DEA environmental assessment in time horizon: Radial approach for Malmquist index measurement on petroleum companies

Energy Economics 51 (2015) 329–345

Contents lists available at ScienceDirect

Energy Economics journal homepage: www.elsevier.com/locate/eneco

DEA environmental assessment in time horizon: Radial approach for Malmquist index measurement on petroleum companies Toshiyuki Sueyoshi a,⁎, Mika Goto b,1 a

New Mexico Institute of Mining & Technology, Department of Management, 801 Leroy Place, Socorro, NM 87801, USA Tokyo Institute of Technology, Department of Value and Decision Science, Graduate School of Decision Science and Technology, W9-41, 2-12-1, Ookayama, Meguro-ku, Tokyo 152-8552, Japan b

a r t i c l e

i n f o

Article history: Received 16 May 2015 Received in revised form 19 June 2015 Accepted 1 July 2015 Available online 5 August 2015 JEL classification: C18 C61 Q54 Q56 Keywords: Environmental assessment DEA Time series Malmquist index Petroleum

a b s t r a c t The climate change and various pollutions have been influencing our societies and economies. The environmental assessment, to be discussed in this study, is increasingly important because it serves as an initial step toward pollution prevention. Corporate leaders, policy makers, researchers and individuals who are interested in environmental protection have been paying attention to the assessment so that they can prepare policy suggestions on the global warming and climate change. As a methodology for the assessment, this study proposes a use of Data Environment Analysis (DEA) in a time horizon. Most of data sets on the climate change are sampled in a time series where the performance of organizations fluctuates every moment. In applying the DEA environmental assessment to such a data set, it is necessary for us to classify outputs into desirable (e.g., oil production) and undesirable (e.g., CO2 emission) categories because all organizations usually produce not only desirable but also undesirable outputs as a result of their economic activities. To unify the two different types of outputs, this study incorporates the concept of natural and managerial disposability into the computational framework of DEA and extends them into a time horizon. For the research purpose, this study incorporates Malmquist index into the proposed DEA environmental assessment to examine an occurrence of a frontier shift among multiple periods. The frontier shift indicates a technology progress and/or managerial innovation during an observed period. The index is further separated into four subcomponents in a time horizon. These subcomponents are differently expressed under the natural and managerial disposability. Thus, eight different subcomponents on the Malmquist index are proposed to measure the frontier shift. As an application, this study uses the proposed DEA approach to examine whether the frontier shift (due to technology progress) occurs or not in the petroleum industry from 2005 to 2009. Our empirical study finds that the industry has not exhibited any major frontier shift under natural disposability, but showing a considerable frontier shift under managerial disposability. In other words, the petroleum firms have improved their environmental performance by eco-technology to reduce an amount of CO2 emission during the observed annual periods. © 2015 Elsevier B.V. All rights reserved.

1. Introduction

⁎ Corresponding author. Tel.: +1 575 835 6452; fax: +1 575 835 5498. E-mail addresses: [email protected] (T. Sueyoshi), [email protected] (M. Goto). 1 Tel.: +81 3 5734 2627.

http://dx.doi.org/10.1016/j.eneco.2015.07.010 0140-9883/© 2015 Elsevier B.V. All rights reserved.

The climate change becomes a major policy issue all over the world. The climate change, due to global warming, implies an increase in average global temperature regarding air, sea and land on the earth. Natural events and human activities, including all industrial and economic activities, contribute to an increase in average global temperature. The change is primarily caused by an increase in “greenhouse” gases such as carbon dioxide (CO2). The change may occur in our global economy where commercial activities link together in the world market. To combat the climate change and global warming, this study proposes the use of Data Envelopment Analysis (DEA) as a holistic

330

T. Sueyoshi, M. Goto / Energy Economics 51 (2015) 329–345

methodology for environmental assessment. The DEA2 has long served as a managerial method to evaluate the performance of various organizations in public and private sectors. It is true that DEA has already established the reputation as one of very popular management science/ operations research approaches. See, for example, the article of Glover and Sueyoshi (2009) that discussed the history of DEA from the contributions of Professor Cooper in management science/operations research, dating back to its linkage with L1-regression developed in the 18th century. See also Ijiri and Sueyoshi (2010) that described his philosophical background on public accounting and public economics that became a conceptual backbone for DEA development. Departing from various conventional uses in performance evaluation, DEA has been recently applied for environmental assessment. For example, see Zhou et al. (2008) that summarized more than 100 articles in environment and energy studies. A contribution of DEA environmental studies was that they found the importance of an output separation into desirable and undesirable categories because production activities produced not only desirable but also undesirable outputs (Färe et al., 1989). The existence of undesirable outputs (e.g., greenhouse gases) is a serious problem in modern business. The finding on the output separation was a major contribution, indeed, in the area of DEA environmental assessment. To unify desirable and undesirable outputs into a computational framework, many research works have been recently explored, various models and methodologies regarding DEA environmental assessment in the past decades. They include Dyckhoff and Allen (2001), Korhonen and Luptacik (2004), Kumar (2006), Liang et al. (2004), Oude Lansink and Bezlepkin (2003), Pasurka (2006), Picazo-Tadeo et al. (2005), Ramanathan (2002), Triantis and Otis (2004), Zaim (2004), Zhou et al. (2008, 2010) and many other articles. Acknowledging their previous contributions in DEA environmental assessment, this study needs to mention that they have not yet systematically documented how to assess the performance of organizations, which produce both desirable and undesirable outputs, in a time horizon. An exception can be found in Zhou et al. (2010). A difference between their studies and this study is that they did not make any linkage with disposability concepts, such as natural and managerial disposability, which describe corporate strategies to a regulation change on undesirable outputs. In contrast, this study incorporates such disposability concepts into DEA formulations as proposed by Sueyoshi and Goto (2013d) and Sueyoshi et al. (2013b).

The purpose of this study is to describe the importance of natural and managerial disposability for DEA environmental assessment in a time horizon. The disposability concepts are linked to the Malmquist index measurement. After completing the methodological setting on DEA environmental assessment, this study applies the proposed approach to measure the performance of petroleum firms in the world. The remainder of this study is organized as follows: Section 2 discusses the importance of DEA in environmental assessment and sustainability development. Section 3 reviews strategic concepts related to disposability. This section extends the disposability concepts into a time horizon. Section 4 discusses how to unify desirable and undesirable outputs under natural disposability in a time horizon. Section 5 shifts our description to managerial disposability in a time horizon. Section 6 summarizes comments on the proposed approach. Section 7 documents an illustrative example regarding the petroleum industry and prepares business implications for the industry. Section 8 concludes this study along with future extensions. 2. Importance of DEA in measuring environmental performance Fig. 1 visually describes the importance of DEA in a social intelligence process for both reducing the amount of various environmental pollutions and enhancing the status of sustainability. Each organization in public and private sectors needs all of such intelligence capabilities to mitigate the amount of industrial pollution. A methodology selection (e.g., DEA) is determined as part of such an intelligence process, where “intelligence” implies a social capability of an organization (e.g., an energy company in a private sector or United Nations in a public sector) for holistic adjustment to various changes (e.g., a regulation change on industrial pollution), so not directly linking to any conventional engineering implication (e.g., artificial intelligence in computer science). Of course, such a social capability depends upon the utilization of a

Start

Crisis sensing capability

Crisis

No Felt crisis Yes Successful ?

2

DEA has been extensively used for environmental assessment. See Glover and Sueyoshi (2009) and Ijiri and Sueyoshi (2010) for their historical descriptions on DEA developments from the contribution of Professor William W. Cooper. DEA applications on environmental assessment can be found in a series of studies (Sueyoshi and Goto, 2009a, 2009b, 2010a,2010b, 2011a,2011b,2011c; Sueyoshi et al, 2009, 2010). An important feature of these studies is that they have developed a computational framework, but lacking a conceptual framework for DEA environmental assessment. The first article, which has discussed the conceptual framework such as natural and managerial disposability, can be found in Sueyoshi and Goto (2012a). Then, the natural and managerial disposability has served a conceptual basis for proceeding research efforts on DEA environmental assessment. See, for example, Goto et al. (2014), Sueyoshi and Goto (2012b, 2012d, 2012e, 2012f, 2012g, 2012h, 2012i, 2012j, 2012k, 2013a, 2013c, 2013d, 2014a, 2014b, 2014c, 2014d, 2015), Sueyoshi and Yuan (2015) and Sueyoshi et al. (2013a, 2013b). The disposability concepts are linked to an occurrence of desirable congestions, or eco-technology innovation, by their research efforts. In some of the articles, all inputs are separated into two categories under the two disposability concepts. Moreover, a conventional use of DEA was applied to renewable energy assessment (Sueyoshi and Goto, 2014c) and its combination with another methodology (e.g., Sueyoshi and Goto, 2012c, 2013b). DEA environmental assessment applied to U.S. industrial sectors can be found in Sueyoshi and Wang (2014a, 2014b) and Wang et al. (2014). The important feature of these studies is that they have used UENM and UENM(DC) for not only efficiency measurement but also investment opportunity assessment for technology innovation. The two measures stand for Unified Efficiency under Natural and Managerial (UENM) disposability and Desirable Congestion (DC), respectively. Finally, it is important to note that DEA can be used for not only efficiency measures but also other types of important economic measures related to social achievement, policy direction and corporate strategy in public and private sectors (e.g., Sueyoshi, 1997, 1999a,1999b, 2001, 2004, 2005, 2006; Sueyoshi and Goto, 2001, 2009b,2009c,2009d, 2011c, 2012c).

End Sustainability-making capability

Achievement assessment capability

Social sustainability

Production factor determination capability

Implementation

Policy/strategy making capability

Empirical results

Performance assessment capability

Corporate sustainability

Inputs

Desirable outputs

Measurement capability

Methodology (DEA)

Fig. 1. Position of DEA in environmental assessment.

Undesirable outputs

T. Sueyoshi, M. Goto / Energy Economics 51 (2015) 329–345

data processing ability (i.e., on a modern personal computer) that can simultaneously deal with many big data sets related to environmental protection. As an initial step, an organization (e.g., a petroleum firm in this study) needs to identify that it faces a serious crisis due to industrial pollution (e.g., air and/or water pollutions). As a result of pollution, consumers do not purchase products from a dirty-imaged company. They purchase products from a green company even if the prices are much higher than those of the dirty-imaged company. More seriously, a very large opportunity cost often occurs along with industrial pollutions that make a serious damage on each organization. For example, the disaster of Fukushima Daiichi nuclear power plant, occurred on March 11, 2011, was such an example of the opportunity cost. This type of opportunity cost is much larger than any cost components in modern business. It is necessary for the organization to have a “sensing capability” by which it can identify the existence of a serious business crisis due to industrial pollutions. Such a sensing capability may be often found in an individual member from the top to the bottom or a group of members within the organization. A result of the sensing capability, incorporated in the organization, is referred to as “felt crisis” in this study. The felt crisis is extended for serving as a necessity of “social sustainability” in a public sector or “corporate sustainability” in a private sector. The concept of “social sustainability”, supported by many international organizations such as United Nations, is related to global social responsibility and social welfare by preventing the climate change and global warming that have been gradually changing our ecological and economic systems. The concept of social sustainability contains world-wide implications in a long-term horizon. In contrast, “corporate sustainability” has another type of implication, so being different from the social sustainability, related to modern business perspectives. That is, the corporate sustainability is closely related to its survivability via a public image as a good corporate citizen. Moreover, the opportunity cost (e.g., damage due to industrial pollutions), which is much larger than any production-related cost items, may terminate its existence as a going concern. Thus, it is important for us to clearly distinguish between “social” and “corporate” sustainability concepts in discussing between world-wide policy issues (e.g., the global warming and climate change) and modem corporate behaviors for preventing industrial pollutions. After identifying the organizational objective (social or corporate sustainability), each organization needs to determine what consists of production factors (i.e., inputs, desirable and undesirable outputs) for environmental assessment. This type of social intelligence is referred to as “production factor determination capability” in this study. The DEA, as a holistic approach, is used in this stage as one of many methodological alternatives for assessing the level of social or corporate sustainability. Some member(s) should have the analytical capability to apply DEA for environmental assessment. This type of social intelligence is referred to as “measurement capability”. After applying DEA for performance assessment, the organization can obtain empirical results, indicating the level of sustainability that is measured by relatively comparing its performance with others. This is referred to as “performance assessment capability”. Based upon the empirical results, the organization needs to prepare policy/strategy for pollution prevention. The type of intelligence is referred to as “policy/strategy making capability”. The organization implements the policy or strategy for pollution reduction. The type of intelligence is referred to as “achievement assessment capability”. If the implementation is unsuccessful, the result brings the necessity of restarting the crisis feeling within the organization. A gradual improvement process is necessary in repeating the whole social intelligence process, as depicted in Fig. 1, until it can eliminate the crisis feeling due to environmental pollutions. Therefore, the pollution reduction effort needs to be explored in a time horizon, as discussed in this study. Finally, note that if one part of such intelligence capacities does not exist in the organization, then it will be unable to survive in our modern society and business. Such is the destination of dirty-imaged companies.

331

3. Previous studies and strategic concepts on DEA dynamics 3.1. Previous DEA studies Two groups of research were closely related to DEA in a time horizon. One of the two groups was due to Malmquist (1953). His study documented how to measure production indexes between different regions. Other production economists, including Bjurek (1996), Bjurek and Hjalmarsson (1995) and Grifell-Tatje and Lovel (1995), applied the Malmquist index3 to DEA dynamics and efficiency analysis. The Malmquist index measurement, proposed in the previous studies, has methodological strengths and drawbacks. A contribution of this group was that the index measurement was introduced and separated into its subcomponents. Consequently, it was possible for us to measure both a shift of an efficiency frontier and an influence of each subcomponent on the Malmquist index. That was a contribution, indeed. In contrast, the index measurement had a drawback. That is, as found in production economics, the previous measurement depended upon an assumption that production activity was characterized by a functional form(s). Of course, the index and its related subcomponents can be identified by DEA in the manner that we can avoid specifying the functional form, as discussed in this study. Furthermore, it was expected that production technology always shifted an efficiency frontier toward better performance in an observed period. However, such underlying assumptions were not always satisfied in many real performance assessments. It is necessary for us to consider the index measurement in which a frontier shift may not occur or an efficiency frontier retreats itself in the worst case. In addition to the economic approach, management scientists (e.g., Bowlin, 1987) were interested in the development of “DEA window analysis”. The methodology examined how much an efficiency score was changed by shifting a combination of adjacent periods, often referred to as a “window”. As an extension, Thore et al (1994) and Goto and Tsutsui (1998) combined the window analysis with the Malmquist index measurement. The combined measure was referred to as “Malmquist productivity index”. An important feature of the window analysis was that it could avoid the assumption that an efficiency frontier did not retreat. Even if a crossover occurred among efficiency frontiers, the window analysis pooled observations for a few consecutive periods into a window on which a new efficiency frontier was identified. Consequently, a group of efficiency scores was smoothed over time and these efficiency scores were determined by comparing these achievements with a newly established efficiency frontier within the window. That was a contribution, indeed. A drawback of the window analysis was that it lacked an analytical scheme to decompose the performance measurement into its subcomponents, as found in the Malmquist index measurement. The combination between the Malmquist index and the window analysis could be found in conventional DEA studies such as Sueyoshi and Aoki (2001) and Sueyoshi and Goto (2001), as well. Position of this study: All the previous studies on DEA dynamics considered only desirable outputs and inputs, so not paying attention to the existence of undesirable outputs. Since DEA environmental assessment needs to consider both desirable and undesirable outputs in a unified

3 There are several index measures in production economics such as Malmquist, Malmquist–Luenberger, Laspeyres, Paashe, Marshall–Edgeworth, Fisher, and Divisia indexes. To measure a shift among efficiency frontiers in a time horizon, Malmquist and Malmquist–Luenberger indexes were conventionally used in many studies. For example, Bjurek (1996), Bjurek and Hjalmarsson (1995), Sueyoshi, and Aoki (2001), Zhou et al. (2010) and Sueyoshi and Goto (2013d) documented how to measure a frontier shift by the Malmquist index. Meanwhile, Kumar (2006) used the Malmquist–Luenberger index for the frontier shift measurement among multiple periods. An important feature of these approaches was that they separated subcomponents of each index and measures the level of each subcomponent in term of the frontier shift.

332

T. Sueyoshi, M. Goto / Energy Economics 51 (2015) 329–345

framework, this study attempts to develop a new analytical framework that incorporates the concept of natural and managerial disposability into the Malmquist index measurement. As a consequence of such a combination, this study explores the DEA environmental assessment that can measure a shift of an efficiency frontier in a time horizon. This type of research has been never explored in the previous DEA studies. Exceptions can be found in Sueyoshi and Goto (2013d) and Sueyoshi et al. (2013b). Finally, it is important to note that this study uses “efficiency” when the measure exists between 0% (full inefficiency) and 100% (full efficiency). Meanwhile, this study uses “index” when the measure may be above the efficiency range, so being more than unity. Furthermore, the increase or the decrease implies a change on some or all components of the directional vector, hereafter.

Moreover, the opportunity cost, often associated with environmental problems, is much larger than any operation cost in modern businesses so that corporate leaders need to pay serious attention to various environmental protections. This type of strategy has been long supported by corporate strategists in U.S. business schools (e.g., Porter and van der Linde, 1995). To describe the concept of natural and managerial disposability by an axiomatic expression, let us consider X ∈ Rm + as an input vector with m components, G ∈ Rs+ as a desirable output vector with s components and B ∈ Rh+ as an undesirable output vector with h components. All of them are column vectors with strictly positive components. The concept of natural and managerial disposability is specified by the following vectors of production factors, respectively, under constant RTS (Returns to Scale) and constant DTS (Damages to Scale: corresponding to RTS on undesirable outputs):

3.2. Strategic concepts: natural and managerial disposability Before discussing DEA environmental assessment in a time horizon, it is necessary for us to discuss two strategic concepts on desirable and undesirable outputs from environmental protection. One of the two strategic concepts, referred to as “natural disposability”, indicates that a firm decreases a directional vector of inputs to decrease a vector of undesirable outputs. Given a reduced vector of inputs, the firm increases a directional vector of desirable outputs as much as possible. For example, let us consider a coal-fired power plant where the CO2 emission is produced by coal combustion. The coal is used as an input for the operation of a coal-fired power plant. Consequently, if the coal-fired power plant reduces the amount of coal combustion, the reduction immediately decreases the amount of CO 2 emission at the level that it can satisfy the amount determined by governmental regulation. Given the reduced coal combustion, the coal-fired power plant maximizes the amount of electricity generation. That is a “natural disposability”. In this case, the coal-fired power plant may attain the reduction of CO2 emission with a limited corporate effort at the level required by governmental regulation. A cost concern associated with the natural disposability is total operational cost. It is easily expected that the total operation cost may decrease but an average or marginal operation cost increases under the natural disposability because of less generation. This type of strategy has been long supported by most of production economists (e.g., Palmer et al., 1995) and DEA researchers. The other strategic concept, referred to as “managerial disposability”, indicates an opposite case of the natural disposability. Under the disposability concept, a firm can increase a directional vector of inputs to decrease a vector of undesirable outputs by utilizing ecotechnology innovation on undesirable outputs. Given the increased input vector, the firm increases a directional vector of desirable outputs as much as possible. For example, a coal-fired power plant increases the amount of coal combustion so that it can increase the amount of electricity generation. Here, 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 high quality coal with less CO2 emission and/or an engineering effort to utilize new ecogeneration technology (e.g., clean coal technology). Management of the power plant considers a change on environmental regulation as a business opportunity. The challenge of the power plant is a corporate effort for environmental protection, so implying “managerial disposability”. A cost concern associated with the managerial disposability is an opportunity cost, implying that consumers do not purchase electricity from a dirty-imaged old power plant. Rather, they prefer purchasing electricity from a clean-imaged power plant even if the electricity price is more expensive than that of the dirty-imaged power plant. Thus, the opportunity cost really poses a risk to the management of power plants. It is easily imagined that a total operation cost may increase because of eco-technology investment but an average or marginal operational cost decreases under managerial disposability because of more generation.

8 9 < = n n n X X X ðG; BÞ : G ≤ G jλ j; B ≥ B jλ j; X ≥ X j λ j & λ j ≥ 0 ð j ¼ 1; ::; nÞ & : ; j¼1 j¼1 j¼1 8 9 < = n n n X X X G jλ j; B ≥ B jλ j; X ≤ X j λ j & λ j ≥ 0 ð j ¼ 1; ::; nÞ ; P m ðX Þ ¼ ðG; BÞ : G ≤ : ; j¼1 j¼1 j¼1

P n ðX Þ ¼

where the subscript (j) stands for the j-th DMU (Decision Making Unit: an organization to be examined by DEA) and λj indicates the j-th structural or intensity variable (j = 1, .., n). The two superscripts (n and m) indicate natural and managerial disposability concepts, respectively. The difference between the two disposability concepts is that production technology under natural disposability, or P n(X), has n

the inequality constraints on inputs: X ≥ ∑ X j λ j . In contrast, that of j¼1

m

n

the managerial disposability, or P (X), has X ≤ ∑ X j λ j . j¼1

Comparison with previous disposability concepts: To specify the position of natural and managerial disposability, this study needs to return to the pioneering work of Färe et al. (1989, pp. 91–92) that has specified the weak and strong disposability. The two disposability concepts are defined by the following vector notation on the two output vectors, respectively: 8 9 < = n n n X X X ðG; BÞ : G ≤ G jλ j; B ¼ B jλ j; X ≥ X j λ j & λ j ≥ 0 ð j ¼ 1; ::; nÞ & : ; j¼1 j¼1 j¼1 8 9 < = n n n X X X G jλ j; B ≤ B jλ j; X ≥ X j λ j & λ j ≥ 0 ð j ¼ 1; ::; nÞ ; P s ðX Þ ¼ ðG; BÞ : G ≤ : ; j¼1 j¼1 j¼1

P w ðX Þ ¼

where the two superscripts (w and s) indicate weak and strong disposability, respectively. The production technology under the weak disposability incorporates the concept of “congestion” on undesirable outputs, or “undesirable congestion” in this study. The concept indicates that some enlarged component(s) of an input vector increases some component(s) of an undesirable output vector but decreases some component(s) of a desirable output vector. Thus, this study considers that some enhanced component(s) of an undesirable output vector leads to a decrease in some component(s) of a desirable output vector under the weak disposability. The equality   n constraints B ¼ ∑ B j λ j under the weak disposability make it posj¼1

sible to incorporate such an occurrence of undesirable congestion in DEA environmental assessment. In contrast, the strong disposability does not consider such an occurrence of undesirable congestion. Lessens from the weak and strong disposability: First, the strong and weak disposability concepts are formulated under the assumption that “undesirable outputs are byproducts of desirable outputs”. Therefore,

T. Sueyoshi, M. Goto / Energy Economics 51 (2015) 329–345 n

n

j¼1

j¼1

the strong disposability has G≤∑ G j λ j and B ≤∑ B j λ j in such a manner that both have the same inequality in these specifications on desirable and undesirable outputs. The weak disposability is formulated in the manner that it can identify an occurrence of undesirable (conventional) n

congestion by reorganizing the output constraints such as B ¼ ∑ B j λ j . j¼1

Acknowledging the importance of the previous contributions in production economics, this study needs to shift the conceptual framework from the weak and strong disposability to the natural and managerial disposability. The rationale is because the two types of outputs are connected to each other as specified by the assumption of byproducts. However, we consider that all DMUs increase the desirable output vector, while they attempt to decrease an undesirable output vector as much as possible so that the two types of output vectors are n

n

j¼1

j¼1

expressed by G≤∑ G j λ j and B ≥ ∑ B j λ j . Here, it is important to note that this study does not look for an occurrence of undesirable congestion, as found in the weak disposability, rather looking for an occurrence of “desirable congestion”, or ecotechnology innovation on pollution prevention under managerial disposability. This study does not discuss how to identify such an occurrence of desirable congestion. See Sueyoshi and Goto (2014b), Sueyoshi and Wang (2014a, 2014b) and Wang et al. (2014) for a detailed description on desirable congestion for pollution prevention. An important feature of their studies is that they allocate equality constraints on desirable outputs, not undesirable outputs as found in the weak disposn

ability. Thus, their formulations have G ¼ ∑ G j λ j under the assumption j¼1

on by-products so that they can identify the occurrence of desirable congestion, or eco-technology innovation, on undesirable outputs. Thus, this study agrees with the research of Färe et al. (1989, pp. 91– 92) in terms of the importance of allocating equality constraints, but disagrees with them on the allocation on which type of outputs the equality constraints are assigned in DEA formulations. As formulated by Sueyoshi and Goto (2014b), Sueyoshi and Wang (2014a, 2014b) and Wang et al. (2014), it is necessary for us to allocate equality constraints, or no slack variable, to desirable outputs under managerial disposability in their formulations. In contrast, an occurrence of undesirable congestion can be measured by allocating the equality constraints (because of no slack variable) to undesirable outputs under natural disposability under which the first priority is operational performance and the second priority is environmental performance. At the end of this section, the desirable congestion, discussed above, implies that some enlarged component(s) of an input vector increases some component(s) of a desirable output vector but decreases some component(s) of an undesirable output vector. The situation is attained by eco-technology innovation for pollution prevention. An underlying premise of the natural and managerial disposability discussed in this study is that technology development makes an occurrence of desirable congestion. Consequently, this study considers that the eco-technology innovation can solve various pollution problems so that we can enhance the status of sustainability. 3.3. Malmquist Index To extend the concept of natural and managerial disposability into a time horizon, this study prepares two figures to intuitively describe the measurement of the Malmquist Index. A visual description in the two figures serves as a conceptual basis for computing eight subcomponents (= 4 subcomponents × 2 disposability concepts) related to the Malmquist Index under natural and managerial disposability. Fig. 2 depicts a frontier shift from the p-th period to the t-th period under natural disposability in which each DMU attempts to enhance

333

the operational efficiency4 as the first priority and the environmental efficiency as the second priority. Two DMUs are listed as {a} and {c} along with the p-th and t-th periods. Two curves indicate efficiency frontiers for the two periods. For our visual convenience, Fig. 2 considers a single input (x) and two desirable outputs (g1 and g2). The visual description can be easily extendable to multiple inputs and desirable outputs in the proposed approach. In Fig. 2, ap stands for an observed performance of DMU{a} at the pth period, which is a base period. Meanwhile, ct indicates an observed performance of DMU{c} at the t-th period for t = p, p + 1, ..,T. The symbol (o) stands for the origin in the figure. The frontier shift occurs toward a north-east direction under the assumption that technology progress and/or managerial enhancement on desirable outputs occur between the two periods. Thus, the north-east direction of a frontier shift is due to the concept of natural disposability. For our visual convenience, the amount of undesirable outputs is considered as the same between the two periods. In Fig. 2, the performance of ap is projected to aep on the efficiency frontier of the p-th period and aet on the efficiency frontier of the t-th

4 According to Sueyoshi and Goto (2015), the concept of “technical efficiency” was first proposed by Michael James Farrell, who was an applied economist at University of Cambridge. This study does not use the term of “technical efficiency”, rather using “operational efficiency”. The rationale, first discussed by Sueyoshi and Goto (2015), explains why the term is used for DEA environmental assessment by reviewing the three articles (Farrell, 1954, 1957; Farrell and Fieldhouse, 1962). The first article (Farrell, 1954: An application of activity analysis to the theory on the firm) was prepared when he visited Yale University where he could meet T.C. Koopmans and J. Tobin. In the article (1954, p. 292), he discussed “activity analysis”, proposed by Koopmans, which could explore the corporate behavior of a firm by applying linear programming. In his article, the production relationship between production factors could be expressed by a static model in multiple periods. As a result, linear programming could be applicable to the assessment of corporate behavior. The second article (Farrell, 1957: The measurement of productive efficiency) was innovative and it was closely related to the classical DEA development in terms of providing the methodology with a conceptual basis. The article discussed an efficient production function, inspired by the activity analysis of linear programming (1957, p. 11) and started discussing an efficiency measure, referred to as “technical efficiency”, which was first discussed in Debreu's “coefficient of resource utilization” (Debreu, 1951). In addition to the concept of technical efficiency, According to his article (1957, p. 255), “an efficient production function might be expressed by a theoretical function specified by “engineers”. However, such an engineering-based empirical function was complicated and practically impossible to measure the theoretical efficiency function from the perspective of production economics. This study pays attention to the fact that Farrell (1957) has used the term “technical efficiency” because of his awareness on the engineering perspective, following Debreu (1951). Here, we may have simple questions such as “what engineering was” and “what type of technology was” in his economic context. It is very clear to us that the production technology in the middle of the 20th century is very different from the current one in the beginning of the 21st century. Fully acknowledging his contribution in production economics, this study does not use the term “technical efficiency” to avoid our confusion with “technology innovation” on industrial pollution that is the gist of this study. The second article (1957, p. 255 and p. 260) also discussed “price efficiency” and “overall efficiency” under increasing and diminishing RTS. These economic concepts have long provided us with a conceptual basis for DEA. No wonder why many studies have discussed his contribution as a staring study of DEA even if he did not mention anything on DEA. Finally, the third article (Farrell and Fieldhouse, 1962: Estimating efficient production function under increasing returns to scale) extended Farrell's previous study (1967) by discussing a linear programming structure that was solved by the simplex method of linear programming (1967, pp. 265–266). Their study documented two interesting concerns from our research perspective. One of the interesting concerns was that they knew an occurrence of degeneracy, or multiple solutions, if a data set contained zero and/or linear dependency among production factors. The other concern was that they discussed the importance of a dual formulation, not discussed by production economists even nowadays. It is easily imagined that their appendix on the method of computation (1967, pp. 264–267) was guided by “Alan Hoffman”, as a reviewer of their manuscript, who was an operations researcher. See Sueyoshi and Sekitani (2009). Consequently, their description on computation is still useful in modern DEA algorithmic development. It may be true that many DEA researchers have been long discussing the concept of technical efficiency, due to Farrell's engineering concern, but not paying serious attention the importance of a dual formulation, as discussed by their works (1967). In reviewing their study (1967), this study thinks that the collaboration between production economics and operations research/management science is essential in extending new research dimensions on DEA and its applications for environmental assessment.

334

T. Sueyoshi, M. Goto / Energy Economics 51 (2015) 329–345

Fig. 2. Frontier shift under natural disposability. (a) An efficiency frontier shifts toward an increase of desirable outputs without any crossover between the two periods. The natural disposability implies that the first priority is operational performance and the second priority is environmental performance. The figure assumes that undesirable outputs are same on all DMUs, so dropping these influences on the frontier shift. (b) The figure assumes that there is no occurrence of multiple projections and multiple reference sets. (c) A unique projection from an observation to two efficiency frontiers are for our visual convenience. This study fully understands that a real projection(s) for DEA assessment is more complicated than the one depicted in the figure. (d) For our visual convenience, the figure assumes that an inefficient DMU changes its location onto an efficiency frontier by a L2-metric projection although it should be measured by a L1-metric projection in reality. (e) Source: Sueyoshi and Goto (2013d).

period, respectively, where the superscript (e) indicates an efficiency frontier. In the two cases, this study assumes a unique projection and a unique reference set in the two periods, as discussed in Fig. 2. Under the same assumption, the performance of ct can be projected to cep on the efficiency frontier of the p-th period and cet on the efficiency frontier of the t-th period, respectively. This type of projection, as depicted in Fig. 2, occurs under constant RTS to avoid an infeasible solution in a computer code. A geometric mean, which is widely used to measure an average of the two line segments (aet − aep and cet − cep), indicates the degree of a frontier shift from the p-th period to t-th period. The geometric mean, referred to as a “Malmquist Index”, is used in the assessment and it is specified by the following notation: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u e e 0a sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u t 0ct e e u 0a 0a 0c p 0c t t ¼ u e te ; INtp ¼ 0aep 0cep u t 0ap 0cp 0ap 0ct

ð1Þ

Fig. 3. Frontier shift under managerial disposability. (a) An efficiency frontier shifts toward a decrease in undesirable outputs without any crossover between the two periods. The managerial disposability implies that the first priority is environmental performance and the second priority is operational performance. The figure assumes that desirable outputs are same on all DMUs, so dropping these influences on the frontier shift. (b) See the note of Fig. 2. (c) Source: Sueyoshi and Goto (2013d).

enhancement on undesirable outputs occur between the two periods. The south-west direction of a frontier shift is due to managerial disposability. For our visual convenience, the amount of desirable outputs is same on all DMUs between the two periods in Fig. 3. The performance of dp is projected onto dep on the efficiency frontier of the p-th period and det on the efficiency frontier of the t-th period, respectively, in Fig. 3. Meanwhile, the performance of qt can be projected to qep on the efficiency frontier of the p-th period and qet on the efficiency frontier of the t-th period, respectively. This type of projection occurs under constant DTS (Damages to Scale: corresponding to RTS on undesirable outputs) to maintain a computational feasibility for avoiding an infeasible solution. The Malmquist Index, which measures an average of the two line segments (dep − det and qep − qet ), is expressed by the following notation: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u e e 0d 0q sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u p p e e 0dp 0qp u 0dp 0q t u IM p ¼ ¼ u e te ; e t 0dt 0qt 0dt 0qet 0dp 0qt

ð2Þ

where IMtp stands for the Malmquist Index (I) between the p-th and the t-th periods under managerial (M) disposability. 4. Formulations under natural disposability

where INtp stands for the Malmquist Index (I) between the p-th and the t-th periods under natural (N) disposability. Shifting our description from natural disposability to managerial disposability, Fig. 3 depicts a frontier shift from the p-th period to the t-th period in which each DMU attempts to enhance the environmental efficiency as the first priority and the operational efficiency as the second priority. For our visual convenience, Fig. 3 considers a single input (x) and two undesirable outputs (b1 and b2) for our visual convenience. Two curves indicate efficiency frontiers in the two periods. In Fig. 3, dp stands for the observed performance of DMU{d} at the p-th period as a base period. Meanwhile, qt indicates an observed performance of the DMU at the t-th period for t = p, p + 1, ..,T. A frontier shift occurs toward a south-west direction under the assumption that eco-technology progress (e.g., clean coal technology) and/or managerial

To prepare DEA environmental assessment in a time horizon, this study considers n DMUs whose unified (operational and environmental) efficiency scores are examined by DEA formulations. As depicted in Fig. 2, this study considers a frontier shift from the p-th period to the t-th period where the p-th period is a base period and the t-th period is a period to be compared with the base period. The t-th period is expressed by t = p, p + 1, …, T in the proposed environmental assessment. In DEA, there are n DMUs (j = 1,.., n) whose performance is relatively compared by each other. The j-th DMU uses a column vector of inputs (Xj) in order to yield not only a column vector of desirable outputs (Gj) but also a column vector of undesirable outputs (Bj) where Xj = (x1j, x2j,.., xmj)Tr, Gj = (g1j, g2j,.., gsj)Tr and Bj = (b1j, b2j,.., bhj)Tr. The superscript “Tr” indicates a vector transpose. It is assumed that Xj N 0, Gj N 0

T. Sueyoshi, M. Goto / Energy Economics 51 (2015) 329–345

and Bj N 0 for all j = 1, ..,n for our analytical convenience. All components of each column vector are strictly positive in the three vectors. To compare the performance of all DMUs (J) between the two periods (p and t), this study adds subscripts (p and t) to J so that Jp and Jt stand for all DMUs at the p-th period (as the base period) and the t-th period, respectively. The conceptual framework for Eq. (1) under natural disposability can be expressed by the following unified efficiencies and index measures: ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi v u e e u u 0ap 0ct 0at 0ct sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u u u 0aep 0cep u 0ap 0ct UENp IUINt→p 0aet 0cet t t u u ⇒ INp ¼ ; ¼ INp ¼ e e ¼u 0aep 0cep u IUINp→t UEN t t 0ap 0cp t 0ap 0ct e e 0at 0ct 0ap 0ct

335

all slacks. This study sets εs = 0.00001 for our computation. The small number was conventionally considered as the non-Archimedean small number in the DEA community. But, none knows it in reality. Therefore, the number is different from the non-Archimedean small number in this study. The data range adjustments (R) in Model (4) are determined by the upper and lower bounds of production factors. These upper and lower bounds are specified by the following manner: n  o n  o−1 max xi j  j ∈ J p ∪ :: J t−1 ∪ J t − min xi j  j ∈ J p ∪ :: J t−1 ∪J t ; n  o n  o−1 −1 max g r j  j ∈ J p ∪ :: J t−1 ∪J t − min g r j  j ∈ J p ∪ :: J t−1 ∪ J t & Rgr ¼ ðm þ s þ hÞ  n  o n  o−1 −1 b   R f ¼ ðm þ s þ hÞ max b f j j ∈ J p ∪ :: J t−1 ∪ J t − min b f j j ∈ J p ∪ :: J t−1 ∪J t : −1

Rxi ¼ ðm þ s þ hÞ





ð3Þ The degree of UENp of the k-th DMU in the p-th period is determined where UENp stands for unified efficiency under natural disposability in the p-th period. UENt stands for the same unified efficiency in the t-th period. The two efficiency scores always exist between 0 (full inefficiency) and 1 (full efficiency). IUINp → t stands for inter-temporal unified index from the p-th period to the t-th period under natural disposability. IUINt → p stands for the same index from the t-th period to the p-th period. The two indexes may become larger than unity, depending upon an occurrence of a crossover between the efficiency frontiers. All the efficiencies and indexes of Eq. (3) are measured under not only natural disposability but also constant RTS and constant DTS. The condition on constant RTS and constant DTS is important to avoid an infeasible solution in a computer code where we measure the two inter-temporal unified indexes. In examining Eq. (3), the left hand side of INtp is originated from Fig. 2. Meanwhile, the right hand side expresses the decomposed structure of INtp. The structural change makes it possible to measure the two unified efficiencies and the two index measures by DEA environmental assessment. Thus, INtp can measure the degree of a frontier shift from the p-th period to the t-th period by examining its subcomponents, all of which are combined together into the Malmquist index under natural disposability. This study considers the index as a total measure related to the frontier shift. As formulated in Eq. (3), INtp is separated into four subcomponents under natural disposability. First, the degree of UENp regarding the kth DMU in the p-th period is measured by the following model: 2 3 m s h X X X x− g b x g b Ri di þ Rr dr þ Rf df 5 Maximize ξ þ εs 4 s:t:

X j∈ J p X

x−

xi j λ j þ di

¼ xik ;

g

g r j λ j −dr −ξg rk ¼ g rk ;

ðk ∈ J p & r ¼ 1 ; ::; sÞ;

X

f ¼1

where the inefficiency score and all slack variables are determined on the optimality of Model (4). The equation within the parenthesis, obtained from the optimality of Model (4), indicates the level of unified inefficiency under natural disposability. The unified efficiency is obtained by subtracting the level of inefficiency from unity. The superscript (*) indicates optimality. The degree of UENp can be less than unity, indicating an existence of some level of inefficiency. Meanwhile, if the degree becomes unity, then it indicates the status of full efficiency. Second, the degree of UENt regarding the k-th DMU in the t-th period is measured by the following model:

2 3 m s h X X X x− g b x g b Maximize ξ þ εs 4 Ri di þ Rr d r þ Rf df 5 s:t:

X X

i¼1 x−

xi j λ j þ d i

j∈ J t

r¼1

¼ xik ;

f ¼1

ðk ∈ J t & i ¼ 1; :: ; mÞ;

g

gr j λ j −dr −ξg rk ¼ g rk ;

ðk ∈ J t & r ¼ 1; :: ; sÞ;

ð5Þ

b

b f j λ j þ d f þ ξb fk ¼ b f k ; ðk ∈ J t & f ¼ 1 ; :: ; hÞ; x−

λ j ≥0 ð j∈J t Þ; ξ : URS; di ≥ 0 ði ¼ 1; ::; mÞ; g b dr ≥0 ðr ¼ 1; ::; sÞ and d f ≥ 0 ð f ¼ 1; ::; hÞ; ð4Þ

b

b f j λ j þ d f þ ξb fk ¼ b f k ; ðk ∈ J p & f ¼ 1 ; ::; hÞ;

λ j ≥0 ðj ∈ J p Þ; g

r¼1

i¼1

j∈ J t

j∈ J p

dr ≥0

0 13 m s h X X X x− g b x g b Ri d i þ Rr dr þ R f d f A5; UENp ¼ 1−4ξ þ εs @ 

X

ðk ∈ J p & i ¼ 1; ::; mÞ;

j∈ J p

2

j∈ J t

f ¼1

r¼1

i¼1

by

ξ : URS;

x− di

≥0

ði ¼ 1; ::; mÞ;

b

ðr ¼ 1; ::; sÞ and d f ≥ 0 ð f ¼ 1; ::; hÞ;

where d xi −(i = 1, … , m), d gr (r = 1, … , s) and d bf (f = 1, .., h) are all slacks related to inputs, desirable and undesirable outputs, respectively. The slacks can be considered as decision variables. λ = (λ1, …, λn)T is a column vector of unknown variables, often referred to as “structural” or “intensity” variables, that are used for connecting the input vector and the two output vectors. A scalar value (ξ), which is unrestricted (URS), stands for a unified inefficiency measure. The degree of inefficiency corresponds to a distance between an efficiency frontier and an observed vector of desirable and undesirable outputs. Another scalar value (εs), which is incorporated into Model (4), stands for a small number for indicating the relative importance between the inefficiency measure and the sum of

where the superscript (p) of Model (4) is replaced by the other superscript (t) in Model (5). There is no other change between Models (4) and (5). The degree of UENt is determined by

2

0 13 m s h X X X x− g b x g b UENt ¼ 1−4ξ þ εs @ Ri di þ Rr dr þ R f d f A5; 

i¼1

r¼1

f ¼1

where the inefficiency score and all slacks are determined on the optimality of Model (5). The unified efficiency score is always less than unity for some level of inefficiency or equal unity for the status of full efficiency.

336

T. Sueyoshi, M. Goto / Energy Economics 51 (2015) 329–345

Third, the degree of IUINp → t regarding the k-th DMU in the p-th period is determined by the following model: 2 3 m s h X X X x x− g g b b5 4 Ri di þ Rr dr þ Rfdf Maximize ξ þ εs s:t:

X j∈ J t X

f ¼1

r¼1

i¼1

xi j λ j þ d x− ¼ xik ; i

ðk ∈ J p & i ¼ 1; :: ; mÞ;

g

ðk ∈ J p & r ¼ 1 ; :: ; sÞ;

g r j λ j −dr −ξg rk ¼ g rk ;

ð6Þ

tionship between the two indexes (i.e., IUINp → t and IUINt → p) and an occurrence of a frontier crossover between the two periods can be summarized as follows:

j∈ J t

X

b

b f j λ j þ d f þ ξb f k ¼ b f k ; ðk ∈ J p & f ¼ 1 ; :: ; hÞ;

j∈ J t

≥ 0 ði ¼ 1; ::; mÞ; λ j ≥ 0 ð j∈ J t Þ; ξ : URS; d x− i g b dr ≥ 0 ðr ¼ 1; ::; sÞ and d f ≥ 0 ð f ¼ 1; ::; hÞ;

where an efficiency frontier consists of DMUs in the t-th period and a DMU to be examined by Model (6) is selected from a group of DUMs in the p-th period. The degree of IUINp → t regarding the k-th DMU is determined by 2

0 13 m s h X X X A5; ¼ 1−4ξ þ εs @ R xi d x− þ R gr d g R bf d b i r þ f r¼1

i¼1

f ¼1

where the inefficiency score and all slacks are obtained from the optimality of Model (6). The equation within the parenthesis, obtained from the optimality of Model (6), indicates the inefficiency part for the inter-temporal unified index. The index is obtained by subtracting the inefficiency level from unity. In a use of the index measurement, this study pays attention to the following concern. If the index of a DMU is more than or equals unity because of negative ξ*, then it indicates a possible occurrence of a frontier crossover between the two periods because a technology progress does not occur between them. In contrast, if the index is less than unity, then it indicates no occurrence of the frontier crossover, so indicating that there is a frontier shift due to the technology progress. In that case, ξ* becomes positive or zero so that the index becomes less than or equal unity. Finally, the degree of IUINt → p regarding the k-th DMU in the t-th period is determined by the following model: 2 3 m s h X X X x x− g g b b5 4 Ri di þ Rr dr þ Rf df Maximize ξ þ εs X

x−

¼ xik ;

ðk ∈ J t & i ¼ 1; :: ; mÞ; ðk ∈ J t & r ¼ 1 ; :: ; sÞ;

j∈ J

Xp

ð7Þ

b

b f j λ j þ d f þ ξb fk ¼ b fk ; ðk ∈ J t & f ¼ 1 ; :: ; hÞ;

j∈ J p x−

λ j ≥ 0 ðj ∈ J p Þ; ξ : URS; di

≥ 0 ði ¼ 1; ::; mÞ;

b

≥ 0 ðr ¼ 1; ::; sÞ; and d f ≥ 0 ð f ¼ 1; ::; hÞ;

where an efficiency frontier consists of DMUs in the p-th period and a DMU to be examined is selected from a group of DUMs in the t-th period. The degree of IUINt → p regarding the k-th DMU is determined by 2

IUIN t→p

0 13 m s h X X X b b ¼ 1−4ξ þ εs @ R xi d x− þ R gr d g R f d f A5; i r þ 

i¼1

Finally, it is important to note that even if the index of a DMU indicates an occurrence of the frontier crossover, we cannot immediately conclude an occurrence of the whole frontier crossover because the final decision depends upon the indexes of the other DMUs. 5. Formulations under managerial disposability By shifting our description from natural disposability to managerial disposability, the conceptual framework on Eq. (2), or the Malmquist Index (IM tp ) under managerial disposability, can be expressed by the following unified efficiencies and indexes as depicted in Fig. 3:

IMtp ¼

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u e e u 0dp 0qp sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u 0dp 0q UEM p IUIM t→p t u t ⇒ IM ; ¼ ¼ u e p IUIM p→t UEMt t 0det 0qet 0dt 0qet 0dp 0qt

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e 0dp 0qep

ð8Þ

f ¼1

r¼1

i¼1

xi j λ j þ di

j∈ J p X g g r j λ j −dr −ξg rk ¼ grk ;

g dr

IUINp → t ≥ 1 ⇔ An occurrence of a frontier crossover (no technology progress) IUINp → t b 1 ⇔ No occurrence of a frontier crossover (a technology progress), IUINt → p N 1 ⇔ No occurrence of a frontier crossover (a technology progress) and IUINt → p ≤ 1 ⇔ An occurrence of a frontier crossover (no technology progress).



IUINp→t

s:t:

where the inefficiency score and all slacks are obtained from the optimality of Model (7). In a use of the index, if the index of a DMU becomes more than unity because of negative ξ*, then it indicates no occurrence of a frontier crossover between the two periods. In contrast, if the index is less than or equal unity, then it indicates an occurrence of the frontier crossover. The classification is opposite to that of IUINp → t. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi UEN p IUIN t→p Considering the structure of Eq. (3), or INtp ¼ IUINp→t UENt , the rela-

r¼1

f ¼1

where UEMp stands for unified efficiency under managerial disposability at the p-th period. UEMt stands for the same unified efficiency at the t-th period. IUIMp → t stands for inter-temporal unified index from the p-th period to the t-th period under managerial disposability. IUIMt → p stands for the same unified index from the t-th period to the p-th period. All the subcomponents of IMtp are measured under constant DTS. In examining Eq. (8), the left hand side of IMtp is originated from Fig. 3. Meanwhile, the right hand side expresses the decomposed structure of IM tp. The structural change makes it possible for us to measure the two unified efficiencies and the two index measures by DEA environmental assessment. Thus, IMtp can measure the degree of a frontier shift from the p-th period to the t-th period by examining its subcomponents, all of which are combined together into the Malmquist index under managerial disposability. This study considers the index as a total measure related to the frontier shift. As formulated in Eq. (8), IM tp is separated into four subcomponents under managerial disposability. First, the degree of UEM p

T. Sueyoshi, M. Goto / Energy Economics 51 (2015) 329–345

regarding the k-th DMU in the p-th period is measured by the following model:

s:t:

X

s:t:

f ¼1

r¼1

¼ xik ;

Third, the degree of IUIMp → t regarding the k-th DMU in the p-th period is determined by the following model: 2 3 m s h X X X x xþ g g b b5 4 Maximize ξ þ εs Ri di þ Rr dr þ Rfdf

2 3 m s h X X X Maximize ξ þ εs 4 R xi d xþ R gr d gr þ R bf d bf 5 i þ i¼1 xþ xi j λ j −di

X

ðk ∈ J p & i ¼ 1; :: ; mÞ;

j∈ J t X

ðk ∈ J p & r ¼ 1 ; :: ; sÞ;

X

j∈ J p

X

g g r j λ j −dr −ξg rk

¼ g rk ;

j∈ J

Xp

b f jλ j þ

b df

ð9Þ

≥ 0 ði ¼ 1; ::; mÞ;

b f j λ j þ d bf þ ξ b fk ¼ b f k ; ðk ∈ J p & f ¼ 1 ; :: ; hÞ;

2

IUIM p→t

where the inefficiency score and all slacks are determined on the optimality of Model (9). The equation within the parenthesis, obtained from the optimality of Model (9), indicates the part of unified inefficiency under managerial disposability. The unified efficiency is obtained by subtracting the level of inefficiency from unity. Thus, the unified efficiency always belongs to the range between 0 (full inefficiency) and 1 (full efficiency) under managerial disposability. Second, the degree of UEMt regarding the k-th DMU in the t-th period is measured by the following model:

f ¼1

r¼1

¼ xik ;

g

b f jλ j þ

b df

ðk ∈ J t & r ¼ 1 ; :: ; sÞ;

X j∈ J p X

ð10Þ

þ ξb fk ¼ b f k ; ðk ∈ J t & f ¼ 1 ; :: ; hÞ;

j∈ J t

f ¼1

where the inefficiency score and all slacks are determined on the optimality of Model (11). In a use of the index, this study pays attention to the following concern. If the index of a DMU is more than or equal unity because of negative ξ*, then it indicates an occurrence of a frontier crossover between the two periods. There is no eco-technology progress between the two periods. In contrast, if the index is less than unity because of positive ξ*, then it indicates no occurrence of the frontier crossover, so indicating that there is a frontier shift due to eco-technology progress between the two periods. Finally, the degree of IUIMt → p regarding the k-th DMU in the t-th period is determined by the following model:

s:t:

ðk ∈ J t & i ¼ 1; :: ; mÞ;

g r j λ j −dr −ξg rk ¼ g rk ;

r¼1

2 3 m s h X X X x xþ g g b b Maximize ξ þ εs 4 Ri di þ Rr dr þ Rfdf5

2 3 m s h X X X x xþ g g b b5 4 Maximize ξ þ εs Ri di þ Rr dr þ Rfdf i¼1 xþ xi j λ j −di

0 13 m s h X X X  x xþ g g b b A5 4 @ ¼ 1− ξ þ εs Ri di þ Rr dr þ Rfdf ; i¼1

f ¼1

r¼1

i¼1

j∈ J t X

ð11Þ

where an efficiency frontier consists of DMUs in the t-th period and a DMU to be examined is selected from a group of DUMs in the p-th period. The degree of IUIMp → t regarding the k-th DMU in the p-th period is measured by

2 0 13 m s h X X X  g g b b A5 UEMp ¼ 1−4ξ þ εs @ R xi d xþ þ R d þ R d ; r r f f i

j∈ J t X

ðk ∈ J p & r ¼ 1 ; :: ; sÞ;

b

The degree of UEMp is determined by

s:t:

g r j λ j −d gr −ξ grk ¼ g rk ;

≥ 0 ði ¼ 1; ::; mÞ; λ j ≥ 0 ð j ∈ J t Þ; ξ : URS; d xþ i g b dr ≥ 0 ðr ¼ 1; ::; sÞ; and d f ≥ 0 ð f ¼ 1; ::; hÞ;

≥ 0 ðr ¼ 1; ::; sÞ; and d f ≥ 0 ð f ¼ 1; ::; hÞ:

X

ðk ∈ J p & i ¼ 1; :: ; mÞ;

j∈ J t

þ ξb f k ¼ b f k ; ðk ∈ J p & f ¼ 1 ; :: ; hÞ; xþ

g dr

f ¼1

r¼1

i¼1

xi j λ j −d xþ i ¼ xik ;

j∈ J t

j∈ J p

λ j ≥ 0 ðj ∈ J p Þ; ξ : URS; di

337

xþ

λ j ≥ 0 ð j ∈ J t Þ; ξ : URS; di ≥ 0 ði ¼ 1; ::; mÞ; g b dr ≥ 0 ðr ¼ 1; ::; sÞ and d f ≥ 0 ð f ¼ 1; ::; hÞ;

where the superscript (p) in Model (9) is replaced by the other superscript (t) in Model (10). There is no other change between Models (9) and (10). The degree of UEMt regarding the k-th DMU in the t-th period is measured by

ðk ∈ J t & i ¼ 1; :: ; mÞ;

gr j λ j −d gr −ξg rk ¼ g rk ;

ðk ∈ J t & r ¼ 1 ; :: ; sÞ;

j∈ J p

X

b f j λ j þ d bf þ ξb fk ¼ b f k ; ðk ∈ J t & f ¼ 1 ; :: ; hÞ;

j∈ J p

λ j ≥ 0 ðj ∈ J p Þ; ξ : URS; d xþ i ≥ 0 ði ¼ 1; ::; mÞ; g

b

dr ≥ 0 ðr ¼ 1; ::; sÞ and d f ≥ 0 ð f ¼ 1; ::; hÞ: ð12Þ where an efficiency frontier consists of DMUs in the p-th period and a DMU to be examined is selected from a group of DUMs in the t-th period. The degree of IUIMt → p is measured by " 

IUIMt→p ¼ 1− ξ þ εs

m X i¼1

0 13 m s h X X X xþ g b x g b UEM t ¼ 1−4ξ þ εs @ Ri di þ Rr dr þ R f d f A5;

f ¼1

r¼1

i¼1

xi j λ j −d xþ i ¼ xik ;

R xi d xþ þ i

s X r¼1

R gr d g r þ

h X

!# R bf d b f

;

f ¼1

2



i¼1

r¼1

f ¼1

where the inefficiency measure and all slacks are determined on the optimality of Model (10). Both UEMp and UEMt are always less than or equal unity under managerial disposability.

where the inefficiency score and all slack variables are determined on the optimality of Model (12). In a use of the index measurement, if the index is more than unity due to negative ξ*, then it indicates no occurrence of a frontier crossover between the two periods because it indicates an eco-technology progress. In contrast, the index is less than or equal unity, then it may indicate a possible occurrence of the frontier crossover. The classification is opposite to that of IUIMp → t.

338

T. Sueyoshi, M. Goto / Energy Economics 51 (2015) 329–345

Considering the structure of Eq. (8), or IM tp ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

UEMp IUIMt→p IUIMp→t UEMt ,

the

relationship between the two indexes (i.e., IUIMp → t and IUIMt → p) and an occurrence of a frontier crossover between the two periods can be summarized as follows: IUIMp → t ≥ 1 ⇔ An occurrence of a frontier crossover (no ecotechnology progress), IUIMp → t b 1 ⇔ No occurrence of a frontier crossover (an ecotechnology progress), IUIMt → p N 1 ⇔ No occurrence of a frontier crossover (an ecotechnology progress) and IUIMt → p ≤ 1 ⇔ An occurrence of a frontier crossover (no ecotechnology progress). Finally, as mentioned previously, even if a DMU indicates an occurrence of a frontier crossover, we cannot immediately conclude the occurrence of the whole frontier crossover between the two periods. The final decision depends upon the indexes of the other DMUs.

horizon. This study needs to discuss it in detail, here. In business reality, a technology progress may not occur so that a frontier may retreat among multiple periods in many applications. Figs. 4 and 5 depict such an occurrence of a frontier crossover between the t-1th and t-th periods under natural or managerial disposability, respectively. The occurrence of such a frontier crossover influences the measurement of IUINp → t under natural disposability and IUIMp → t under managerial disposability. Assuming that the frontier crossover occurs between the two periods (t-1 and t periods), the degree of IUINp → t is measured by 2 3 m s h X X X x x− g g b b5 4 Ri di þ Rr dr þ Rf df Maximize ξ þ εs s:t:

X

ðk ∈ J p & i ¼ 1; :: ; mÞ;

g r j λ j −d gr −ξg rk ¼ g rk ;

ðk ∈ J p & r ¼ 1 ; :: ; sÞ;

j∈ J t−1 ∪ J t

X

j∈ J t−1 ∪ J t

X

b f j λ j þ d bf þ ξb fk ¼ b f k ; ðk ∈ J p & f ¼ 1 ; :: ; hÞ;

j∈ J t−1 ∪ J t

6. Malmquist index measurement: extension The Malmquist index measurement under natural and managerial disposability has five unique features, all of which can be specified as follows: First, the inefficiency score (ξ) is unrestricted in all models so that it can take any sign. The unrestricted score makes it possible that the objective value in Models (6), (7), (11) and (12) can become negative. As a result, the degree of these index numbers may be more than unity. This unique feature is important for DEA environmental assessment in a time horizon. Many DEA studies in production economics formulate DEA models in which all decision variables, including an efficiency score, are non-negative in their signs. It is unacceptable for this study because their DEA formulations are limited in their applications for time series. Second, this study assumes that all models in Sections 3 and 4 can uniquely produce a DEA solution. However, the assumption is not always true because they may suffer from an occurrence of multiple solutions (e.g., multiple projections and reference sets) on an efficiency frontier. If such a problem occurs in a computer code, it is necessary for us to incorporate Strong Complementary Slackness Conditions (SCSCs) to uniquely identify a DEA solution. This study does not discuss the use of SCSCs in the proposed approach for time series analysis. That is a future extension of this study. Third, all DEA models assume constant RTS and constant DTS in order to avoid an infeasible solution by dropping the side constraint n

∑ λ j ¼ 1 from all the formulations. The assumption is due to only our

f ¼1

r¼1

i¼1

xi j λ j þ d x− ¼ xik ; i

x−

λ j ≥0 ð j ∈ J t−1 ∪J t Þ; ξ : URS; di ≥ 0 ði ¼ 1; ::; mÞ; g b dr ≥0 ðr ¼ 1; ::; sÞ and d f ≥ 0 ð f ¼ 1; ::; hÞ: ð13Þ In a similar manner, the degree of IUIMp → t is measured by 2 3 m s h X X X x xþ g g b b5 4 Maximize ξ þ εs Ri di þ Rr dr þ Rf df s:t:

X j∈ J t−1 ∪ J t

X

f ¼1

r¼1

i¼1 xþ

xi j λ j −di

¼ xik ;

ðk ∈ J p & i ¼ 1; :: ; mÞ;

g

g r j λ j −dr −ξg rk ¼ g rk ;

ðk ∈ J p & r ¼ 1 ; :: ; sÞ;

j∈ J t−1 ∪ J t

X

j∈ J t−1 ∪ J t

b

b f j λ j þ d f þ ξb fk ¼ b f k ; ðk ∈ J p & f ¼ 1 ; :: ; hÞ; xþ

λ j ≥0 ð j ∈ J t−1 ∪J t Þ; ξ : URS; di ≥0 ði ¼ 1; ::; mÞ; g b dr ≥0 ðr ¼ 1; ::; sÞ and d f ≥0 ð f ¼ 1; ::; hÞ: ð14Þ The union set (j ∈ Jt − 1 ∪ Jt) is easily extendable to three or more periods in Models (13) and (14). Models (13) and (14) depend upon Period Block (PB) during which a frontier crossover occurs. In that case, it is possible to extend the block to JPB = Jp ∪ Jt ‐ 1 ∪ Jt ∪ ⋯ ∪ Jz in the two models where z stands for the last year of the frontier crossover.

j¼1

computational convenience. We may have an infeasible solution under the assumption of variable RTS and variable DTS. This study will discuss how to reorganize the proposed formulations, including the condition of variable RTS and variable DTS. That is another future extension of this study. Fourth, the measurement of IUINp → t and IUIMp → t assumes that all DMUs in the p-th period can access technology in the t-th period. The assumption may be slightly unrealistic in modern business because the t-th period is the future event for DMUs in the p-th period. The Malmquist index measurement was originally used to examine a frontier shift among multiple regions. In that case, the difference between p-th and t-th regions does not have such a problem in terms of a technology progress. However, when DEA extends the index measurement from regional analysis to time series, we have such a difficulty in the dynamic assessment. This type of difficulty will be overcome as a future extension of this study, as well. Finally, a frontier crossover may occur among multiple periods. The concern is important in DEA environmental assessment in a time

Fig. 4. Frontier crossover between t-1 th and t-th periods under natural disposability.

T. Sueyoshi, M. Goto / Energy Economics 51 (2015) 329–345

339

Gas

Oil Refining

Pipeline Transport

Power Generation

Primary Chemicals

Environmental Fuels Upgrading

Specialty Chemicals

Distribution (Pipeline/Rail/ Truck)

Distribution (Pipeline/ Rail/ Truck)

Marketing and Sales

Marketing and Sales

Data and Market Information

Fig. 5. Frontier crossover between t-1 th and t-th periods under managerial disposability.

7. An illustrative example The petroleum industry is usually separated into two business functions. One of the two functions is related to “upstream” (e.g., exploration, development and production of crude oil or natural gas). Fig. 6 depicts business components for the upstream. The other function is related to “downstream” (e.g., oil tankers, refineries, storages and retails). Fig. 7 depicts business components for the downstream. This study measures only the performance of oil companies in the upstream. See Sueyoshi and Wang (2014b) for DEA environmental assessment that was applied to examine the upstream and downstream

Marketing and Sales

Marketing and Sales

Client

DOWNSTREAM

Production Control

Technology and signal Processing Fig. 7. Business components for downstream. Source: Crain and Abraham (2008).

UPSTREAM Geotech Analysis

Expro Rights Acquisition

Exploration/ Evaluation/ Delineation

Finance/Risk management

Technical and Market Evaluation

Facility Development

Production

Gas Processing

Crude Upgrading & Gas-to-Liquids

Transport: Marine (LNG) and Pipeline

Trading and Hedging

Transport Marine and Pipeline Oil

Gas

Fig. 6. Business Components for Upstream. Source: Crain and Abraham (2008).

of oil firms in the United States. It is widely known that international oil companies have dominated the downstream market so that it is not necessary to measure the performance of petroleum firms in the downstream. However, the comparison between this study and their study (2014b) provides us with new business implications regarding the petroleum industry. Note that Figs. 6 and 7 are obtained from Crain and Abraham (2008). To compare the performance of petroleum firms in terms of their functions for upstream, this study selects twelve oil firms whose equities are partially or completely owned by their governments. See Sueyoshi and Goto (2012a). This type of petroleum firms can be considered as National Oil Companies (NOCs) because they are under governmental influence. This study also selects five private petroleum firms whose governmental ownership is zero. All the firms are internationally well known as International Oil Companies (IOCs), often referred to as “Major”. The NOCs include the following public firms: (a) China National Offshore Oil Corporation (CNOOC) in China, (b) Eni in Italy, (c) Gazprom in Russia, (d) Industrija Nafte (INA) in Croatia, (e) MOL Hungarian Oil and Gas Company (MOL) in Hungary, (f) Österreichische Mineralölverwaltung (OMV) in Austria, (g) Petroleum Development Oman (PDO) in Oman, (h) Petroleos Mexicanos (Pemex) in Mexico, (i) Petrobras Brazil (Petrobras) in Brazil, (j) PetroChina Company Limited (PetroChina) in China, (k) Saudi Aramco in Saudi Arabia, and (l) Statoil in Norway. Meanwhile, the IOCs include the following private firms: (a) British Petroleum (BP) in the United Kingdom, (b) Chevron in the United States, (c) Total in France, (d) ExxonMobil in the United States, and (e) Shell in Netherlands.

340

T. Sueyoshi, M. Goto / Energy Economics 51 (2015) 329–345

The proposed DEA approach evaluates the performance of the total 17 (= 12 national + 5 international) petroleum firms based upon their four inputs (i.e., the amount of oil reserve, the amount of gas reserve, the total operating cost and the number of employees), two desirable outputs (the amount of oil production and the amount of gas production) and a single undesirable output (the amount of CO2 emission). The observed annual periods are from 2005 to 2009. Table 1 summarizes descriptive statistics of the data set used in this study. This research obtains the data set from Sueyoshi and Goto (2012a). See the supplemental section of this study that provides the whole data set. Table 2 documents unified efficiency measures of seventeen oil firms, all of which are measured by Models (4) and (5). The average of NOCs (total average: 0.980) and that of IOCs (total average: 0.921) are listed at the bottom of the table. The table indicates that NOCs outperform IOCs in terms of their unified efficiencies under natural disposability on average. Table 3 summarizes the degree of IUINp → t regarding all oil firms under natural disposability. Eq. (3) indicates that IUINp → t is the denominator of the Malmquist index under natural disposability. In the measurement, an efficiency frontier consists of DMUs in the t-th period and a DMU to be examined by Model (6) is selected from a group of DUMs in the p-th period. As summarized in the table, most of NOCs exhibited more than unity. Exceptions (i.e., less than unity) were found in DMUs {2, 4 and 10}. This result indicates that a frontier crossover has occurred between the base year (1995) and the other annual periods in their operational performance of NOCs. In contrast, the index numbers were less than or equal unity, as found in IOCs. An exception was found in DMU {17}. This result indicates that a frontier crossover has occurred in most of NOCs, but it has not occurred in most of IOCs during all observed annual periods. In other words, a technology progress did not occur in the performance of NOCs from 2005 to 2009, but the progress was found in the performance of IOCs. Table 4 summarizes the degree of IUINt → p regarding all oil firms under natural disposability. Eq. (3) indicates that IUINt → p is the numerator of the Malmquist index under natural disposability. In the measurement, an efficiency frontier consists of DMUs in the p-th period and a DMU to be examined by Model (7) is selected from a group of DUMs in the t-th period. In the measurement, if the index is more than unity, as found in most of NOCs and IOCs in Table 4, then it indicates that there is no frontier shift between the two periods. In contrast, if the

index is less than or equal unity, then it may indicate a possible occurrence of the frontier shift. The indexes summarized in Table 4 indicated that there was a technology progress in most of NOCs and IOCs from 2005 to 2009. Table 5 summarizes the degree of INtp (the Malmquist Index between the p-th and the t-th periods under natural disposability) of all oil firms that is determined by combining the computational results in Tables 2, 3 and 4. The index serves as the total measure of a frontier shift under natural disposability in the observed annual periods. Such a combination is computed by Eq. (3). The Malmquist indexes were the averages, as geometric means, of the two inter-temporal unified indexes between the p-th period (2005) and t-th period (from 2006 to 2009) along with their unified efficiencies measured under natural disposability. The indexes summarized in Table 5 indicated that, on average, NOCs exhibited a frontier shift with an increase by 1.1% from the base period. Meanwhile, IOCs exhibited a frontier shift with an increase by 7.5%. The increase was due to technology innovation and/or a managerial effort for adapting business and regulation changes during the observed periods. See the averages at the bottom of the last column of Table 5. Table 6 documents the unified efficiency scores of seventeen oil firms, all of which are measured by Models (9) and (10). The average of NOCs (total average: 0.643) and that of IOCs (total average: 0.547) are listed at the bottom of the last column in Table 6. As summarized in Table 6, NOCs outperform IOCs in terms of their unified efficiencies under managerial disposability. Table 7 summarizes the degree of IUIMp → t regarding all oil firms under managerial disposability. Eq. (8) indicates that IUIMp → t is the denominator of the Malmquist index under managerial disposability. In the measurement, an efficiency frontier consists of DMUs in the t-th period and a DMU to be examined by Model (11) is selected from a group of DUMs in the p-th period. In the table, if the index of DMUs, like DMU {11}, is more than or equal unity, then it indicates a possible occurrence of a frontier crossover between the two periods. In contrast, if the index is less than unity, then it indicates no occurrence of the frontier crossover. See the other DMUs whose indexes were less than unity. Thus, the indexes of Table 7 indicated that a frontier crossover was not found in most of DMUs during all observed annual periods. An exception was found in DMU {11}. The oil company {11} attained the advanced level of petroleum technology, so being not necessary on technological improvement during the observed periods. In other words, there was a technology progress and/or managerial

Table 1 Descriptive statistics (2005–2009). Production factors Year

Statistics

2005

Average Max. Min. St.Dev. Average Max. Min. St.Dev. Average Max. Min. St.Dev. Average Max. Min. St.Dev. Average Max. Min. St.Dev.

2006

2007

2008

2009

Oil reserve

Gas reserve

Operating cost

No. of employee

Oil production

Gas production

CO2 emission

100 million barrels

100 billion cubic feet

Billion $

1000

Million barrels/day

Billion cubic feet/day

Million tons

78.761 311.248 0.513 102.647 85.350 310.233 0.632 106.073 94.236 334.078 0.710 115.522 111.949 407.740 0.749 146.970 84.626 276.187 0.760 97.091

79.526 439.220 2.696 100.391 80.133 446.000 2.929 102.015 81.967 466.502 3.288 106.394 81.958 447.780 3.584 101.725 87.460 539.168 4.019 122.195

1.828 9.065 0.023 2.138 1.822 8.912 0.023 2.102 1.781 8.532 0.023 2.004 1.770 8.900 0.025 2.061 1.717 7.900 0.023 1.845

3.674 9.251 0.178 3.135 3.925 9.334 0.197 3.163 3.998 9.384 0.167 3.130 4.161 9.095 0.206 3.208 4.250 9.273 0.200 3.266

45.609 138.000 3.360 42.007 46.692 146.000 3.360 44.072 47.152 141.000 3.358 44.560 48.101 150.000 3.188 46.490 48.052 163.000 3.404 48.247

207.911 2598.000 0.697 617.334 207.583 2599.000 0.894 617.694 206.625 2599.000 0.885 617.912 215.147 2599.000 0.837 616.135 209.040 2601.000 0.710 617.795

352.642 2395.000 10.516 559.410 364.863 2485.000 10.294 580.191 369.114 2538.000 7.310 593.443 375.492 2630.000 10.271 614.954 389.911 2752.000 11.613 643.984

(a) Max. and Min. indicate maximum and minimum, respectively. St. Dev. Stands for standard deviation of each data set.

T. Sueyoshi, M. Goto / Energy Economics 51 (2015) 329–345

341

Table 2 Unified efficiency under natural disposability. No.

Company and country (government ownership)

2005

2006

2007

2008

2009

Average

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

China National Offshore Oil Corporation (CNOOC): China (71%) Eni: Italy (30%) Gazprom: Russia (51%) Industrija Nafte (INA): Croatia (75%) Hungarian Oil and Gas Company (MOL): Hungary (25%) Österreichische Mineralölverwaltung (OMV): Austria (32%) Petroleum Development Oman (PDO): Oman (60%) Petroleos Mexicanos (Pemex): Mexico (100%) Petrobras Brazil (Petrobras): Brazil (32%) PetroChina Company Limited (PetroChina): China (90%) Saudi Aramco: Saudi Arabia (100%) Statoil: Norway (71%) British Petroleum (BP): UK (0%) Chevron: USA (0%) Total: France (0%) ExxonMobil: USA (0%) Shell: Netherland (0%) Average of NOCs (1–12) Average of IOCs (13–17)

1.000 0.938 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.928 0.995 0.905 0.981 1.000 0.995 0.962

1.000 1.000 1.000 0.956 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.943 1.000 0.869 0.809 1.000 0.996 0.924

1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.924 1.000 0.868 0.921 1.000 1.000 0.943

1.000 0.970 1.000 0.981 0.462 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.927 1.000 0.789 0.902 0.972 0.951 0.918

1.000 1.000 1.000 1.000 0.499 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.940 0.931 0.804 0.779 0.846 0.958 0.860

1.000 0.981 1.000 0.987 0.792 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.932 0.985 0.847 0.878 0.964 0.980 0.921

(a) The number within ( ) for each firm indicates the level of governmental ownership. (b) NOC and IOC stand for National and International Oil Companies, respectively. (c) The base period is 2005. The unified efficiency was computed by the annual performance of 17 oil firms. (d) All the unified efficiency scores in the table are computed by Models (4) and (5).

innovation in the environmental performance of NOCs (total average: 0.612) and IOCs (total average: 0.446) on most of oil firms from 2005 to 2009.

Table 3 Inter-temporal unified index under natural disposability (IUINp → t). No. Company and country (government ownership)

2006

1

1.103 1.140 1.565 1.192 1.250

2 3 4 5 6

7 8 9 10 11 12 13 14 15 16 17

China National Offshore Oil Corporation (CNOOC): China (71%) Eni: Italy (30%) Gazprom: Russia (51%) Industrija Nafte (INA): Croatia (75%) Hungarian Oil and Gas Company (MOL): Hungary (25%) Österreichische Mineralölverwaltung (OMV): Austria (32%) Petroleum Development Oman (PDO): Oman (60%) Petroleos Mexicanos (Pemex): Mexico (100%) Petrobras Brazil (Petrobras): Brazil (32%) PetroChina Company Limited (PetroChina): China (90%) Saudi Aramco: Saudi Arabia (100%) Statoil: Norway (71%) British Petroleum (BP): UK (0%) Chevron: USA (0%) Total: France (0%) ExxonMobil: USA (0%) Shell: Netherland (0%) Average of NOCs (1–12) Average of IOCs (13–17)

0.907 1.300 1.086 1.108

2007

0.898 1.184 1.009 1.172

2008

0.774 1.175 0.993 1.189

2009

0.925 1.105 0.978 1.281

Table 8 summarizes the degree of IUIMt → p regarding all oil firms under managerial disposability. Eq. (8) indicates that IUIMt → p is the numerator of the Malmquist index under managerial disposability. In this measurement, an efficiency frontier consists of DMUs in the p-th period and a DMU to be examined by Model (12) is selected from a group of DUMs in the t-th period. In the measurement, if the index of

Average

0.876 1.191 1.017 1.188

1.205 1.328 1.245 1.218 1.249

Table 4 Inter-temporal unified index under natural disposability (IUINt → p). No. Company and country (government Ownership)

2006

1

1.091 1.134 1.227 1.236 1.172

2 3 4 5

1.246 1.364 1.372 1.460 1.360 6 1.074 1.120 1.240 1.143 1.144 1.118 1.176 1.238 1.098 1.157

7

1.050 1.057 0.977 1.001 1.021

8

1.032 1.025 0.879 0.928 0.919 0.774 1.072 1.104 0.914

9

1.088 1.238 0.880 0.918 0.890 0.889 1.084 1.148 0.932

1.090 1.220 0.941 1.070 0.825 0.918 1.026 1.173 0.956

1.190 1.213 0.831 0.892 0.859 0.757 1.198 1.150 0.907

1.100 1.174 0.883 0.952 0.873 0.835 1.095 1.144 0.928

(a) In the measurement, an efficiency frontier consists of DMUs in the t-th period and a DMU to be examined by Model (6) is selected from a group of DUMs in the p-th period. Most of NOCs exhibited more than unity. Exceptions (i.e., less than unity) were found in DMUs {2, 4 and 10}. This result indicates an occurrence of a frontier crossover between the base year (2005) and other annual periods in their operational performance of NOCs. In contrast, the index numbers were less than or equal unity, as found in IOCs. An exception was found in DMU {17}, for example. This result indicated that a frontier crossover occurred in most of NOCs, but it did not occur in most of IOCs during all observed annual periods. In other words, a technology progress did not occur in the operational performance of NOCs from 2005 to 2009, but the progress was found in the performance of IOCs.

10 11 12 13 14 15 16 17

China National Offshore Oil Corporation (CNOOC): China (71%) Eni: Italy (30%) Gazprom: Russia (51%) Industrija Nafte (INA): Croatia (75%) Hungarian Oil and Gas Company (MOL): Hungary (25%) Österreichische Mineralölverwaltung (OMV): Austria (32%) Petroleum Development Oman (PDO): Oman (60%) Petroleos Mexicanos (Pemex): Mexico (100%) Petrobras Brazil (Petrobras): Brazil (32%) PetroChina Company Limited (PetroChina): China (90%) Saudi Aramco: Saudi Arabia (100%) Statoil: Norway (71%) British Petroleum (BP): UK (0%) Chevron: USA (0%) Total: France (0%) ExxonMobil: USA (0%) Shell: Netherland (0%) Average of NOCs (1-12) Average of IOCs (13-17)

1.037 1.615 0.991 1.028

2007

1.016 1.719 1.124 1.207

2008

1.025 1.355 1.016 0.485

2009

1.080 1.330 1.093 0.566

Average

1.039 1.505 1.056 0.821

1.075 1.163 1.098 1.108 1.111

1.252 1.289 1.283 1.282 1.276 1.103 1.211 1.401 1.445 1.290 0.989 0.981 0.990 1.074 1.008 1.111 1.201 1.330 1.333 1.244 0.999 1.274 0.950 1.102 0.854 1.001 1.102 1.130 1.002

0.947 1.273 0.929 1.113 0.875 1.014 1.143 1.189 1.015

0.946 1.400 0.965 1.077 0.861 1.002 1.244 1.130 1.030

0.848 1.197 1.039 1.025 0.870 1.004 0.946 1.133 0.977

0.935 1.286 0.971 1.079 0.865 1.005 1.109 1.145 1.006

(a) In the measurement, an efficiency frontier consists of DMUs in the p-th period and a DMU to be examined by Model (7) is selected from a group of DUMs in the t-th period. In the measurement, if the index is more than unity, as found in most of NOCs and IOCs, then it indicates that there is no frontier shift between the two periods. In contrast, if the index is less than or equal unity, then it may indicate a possible occurrence of the frontier shift. The indexes indicated that there was a technology progress in most of NOCs and IOCs from 2005 to 2009.

342

T. Sueyoshi, M. Goto / Energy Economics 51 (2015) 329–345

Table 5 Malmquist index under natural disposability.

Table 7 Inter-temporal unified index under managerial disposability (IUIMp → t). No. Company and country (government ownership)

2006

0.995 0.997 0.885 1.018 0.974

1

0.634 0.577 0.539 0.536 0.571

1.036 1.115 0.977 0.963

1.061 1.123 1.028 0.965

2 3 4 5

0.944 0.936 0.939 0.954 0.943

6

1.002 0.972 0.967 0.937 0.970

7

1.013 1.040 1.063 1.125 1.060

8

0.941 0.914 0.894 0.989 0.934

9

1.029 1.066 1.167 1.154 1.104

10

0.984 1.115 1.032 1.087 0.984 1.253 1.014 1.009 1.074

11 12 13 14 15 16 17

No. Company and country (government ownership)

2006

1 2 3 4 5 6

7 8 9 10 11 12 13 14 15 16 17

China National Offshore Oil Corporation (CNOOC): China (71%) Eni: Italy (30%) Gazprom: Russia (51%) Industrija Nafte (INA): Croatia (75%) Hungarian Oil and Gas Company (MOL): Hungary (25%) Österreichische Mineralölverwaltung (OMV): Austria (32%) Petroleum Development Oman (PDO): Oman (60%) Petroleos Mexicanos (Pemex): Mexico (100%) Petrobras Brazil (Petrobras): Brazil (32%) PetroChina Company Limited (PetroChina): China (90%) Saudi Aramco: Saudi Arabia (100%) Statoil: Norway (71%) British Petroleum (BP): UK (0%) Chevron: USA (0%) Total: France (0%) ExxonMobil: USA (0%) Shell: Netherland (0%) Average of NOCs (1–12) Average of IOCs (13–17)

2007

1.030 1.205 1.055 1.015

0.933 1.014 1.030 1.099 1.012 1.103 1.027 1.015 1.054

2008

1.131 1.074 1.021 0.939

0.932 1.071 1.014 1.001 1.094 1.090 1.117 1.007 1.063

2009

1.046 1.097 1.057 0.941

0.844 0.993 1.112 1.108 1.068 1.293 0.967 1.013 1.109

Average

0.923 1.048 1.047 1.074 1.040 1.185 1.031 1.011 1.075

(a) The Malmquist indexes are the averages, in geometric means, of the two intertemporal unified indexes between the p-th period (2005) and t-th periods (from 2006 to 2009) along with their unified efficiency under natural disposability. On the average, NOCs showed a frontier shift with an increase with 1.1% from the base period. Meanwhile, IOCs showed a frontier shift with an increase with 7.5%, both of which were due to technology innovation on desirable outputs between the two periods.

a DMU is more than unity, then it indicates no occurrence of a frontier crossover between the two periods, so indicating an eco-technology progress. In contrast, if the index is less than or equal unity, then it indicates an occurrence of the frontier crossover. The indexes summarized in Table 8 indicated that a frontier crossover was found in most of DMUs during all observed annual periods. Exceptions were found in DMUs {3, 7, 10 and 12}. In other words, there was no eco-technology progress and/or managerial innovation in the environmental

China National Offshore Oil Corporation (CNOOC): China (71%) Eni: Italy (30%) Gazprom: Russia (51%) Industrija Nafte (INA): Croatia (75%) Hungarian Oil and Gas Company (MOL): Hungary (25%) Österreichische Mineralölverwaltung (OMV): Austria (32%) Petroleum Development Oman (PDO): Oman (60%) Petroleos Mexicanos (Pemex): Mexico (100%) Petrobras Brazil (Petrobras): Brazil (32%) PetroChina Company Limited (PetroChina): China (90%) Saudi Aramco: Saudi Arabia (100%) Statoil: Norway (71%) British Petroleum (BP): UK (0%) Chevron: USA (0%) Total: France (0%) ExxonMobil: USA (0%) Shell: Netherland (0%) Average of NOCs (1–12) Average of IOCs (13–17)

0.320 1.016 0.177 0.515

2007

0.284 0.898 0.155 0.397

2008

0.386 0.834 0.217 0.611

2009

0.230 0.839 0.124 0.288

Average

0.305 0.897 0.168 0.453

0.621 0.574 0.561 0.485 0.560

0.810 0.788 0.765 0.762 0.781 0.376 0.344 0.339 0.315 0.344 0.357 0.320 0.353 0.293 0.331 0.994 0.976 1.616 0.933 1.130 1.041 0.741 0.494 0.509 0.434 0.391 0.513 0.633 0.468

1.095 0.700 0.436 0.393 0.379 0.326 0.425 0.592 0.392

1.087 0.692 0.640 0.634 0.584 0.528 0.676 0.667 0.612

1.247 0.606 0.357 0.285 0.307 0.262 0.345 0.555 0.311

1.118 0.685 0.482 0.455 0.426 0.377 0.490 0.612 0.446

(a) In the measurement, an efficiency frontier consists of DMUs in the t-th period and a DMU to be examined by Model (11) is selected from a group of DUMs in the p-th period. In the table, if the index of DMUs, like DMU {11}, is more than or equal unity, then it indicates a possible occurrence of a frontier crossover between the two periods. In contrast, if the index is less than unity, then it indicates no occurrence of the frontier crossover. See the other DMUs whose indexes were less than unity. Thus, the indexes indicated that a frontier crossover was not found in most of DMUs during all observed annual periods. An exception was found in DMU {11}. There was an eco-technology progress and/or managerial innovation in the environmental performance of NOCs (total average: 0.612) and IOCs (total average: 0.446) on most of oil firms from 2005 to 2009.

performance of NOCs (total average: 0.803) and IOCs (total average: 0.792) from 2005 to 2009. Table 9 summarizes the degree of IM tp (the Malmquist Index between the p-th and the t-th periods under managerial disposability) of all oil firms that is determined by combining the computational

Table 6 Unified efficiency under managerial disposability. No.

Company and country (government ownership)

2005

2006

2007

2008

2009

Average

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

China National Offshore Oil Corporation (CNOOC): China (71%) Eni: Italy (30%) Gazprom: Russia (51%) Industrija Nafte (INA): Croatia (75%) Hungarian Oil and Gas Company (MOL): Hungary (25%) Österreichische Mineralölverwaltung (OMV): Austria (32%) Petroleum Development Oman (PDO): Oman (60%) Petroleos Mexicanos (Pemex): Mexico (100%) Petrobras Brazil (Petrobras): Brazil (32%) PetroChina Company Limited (PetroChina): China (90%) Saudi Aramco: Saudi Arabia (100%) Statoil: Norway (71%) British Petroleum (BP): UK (0%) Chevron: USA (0%) Total: France (0%) ExxonMobil: USA (0%) Shell: Netherland (0%) Average of NOCs (1–12) Average of IOCs (13–17)

0.644 0.395 1.000 0.222 0.702 0.753 0.992 0.385 0.364 1.000 1.000 0.901 0.588 0.695 0.564 0.533 0.699 0.696 0.616

0.661 0.354 1.000 0.187 0.616 0.379 1.000 0.307 0.371 1.000 1.000 0.889 0.598 0.501 0.471 0.368 0.560 0.647 0.500

0.631 0.299 1.000 0.208 0.424 0.373 1.000 0.265 0.337 1.000 1.000 0.796 0.507 0.418 0.408 0.325 0.517 0.611 0.435

1.000 0.499 1.000 0.300 0.559 0.371 1.000 0.250 0.430 1.000 0.954 0.845 0.958 0.760 0.767 0.616 1.000 0.684 0.820

0.705 0.293 1.000 0.144 0.291 0.292 0.955 0.182 0.299 1.000 1.000 0.780 0.422 0.327 0.335 0.280 0.459 0.578 0.364

0.728 0.368 1.000 0.212 0.518 0.433 0.989 0.278 0.360 1.000 0.991 0.842 0.615 0.540 0.509 0.424 0.647 0.643 0.547

(a) NOCs (total average: 0.643) outperformed IOCs (total average: 0.547) in unified efficiency under managerial disposability. See the bottom of the last column. (b) The base period is 2005. The unified efficiency was computed by the annual performance of 17 oil firms. (c) All the unified efficiency scores in the table are computed by Models (9) and (10).

T. Sueyoshi, M. Goto / Energy Economics 51 (2015) 329–345 Table 8 Inter-temporal unified index under managerial disposability (IUIMt → p). No. Company and country (government ownership)

2006

1 2 3 4 5 6

7 8 9 10 11 12 13 14 15 16 17

China National Offshore Oil Corporation (CNOOC): China (71%) Eni: Italy (30%) Gazprom: Russia (51%) Industrija Nafte (INA): Croatia (75%) Hungarian Oil and Gas Company (MOL): Hungary (25%) Österreichische Mineralölverwaltung (OMV): Austria (32%) Petroleum Development Oman (PDO): Oman (60%) Petroleos Mexicanos (Pemex): Mexico (100%) Petrobras Brazil (Petrobras): Brazil (32%) PetroChina Company Limited (PetroChina): China (90%) Saudi Aramco: Saudi Arabia (100%) Statoil: Norway (71%) British Petroleum (BP): UK (0%) Chevron: USA (0%) Total: France (0%) ExxonMobil: USA (0%) Shell: Netherland (0%) Average of NOCs (1–12) Average of IOCs (13–17)

2007

2008

2009

343

Table 9 Malmquist index under managerial disposability. Average

No. Company and country (government ownership)

2006

0.675 0.722 1.268 0.819 0.871

1

1.018 1.131 1.231 1.182 1.141

0.432 1.015 0.234 0.841

0.449 1.142 0.266 0.744

2 3 4 5

0.482 0.514 0.487 0.488 0.493

6

1.276 1.307 1.316 1.247 1.286

7

0.332 0.343 0.327 0.309 0.328

8

0.378 0.383 0.348 0.375 0.371

9

1.364 1.768 1.272 2.436 1.710

10

0.985 1.054 0.816 0.684 0.643 0.502 0.765 0.756 0.682

11 12 13 14 15 16 17

0.414 1.160 0.294 0.749

0.951 1.001 0.888 0.738 0.722 0.560 0.915 0.800 0.764

0.462 1.204 0.283 0.679

0.899 1.040 1.174 0.912 0.942 0.714 1.338 0.799 1.016

0.489 1.190 0.255 0.708

0.883 1.094 0.756 0.630 0.690 0.510 0.950 0.858 0.707

0.930 1.047 0.908 0.741 0.749 0.571 0.992 0.803 0.792

(a) In the measurement, an efficiency frontier consists of DMUs in the p-th period and a DMU to be examined by Model (12) is selected from a group of DUMs in the t-th period. If the index of a DMU is more than unity, then it indicates no occurrence of a frontier crossover between the two periods, so indicating an eco-technology progress. In contrast, if the index is less than or equal unity, then it indicates an occurrence of the frontier crossover. The indexes indicated that a frontier crossover was found in most of DMUs during all observed annual periods. Exceptions were found in DMUs {3, 7, 10 and 12}. In other words, there was no eco-technology progress and/or managerial innovation in the environmental performance of NOCs (total average: 0.803) and IOCs (total average: 0.792) from 2005 to 2009.

results in Tables 6, 7 and 8. The index serves as a total measure of a frontier shift under managerial disposability in the observed annual periods. Such a combination is computed by Eq. (8). The Malmquist indexes are the total averages, as geometric means, of the two inter-temporal unified indexes between the p-th period (2005) and t-th periods (from 2006 to 2009) along with their unified efficiencies measured under managerial disposability. The index numbers summarized in Table 9 indicated that, on average, NOCs showed a frontier shift with an increase of 25.7% from the base period. Meanwhile, IOCs showed a frontier shift with an increase of 51.8% on average, both were due to technology innovation on undesirable outputs and/or a managerial effort to adapt a regulation change. See the bottom of the last column of Table 9. Policy implication: The Malmquist index (INtp) under natural disposability indicated that the frontier shift occurred in both NOCs and IOCs under the disposability where their operational performance is the first priority and environmental performance is the second priority. The degree on the frontier shift of NOCs (total average: 1.1%) was less than IOCs (total average: 7.5%). In a similar manner, the Malmquist index (IM tp) under managerial disposability indicated that the frontier shift occurred in both NOCs and IOCs under the disposability where their performance criterion was the opposite of the natural disposability. The degree of the frontier shift of NOCs (total average: 25.7%) was less than that of IOCs (total average: 51.8%). The results implied that both NOCs and IOCs had paid attention to their pollution prevention. Since IOCs needed to operate in a global oil market, they paid more serious attention to environmental regulations than NOCs whose operations were usually limited within their own nations. The environmental regulation on NOCs was less restricted than that of IOCs. In other words, strict regulation

China National Offshore Oil Corporation (CNOOC): China (71%) Eni: Italy (30%) Gazprom: Russia (51%) Industrija Nafte (INA): Croatia (75%) Hungarian Oil and Gas Company (MOL): Hungary (25%) Österreichische Mineralölverwaltung (OMV): Austria (32%) Petroleum Development Oman (PDO): Oman (60%) Petroleos Mexicanos (Pemex): Mexico (100%) Petrobras Brazil (Petrobras): Brazil (32%) PetroChina Company Limited (PetroChina): China (90%) Saudi Aramco: Saudi Arabia (100%) Statoil: Norway (71%) British Petroleum (BP): UK (0%) Chevron: USA (0%) Total: France (0%) ExxonMobil: USA (0%) Shell: Netherland (0%) Average of NOCs (1–12) Average of IOCs (13–17)

1.226 1.000 1.253 1.364

2007

1.386 1.136 1.422 1.768

2008

0.972 1.201 0.982 1.181

2009

1.691 1.191 1.781 2.436

Average

1.319 1.132 1.359 1.687

1.243 1.345 1.328 1.611 1.382

1.250 1.283 1.306 1.304 1.286 1.052 1.205 1.218 1.440 1.229 1.020 1.137 0.914 1.247 1.079 1.171 1.345 0.887 1.615 1.255 0.973 1.201 1.274 1.364 1.331 1.364 1.364 1.148 1.340

0.932 1.273 1.537 1.768 1.622 1.679 1.706 1.280 1.662

0.931 1.266 1.060 1.147 1.088 1.081 1.176 1.118 1.111

0.841 1.444 1.717 2.168 1.945 1.926 2.048 1.482 1.961

0.919 1.296 1.397 1.612 1.497 1.512 1.574 1.257 1.518

(a) The Malmquist indexes are the total averages, as geometric means, of the two intertemporal unified indexes between the p-th period (2005) and t-th periods (from 2006 to 2009) along with their unified efficiencies measured under managerial disposability. The index numbers indicated that, on average, NOCs showed a frontier shift with an increase of 25.7% from the base period. Meanwhile, IOCs showed a frontier shift with an increase of 51.8%, both of which were due to eco-technology innovation on undesirable outputs and/or a managerial effort to adapt a regulation change.

on environment may produce an opportunity for technology innovation in the petroleum industry, as discussed by corporate strategists in U.S. business schools (e.g., Porter and van der Linde, 1995). Comparison with previous studies: Sueyoshi and Wang (2014b) utilized the DEA environmental assessment to measure the corporate sustainability of petroleum firms in the United States. The U.S. petroleum industry, consisting of private firms, is functionally separated into integrated and independent companies. The integrated companies, referred to as “Major”, have their large supply chains for both upstream and downstream. Meanwhile, U.S. independent companies focus upon the upstream function like NOCs in this study, but not having the downstream function in their business operations. Their empirical comparison between the two groups of U.S. petroleum firms identified that the integrated companies (i.e., IOCs) outperformed the independent companies because a large supply chain incorporated into the former group provided them with both a scale merit in their operations and an opportunity to obtain consumer's opinions on their business operations. As an extension of Sueyoshi and Goto (2012a) that investigated the performance of NOCs and IOCs as a pooled data by a non-radial approach, this study investigated a frontier shift and its related subcomponents during the observed period (2005–2009) by a radical approach. The previous study did not have an analytical capability on time series because it was structured by the non-radial measurement. This study finds that the industry has not exhibited any major frontier shift under natural disposability, but showing a considerable frontier shift under managerial disposability. In other words, the petroleum firms have improved their environmental performance by ecotechnology innovation to reduce an amount of CO2 emission, but not so much on operational performance during the observed period. Thus, the empirical finding of this study is consistent with the one

344

T. Sueyoshi, M. Goto / Energy Economics 51 (2015) 329–345

obtained from the research effort of Sueyoshi and Wang (2014b). This study supports that business implications obtained by their study can be applied to not only the U.S. petroleum firms but also other oil firms in the world. 8. Conclusion and future extensions This study incorporated an economic concept, or the Malmquist index, to measure a frontier shift among different periods into DEA environmental assessment. A contribution of this study was that it linked the index to natural and managerial disposability. Consequently, the Malmquist index measurement was separated into eight different subcomponents (4 subcomponents × 2 disposability concepts). All subcomponents provided us with information on how a frontier shift occurred among different periods in a time horizon. As an illustrative example, this study applied the proposed approach to measure a frontier shift in the petroleum industry. The empirical finding implied that both NOCs and IOCs had paid attention to their environmental protections. Furthermore, IOCs paid more serious attention to the environmental concerns than NOCs because the former group had to operate in a global oil/gas market and the operation of the latter group was usually limited within their own nations. Thus, the environmental regulation on NOCs was less restricted than that of IOCs. In other words, strict environmental regulation may produce an opportunity for technology innovation in the petroleum industry, as discussed by corporate strategists in U.S. business schools. The proposed DEA approach has four research tasks to be overcome in the future. First, this study has documented only an illustrative example related to the petroleum industry from 2005 to 2009. The time horizon within the data set should be expanded to obtain long-term policy implications concerning their operational and environmental performance. See, for example, Sueyoshi and Wang (2014b). That is a drawback of this study to be overcome in the future. Second, this study needs to develop a new computational framework in DEA by incorporating the concept of cost and future energy uncertainty. This study does not consider the research task on cost and a better fuel mix for the development of a sustainable society. The stochastic DEA will be a promising approach for the research task. Third, it is possible to measure the type of RTS and that of DTS in a time horizon. See, for example, Sueyoshi and Goto (2012d). The proposed DEA approach assumes constant RTS and constant DTS to obtain computational feasibility on a computer code. The determination on RTS and DTS in a time horizon will be explored as a future extension of this study. Finally, the proposed approach usually does not work on a data set that contains zero and negative values in production factors. As an extension, it is necessary for us to develop a new approach to handle the data set with zero and/or negative values. In conclusion, it is hoped that this study makes a contribution for DEA environmental assessment. We look forward to seeing future research extensions, as discussed in this article. Acknowledgement This work was supported by a Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (KAKENHI) 26285050. References Bjurek, H., 1996. The Malmquist total factor productivity index. Scand. J. Econ. 98, 303–3013. Bjurek, H., Hjalmarsson, L., 1995. Productivity in multiple output public services: a quadratic frontier function and the Malmquist index approach. J. Public Econ. 56, 447–460. Bowlin, W.F., 1987. Evaluating the efficiency of US air force real-property maintenance activities. J. Oper. Res. Soc. 38, 127–135. Crain, D.W., Abraham, S., 2008. Using value-chasing analysis to discover customers' strategic needs. Strateg. Leadersh. 36, 29–39. Debreu, G., 1951. The coefficient of resource utilization. Econometrica 19, 273–292. Dyckhoff, H., Allen, K., 2001. Measuring ecological efficiency with data envelopment analysis (DEA). Eur. J. Oper. Res. 132, 312–325.

Färe, R., Grosskopf, S., Lovel, C.A.K., Pasurka, C., 1989. Multilateral productivity comparison when some outputs are undesirable: a nonparametric approach. Rev. Econ. Stat. 71, 90–98. Farrell, M.J., 1954. An application of activity analysis to the theory of the firm. Econometrica 22, 291–302. Farrell, M.J., 1957. The measurement of productive efficiency. J. R. Stat. Soc. Ser. A 120 (Part 3), 253–290. Farrell, M.J., Fieldhouse, M., 1962. Production functions under increasing returns to scale. J. R. Stat. Soc. Ser. A (General) 125, 252–267. Glover, F., Sueyoshi, T., 2009. Contributions of Professor William W. Cooper in operations research and management science. Eur. J. Oper. Res. 197, 1–16. Goto, M., Tsutsui, M., 1998. Comparison of productive and cost efficiencies among Japanese and US electric utilities. OMEGA 26, 177–194. Goto, M., Ootsuka, A., Sueyoshi, T., 2014. DEA (data envelopment analysis) assessment of operational and environmental efficiencies on Japanese regional industries. Energy 66, 535–549. Grifell-Tatje, E., Lovel, C.A.K., 1995. A note on the Malmquist productivity index. Econ. Lett. 47, 167–175. Ijiri, Y., Sueyoshi, T., 2010. Accounting essays by Professor William W. Cooper: revisiting in commemoration of his 95th birthday. ABACUS: J. Account. Finance Bus. Stud. 46, 464–505. Korhonen, P.J., Luptacik, M., 2004. Eco-efficiency analysis of power plants: an extension of data envelopment analysis. Eur. J. Oper. Res. 154, 437–446. Kumar, S., 2006. Environmentally sensitive productivity growth: a global analysis using Malmquist–Luenberger index. Ecol. Econ. 56, 280–293. Liang, L., Wu, D., Hua, Z., 2004. MES-DEA modeling for analyzing anti-industrial pollution efficiency and its application in Anhui province of China. Int. J. Global Energy Issues 22, 88–98. Malmquist, S., 1953. Index number and indifferences surfaces. Trab. Estad. 4, 209–2042. Oude Lansink, A., Bezlepkin, I., 2003. The effect of heating technologies on CO2 and energy efficiency of Dutch greenhouse firms. J. Environ. Manag. 68, 73–82. Palmer, K.W., Oates, W.E., Portney, P.R., 1995. Tightening environmental standards— the benefit–cost or the no-cost paradigm. J. Econ. Perspect. 9, 119–132. Pasurka Jr., C.A., 2006. Decomposing electric power plant emissions within a joint production framework. Energy Econ. 28, 26–43. Picazo-Tadeo, A.J., Reig-Martinez, E., Hernandez-Sancho, F., 2005. Directional distance functions and environmental regulation. Resour. Energy Econ. 27, 131–142. Porter, M.E., van der Linde, C., 1995. Toward a new conception of the environment competitiveness relationship. J. Econ. Perspect. 9, 97–118. Ramanathan, R., 2002. Combing indicators of energy consumption and CO2 emissions: a cross-country comparison. Int. J. Global Energy Issues 17, 214–227. Sueyoshi, T., 1997. Measuring scale efficiencies and returns to scale of Nippon Telegraph & Telephone in production and cost analyses. Manag. Sci. 43, 779–796. Sueyoshi, T., 1999a. DEA-discriminant analysis in the view of goal programming. Eur. J. Oper. Res. 115, 564–582. Sueyoshi, T., 1999b. DEA duality on returns to scale (RTS) in production and cost analyses: an occurrence of multiple solutions and differences between production-based and cost-based RTS estimates. Manag. Sci. 45, 1593–1608. Sueyoshi, T., 2001. Extended DEA-discriminant analysis. Eur. J. Oper. Res. 131, 324–351. Sueyoshi, T., 2004. Mixed integer programming approach of extended DEA-discriminant analysis. Eur. J. Oper. Res. 152, 45–55. Sueyoshi, T., 2005. Financial ratio analysis of the electric power industry. Asia-Pac. J. Oper. Res. 22, 349–376. Sueyoshi, T., 2006. DEA-discriminant analysis: methodological comparison among eight discriminant analysis approaches. Eur. J. Oper. Res. 169, 247–272. Sueyoshi, T., Aoki, S., 2001. A use of a nonparametric statistic for DEA frontier shift: the Kruskal and Wallis rank test. OMEGA 29, 1–18. Sueyoshi, T., Goto, T., 2001. Slack-adjusted DEA for time series analysis: performance measurement of Japanese electric power generation industry in 1984–1993. Eur. J. Oper. Res. 133, 232–259. Sueyoshi, T., Goto, M., 2009a. Can environmental investment and expenditure enhance financial performance of US electric utility firms under the clean air act amendment of 1990? Energy Policy 37, 4819–4826. Sueyoshi, T., Goto, M., 2009b. Can R&D expenditure spending avoid corporate bankruptcy? Comparison between Japanese machinery and electric equipment industries using DEA-Discriminant Analysis. Eur. J. Oper. Res. 196, 289–311. Sueyoshi, T., Goto, M., 2009c. DEA-DA for bankruptcy-based performance assessment: misclassification analysis of the Japanese construction industry. Eur. J. Oper. Res. 199, 576–594. Sueyoshi, T., Goto, M., 2009d. Methodological Comparison between DEA (Data Envelopment Analysis) and DEA-DA (Discriminant Analysis) from the perspective of bankruptcy assessment. Eur. J. Oper. Res. 199, 561–575. Sueyoshi, T., Goto, M., 2010a. Measurement of a linkage among environmental, operational and financial performance in Japanese manufacturing firms: a use of data envelopment analysis with strong complementary slackness condition. Eur. J. Oper. Res. 207, 1742–1753. Sueyoshi, T., Goto, M., 2010b. Should the US clean air act include CO2 emission control? Examination by data envelopment analysis. Energy Policy 38, 5902–5911. Sueyoshi, T., Goto, M., 2011a. Operational synergy in the electric utility industry under the influence of US deregulation policy: a linkage to financial performance and corporate value. Energy Policy 39, 699–713. Sueyoshi, T., Goto, M., 2011b. DEA approach for unified efficiency measurement: assessment of Japanese fossil fuel power generation. Energy Econ. 33, 195–208. Sueyoshi, T., Goto, M., 2011c. A combined use of DEA (data envelopment analysis) with strong complementary slackness condition and DEA-DA (discriminant analysis). Appl. Math. Lett. 24, 1051–1056.

T. Sueyoshi, M. Goto / Energy Economics 51 (2015) 329–345 Sueyoshi, T., Goto, M., 2012a. Data envelopment analysis for environmental assessment: comparison between public and private ownership in petroleum industry. Eur. J. Oper. Res. 216, 668–678. Sueyoshi, T., Goto, M., 2012b. DEA radial measurement for environmental assessment and planning: desirable procedures to evaluate fossil fuel power plants. Energy Policy 41, 422–432. Sueyoshi, T., Goto, M., 2012c. Efficiency-based rank assessment for electric power industry: a combined use of data envelopment analysis (DEA) and DEA-discriminant analysis (DA). Energy Econ. 34, 634–644. Sueyoshi, T., Goto, M., 2012d. Returns to scale and damages to scale under natural and managerial disposability: strategy, efficiency and competitiveness of petroleum firms. Energy Econ. 34, 645–662. Sueyoshi, T., Goto, M., 2012e. Environmental assessment by DEA radial measurement: U.S. coal-fired power plants in ISO (independent system operator) and RTO (regional transmission organization). Energy Econ. 34, 663–676. Sueyoshi, T., Goto, M., 2012f. Weak and strong disposability vs. natural and managerial disposability in DEA environmental assessment: comparison between Japanese electric power industry and manufacturing industries. Energy Econ. 34, 686–699. Sueyoshi, T., Goto, M., 2012g. DEA radial and non-radial models for unified efficiency under natural and managerial disposability: theoretical extension by strong complementary slackness conditions. Energy Econ. 34, 700–713. Sueyoshi, T., Goto, M., 2012h. Returns to scale, damages of scale, marginal rate of transformation and rate of substitution in DEA environmental assessment. Energy Econ. 34, 905–917. Sueyoshi, T., Goto, M., 2012i. Returns to scale and damages to scale with strong complementary slackness conditions in DEA environmental assessment: Japanese corporate effort on environmental protection. Energy Econ. 34, 1422–1434. Sueyoshi, T., Goto, M., 2012j. DEA environmental assessment of coal fired power plants: methodological comparison between radial and non-radial models. Energy Econ. 34, 1854–1863. Sueyoshi, T., Goto, M., 2012k. Returns to scale and damages to scale on U.S. fossil fuel power plants: radial and non-radial approaches for DEA environment assessment. Energy Econ. 34, 2240–2259. Sueyoshi, T., Goto, M., 2013a. Returns to scale vs. damages to scale in data envelopment analysis: an impact of U.S. clean air act on coal-fired power plants. OMEGA 41, 164–175. Sueyoshi, T., Goto, M., 2013b. A Use of DEA-DA to measure importance of R&D expenditure in Japanese information technology industry. Decis. Support. Syst. 54, 941–952. Sueyoshi, T., Goto, M., 2013c. A comparative study among fossil fuel power plants in PJM and California ISO by DEA environmental assessment. Energy Econ. 40, 130–145. Sueyoshi, T., Goto, M., 2013d. DEA environmental assessment in a time horizon: Malmquist index on fuel mix, electricity and CO2 of industrial nations. Energy Econ. 40, 370–382. Sueyoshi, T., Goto, M., 2014a. DEA radial measurement for environmental assessment: a comparative Study between Japanese chemical and pharmaceutical firms. Appl. Energy 115, 502–513.

345

Sueyoshi, T., Goto, M., 2014b. Investment strategy for sustainable society by development of regional economies and prevention of industrial pollutions in Japanese manufacturing Sectors. Energy Econ. 42, 299–312. Sueyoshi, T., Goto, M., 2014c. Photovoltaic power stations in Germany and the United States: a comparative study by data envelopment analysis. Energy Econ. 42, 271–288. Sueyoshi, T., Goto, M., 2014d. Environmental assessment for corporate sustainability by resource utilization and technology innovation: DEA radial measurement on Japanese industrial sectors. Energy Econ. 46, 295–307. Sueyoshi, T., Goto, M., 2015. DEA environmental assessment on coal-fired power plants in U.S. north-east region by DEA non-radial measurement. Energy Econ. 50, 125–139. Sueyoshi, T., Sekitani, K., 2009. An occurrence of multiple projections in DEA-based measurement of technical efficiency: theoretical comparison among DEA Models from desirable properties. Eur. J. Oper. Res. 196, 764–794. Sueyoshi, T., Wang, D., 2014a. Radial and non-radial approaches for environmental assessment by data envelopment analysis: corporate sustainability and effective investment for technology innovation. Energy Econ. 45, 537–551. Sueyoshi, T., Wang, D., 2014b. Sustainability development for supply chain management in U.S. petroleum industry by DEA environmental assessment. Energy Econ. 46, 360–374. Sueyoshi, T., Yuan, Y., 2015. China's regional sustainability and diversity: DEA environmental assessment on economic development and air pollution. Energy Econ. 49, 239–256. Sueyoshi, T., Goto, M., Shang, J., 2009. Core business concentration vs. corporate diversification in the US electric utility industry: synergy and deregulation effects. Energy Policy 37, 4583–4594. Sueyoshi, T., Goto, M., Ueno, T., 2010. Performance analysis of U.S. coal-fired power plants by measuring three DEA efficiencies. Energy Policy 38, 1675–1688. Sueyoshi, T., Goto, M., Snell, M.A., 2013a. DEA environmental assessment: measurement of damages to scale with unified efficiency under managerial disposability or environmental efficiency. Appl. Math. Model. 37, 7300–7314. Sueyoshi, T., Goto, M., Sugiyama, M., 2013b. DEA window analysis for environmental assessment in a dynamic time shift: performance assessment of U.S. coal-fired power plants. Energy Econ. 40, 845–857. Thore, S., Kozmetsky, G., Phillips, F., 1994. DEA of financial statements data: the US computer industry. J. Prod. Anal. 5, 229–248. Triantis, K., Otis, P., 2004. Dominance-based measurement of productive and environmental performance for manufacturing. Eur. J. Oper. Res. 154, 447–464. Wang, D., Li, S., Sueyoshi, T., 2014. DEA environmental assessment on U.S. industrial Sectors: investment for improvement in operational and environmental performance for corporate sustainability. Energy Econ. 45, 254–267. Zaim, O., 2004. Measuring environmental performance of state manufacturing through changes in pollution intensities: a DEA framework. Ecol. Econ. 48, 37–47. Zhou, P., Ang, B.W., Poh, K.L., 2008. A survey of data envelopment analysis in energy and environmental studies. Eur. J. Oper. Res. 189, 1–18. Zhou, P., Ang, B.W., Han, J.Y., 2010. Total factor carbon emission performance: a Malmquist index analysis. Energy Econ. 32, 194–201.