Data Envelopment Analysis in Energy and Environmental Economics: An Overview of the State-of-the-Art and Recent Development Trends

Measurement of environmental and energy economics presents an analytical foundation for environmental decision making and policy analysis. Applications of data envelopment analysis (DEA) models in the assessment of environmental and energy economics are increasing notably. The main objective of this review paper is to provide the comprehensive overview of the application of DEA models in the fields of environmental and energy economics. In this regard, a total 145 articles published in the high-quality international journals extracted from two important databases (Web of Science and Scopus) were selected for review. The 145 selected articles are reviewed and classified based on different criteria including author(s), application scheme, different DEA models, application fields, the name of journals and year of publication. This review article provided insights into the methodological and conceptualization study in the application of DEA models in the environmental and energy economics fields. This study should enable scholars and practitioners to understand the state of art of input and output indicators of DEA in the fields of environmental and energy economics.


Introduction
Data Envelopment Analysis (DEA) is a non-parametric multi input-output linear approach for the calculation of energy efficiency that measures the relative efficiency of a set of comparable Decision-Making Units (DMUs) [1]. DEA was introduced by Farrell [2] and it is a relatively technical efficient approach using operations research methods to calculate the weights assigned to the inputs and outputs of the DMUs being assessed. The actual input-output data values are then multiplied by the calculated weights to determine the efficiency scores [3]. The key contribution of DEA to efficiency analysis, and empirical production analysis in general, is the possibility to approximate unobservable production technologies from empirical input output data of DMUs without imposing overly restrictive parameter assumptions [3]. In recent years, several types of DEA method have been introduced for measuring the relative efficiency of DMUs. Ji et al. [4] introduced the hybrid Additionally, some previous studies have reviewed the application of various methods such as DEA, structural equation modeling and multiple criteria decision-making (MCDM) techniques in different areas [26][27][28][29][30][31][32][33][34][35][36][37][38][39]. For example, a review of ranking methods (Adler et al. [40]), research in efficiency and productivity (Emrouznejad et al. [41]; Emrouznejad and Yang [42]), fuzzy DEA (Hatami-Marbini et al. [43]), energy and environmental studies (Zhou et al. [44]), operation research (Liu et al. [45], Cook and Seiford [46], Kuah et al. [47]), measuring efficiency in the context of higher education (Johnes [48]), performance measurement and evaluation (Cooper et al. [49]), environmental efficiency evaluation (Song et al. [50]), network DEA (Kao [51]), or energy efficiency (Mardani et al. [1]). While previous scholars have reviewed the application of DEA methods in different areas, we believe that there is a need for a review of the most important recent studies conducted in the considered area. In addition, researchers think that there is a need for a comprehensive paper, combining the available studies and methods. The presented review attempts to describe some previous studies that employed the considered methods and techniques. In addition, this paper attempts to discuss the exponentially growing interest in the DEA models and provide a comprehensive literature survey of the current DEA methodologies and applications. This study contributes to the theory of DEA and current body of knowledge by evolving a classification structure with practical considerations, structurally reviewing the literature with the aim of presenting a guide to these studies of DEA methods offered by previous scholars, and some recommendations for future studies. Moreover, the current study takes into consideration some new perspectives in reviewing the articles, author(s) and year application area and scope, study purpose as well as results and outcomes. The structure of the paper is organized as follows: Section 2 presents an example of DEA model. Section 3 provides the research methods used for this study. Section 4 presents the results. Section 5 discusses the conclusions, limitations and recommendations for future studies.

Literature Review
A DEA model was presented for the first time by Charnes, Cooper and Rhodes [52] (the so-called CCR model) for measuring the technical efficiency based on decision making units (DMUs) assuming constant returns to scale which consider multiple outputs and multiple inputs. After Charnes et al. [52], Banker et al. [53] (BCC) extended the CCR model to allow variable returns to scale and showed that solutions to both CCR and BCC allowed a decomposition of CCR efficiency into technical and scale components.
The generic multiplicative and envelopment BCC models are in the form of Models (1) and (2): where X ij shows the vector of i-th inputs for j-th DMU.
v i shows the weight to be determined of j-th input. Y rj shows the vector of l-th outputs for j-th DMU.
µ r shows the weight to be determined of j-th output. n shows the number of DMUs. s shows the number of inputs. r shows the number of outputs.
If θ is the variable corresponding to the first constraint of the initial problem and λ j is the variable corresponding to other constraints, then the following envelopment model can be obtained: where λ j is the corresponding variable, λ j Y rj shows the vector of r-th inputs for j-th DMU. λ j x ij shows the vector of i-th outputs for j-th DMU.

Cross-Efficiency Calculation
The cross-efficiency is the level of efficiency that is obtained by considering the available resources and the value (weight) of inputs and outputs of the model. Equation (3) shows the method of calculation of the cross-efficiency of the DMUs based on the method proposed by [54]: This mathematical model is founded upon a generic DEA structure of the BCC type but allows the breakdown points (cross-efficiency scores) to be used for integrating efficiency improvement policies through better use of resources. Equation (4) illustrates the general form of the multiplicative-envelopment BCC-I model: where µ k i shows the importance of output r, α r shows the ratio of the importance of inputs and functional area, u n r shows the importance of output r; Y rj shows the value of output r in the unit j and x rj shows the value of input i in the unit j.

Review Method
In this review paper, we conducted a review regarding the application of DEA methods in the fields of environmental and energy economics. Denyer and Tranfield [55] indicated that, the aim of a review is to find relevant existing studies based on research questions, to evaluate and synthesize their respective contributions and to report the evidence in a way that clear conclusions with regard to further research and managerial practice can be drawn. Our search strategy consisted of looking for relevant studies within scientific literature sources, represented by academic studies published in peer-reviewed journals. To identify the published papers in field of environmental and energy economics and DEA methods we searched two online databases (Web of Science and Scopus) between 2000 and 2018 to identify eligible articles. The selected articles were then classified and reviewed based on authors, application scheme, DEA models, application fields, number of publications, journal distribution and publication year. In the following sections, we briefly present the articles and related literature based on the above classifications.

Distribution of Articles Based on DEA Models and Application Scheme
In recent years the applications of DEA have increased in field of environmental and energy economics, in areas, for example; energy performance [56][57][58][59][60][61][62], energy savings [63][64][65][66][67][68][69], and energy efficiency [70][71][72][73][74][75][76][77][78][79], Shi et al. [80][81][82][83][84][85][86][87][88][89]. In this regard, various DEA models were employed in different industries and sectors such as non-radial DEA, bootstrap DEA, CCR and BCC models, DEA window analysis, non-radial and constant returns to scale ( [90] used a non-radial DEA in the non-ferrous metals industry. Lin and Du [57] applied a non-radial DEA for assessment of energy and CO 2 emissions performance by using panel data set of 30 provinces. Iribarren et al. [59] developed a non-radial and constant returns to scale (CRS) method for the wind energy industry. Bian et al. [66] employed non-radial DEA for evaluating of energy saving and CO 2 emission in the various provinces, municipalities and autonomous regions of China. Fang et al. [56] used CCR and BCC DEA models for coal mining companies. Ebrahimi and Salehi [85] applied DEA-CCR and BCC models to the production of button mushrooms. Nabavi-Pelesaraei et al. [84] employed DEA CCR and BCC models in the study of orange production. Khoshnevisan et al. [3] utilized CCR and BCC models in cucumber production. Mousavi-Avval et al. [82] used CCR and BCC models in canola production. Shi et al. [80] employed CCR and BCC models for 28 Chinese administrative regions to examine industrial energy efficiency. Yeh et al. [79] examined the energy utilization efficiency of 31 DMUs of China and Taiwan by using a CCR-DEA model. Song et al. [65] studied energy savings using nearly 20 years of data by application of a CCR-DEA model. Mandal and Madheswaran [69] applied BCC DEA to cement companies. Han et al. [91] used CRS-DEA in industrial departments. Geng et al. [92] applied CCR DEA in the process of complex chemical manufacture. Nabavi-Pelesaraei et al. [93] employed CCR and BCC DEA in paddy production. Chen et al. [94] used CCR DEA in the petrochemical industries. Liu et al. [62] applied CRS and VRS DEA to the wind power industry. Nazarko and Chodakowska [95] used SFA-DEA labour efficiency analysis in the construction industry. Nazarko and Chodakowska [96] used the Tobit regression and DEA approach for labour productivity analysis in the construction sectors in different European nations. Banaeian et al. [87] utilized the CRS and VRS DEA for evaluating strawberry yields. Lee et al. [64] used CRS and VRS DEA for different types of efficient electricity, gasoline oil and coal savings studies.
Wang and Wei [81] examined the industrial energy and emissions efficiency by using VRS model in the 30 major Chinese cities. Mohammadi et al. [77] employed the CRS-DEA in the study of rice paddy production. Zhou et al. [97] applied VRS DEA to examine congestion assessment and energy efficiency in the 19 APEC countries. Toma et al. [98] used CRS and VRS DEA for efficiency of the agricultural industry. Moutinho et al. [99] developed VRS and CRS-DEA for environmental and economic efficiency in the European countries. Kim et al. [100] used CRS and VRS in the healthcare industry. Yu et al. [101] employed CRS and VRS DEA models for assessing sustainable development in 34 major cities. Wang et al. [58] used DEA window analysis based on labor and capital stock for evaluating the energy and emission performance of Chinese regions. Vlontzos and Pardalos [102] employed a DEA window analysis in agricultural production. Chen et al. [103] utilized a DEA window analysis for transportation efficiency in cities. Lin et al. [104] applied a DEA window analysis in the manufacturing industries. Chang et al. [75] used a DEA-SBM model for assessing of the environmental performance in the top Fortune 500 companies. Chen and Jia [105] employed an SBM-DEA method for environmental efficiency analysis in the 31 China's regional industry. Hu and Liu [106] utilized slacks-based-DEA in the construction industry. Song and Zheng [107] applied an SBM DEA model for evaluating the efficiency in thermoelectric enterprises. Guo et al. [108] employed an SBM-DEA model to evaluate natural resource allocation in the 26 provincial regions of China. Chu et al. [109] used an SBM-DEA model in the transportation system. Li et al. [110] applied a DEA-SBM model for assessment of efficiency in photovoltaic companies. Shin et al. [111] applied an SBM-DEA model in the manufacturing industry. Masuda [112] utilized the SBM model in rice production. Wang et al. [113] employed an SBM-DEA model in the manufacturing sector. Pang et al. [86] integrated the directional distance function (DDF) and SBM to assess the total clean energy use of 86 countries. Hu and Kao [63] combined the SBM-DEA and radial DEA in the 17 APEC economies for their energy-saving targets. Welch and Barnum [72] used a DEA-MBP model for the efficiency of electricity generation. Rezaee et al. [70] integrated the DEA-bargaining game models for thermal power plants. Wu et al. [67] used a two-stage network DEA to evaluate emission reduction efficiency and energy saving in the 30 municipalities, provinces, and autonomous of China's regional. Gan et al. [114] integrated the triangular fuzzy numbers (TFNs), AHP and DEA in a renewable energy project. He et al. [115] integrated the DEA, fuzzy artificial neural network (FANN) and rough set theory (RS) to assess industrial energy efficiency in the provincial industry sectors. Wang et al. [116] integrated the DEA, decision tree and K-means clustering for twenty-five global cities. Li and Lin [117] combined a non-radial and double-bootstrap for energy consumption performance across 30 Chinese provinces. Li and Lin [118] integrated the stochastic frontier analysis (SFA) and DDF DEA in the manufacturing sector. Distributions of other DEA models with application schemes and fields are presented in Table 1.

Distribution of Paper Based on Journal Selection
This review paper attempts to cover all recently published papers regarding the application of DEA models in the environmental and energy economics areas. According to Table 2 and Figure 1, 45 high-quality journals published several articles on the application of DEA models in these fields. Li, et al. [163] 30 provinces CRR and BCC DEA Efficiency of Water-Energy

Distribution of Paper Based on Journal Selection
This review paper attempts to cover all recently published papers regarding the application of DEA models in the environmental and energy economics areas. According to Table 2 and Figure 1, 45 high-quality journals published several articles on the application of DEA models in these fields.   In this regard, Journal of Cleaner Production ranks first, with 17 publications. The second was Journal of Sustainability. In addition, Journal of Energy and Journal of Energy Policy occupy the third and fourth ranks with 14 and 12 articles, respectively. Other important journals in these areas were Journal of Energies, Journal of Renewable and Sustainable Energy Reviews and Applied Energy. The information regarding the distribution of other journals is provided in Table 2 and Figure 1.

Distribution of Paper Based on Keywords Networks by VOS-Viewer
In this section of the paper for visualization, we searched several keywords related to the applications of DEA in energy and environmental economics such as DEA and energy efficiency (1103 records), DEA and environmental efficiency (1359 records), DEA and energy economics (23 records), DEA and environmental economics (44 records), energy performance and DEA (707 records), efficiency performance and DEA (4805 records), CO2 emissions and DEA (374 records), energy consumption and DEA (421 records) energy saving and data envelopment analysis (183 records) energy use efficiency and DEA (804), and total factor efficiencies and DEA (531 records). In Figure 3 we show the keywords which come up repeatedly in published papers dealing with the application of DEA in the assessment of energy and environmental economics in the Web of Science (WoS) database.

Distribution of Paper Based on Keywords Networks by VOS-Viewer
In this section of the paper for visualization, we searched several keywords related to the applications of DEA in energy and environmental economics such as DEA and energy efficiency (1103 records), DEA and environmental efficiency (1359 records), DEA and energy economics (23 records), DEA and environmental economics (44 records), energy performance and DEA (707 records), efficiency performance and DEA (4805 records), CO 2 emissions and DEA (374 records), energy consumption and DEA (421 records) energy saving and data envelopment analysis (183 records) energy use efficiency and DEA (804), and total factor efficiencies and DEA (531 records). In Figure 3 we show the keywords which come up repeatedly in published papers dealing with the application of DEA in the assessment of energy and environmental economics in the Web of Science (WoS) database.

Distribution of Paper Based on Keywords Networks by VOS-Viewer
In this section of the paper for visualization, we searched several keywords related to the applications of DEA in energy and environmental economics such as DEA and energy efficiency (1103 records), DEA and environmental efficiency (1359 records), DEA and energy economics (23 records), DEA and environmental economics (44 records), energy performance and DEA (707 records), efficiency performance and DEA (4805 records), CO2 emissions and DEA (374 records), energy consumption and DEA (421 records) energy saving and data envelopment analysis (183 records) energy use efficiency and DEA (804), and total factor efficiencies and DEA (531 records). In Figure 3 we show the keywords which come up repeatedly in published papers dealing with the application of DEA in the assessment of energy and environmental economics in the Web of Science (WoS) database.   In the final step of the visualization process, we provide the relationships between keywords by using VOS-viewer for generating keyword networks. The most important keywords are located in the center of the map (Figure 4). Each point shows a word, the font size of a word and related sizes as well as the frequency of that word. According to Figure 4, the word that has indicated in the most of the published papers showing the strongest relationships with other words. According to Figure 4, the keyword "efficiency" had the strongest relationships to other keywords compared to other keywords. The results of other keywords are represented in Figure 4. VOS-viewer allowed us to join the most important words into relevant clusters shown in different colours. In addition, there are three different clusters regarding the analysis of co-occurrence of keywords. The details of the three clusters with important keywords are presented in Figure 4. In the final step of the visualization process, we provide the relationships between keywords by using VOS-viewer for generating keyword networks. The most important keywords are located in the center of the map (Figure 4). Each point shows a word, the font size of a word and related sizes as well as the frequency of that word. According to Figure 4, the word that has indicated in the most of the published papers showing the strongest relationships with other words. According to Figure  4, the keyword "efficiency" had the strongest relationships to other keywords compared to other keywords. The results of other keywords are represented in Figure 4. VOS-viewer allowed us to join the most important words into relevant clusters shown in different colours. In addition, there are three different clusters regarding the analysis of co-occurrence of keywords. The details of the three clusters with important keywords are presented in Figure 4.

Conclusions
In this section, we discuss the application of DEA for assessment of energy and environmental economics fields. According to results of this review article, there are various types of DEA models that have been used in different fields of energy and environmental economics. According to the current literature review, these areas have attracted much interest in the last two decades, spawning a number of studies, and many literature reviews have been undertaken, therefore, there are a number of key challenges regarding these subjects which can be interesting for discussion. This is the first review paper to comprehensively review the application of DEA models in the evaluation of energy and environmental economics. Notwithstanding the contributions offered in this review paper, the findings were to be considered in light of many limitations. As we classified the selected articles in different application areas, there are other issues for more discussion. For example; this review paper provided insights into the methodological and conceptualization study in the application of DEA models in energy and environmental economics fields. This review study should enable scholars and practitioners to understand the state of art of inputs and outputs indicators in the fields of DEA models and environmental and energy economics. This review article attempted to present an overview of the body of 145 published articles in 45 different international journals in the field of environmental and energy economics and DEA models in different parts of papers such as title, keywords, abstract, introduction, methodology, results, and conclusion. This research review

Conclusions
In this section, we discuss the application of DEA for assessment of energy and environmental economics fields. According to results of this review article, there are various types of DEA models that have been used in different fields of energy and environmental economics. According to the current literature review, these areas have attracted much interest in the last two decades, spawning a number of studies, and many literature reviews have been undertaken, therefore, there are a number of key challenges regarding these subjects which can be interesting for discussion. This is the first review paper to comprehensively review the application of DEA models in the evaluation of energy and environmental economics. Notwithstanding the contributions offered in this review paper, the findings were to be considered in light of many limitations. As we classified the selected articles in different application areas, there are other issues for more discussion. For example; this review paper provided insights into the methodological and conceptualization study in the application of DEA models in energy and environmental economics fields. This review study should enable scholars and practitioners to understand the state of art of inputs and outputs indicators in the fields of DEA models and environmental and energy economics. This review article attempted to present an overview of the body of 145 published articles in 45 different international journals in the field of environmental and energy economics and DEA models in different parts of papers such as title, keywords, abstract, introduction, methodology, results, and conclusion. This research review examined the different models of DEA by considering the related journals based on application scheme, DEA models, scope, results, and publication year.
Some of the previous studies used a non-radial DEA approach for environmental and energy performance, however, further studies would be integrated the environmental non-radial DEA approach with some other techniques such as statistical inference to predict the environmental and energy performance based on time series data. In addition, further investigations could use the stochastic and fuzzy data for improving the energy efficiency and energy performance. In addition, some of the past published papers focused on environment and energy efficiency for improving environment DEA cross-model (DEACM), in this regard, future studies can use the high-dimension initial data by principal component analysis. The SFA model is used for analysis of energy and environmental efficiency, therefore, the further investigations would use other techniques and compare these results with their results. Structural equations modelling (SEM) is a technique for regression analysis, therefore, further studies would integrate the SEM approach with DEA models. Guo et al. [108] evaluated the efficiency of emission reduction and energy saving by modifying an SMB. Therefore, future scholars can focus on the allocation for decreasing the emission and energy based on decentralized and centralized views. Zhang and Chen [164] used the DEA based on DDF for assessing the dynamic performance of energy portfolios in the daily fossil-fuel prices between 2006 and 2015. Regarding this, further investigation would focus on the different commodities based on energy portfolios and their effect of risk and return volatility. Angulo-Meza et al. [165] evaluated the eco-efficiency of agricultural sectors by using a multiple objective DEA approach. Consequently, future articles can extend the proposed model of this study by developing the different methods such as decision support system. In addition, future works would use the multiple objective DEA approach to evaluate the economic perspectives of eco-efficiency assessment. Meng et al. [166] integrated the DEA model and TOPSIS approach to evaluating the dynamic energy efficiency, thus, further studies would integrate the DEA model with other decision-making approaches and fuzzy decision-making methods.
Regarding the journal selection, this review study found that the Journal of Cleaner Production had the highest number of published paper followed by Journal of Sustainability, Journal of Energy, Journal of Energy Policy, Journal of Energies, Journal of Renewable and Sustainable Energy Reviews and Applied Energy.
Moreover, this review paper found that in recent years the application of DEA models has increased and the results of this study demonstrated that in the year of 2014, authors published 40 papers with compare to other years.
There are some limitations to this particular review paper which provides recommendations and opportunities for further investigation. First, this review categorized the published papers in the fields of DEA and environmental and energy economics, therefore it is an opportunity for further study to classify the published papers based on different application areas. Moreover, this study categorized the selected papers based on DEA models, thus further research would examine more details about methodological parts such as benchmark ranking method, multivariate statistics, cross-efficiency ranking methods, ratios discriminant analysis, linear discriminant analysis, canonical correlation analysis, inefficient decision-making units, DEA and MCDM methods, super-efficiency ranking techniques, inputs and outputs indicators and, fuzzy DEA principles, efficiency measures. Moreover, in Section 2 this paper presented an example of DEA models based on CCR-DEA and BCC-DEA, therefore, researchers could further focus on other different DEA models such as SBM-DEA, DEA window analysis, stochastic network DEA, fuzzy dynamic network-DEA, fuzzy network SBM model, network DEA and stochastic DEA.