 1

and managerial disposability share the same condition, or G   G j  j & B   B j  j . The underlying implication is that DMUs can reach production frontiers by increasing desirable outputs or reducing undesirable outputs. To extend Equations (2) and (3) into the proposed DEA formulations, this study specifies the following three types of data ranges (R) according to the upper and lower bounds of production factors:

Rix   m  s  h 

1

1

ij

Rrg   m  s  h  Rbf   m  s  h 

 max x | j  1,..., n   min x | j  1,..., n ,  max g | j  1,..., n   min g | j  1,..., n ,  max b | n  1,..., n   min b | n  1,..., n .

1

1

ij

1

rj

rj

(4)

1

fj

fj

The purpose of the three ranges is that DEA results can avoid an occurrence of zero in dual variables (multipliers). Such an occurrence implies that corresponding production factors are not utilized in DEA applications. The occurrence is problematic. Therefore, this study incorporates the data ranges into the proposed formulations.

3.2 Radial Approach This study utilizes a radial approach according to the previous studies such as Sueyoshi and Yuan (2017) and Sueyoshi et al. (2017a). The level of UEN on the k-th DMU is determined by the following radial model (Sueyoshi and Goto, 2018):

m

s

h

i 1

r 1

f 1

Maximize    s (  Rix dix    Rrg d rg   Rbf d bf ) n

s.t.

x  xij  j  di

 xik (i  1, .. , m),

j 1 n

 g rj  j

j 1

  g rk  g rk (r  1 , .. , s),

 d rg

n

 b fj  j

(5)

 d bf   b fk  b fk (f  1 , .. , h),

j 1 n

 j 1 ,

j 1

λ j  0 (j  1, .. ,n),  :URS, dix   0 ( i  1,..,m ), d rg  0 ( r  1,..,s ) & d bf  0 ( f  1,..,h ).

The level of UEN is defined by subtracting the unified inefficiency measured by Model (5) from unity, which can be specified as follows: m

s

h

i 1

r 1

f 1

UENvR  1  [  *   s (  Rix dix *   Rrg drg*   Rbf d b* f )].

(6)

Here, the superscript (R) stands for the radial measurement and the subscript (v) represents variable RTS. All variables on an inefficiency score and slacks used in Equation (6) are obtained from the optimality of Model (5). The superscript (*) indicates the status of optimality. Meanwhile, sector sustainability in this study is defined as the unified efficiency improvements, after in line with Sueyoshi and Yuan (2016, 2017). Unified efficiency measures in this study can capture the efficiency changes in production inputs, desirable outputs and undesirable outputs. In this regard, sector sustainability means overall improvements in unified efficiency. In a similar manner, the degree of UEM of the k-th DMU is determined by the following radial model under managerial disposability (Sueyoshi and Goto, 2018):

m

s

h

i 1

r 1

f 1

Maximize    s (  Rix dix    Rrg d rg   Rbf d bf ) n

s.t.

x  xij  j  di

 xik (i  1, .. , m),

j 1 n

 grj  j

j 1

  g rk  g rk (r  1 , .. , s),

 drg

n

 b fj  j

 d bf   b fk  b fk (f  1 , .. , h),

j 1

(7)

n

 j  1 ,

j 1

λ j  0 (j  1, .. , n),  :URS, dix+  0 ( i  1,..,m ), drg  0 ( r  1,..,s ) & d bf  0 ( f  1,..,h ). The level of UEM is defined as follows: m

s

h

i 1

r 1

f 1

UEM vR  1  [ *   (  Rixdix *   Rrg d rg*   Rbf d b* f )],

(8)

where the subscript (v) stands for variable DTS. This study needs to note the following three concerns. First, the most important feature of Models (5) and (7) is that they incorporate an inefficiency score (  ) in these formulations. The measure is applied to both desirable and undesirable outputs. This analytical feature cannot be found in no-radial approach that does not have such an inefficiency score. Second, the difference between Models (5) and (7) can be found in the input vector. That is, Model (5) uses  d ix  to express the natural disposability, while Model (7) uses  d ix  to express the managerial disposability. There is no other difference between the two radial models. Finally, this type of assessment by the two radial models is originated from Debreu-Farrell measure because of the inefficiency score (  ).

3.3 Non-radial Approach This study uses a non-radial approach according to the previous studies such as Sueyoshi and Goto (2012b) and Sueyoshi et al. (2017a). The level of unified efficiency of the k-th DMU under natural disposability is determined by the following non-radial model (Sueyoshi and Goto, 2018): Maximize  (

s.t.

m



Rix dix  

s



g g Rr d r 

i 1 r 1 n  xij  j  dix  j 1 n g  dr  grj  j j 1 n  b fj  j j 1 n  j 1, j 1

h



f 1

Rb d b ) f f  xik (i  1, .. , m),  g rk (r  1 , .. , s),

(9)  d b  b fk (f  1 , .. , h), f

λ j  0 (j  1, .. , n), dix   0 ( i  1,..,m ), g dr  0 ( r  1,..,s ) & d b  0 ( f  1,..,h ). f

Model (9) drops the inefficiency score, as found in the radial measurement, and determines the level of inefficiency by only the total amount of slack variables on the optimality of Model (9). The level of UEN is defined as follows: UENvNR  1   (

m



i 1

Rix dix * 

s



r 1

g g* Rr d r 

h



f 1

Rbf d b* f ),

(10)

where all the slack variables are obtained on the optimality of Model (9). The superscript (NR) stands for non-radial measure. In a similar manner, the level of UEM of the k-th DMU is determined by the following non-radial model (Sueyoshi and Goto, 2018):

Maximize  (

s.t.

m



Rix dix  

s



g g Rr d r 

h



Rb d b ) f f

i 1 r 1 f 1 n  xik (i  1, .. , m),  xij  j  dix  j 1 n g  dr  g rk (r  1 , .. , s),  g rj  j j 1 n  d b  b fk (f  1 , .. , h),  b fj  j f j 1 n  j 1, j 1 λ j  0 (j  1, .. , n), dix   0 ( i  1,..,m ), g d r  0 ( r  1,..,s ) & d b  0 ( f  1,..,h ). f

(11)

The level of UEM is defined as follows: m s h g g* UEM vNR  1   (  Rix dix *   Rr d r   Rbf d b* f ), i 1 r 1 f 1

(12)

where all the slack variables are obtained on the optimality of Model (11). Note that Models (9) and (11) are originated from Pareto-Koopmans measurement. Thus, these models are based upon Pareto optimality. Hence, it does not need the inefficiency score to determine the degree of unified efficiency measures.

3.4 Intermediate approach So far, only two studies have proposed a new use of the intermediate approach. Sueyoshi and Yuan (2017) have first proposed the new approach. Sueyoshi et al. (2017a) have extended the approach by comparing it with the other two (i.e. radial and nonradial) approaches. The level of unified efficiency of the k-th DMU under natural disposability is determined by the following intermediate model (Sueyoshi and Yuan, 2017):

s h m s h 1 (   rg    bf )   s (  Rix dix    Rrg d rg   R bf d bf ) s  h r 1 f 1 i 1 r 1 f 1

Maximize

n

x  xij  j  di

s.t.

 xik

j 1 n

 g rj  j

j 1

 drg

  rg g rk  g rk (r  1,..,s),

 rg n

 b fj  j

j 1

(i  1,..,m),

1

( r  1,..,s ),

 d bf   bf b fk  b fk (f  1,..,h),

 bf

1

(13)

( f  1,..,h ),

n

 j

j 1

= 1,

 rg  0 ( r  1,..,s ),  bf  0 ( f  1,..,h ), λ j  0 (j  1, .. , n), dix   0 ( i  1,..,m ), d rg  0 ( r  1,..,s ) & d bf  0 ( f  1,..,h ).

The important feature of the intermediate model is that it separates the inefficiency score (  ) into its subcomponents related to desirable and undesirable outputs, or

 rg ( r  1,..,s ) and  bf ( f  1,..,h ) , respectively. The level of unified efficiency of the k-th DMU under managerial disposability is defined as follows: UENvI  1  [

s h m s h 1 x x * (  rg*    b*   Rrg drg*   Rbf d b* f )   s (  Ri di f )], (14) s  h r 1 f 1 i 1 r 1 f 1

where the superscript (I) stands for an intermediate approach. The average on the sum of inefficiency components on desirable and undesirable outputs is used to determine the degree of UEN, as found in Model (14). Meanwhile, the level of unified efficiency of the k-th DMU under managerial disposability is determined by the following model (Sueyoshi and Yuan, 2017):

Maximize

s h m s h 1 (   rg    bf )   s (  Rix dix    Rrg d rg   Rbf d bf ) s  h r 1 f 1 i 1 r 1 f 1 n

s.t.

x  xij  j  di

 xik (i  1,..,m),

j 1 n

 grj  j

j 1

 drg

  rg g rk  g rk (r  1,..,s),

 rg n

 b fj  j

j 1

 d bf 

1

( r  1,..,s ),

(15)

 bf b fk  b fk (f  1,..,h),  bf

1

( f  1,..,h ),

n

 j

j 1

=1

 rg  0 ( r  1,..,s ),  bf  0 ( f  1,..,h ), λ j  0 (j  1, .. , n), dix+  0 ( i  1,..,m ), d rg  0 ( r  1,..,s ) & d bf  0 ( f  1,..,h ).

Then, the level of unified efficiency (UEM) under managerial disposability is defined as follows: UEM vI  1  [

s h m s h 1 x x * (  rg*    b*   Rrg drg*   Rbf d b* f )   s (  Ri di f )] (16) s  h r 1 f 1 i 1 r 1 f 1

Here, the components of an inefficiency score and slack variables are determined on the optimality of Model (15). In considering Models (13) and (15), the inefficiency score (  ) is separated into

 rg ( r  1,..,s ) and  bf ( f  1,..,h ) , respectively. A computational problem is that they may be more than unity. To avoid the problem, the two models incorporates

rg  1 ( r  1,..,s ) and  bf  1 ( f  1,..,h ) in their formulations.

3.5 Structural Differences among Three Approaches This study summarizes five differences among the three approaches. First, the three approaches have originated from these corresponding conventional optimality concepts, which are generally classified into radial (i.e. Debreu-Farrell type of efficiency measurement) and non-radial (i.e. Pareto-Koopmans type of efficiency measurement) category. This study adds an intermediate model between them as the third alternative that is originated from the Russell measure. Note that the proposed intermediate approach is based upon inefficiency measurement, not efficiency as found in the Russell measure. See Sueyoshi and Goto (2018) for a detailed description on the Russell measure. Second, the three approaches for environmental assessment have different objective functions. The radial approach is designed to maximize a level of unified inefficiency. The sum of slacks related to all production factors is incorporated into the objective function to avoid an occurrence of zero in their corresponding dual variables (i.e. multipliers). The occurrence of zero means that the corresponding production factor is not fully utilized in the DEA assessment. Thus, such an occurrence is very problematic. The non-radial approach is designed to maximize the total amount of slacks, indicating the level of unified inefficiency in the objective function. The intermediate approach separates all the components of an inefficiency score and maximizes them along with the sum of all slacks. These inefficiency components function like slacks. The purpose of slacks is to avoid the occurrence of zero in these corresponding dual variables.

Third, the radial approach incorporates a unification process between desirable and undesirable output vectors, which have opposite directions on optimization. Thus, the approach is an output-oriented measurement. In contrast, the non-radial approach measures a level of inefficiency by the sum of slacks so that the unification is an outputoriented and input-oriented combined measurement. The intermediate approach separates the components of an inefficiency measure related to desirable and undesirable outputs and then it measures the average of these components. Thus, the approach is an output-oriented measurement. Fourth, the magnitude difference in DMUs may influence the degree of unified efficiency scores of the three approaches. The non-radial approach usually produces efficient DMUs and inefficient ones whose magnitudes are close to unity. This result is mathematically acceptable, but managerially unacceptable. Therefore, they suggested a use of “slack-adjusted radial measure”, which serves as a conceptual basis of the radial measurement of this study. The proposed intermediate approach can separate the degree of unified inefficiency by decomposing its inefficiency components so that the degree of unified efficiency may have a wide range of distribution than the radial and nonradial measures. Finally, the radial and intermediate approaches use a very small number (e.g.  s = 0.0001) to reduce an influence of slacks on their unified efficiency measures. Meanwhile, the non-radial approach uses a small number (e.g.  = 1 or 2) to control the degree of a unified efficiency measure as a magnitude control factor.

3.6 Sub-group Technologies and Group Frontier This study incorporates the concept of a group-frontier3, often called as metafrontier by Chinese researchers, into the proposed three approaches by following Chiu et al. (2012), Zhou et al. (2012), Zhang et al. (2013) and Yao et al. (2015). The purpose of the concept incorporation leads to a statistical inference for examining by the rank sum test regrading whether there are significant differences between multiple groups (e.g. coastal and inland provinces) in the proposed performance assessment. Here, the group-frontier is defined according to the observations of specific z group. Following Battese and Rao (2004) and O’Donnell et al. (2007), this study specifies each frontier of the  -th group on a production and pollution possibility set as follows:

T   P  X  can produce G and B for  = 1, 2, .., z.

(17)

The group-frontier is defined as the following one for covering a union set of all production technology sets of all z groups:

T G  T 1  T 2  ...  T z

(18)

According to Equation (18), as an extension of Model (1), this study differentiates group performances, using radial, non-radial and intermediate approaches, respectively, under natural or managerial disposability.
To visually describe the concept of group-frontier in DEA environmental assessment, Figure 1 depicts two sub-frontiers and a group frontier, covering the two sub-groups. An important feature of the group-frontier is that we can measure the

performance of DMUs, belonging to each sub-group, by using the group frontier. For example, the degree of efficiency on DMU {a} is determined by the ratio distance of 0a/0a* on the group frontier. The efficiency measure, or 0a/0a’, is originally used on the frontier of the first sub-group. As depicted in Figure 1, the performance on unified (operational and environmental) efficiency on DMU{a} is enhanced by increasing the amount of a desirable output, so enhancing its operational performance or reducing an undesirable output, so enhancing its environmental performance. In each case, an input is considered as the same amount for our visual convenience. The unified efficiency incorporates the two possibilities for performance enhancement.

4. Data Set This study uses the data set on fossil fuel power plants in 2015 across provinces in China. Every province (or province-equivalent, called province in short) is considered as a separate DMU. This study does not cover the data of Tibet, Hong Kong and Macau, due to data availability. There are three production inputs, one desirable output and one undesirable outputs. Production inputs are calculated by installed capacity (KK, 104 KW), labor (L, persons) and energy (E, 104 tce). Desirable output is calculated by electricity generated (G, 108 kWh). Undesirable outputs are calculated by CO2 (B, 104 tons). The data set on installed capacity of fossil fuel power plants is from Wind Database (2017), without covering installed capacity less than 6000 KW. Labor input is the employed persons at year-end and the source is National Bureau of Statistics of China

(2016a). Energy consumption is measured by 14 types of fossil fuel consumption and the source is National Bureau of Statistics of China (2016b). Desirable output is measured by thermoelectricity and the source is National Bureau of Statistics of China (2016b). The data set on undesirable outputs is measured by the amount of CO2 emissions that is calculated by energy consumption. The calculating method is from Du (2010), which can be expressed as follows:

CO2   CO2i   ( Ei  EFi ) i

(19)

i

where subscript i stands for different types of energy. E stands for energy consumption. EF stands for emission factor. This study considers seven types of energy consumption. The related data are from National Coordination Committee on Climate Change and Energy Research Institute of National Development and Reform Commission (2007), IPCC (2006) and National Bureau of Statistics of China (2016b).
Table 2 summarizes the descriptive statistics of production variables, wherein Ave., S.D., Min. and Max. stand for mean, standard deviation, minimum and maximum, respectively. This study examines the mean of the observed data as an example. As production inputs, fossil fuel power plants in coastal provinces have relatively largesized average installed capacity and fossil fuel consumption. However, small-sized labor inputs in the other province group. In terms of outputs, fossil fuel power plants in coastal provinces have relatively large-sized average electricity generated and CO2 emissions. Thus, it is observed in Table 2 that there are significant differences in production variables between coastal and inland provinces.

5. Empirical Results 5.1 Performance Measures on Two Regional Groups This section considers unified efficiency measures under natural and managerial disposability, separately. The left hand side of Table 3 lists the results of GUEN under natural disposability, along with Figure 2, which provide a graphical illustration. The right hand side of Table 3 also reports their results of GUEM under managerial disposability, along with Figure 3, which provides a graphical illustration. Hereafter, this study adds group (G) to the unified efficiency measures in the manner that they become GUEN under natural disposability and GUEM under managerial disposability. The rationale on the use of G is that fossil fuel power plants are measured on the basis of the group frontier for Chinese coastal and inland provinces.

Table 3, along with the two figures, provides us with three important empirical results. First, slight differences are found in the status of unified efficiency measures among different approaches. For example, the table indicates that the three approaches produce almost the same rank of China’s provinces. To explain it further, let us consider the GUEN measures as an example. Eleven provinces attained the status of efficiency in term of GUEN according to intermediate, radial and non-radial approaches. They produced the same provinces on the group frontier, so being efficient in their statuses. Thus, their ranking statuses are almost same for empirical differences from using the three approaches.

Second, there are empirical differences in the magnitude of unified efficiency measures from using the three approaches. Let us consider the results of GUEN and GUEM. The quantitative comparison indicates that the two measures, obtained by the intermediate approach, are generally less than those of non-radial approach. Furthermore, these measures obtained by radial approach are usually less than those of the non-radial approach. Thus, their magnitudes are influenced by the three approaches. Finally, there are differences between GUEN and GUEM. Table 4, obtained from Table 3, indicates correlation coefficients from using the three approaches. There are high correlations for these performance measures related to GUEN. Such high correlations may be found in GUEM, as well. In contrast, such high corrections are not found between GUEN and GUEM. The GUEN under natural disposability measures the performance of provinces under the condition that their operational achievements are the first priority and their environmental protections are the second priority. In contrast, the GUEM under managerial disposability has an opposite priority (i.e. economic achievement: second and environmental protection: first). Thus, the policy difference is confirmed from Table 4. So, different disposability concepts are associated with different policy directions in the fossil fuel power plants in Chinese provinces. Policy implication: There is a methodological bias in any empirical studies, including this research. Thus, it is important for us to examine different methodologies, as documented in this study, to obtain reliable suggestions for guiding a policy issue(s) on Chinese fossil fuel power plants.

5.2 Rank Sum Test for Group Heterogeneity

This subsection discusses the existence of group heterogeneity. Table 5 reports the results of Mann–Whitney U-test between coastal and inland provinces under natural and managerial disposability. The major purpose is to statistically examine whether there is group heterogeneity between them. See Appendix of this study for a description on the rank sum test used in this section.
Table 5 provides us with two interesting concerns. One finding is that under natural disposability, there are significant differences in unified efficiency between coastal and inland provinces. As for intermediate approach, the null hypotheses are rejected at the significance level of 1%, implying that there are considerable differences in provinces between coastal and inland provinces in terms of these GUEN measures. There are similar results by radial and non-radial approaches. The other finding is that under managerial disposability, there is no significant group heterogeneity between coastal and inland provinces. In unified efficiency (i.e. GUEM), the null hypotheses cannot be rejected for all three approaches. Policy Implication: The rank sum tests on GUEN statistically reject the three null hypotheses. The statistical results indicate that Chinese provinces have paid attention to their economic (so, operational) developments more than environmental protection. The implication is confirmed by the proposed three approaches. In contrast, the rank sum tests on GUEM cannot statistically reject the three null hypotheses because the operations of power plants in all provinces have been under governmental regulations

and international pressure4 on air pollution. Therefore, no major difference exists between the power operations of these provinces.

6. Conclusion and Future Extension The DEA approaches were usually classified into two categories, i.e. radial and non-radial approaches. Recently, a new approach (i.e. intermediate approach) was proposed as the third alternative. Along with such a research development trend, this study compared methodological differences among the three approaches under group heterogeneity and two (i.e. natural and managerial) disposability concepts. Moreover, this study proposed how to statistically examine whether the heterogeneity existed between the two groups by the Mann–Whitney rank sum test. To document the applicability of DEA environmental assessment, this study examined the performance of Chinese fossil fuel power plants across provinces in 2015. Our conclusions are as follows. First, Chinese provinces have paid attention to their operational efficiencies more than their environmental ones under the governmental “catching-up” policy5. Second, coastal provinces have outperformed inland provinces in terms of efficiency measures on the operation of fossil fuel power plants. Thus, there was a regional imbalance between the two groups of provinces. The Chinese government needs to discuss resource allocation and technology diffusion (e.g. clean coal technology and/or fuel shift from coal to natural gas or renewable generation) to inland provinces in the manner that their fossil fuel power plants can attain high operational efficiencies, so enhancing the level of sector sustainability. Finally, these power plants in all provinces have been operating under governmental regulations and

international pressure on air pollution. Consequently, this study cannot find a major difference in their environmental efficiencies among Chinese provinces. It is true that this study is not perfect because it contains four empirical and methodical drawbacks. All of them should be overcome as the future extensions of this study. First, Tibet, Hong Kong and Macau are not listed in our data set. The proposed DEA model does not incorporate energy investment, as well, which influences the operational performance and environmental prevention of the power plants examined in this study. Second, it is necessary for this study to incorporate a time horizon into the proposed DEA approach, as discussed by Sueyoshi and Goto (2018). Third, the inputs used in this study may be separated into two groups under natural and managerial disposability concepts. For example, an amount of investment for preventing industrial pollution may be categorized as the input under managerial disposability. The other inputs are categorized under natural disposability. Then, this study can measure the other types of efficiency measures. Finally, as a methodology for sector sustainability, the proposed approach needs to several scale related measures (e.g. RTS: Returns to Scale) into the proposed frameworks. The extension may provide us practical implications on Chinese fossil fuel power plants. In conclusion, it is hoped that this study makes a contribution in DEA environmental assessment for social sustainability enhancement and regional development. We look forward to seeing future extensions as discussed in this study.

Acknowledgements The authors are grateful to the anonymous referees for their valuable suggestions. This paper is supported by the National Natural Foundation of China (Grant No. 71403147), the Ministry of Education Research of Social Sciences Youth Funded Projects (Grant No. 13YJC790065), Shandong Social Science Planning Fund Program (Grant No. 12DJJJ12) and Young Scholars Program of Shandong University (Grant No. 2016WLJH02).

Footnote 1. To describe RTS in DEA environmental assessment, we measure the degree of scale elasticity (eg) between an input (x) and a desirable output (g). Let us consider a simple case in which a supporting hyperplane is mathematically expressed by vx - ug + wb +  = 0. For our descriptive convenience, all production factors consist of a single component. Here, the undesirable output (b) is additionally incorporated in the equation. The symbols (v, u and w) are parameters of a supporting hyperplane, indicating the degree of each slope regarding the supporting hyperplane. All the parameters are positive in their signs. An exception is  that is unrestricted in the sign and it indicates an intercept of the dg v supporting hyperplane .Using the supporting hyperplane, we obtain = and dx u

g v   wb =  . Consequently, the scale elasticity between g and x is measured ux x u   wb   dg g by eg =      1  1   . The degree of the scale elasticity (eg) vx    dx   x  related to a desirable output is classified by  and w by the following rule:

(a)

eg > 1  Increasing RTS    wb  0 , (b) eg = 1  Constant RTS    wb  0 and (c) eg < 1  Decreasing RTS    wb  0 .

2. To discuss DRS, let us consider scale elasticity ( eb ) between an input and an undesirable output. We consider that a supporting hyperplane is - vx - ug+ wb +  = 0 where the three production factors consist of a single component. Then,

we have

db v b v   ug = and   . Consequently, the scale elasticity related x w wx dx w

 db   b    ug  to an undesirable output is measured by eb       1  1   . The vx   dx   x   scale elasticity ( eb ) related to an input and an undesirable output is determined by  and u as follows:

(a) eb > 1  Increasing DTS    ug > 0, (b)

eb = 1  Constant DTS    ug = 0

and (c) eb < 1  Decreasing

DTS    ug < 0. 3. There are several studies that address group heterogeneity issues in China. For example, Wang et al. (2013) argued that there were significant differences in energy efficiency and technology gaps between east, central and west provinces in China. Fei and Lin (2016) argued that China’s agricultural sectors had regional differences. Battese et al. (2004) argued that efficiency scores might be biased, without considering substantial differences in production technologies among different groups. To address the group heterogeneity, meta-frontier method was frequently used in Wang et al. (2013), Munisamy and Arabi (2015) and Li and Lin (2017). 4. In 2015, the Chinese government committed to peaking carbon dioxide emissions by 2030, reducing carbon dioxide emissions per unit of GDP by 60% to 65% relative to the 2005 levels, and increasing the share of non-fossil fuels in terms of total primary energy consumption to around 20%. The intended nationally determined contributions of China can be found in 2015. http://www.scio.gov.cn/xwfbh/xwbfbh/wqfbh/2015/20151119/xgbd33 811/Document/1455864/1455864.htm. 5. The catching-up policy implies that inefficient DMUs improve efficiency by adopting more efficient technologies that are used by efficient DMUs (Zhang et al., 2013).

Appendix Mann-Whitney Rank Sum Test: To examine statistically a null hypothesis (i.e. no difference between two groups of observations), this study applies the Mann-Whitney rank sum test to the rank of two groups of observations (e.g, Chinese power plants in this study). In the rank sum test, all provinces are ranked by their unified efficiency

scores from the greatest to the least in most of cases although the ranking order may be changed by the purpose of its application. The formulation used for the rank sum test is as follows: n n  1 n n  1 U  n1  n 2   1 1   R1 or U  n1  n 2   2 2   R2 . 2 2

(A-1)

Here, n1 and n2 represent the number of observations in the first group (G1) and that of observations in the second group (G2), respectively.  R1 and  R2 represent the sum of the ranks of each group, respectively. Note that the two equations of (A-1) may produce two different values, but the two always produce a same statistic. It is mathematically approximated that each group follows a normal distribution that has a mean expressed by n1n2 2 and a variance expressed by n1n2 ( n1  n2  1 ) 12 if a sample size is more than 20. See Mann and Whitney (1947). Hence, the statistic:

  [U  n1n2 / 2 ]

n1n2 ( n1  n2  1) 12

(A-2)

follows a standard normal distribution N(0,1). See Hollander and Wolfe (1999) for a description regarding how to deal with a case where many firms are on a same rank.

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Figure 1: Meta Frontier and Group Frontiers: Two Groups Note: [1] This figure depicts two group frontiers and a meta frontier, covering the two sub-groups. An important feature of the meta-frontier is that we can measure the performance of DMUs, belonging to each group, by using the meta frontier. Coastal region

Inland region

1.0

0.9

0.7

0.6

0.5

Intermediate Radial Non-Radial

0.4

BJ TJ HEB LN SH JS ZJ FJ SD GD GX HAN SX IM JL HLJ AH JX HEN HUB HUN CQ SC GZ YN SAX GS QH NX XJ

MUEN

0.8

Figure 2: MUEN under Natural Disposability

Coastal region

Inland region

1.0

0.9

0.7

0.6

0.5

Intermediate Radial Non-Radial

0.4

BJ TJ HEB LN SH JS ZJ FJ SD GD GX HAN SX IM JL HLJ AH JX HEN HUB HUN CQ SC GZ YN SAX GS QH NX XJ

MUEM

0.8

Figure 3: MUEM under Managerial Disposability

Table 1: Recent DEA Environmental Studies on Group Heterogeneity Authors

Coverage

Desirable outputs

Kuosmanen (2012) Zhang and Choi (2013)

Electricity Energy transmitted, networks, Finland network length, customers Power plants, Electricity China and Korea

Wang et al. (2013)

Regional GDP, China [1]

Adler et al. (2013)

Undesirable outputs

Inputs [2]

Groups or environment variables

Total cost

Underground cables

L, capacity, E

China, Korea

Regional GDP

L, KK, E

East, central, west

Airport, Europe

Aeronautical and nonaeronautical revenues

Staff costs, declared and terminal capacity

Intermediate outputs

Li and Lin (2015)

Regional GDP, China

Regional GDP

L, KK, E

East, Central, West

Munisamy and Arabi (2015)

Power plant, Iran

Electricity

Capacity, fuel

Electricity of steam, gas and hydro

Fei and Lin (2016)

Agriculture, China

Agricultural output

L, KK, E

East, central, west

CO2

Generation deviation, total emissions

Xie et al. (2017)

Industry, China

Industrial output

CO2

L, KK, E

Emission reduction strategies

Li and Lin (2017)

Heavy and light industry, China

Industrial output

CO2, SO2, COD

L, KK, E

Heavy, light industry

Total cost

Distance to road, HV lines underground, Forest [3]

Bjørndal et al. (2017)

Electricity Costumers, high networks, voltage lines, network Norway stations [1] Note: GDP indicates Gross Domestic Product. [2] L, KK and E stands for labor, capital and energy respectively. [3] HV stands for high voltage.

Table 2: Descriptive Statistics Desirable Production input [1] output Region

Coasta l region

Indicato r

E

Ave. S.D.

104 kW 3887 2844

104 tce 5361 4399

Min.

16371

461

Ave. S.D. Min. Max.

China’ s averag e

KK

person s 98674 66893

Max. Inland region

L

Ave. S.D.

23692 7 10709 2 51028 17198 21348 0 10372 5 56932

G

Undesirable output B

108 kWh

104 tons

1746 1450

11454 9738

694

234

1519

8380

13869

4502

30829

2908

4104

1193

9123

1901 318

3371 437

900 122

7581 965

7268

14000

3422

31517

3299

4607

1414

10055

2329

3794

1161

8426

Min.

16371 318 437 122 965 23692 Max. 8380 14000 4502 31517 7 Sources: Wind Database (2017) and National Bureau of Statistics of China (20092016a, 2009-2016b). Note: [1] Inputs include labor (L, persons), installed capacity (KK, 104 KW) and energy (E, 104 tce). Desirable output is electricity generated (G, 108 kWh). Undesirable output is CO2 (B, 104 tons).

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Table 3: Performance Measures under Two Disposability Concepts MUEN MUEM Province Provinces [2] IM [1] RA NRA IM RA NRA Group BJ 1.000 1.000 1.000 1.000 1.000 1.000 TJ 0.964 0.970 0.992 0.850 0.858 0.829 HEB 1.000 1.000 1.000 1.000 1.000 1.000 LN 0.856 0.856 0.914 0.828 0.921 0.850 SH 1.000 1.000 1.000 0.920 0.960 0.873 JS 1.000 1.000 1.000 1.000 1.000 1.000 ZJ 1.000 1.000 1.000 1.000 1.000 1.000 FJ 0.899 0.903 0.952 0.893 0.930 0.853 SD 1.000 1.000 1.000 1.000 1.000 1.000 GD 1.000 1.000 1.000 1.000 1.000 1.000 GX 0.857 0.862 0.900 1.000 1.000 1.000 HAN 1.000 1.000 1.000 0.683 0.844 0.945 SX 0.918 0.922 0.939 0.909 0.944 0.814 Inland region IM 0.850 0.931 0.871 1.000 1.000 1.000 JL 0.648 0.675 0.886 0.594 0.836 0.860 HLJ 0.776 0.782 0.857 0.784 0.889 0.906 AH 0.957 0.962 0.967 0.946 0.953 0.835 JX 0.910 0.916 0.919 0.934 0.946 0.934 HEN 0.932 0.932 0.846 0.926 0.941 0.917 HUB 0.932 0.936 0.910 0.955 0.962 0.946 HUN 0.891 0.893 0.884 0.971 0.989 0.985 CQ 0.866 0.866 0.967 0.810 0.884 0.892 SC 0.792 0.792 0.808 1.000 1.000 1.000 GZ 0.798 0.799 0.895 0.765 0.809 0.853 YN 0.556 0.653 0.902 1.000 1.000 1.000 SAX 0.940 0.953 0.946 0.930 0.934 0.858 GS 0.843 0.843 0.914 0.844 0.865 0.882 QH 1.000 1.000 1.000 1.000 1.000 1.000 NX 1.000 1.000 1.000 0.813 0.841 0.774 XJ 1.000 1.000 1.000 0.884 0.898 0.758 Coastal region 0.965 0.966 0.980 0.931 0.959 0.946 Average Inland region 0.867 0.881 0.917 0.893 0.927 0.901 [1] Note: IM, RA and NRA stand for intermediate approach, radial approach and nonradial approach, respectively. [2] China’s provinces (or province-equivalents) are listed as follows: BJ: Beijing; TJ: Tianjin; HEB: Hebei; SX: Shanxi; IM: Inner Mongolia; LN: Liaoning; JL: Jilin; HLJ: Heilongjiang; SH: Shanghai; JS: Jiangsu; AH: Anhui; CQ: Chongqing; FJ: Fujian; GS: Gansu; GD: Guangdong; GX: Guangxi; GZ: Guizhou; HAN: Hainan; HEN: Coastal region

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Henan; HUB: Hubei; HUN: Hunan; JX: Jiangxi; NX: Ningxia; QH: Qinghai; SAX: Shaanxi; SC: Sichuan; YN: Yunnan; SD: Shandong; XJ: Xinjiang; ZJ: Zhejiang.

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Table 4: Correlation Coefficients among Unified Efficiency Measures Efficiency measures

Method s IM [2]

IM 1.0000

MUEN RA

NRA

IM

MUEM RA NRA

1.000 MUEN 0 0.728 NRA 0.7094 1.0000 0 0.371 1.000 IM 0.3049 0.1072 1 0 0.249 0.914 1.000 MUEM RA 0.1833 0.0422 3 1 0 0.026 0.590 0.739 1.000 NRA 0.0207 5 0.0878 8 4 0 [1] Note: MUEN: unified efficiency under meta-frontier and natural disposability. MUEM: unified efficiency under meta-frontier and managerial disposability. [2] IM: Intermediate approach, RA: Radial approach and NRA: Non-radial approach. [1]

RA

0.9838

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Table 5: Mann–Whitney U-test between Coastal and Inland Provinces Under Natural disposability UPHypothesis

[1]

statistics value [2]

IM [3]

Ho: Mean(MUEN of Coast ) = Mean(MUEN of Inland)

46.000***

0.008

49.000**

0.012

39.000***

0.003

U-

P-

statistics

value

77.000

0.200

72.000

0.134

73.000

0.146

[4]

Ho: Mean(MUEN of Coast) = Mean(MUEN of RA Inland) NR A

Ho: Mean(MUEN of Coast) = Mean(MUEN of Inland)

Under Managerial disposability

Hypothesis

Ho: Mean(MUEM of Coast) = Mean(MUEM of IM Inland) Ho: Mean(MUEM of Coast) = Mean(MUEM of RA Inland) NR A

Ho: Mean(MUEM of Coast)= Mean(MUEM of Inland)

Note: [1] Ho indicates a null hypothesis, assuming that the average of the power plants in coastal provinces is the same as that of the inland provinces. The tests on MUEN statistically reject the three null hypotheses. The statistical results indicate that Chinese provinces have paid attention to their economic developments more than 44

environmental protection. In contrast, the tests on MUEM cannot statistically reject the three null hypotheses because the operations of power plants in all provinces have been under governmental regulations and international pressure on air pollution. [2] *** denotes that the significance level is 1%. ** denotes that the significance level is 5% and ** denotes that the significance level is 10%. [3] IM: Intermediate approach, RA: Radial approach and NRA: Non-radial approach. [4] All provinces are classified into coastal group and inland group.

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