A generalized MCDA–DEA (multi-criterion decision analysis–data envelopment analysis) approach to construct slacks-based composite indicator

Energy xxx (2014) 1e9

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A generalized MCDAeDEA (multi-criterion decision analysisedata envelopment analysis) approach to construct slacks-based composite indicator H. Wang* Department of Industrial and Systems Engineering, National University of Singapore, Singapore

a r t i c l e i n f o

a b s t r a c t

Article history: Received 8 September 2014 Received in revised form 30 October 2014 Accepted 14 November 2014 Available online xxx

This paper presents a generalized framework to construct composite indicator, which can be used in static and dynamic analysis. By grouping DMUs (decision making units) first, the proposed approach is more flexible to derive weights for entities featuring diverse characteristics. A more neutral set of weights can be obtained through investigating the lower and upper bound of possible weights. Subsequently, we introduce a slack-based composite indicator from the perspective of distance function, which facilitates studying entities' improvement potential in sub-indicators. Furthermore, the slacks-based composite indicator is combined with the Malmquist index to conduct dynamic assessment, aiming to quantify the evolvement of composite indicator over time and the underlying driving forces. To illustrate the usefulness of the proposed approach, it is applied to construct the Sustainable Energy Index for 109 countries worldwide in 2005e2010. Our results show that the high-income country group has the best sustainable energy performance among all the three country groups in 2010. The dynamic assessment indicates the worldwide sustainable energy development level declined during 2005e2010, and the efficiency change was the main negative driving force. More discussions and implications are presented in the paper. © 2014 Elsevier Ltd. All rights reserved.

Keywords: Data envelopment analysis Multi-criteria decision analysis Slacks-based composite indicator Malmquist index

1. Introduction CI (composite indicator) is a useful tool to conducting assessment and comparison when MCDA (multi-criterion decision analysis) problem arises. The main advantage of CI is it can represent the overall information of entities in a comprehensive way even sub-indicators are controversial. CI has been attracting increasingly attention from the academia and publics because it is quite easy to use and understand. Currently CI has been widely applied in realworld problems. For instance, World Bank develops a CI to measure countries' development level.1 Particularly, in recent years CI has also been applied in the performance assessment in energy and environmental studies. As an example, a great number of organizations and researchers have devoted to construct the environmental sustainability index or environmental performance index, which is essentially a CI considering economic, environmental and social aspects simultaneously [1e3].

* Tel./fax: þ65 93720102. E-mail address: [email protected]. 1 http://data.worldbank.org/data-catalog/world-development-indicators.

With popularity and importance in application growing, constructing CI becomes a fundamental work. Recently, a joint study by the OECD and the Joint Research Centre of the European Commission outlines several key steps to build a CI, from establishing analytical framework to processing data and final test [4]. In the whole workflow, a critical question is how to weight and aggregate sub-indicators into a CI. Nevertheless, weighting and aggregating sub-indicators is still an open question. In the literature, a number of methods have been used to derive weights and different results can be obtained. They include, for example, AHP (analytic hierarchy process) method [5e8], PCA (principal component analysis) method [9], grey relation analysis [10] and Delphi method [11,12]. One common feature of those approaches is they need certain prior information on subindicators and comparison among them, based on which the weights can be determined. However, this feature makes those approaches frequently criticized, mainly due to the objective in deriving weights cannot be guaranteed. Alternatively, another line of research in this field is to employ the DEA (data envelopment analysis) method to weight subindicators. Distinct from those aforementioned methods, DEA is a

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Please cite this article in press as: Wang H, A generalized MCDAeDEA (multi-criterion decision analysisedata envelopment analysis) approach to construct slacks-based composite indicator, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.11.051

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H. Wang / Energy xxx (2014) 1e9

non-parametric approach that does not require any prior information on sub-indicators/variables, and can derive a set of weights endogenously for all DMUs (decision making units). This characteristic of DEA makes it possible to solve the issue of objective. In the literature, DEA has been widely used in the MCDA area to address decision problems. Stewart [13] argues that DEA and MCDA share certain similarities and coincide in formulation. A number of researchers adopt DEA in empirical MCDA studies. See, for example, [14e18]. In the area of constructing CI, DEA has also been popular for years as it is desirable in obtaining a ‘fair’ set of weights for all DMUs. Examples of such studies are [19e22]. In principle, the weights derived from DEA method can be divided into two categories. The first category is common weights, which implies all DMUs share the same set of weights to construct CI. The underlying rationale is that using the same set of weights for all DMUs is strictly fair and consistent. For instance, Hatefi and Torabi [23] propose a common-weights DEA model and demonstrate its usefulness by comparing it with some parallel methods; Emerson and Esty [1] and Karsak and Ahiska [24] introduce a common-weights model and apply it to the technology selection problem; Kao [25] study Taiwan's forest after reorganization by combining the Malmquist performance index and a commonweight DEA model. On the contrary, some researchers argue that DMUs should have certain freedom to choose their own preference such that maximizes individual performance. This category can be identified as differentiated weights. For instance, Zhou and Ang [26] introduce two DEA models to calculate the differentiated weights and further construct the Sustainable Energy Index for APEC countries. By employing the differentiated weights, Zhou and Ang [27] evaluate the Human Development Index in the multiplicative form for 27 countries in 2005. Nevertheless, the two categories of weights may represent two extremes of weighting subindicators. When decision makers face large-scale assessment, considerable heterogeneity may exist among DMUs and is likely to impact the assessment. In such context, it would be necessary to realize the stakeholders' preference and account for the potential heterogeneity. However, this goal cannot be achieved using existing approaches. Besides, previous studies on CI only focus on the static assessment, which is just for a particular time period, whereas the dynamic evolvement of CI cannot be revealed with existing methods. The purpose of this paper is to fill the aforementioned gaps, and the contribution of this paper would be threefold. First, this study attempts to establish a generalized framework that is more flexible in deriving weights for DMUs featuring varied characteristics, in which potential heterogeneity among DMUs can be accounted for. Second, we further introduce a slacks-based composite indicator, which can help rank DMUs' performance as well as investigate their improvement potential. Third, we combine the slacks-based composite indicator and the Malmquist index to track the dynamic evolvement of CI over time. As such, based on the proposed approach, a comprehensive analysis of CI, both statically and dynamically, can be conducted. The rest of this paper is organized as follows. Section 2 introduces and discusses methodological issues. Section 3 presents a case study using the proposed approach and discusses the results obtained. Section 4 concludes the whole study. 2. Methodology 2.1. Weighting sub-indicators In large-scale assessment, noticeable heterogeneity may exist among DMUs. In such case, choosing either common or differentiate weights could be somewhat ‘unfair’ for some entities since DMUs might feature different characteristics. In order to account for the

potential heterogeneity, all the DMUs can be first categorized according to certain criterion. In each group, DMUs would share similar production technology or development level, and therefore it is appropriate to derive common weights within each group. In this manner, the weights for each group might be different. Suppose N DMUs are under assessment using M sub-indicators (m ¼ 1; :::; M). We further assume that all the N DMUs can be divided into L groups (l ¼ 1,…,L), and the group l contains Sl DMUs (i ¼ 1; :::; Sl ). Then the following model can be proposed to assess DMUs' performance.

minK s:t:K  maxðdil Þ; ci; l M P w1lm xilm þ dil ¼ 1; i ¼ 1; :::; Sl ; l ¼ 1; :::; L m¼1 M P m¼1

(1)

w1lm ¼ 1; c l

w1lm  ε; c l; m where x denotes sub-indicators, d refers to slacks, and xilm is the value for the mth sub-indicator of the ith DMU in the lth group. w1lm denotes the weight associated with the mth sub-indicator for the lth group. ε is an arbitrary small positive number, which is to ensure the weight for any sub-indicators higher than zero. It should be noted that sub-indicators might have different unit and varied scale in value, which potentially affect the performance assessment. To cope with this problem, a common practice is to normalize the raw data for sub-indicators. We shall adopt this useful procedure before performing model (1) in the following analysis. Distinct from conventional DEA models, w1lm in model (1) can be considered as weight, and thus its sum should be equal to unity. Model (1) seeks to minimize the slacks for each DMU and maximize their performance. By grouping DMUs into different categories, the weights in each group are also expected to be different. As such, groups of DMUs have certain flexibility to choose their own most appropriate weights. It can be found that model (1) is similar to that proposed in Hatefi and Torabi [23]. However, a key difference is that we introduce groups in model (1) and ensure the sum of weights equal to unity, which might make the present model more reasonable and flexible. In the literature, a number of researchers employ methods similar with model (1) to weight sub-indicators. Examples of such studies are Bellenger and Herlihy [28] and Reig-Martínez [29]. One reason that such weight is preferred is it can endogenously maximize all DMUs possible performance under constraints. Nevertheless, it might not be comprehensive to solely investigate the possible ‘best’ weights. Zhou et al. [26] employ a variation of DEA model to calculate the possible ‘worst’ weights for DMUs, which aims to reduce the number of efficient DMUs from their original model. The ‘worst’ weights can also be considered as the lower bound of possible weights assigned to sub-indicators, and therefore provide certain complementary information besides model (1). Following the idea, we shall adopt model below to calculate the ‘worst’ weights for sub-indicators within each DMUs group.

maxK s:t:K  minðdil Þ; c i; l M P w2lm xilm þ dil ¼ 1; i ¼ 1; :::; Sl ; l ¼ 1; :::; L m¼1 M P

m¼1 w2lm

w2lm

(2)

¼ 1; c i; l

 ε; c l; m

Please cite this article in press as: Wang H, A generalized MCDAeDEA (multi-criterion decision analysisedata envelopment analysis) approach to construct slacks-based composite indicator, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.11.051

H. Wang / Energy xxx (2014) 1e9

where w2lm refers to the weight associated with mth sub-indicator in the lth group. Unlike model (1), model (2) seeks to maximizes all slacks and thus minimizes all weighted sub-indicators' value. Essentially, model (2) measures how far each entity can be away from the best practice frontier. Model (2) can give a set of weights under which all the DMUs have their possible worst performance. Hence, such result can be regarded as the lower bound of possible weights. Considering the ‘best’ weights (upper bound) and ‘worst’ weights (lower bound) simultaneously, we can use their weighted sum as the final weights.

wlm ¼ a,w1lm þ ð1  a Þ,w2lm

(3)

The specification of a is dependent on decision maker's preference. Without any prior information available, it could be neutral to set a ¼ 0:5, which leads the final weight, i.e. wlm , equal to simple arithmetic mean of w1lm and w2lm . Compared with the weights derived solely from model (1) or (2), Eq. (3) allows people to reach a compromise between the ‘best’ and ‘worst’ possible weights, which helps reflect decision makers' attitude on the assessment. 2.2. Slacks-based composite indicator Conventionally, once the weights calculated, it can be directly used to construct CI in additive or multiplicative form, and subsequently conducting ranking. However, apart from ranking result, we cannot extract more information from such CI. For instance, it would be interesting to study DMUs' improvement potential in sub-indicators, which can direct DMUs' future development. Motived by this question, we shall investigate DMUs' slacks in subindicators, based on which an alternative CI can be constructed. For the M sub-indicators, suppose there are P input-type indicators (p ¼ 1; :::; P) and Q output-type indicators (q ¼ P þ 1; :::; M). Then the slacks for sub-indicators can be calculated through the following model. M X lil ¼ max wlm sm m¼1 P s:t: zil xilp þ sp ¼ xop ; p ¼ 1; :::; P P i;l zil xilq  sq ¼ xoq ; q ¼ P þ 1; :::; M i;l P zil ¼ 1

(4)

i;l

zil  0; sm  0; c i; l; m where zil is intensity variable,2 subscript o denotes the DMU under evaluation (o ¼ 1; :::; N) and s refers to slacks. By including the equation that the sum of intensity variables equals to unity, model (4) imposes the assumption of VRS (variable returns to scale). By performing model (4), we can evaluate each DMU's weighted slacks, which is also its distance away from the best practice frontier constructed by all observations. In essential, model (4) is a nonradial weighted additive DEA model that seeks to maximize the weighted slacks of all sub-indicators. Due to its non-radial property, model (4) is able to capture potential slacks exhaustively [30,31]. In DEA literature, weights in the objective function, i.e. wlm in model (4), can be specified differently within various models. For instance, the RAM (range adjusted measure) [32] and the SBM (slacks-based model) [33] have different weights for slacks in their objective functions. Since the purpose of this study is to construct CI, the

2 It should be noted that there is no direct relationship between zil and wlm , though both are essentially related with intensity variables in DEA models.

3

weights obtained from Eq. (3) can be used as it reflects the comparative importance of sub-indicators. As such, model (4) can evaluate the weighted slacks of DMU. We then further define the following composite indicator.

CIil ¼ 1  lil

(5)

Essentially, CIil in Eq. (5) attempts to measure an entity's performance through the weighted slacks in sub-indicators, and thus we shall name the CI in Eq. (5) as the SBCI (slacks-based composite indicator). It can be found that the value of SBCI would fall in the interval [0,1], and therefore can be directly used as a standard indicator. A higher value of SBCI implies better performance with respect to the best practice frontier. If a DMU possesses unity for its SBCI, it means this DMU is located on the frontier, and hence possesses the best performance. In this way the assessment can be conducted by ranking DMUs according to their value of the SBCI. Other than ranking DMUs, the calculation process of SBCI can provide additional informative results on the slacks. Through examining the slacks for each sub-indicator, we can also study DMUs' potential to improve towards the frontier, as well as its main disadvantaged aspect. Hence, more specific implications can be drawn from such assessment.

2.3. Malmquist performance index for slacks-based composite indicator The SBCI constructed in Eq. (5) can help assess entities' performance in a particular time period, which is therefore a static assessment. Apart from the static study, researchers and policymakers may also be interested in how entities' performance would evolve over time. Different from the static study, such timeseries analysis should be a dynamic study. In the CI literature, it is rare to analyse time-series data. A common difficult is hard to measure and interpret the changes in CI over time [34]. Through using the SBCI, however, we are able to study and reasonably interpret such changes. The key reason is that the SBCI is formulated through DMUs' weighted distance away from the best practice frontier, and thus we may calculate this distance in different time periods and compare them. In DEA and productivity studies, one common approach to conduct dynamic analysis is to use the Malmquist index [35,36], which can measure the total performance change over time and its drivers [37]. See, for example, Wang et al. [38], Wang et al. [39] and Goto et al. [40]. In virtue of the Malmquist index, we shall define the following index to capture the change of SBCI over time.

   #1=2 SBCI t t þ 1 SBCI tþ1 t þ 1   ¼ SBCI t ðtÞ SBCItþ1 t "

MSBCIttþ1

(6)

where t denotes time period, and SBCI t ðt þ 1Þ is the value of the slacks-based composite indicator for an entity evaluated in t þ 1 using the best practice frontier in t. Given any particular entity, the first ratio in the bracket in the right-hand side of Eq. (6) is to measure the change of entity between time t and t þ 1 with respect to the best practice frontier in year t. To avoid arbitrarily selection of base year, the changes with respect to the frontier in year t þ 1, i.e. the second ratio in the bracket, is also presented. Then the eventual Malmquist performance index is the geometric mean of the two ratios. It can also be observed that the value of MSBCI would fall in the interval ð0; þ∞Þ. With a MSBCI less than 1, it implies the SBCI of a given entity has deteriorated during the time period. When MSBCI is larger than 1, it would be an

Please cite this article in press as: Wang H, A generalized MCDAeDEA (multi-criterion decision analysisedata envelopment analysis) approach to construct slacks-based composite indicator, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.11.051

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H. Wang / Energy xxx (2014) 1e9

Table 1 Descriptive statistics for the three country groups in 2010.

Low-income group

Middle-income group

High-income group

Min Mean Median Max St. Dev Min Mean Median Max St. Dev Min Mean Median Max St. Dev

CO2 emissions intensity (kg per 2005 US$ of GDP)

Energy intensity (kg of oil equivalent per $1000 GDP (constant 2005 PPP))

Share of electricity produced from renewable (%)

0.3221 0.7229 0.5285 2.0940 0.5002 0.2477 1.0457 0.6803 4.8598 0.8789 0.0798 0.4489 0.2721 2.6690 0.4987

138.9802 353.8228 289.4055 1138.4241 278.1649 77.1938 193.2736 163.6108 556.2341 103.8792 45.9776 166.4325 136.1136 686.2494 116.2256

0.6431 47.4304 50.4113 99.5563 41.1896 0.3725 36.9705 29.1403 99.9868 29.9259 0.0000 29.7390 18.2419 99.9883 28.3231

indication that the performance of this particular entity has been improved. Furthermore, similar to the Malmquist index, the MSBCI can be decomposed into two components:

MSBCIEttþ1 ¼

  SBCI tþ1 t þ 1 SBCI t ðtÞ     1=2 SBCI t t þ 1 SBCI t t     SBCI tþ1 t þ 1 SBCI tþ1 t

(7)

 MSBCITttþ1 ¼

(8)

where MSBCIE denotes efficiency change, and MSBCIT refers to the technological change. Given a particular DMU, Eq. (7) is the direct ratio of SBCI value for any two consecutive time periods, which serves to measure the relative change in entity's performance in t and t þ 1. Due to the performance can also be interpreted as efficiency with respect to the best practice frontier, Eq. (7) would be able to reflect the efficiency change behind the changes in SBCI. On the other hand, Eq. (8) captures how the best practice frontier evolves over time. Therefore, it can represent how the best performance among DMUs and related technology develop. As a result, this component is denoted as technological change. In this way we can conduct the dynamic analysis of SBCI and further investigate the driving forces of changes in MSBCI. Compared with other existing approaches in MCDAeDEA area, the method presented in this Section is a generalized framework to constructing CI. The key merits of the proposed approach include: (1) having more flexibility in deriving weights for DMUs featuring varied characteristics; (2) by calculating the upper and lower bound of possible weights, policy-makers' preference can be realized flexibly through the weighted sum in Eq. (3); (3) able to investigate DMUs' improvement potential in sub-indicators through the calculation of SBCI; (4) fulfilling the dynamic analysis of CI and study the underlying driving forces. Thus, using the proposed approach can conduct a comprehensive multi-criteria static and dynamic assessment. 3. Case study To illustrate the usefulness of the proposed approach in Section 2, we shall apply it to examine economies' sustainable energy development level worldwide.

and publics across the world. Generally, the major concern people have are energy consumption, climate change as well as economy growth. To save energy resource, mitigate climate change and simultaneously drive economy, improving energy efficiency is an economically efficient option which has been widely adopted over the world [41]. Energy intensity is often used as a single indicator for tracking energy efficiency trend. Among various climate change factors, the most important one is CO2 emission. Although fossil fuel combustion is still the primary source for CO2 emissions, other factors, e.g. energy structure, also have an impact on CO2 emissions and its intensity. For this reason, CO2 emission intensity can provide complement information to show the full picture of energy use and climate change trend. Furthermore, nowadays many countries have set constraints on CO2 emissions, either total amount or intensity, to achieve the goal of low-carbon development. In particular, energy-intensity sectors face substantial pressure. To eliminate the negative impacts of such restrictions, nowadays industry and government are putting more efforts on developing and utilizing renewable energy, which is almost free from greenhouse gas emissions. Typically renewable energy cannot be utilized directly, but should be transformed into electricity first and then distributed to end-users. In this sense, the share of electricity production from renewable source is also a vital aspect in assessing an economy's sustainable energy development level. In the literature, the three aspects, i.e. energy utilization, climate change and renewable energy development, are frequently used to examine countries' sustainable energy performance. The main reason is the three points are highly representative for a country's energy and environmental development level (Yale Center for Environmental Law and Policy et al., 2012). For example, Zhou et al. [26] construct the SEI (sustainable energy index) considering the three aspects. Following previous works, we shall select the three sub-indicators, i.e. energy intensity, CO2 emissions intensity and the share of electricity production from renewable source, to construct a slacks-based composite indicator to assess economies' sustainable energy development level. Due to the data availability, we select 109 countries to conduct the assessment between 2005 and 2010. All the data is collected from the World Bank database.3 Typically, the three sub-indicators would be varied significantly among countries with national development level. For instance, developed countries' economy structure may lean more to service sector, and thus its energy intensity might be low compared to the

3.1. Data At present, national development in a low-carbon and sustainable way has attracted increasingly attention from the government

3 http://data.worldbank.org/. The raw data used in this paper is available upon request.

Please cite this article in press as: Wang H, A generalized MCDAeDEA (multi-criterion decision analysisedata envelopment analysis) approach to construct slacks-based composite indicator, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.11.051

H. Wang / Energy xxx (2014) 1e9 Table 2 Weights of sub-indicators for the three groups in 2010. Sub-indicator

Low-income group

Middle-income group

High-income group

CO2 emissions intensity Energy intensity Share of electricity production from renewable

0.0075 0.4575 0.5350

0.2310 0.5453 0.2237

0.0666 0.7502 0.1831

developing economies. In order to account for this heterogeneity, we shall first group all the economies into three categories according to their national income. Based on the World Bank's criterion, the 109 economies can be divided into 11 low-income countries, 59 middle-income countries and 39 high-income countries.4 Table 1 summarizes the descriptive statistics for the three groups in 2010. It can be observed from Table 1 that energy intensity and the share of electricity production from renewable sources averagely decreases with country's income increases. However, for the CO2 emission intensity, the middle-income group has the highest mean value, followed by the low-income group. Generally, the three groups exhibit notable difference in the three sub-indicators, and therefore it is reasonable to categorize all the entities before conducting the assessment. Using the data collected, we shall apply the method proposed in Section 2 to construct the slacks-based composite indicator, SEI, based on which the static and dynamic assessment can be conducted. For the static assessment, we shall select 2010 as the base year, whereas the evolvement of SEI during 2005e2010 will be examined in the dynamic assessment.

3.2. Sustainable energy index in 2010 Note that in model (1) and (2) all the variables are output-type, and thus we first need to transform the data for CO2 emission intensity and energy intensity by taking their reciprocal. Subsequently all the data are normalized for weighting the three subindicators. By performing the models (1)e(3), the weights for the three sub-indicators in 2010 can be obtained, as summarized in Table 2. From Table 2 we can observe that the weights for the three country groups are significantly different. For countries in the lowincome group, the share of renewables in electricity production takes the most important role, followed by energy intensity. For the middle- and high-income group, energy intensity carries more priority. However, the specific values of the weights are apparently different among groups, which might indicate that they face different energy utilization and emissions situation. Based on the weights obtained, we further apply it to model (4) and calculate the SEI for the 109 countries, as shown in Table 3. Generally, the average SEI value for all the 109 economies in 2010 is 0.7889, which implies that the global SEI has the potential to improve by roughly 21% compared with the best practice frontier. More specifically, the average values of SEI for the three groups, i.e. low-income, middle-income and high-income, are 0.6143, 0.7802 and 0.8514, respectively. 7 countries are observed possessing unity for the SEI value, indicating that they are located on the best practice frontier. Among the efficient DMUs, 2 of them come from

4 Economies are categorized into three groups according to the per capita GNI in 2012, calculated using the World Bank Atlas method. The three groups are: low income ($1035 or less); middle income ($1036 e $12,615); and high income ($12,616 or more).

5

the middle-income group, i.e. Albania and Costa Rica, and the other 5 countries belongs to the high-income group, i.e. Hong Kong, Iceland, Norway, Singapore and Switzerland. Moreover, totally 62 countries have a SEI score higher than the average level, whereas the other 47 economies are on the lower side. In particular, China receives a SEI of 0.6428, and the U.S. has 0.7833, both of which are lower than the global average level. This fact might suggest the two giant economies and energy consumers have potential to contribute more to the international sustainable development. Fig. 1 shows the distribution of SEI for the three groups. In general, it can be observed that the SEI is likely to increase with national income rising. The high-income group has the best performance since it has a comparatively high average of SEI value, followed by the middle-income group. In addition, the deviation for the low- and middle-income group is large, while that of highincome group is relatively small. This fact might suggest the countries in the high-income group have a more consistent performance. To more rigorously compare the performance among the three groups, we shall perform the KruskaleWallis rank-sum-test, which has been frequently adopted in DEA score ranking exercises [42,43], to examine the following hypothesis.5 Null hypothesis: The three groups of countries have identical performance in terms of SEI. The hypothesis test results show that the null hypothesis should be rejected at the 1% level of significance, implying the three groups don't have identical performance in terms of SEI. Consolidating the above results, it can be concluded that the high-income group of countries has the best sustainable energy development performance, while the low-income group would have more improvement potential in the area of energy utilization and sustainable development. Other than ranking countries according to their SEI value, we can also investigate individual country's potential of improvement since the SEI is measured through slacks in each sub-indicator. In this sense, we can better understand countries' key challenge and perspective in sustainable energy development. Take China as an example, the slacks for the three sub-indicators, i.e. CO2 emissions intensity, energy intensity and the share of electricity production from renewables, respectively are 1.7598 kg/US$, 93.8108 kg/1000 US$ and 81.1527%.6 This potential for improvement is also the distance from the best practice frontier of that particular group, i.e. the middle-income group for China. One interesting point is that the improvement potential for China's renewable share in electricity production is quite high. A possible reason is that China currently needs huge amount of electricity to drive its industry and economy. Although the total volume of electricity generated from the renewable sources is increasing, the share in the total electricity generation is still limited, compared with other countries in its group. If China is able to implement considerable effective actions to achieve this improvement potential, its performance in the three sub-indicators would become 0.3993 kg/US$, 182.0788 kg/1000US$ and 99.9856%. As such, China would be the best player in its group in the sense of sustainable energy development.

5 As one anonymous referee suggested, the KruskaleWallis test is more suitable in the current case than other pair-wise rank sum tests, e.g. WilcoxoneManneWhitney test. The reason is that KruskaleWallis test is able to simultaneously compare multiple populations without assuming they follow normal distribution. See Hollander and Wolfe [44] for more details on the KruskaleWallis rank-sum-test. 6 The slacks for other countries in 2010 are provided in Appendix A.

Please cite this article in press as: Wang H, A generalized MCDAeDEA (multi-criterion decision analysisedata envelopment analysis) approach to construct slacks-based composite indicator, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.11.051

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H. Wang / Energy xxx (2014) 1e9

Table 3 SEI of 109 countries in 2010. Group

Country

SEI

Group

Country

SEI

Group

Country

SEI

Middle Middle High High High High High High Middle High Middle Middle Low Middle High Middle High Middle Middle High Middle High High Middle High Middle Middle Middle Middle Middle High High Middle Low High High High

Albania Costa Rica Hong Kong SAR, China Iceland Norway Singapore Switzerland Uruguay Namibia Austria Colombia Brazil Tajikistan Peru Sweden Georgia Portugal Zambia Congo, Rep. New Zealand El Salvador Denmark Spain Panama Croatia Cameroon Gabon Sudan Guatemala Angola Ireland Italy Sri Lanka Kyrgyz Republic Latvia United Kingdom Chile

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9924 0.9815 0.9611 0.9467 0.9441 0.9431 0.9378 0.9328 0.9326 0.9324 0.9316 0.9280 0.9249 0.9175 0.9124 0.9044 0.9044 0.9024 0.9018 0.9002 0.8980 0.8965 0.8939 0.8925 0.8903 0.8890 0.8852 0.8658 0.8657 0.8623

High Middle Middle High High High High Middle High High High Middle Middle Middle Middle High Middle Middle High Middle High Middle High High Middle Middle High High High Middle Middle High Middle Middle Middle Middle Middle

France Ecuador Montenegro Germany Greece Canada Japan Armenia Luxembourg Slovenia Netherlands Ghana Honduras Turkey Nicaragua Lithuania Venezuela, RB Philippines Finland Romania Slovak Republic Dominican Republic Belgium Israel Mexico Morocco United States Australia Poland Bolivia Macedonia, FYR Czech Republic Hungary Lebanon Tunisia Cote d'Ivoire Pakistan

0.8602 0.8580 0.8570 0.8544 0.8470 0.8467 0.8404 0.8365 0.8342 0.8342 0.8276 0.8276 0.8240 0.8144 0.8141 0.8132 0.8114 0.8063 0.8043 0.8040 0.8033 0.7997 0.7993 0.7957 0.7943 0.7849 0.7833 0.7812 0.7781 0.7662 0.7659 0.7632 0.7591 0.7578 0.7558 0.7529 0.7513

Middle High Low Middle Middle Middle High Middle Middle Low Middle Middle Middle Middle Middle Middle Middle Middle Middle High Middle Low Middle Middle Low Low Middle Middle Middle Low Low High Low Middle Low

Senegal Korea, Rep. Kenya Azerbaijan Bosnia and Herzegovina Algeria Estonia Indonesia Nigeria Togo India Malaysia Vietnam Bulgaria Egypt, Arab Rep. Thailand Jordan Syrian Arab Republic Belarus Russian Federation China Tanzania Moldova South Africa Congo, Dem. Rep. Haiti Iraq Kazakhstan Ukraine Cambodia Bangladesh Trinidad and Tobago Eritrea Uzbekistan Benin

0.7500 0.7478 0.7388 0.7311 0.7146 0.7145 0.7095 0.7080 0.7074 0.7047 0.7034 0.7025 0.7023 0.7004 0.6992 0.6752 0.6712 0.6607 0.6557 0.6517 0.6428 0.6363 0.6195 0.6189 0.6127 0.5623 0.5568 0.5040 0.4623 0.4525 0.4518 0.3888 0.3858 0.3849 0.3846

Notes: High denotes high-income country group, and similarly for the Middle and Low.

3.3. Malmquist sustainable energy index in 2005e2010 By using the Malmquist performance index defined in Section 2, we can further study the evolvement of SEI for the 109 countries during 2005 and 2010. In the current context, we shall name the resulting index as MSEI (malmquist sustainable energy index). Moreover, its two components are denoted as MSEIT and MSEIE, for technological change and efficiency change, respectively. According

Fig. 1. Box plot of SEI for the three groups.

to Eqs. (6)e(8), the cumulative change of MSEI and its driving forces for the three groups can be calculated, as shown in Figs. 2e4. For the MSEI, all the three groups show decline during the period 2005e2010, though the high-income group exhibits a more moderate trend. At the end of this period, the cumulative MSEI for the three groups are 0.9715, 0.9971 and 0.9885, respectively. Of the three groups, the decline in the middle-income group is the most minor, while the fall for the low-income group is more substantial. The result suggests that the worldwide sustainable energy performance has declined in this period. A possible explanation is that the energy intensity and CO2 emission intensity have increased rapidly as economy development is still most societies' primary concern. For individual countries, the most outstanding progress was made

Fig. 2. Cumulative changes in MSEI for the three groups, 2005e2010.

Please cite this article in press as: Wang H, A generalized MCDAeDEA (multi-criterion decision analysisedata envelopment analysis) approach to construct slacks-based composite indicator, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.11.051

H. Wang / Energy xxx (2014) 1e9

7

Table 4 Average SEI for the three country groups using the three models, 2010.

Fig. 3. Cumulative changes in MSEIT for the three groups, 2005e2010.

in Uzbekistan during this period since its cumulative MSEI is 1.5911, indicating that its sustainable energy development status in 2010 had improved by roughly 59% compared to the 2005 level. On the contrary, Congo shows a significant deterioration in terms of SEI as its MSEI decreased by 28% in 2005e2010. Furthermore, Figs. 3 and 4 show the driving forces for the changes in MSEI of the three country groups. It can be observed that high-income group shows a mild trend in both efficiency change and technological change. However, the variation of low-income group is more significant. Generally, the cumulative MSEIT is greater than unity for low- and middle-income group, i.e. 1.0533 and 1.0998, respectively. On the other hand, the cumulative MSEIT of high-income group is 0.9905. The result implies that the best practice frontier for low- and middle-income group has been progressed outward during 2005 and 2010, whereas that of highincome group almost stays unchanged. A potential reason is that the spreading technology diffusion enables low- and middleincome countries to improve energy utilization efficiency and adopt more renewable energy technologies. For the MSEIE, it can be observed that all the three groups exhibit a declining trend. The cumulative MSEIE in 2010 is 0.9223, 0.9066 and 0.9979 for the low-, middle- and high-income group, respectively. Again, the highincome group shows a temperate changing trend. Considering the two components of MSEI, it can be found that the technological change contributes positively to the improvement of sustainable energy performance, whereas the efficiency change is the main negative factor. 3.4. Comparison with Zhou et al. [26]'s and Hatefi and Torabi [23]'s models To further demonstrate the robustness and advantage of the approach proposed in this paper, we shall empirically compare it with some earlier methods. In existing literature, two methods are selected for comparison. The first one is the differentiated weights

Country group

Zhou et al. [26]

Hatefi and Torabi [23]

The proposed model

Low Middle High

0.3225 0.3339 0.4183

0.1885 0.3066 0.3560

0.6143 0.7802 0.8514

DEA method proposed in Zhou et al. [26], and the other is the common weight DEA method given in Hatefi and Torabi [23]. The reason for choosing the two methods is the differentiated and common weight approaches are two representatives in CI field. As a compromise, this study makes use of the combination of the two ideas. The purpose is to account for potential heterogeneity among groups of entities, and to set a relative fair baseline for comparison among entities within the same group. Hence, we shall compare the three models numerically by using the foregoing case study. For illustration purpose, here we only calculate the SEI of the 109 countries in 2010 following the three models, respectively.7 The results of Zhou et al.'s and Hatefi and Torabi's approaches are provided in Appendix C. It can be seen that the SEI values obtained from the three models are diverse. For the ranking of countries, however, certain similarities can be spotted. For instance, all the three methods locate Hong Kong on the best practice frontier, and show Switzerland and Albania having top performance in sustainable energy development. On the other hand, Trinidad and Tobago, Ukraine and Uzbekistan are found at the lower end of SEI ranking. As shown in Table 4, all the three methods indicate that the average SEI value would rise with countries' income increased. Moreover, the correlations between the three models are evaluated through the Spearman's rank correlation test [45]. Table 5 shows that there exist significant correlations among the three methods. In particular, Zhou et al.'s method and the proposed method in this paper have a strong correlation with a Spearman's coefficient of 0.9284. This might be an indication that the proposed method is robust and efficient in ranking DMUs. Besides the ranking of countries by means of SEI, some advantages in application can be observed for the proposed method. First, the SEI value obtained from the proposed method in this paper can be meaningfully interpreted as weighted distance from the best practice frontier. In this manner, the information on slacks of subindicators can be extracted, which could help direct future improvements of DMUs. Second, as shown in Sections 3.3, the proposed method can further investigate the dynamic performance of SEI, while Zhou et al.'s and Hatefi and Torabi's methods are only able to give static analysis. Hence, the proposed method allows conducting more comprehensive and informative analysis on CI. 4. Conclusion The main objective of this paper is to extend existing approaches in MCDA-DEA field by establishing a generalized framework to constructing CI. Through grouping DMUs first and calculating the possible ‘best’ and ‘worst’ weights, the proposed approach is able to yield a more flexible and neutral set of weights for sub-indicators. Instead of directly calculating the value of CI in additive or multiplicative form, we introduce the slacks-based composite indicator by employing a non-radial additive DEA model. Hence, the slacks-based indicator can be interpreted from

Fig. 4. Cumulative changes in MSEIE for the three groups, 2005e2010.

7 The Zhou et al.'s and Hatefi and Torabi's methods are briefly described in Appendix B.

Please cite this article in press as: Wang H, A generalized MCDAeDEA (multi-criterion decision analysisedata envelopment analysis) approach to construct slacks-based composite indicator, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.11.051

8

H. Wang / Energy xxx (2014) 1e9

Table 5 Spearman's correlation coefficient between the three models. [6] Zhou et al. [26] Zhou et al. [26] Hatefi and Torabi [23] The proposed model

1.0000 0.7098 (0.0000) 0.9284 (0.0000)

Hatefi and Torabi [23]

The proposed model

1.0000 0.6949 (0.0000)

1.0000

Note: The number in the parenthesis is the p-value of the test.

the perspective of distance function. Besides ranking DMUs, examining the slacks can reveal DMUs' potential for improvement in sub-indicators. Furthermore, the proposed slacks-based composite indicator can facilitate dynamic assessment. As such, the evolvement of composite indicator over time and its underlying driving forces can be studied. With the methodological improvements, we construct the Sustainable Energy Index for 109 countries worldwide. Considering the potential heterogeneity in economic development, the 109 countries are first divided into 3 groups, i.e. low-income, middleincome and high-income group, according to their national income. The empirical results show that the high-income group has the highest SEI value among the three country groups, followed by the middle-income group. Scrutiny on the slacks of sub-indicators for individual country could help better understand their improvement potential in each aspect. Furthermore, we conduct the dynamic assessment examining the evolvement of SEI for all the 109 countries during 2005e2010. The results imply that the worldwide sustainable energy development level has declined in this period, and the efficiency change is the main negative driving force. Inevitably, there exist certain limitations in the present study. One potential question is how to precisely formulate decision makers' preference, which would advance the present methods to be more applicable. Besides, additional factors/sub-indicators, e.g. energy structure and R&D in energy technology, could be taken into consideration in further research to construct the sustainable energy index. In this manner we can obtain more comprehensive information on how countries utilize energy in a sustainable way. Acknowledgement The author would like to thank the editor and anonymous referees for their constructive comments, which help to vastly improve this paper. The author is also grateful to Prof Peng Zhou at the Nanjing University of Aeronautics and Astronautics, Prof K.L. Poh and Prof B.W. Ang at the National University of Singapore for their valuable inputs on an earlier version of this paper. Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.energy.2014.11.051. References [1] Emerson J, Esty DC, Levy MA, Kim CH, Mara V, de Sherbinin A, et al. Environmental Performance Index. New Haven: Yale Center for Environmental Law and Policy; 2010. p. 2010. [2] Esty D. 2006 pilot environmental performance index. Yale Center for Environmental Law & Policy, Yale University; 2006. [3] Emerson JW, Hsu A, Levy MA, de Sherbinin A, Mara V, Esty DC, et al. Environmental Performance Index and Pilot Trend Environmental Performance Index. New Haven: Yale Center for Environmental Law and Policy; 2012. p. 2012. [4] Nardo M. Handbook on constructing composite indicators-methodology and user guide. OECD Publishing; 2008. s-Beltra n Pablo, Chaparro-Gonz [5] Aragone alez Fidel, Pastor-Ferrando JuanPascual, Pla-Rubio Andrea. An AHP (Analytic Hierarchy Process)/ANP (Analytic

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