DEA radial measurement for environmental assessment and planning: Desirable procedures to evaluate fossil fuel power plants

Energy Policy 41 (2012) 422–432

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Energy Policy journal homepage: www.elsevier.com/locate/enpol

DEA radial measurement for environmental assessment and planning: Desirable procedures to evaluate fossil fuel power plants Toshiyuki Sueyoshi a,n, Mika Goto b a b

New Mexico Institute of Mining & Technology, Department of Management, 801 Leroy Place, Socorro, NM 87801, USA Central Research Institute of Electric Power Industry, 1-6-1, Otemachi, Chiyoda-ku, Tokyo 100-8126, Japan

a r t i c l e i n f o

a b s t r a c t

Article history: Received 31 March 2011 Accepted 3 November 2011 Available online 7 December 2011

Energy policy depends on a proper use of methodology in guiding a large energy issue such as the global warming and climate change. DEA is one of such methodologies that are often used for preparing environmental policy, which is closely linked to various energy issues. Unfortunately, the use of DEA applied to environmental policy is insufficient, often misguiding policy makers and other individuals who are involved in energy issues. This study provides three guidelines for a use of DEA in preparing environmental assessment. First, it is important to prepare both primal and dual formulations to confirm whether information regarding all production factors (i.e., inputs, desirable and undesirable outputs) is fully utilized in DEA assessment. Second, DEA has model variations in radial and non-radial measurements. It is necessary for us to examine environmental issues by different models in order to avoid a methodological bias existing in those empirical studies. Finally, DEA environmental assessment needs to incorporate the concept of natural and managerial disposability. The natural disposability indicates that a firm negatively adapts a regulation change on undesirable outputs. In contrast, the managerial disposability indicates that a firm positively adapts the regulation change because the firm considers the regulation change as a new business opportunity. & 2011 Elsevier Ltd. All rights reserved.

Keywords: Energy policy Environmental assessment Data envelopment analysis

1. Introduction Charnes et al. (1988) have first discussed a problem of a methodological bias in guiding a large policy issue, such as the global warming and climate change, which often need our multiple disciplinary efforts. The methodological bias simply indicates that different methods produce different empirical results. They have claimed ‘‘the difference in results obtained by the two methods of analysis points up a need for drawing on persons from multiple disciplines who are capable of checking each other’s methodologies when important policy decisions may be influenced by results’’. To avoid the methodological bias in policy studies, researchers and policy makers should not make an immediate conclusion based upon empirical results obtained from a single discipline (e.g., economics). In particular, when addressing a large policy issue on energy, an approach originated from economics is often used as a conceptual and methodological basis. Policy makers often do not pay attention to alternative approaches that originate from other disciplines. Thus, it is important for us to combat a methodological bias by applying an alternative approach to a large policy issue on energy.

n

Corresponding author. E-mail addresses: [email protected] (T. Sueyoshi), [email protected] (M. Goto). 0301-4215/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.enpol.2011.11.003

The research of Charnes et al. (1988) prepared their message more than twenty years ago. However, their message is still valid and important in current research on energy policy. To document the validity of their message, this study examines a use of DEA (Data Envelopment Analysis) as a methodology for guiding modern energy issues from the perspective of economics and management science. Both economics and management science conceptually link each other in DEA, but providing different methodological perspectives in their empirical studies. Thus, this study is concerned with a combined use of two disciplines that can avoid the problem of a methodological bias in DEA energy studies. That is the purpose of this study. Before describing the methodological issue in energy policy, this study needs to mention that DEA has been long serving as a managerial method to evaluate the performance of various organizations in public and private sectors. See Emrouznejad et al. (2008) that summarized previous DEA contributions in the past three decades. A major contributor of DEA is Professor William W. Cooper (University of Texas at Austin). Glover and Sueyoshi (2009) discussed DEA theories, models and algorithms from the contributions of Professor Cooper, dating back to the 18th century. Ijiri and Sueyoshi (2010) discussed his contributions in accounting and economics that became a conceptual backbone of DEA development. In returning to energy policy, we have been recently paying serious attention to the global warming and climate change

T. Sueyoshi, M. Goto / Energy Policy 41 (2012) 422–432

mainly due to an increase in CO2 emission. Almost all organizations in private and public sectors are required to make their efforts to reduce the amount of CO2 emission and other types of various pollutions. In response to the environmental issue, many researchers applied DEA to measure the performance of energyrelated organizations in public and private sectors. For example, Zhou et al. (2008) summarized more than 100 DEA applications in environment and energy studies. Cooper et al. (1996) provided a summary of more than 100 previous studies on how OR/MS (Operations Research/Management Science) methods were useful in preventing air pollution issues. A contribution of previous DEA studies in production economics was that they found the importance of an output separation into desirable (good) and undesirable (bad) outputs. That was a contribution, indeed. Such previous research efforts in the past decade included Bevilacqua and Braglia (2002); Korhonen and Luptacik (2004); Kumar (2006); Pasurka (2006); Picazo-Tadeo et al. (2005); Triantis and Otis (2004); Yang and Pollitt (2010); Zaim (2004); Zhou and Ang (2008); Zhou et al. (2008) and many other articles. An important feature of their studies in production economics is that they have used DEA radial models to unify desirable and undesirable outputs. In contrast, Sueyoshi and Goto (2010a, 2010b, 2011a, 2011b, 2011c, forthcoming-b, 2012, forthcoming-c) and Sueyoshi et al. (2010) utilized DEA non-radial models (e.g., RAM: Range-Adjusted Measure and its extensions in management science) because the non-radial measurement can more easily unify desirable and undesirable outputs than the radial measurement. See Sueyoshi and Goto (forthcoming-d) for their extension to the radial measurement. The remainder of this study is organized as follows: Section 2 reviews economic concepts used in previous studies on DEA environmental assessment. This review provides us with conceptual and methodological criteria that need to satisfy for the preparation of DEA environmental assessment. This section also discusses a new conceptual definition on natural and managerial disposability that is originated from business strategy. Based on the concept of natural and managerial disposability, Section 3 proposes a new radial model to determine the unified (operational and environmental) efficiency of various organizations in energy industries. Section 4 describes a DEA model under natural disposability. Section 5 discusses it under managerial disposability. Using a real data set on U.S. fossil fuel (coal and natural gas) power plants, Section 6 documents how to use the proposed approach for assessing and planning of these power plants. Section 7 concludes this study along with future extensions.

2. Previous contributions in DEA environmental assessment 2.1. Economic concepts Weak or Strong Disposability: A pioneering work was done by ¨ et al. (1989) who distinguished the concept of disposability Fare by weak and strong disposability on undesirable outputs. Follow¨ et al. (1989, pp. 91–92), let us consider X A Rm ing Fare þ as an input vector, G A Rsþ as a desirable (good) output vector and B A Rhþ as an undesirable (bad) output vector. All are column vectors. Production technology (P) can be considered as the mapping s P:X A Rm þ -PðXÞ D R þ , where the output set P(X) denotes a set of all output vectors producible by the input vector X. The ‘‘weak disposability’’ on desirable outputs is specified by GAP(X) ) yGAP(X) for all 0r y r1. Meanwhile, the ‘‘strong disposability’’ on desirable outputs is specified by G0 rGAP(X) ) G0 AP(X), where G0 is another output vector. Considering both undesirable and desirable output vectors, their study (1989, p. 92) has specified an output vector as (G, B). Then, the weak disposability is specified by the following vector

423

notation on the two output vectors: Pw ðXÞ ¼ fðG,BÞ : G r XZ

Xn j¼1

Xn j¼1

Gj lj ,B ¼

Xn j¼1

Bj lj ,

X j lj , lj Z 0 ðj ¼ 1,::,nÞg:

Here, the subscript (j) stands for the jth DMU and lj indicates the jth intensity variable (j ¼1,y,n). In the specification, desirable outputs are strongly disposable, but undesirable outputs are P weakly disposable. The inequality constraints ðG r nj¼ 1 Gj lj Þ allow a feasible vertical extension, reflecting the strong disposability of desirable outputs. The production technology under weak disposability incorporates a situation of ‘‘congestion’’ on undesirable outputs where an increase in undesirable outputs decreases the vector of desirable outputs. The equality constraints P ðB ¼ nj¼ 1 Bj lj Þ indicate such congestion by weak disposability on undesirable outputs. The strong disposability is specified by the following vector notation on the two output vectors Ps ðXÞ ¼ fðG,BÞ : G r XZ

Xn j¼1

Xn j¼1

Gj lj ,B r

Xn j¼1

Bj lj ,

X j lj , lj Z 0 ðj ¼ 1,::,nÞg:

P The inequality constraints ðB r nj¼ 1 Bj lj Þ allow for strong disposability on undesirable outputs. The following three concerns are important in understanding the weak and strong disposability. First, the economic concept on weak and strong disposability attracted considerable attention among production economists. For example, Korhonen and Luptacik (2004) proposed seven radial models, originated from the original ratio form, to examine an emission reduction program of twenty-four power plants. In addition to the weak and ¨ and Grosskopf (2004) discussed a nullstrong disposability, Fare joint relationship between desirable and undesirable outputs. In our understanding, the relationship indicates that undesirable outputs can be produced only if desirable outputs are produced. They discussed it oppositely. Second, although the importance of weak and strong disposability was widely accepted by many researchers in production economics, the economic concept was not perfect and insufficient in DEA environmental assessment. For example, Kuosmanen (2005) questioned on the validation of weak disposability. He claimed that the weak disposability implicitly assume that all firms apply uniform abatement factors. Then, he proposed a DEA radial model that incorporates the weak disposability for undesirable outputs, but allowing for differences in disposability factors across firms. ¨ Finally, a major problem of Fare et al. (1989), not clearly discussed in previous studies for production economics, is that they have conceptually discussed economic requirements on weak and strong disposability. However, they have never sufficiently specified a mathematical formulation to measure the concept of disposability. Consequently, the concept of weak and strong disposability has long dominated the previous studies on DEA environmental assessment. However, they have used many different models (mainly radial model) to assess the performance of environmental protection efforts. Simply saying, different studies used different formulations for DEA environmental assessment. Thus, the concept of disposability suffers from an occurrence of multiple radial models in the previous studies. The methodological issue, originated from production economics, needs to be explored in this study from the perspective of management science and it is extended further into a proper use of DEA for environmental assessment.

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2.2. DEA formulations under weak and strong disposability To describe more analytically the unique features of weak and strong disposability, this study reviews radial models proposed by Yang and Pollitt (2010) as an illustrative example. Weak Disposability: To describe their formulations, let us consider n DMUs (Decision Making Units) whose operational and environmental efforts are examined by DEA. The jth DMU (j¼1,y,n) uses a column vector of inputs (Xj) in order to yield not only a column vector of desirable (good) outputs (Gj), but also a column vector of undesirable (bad) outputs (Bj), where Xj ¼ðx1j ,x2j ,::,xmj ÞT , Gj ¼ ðg 1j ,g 2j ,::,g sj ÞT and Bj ¼ ðb1j ,b2j ,::,bhj ÞT : Here, the superscript ‘‘T’’ indicates a vector transpose. It is assumed that Xj 40, Gj 40 and Bj 40 for all j ¼1,y,n for our mathematical convenience. Yang and Pollitt (2010) has proposed three radial models. Since this study is interested in the concept of weak and strong disposability, we pay attention to their two radial models related to the concept on disposability. First, the unified (operational and environmental) efficiency of the kth DMU under weak disposability is measured by the following radial model (Yang and Pollitt, 2010, p. 4442): Minimize y n X s:t:  xij lj þ yxik Z0

Maxmize s:t:

g rj lj

Z g rk



bf j lj þ ybf k ¼ 0

ð1Þ

Here, the efficiency score is measured by y in Model (1). The column vector l ¼(l1,...,ln)T stands for unknown variables (often referred to as ‘‘structural’’ or ‘‘intensity’’ variables) for connecting the input vector, desirable and undesirable output vectors. The symbol (URS) implies ‘‘unrestricted’’. The unified efficiency is determined by yn obtained on optimality of Model (1). According to Yang and Pollitt (2010, p. 4442), the model is formulated under ‘‘weak disposability’’ because the third group of constraints for undesirable outputs has equality. In addition to their description, this study needs to mention that Model (1) is a radial model with input and undesirable output-orientation. The production possibility set for Model (1) is structured by constant RTS (Returns to Scale) because the equation (the sum of lambdas is unity) is not incorporated in Model (1). Yang and Pollitt (2010) did not specify y:URS in Model (1), but this study specifies it as formulated in Model (1). If we do not specify it in Model (1), we have a difficulty in preparing the dual formulation of Model (1). Strong Disposability: The second model is formulated under ‘‘strong disposability’’ as follows (Yang and Pollitt, 2010):

ði ¼ 1,. . .,mÞ,

j¼1 n X

g rj lj

Z g rk

ðr ¼ 1,. . .,sÞ,

j¼1



n X

bf j lj þ ybf k Z 0

ðf ¼ 1,. . .,hÞ,

j¼1

lj Z0 ðj ¼ 1,. . .,nÞ and y : URS:

m X

i¼1

ðf ¼ 1,. . .,hÞ,

j¼1

Minimize y n X s:t:  xij lj þ yxik Z0



m X

lj Z0 ðj ¼ 1,. . .,nÞ and y : URS:

ur g rk

vi xij þ

ð2Þ

Here, the difference between Models (1) and (2) is that the third group of constraints in Model (1) is reformulated by

s X

ur g rj 

r¼1

i¼1

ðr ¼ 1,. . .,sÞ

j¼1 n X

s X r¼1

ði ¼ 1,. . .,mÞ,

j¼1 n X

inequality. No other change is found between Model (1) and Model (2). Models (1) and (2) have two important features, both of which are not discussed in the research of Yang and Pollitt (2010). One of the two features is that they measure the level of reduction on inputs and undesirable outputs by an efficiency score (y). However, the efficiency score is not applicable to desirable outputs in the two radial models. The treatment is because the directional vector of desirable outputs is the opposite to the directional vector of inputs and undesirable outputs. Thus, their treatment may be slightly insufficient in assessing the operational and environmental performance of power plants. This indicates a difficulty in unifying desirable and undesirable outputs by the radial measurement. The other feature is that Models (1) and (2) specify a single-sided directional vector of inputs such as P  nj¼ 1 xij lj þ yxik Z0 (i¼ 1,y,m). This analytical feature is by far different from the non-radial measurement, proposed by a series of studies by Sueyoshi and Goto (2010b, 2011a, 2011b, 2011c, forthcoming-b, 2012, forthcoming-c) that incorporate both-sided directional vectors of inputs. Returning to Model (1), the model has the following dual formulation:

vi xik

h X

wf bf j

r0

ðj ¼ 1,. . .,nÞ,

f ¼1

þ

h X

wf bf k ¼ 1

f ¼1

vi Z0 ði ¼ 1,. . .,mÞ, ur Z0 and wf : URS ðf ¼ 1,. . .,hÞ:

ðr ¼ 1,. . .,sÞ, ð3Þ

Here, dual variables vi Z0 (i¼1,y,m), ur Z0 (r ¼1,y,s) and wf: URS (f¼1,y,h) are associated with the first, second and third groups of constraints in Model (1). It is important to note that the dual formulation of Model (2) under strong disposability can be obtained by changing from wf:URS (f¼1,y,h) to wf Z0 (f¼1,y,h). The change seems very minor, but the change produces a major difference between Model (3) and the dual of Model (2) because Model (3) can find an occurrence of ‘‘congestion’’, but the latter cannot. Here, the concept of congestion in production economics conventionally implies that an increase in an input results in a decrease in an output without changing the other inputs and outputs. However, the congestion of Model (3) is measured with respect to undesirable outputs, which is different from the conventional definition on congestion, because the conventional one is related to inputs, not undesirable outputs. In addition to the issue of congestion, Models (1) and (2) have two different features, all of which have never been discussed in Yang and Pollitt (2010). One of the two features is that P yn ¼ sr ¼ 1 unr g rk is attained on optimality of the two radial models. If unr becomes zero for some r, the rth desirable output does not determine the level of unified efficiency. Even if grk is one million, unr g rk ¼0 because unr is zero. In this case, the rth desirable output is not fully utilized in the efficiency measurement. Thus, it is difficult to accept the empirical results obtained from Models (1) and (2) as an empirical basis for preparing policy implications. This is a problem in the occurrence of zero in dual variables. Many previous studies in production economics, including Yang and Pollitt (2010), did not pay attention on the existence of this type of problem because they did not examine the dual formulations of their models. The other feature is that the efficiency score (y) works as a uniform abatement factor on undesirable outputs in Model (1).

T. Sueyoshi, M. Goto / Energy Policy 41 (2012) 422–432

The influence on the efficiency score is determined by an occurrence of zero in slacks in the constraints related to undesirable outputs. For example, if a dual variable(s) is positive, then the corresponding constraint(s) becomes binding (so, zero in its corresponding slack) so that the uniform abatement occurs on undesirable outputs. In contrast, if a dual variable becomes zero, we cannot identify the occurrence of uniform abatement on the undesirable outputs because a slack is positive. This type of linkage between primal and dual formulations is due to CSCs (Complementary Slackness Conditions) in linear programming. Many researchers in management science usually pay attention to the CSCs between Models (1) and (2) and their dual formulations. See Sueyoshi and Sekitani (2009) for a detailed description on CSCs in DEA. 2.3. Strategic concepts Natural Disposability: The first concept, referred to as ‘‘natural disposability’’, indicates that a firm decreases the directional vector of inputs to decrease the vector of undesirable outputs. Given the reduced input vector, the firm simultaneously attempts to increase the vector of desirable outputs. For example, let us consider a coal fired power plant where CO2 emission is produced by coal combustion. The coal is used as an input for the operation of a coal fired power plant. If the power plant may decrease the amount of coal, then the reduction immediately decreases the amount of CO2 emission until it reaches the level of governmental regulation or international agreement. Given the reduced vector of inputs, the power plant attempts to increase the amount of electricity as much as possible. Thus, the natural disposability indicates an environmental strategy that negatively adapts a change in regulation on undesirable outputs. Managerial Disposability: The second concept, referred to as ‘‘managerial disposability’’, indicates an opposite direction of the input vector. The concept indicates that a firm can increase the input vector to decrease the vector of undesirable outputs and increase the vector of desirable outputs by new technology innovation and/or new management. The firm considers a regulation change on undesirable outputs as a new business opportunity. For example, the coal fired power plant increases the amount of coal for combustion so that it can increase the amount of electricity. Here, even if the power plant increases the amount of coal, the increase can reduce the amount of CO2 emission by a managerial effort by using a high quality fuel with less CO2 emission and/or an engineering effort to utilize new generation technology (e.g., clean coal technology and CCGT: CombinedCycle Gas Turbine for power generation) that can reduce the amount of CO2 emission. Thus, the managerial disposability indicates an environmental strategy that positively adapts the change on regulation to undesirable outputs. The two types of disposability, mentioned above, originate from environmental strategy to adapt a regulation change on undesirable outputs (e.g., CO2 emission). The natural disposability negatively adapts the regulation change, while the managerial disposability positively adapts the regulation change by considering the regulation change as a new business opportunity. Production technology to express natural and managerial disposability is formulated by the following output vectors, respectively:

The difference between the two concepts on disposability is that production technology under natural disposability, or Pn(X), has the P inequality constraints on inputs: X Z nj¼ 1 X j lj . Meanwhile, that of P m the managerial disposability, or P (X), has X r nj¼ 1 X j lj . The unification of the two disposability sets produces the following output set Pu ðXÞ ¼ P n ðXÞ [ Pm ðXÞ: In this unification, where [ stands for a union set, an efficiency frontier (EF) is for both desirable and undesirable outputs. The level of unified efficiency on a DMU is identified on EF in this study. Table 1 summarizes two structural differences between the weak/strong disposability and the natural/managerial disposability. As mentioned previously, the conventional definition on congestion in Table 1 implies that an increase in an input vector decreases a desirable output vector due to a capacity limit. However, the concept of congestion under weak disposability implies that an increase in an undesirable vector decreases a desirable output vector due to a capacity limit. Thus, the congestion under weak and strong disposability is different from its conventional definition in production economics. See Sueyoshi and Goto (forthcoming-e) on the claim. ¨ et al. (1989, pp. 91–92) considered It is important to note Fare P the strong disposability as B r nj¼ 1 Bj lj as listed above. HowP ever, Yang and Pollitt (2010, p. 4442) treated it as B Z nj¼ 1 Bj lj . Thus, the location of an efficiency frontier in the former study is opposite to that of the latter study, rather than being close to the natural disposability discussed in this study. Desirable Procedures on Environmental Assessment: Reviewing the recent studies on DEA environmental assessment (e.g, Watanabe and Tanaka, 2007; Zhou and Ang, 2008; Mandal and Madheswaran, 2010; Yang and Pollitt, 2010) published in this journal, this study finds the following three concerns on DEA environmental assessment. (a) Dual Formulation: First, all the previous research efforts in production economics (including publications in this journal) did not pay attention to dual formulations even though these formulations had a close linkage with primal formulations proposed in their studies. Consequently, many previous publications neglected the fact that when a dual variable(s) becomes zero, its corresponding production factor(s) is not fully utilized in DEA assessment. They collected a data set for their empirical Table 1 Structural differences between two disposability combinations. Weak and strong disposability

Natural and managerial disposability

Undesirable outputs P (a) B ¼ nj¼ 1 Bj lj for weak P disposability and B r nj¼ 1 Bj lj for

(a) B Z

strong disposability. (b) An important difference between the two is that the weak disposability can measure the status of congestion on undesirable outputs. In contrast, the strong disposability does not measure the status of congestion.

8 9 n n n n < = X X X X P ðXÞ ¼ ðG,BÞ: G r Gj lj , BZ Bj lj , X Z X j lj , lj ¼ 1, lj Z 0 ðj ¼ 1,::,nÞ : : ;

Desirable outputs P G r nj¼ 1 Gj lj for both weak and

8 9 n n n n < = X X X X Gj lj , B Z B j lj , X r X j lj , lj ¼ 1, lj Z 0 ðj ¼ 1,::,nÞ : P m ðXÞ ¼ ðG,BÞ: G r : ;

Inputs P X Z nj¼ 1 X j lj for both weak and

n

j¼1

j¼1

j¼1

j¼1

j¼1

j¼1

j¼1

j¼1

425

strong disposability.

strong disposability.

Pn

j¼1

Bj lj for both natural and

managerial disposability (b) The concept of natural and managerial disposability does not have any linkage to the measurement of congestion in this study. Sueyoshi and Goto (forthcoming-e) has discussed an occurrence of congestion under natural and managerial disposability. Gr

Pn

j¼1

Gj lj for both natural and

managerial disposability.

XZ

Pn

j¼1

X j lj for natural Pn

disposability and X r

j¼1

managerial disposability.

X j lj for

426

T. Sueyoshi, M. Goto / Energy Policy 41 (2012) 422–432

analyses, believing that DEA could fully utilize information on the data set. However, the truth is opposite to their expectation. It is also true that DEA is not a perfect methodology, having strengths and drawbacks in applying it for empirical studies. Therefore, the examination of dual variables is important for confirming whether information on all production factors is fully utilized in DEA environmental assessment. Moreover, the occurrence of zero in many dual variables produces many efficient DMUs. The result is mathematically acceptable, but managerial unacceptable. It is required that DEA needs to restrict dual variables to be positive so that it can reduce the number of efficient DMUs. See Sueyoshi and Goto (2011d, forthcoming-a) for a detailed description on how to handle the problem. (b) Radial/Non-Radial Models: Second, DEA has many model variations, all of which are generally classified into radial and nonradial models. See Sueyoshi and Sekitani (2009) for a detailed description on analytical features of radial and non-radial models. DEA models used in previous studies on environmental assessment mainly belonged to the radial measurement, not the nonradial measurement. It is better for DEA environmental studies to examine their empirical results from not only the radial measurement (or so-called ‘‘Debreu–Farrell measurement’’), but also the non-radial measurement (or so-called ‘‘Pareto-Koopmans measurement’’). See Glover and Sueyoshi (2009) for a detailed description on the history of DEA, dating back to the 18th century, which discusses such analytical differences. (c) Natural and Managerial Disposability: Finally, the concept of weak and strong disposability dominated previous studies on DEA environmental assessment in not only production economics and other energy areas. Many researchers, except Kuosmanen (2005), did not make any question on the validity of the economic concept. Of course, this study clearly acknowledges the historical importance and contribution of weak and strong disposability in environmental assessment. However, the economic concept does not consider a possible incorporate of technology innovation for environmental protection in DEA environmental assessment. Therefore, the economic concept cannot serve as a conceptual basis for DEA environmental assessment in the 21st century where the technology innovation plays a major role in environmental protection and assessment. Thus, it is better for us to examine the natural and managerial disposability, originated from environmental strategies for a regulation change, into DEA environmental assessment. Finally, the use of natural and managerial disposability needs to be examined along with the concept of weak and strong disposability. 3. Unfired efficiency under natural and managerial disposability 3.1. Non-radial formulation

m X

xþ

Rxi ðdi

x

þ di Þ þ

n X

s X

xþ

xij lj di

j¼1

x

g

Rgr dr þ

r¼1

i¼1

s:t:

g

g rj lj dr ¼ g rk

ðr ¼ 1,. . .,sÞ

j¼1 n X

b

bf j lj þdf ¼ bf k

ðf ¼ 1,. . .,hÞ,

lj ¼ 1, lj Z 0

ðj ¼ 1,. . .,nÞ,

j¼1 n X j¼1 xþ

di

Z0

g dr Z 0

x

ði ¼ 1,. . .,mÞ, di Z 0 ði ¼ 1,. . .,mÞ, b

ðr ¼ 1,. . .,sÞ, and df Z 0 ðf ¼ 1,. . .,hÞ:

x di

g dr

ð4Þ

b df

Here, (i¼1,y,m), (r ¼1,y,s) and (f¼1,y,h) are all slack variables related to inputs, desirable (good) and undesirable (bad) x outputs, respectively. The slack variable (di ) related to the ith xþ

input is separated into its positive and negative parts (di and x di Þ. They are incorporated together in the first group of constrains of Model (4). l ¼(l1,y,ln)T is a column vector of unknown variables (often referred to as ‘‘structural’’ or ‘‘intensity’’ variables) used for connecting the input and output vectors by a convex combination. Since the sum of the structural variables is restricted to be unity in Model (4), the production possibility set for Model (4) is structured under variable RTS and variable DTS (Damages to Scale: it corresponds to RTS in the case of undesirable outputs). See Sueyoshi and Goto (2011c, forthcoming-c) for fa detailed description on DTS. The ranges in Model (4) are determined by the upper and lower bounds on inputs and those of desirable and undesirable outputs. The upper and lower bounds of inputs are specified by xi ¼ maxfxij g j

and x i ¼ minfxij g for all i. The range for inputs becomes j

Rxi ¼ 1=½ðmþ s þ hÞðxi x i Þ for all i. The upper and lower bounds of desirable outputs are g r ¼ maxfg rj g and g r ¼ minfg rj g for all r. The j

j

range for desirable outputs becomes Rgr ¼ 1=½ðmþ s þ hÞðg r g r Þ for all r. The upper and lower bounds of undesirable outputs are mathematically expressed by bf ¼ maxfbf j g and b f ¼ minfbf j g for j

j

all f. Then, Rbf ¼ 1=½ðm þs þ hÞðbf b f Þ for all f indicate the range for undesirable outputs. This study does not describe the important feature of Model (4) further because such a description can be found in a series of studies by Sueyoshi and Goto (2010b, 2011a, 2011b, 2011c, forthcoming-b, 2012, forthcoming-c). An exception is that it is not necessary for Model (4) to have an efficiency score (y) because Model (4) measures the level of inefficiency by examining only slacks related to production factors. The analytical feature of Model (4) is important in unifying desirable and undesirable outputs. That is, the non-radial measurement can more easily unify desirable and undesirable outputs than that radial measurement. 3.2. Radial formulation

This study starts reviewing a non-radial model for DEA environmental assessment and then extends it to the radial measurement to maintain a descriptive consistency with the previous studies such as Yang and Pollitt (2010). The non-radial model under natural and managerial disposability, proposed by Sueyoshi and Goto (e.g., 2010a, 2010b, 2011c, 2012b, 2012c), is formulated as follows:

Maximize

n X

þ di ¼ xik

h X

Following Sueyoshi and Goto (2012d), this study extends Model (4) to the following radial model: 2 3 m s h X X X xþ x g b Maximize x þ e4 Rxi ðdi þ di Þ þ Rgr dr þ Rbf df 5 r¼1

i¼1

s:t:

n X

xþ xij lj di

x þdi

¼ xik

f ¼1

ði ¼ 1,. . .,mÞ,

j¼1 b

Rbf df

f ¼1

n X

n X

ði ¼ 1,. . .,mÞ,

g

g rj lj dr xg rk ¼ g rk

ðr ¼ 1,::,sÞ,

j¼1

j¼1

b

bf j lj þ df þ xbf k ¼ bf k

ðf ¼ 1,. . .,hÞ,

T. Sueyoshi, M. Goto / Energy Policy 41 (2012) 422–432 n X

427 xþ

lj ¼ 1, lj Z0

implies a simultaneous occurrence of di on optimality of Model (5).

ðj ¼ 1,. . .,nÞ,

j¼1

x : URS, dxi þ Z0 ði ¼ 1,. . .,mÞ, dx i Z 0 ði ¼ 1,. . .,mÞ, g

b

dr Z0 ðr ¼ 1,. . .,sÞ, and df Z 0

ðf ¼ 1,. . .,hÞ:

4. Unified efficiency under natural disposability ð5Þ

A scalar value (x), standing for an inefficiency score, is unrestricted (URS) in Model (5). The existence of the ranges indicates that Model (5) can always produce positive dual variables so that information on all production factors is utilized in the DEA environmental assessment. A scalar value (e) stands for a small number. This study sets it as 0.0001 for our computation convenience. The small number should be selected in a range that the efficiency score of all DMUs locate between zero (standing for full efficiency) and one (standing for full inefficiency). In the case when we cannot determine the small number, it is possible to specify it as zero. In this case, Model (5) may face an occurrence of zero in dual variables. The magnitude of unified efficiency is measured by 2 0 13 m s h X X X n n xn x xþn g gn b bn A5 4 @ y ¼ 1 x þ e Ri ðdi þdi Þ þ Rr dr þ Rf df r¼1

i¼1

To extend Model (5) further, this study reorganizes the DEA model by incorporating the concept of natural disposability. The unified efficiency under natural disposability is measured by the following radial model: 2 3 m s h X X X x g b Maximize x þ e4 Rx d þ Rg d þ Rb d 5

s:t:

x

xþ

n X

n X

x

x

the nonlinear conditions: di di ¼ 0 (i¼1,y,m), implying that the two slack variables are mutually exclusive. Consequently, a xþ x simultaneous occurrence of both di 40 and di 4 0 (i¼1,y,m) is excluded from the optimal solution of Model (5). When Model (5) has such a simultaneous occurrence, a computer code may produce ‘‘an unbounded solution’’ because of violating the nonlinear conditions. In order to make Model (5) satisfy the nonlinear conditions, this study suggests the following two computational alternatives: (a) One of the two alternatives is that Model (5) incorporates the nonlinear conditions into the formulation as side constraints x þ x and then we solve Model (5) with di di ¼ 0 (i¼1,y,m) as a nonlinear programming problem. (b) The other alternative is that Model (5) incorporates the followxþ x þ þ  ing side constraints: di r Mziþ , di r Mz i , zi þzi r1, zi and  zi : binary (i¼1,...,m) into the formulation and we solve Model (5) with the side constraints as a mixed integer programming problem. Here, M stands for a very large number that we need to prescribe before our computational operation.

n X

f

f

f ¼1

x

ði ¼ 1,. . .,mÞ,

g

ðr ¼ 1,. . .,sÞ

xij lj þ di ¼ xik g rj lj dr xg rk ¼ g rk b

bf j lj þ df þ xbf k ¼ bf k

ðf ¼ 1,. . .,hÞ,

j¼1

lj ¼ 1, lj Z 0

ðj ¼ 1,. . .,nÞ,

j¼1

x : URS, dxi Z0 ði ¼ 1,. . .,mÞ, g

dr Z0 ðr ¼ 1,. . .,sÞ,

b

and

df Z0

ðf ¼ 1,. . .,hÞ:

ð7Þ x

Model (7) considers only single-sided input deviations þdi (i ¼1,y,m) of Model (5) to attain the natural disposability. As mentioned previously, the natural disposability implies that a firm decreases the directional vector of inputs to decrease the vector of undesirable outputs. Given the reduced input vector, the firm simultaneously attempts to increase the vector of desirable outputs. In the case of a coal fired power plant, the coal is used as an input for the operation of the power plant. Under natural disposability, the power plant decreases the amount of coal. The reduction immediately decreases the amount of CO2 emission until it reaches the level of governmental regulation and/or an international agreement on the gas emission. Given the reduced vector of inputs, the power plant attempts to increase the amount of electricity. A unified efficiency score (yn) of the kth DMU under natural disposability becomes 2 0 13 m s h X X X n n x xn g gn b bn A5 4 @ : ð8Þ y ¼ 1 x þ e Ri di þ Rr dr þ Rf df r¼1

i¼1

f ¼1

The inefficiency score and all slack variables are determined on optimality of Model (7). The equation within the parenthesis, obtained from the optimality of Model (7), indicates the level of unified inefficiency under natural disposability. The unified efficiency is obtained by subtracting the level of inefficiency from unity. Model (7) has the following dual formulation: Minimize

m X

vi xik 

m X

s X

ur g rk þ

r¼1

i¼1

s:t: Infeasibility in Dual Formulation of Model (5): It is important to note that Model (5) has a feasible solution. However, it may also produce an unbounded solution because the dual formulation is infeasible. In this case, we must depend on one of the above two alternatives. Both usually produce a similar optimal solution. See Sueyoshi and Goto (2011b) for a computational comparison on the two approaches. Here, the unbounded solution implies the violation of the nonlinear conditions, not a conventional unbounded solution (where an optimal objective value becomes infinite) in linear programming. The violation, indicated by an unbounded solution,

r

j¼1

n X

objective function of Model (5) indicates di þdi ¼ 9di 9. The input slacks in the first group of constraints in Model (5) indicate xþ x x di di ¼ di . The variable transformation of input slacks needs

r

r¼1

j¼1

ð6Þ where xn and slacks within the parentheses are all obtained from optimality of Model (4). They indicate the level of unified inefficiency. The level of efficiency is obtained by subtracting the level of inefficiency from unity, as formulated in Eq. (6). Returning to Model (5), this study needs to mention that the two slacks related to the ith input are mathematically defined as xþ x x x x x di ¼ ð9di 9 þ di Þ=2 and di ¼ ð9di 9di Þ=2. The parenthesis in the

i

i

i¼1

f ¼1

xþ

x

4 0 and di 40 for some i

vi xij 

i¼1

s X

wf bf k þ s

f ¼1

ur g rj þ

r¼1 s X

h X

h X

wf bf j þ s Z 0

ðj ¼ 1,. . .,nÞ,

f ¼1

ur g rk þ

r¼1

h X

wf bf k

¼1

f ¼1

vi Z eRxi

ði ¼ 1,. . .,mÞ, Rgr

ur Z e

ðr ¼ 1,. . .,sÞ, Rbf

wf Z e

ðf ¼ 1,. . .,hÞ,

s : URS:

ð9Þ

428

T. Sueyoshi, M. Goto / Energy Policy 41 (2012) 422–432

where vi (i¼1,y,m), ur (r¼1,y,s), wf (f¼1,y,h) are all dual variables related to the first, second and third groups of constraints in Model (9). The dual variable (s) is obtained from the fourth equation of Model (9). The objective value of Model (7) equals that of Model (9) on optimality. Each dual variable indicates the level of increase in unified inefficiency under natural disposability due to a unit increase in each production factor. For example, a unit increase in the fth undesirable output yields the rate of change (wf) in the unified inefficiency under natural disposability.

s:t:



m X

vi xij 

i¼1

s X

ur g rj þ

r¼1 s X

h X

wf bf j þ s Z0

ur g rk þ

r¼1

h X

wf bf k

¼1

f ¼1

vi Z eRxi

ði ¼ 1,. . .mÞ, ur Z e

Rgr

ðr ¼ 1,. . .,sÞ, wf Z eRbf

i

i

s:t:

n X

r

r

r¼1

i¼1

f

f

f ¼1

x

ði ¼ 1,. . .,mÞ,

g

ðr ¼ 1,. . .,sÞ,

xij lj di ¼ xik

j¼1 n X

g rj lj dr xg rk ¼ g rk

j¼1 n X

b

bf j lj þ df þ xbf k ¼ bf k

ðf ¼ 1,. . .,hÞ,

lj ¼ 1, lj Z0

ðj ¼ 1,. . .,nÞ,

j¼1 n X j¼1

x : URS, dxi Z0 ði ¼ 1,. . .,mÞ, g

b

dr Z0 ðr ¼ 1,. . .,sÞ, and df Z 0

ðf ¼ 1,. . .,hÞ:

ð10Þ x

Model (10) considers only single-sided input deviations di (i¼1,y,m) in Model (7) to attain the status of managerial disposability. A unified efficiency score (yn) of the kth DMU under managerial disposability is measured by 2 0 13 m s h X X X n n x n g n b n x g b ð11Þ y ¼ 14x þ e@ Ri di þ Rr dr þ Rf df A5 r¼1

i¼1

f ¼1

Here, the inefficiency score and all slack variables are determined on optimality of Model (10). The equation within the parenthesis, obtained from the optimality of Model (10), indicates the level of unified inefficiency under managerial disposability. The unified efficiency is obtained by subtracting the level of inefficiency from unity. Model (10) has the following dual formulation: Minimize



m X i¼1

vi xik 

s X r¼1

ur g rk þ

h X f ¼1

wf bf k þ s

ðf ¼ 1,. . .,hÞ,

s : URS:

5. Unified efficiency under managerial disposability The managerial disposability indicates an opposite concept to the natural disposability that a firm considers a regulation change on undesirable outputs as a new business opportunity. They invest in new technology so that they can increase an input vector to produce both an increase in the vector of desirable outputs and a decrease in the vector of undesirable outputs. Returning to the case of a coal fired power plant, the power plant can increase the amount of coal for combustion so that it can increase the amount of electricity. Even if the power plant increases the amount of coal combustion, the increase can reduce the amount of CO2 emission by a managerial effort by using a high quality fuel with less CO2 emission and/or an engineering effort to utilize new generation technology (e.g., clean coal technology and CCGT) that can reduce the amount of CO2 emission. The unified efficiency under managerial disposability is measured by the following radial model: 2 3 m s h X X X x g b x g b Maximize x þ e4 R d þ R d þ R d 5

ðj ¼ 1,. . .,nÞ,

f ¼1

ð12Þ

where vi (i¼1,y,m), ur (r ¼1,y,s), wf (f ¼1,y,h) are all dual variables related to the first, second and third groups of constraints in Model (10). The dual variable (s) is obtained from the fourth equation of Model (10). The objective value of Model (10) equals that of Model (12) on optimality. Each dual variable indicates the level of increase in unified inefficiency under managerial disposability due to a unit increase in each production factor. For example, a unit increase in the fth undesirable output yields the rate of change (wf) in the unified inefficiency under managerial disposability.

6. Environmental assessment and planning 6.1. U.S. coal fired power plants According to the web site (http://www.sierraclub.org/cleanair/ factsheets/power.asp#cite4) of Sierra Club (2008), we have not changed fossil fuels, in particular dirty coal, to generate electricity although amazing technological advancements occurred in the last century. More than half of the electricity generated in the United States comes from coal. As the producers of the largest share of U.S. energy, coal fired power plants are also one of the dirtiest sources of electricity. Power plants are a major source of air pollution, with coal fired power plants spewing approximately 59% of total U.S. sulfur dioxide (SO2) pollution and approximately 18% (NOx) every year. Coal fired power plants are also the largest polluter of toxic mercury and the largest contributor of hazardous air toxics. They release approximately about 50% of particle pollution. Additionally, power plants release over 40% of total U.S. carbon dioxide emissions that is a prime contributor to the global warming and climate change. See the data sources http://www.eia.doe.gov/oiaf/ 1605/ggrpt/carbon.html#total and http://www.epa.gov/ttn/chief/ trends/index.html#tables. Sulfur dioxide, which can travel a long distance in the atmosphere before falling down to the land, can cause problems on its own as well as when it combines with other pollution to form other dangerous compounds. Acid rain, or acid deposition, occurs when SO2 and NOx react with water and oxygen in the atmosphere to make acidic compounds, most commonly sulfuric and nitric acid. These acidic compounds then either mix with natural precipitation and fall to the earth as acid rain, or remain dry and then settle to the ground. In the United States, coal fired power plants are the single largest source of SO2 pollution (approximately 66% of total SO2 is emitted from the electric power sector in 2008, and the main contributor of the emission of the sector is coal fired power plants) and the second largest source of NOx pollution. See http://www.epa. gov/ttn/chief/trends/ index.html#tables. Thus, the acid rain destroys our ecosystems, including streams and lakes, by changing their delicate pH balance and thereby, making them unable to support our life. Although coal fired power plants account for approximately 49% of electricity produced in the United States in 2007

T. Sueyoshi, M. Goto / Energy Policy 41 (2012) 422–432

(http://www.eia.doe.gov/cneaf/electricity/epa/epa_sum.html), they have been responsible for over 81% of the carbon dioxide (CO2) pollution from the electric power sector in 2007. Coal fired power plants have the highest output rate of CO2 per unit of electricity among all fossil fuels. See http://www.eia.doe.gov/oiaf/ 1605/ggrpt/carbon. html#electric. Because of such various pollution problems, this study recommends a use of DEA to evaluate the performance of U.S. coal fired power plants. Using a data set on U.S. coal fired power plants, this study discusses that the proposed two guidelines (i.e., dual formulation and natural and managerial disposability) are useful for DEA environmental assessment and planning. Since Sueyoshi and Sekitani (2009) have compared radial and non-radial models; this study does not discuss differences among them, rather focusing upon the importance of the remaining other two guidelines. No previous study compared the performance of coal fired power plants under weak, strong, natural and managerial disposability. This study is the first research to document such performance comparison under the four disposability concepts.

429

6.2. For environmental assessment This study documents empirical differences among weak, strong, natural and managerial disposability in assessing the performance of fossil fuel power plants. Then, we document a use of the proposed DEA approach under natural and managerial disposability for environmental planning by utilizing new generation technology. Table 2 summarizes a data set used for this illustration. The data set consists of two inputs (nameplate capacity and fuel consumption), one desirable output (net generation) and three undesirable outputs (SO2, NOx and CO2). The data source is U.S. EIA (Energy Information Administration) electricity data (http://www.eia.gov/cneaf/electricity/page/data.html) and U.S. EPA (Environmental Protection Agency) clean air markets data (http://camddataandmaps.epa.gov/gdm/). We sampled 390 U.S. coal and natural gas power plants for the year 2009. This study uses part of the data set for our illustrative purpose. Table 3 summarizes an efficiency score and dual variables obtained from Model (3) under strong disposability. To maintain

Table 2 An illustrative example. Plant

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Nameplate capacity

Fuel consumption

Net generation

MW

1000 MMBtu

GWh

2842 138 1417 1969 721 538 110 257 349 1129 1207 85 559 2390 1429 574 1010 138 183 752

122,482 3855 52,698 51,648 51,927 32,907 6,510 20,258 27,868 74,881 13,523 61 7929 146,042 70,867 5589 75,739 64 676 1559

14,087 261 5207 4,688 4,465 3026 592 1836 2656 7236 1521 4 688 14,620 7097 722 6840 2 45 132

SO2 Ton 37,109.314 3925.846 5027.653 12,861.358 11,720.507 5644.990 2,679.396 1308.302 1948.292 7955.926 2.933 0.093 642.152 7156.835 20,576.961 1.650 18,012.943 0.020 0.199 0.425

NOx

CO2

Ton

1000 Ton

8,440.868 795.335 5373.364 3526.372 4589.779 3193.010 1273.507 3607.039 4355.391 9211.297 103.511 0.910 1010.558 5903.727 4401.534 30.376 14,346.412 19.904 233.665 191.427

11,424.864 365.722 5695.994 5278.828 5265.576 3496.782 766.309 2164.309 2892.501 8441.262 580.963 3.162 580.239 15,588.088 7687.792 326.848 8,509.161 3.849 39.330 84.140

Table 3 Unified efficiency and dual variables: Model (3) under strong disposability. Plant

Efficiency score

Nameplate capacity

Fuel consumption

Net generation

SO2

NOx

CO2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1.000 0.578 0.930 0.771 0.925 0.905 0.880 0.975 1.000 0.970 1.000 0.544 0.718 1.000 0.923 1.000 0.933 0.274 0.511 0.682

0.131 0.394 0.065 0.029 1.190 0.618 2.742 2.328 0.515 0.183 0.000 0.000 0.687 0.393 0.269 0.000 0.252 0.000 0.000 0.000

0.005 0.245 0.016 0.018 0.000 0.019 0.107 0.000 0.029 0.010 0.000 8.883 0.033 0.000 0.008 0.000 0.010 15.663 0.761 0.342

0.071 2.212 0.179 0.165 0.207 0.299 1.487 0.531 0.377 0.134 0.657 133.971 1.043 0.068 0.130 1.385 0.136 121.257 11.477 5.159

0.000 0.000 0.009 0.000 0.000 0.000 0.000 0.307 0.008 0.003 340.948 0.000 0.071 0.000 0.000 483.567 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.031 0.008 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.010 0.004 6.654 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 144.011 0.528 0.000 0.000 0.000 0.000 0.000 12.337 5.545

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T. Sueyoshi, M. Goto / Energy Policy 41 (2012) 422–432

the strong disposability, Model (3) needs to change wf:URS (f¼1,y,h) to wf Z0 (f¼1,y,h) in the formulation. The objective value of Model (2) equals that of Model (3) under strong disposability on optimality. An important finding in Table 3 is that Model (3) under strong disposability produces zero in many dual variables. For example, see the last three columns of Table 3 where most of power plants have zero in these dual variables. This result clearly indicates that information on the three gases (CO2, SO2 and NOx) is not fully utilized in the performance evaluation of Model (2) or its dual formulation (3) with strong disposability. Thus, it is difficult to accept the computational results produced by Model (2) or (3) as the environmental assessment of coal and natural gas fired power plants. This type of problem (an occurrence of zero in many dual variables) can also be found in Model (1) under weak disposability. Yang and Pollitt (2010) have claimed that their models can be used for guiding the energy policy of Chinese coal fired power plants. However, Table 3 clearly indicates the invalidation of their claim. This type of problem occurs because they have never examined their dual formulations. Table 4 summarizes the unified efficiency of twenty coal and natural gas fired power plants measured by Models (1) under weak disposability, Model (2) under strong disposability, Model (7) under natural disposability and Model (9) under managerial disposability. DEA evaluation under the four types of disposability indicates that the five plants (1, 11, 12, 14 and 16) are rated as efficient in Table 4. The remaining other plants exhibit some level of inefficiency in at least one efficiency measure. An important result can be found in Model (1) under weak disposability that produces 14 efficient plants among 20 power plants. The rationale on why the computational result occurs is because deal variables of Model (1) have zero in many dual variables, as found in Table 3. The computational result (i.e., zero in dual variables) in Table 3 is also obtained under the strong disposability. The computational results in Table 4 indicate that the weak disposability produces zero in more dual variables than the strong disposability. As a result, Model (1) under weak disposability produces more efficient power plants than Model (2) under the strong disposability. Meanwhile, Model (7) under natural disposability and Model (9) under managerial disposability have the same problem of Table 4 Unified efficiency measured by radial models (1), (2), (7) and (9). Plant Unified efficiency score

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Model (1) under Model (2) under Model (7) under natural strong weak disposability disposability disposability

Model (9) under mangerial disposablity

1.000 1.000 0.993 0.855 1.000 0.939 1.000 1.000 1.000 1.000 1.000 0.552 0.944 1.000 1.000 1.000 1.000 1.000 1.000 0.826

1.000 0.425 0.855 1.000 0.780 0.706 0.403 0.613 0.721 0.793 1.000 1.000 0.601 1.000 0.826 1.000 0.675 1.000 0.763 1.000

1.000 0.578 0.930 0.771 0.925 0.905 0.880 0.975 1.000 0.970 1.000 0.544 0.718 1.000 0.923 1.000 0.933 0.274 0.511 0.682

1.000 0.762 0.897 0.789 0.906 0.930 1.000 1.000 1.000 0.928 1.000 1.000 0.771 1.000 0.891 1.000 1.000 1.000 0.654 0.739

many efficient plants even if their dual variables are all positive. The rationale is because the restriction on dual variables is not restrictive in such a level that it can reduce the number of efficient power plants. Note that this type of problem under natural and managerial disposability can be easily solved by the approach proposed by Sueyoshi and Goto (2011d, forthcoming-a), as mentioned previously. To discuss a methodological bias in Table 4, this study pays attention to an example plant (the 12th power plant). The power plant is evaluated as efficient (100%) under natural and managerial disposability, but it is evaluated as inefficient (55.2% and 54.4%) under weak and strong disposability. The efficiency scores on the 12th power plant indicate that different disposability concepts produce different efficiency measures. Thus, it is important for research to carefully examine a rationale concerning why such a discrepancy occurs in their DEA measures. At this stage, it is difficult for us to determine why such a discrepancy occurs under four disposability concepts and which disposability concept is better or not. Rather, it is important for us to understand the existence of a methodological bias in any DEA environmental assessment. Policy implication: It is better for us to examine several different disposability concepts in guiding energy and environmental policy. If we depend on only weak and strong disposability, our empirical results may misguide policy makers and other individuals who are interested in energy policy. To avoid such a methodological bias, we need to examine other alternative concepts, such as natural and managerial disposability, originated from an environmental strategy to adapt a regulation change on undesirable outputs. In particular, energy and environmental policy is usually very large and influential on not only the energy industry, but also the other industries in the world. Therefore, a careful examination on the methodology issue, along with different concepts of disposability, is very important in conducting DEA environmental assessment. 6.3. For environmental planning Besides a use for assessment as documented in Section 6.2, the proposed DEA approach can be utilized for environmental planning. To describe how to use it for environmental planning, this study pays attention to the first power plant whose unified efficiency scores are all 100% under the four disposability concepts. Let us consider that the power plant introduces new generation technology (e.g., high efficiency gas turbine technology such as CCGT for power generation) that can reduce the emission amount of the three gasses and increase the amount of electricity. For the planning purpose, this study considers the following five cases on the first power plant: (a) 10% increase in inputs, 10% increase in a desirable output and 10% decrease in undesirable outputs. (b) 10% increase in inputs, 20% increase in a desirable output and 20% decrease in undesirable outputs. (c) 10% increase in inputs, 30% increase in a desirable output and 30% decrease in undesirable outputs. (d) 10% increase in inputs, 40% increase in a desirable output and 40% decrease in undesirable outputs. (e) 10% increase in inputs, 50% increase in a desirable output and 50% decrease in undesirable outputs. It is assumed that the remaining other plants use the current production factors as summarized in Table 2. Under the five scenarios, this study is interested in examining how the unified efficiency scores of the twenty power plants, measured by Model (5) under both natural and managerial disposability, shift from their original efficiency scores.

T. Sueyoshi, M. Goto / Energy Policy 41 (2012) 422–432

Table 5 A shift of unified efficiency by innovation in first power plant: Models (5). Plant

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Unified efficiency Original

Case (a)

Case (b)

Case (c)

Case (d)

Case (e)

1.000 0.405 0.855 0.789 0.717 0.706 0.403 0.613 0.721 0.793 1.000 1.000 0.601 1.000 0.826 1.000 0.660 1.000 0.654 0.739

1.000 0.405 0.834 0.724 0.657 0.662 0.406 0.608 0.714 0.771 1.000 1.000 0.602 1.000 0.756 1.000 0.603 1.000 0.654 0.742

1.000 0.405 0.808 0.651 0.590 0.613 0.408 0.598 0.702 0.745 1.000 1.000 0.603 1.000 0.680 1.000 0.538 1.000 0.654 0.744

1.000 0.405 0.777 0.576 0.518 0.559 0.410 0.584 0.686 0.713 1.000 1.000 0.604 1.000 0.580 1.000 0.470 1.000 0.654 0.746

1.000 0.389 0.739 0.494 0.442 0.497 0.411 0.565 0.664 0.674 1.000 1.000 0.602 1.000 0.482 1.000 0.400 1.000 0.654 0.748

1.000 0.318 0.691 0.407 0.363 0.427 0.335 0.536 0.633 0.624 1.000 1.000 0.562 1.000 0.386 1.000 0.326 1.000 0.654 0.749

Note: Model (5) measures the unified efficiency under natural and managerial disposability.

Table 5, summarizing the shift of their unified efficiency scores, indicates two findings. One of the two findings is that the innovational change of the first plant does not change all efficient plants (1), (11), (12), (14), (16) under the five scenarios, where all plants are rated as efficiency under the four disposability concepts except the plant (12) that is rated as efficient under natural and managerial disposability. If the first power plant wants to dominate a power exchange market as a clean generator, it needs more technology innovation than the level required by the five scenarios so that it can change the efficiency status (from efficiency to inefficiency) of the other efficient power plants. The other finding is that the change of technology innovation influences on other inefficient power plants. They exhibit a decreasing trend in their unified efficiency scores. This declining trend implies that the new generation technology introduced in the first power plant may be a pressure on other inefficient power plants. The other power plants may introduce new generation technology for clean air in order to avoid a decrease in their unified efficiency scores. Policy implication: DEA can be used for not only environmental assessment, but also future planning. For example, the use of DEA models for environmental planning makes us possible to predict an expected change in ranking or a relative position of power plants when a specific power plant introduces new technology. Such a use of DEA may serve as an empirical basis for preparing environmental strategy. This methodological capability is because the proposed DEA approach can measure the unified efficiency of coal fired power plants under natural and managerial disposability, where the managerial disposability can measure the performance of coal fired power plants equipped with new technology and new management. The capability to measure new technology innovation is important in planning energy policy and environmental strategy regarding fossil fuel power plants.

7. Conclusion and future extensions Energy policy is a very important research area from academic and practical perspectives. Usually, an energy problem becomes a large policy issue because almost all industries in many nations

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connect each other by energy. A policy making process on energy depends on a proper use of methodology for guiding the policy issue. Recently, a use of DEA has been proposed as a methodology for energy studies by many researchers in economics and other policy-related studies. Acknowledging the previous DEA contributions in energy policy, this study found that the previous uses of DEA applied to energy and environment policy were methodologically biased as discussed by Chaners et al. (1988). Their uses of DEA environmental assessment occasionally misguided policy makers and other individuals related to energy policy. To overcome such a situation, this study provided three guidelines regarding a use of DEA for preparing environmental assessment and planning. First, the use of DEA needs to prepare not only a primal formulation, but also its dual formulation to enhance the quality of an empirical study. Using the dual formulation, it is possible for us to confirm whether information on all production factors is fully utilized in DEA assessment. Second, DEA has many model variations for radial and non-radial measurements, as documented in Sueyoshi and Sekitani (2009). It is necessary for us to pay attention to different DEA models in order to avoid a methodological bias existing in their empirical studies. Finally, DEA environmental assessment needs to incorporate the concept of natural and managerial disposability in addition to the conventional concept of weak and strong disposability. The concept of natural and managerial disposability originated from adaptive strategy to a regulation change to undesirable outputs (e.g., NOx, SO2 and CO2). Thus, the concept of natural and managerial disposability provides DEA environmental assessment with a strategic perspective (e.g, technology innovation for clean air) that cannot be found in the economic concept of weak and strong disposability. Under natural disposability, a firm decreases an input vector at the level that the emission of undesirable outputs can satisfy a policy guideline required by a government or an international agreement. The firm attempts to produce desirable outputs as much as possible at the decreased level of inputs. This type of negative adaptation strategy is often found in firms that do not have enough capital to invest in environmental protection. In contrast, the managerial disposability implies an environmental strategy in which a firm positively considers the regulation change on undesirable outputs. The firm invests in new technology and/or new management both to increase the amount of desirable outputs and to decrease the amount of undesirable outputs. The investment increases a cost in a short run, but reduces opportunity and operation costs in a long run. The increased desirable outputs, along with the reduced costs, increase revenue in a long run. The opportunity cost (i.e., electricity users change an electricity supplier and/or use an alternative energy source) is very important when we consider the environmental strategy of electric power firms. As a future extension, this study needs to explore economic and managerial features on DEA. For example, it is important for us to investigate the relationship between an amount of investment for new environmental technology on renewable energies and DEA results in terms of electricity generation under various cases of fuel mixture. No study has discussed such a research issue. Furthermore, this study needs to compare the concept of weak and strong disposability from the non-radial measurement (Pareto–Koopmans measurement). Conversely, the concept of natural and managerial disposability needs to be examined from the radial measurement (Debreu–Farrell measurement). This study exists on such a research direction as the initial step. We need to examine the issue from other important issues such as congestion and RTS/DTS. That is another important research extension.

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Finally, it is important to mention that DEA environmental assessment belongs to the initial stage of its development. There are many research tasks for future development. It is hoped that this study can make a contribution in the environmental assessment and planning. We look forward to seeing future research extensions, as discussed in this study.

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